Structural control for civil and infrastructure engineering: proceedings of the 3rd international workshop on structural control: Paris, France 6-8 July 2000

ii9/(0 + c ii

/7 {t) + kn
V8(p,,8(p„ (4) "»2i„ {t)+k22I(t) + cn(pI(t) + kn(p,(t)+mn(i>II{t) + cl2(pII{t) + ku(pI1(t) =

=

-r'xUgxii)-r'yugy{t)-f's

m21cp; (r) + c2l(p, (t) + k2l(p, (t) + m22ipn {t) + c22
= -#«(')- X*(0-//

ruling the combined response of the structure (Fig.9).

in

a)

b)

Figure 9. Combined system response.

(5)

67

In the following section this case will be considered in order to model the analysis of a possible control device. 3 3.1

A control strategy for small oscillations The motion of the arch model with a variable length tie-rod

As an example of the possibility to control the dynamic response in some common masonry structural pattern, suppose that the previously considered arch model is equipped with a tie-rod, whose length is ruled by a control algorithm. It results a two-mode behavior, referred to the arch equipped with an extensible tie. Marking by x the position vector of the generic current point and assuming for a clockwise rotation cp^ (pn < 0, the instantaneous configuration at time t is obtained by the superposition of the two modes (Fig.8) as follows s(x,f) =

(6)

Design of the control algorithm

In order to keep into account the insertion of the elongable tie-rod, one goes to calculate the length variation M A£{t) = A£I(?I{t) + A£„
(7)

where M{ and Mu are the two single-mode elongations for unitary parameters

x t =

( ) -^r''a=-MJL

(8)

and the structure is reduced to a single-degree-of-freedom system. In fact, by introducing the second Eq.(8) into Eq.(4) one gets mn(i>I{t) + cn(pI(t)+kn(p,{t)+m12(i>„(t) + -a + c (p„ (t) + *

, (t) + k2l„ (t) +

=0

+ C22

(9)

68

and substituting a = A£Il/&£I,X(t) follows

here the first Eq.(8) for cpXO. with the positions = A£{t)/A£l, the equation of the motion can be written as

Mcp„ (t)+ C(p„ (t) + K(p„ (t) + QX{t) + Rk{t) + SX{t) =F(t)

(10)

with M = a2/n11-a(7n21+/^2)+m22;C=a2cn-0((c12+c21)+c22;Ar=a2^11-o((/c12+^21)+/t22 (11) Q = m2l - a m , , ;R = c2l -acn ;S = k2l-akn (12) F{t)=-{r;-ar'x)iigx{t)-{r;-ar'y)iiJ)-{f;-af;) 3.3

(13)

The "intelligent" tie-rod and the control algorithm

In Eq.(10) A(t) can play the role of a control variable. Assuming the control law in the (linear) form

M') = W „ ( 0

(14)

Eq.(10) becomes Mcij>a{t)+Cein{t) + Ke
(15)

where MC=M+Qy;

Cc=C + Ry; KC=K + S\\f

(16)

are the controlled structure parameters. The search of the optimal control factor \|/„ can be reduced to the problem to find the constrained minimum of the impulsive response function norm [4]. Having determined the controlled system characteristics (damping coefficient £c and frequency coc), depending on \|/, and the standard forcing function j{i)

the Eq.(15) of the controlled motion can be written in the standard form

(p//(f)+2Cccoc(p//(r)+co2(p„(0 = / ( 0

(18)

69

and the structural oscillation can be expressed by the introduction of the impulsive response function A(r/C,(D)=e-^^foi);

co, = ( 0 ^ ^ "

d9)

by the equation


(20)

o

where it has been put hc(x) = h(x /£c, coc). Remembering Eq.(14), the instantaneous elongation of the tie is given by X(t) = y'fhc{t-T)f{x)dT: o

(21)

The objective of the control is to keep as small as possible the oscillation amplitude cp/XO without requiring too large elongation of the tie. To this aim, consider that by the Schwartz inequality one gets (f,l(t)<WfitfH^tl^) \ft6 (0,T)

(22)

where T is the duration of the ground shaking and

\\f(tf Jjf^^H^^Jfh^^ljf 0

=)n^-M%^c)=)hl[Q)dB (23) 0

0

0

From the above bounds one gets «P„»=njfflJ
™ =^\X^\flL^^)>

(24) Lfcto) = H-H(C)co)

In order to realize an effective and energetically economic control the maximum value of the tie length X^ has to be maintained under a certain predefined threshold X0 = \\f\[L0 while minimizing the norm of the response operator. In other words it is required to solve the following optimization problem

70

{FIND min//(Cc,coc) (25) [SUB

U//(C c ,co c )
0 30 - , Norm H

Norm L . r

2000

°

o.oo

0.00 -400.00

0.00

400.00

Control coefficient v A(, Figure 10. Diagram of the norms Hc,Lc, Sc, versus the control coefficient *P.

The diagram of the response norm versus the control coefficient \|/ (Fig. 10) shows that the lowest values of Hc are reached for negative values of \|/. The uncontrolled and controlled response for \|/ =0 (the case of non-stretch tie) can be analyzed, under the hypothesis of small displacements from Fig.l 1. Moreover, a comparison of this case with the Bode diagrams provided for the extensible tie equipped arch, with \\i =300/Mj, points out (Fig.l 1) a further remarkable increase of the damping capacity and of the structural stiffness. Good results are also obtained, as one can evaluate from Fig. 10, choosing a more binding value of the control norm, namely giving more weight to the energetic economy. As one would choose large negative values of the control coefficient in such a manner to accomplish, at the same time, the double effect of minimizing costs while maximizing the control effectiveness, particular attention has to be paid to prevent compression in the tie. 4

Discussion

The paper is inspired by the need that is highly felt, especially in countries that are rich of monumental constructions, to improve the safety and the survival probability of these objects with regard to exceptional load conditions, such as earthquakes and strong wind gusts. Control technology offers a perspective to achieve modernisation

71 200.00^ Phase (deg)

Magnitude (db)

Uncontrolled

100.00

• Controlled • Non-stretch tid

0.00

0.0004

~i—'—r 0.00

40.00

80.00 120.00 160.00 Frequency (Hz)

200.00

0.00

40.00

80.00

120.00

160.00

200.00

Frequency (Hz)

Figure 11. Bode diagram transfer function from ground acceleration to the rotations for ¥ = 0 (non-stretch tie) and ¥ =-300/A^;: (controlled tie).

in the field of the building industry and to have a different conceivement of the structural design. The paper attempts at setting the basis for applying the new technology to the old buildings with the hope that such a combination can produce unexpected good results. The device here considered is pretty simple and represents the natural conceptual consequence of the traditional tie technology. The control law also meets the maximum simplicity requirement, but it seems that the result of such complexity abatement is a very consistent attenuation of the risk of the considered structure. If one looks at the matter in its entireness, one can realise that the task to develop specialist control techniques for existing masonry buildings involves at least two problems. First of all, at present dynamics of masonry structures are not supported by a well consolidated and generally agreed theoretical support. Secondly, control devices suited for masonry and monumental fabrics have not yet been identified; therefore the future development will be conditioned by the elaboration of a well founded theoretical basis for dynamic analysis of masonry structures and by the conceivement of new actuation and monitoring systems that are specialised to such building typologies. 5

Acknowledgements

Paper supported by grants of the Italian National Research Council (C.N.R.). References 1.

Augusti, G., Martin, J. B., O' Keeffe, J. D., An approximate method of analysis for pulse-loaded rigid-plastic structures, 2° Congresso Canadese di Meccanica Applicata, Ontario, (1969).

72

2. 3.

4.

5.

6.

7.

Augusti, G., Mode approximations for rigid-plastic structures supported by an elastic medium, ARPA E63, Rhode Island, 6, pp. 809-827, (1970). Baratta, A., Cennamo, C , Voiello, G., Approssimazione modale della risposta di strutture rigido-plastiche sotto carico dinamico, XII Congresso Nazionale dell'Associazione Italiana di Meccanica Teorica e Applicata, Napoli, (1995). Baratta, A., Cennamo, C , Voiello, G. , Norm solutions and optimized linear control for mdof structures, 1° WCSC, Los Angeles, U.S.A. Vol. 3, FP1/6372, (1994). Baratta, A., Cennamo, C , Corbi, O., A modal approach to active control of masonry arches, Model and Simulation-Based Engineering, Atlanta (Georgia), U.S.A., Vol. 1, 545-550, (1998). Binetti, A., Cennamo, C , Risposta dinamica di strutture non reagenti a trazione mediante tecniche di approssimazione modale, XIII Congresso Nazionale dell'Associazione Italiana di Meccanica Teorica e Applicata, Siena, (1997). Heyman J., The Stone Skeleton, Int. Journ. of Solids and Structures, 2, pp. 269-279., (1966).

MODELING A N D N U M E R I C A L ISSUES IN T H E A C T I V E CONTROL OF FLEXIBLE S T R U C T U R E S F. BOURQUIN Laboratoire des Materiaux et des Structures du Genie Civil, UMR113 LCPC/CNRS, Champs-sur-Marne, France M. COLLET Laboratoire de Mecanique Appliquee, Besancon, France L. RATIER Laboratoire de Modelisation et Mecanique des Structures URA 1776 CNRS UPMC/ENSAM/ENS de Cachan, Paris, France LMSGC

1

Introduction

This paper aims at highlighting the importance of choosing adequately the continuous mechanical model and its approximations when designing and implementing active control laws. Of course, the starting point of most works in the area of control engineering is usually a given finite (or infinite) dimensional system ^ | = Ax + Bu, or sometimes even a partial differential equation. For example, the control benchmarks posted on the web give the matrices. However, the question of how to discretize consistently the corresponding control problem remains of primary importance in view of control design and response simulation, although a number of papers have appeared in the applied mathematics litterature in the past two decades. Moreover, the question of the mechanical modelling of the system to be controlled proves of paramount importance in view of experimental implementation : in particular, the choice of mechanical unknowns, displacements or stresses, is shown here to impact on the performance of the resulting control algorithm. The outline of this paper is as follows : in the next section, a fast control law that has been introduced in 9 and successfully implemented 7 is taken as an example. It is explained and applied to a beam. Here, a boundary displacement is imposed. In view of computations, a "very weak" formulation is introduced which is unusual in structural mechanics. It will be noted that a classical formulation leads in this case to a generally unstable discrete closed-loop system although the continuous closed-loop system is stable. But the discrete very weak formulation yields a structural response asymptotically independent of the discretization parameters. More importantly, the

73

74

associated discrete closed-loop system enjoys a uniform exponential stability, independent of the discretization parameter. In section 3 a few experimental results are recalled. The resulting control law proves practically efficient and easily implementable. Finally, for a given structure and a given set of actuators, the choice of the mechanical unknown, displacement or stress, is shown to influence the efficiency and stability of the experimental controller. Section 4 is devoted to the dual control synthesis, based on a dual formulation of the beam. In section 5, a mixed primal dual control synthesis that takes advantage of both primal and dual formulations simultaneously is introduced. 2

Rapid stabilization of beams : primal formulation

Let us consider a simply supported Euler-Navier-Bernoulli beam of length L. Let p, E, A, I denote its mass density, Young's modulus, cross-sectional area and inertia respectively. For the sake of simplicity, the mass density per unit length pA and the stiffness EI are supposed to be constant. The transverse displacement y{x,t) satisfies f

pAduy + EIOxxxxy

=0

y(o,t) = v(t)

[0, L] x [0, T]

[o,T]

y(L, t) = dxxy(0, t) = dxxy(L, t)=0 ly(x,0)=y°(x), dty(x,0)=y1(x)

{Z l)

[0, T] [0,L].

'

Here the beam is controlled through the imposed transverse displacement of the left end point, and the horizon T can be arbitrarily large. Following Komornik 9 , in order to design the full state feedback law v(t) = T (y(t), dty{t)), the adjoint state is introduced : let
=0

[0, L] x [0, S] [0,5] [0,L],

(2.2)

where s denotes a fictitious time, and S a fictitious time horizon. The displacement field tp depends linearly on the initial conditions {(p°, ip1} . Hence, for any value of w, one can define the bilinear controllability gramian 1

O

1

au,s{W°,

rs J

e-2usEIdxxM0,s)EIdxxx^>(0,s)

ds — (2.3)

where (p denotes the solution of (2.2) with initial conditions {<£°, tp1 } . Following Lebeau 10 , who proved much more general results for the two-dimensional

75

simply supported plate, we can state that, for any smooth enough displacement and velocity fields z° and z1, there exists a unique solution {y? 0 ,^ 1 } of the variational equation aa,s{{
V ^

1

} .

(2.4)

Jo

Define the operator C by just writing {ip0,^1} = C{zQ,z1} and denote by P\ the projection on the first component of a pair of real numbers, i.e. Px ({a, b}) = a. In this setting, the proposed feedback reads v(t) = -EI0XXX

(PiC{y(t),dty(t)})

(x = 0).

(2.5)

Provided the function e~2u$ is slightly modified, Komornik proved 9 wellposedness for related equations as well as the estimate ||{2/(t),<9tj/(^)}||U) < Ce~2ut IK^Ay 1 }!! for some constant C, where ||.||^ stands for some weak energy of the state, that is called here the w-energy. The constant C depends exponentially on u 8 . Above stability estimate can be enhanced in some cases 12

Of course, there is no reason why y°(x — 0) = v(t = 0) although this condition would be requested for compatibility. And this condition is almost never satisfied. The w-energy allows for this lack of compatibility and the response of the structure is defined in a "very weak" sense. However, a smoothing procedure that postprocesses the control law restaures artificially the compatibility, thus decreasing dramatically the control spill-over of the resulting law 5 . In view of computing this feedback, an ad hoc formulation of the beam equation and a suitable mode superposition method are introduced, as in 4 and 5 . In order to let the control enter in the formulation, you need integrate four times by parts in space since the actuator is assumed to impose a displacement. Therefore, the following unusual starting formulation is used : /„ pAdtty{t)w

+ J0 EIy(t)dxxxxw

v(t) = -EIdxxxPi

= -v{t)EIdxxxw(x \/w (£{y(t),dty(t)}) (x = 0)

= 0) (2.6)

where part of the second equation will be put in a standard variational form, and where the virtual displacement fields w are assumed to be smooth enough. At this point, direct use of finite element techniques would require special care since usual test functions do not have square-integrable fourth order derivatives. Now let (Xi,6i)iz^ denote the family of eigenvalues and normal modes

76

of the simply supported beam, and VN =

Span {6i}. The modes are asi = l,N sumed to be normalized so as to have a unit mass. For every pair of functions {z°,z1}, define {tp%,
(W°N,¥>N}

> {'P'N^'PN})

= f (z1^ - z°ipN) V{5v>y]v} = £N {Z0^1} . Then, similarly to 4 , for any pair of integers M and TV, an approximation yM,N(t) — J2i=1 ai(t)6i, (with smooth «i ) of the displacement of the controlled beam satisfies the equation Jo PA9ttyM,N(t)wM

+ J0 EIyM,N(t)dxxxxwM

= -VM,N(t)EWxxxWM(x = 0) VwM e VM VM,N(t) = -EIdxxxPi {CN {yM,N{t),dtyMN(t)})

I

VMMO)

=

pM

V° ,

(2.8) (2-9) (x = 0)

M l

dtyM:N(0) = JP y ,

where PM stands for the projection over the first M modes of the beam. In practice, M is large or even infinite but N must be kept as small as possible. That both numbers are assumed to be different enables one to simulate control spill-over effects but has no impact on the control design. We can prove mathematically (see 3 for the wave equation) that the displacement field j/M,iv(£) enjoys the same stability property as above for M = N. This property holds uniformly with respect to the number of modes. The approximation of the control law, i.e. the resolution of (2.7) is detailed in 4 and 2 for a related problem. Remark : notice that yN(x = 0) = 0 ! whereas a non-zero displacement is imposed at that location. It is very tempting to try to modify above formulation in order to allow the approximate response to assume the value of the imposed displacement at the actuator location. To do that, a natural and popular way consists of adding and weighting a static displacement field which does not vanish at the actuator location : in this case we would have N

yN = Pz + ^T otiOi, z(x = 0) = 1,

P=v

i=i

and the equation for the dynamical part of the response could be obtained by just plugging this decomposition into the standard variational formulation

77

of the beam problem, thus leading to another finite-dimensional system. But it turns out that for any kind of full state feedback, this system is always unstable! See n for a proof. Therefore, it is not useful to simulate the real beam which is stable. 3

A few experimental results

(D

capteur 3 f

\

Condition]leur

U O <

capteur 2

capteur 1

^™ capteur

^

Filtre modal

fdenvation

Gain de Komornik ( DAC ) J

Pot vibrant —

Ampli

Figure 1. experimental setting for the primal algorithm The experimental implementation of this feedback is detailed in n and preliminary results have been presented in 6 , 7 . The advantages of the proposed feedback are multifold. First, efficiency proves at least as good as, and often better than, more conventional laws n , 1 . Second, the implementation does not require solving any Riccati equation but only a well-conditionned positive definite linear system of small size. The approximation error is under control. Most of the data needed for implementation can be measured. The entries of the gramian matrix depend weekly on the normal mode shapes. Robustness with respect to mass distribution has been proved experimentally n . Finally there is a single parameter to tune, and not a whole matrix as for the LQ strategy. However, the parameter w which is directly related to the expected decay rate cannot be tuned as large as you want because of instabilities which are probably due to observation and control spill-over but also to the actuator dynamics and a coupling of both phenomena. A low-pass filter is used of course but the modes responsable for spill-over and the internal mode of the actuator are very close to the frequency range of interest. Therefore, an effi-

78

TIME (s)

Figure 2. primal formulation : the first 3 modal contributions to the response of the beam, w = 2

cient filter will deteriorate the efficiency of the control law. In our case, the limited efficiency is amplified because of control-structure interaction, since the shaker has some resonance around 40 Hz. 4

Dual control synthesis

(D

capteur 3

Filtre modal

Calcul des contributions "l du moment et de sa d6riv6j

3-i

capteur 2

Gain de Komomik (Double integration"")

capteur 1

Pot vibrant

QK1Q-

( DAC )

Figure 3. experimental setting for the dual algorithm

In order to prevent from spill-over at "high frequencies", a dual formulation of the problem is advocated. By just writing down the equation solved

Figure 4. dual formulation : the first 3 modal contributions to the response of the bearr w=1

by the bending moment, t

pAdttM + EIdxxxxM

I

d,xM{0,t) =-pAdtMt)

=0

[0, L] x [0,T]

[0,T]

M(L, t) = M(0, t) = dxxM(L, t) = 0 M{x,0) = M°(x), dtM(x,0)=:Ml(x) {M°(x) = EIdxxy°(x), M1(x)=EIdxxy1(x)

[0, T] [0,L] [0,L]

we recognize here a similar equation as before. Therefore, we may use a similar control strategy : find u, such that if you impose dxxM(0,t) = u, then M —t 0 exponentially fast. Since now the bending moment is controlled through its "own bending moment", a new gramian is needed : fS <™,s ({{
fu,s(s)dx(PN(0,s)dx!pN(0,s)ds

Jo

where
= / Jo

{M'N{t)$% - MN(t)iplN)

€

80

where MM denotes an estimation of the bending moment of the real beam, and set uN(t) = EIdxip°N(t)(x

= 0)

Then compute Vd = —r / ds

uN(r)dT

To this end you have to filter out the very low frequencies that would otherwise be overamplified and do as follows : UN

•

> J-

-

> ~

S

> S

>

Vd

S

where T stands for a 2nd order high-pass filter, with a 0.1 Hz cut-off frequency. The fundamental frequency of the beam is 2.5 Hz. Now, computing M^ from displacement measurements is not necessarilly easy but we may take advantage of the dynamical properties of the normal modes to define robust and easily implementable formulas for the right-hand side of the controller equation. This will be explained in a more detailed paper. A global similar efficiency as with the primal formulation is obtained but there is no more spill-over at "high frequencies". The efficiency still remains limited by the necessary high-pass filtering. Loosely speaking, this "dual" control law proves slightly less efficient for the fundamental mode than the "primal" one but behaves nicer at higher frequencies. 5

Mixed primal dual control synthesis

Based on above conclusions, the new idea writes as follows : by just using each feedback in the frequency range where it is efficient and where there is no spill-over effect, provided both regions overlap, and they do, one could certainly increase the gain and ask for more efficiency. We propose here the additive blending v

= 2 $PVP

+

GdVd)

where vp denotes the control obtained with the primal formulation and Vd denotes the control obtained from the dual one, and where Qp and Gd stand for gentle 1st order filters defined here as

^( S ) = TTT:

gd{s)=

lf^

»r = 10Hz

"d = 20Hz

81

OP

capteur 3

Filtre modal

^ derivation

Calcul des contributions du moment et de sa derive

capteur 2

Gain de Komomik primal

Gain de Komomik dual

capteur 1

(filtre passe bas )

(Double integration )

X

capteur Potvjbniil

F i g u r e 5. e x p e r i m e n t a l s e t t i n g for t h e p r i m a l d u a l s y n t h e s i s

. xio

TEMPS (s)

Figure 6. primal dual synthesis : the first 3 modal contributions to the response of the beam, u = 5

As anticipated, the parameter ui can now be increased and a much better efficiency is observed. In half a second all the vibrations of the beam get damped. The new higher efficiency limitation seems to be due to above choice

82

TEMPS (s)

Figure 7. primal dual synthesis : the "weak energy" of the controlled beam, ui = 5

of weighting parameters. We then expect to increase the potential efficiency by just modifying above decomposition. In terms of computational time, the resulting strategy is only twice as expensive as the previous one. 6

Concluding remarks • An apparently new way of blending mechanical formulations and associated low and high pass filters to define control laws proves much more efficient than previous strategies based on a single mechanical formulation. This remark may open the way to new classes of control algorithms that are both efficient and practically stable. • In particular, the mixed primal dual control synthesis may be of interest in the case of high modal densities which is the case of many, if not all, complex structures. • A thorough analytical investigation is needed to fully understand and enhance the properties of the new class of control algorithms.

83

• The dual formulation shares common features with IFF x . For example, stresses are "measured", and finally time-integrated. Therefore combining IFF and DVF might also be of interest. References 1. Y. Achkire and A. Preumont. Active tendon control of cable-stayed bridges. J. Earthquake Engineering and Structural Dynamics, 25:585597, 1996. 2. F. Bourquin. A numerical approach to the exact controllability of eulernavier-bernoulli beams. Proceedings of the First World Conference on Structural Control, Pasadena (California), pages 120-129, 1994. 3. F. Bourquin. Approximation for the fast stabilization of the wave equation from the boundary. In Proceedings of MMAR2000, Poland, 08-2000, 2000. 4. F. Bourquin, J-S. Briffaut, and M. Collet. On the feedback stabilization: Komornik's method. In Proceedings of the second international symposium on active control in mechanical engineering, Lyon, France, 1997. 5. F. Bourquin, J-S. Briffaut, and M. Collet. Smoothed fast stabilization. In Proceedings of the second world Conference on structural control, Kyoto, 1998. 6. F. Bourquin, J-S. Briffaut, M. Collet, M. Joly, and L. Ratier. Fast control algorithms for beams : experimental results. In Proceedings of Forum Acousticum 1999, Berlin, 1999. 7. F. Bourquin, M. Collet, M. Joly, F. Lene, and L. Ratier. An efficient control algorithm for beams : experimental results. In Proceedings of ACTIV1999, Florida, 12-99, 1999. 8. J-S. Briffaut. methodes numeriques pour le controle et stabilisation rapide des structures. PhD thesis, Ecole Nationale des Ponts et Chaussees, Paris, 1999. 9. V. Komornik. Rapid boundary stabilization of linear distributed systems. Siam J. Control and Optimization, 35(5):1591-1613, 1997. 10. G. Lebeau. Controle de l'equation de schrodinger. J. Math. Pures Appl., 71:267-291, 1992. 11. L. Ratier. stabilisation rapide des structures et raise en oeuvre experimentale. PhD thesis, ENS Cachan, France, 2000. en preparation. 12. J. Urquiza. Controle et stabilisation des structures haubanes. PhD thesis, Universite P. et M. Curie, Paris, France, 2000. under review.

STRUCTURAL CONTROL OF BRIDGES: RECENT EXPERIENCES IN CABLE-STAYED BRIDGES JOAN R. CASAS Escuela Tecnica Superior de Ingenieros de Caminos, Canales y Puertos (UPC) Gran Capitan s/n. Modulo CI. 08034 Barcelona, Spain E-mail: [email protected] The paper presents different case studies on dynamic testing of cable-stayed bridges as the first necessary step to develop afterwards an efficient strategy for the structural control of such important structures. The model identification process and the calibration of the most accurate dynamic model to predict the actual real behavior of the bridges are presented. Based on the feasibility of obtaining an up-dated calibrated model of the performance of such complex structures, as shown in the paper through 3 case studies, the last part of the presentation is devoted to the most appropriate techniques of active structural control to be applied in those structures taking into account the presence of cables in the structure itself. Finally, a theoretical example of the application of a decentralized strategy of structural control is applied to an existing bridge subjected to earthquake excitation. Prospective applications of long-term monitoring to develop in the near future smart cable-stayed bridges are also presented.

1

Introduction

A correct and efficient strategy of active control in a bridge is feasible only if an updated calibrated dynamic model of the real bridge is available. This may be difficult to obtain using only the theoretical data and information from the existing drawings. Although these general considerations are valid for most structures, they are especially relevant in the case of bridges, partly due to the usual lack of nonstructural elements that may affect the actual (measured) stiffness and damping, as compared with the same properties computed with numerical or analytical models. In the case of complex structures as cable-stayedbridges this difficulty becomes still more evident. However, the use of dynamic tests has been recognised as an effective method for data collection of mass, stiffness and damping properties. The results from a dynamic tests may be very usefull to up-date and calibrate a dynamic model of the real constructed bridge. This will be shown in the following 3 case studies of dynamic tests performed in cable-stayed bridges. 2

Alamillo bridge

The Alamillo bridge is one of the seven bridges built in Sevilla (Spain) because of the Universal Exhibition EXPO-92 (figure 1). The deck of the bridge (200 m span) is a hexagonal steel box girder with 4.40 m depth. Every 4 m two lateral cantilevers 13.20 m in width formed of steel ribs support a reinforced concrete slab of 23 cm thickness forming the traffic carriageway. The pedestrians pass over the upper flange of the steel box. The deck is connected to the pylon by 13 pairs of parallel stays. The pylon is a composite (steel-concrete) structure. The height of the pylon is 85

86 134.25 m. The pylon has an inclination- of 32° to the vertical, which makes it possible to balance the forces in the cable stays without the use of back-stays. A description of the bridge and the construction process can be found in [1]. A dynamic test was performed in the bridge to determine the modal properties to validate the mathematical and full-aerolastic models used in the design [2,3]. The main results concerning the dynamic parameters of the bridge and their comparison with theoretical ones are summarized in table 1. As deduced from the table, the agreement between dynamic parameters of the real bridge and theoretical and scaled models (tested in wind-tunnel) was completely satisfactory.

Figure 1: Alamillo bridge (Sevilla, Spain) Table 1. Natural frequencies in the Alamillo bridge

Vibration mode

| |

3

Transverse pylon 1 Longitudinal (pylon + Longitudinal (pylon + Transverse deck 1 Longitudinal (pylon + Torsion deck 1 Transverse pylon 2 Longitudinal (pylon + Torsion deck 2 Longitudinal (pylon + Transverse deck 2

Theoretica f(Hz) 0.292 0.373 0.610 1.088 1.191 1.235 1.583 2.196 2.298 2.312 3.244

Aerolasti f(Hz) 0.30 0.39 0.65 1.20 1.19 1.11 1.67 1.97 2.19 — 3.4

Actual f(Hz) 0.30 0.40 0.66 — 1.205 1.155 1.537 2.155 2.295 2.78 —

Chaco-corrientes bridge over the Parana River (Argentina)

The Chaco-Corrientes Bridge consists of two independent half-bridges with prestressed concrete deck and two main longitudinal box girders made of precast segments. It has a central free span of 245 m between pylon axes and lateral spans

87

of 112.5 m. (Fig. 2). The bridge was completed in 1973; during the first 10 years of service, the bridge vertical profile suffered significant creep deformations that caused deterioration/loss of the elastomeric supports of the simple supported spans connecting the half bridges, and produced a systematic slowdown of traffic on the bridge due to the loss of vertical alignment of the road surface.

Figure 2: Chaco-Corrientes Bridge (Corrientes, Argentina)

In order to compensate for the accumulated deformations, the bridge Owner/Operator decided to replace all original stays before formulating a programme for cable re-stressing to compensate for the creep deformations. To assist in that process, a series of ambient vibration tests and impulsive tests were performed in order to define with sufficient accuracy the degree 'of geometrical corrections that could be introduced while complying with structural safety requirements. The dynamic tests were judged to be a reliable method to determine the current deck stiffness, since the actual static displacements measured during replacement of the cables are highly sensitive to temperature gradients, and therefore are not sufficiently accurate for this purpose. A series of ambient vibration measurements were performed on the bridge at the sections where the groups of stays are fixed to the deck [4]. Typical Normalized Spectral Density Functions (NSDF) of the vertical component of accelerations are shown in Fig. 3 from which the natural frequencies in Table 2 are obtained. QJ X3

1000

^ E

aoo

TO

600

J ^

400 200

0.587 ' 2-404

0 -K^--^ 6

8

10

12

14

16

18

Frequency [Hz]

Figure 3: Typical Normalized Spectral Density Functions (NSDF)

20

88 Table 2. Measured Natural Frequencies by NSDF and Phase Dispersion Procedures

Frequency of picks 1 2 3 4 5 6 7 8 9

ANPSD [Hz] 0.567 1.621 2.404 4.058 11.810 13.013 -

Phase Dispersion [Hz] 0.540 1.648 2.384 2.948 4.043 9.208 11.826 13.104 14.173

The cable forces due to permanent loads were also measured indirectly by means of records of transverse vibrations of the cables. The locked-type cables have low bending stiffness in relation to their mass and axial force, and consequently present little dispersion of the transverse waves. In this way an up-dated model of the cables was obtained too. 4

Zarate-Brazo Largo bridges over the Parana river (Argentina)

As depicted in Fig. 4 they are two almost identical cable-stayed bridges with four roadway lanes and one railway line on a steel deck (330 m central span and 110 m lateral spans) that conform together with the access viaducts, the so-called ZarateBrazo Largo Road/Rail Complex. One of the cables failed unexpectedly due to the combination of factors that had been ignored due to lack of proper maintenance, under permanent and normal traffic loads and normal meteorological conditions. The main reason behind the sudden rupture was the important degree of corrosion of the parallel wire cables mainly close to the bottom anchorages.

Figure 4: Cable-stayed part of the Zarate-Brazo Largo Bridge Complex (Argentina)

89

The objective of measurements of deck vibrations is to determine through tests the most significant natural frequencies of the cable stayed bridges of ZBL in order to calibrate the numerical models used in the evaluation of traffic and wind effects. Table 3 summarizes the main natural frequencies involving vertical components of displacement. In summary, the three lowest frequencies of the dominant modes of both bridges that involve vertical deck vibrations of the two ZBL bridges are: 0.44 Hz, 0.58 Hz and 0.63 Hz Table 3. Natural frequencies of ZBL Brigde [Hz]

Parana de las Parana Guazii Bridge Palmas Bridge 0.441 0.436 1 0.584 0.572 2 0.641 0.632 3 0.688 0.672 4 0.762 0.749 5 0.930 0.914 6 0.968 0.969 7 1.003 0.994 8 1.074 1.072 9 1.111 1.112 10 1.153 1.160 11 1.223 1.221 12 1.270 1.267 13 1.352 1.345 14 1.393 1.399 15 1.508 1.496 16 These measured frequencies provided useful information in two respects: i) The structural behaviour of the bridge. The new set of measurements confirm that the behaviour of the two bridges is in agreement with the numerical model and in close agreement with measurements performed at the end of construction. ii) Provided actual field data to calibrate the numerical model used to assess the structural safety of the bridges (deck, cables and pylons) after 22 years of service. Mode

A set of dynamic tests in the cables were also performed to provide a complete and updated set of natural periods and cable forces under permanent loads of all cables to serve as reference values and to provide the "initial" forces for cable replacement operations in the future, and also to help identify possible changes of cable stiffness with respect to the reference state at the end of construction (1977). The anchor pendulums are steel trust that link the deck with the anchor pier of the bridge. To evaluate their actual condition and effectiveness in anchoring the deck at this point, a set of measurements of the vertical displacement at their location were

90 carried out. This is a very important point because the incorrect performance of the anchor pendulums derives in the modification of the boundary conditions at the end of the bridge, and this may affect in a very relevant way the dynamic behaviour of the bridge. It has important influence in updating the theoretical model too. The relative vertical displacements between the top of the pendulums and the top of the anchor piers was recorded under normal traffic conditions. These records show variations of vertical displacements caused by traffic loads with changing signs depending on the instantaneous position of the moving load. For the purpose of comparing the experimental results with predictions by the numerical model, the influence line of the reaction at the pendulum was computed with the model of the bridge, and superimposed in scaled form with typical displacement records generated by a single truck moving along the bridge. These results are shown in Fig. 5. The pendulum displacements differ significantly from the computed influence line. Therefore the assumption of fixed zero displacement is not valid.

0

50

100

150

200

250

300

350

400

Distance [m]

Figure 5: Theoretical and measured influence lines of the force on roadway pendulum

5

Application to active control of cable-stayed bridges

We have shown how the calibration of the theoretical dynamic model for a cablestayed bridge can be performed via dynamic testing. This makes possible to get a very accurate model to predict the real dynamic behavior of the bridge. Thus, the techniques of active control can be used in a more efficient way. In the following we will see an application of active control in a cable-stayed bridge. Although the active control is only theoretical and simulated, the bridge is real. The idea is to design an automatic control system for a cable-stayed bridge to actively counteract external environmental forces generated by earthquakes. The introduction of this intelligent feature in the structure turns an otherwise passive bridge into a smart bridge, capable of reducing the amplitude of the deflections of

91

its deck down to a desired level automatically. The control strategy proposed here uses a subset of the stay cables as active tendons to provide control forces through appropriate actuators. Each individual actuator is controlled by a decentralized controller that only uses local linear velocity and local linear relative displacement information. The effectiveness of the control algorithm is tested on a threedimensional model of the Quincy Bayview bridge [5,6]. The length of the main span is 297 m, and the length of each of the side spans is 145 m. The width of the deck is 13.2 m (from cable center to cable center). The bridge has a total of 56 stay cables. This paper uses the same bridge modeling philosophy outlined in [5,6]. The values of the modal frequencies found with the finite element model developed here differ from those found in [5,6] very slightly. The computed mode shapes, however, are almost the same for the first 20 modes. Therefore, we can conclude that we have a very accurate model of the bridge, as this has been compared with the results coming from a dynamic test in the real bridge. The finite element model uses 213 three-dimensional beam elements (six degrees of freedom per node) for the deck and towers, and 56 one-dimensional truss elements. The first 10 modal frequencies (in Hz) computed from the finite element dynamic model of the bridge are the following: 0.38, 0.45,0.52, 0.55, 0.60, 0.65, 0.70, 0.74, 0.80, 0.82. Before to proceed with the controller design, we need to assess the uncontrolled bridge performance in the presence of seismic excitation. Let such an excitation be provided by the corrected vertical acceleration record of the Taft Earthquake. Most of its energy is concentrated in the range of 0 to 13 Hz. This is a good test signal to assess uncontrolled performance, since it can provide a high enough level of excitation to practically every on of the lower vertical modes of the bridge. Figure 6 shows the bridge's deck vertical deflections at t = 2 and 10 seconds. The maximum deck vertical deflection is 0.18 meters. After observing the vertical deflections of the deck of the uncontrolled bridge caused by the earthquake, it was decided to place 6 couples of active controllers. The design of the decentralized active control system is fully explained in [7].

''

j

A^

i

i

&

100

200 300 400 posfem ikMgbndgc deck n m a t r s

OTffl ICO

299 300 400 postisHt itoog bridjp deck ift i w t m

Figure 6 : Vertical deflections along span for t= 2 s (left) and t = 10 s (right)

$00

92

Then the controlled response of the bridge in the presence of the same seismic input (Taft earthquake vertical acceleration component) is shown in Figure 7. In this case, the maximum deflection is only 0.016 m. Although only local information has been used to control the entire bridge, the deflections have been reduced substantially.

tinrc * i seconds

posiisa afeng bridsss <*ecte an meKas

Figure 7 : Controlled response of the bridge using decentralized active control in 12 stays

Acknowledgements The authors acknowledge the partial support provided by the Spanish Ministry of Education (CICYT) through Research Project TAP99-1079-C03-C01. References 1. A.C. Aparicio and J.R. Casas. The Alamillo cable-stayed bridge: special issues faced in the analysis and construction. Proceedings of the Institution of Civil Engineers (Structures and Buildings), Vol. 122, pp. 432-450 (1997) 2. J.R. Casas. Full-scale dynamic testing of the Alamillo cable-stayed bridge in Sevilla (Spain). Earthquake Engineering and Structural Dynamics, Vol. 24, pp. 35-51(1995) 3. J.R. Casas. A combined method for measuring cable forces: The cablestayed Alamillo bridge, Spain. Structural Engineering International, Vol. 4, N.4, pp. 235-240 (1994) 4. C. Prato, M.A. Ceballos, J.R. Casas, A.C. Aparicio. Interpretation of ambient vibration records for restitution of deck profile of the ChacoCorrientes cable-stayed bridge. Proceedings of Structural Faults and Repair 97. M.C. Forde Editor, pp. 387-394 (1997) 5. J.C. Wilson and W. Gravelle. Modelling of a cable-stayed bridge for dynamic analysis. Earthquake Engineering and Structural Dynamics, Vol. 20, pp. 707-721(1991) 6. J.C. Wilson and T. Liu. Ambient Vibration measurements on a cable-stayed bridge. Earthquake Engineering and Structural Dynamics, Vol. 20, pp. 723747 (1991) 7. M.E. Magafia, J. Rodellar, J.R. Casas, J. Mas. Active control of cable-stayed bridges. Smart Structures, Nato Science Series, pp. 193-202 (1999)

SOME IMPLEMENTATIONAL ISSUES I N S T R U C T U R A L CONTROL S.Y. CHU, T.T. SOONG AND A.M. REINHORN Department of Civil, Structural, and Environmental Engineering, State University of New York at Buffalo, Buffalo, NY 14260, USA In structural control, a number of practical issues arise when a control strategy is implemented in practice. These include discrete-time control, time delay, model construction and experimental verification. This paper proposes a procedure which can be used as a bridge between theoretical algorithm development and practical implementation. To demonstrate this procedure, a discrete-time output feedback model with time delay is used as the foundation for designing an optimal control system. It is then implemented inside a controller PC with an independent Digital Signal Processor (DSP) to carry out the calculation of required control force and also perform the function of data acquisition through communication with the Analog to Digital Converter(ADC) and the Digital to Analog Converter(DAC). Another simulator PC with the similar dedicated hardware which simulates the real-time response of the identified feedback model is then constructed to verify the real-time control effect. The integrated system not only verifies the effectiveness of the digital controlled system but also provides an economical pre-implementation testing base.

1

Introduction

Although a number of control problems are theoretically solvable, such as modeling errors, spillover effects, structural nonlinearities, limited numbers of sensors and controllers, discrete-time approach, and time delay effect 9 , the necessary knowledge about a practical control system is required in order to translate theoretical developments into practice. For example, the basic knowledge to handle digital data discretized from analog measurements and some important factors such as the transformation from theoretical simulation values to practical signals or the effects of saturation is needed *. The generalized hardware function of an active control system is represented by the block diagram in Fig. (1). The response of structure under external excitation, the active device status, the remote control status, and the fail-safe monitoring status of the Active Control Force Generation System (ACFGS) (usually continuous analog voltage signals) are measured by the measuring equipment and then sent to the Custom-Designed Signal Interface System(CDSIS). The required signals are collected together and sent to the Digital Control System(DCS) via the Data Acquisition System to perform the major control pro-

93

94

cess. The required control force command and the remote control command are generated by the control command calculator and send to the ACFGS through the CDSIS 3 . Apart from the hardware equipment, the core of an active control system is the control software that generates the appropriate control command signals based on the response of the controlled structure according to the proposed control algorithm, and sends out the remote control command based on continuously monitoring of the outputs of the controlled structure to trigger the operation of the ACFGS. The required knowledge for programming such as, access to the hardware issues, analog I/O issues, fixedand floating- point arithmetic issues, saturating issues, fixed- and floatingpoint scaling issues, error detection and correction issues, and communication interface issues have to be understood clearly 6 . Some important modules should be provided by the microcode so as to be able to conduct the control process and also perform the required issues with more flexibility 3 . Especially the required theoretical development and experimental counterparts like Discrete-Time Control Analysis and Design, Development of Appropriate Control Algorithm, Analytical Simulation Tools, and Integrated Emulation Simulator should also be constructed to perform the complete procedure. In this paper, a discrete-time output feedback control algorithm with time delay is proposed as the design base. And a hybrid mass damper (HMD) model is used to demonstrate the required considerations and procedures while implementing a theoretical control law. A digital control system which contains a dedicated PC with an independent DSP is used as a digital control processor(DCP) in this study to develop robust control algorithms and modules for implementation. A simulator PC which emulates the real-time response of a theoretic structure model based upon the discrete-time approach is constructed in the laboratory to verify implementation procedures. 2 2.1

Theoretical Development Discrete-Time Direct Output Feedback Control Algorithm with Time Delay

The equation of motion of an n-DOF discrete-parameter structure under dynamic loading w(t) and time delayed control force u(f - td) can be written in state-space form as *(*) = [Ac]x(t) + [Bc]n(t - td) + [Ee]v(t)

(1)

where x(t) is the state vector and [Ac], [Bc], a,nd[Ec] are the system matrix, the controller location matrix and the external loading location matrix,

95

respectively. System stability of the time-delayed continuous-time control system is examined throughout by analyzing system modal properties after time-delayed control 2 . The use of digital computer to conduct control performance is now common in the control industry, thus the discrete-time control algorithm is inevitably necessary. Assuming the sampling period of the measurement is T, the control force delay time td can be split into an integer of the sampling period and a fraction. Define an integer I and a positive number m such that td = (i — m) T and £ > l , 0 < m < l . With the assumption of zero-order hold, the solution of Eq. (1) in discrete-time format is x(fc + 1) = [A]x{k) + [£i]u(fc - I) + [B a ]u(* - / + !) + [E]w(k)

(2)

where [A] = e^T,[B1] = [AC}-\[A] - [A}™)[BC], [B2] = [AC]^([A]™ [I])[BC], and [E] = [Ac]'1 ([A] - [I\)[EC]. In direct output feedback, the control forces are calculated directly from the multiplication of delayed output measurements by constant feedback gains. Thus, u(fc — £) = [G][D]x(k — (.). In order to represent Eq. (2) as the traditional first-order difference state equation, we need to define a new augmented state vector x(fc) which includes the control force vectors from u(k — 1) to u(fc — t). Then the new first-order difference equation will be x(fc + 1) = [A]x(k) + [B]u(fc) + [E]w(k)

(3)

where

[A] =

[A] [Bi] [B2] 0 0 0 -[I] 0 0 0 0 m

• •

• o•

0

• •

0

• o

, [B] =

0 0

0 0

0 0

0 0

• • [T\ . . 0 .

\[E]

•

0 0

0 0 , [E] =

0

Lm-J

(4)

0 . 0

with the modified output matrix [D] = [ [D] 0 0 ... 0]. For a controllable and observable system, there exists an optimal output feedback gain matrix [G] such that the discrete quadratic performance index oo

J = £{x T (fc)[Q]x(fc) + uT(fc)[iqu(fc)}

(5)

fc=0

is minimized subject to the system constraint. In Eq. (5), [Q] is a positive semi-definite augmented response weighting matrix constructed from [Q] and [R] is a positive definite control force weighting matrix. If the control system

96

performs well under random excitation, it will work equally well for random initial conditions, and vice versa. Consider the system under random initial disturbance XQ = [ x(0) 0 0 ... 0 ] , the discrete-time optimal output feedback gain matrix [G] satisfies the following simultaneous linear algebraic equations 4 , 5 : ([A] + [B][G][D])T[H]{[A] + [B][G][D]) - [H] + {[Q] + [D]T[G]T[R][G\[D]) = 0 (6) {[A] + [B][G][D])[L]([A] + [B][G]{D])T - [L] + [Xo] = 0 (7) [5]T[S]([A] + [B][G][D])T[L][D]T + [R][G][D][L][Df = 0 (8) where [H] = £ ~ o { [ ( M + [B}[G][D})T([Q] + [D]TMT[K\[G\[D]){[A] -T [B][G][D])k}, [L] is the Lagrangian multiplier matrix, and [X0]

+

x0 • x 0 .

2.2

Numerical Model and Analytical

Simulation

For a structure with a hybrid mass damper under earthquake loading xg(t) and time delayed active control force u(t-£<j) as shown in Fig. (2), the equation of motion of the system can be represented as XBr(t) XDB(t)

+

2£BUJB

—2/J,£DU>D

{ XBr(t) 1

0

2/^DWD

1 XDB(t) j

/ XBr(t) \ _

^i

u(t - td) +

w% ftu2D -1 -A*

,(*)

(9)

where XBT and XDB are the relative displacement of the system and the relative displacement of the damper with respect to the system, respectively. The parameters of the system 7 are given in Table(l). If we choose UD — 0 and £D — 0, the HMD system becomes an AMD system and if you force u = 0 it becomes a PTMD system. The pattern of sensor types are symbolized by X and V. For example, XDVD indicates that the relative displacement (XDB) and velocity {XDB) of the damper with respect to the system are measured. A study of the theoretical development and numerical simulation results indicates that the XDVD feedback in both HMD and AMD systems is more efficient and acceptable. The active damping ratio £c of AMD system is more sensitive to time delay than the HMD system. Thus AMD XDVD control type will be used in this paper to illustrate the required implemental procedures. The influence of delay time to the active modal frequencies u_c and active damping ratios £c of the controlled system is shown in Fig. (3). From previous

97

experimental results 8 , the calculated delay time of an active-tendon system is close to 40 msec. In order to emulate this real configuration of experimental setup, we set the delay time t d = 40 msec. The corresponding continuous-time modal properties when ta= 0 and 40 msec ( A M D C - T ) are calculated by using the explicit stability formulas proposed by the authors 2 . The discrete-time control gains are calculated based on the same choice of weighting matrices [Q] and [R] as in the continuous-time. Since the real experimental requirement of sampling period is 22 msec, we choose the sampling period T= 20 msec in Eq. (2) to find the discrete-time output feedback optimal control gains. The control effects on modal properties denoted as A M D D _ T are shown in Table (2). In practical implementation, the control gains are saved inside the control program for finding the required control force. The modal damping ratios of A M D C - T ( O ) are reduced dramatically to those of AMDc-x(40) due to the 40 msec time delay. This effect can also be observed if we use the continuous-time gains in the discrete-time modal analysis with sampling period T=20 msec. The mismatch of modal properties between continuous-time and discrete-time is also due to the choice of sampling period. The continuous-time case with T -> 0 is impossible to achieve in real implementation. So the discrete-time modal properties also provide a tool to predict the effectiveness of control under certain sampling period and delay time. If we use the discrete-time optimal gains for the AMD system, A M D , D _ T ( 4 0 ) , the control effect is even better than the ideal continuous-time case without delay. As we check the difference between the control gains, the time delay and sampling period effect had been automatically included inside the optimization process. There is no phase-shift needed for the output feedback control algorithm, and actually it is also difficult to perform the phase-shift modification. There is another important issue that needs to be clarified before we implement the proposed algorithm in real-time application. According to the derivation of discrete-time control gains, the sampling period of applying control force, Tu, should be the same as the sampling period of response measurement, T. In order to predict the response of a continuous-time model correctly, however, we need to simulate the response of the corresponding discrete-time model in a smaller sampling period. From the verification testing, the sampling period of the Real-Time Structural Simulator is chosen as 1.82 msec. The corresponding response of uncontrolled and PTMD systems are verified to be the same as those in the continuous-time approach (Table(4)). The 1940 El Centro earthquake (N-S component) in Fig. (5) is used as the base excitation to verify the control effect and to find the required control forces. The discrete-time analytical solutions are simulated by using Tu— 22 msec and T= 1.82 msec.

98

3 3.1

Experimental Verification Experimental Setup

The integrated pseudo real-time verification system as shown in Fig. (4) is constructed to perform the pre-implementation testing that includes two parts as follows: D S P Controller System: The required control force is calculated by a dedicated controller PC which is equipped with a QPC/C40B TIM Carrier Board with one TMS320C40 processor, a 12-bit A/D Converter Board, and a 12-bit D/A Converter Board. The TMS320C40 is the first of Texas Instruments 'TMS320C4X' generation of floating-point processors that is capable of performing the Programmable Erasable Read-Only Memory (PEROM) function. The Read-Only Memory (ROM) is used to store the programs that are executed repeatedly. This set of data acquisition system is also equipped with a DSPLINK digital system expansion interface, which is a high-speed, bidirectional bus that allows input/output directly to/from the DSP between A/D or D/A converters, without using the I/O bus on the host machine. The proposed control strategy is coded in C / C + + language and is downloaded to the PEROM of DSP to perform independent data acquisition and control force calculation. Real-Time Structural Simulator: The digital structural simulator employed in this experiment utilizes a DT-2801 data acquisition board made by Data Translation Inc. It is configured on a board that plugs into an ISA slut in a PC's expansion bus and features an on-board microprocessor and 8 differential 12-bit A/D input channels and two 12-bit D/A output channels. The actual real-time response is performed by a customer-written program downloaded to the microprocessor on the DT-2801 board. This simulator software is written in C language in order to access the hardware and communicate with A/D and D/A converters. Although the discrete-time model will converge to continuous-time model if the sampling period is close to zero, the time needed to calculate the analytical response of the discrete-time model inside the microprocessor should also take into consideration. The sampling period of the Real-Time Structural Simulator can't be too small in order to provide enough time to perform the calculation. The real sampling period will depend on the algorithm of the program and the numbers of data needed to be recorded. It is thus very important to identify the sampling period with respect to different codes.

99

Real-Time Control Process: To perform the real-time control, the output of the system at each time step is measured by DSP Controller and the required control force is then calculated inside the DSP and send out the analog voltage signal through ADC to actuator to apply the appropriate control force to the system. In this experiment, this control force analog voltage is routed directly into the Real-Time Structural Simulator to perform the pseudo realtime testing. In order to emulate the 40 msec delay time, we set the internal clock inside DSP program as 0.4 kHz (2.5 msec) and the resulting sampling period for response measuring T and control force application Tu is 22 msec. The required time to calculate the control force is also identified as 44 msec. Detail descriptions can be found in Table (3). The internal clock inside RealTime Structural Simulator is set as 1 kHz (1 msec) and the real sampling period to perform the response of the HMD benchmark model is identified as 1.82 msec. This choice of sampling period is verified by experiment to be small enough to emulate the continuous-time response of the HMD benchmark system.

3.2

Experimental

Verification

According to the estimated maximum response, we then setup the scaling factors to conduct the experimental verification as shown in Table (4). If any of the signals either inside the DSP Controller or the Real-Time Structural Simulator exceeds the preset limitation, the program will be terminated automatically to protect the system from saturation which may cause damage in real application. The control effects of the ideal continuous-time control without time delay are compared with the discrete-time analytical solutions and the experimental measurements from the Real-Time Structural Simulator as illustrated in Table(5). Without the action of control force, the experimental results show that the Real-Time Structural Simulator can emulate the response of uncontrolled and PTMD systems very well. And the results of discrete-time analytical analysis are very close to those from real measurements of the experiments. The only exception is the A M D C _ T ( 4 0 ) case, which uses the continuous-time gains inside the implementation of the discrete-time controller. Since the response of this system has exceeded the hardware limitation of the Real-Time Structural Simulator, no further experiments can be conducted unless the preset scaling factors are increased. With the XDVD output feedback type, the required stroke measurements of system with 40 msec delay time (denoted as AMD (40)) are compared with PTMD in Fig. (6). The measurements of absolute acceleration and relative displacement of the

100

AMD system with 40 msec delay time are depicted in Fig. (7). The corresponding control forces calculated by analytical simulation and experimental measurement are compared in Fig. (8). 4

Conclusions

The issues along with the implementional procedures include discrete-time control, time delay, model construction and experimental verification are demonstrated in this paper. The control effects on the HMD benchmark system with time delayed control forces have been investigated thoroughly by both analytical and experimental verification. The proposed discrete-time output feedback optimal control algorithm is proved to provide the desired control effect and stability of the controlled system is also guaranteed. Moreover, the integrated real-time simulation system provides an economic and efficient testing platform. It can also be used to conduct reliability analysis of the integrated system with parameter uncertainty or measurement noise. Acknowledgments This research is supported in part by the National Science Foundation under grant No.CMS9402196 and by the Multidisciplinary Center for Earthquake Engineering Research under grant No.MCEER-992401. References 1. K.J. Astrom and B. Wittenmark, Computer-Controlled Systems: Theory and Design, Prentice Hall, Upper Saddle River, New Jersey, 1997. 2. S.Y. Chu and T. T. Soong. "Time Delay Effect on Direct Output Feedback Controlled Mass Damper Systems", to appear in Proceedings of the 2000 American Control Conference, 2000. 3. S.Y. Chu, T. T. Soong and A.M. Reinhorn. "Integration Issues in Implementation of Active Control Systems", to appear in Proceedings of the Second European Conference on Structural Control, 2000. 4. L.L. Chung, C.C. Lin and S.Y. Chu, "Optimal Direct Output Feedback of Structural Control", J. Engrg. Mech., ASCE, 119, 2157-2173, 1993. 5. L.L. Chung, C.C. Lin and K.H. Liu, "Time-Delay Control of Structure", Earthquake Engrg. and Struct. Dynamics, 24(5), 687-701, 1995. 6. Gene F. Franklin, J. David Powell, and Michael L. Workman, Digital Control of Dynamic Systems, Addison-Wesley Publishing Company, Inc., 1990.

101

7. C.C. Lin, J.F. Wang and Y.C. Gau, "System Identification and Vibration Control of Structures with Tuned Mass Dampers", Proc, 3rd R. 0. C. and Japan Joint Seminar on National Hazards Mitigation, 436-450, 1993. 8. S. McGreevy, T.T. Soong and A.M. Reinhorn, "An Experimental Study of Time Delay Compensation in Active Structural Control", Proc. SEM 6th Modal Analy. Conf., II, 733-739,1987. 9. T.T. Soong, Active Structural Control: Theory and Practice, John Wiley k Sons, Inc., New York, 1990. Table 1. Parameters of the System

System parameters Mass , TUB (kg) N a t u r a l frequency , UJB ( H Z . ) Damping ratio , £g (%) D a m p e r mass ratio , /x = mo/ms P T M D , D a m p e r designed frequency , WB ( H Z . ) P T M D , D a m p e r designed damping ratio , £ D (%)

Parameter values 6897.5 1.00 2.00 0.05 0.93 11.00

Table 2. Control results on modal properties

Cases

td (msec)

[-

N/cm

[G\ - N • sec/cm]

Uncontrolled PTMD

(Hz) 1.00 0.87 1.07

(%) 2.00 6.90 6.31

0.87 1.03 '0.86' 1.08

13.15 7.87 '4.77' 4.49

0.86 1.08 '0.87' 1.03

3.02 3.09 15.87 8.74

Continuous-Time AMDC-T

0

[0

-109.70

0

-7.25]

AMDC-T

40

[0

-109.70

0

-7.25]

0

-7.25]

Discrete-Time with T = 20 msec AMDC-T

40

[0

-109.70

AMDD_T

40

[0

-92.09

0

-12.30]

102 Table 3. Distribution of microcode execution time

Time Description (msec) 40 Target emulated delay time 2.5 Clock-Setup referred to 4 A/D's conversions in parallel 20 Conversion time for all channels (32 ch) on the board / 1 cycle 2 Program execution time / 1 cycle 22 System total sampling time / 1 cycle 44** Active force application delay time ** Achieved delay time needs 2 cycles of program computation

Table 4. Setup of Experimental Scaling Factors

Software/Hardware HMD Model Structural Simulator DSP Controller

yU'lmax

max

max

±30.48 cm (±12 in) ±10 Vdc ±2.5 Vdc

±203.2 cm/sec (±80 in/sec) ±10 Vdc ±2.5 Vdc

±4450 N (±1000 lb) ±10 Vdc ±10 Vdc

Table 5. Maximum response under El Centro earthquake

Cases

(XBr) (cm)max Continuous-Time Analytical Solutici n 15.16 Uncontrolled 0.61 PTMD 0.36 8.76 0.40 9.96 AMDC-T(O) Discrete-Time Analytical Solution 15.24 0.61 Uncontrolled PTMD 0.36 8.76 11.21 0.47 AMDC-T(40) 9.72 0.40 AMD£,_ T (40) Experimental Measurements Uncontrolled 0.61 15.23 PTMD 8.76 0.36 N/A N/A AMDC-T(40) AMD£,_T(40) 0.41 10.15 max

isfs)

max

y^Jmax

(cm)

(N)

29.67 22.58

2687.8

29.76 43.44 23.21

5164.41 2781.4

29.61 N/A 22.72

N/A 2707.37

103

Digital Control System (DCS) Control Command Calculator (CCC) System Information Control Command (Digital) (Digital) j Data Acquisition/Conversion System (DACS) ADC DAC

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System Information (Analog)

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Status Check

Active Control Force Generation System (ACFGS)

Measuring Equipment (Sensors)

Displacement, Velocity, Acceleration, Force

Active Control Force

Excitation

Signals (Analog)

Response

Structure

Real-Time Structure or Structural Simulator Figure 1. The General Hardware Function of Active Control Systems

.

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104 1.1

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0.08

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0.C

Figure 3. Time delay effect on active modal frequencies and active damping ratios of AMD XDVD system 2

Real-Time Structural Simulator

DSP Controller System

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Keyboard

Ti

Monitor

DT2801 Data Acquisition Board

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16 Caunel D/A Converter

Custom-Design Signal Interface System (CDSIS)

Figure 4. The Experimental Setup of the Pseudo Eeal-Time Verification Test System

Figure 5. 1940 El Centro earthquake

105 30

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20

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15 Time (sec) Figure 7. Absolute acceleration and relative displacement with AMD(40) (Experiment)

Figure 8. Control force with AMD(40) (Analytical vs. Experimental)

MONITORING OF INFRASTRUCTURES IN THE MARINE ENVIRONMENT

A.

DEL GROSSO

Department of Structural and Geotechnical Engineering, University of Genoa, Via Montallegro, 1 -116145 Genoa, ITALY e-mail: delgrosso@diseg. unige. it Maintenance, implemented through inspection and rehabilitation cycles, of infrastructures has taken a paramount role in modern civil engineering research because of the very large amount of aged infrastructures existing in the world. Among these infrastructures, those interacting with the marine environment, i.e. port and coastal structures, structures for oil and gas production and transportation, are posing to the engineering community very interesting and challenging problems. After a review of the maintenance strategies more useful for engineered structures in the marine environment, the paper addresses some topics of the longterm monitoring of breakwaters, internal port structures, offshore platforms and submarine pipelines, showing the interdisciplinary aspects arising from these new fields of the civil engineering activity.

1

Introduction

Looking at the scientific and technical journals belonging to the field of civil engineering over the last 20 years, we observe that many new and unconventional problems have been brought to the attention of the engineering community. Moreover, we will also discover that many prestigious journals, well known in other disciplines, are publishing papers somehow related to civil engineering problems. The rationale staying behind this observation, lies in the fact that managing constructed facilities is becoming more critical than building new ones. Economical and social reasons, sometimes more stringent than purely technical reasons, stay underneath this fact, but by no way we could avoid to face the challenges of this highly interdisciplinary context. Especially infrastructure systems form the object of these new developments, because on the one hand they are more subjected to obsolescence and, one the other hand, they involve economical and financial aspects more important than other engineered structures. In addition to aging and physical degradation, infrastructure obsolescence may have different sources. According to Lemer [1], the factors that can cause obsolescence can be grouped into four categories: 1. technological changes, that influence the scope or level of services the infrastructure is to provide; 2. regulatory changes, that impose new requirements on infrastructure; 3. economic or social changes in the market within a region, that alter the demand placed on infrastructure; 107

108

4.

changes in value or behavior of the people who use and own the infrastructure, that similarly alter demands. System management is therefore becoming at least as important as system design in the continuous balancing of safety, usability and profitability of an infrastructure. Such balance introduces the concept of fitness for use. A dynamic measure of the fitness for use can form the basis for decision making by expert panels in establishing if an infrastructure needs intervention. Relative measures of fitness for use can also be very useful in establishing ranking systems, able to help decision makers, responsible for the management of large infrastructure systems, in optimizing investments for repair or replacement. In the simplest form, fitness for use can be expressed by a weighted summation of scores, attributed to the infrastructure according to different criteria: Fu = I ; Wi ^ ,

(1)

where Sj is the score and w( is the corresponding normalized weighting function, such that Zi Wj = 1. However, multiplicative models and different multi-criteria as well as single-criteria measures of the fitness for use can also be introduced, and qualitative methods as well as quantitative, based on complex mathematical models, can be used to perform scoring. Monitoring of an infrastructure involves periodical reassessment of the fitness for use, in order to determine its decay in time and, whenever the measure indicates that a minimum acceptable limit is being reached, refurbishment activities shall be planned. Infrastructures interacting with the marine environment, like ports and facilities for oil and gas exploitation in the continental shelf, represent a very significant casestudy for the above principles, because of their extreme economical importance and because of the concern about the effects that these facilities may produce on the natural environment. Fixed marine structures are primarily designed to withstand environmental forces. Knowledge about phenomena related to environmental dynamics has greatly improved in the recent years, and today's standard design loads are substantially increased with respect to past standards (e.g.: the return period of the design wave has been increased in API standards from 25 to 100 years after the hurricanes in the Gulf of Mexico of 1964 and 1965 [2]). Fatigue, corrosion and material degradation due to chemical and biological phenomena are more severe in the marine than in any other environment. Many coastal structures are inherently subjected to damaging by the sea (rubble-mound breakwaters) or are definitely conceived for being modeled by the waves (berm breakwaters). In addition, interaction with the environment may cause effects that in turn can modify actions on structures ( e.g.: reflected and refracted waves, drag forces, scouring, interaction between sea floor and pipelines, etc.). All the above considerations indicate that life-cycle management of infrastructures in the marine environment cannot be conceived without putting in

109 place fitness for use reassessment and requalification programs based on condition monitoring of structural components. This paper is intended to examine some of the aspects related to structural monitoring in this context, with the aim of calling to evidence the needs for developing and testing innovative technologies. Since monitoring is strictly related to maintenance strategies, a brief summary of the maintenance approaches suitable for application to infrastructures in the marine environment will be presented first. 2

Maintenance strategies

The definition of a maintenance policy shall be a part of the design process, in order to keep costs and benefits into a constant equilibrium during the entire lifetime cycle of an infrastructure. It is noted that, sometimes, infrastructures have very long design lifetime (50 to 70 years or more). The concept linking design, maintenance and risk can be expressed through the minimization of the lifetime cost [3,4]: Qifetae = I + PV(M) + PV(R) + PV(pf Cf)

(2)

where : I is the investment (construction) cost, M is the cost of monitoring, R is the cost of repair, p f is the annual probability of failure, Cf is the cost for the consequences of a failure, and PV is the present value operator. The last term of equation (2) is clearly a measure of the risk or a cost associated to failures. Monitoring techniques are defined in terms of the objectives that monitoring activity should obtain in function of the maintenance strategy adopted. Usually, a distinction is made between corrective and preventive maintenance. A corrective maintenance strategy is adopted when repair or rehabilitation is undertaken after a failure has occurred. This strategy may be suitable only for cases in which the global cost associated to the failure is low. In this case, the role of monitoring is just to detect if, when and where the failure has occurred. A preventive maintenance strategy, instead, is aimed at preventing the occurrence of failure states. Preventive maintenance is suitable when the cost associated with failure is high. Preventive maintenance strategies can further be classified into: 1. state (or condition) based maintenance, 2. time based maintenance, and 3. load based maintenance. State based maintenance is the most general approach. According to this approach, the role of monitoring is to allow detection and evaluation of the state of the system in the real-time, through the definition of an appropriate condition index or, if mathematical reliability models are available, of a reliability index. Several Repair, Evaluation, Maintenance, & Rehabilitation (REMR) programs based on

110

such concepts have been established worldwide by large-scale organizations managing marine infrastructure systems [ 5, 6, 7]. Time based maintenance is applicable when statistical knowledge allows the reliable definition of age-related hazard functions of some system component. In this way, detailed inspection or substitution of the components can be prescheduled. Monitoring is eventually required to improve knowledge on component performances. This method is normally applicable to widely used mechanical components. A load based maintenance strategy can be adopted when probability models are available, allowing to correlate the occurrence of a given intensity of load to the state of the system. Such strategy involves running of detailed inspections and rehabilitation works, only after a given phenomenon has occurred. In this case, the role of monitoring concentrates more on environmental phenomena than on the response of the system. Of course mixed strategies may be adopted for complex systems, especially when fitness for use derives from the superposition of the state of independent subsystems, with different characterization in terms of mechanical complexity and availability of probability models. In the selection of monitoring techniques for the different maintenance strategies, the following aspects should be considered: 1. cost of acquiring data; 2. data processing techniques, 3. information value of the data. The above discussion will be useful in the following paragraphs, where some of the problem related to monitoring of port structures, offshore platforms and pipelines will be addressed. It is anticipated that port structures will receive major consideration. 3

Monitoring of port structures

In port and harbor infrastructure it is necessary to make a distinction among external breakwater structures, internal structures and equipment. 3.1

Breakwater structures

In-service monitoring of breakwater structures may involve different aspects, depending on the type of breakwater and on what the monitoring is aimed at. The specification of in-service monitoring is due to the fact that in many cases monitoring during construction is aimed at optimizing the design/construction process. Construction of large breakwaters usually takes several years to be completed and may involve settlement of the sea bed, erosion by the waves and

111

streams, tilting of caissons etc., and requires a large amount of topographic and bathymetric surveys. In-service monitoring can be aimed at: a) improving knowledge on the site or monitor the effects of the structure on the environment; b) validating design hypotheses or applicable stardards; c) serving as a basis for maintenance operations. In the last case, the design of the monitoring system should be addressed to acquire information able to characterize the state of the entire structure and should fully comply with the criteria discussed in the previous paragraph. A further distinction can be made between vertical wall and rubble mound breakwaters. In the first case, the safety concept is similar to that of any other structure and damaging is not permitted, because it will lead to a major failure state. Monitoring usually involve determination of the water pressure on the vertical walls (to verify design hypotheses), dynamic response of the caissons to impacting waves, structural integrity, permanent settlement or rotations of the caissons. In the second case, damages can be permitted because they are repairable through maintenance and they do not necessarily mean failure. Monitoring shall therefore address the recognition of the damage state suffered by the jetty, in terms of fracture or displacement of their elements both underwater and above water (evolution of the profile), permanent displacements of the crest and characterization of the flow through the body of the breakwater. A common aspect is the monitoring of environmental conditions (wind, waves, streams, dynamics of nearby coastlines) and the evolution of the sea floor close to the breakwater foundation, because it may disclose the tendency to erosion, soil liquefaction or soil failures, causing collapse of the breakwater. It should be noted that the presence of a breakwater always alters the coastal equilibrium state. In both cases, a clear understanding of the potential failure mechanisms is crucial in designing a monitoring program. Important monitoring programs are currently under way in several countries. In the U.S., it is important to underline the activity of the Army Corps of Engineers, that is publishing very useful manuals and guidelines to design and run breakwater monitoring programs [8,9,10]. In addition, USACE is responsible for the conductance of large-scale monitoring of breakwaters and complete coastal engineering projects. A review of the most relevant experiences performed in the US is contained in the works edited by Magoon and Davidson [11]. In Europe, several projects have also been started. The largest and the most complete of them are the monitoring of the rubble mound breakwaters in Zeebrugge [ 12] and in the port of Sines [13 ]. A fairly small but still interesting program is being started in the Port of Genoa, where an old existing breakwater (Duca di Galliera) is being refurbished in order to recover the present damage state. According to the design, the jetty will be transformed into a berm breakwater [14]. It is planned to record the displacements

112

of the crest both during refurbishment and in the long-term, and to monitor the evolution of the critical profiles of the jetty. Monitoring for maintenance purposes is typical of rubble mound breakwaters. Among the different problems, two of them will be addressed in detail: a) detection of global displacements of the crest, and b) monitoring the evolution of the profiles of the jetty. 3.1.1

Displacement monitoring

The spatial distribution of settlement and rotations is of interest for the monitoring of breakwater behavior. Traditionally, displacement monitoring is performed by means of precision topographical surveys. However, modern technologies are available to perform this task and obtain data ready for computer processing. A readily available technology is represented by fixed GPS networks. A review of recent applications of this technique has been presented by Duff [15]. The method will be experimented on the Duca di Galliera Breakwater in the Port of Genoa. A future technology can be represented by satellite interferometric measurements, using fixed networks of corner reflectors [16]. 3.1.2

Profile evolution monitoring

This is the crucial aspect in the monitoring of breakwaters. An evaluation of the effectiveness of the different methods that can be used to this purpose is presented in [3]. Topographical, photogrammetric, and direct surveys using specially designed cranes have been used to monitor evolution of the emerged part of the jetty. Also, interesting applications of image recognition techniques have been used in South Africa by Hough and Phelp [17] to detect the displacement of the elements of a jetty from aerial images. For inspection and survey of the submerged part of the jetty, several traditional methods can be used, from diver's inspection, to side scan sonar bathymetry, etc. However, the interest is increasing towards emerging technologies such the use of ROV, multibeam Sonar and airborne Lidar systems. Especially, vessel operated multibeam Sonars are able to automatically produce accurate digital terrain models (DTM) of the submerged part [18]. Airborne Lidar Systems, such as SHOALS, are the most interesting technology because they can produce with a very reasonable accuracy a DTM of both the emerged and of the submerged parts, up to water depths close to 40 meters in optimal conditions. A review of the recent applications of the SHOALS system can be found in [19]. 3.2

Internal Structures

Internal structures in a port environment that may be subjected to monitoring are constituted by piers, docks, berths, dolphins, transportation facilities and buildings.

113

Such structures are not usually designed to withstand wave actions, but distress and degradation producing loss of functionality end even collapse may be caused, for example, by the following actions: a) Corrosion of steel and degradation of concrete and other materials; b) Excessive earth pressures due to overload on the quays; c) Overloading of slabs; d) Collision of Ships; e) Interaction with the sea floor (instability, erosion or dredging activities) f) External Hazards (earthquake, hurricanes, fire, etc). Corrosion and concrete degradation is one of the major causes of repair, especially after the diffusion of precast prestressed concrete elements that has taken place in the recent years for the construction of pier slabs, and because of the harsh microclimatic environment that sometimes is established between the slabs and the water surface. In a large port, monitoring by inspection usually involves important resources. Great interest is therefore devoted to instrumentation monitoring and some experiment is already going on. In the Port of Genoa, a 400 meter long gravity quay wall has been instrumented with fiber optic sensors to monitor the state of displacement potentially induced by nearby dredging activity [20]. Another application will be started soon, involving monitoring of a prestressed concrete pier slab with fiber optic deformation sensors and conventional sensors for moisture content, inserted in the beams at critical locations. It should be pointed out that fiber optic sensors look to be very suitable for application in this environment. Indeed, in addition to deformation sensing, fiber optic sensors can be developed for chemical, temperature, and other processes, thus allowing a high degree of integration of the data acquisition system. Stability, durability, independency on electrical disturbances, capability of being used in largely distributed networks render this technique superior to other sensing devices. 3.3

Equipment

A very large number of equipment involving important structural problems is used in ports. The degree of fitness for use of the entire infrastructure is largely dependent on the reliability and availability of such structures. Movable bridges, dock gates and locks, cranes and other loading/unloading equipment are among these structures. Structures for these types of application are usually steel structures, with the tendency in time to increase the slenderness (in order to reduce weight) and substitute welded box girders to traditional truss girders. As a consequence, instability to wind and lateral forces, insurgence of non-linear dynamic effects, excess of vibrations, fatigue cracking and steel corrosion are among the most frequently encountered problems for such structures, sometimes leading to

114

unexpected collapses. In addition, many port facilities still make use of existing equipment well beyond their operating life. All such structures are usually subjected to detailed periodical inspection programs but, clearly, great benefits can be expected from instrumental health monitoring experiences. However, despite of the fact that modern equipment is normally operated through computerized systems, monitoring of the structural response is still far from practice. 4

Monitoring of structures for oil and gas exploitation

Structures for oil and gas exploitation are among the most technologically developed structures in the marine environment and, due the their economic and environmental impact, they have also been the first objective for the development of instrumental monitoring techniques. 4.1

Fixed offshore platforms and raisers

Very extensive research and application efforts have been devoted to structural monitoring of fixed offshore platforms. The number of major operating platforms is now about 6,000 worldwide, with approximately one third of them called upon for extended service or reuse [21]. Some oil companies are owning or operating hundreds of such structures. Monitoring and inspection programs also form the subject of API and ISO recommendations. A very large number of papers on the subject can be found in the literature, but a survey of them is out of the scope of this paper. Some basic references can be found in the mentioned works by Bea [21] and by Banon, Bea et al. [ 2]. For the interest of the present discussion, it will be pointed out that technologies such as GPS and fiber optic sensing can also be very useful in upgrading the instrumentation available for platform monitoring. It should be mentioned that, especially in deep waters, oil exploitation is also performed by means of moored or position controlled operating barges or semisubmersible structures or buoys, connected to the well head by means of steel risers. Although risers are connected to the barge and to the well head by means of special joints, they undergo severe stress states because of the relative movements between the barge and the well head. Design and control of risers is one the most interesting structural problems today arising from offshore technology. A very interesting monitoring application to workover risers has been proposed by Osen et al [22]. They have developed a system, based on strain monitoring at the two ends of the riser, able to advise the operating barge about the state of stress in the riser, and drive the repositioning of the barge in order to keep the stress state below allowable limits. In this application, LVDT sensor types are used to pick up

115

strain data. However, Martinelli et al. [23] have shown that, in a similar application, arrays of fiber optic sensors have been able to work satisfactorily. 4.2

Pipelines

Development of marine pipelines for oil and, especially, for gas transportation has been very intensive in the recent years. Very large-scale projects have been realized and even larger projects are under study. It has been recognized [24] that hazards to underwater pipelines mainly (80 percent of reported failures) come from corrosion and third party external sources (navigation, fishing activity). Actually, inspection of existing pipelines is performed by the following tools: a) Intelligent pigs (internal inspection); b) Visual inspection by divers; c) ROV. Interest toward the use of continuous instrumental monitoring and new sensing technologies has been raised up by several parties, but no real applications are known at present. 4.3

Terminals

A very large number of open sea piers are existing worldwide to serve as terminals for oil export and import. Most of them are aged of more than 30 years, and quite a few built in the first decades of the 20th century are still in operation. This situation is posing a management problem to owners and public administrations because of the decision to close, substitute or refurbish the structures of these terminals that has to be taken in several cases. Usually, detailed periodical inspections are required to keep the terminals into operation. Interesting experiences, gathered by the California State Lands Commission have been presented in [25]. Besides these old or conventional types of structures, several projects are under way, aimed at realizing LNG terminals equipped with underwater storage facilities. Although even in this case practical applications are lacking, it is easily understood that instrumental monitoring and use of smart materials and sensors could greatly improve safety of such critical facilities. 5

Conclusions

Monitoring of infrastructures in the marine environment is a very broad subject and requires facing many different problems. From the cases discussed, it can be concluded that, in establishing monitoring programs for marine facilities, consideration shall be given, but shall not be limited to the following aspects:

116

a) lifecycle cost optimization; b) engineering support to decision making, involving structural safety and reliability models, risk analysis and fitness for use models; c) interaction with the marine environment; d) sensing technology; e) data analysis and interpretation. The latter aspect is crucial when continuous automated instrumental monitoring is applied, because of the extremely great amount of information that is gathered from the structural response. This observation lead to individuate data analysis and interpretation as one of the key problems in structural health monitoring for complex infrastructure systems. References 1.

Lemer A. C , Infrastructure Obsolescence and Design Service Life. ASCE Journal of Infrastructure Systems 2 4 (1996) pp. 153-161 2. Banon, H., R. G. Bea, F. J. Bruen, C. A. Cornell, W. F. Krieger, D. A. Stewart, Assessing Fitness for Purpose of Offshore Platforms. I: Analytical Methods and Inspection. ASCE Journal of Structural Engineering 120 12 (1994) pp. 3595-3612 3. De Rouck J., K. De Winne, Full Scale Dynamic Load Monitoring of Rubble Mound Breakwaters. Report MAST2 Project MAS20023, University of Ghent (1994) 4. Moubray J., Reliability Centered Maintenance. Butterworth-Heinemann, Oxford (1991) 5. Chouinard L.E., G. R. Andersen, V. H. Torrey, Ranking Models Used for Condition Assessment of Civil Infrastructure Systems. ASCE Journal of Infrastructure Systems 2 1 (1996) pp. 23-29 6. Staneff S. T., C. W. Ibbs, R. G. Bea, Risk-Management System for Infrastructure-Condition Assessment. ASCE Journal of Infrastructure Systems 1 4 (1995) pp. 221-229 7. De Franco S., P. O'Connor, A. Tallin, F. Puskar, Development of a Risk Based Underwater Inspection Process for Prioritizing Inspections of Large Numbers of Platforms, paper OTC 10846, Offshore Technology Conference (1999) 8. USACE, Design of Breakwaters and Jetties. Publication No. EM 1110-22904, Chapter 12 Performance Monitoring Plan (1986) 9. USACE, Surveys of Coastal Structures. Publication No. CETN-III-41 (1991) 10. USACE, REMR Management Systems for Civil Works. REMR Technical notes OM-MS-1.1 11. Magoon O. T. , D. D. Davidson, Case Histories of the Design, Construction and Maintenance of Rubble Mound Breakwaters. ASCE (1995) 12. Van Damme L., J. De Rouck, Monitoring of Zeebrugge Breakwater. Proceedings Coastal Engineering (1998) pp. 1944-1956

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13. Pita C , F. Abecasis, A. Femandes, Sines Breakwaters Monitoring Program. In Reconstruction of the West Breakwater at Port Sines, Portugal, ASCE (1994) pp. 408-427 14. Fedolino M., P. Grimaldi, S. Stura, G.R. Tomasicchio, The Duca di Galliera Breakwater of the Port of Genoa, in Case Histories of the Design, Construction and Maintenance of Rubble Mound Breakwaters. ASCE (1995) pp. 16-22 15. Duff. K, GPS Monitoring and Control in the Marine Environment, Proc. Int. Conf. Monitoring and Control of Marine and Harbor Structures, Genoa (1999) 16. Dellepiane S., G. Bo, R. De Laurentiis, A. Del Grosso, Remote sensing and Coastal Monitoring: methods and applications. Proc. Int. Conf. Monitoring and Control of Marine and Harbor Structures, Genoa (1999) 17. Hough G., D. Phelp, Digital Image Processing Techniques for the Aerial field Monitoring of Harbor Breakwaters. Proceedings Coastal Engineering (1998) pp. 1787-1799 18. Prickett T., Coastal Structure Underwater Inspection Technologies. USACE Publ. CETN-III-62 (1996) 19. Irish J. L., J.K. McClung, W. J. Lillycrop, Airborn Lidar Bathymetry: the SHOALS System. International Navigation Association Bulletin 103 (2000) pp. 43-53 20. Del Grosso A., D. Inaudi, G. Brunetti, M. Fedolino, Monitoring of the San Giorgio Pier in the Port of Genoa with Fibre Optic Displacement Sensors. Proc. Int. Conf. Monitoring and Control of Marine and Harbor Structures, Genoa (1999) 21. Bea R. G., Reassessment and Requalification of Infrastructure: Application to Offshore Structures. ASCE Journal of Infrastructure Systems 2 2 (1996) pp. 45-53 22. Osen P., B. Johannessen, K. Stromsen, T.G. Werno, Instrumented Monitoring of Workover Risers, paper OTC 8797, Offshore Technology Conference (1998) 23. Martinelli M., A. Melloni, A. Gusmeroli, A. Tonini, P. Guaita, F. Trave, C. Barilla, C. Mariottini, G. Vegetti, C. Preti, G. Pagnoni e M. Pizzorno, Deployment of 32 FOIS Array for off-shore Structure Monitoring in the Adriatic sea, Proc. Int. Conf. Monitoring and Control of Marine and Harbor Structures, Genoa (1999) 24. Carpaneto R., E. Valente, Application of Innovative Monitoring and Sensing Technologies to Improve Safety of Marine Pipelines Against External Hazards. Proc. Int. Conf. Monitoring and Control of Marine and Harbor Structures, Genoa (1999) 25. Eskijian M.L., Structural Monitoring and Control of Marine Oil Terminals in California. Proc. Int. Conf. Monitoring and Control of Marine and Harbor Structures, Genoa (1999)

SEISMIC RETROFIT OF CHURCH BUILDINGS THROUGH BASE ISOLATION

A. DE LUCA, E. MELE AND C. GIAGNUOLO DAPS, Universita' di Napoli, Piazzale Tecchio n.80, Napoli ITALY E-mail: [email protected]

80125,

Base Isolation has demonstrated to be a very efficient means for protecting buildings against destructive earthquakes. The application of base isolation to existing monumental buildings has been made quite extensively in the United States [1-9] to buildings charachterized by structural typologies which are not very close to the older typologies existing in Europe. In this paper the possibilities of application of Base Isolation to church buildings is demonstrated through dynamic numerical analyses which have modeled the entire building. The efficacy of Base Isolation is demonstrated through a comparison of performance with the existing monument and with the monument retrofitted via some techniques which are very common: insertion of rigid diaphragm. It is concluded that the insertion of rigid diaphragm does not always provide better performance and that base isolation could be adopted in most cases for the seismic retrofit of churches.

1

Introduction

Church buildings, which represent a large portion of the Italian monumental heritage, have frequently demonstrated to be very susceptible to damage and partial or total collapse in earthquakes. Masonry churches, in fact, have been designed and constructed for resisting with wide safety margin to vertical loads, but are not able to withstand horizontal actions, which give rise to tensile stress in the masonry elements. In this paper the seismic behaviour and a retrofit solution of a basilica type church (already studied in [10]) is investigated. The plan, facade and the main longitudinal and transversal sections of the church are provided in figure 1. In the schematic plan provided in figure 1 the main macro-elements, appointed respectively as L1-L3 for the longitudinal direction and T1-T5 for the transversal direction, can be derived. Such elements are very repetitive in the church building typology, thus the results of the analyses on this specific case study can be somehow extended to a number of structures having similar characteristics. 2

Structural analysis of the church

In this section the main results of the analyses performed on the structural complex of the church are provided. Dynamic analyses are carried out the by means of a FEM computer code, with reference to the EC8 elastic spectrum (PGA = 0.35g), with the

119

120

aim of evaluating the principal modal shapes, the fundamental periods and the stress distribution in the single structural elements. The FEM model representing the structural system of the church is provided in figure 2. This model consists of 5941 joints 5572 shell elements and 56 frame elements used for timber trusses. PLAN SECTION A - A

(element

u

T4)

-ra.5

I 5.00.

11.6

I5.00|

_L

SECTION B—B ( e l e m e n t FACADE

(element

~^~S~~~~-

0

n

•

ft

2.7

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•

n

1 8.5

LONGITUDINAL SECTION ( e l e m e n t L2)

'f

id.a

T3)

T5)

I I I I I I I I" D • D 0 D

rrrrnrrn

-r

Figure 1. Plan, elevation and sections of the church studied

Figure 2. Finite Element Model of the church

SECTION

C-C

(element

T2)

121

The analyses have evidenced that the fundamental periods of the church (figure 3 and table 1) in the transversal (0.449 sec) and longitudinal direction (0.337 sec) are sufficiently small to advise for a retrofit solution which makes use of base isolation.

\

Ti =0.449 sec

T 3 =0.337 s e c

T2=0.375 sec

Figure 3. Mode shapes and periods of the 3D FEM model. Fixed Base solution

LONGITUDINAL

TRANSVERSAL MODE 1 2 4 10 14 15 16 22 26 38

PERIOD (sec) M / M m (%) SM/M l o l (%) 0.46 0.377 0.293 0.273 0.208 0.189 0.183 0.164 0.153 0.084

42.852 6.3447 2.658 9.686 4.664 2.801 4.547 1.638 2.083 9.88

42.852 49.1967 51.8547 61.5407 66.2047 69.0057 73.5527 75.1907 77.2737 87.1537

MODE 3 9 13 25 27 29 32 39

PERIOD (sec)

M/M tot (%)

ZM/M l 0 , (%)

0.342 0.274 0.211 0.157 0.143 0.129 0.12 0.086

58.563 1.6353 6.6337 1.715 1.975 2.543 1.188 10.993

58.563 60.1983 66.832 68.547 70.522 73.065 74.253 85.246

Table 1. Modal participation factors: church without retrofitting

In figure 4 (a) and 4(b) are provided the schematic plans of the church at different levels. In particular in figure 4(a) the different zones in which rigid diaphragms can be inserted are appointed as A, B, C, D. In figure 4 (b) the location of BIS devices at foundation level are given.

122

Figure 4. Plan of the church at different levels.

3

The BIS retrofit solution

The base isolation system has been designed to shift both the transversal and the longitudinal periods at 2.6 sec. The type of isolators to be inserted at the base of the church are HDRBs (high damping rubber bearings) having the characteristics given in figure 5.

J

t. r l

\ x Nssteel fe

plate

Rubber I

I

D

t r = rubber layer thickness H r =£t r = total rubber height D = diameter; A=(D/Hr)=3 +5 S = (D/4tr) > 30 av=3-10Mpa v = 10% Figure 5. Schematic representation and

main properties of BIS Devices

Given the position of the devices, which can be obtained from figure 4, and satisfying the requirements of figure 5, the dimensions for the isolators which are reported in table 2 have been obtained. Isolator D

K

n° mm mm

I I [

1 400 120

2 600 200

3 600 220

4 400 140

5 24 400 120

25 400 80

26-27-28 650 210

29-30 650 170

Table 2. Dimensions of BIS devices

In the FEM model of the B.I. structural complex a grid of very stiff beams has been introduced above the isolators. For the isolation system an equivalen linear viscous model, which has shown [11] to couple simplicity a satisfactory accuracy in the simulation of the actual HDRB behaviour, has been introduced in the FEM analyses.

123

4

Structural analysis of the BIS retrofit solution

The results of the dynamic analyses show the typical, SDOF type behaviour of B.I. structures. From figure 6 it can be derived that the first three modes are the ones characterizing the deformation of the construction acting as a rigid body on the devices. The modal participation factors (table 3) in the longitudinal and transversal directions confirm that the higher modes involving different deformations are practically not effective.

Ti=2.616 s e c

T 3 =2.5 s e c

T2=2.611 s e c

Figure 6. Modal shapes of the BIS retrofit solution LONGITUDINAL PERIOD (sec) M^Mtot(%) 2M,/Mtol(%)

TRANSVERSAL MODE PERIOD (sec) 1 I 2.616

M/M,ot(%) EM,/M 1O1 (%) I 99.102 | 99.102 I

MODE

I

2

|

2.611

I 99.711 I

99.711

Table 3. Modal participation facor: church with BIS retrofit

5

Analysis of results

The results of the analyses presented in this paper are provided in terms of a comparison of the behaviour of the following cases: • monument as is, which means without any retrofit; • monument retrofitted by inserting rigid diaphragms at different levels (the ones given in fig. 4a; • monument retrofitted through Base isolation which dimensions are given in fig.5 and table 2 and which location is given in fig. 4b.

124 25 Vi/Wtot % 0 without retrofit 20

S3 with rigid diapharagms SI BIS

15

10

5 -

Figure 7. Effect of base isolation and rigid floor on shear distribution on longitudinal and transversal elements. Shears nondimensionalized to toal weight of construction.

Due to the limited space not all the results are provided in this paper. Only the distribution of shears among the different transversal and longitudinal elements are given for the three above mentioned cases. The results are given in figures 7 and 8. From figure 7, in which shears, on all longitudinal (LI to L4) and transversal (Tl to T5) elements, are nondimensionalized to the total weight of the church, it can be derived the consistent reduction of forces when BIS is introduced with respect to the "as is" monument. It is also clear that the insertion of rigid diaphragms strongly concentrates the shears on the stiffer elements both in the longitudinal (LI and L3 elements) and transversal (T2 and T5 elements). The same distribution of shears is given in figure 8. In this case the shears on each element are nondimensionalized to the weight of the same element. This representation obviously confirms the same results but gives some interesting information on the efficacy of adopting the retrofit solution of inserting rigid diaphragms. It is in fact demonstrated that, in this particular case, the element in which shears are concentrated: LI and L3 in longitudinal and T2 and T5 in transversal attract shears which respectively are equal to 200 % and 150% of the weight insisting on the element. It can be easily demonstrated that these values of shears cannot be withstood by the element and therefore the retrofit solution is not appropriate unless other interventions are considered together with insertion of rigid floors.

125 Vi/W, %

L1

L2

L2

L3

T1

T2

T3

T4a

T4b

T4c

T4d

T5

Figure 8. Effect of base isolation and rigid floor on shear distribution on longitudinal and transversal elements. Shears nondimensionalized to weight of element.

In conclusion BIS is a very effective means for retrofitting these type of monuments while insertion of rigid diaphragms does not necessarily improve the seismic behavior. 6

Conclusions

The results of analyses of the "as is" church and BIS retrofit solution have shown that: • It is possible to obtain a particularly simple dynamic behaviour of the church through an appropriate design of the BI system. • BIS leads to large reduction of the strength demands in the structural elements, such to avoid tensile stress, and hence cracking, in the masonry elements. These results appear encouraging and suggest that the BIS can be delineated as a particularly promising strategy in the seismic retrofit of historic churches.

7

Acknowledgements

This research has been supported by the CNR Progetto Finalizzato Beni Culturali.

126

References 1. Honeck, W. And Walters, M, Use of steel in the seismic retrofit of historic Oakland City Hall. Steel Tips, Structural Steel Educational Council. 1994. 2. Buckle I.G. - "Application of base isolation systems to the seismic retrofit of historical buildings in the United States", in: Final Report on the Int. Workshop on the Use of Rubber-Based Bearings for the Earthquake Protection of Buildings, by James M. Kelly, Report UCB/EERC-95/05, 1995, pp.C5-C18. 3. Mayes R.L., Jones L.R., Kelly T.E. - "The economics of seismic isolation in buildings", Proc. of Int. Workshop on Recent Developments in Base Isolation Techniques for Buildings, Tokyo, Jap., 1992. 4. De Luca A., Mele E. - "The seismic isolation in the retrofit of historic buildings", Proc. of USA-Italy Seminar on the Seismic Restoration of Historic Buildings, Los Angeles, July 22-25, 1996. 5. Wyllie L.A. - "The balance between historic preservation and seismic safety can we achieve it?", in: The Seismic Retrofit of Historic Buildings Conf. Workbook, San Francisco, Cal., 1991, pp.5-1 - 5-9. 6. Elsesser E. et al. "Repair of five historic buildings damaged by the Loma Prieta earthquake.", in: The Seismic Retrofit of Historic Buildings Conf. Workbook, San Francisco, Cal., 1991, pp.4-1 - 4-40. 7. Youssef N. et al. - "Passive control of the Los Angeles City Hall". PVP, Seismic, Shock and Vibration Isolation, ASME, Vol. 319, 1995, pp.241-248. 8. Naaseh S. - "Seismic retrofit of San Francisco City Hall. The role of masonry and concrete", Proc. of the 3rd National Concrete & Masonry Eng. Conf., San Francisco, California, 1995, pp.769-795. 9. Seismic Isolation Project Briefs. Buildings, Dynamic Isolation System Inc., Sept. 1995. 10. Mele E., Modano M., De Luca A. The seismic retrofit of historic masonry buildings through BIS: preliminary analysis for application to church typology. Proc. of MONUMENT '98 Workshop on Seismic Performance of Monuments, Lisbon, Portugal, Nov. 1998. 11. Mele, E., De Luca, A., Ramasco, R. The effect of using different device numerical models on the global nonlinear behaviour of base isolated structures. Proc. of 11th WCEE, Acapulco, Mexico, Paper No. 1541. 1996.

TOWARDS A SAFETY CONCEPT FOR BUILDINGS WITH STRUCTURAL CONTROL

UWE E. DORKA University of Rostock, Dept. Of Civil Engineering, Philip Mtiller Str. 20, 23952 Germany E-mail: uwe. dorka @ bau. uni-rostock. de

Wismar,

For many structural control concepts to work effectively, structures must be modified and the control system then becomes safety critical. The control system modifies the loading on the conventional part of the structure. The reliability of this load modification capability is an important safety issue. Simulation models must be used to assess this load modification capability. They are more refined than design models and must be verified. They are not state of the art knowledge. For a realistic safety assessment, failure of the control system must be taken into account. This adds new failure modes un-common to structural engineers. But not every control failure triggers structural failure. A control system confidence can be defined and its required level may be given in codes. These issues are discussed and illustrated on HYDE-systems, a specific passive control concept for earthquake protection.

1

Introduction

Many structural control concepts have been developed in recent years. They can be classified as passive, active, semi active or hybrid. Because it is a new technology, it is often only used as "add on" to improve performance but not as a safety critical component for the structure. On the other hand, it is more and more evident that, in order to fully utilise the advantages of many structural control concepts, the basic conventional structure should be modified. This often makes the control system safety critical. Take Active Mass Dampers (AMDs) as an example. They are most effective in very slender, light weight structures. But when malfunctioning, they may excite such structures much more easily and may even cause collapse. This example illustrates another important safety issue: The structural control system adds new modes of failure that must be considered, some of them probably yet unknown. This raises the question of how unknown failure modes in new technology can be incorporated in a safety concept. The safety concepts of current building codes like UBC or Eurocodes are based on a separate treatment of loads and local structural resistance. This leads to the concept

127

128

of split safety factors. The variability of the loading is taken into account and so is the variability of the material. The uncertainties in modelling the structure is not explicitly included (Fig 1). Since in most cases, only simplified "worst case response" models are used in design (like neglecting the moments due to end restraints of a beam when designing its midspan cross section). It is not common practice (and is of course not necessary for conventional structures) to use a model that can simulate the behaviour of the structure with a certain degree of accuracy. There are no specific provisions in the codes about model accuracy and how it should be verified. Conventional Structure:

Load

^

Structure: Design model

^

Structure: Simulation model

W

Resistance

Structural Control:

Load

P£ mnHifiratinn/

safety check

Resistance

r control svsrem Figure 1.

Design path for conventional structures and comparison to structures with control systems.

In Figure 1 the design path of a structure with control is also given. The control system modifies the loading on the conventional part of structure. A safety critical state is still due to failure of a conventional component (like column or beam), but a malfunction in the control system may cause a loading state triggering such a failure. The reliability of the load modification capability of the control system therefore becomes an important safety issue. In the following, I'd like to discuss the issues raised here in more detail.

129 2

Reliability of Load Modification Capability

The load modification for the structural system is the most important feature of any structural control system. The type of modification depends on the control concept. Let's look at three important passive control concepts for earthquake protection (Fig. 2). Base Isolation (BI) for example filters out a large portion of the loading in the frequency domain. A Tuned Mass Damper (TMD) in contrast draws input energy away from a specific eigenfrequency of the structure and transforms it into its own vibrations. A Hysteretic Device System (Hyde System) on the other hand limits the maximum forces possible to enter a structure and reduces displacements by transforming large amounts of energy into heat. The first two concepts work in the frequency domain and are based on an essentially linear response whereas the Hyde System relies on a strongly non-linear mechanism in the time domain. Each concept works best with different types of structures.

Base Isolation (BI)

Figure 2.

Tuned Mass Damper (TMD)

Hysteretic Device System (Hyde System)

Three important passive structural control concepts: Base Isolation (BI), Tuned Mass Damper (TMD) and Hysteretic Device System (Hyde System).

BI requires a stiff conventional structure with a first eigenfrequency well above the frequency of the BI system. This cancels any vibration in the conventional structure effectively. The remaining low frequency vibration is hardly excited by an

130

earthquake and additionally dampened by the BI system. It becomes a rigid body motion for the conventional structure above the BI system. TMDs require the opposite: Very slender structures with small masses and one very pronounced frequency. The TMD then effectively reduces the response in this frequency, often by an order of magnitude. Typically introduced to reduce service level vibrations, the conventional structure can now be made so slender that an earthquake has hardly any effect. Hyde Systems also require a very soft conventional structure to prevent any damage there. But their primary structure must be stiff-ductile to limit the forces and allow large energy dissipation at small displacements. This reduces overall displacements and keeps the conventional structure in the elastic range. The stiff-ductile primary structure is part of the control system. It contains the Hysteretic Devices (Hydes) [1]. All three systems can easily be transformed into active, semi active or hybrid systems, given there are appropriate devices available. This extension will not change the underlying concept of each control system (and therefore not the basic requirements on the conventional structure) but rather improves its performance or broadens its applicability (like Hybrid Mass Dampers in high rises, where TMDs would become too large). From this brief discussion of various control concepts it is obvious that for each concept to work effectively, a certain basic type of conventional structure should be required and its compliance checked in an application. And to assess the load modification capability in a particular case, structural models are required that can simulate the actual response with an acceptable degree of accuracy. Such "simulation models" must be more refined by nature than the simple "design models" which are the current basis of codes. For a simulation model to be acceptable, it should capture the mean response of the real structure and document its variation. This will allow for an incorporation of the model uncertainty in a probabilistic safety concept. For structures with BI and TMD systems for example, linear models for response evaluations in the frequency domain appear to be appropriate. For structures with Hyde Systems, time domain models should be required because of their strong non-linearities. The structural engineering community is not used to work with simulation models although modern computer technology and software allow their daily use for some time already. In the future, some document written by experts may provide basic modelling guidelines for this purpose. But especially in the introductory phase of a new technology, where we are now with structural control, I believe that each actual

131

model must be checked until experience has provided us with some simple, yet accurate set of modelling guidelines for each control concept. One way to check a simulation model is system identification. For linear models in the frequency domain, inexpensive on site methods are available. For non-linear models, verification is more involved. For Hyde Systems for example, the linear characteristics of the conventional system (SHS) can only be checked without the devices in place. Necessary gaps to allow for the relative displacements imposed at link levels must be checked by inspection. The linear characteristics of the completed structure, including the devices, must also be checked. Having demonstrated the required load modification capability using a verified simulation model that includes a working control system, failure of the control must now be taken into account for a realistic safety assessment. Depending on the type of control system, single or multiple mode failure may cause partial or total collapse of the conventional structure under loading conditions below the design load for a working control system. In active systems, failure is not only "non-performing" but also "over-performing" due to instable control that may occur without any external loading. A control system may have several failure modes not leading to failure of the conventional structure. Therefore, a failed control system does not necessarily constitute a structural failure.

^•s " — -

$£U- .-7=?:: • ,'...;•

:

-

- ~

•i".",.'"

-

-

. . ' " ' - " • ^ • ^

- " * •

.r^Sb '-"

-::~jj

•

1

—:.••• •-::',

...

1

= - • - ' - - I

. 'i v-v-^--\. 75. t Jf-JI I . - .•- -- i

—

. _ • * - . •••'"

• • ' f ; r L . . . . : , .~^V, .^rj:

"—• I • • •

u Figure 3.

•I'V

' \ \

\

v

Deformation of a 5 storey office building with Hyde system in the ground floor (Hyde system not shown).

132

To assess the safety of a structure with control, the failure modes of the control system and their effect on the structure's response must therefore be evaluated in probabilistic terms. Each mode of failure has a probability of occurrence that is dependent on the quality of the control system. It is a probability that increases with time like the probability of occurrence of the respective design event. This leads to a time dependent safety of the structure. To illustrate this, let's look at a Hyde System under earthquake loading. Fig. 3 shows a typical 5-storey office building with one seismic link [2]. The most important parameter of such a system is the limit force in the link, which is provided by the devices there. It depends on the maximum permissible link displacement. This displacement is determined by the elastic limit of the SHS. It is the true limit state of the building because beyond it, there may be plastic deformation or buckling failure of the slender SHS. STD [mm]

5 00^

Design Point FN = 380 kN

3.88-

|

3.25_ 2.63F[kN]

7.00

200 Figure 4.

1 — J1

1

400

600

—1

800

1

1000

Design curve for link forces based on permissible link displacement STDs for retrofitting large panel buildings with one seismic link [3].

To assess the safety against this permissible link deformation for a nominal link force, link displacement standard deviations (STDs) can be calculated by Monte Carlo Simulation. A simulation with 500 earthquake records generated for the same site specific earthquake will give STDs with a confidence of 95%. Modelling uncertainties can be neglected in this calculations because their effect on the variation of the response is small compared to the variability of the earthquake (and the model should be checked for reasons mentioned above). A safety index P then provides the required distance to the permissible link displacement which may also

133

be a nominal value. This procedure has been suggested in [3] for the design of link forces in retrofitting large panel buildings. Calculating the STDs in this way for several nominal link forces provides a curve with a design point (Fig. 4). In terms of a probabilistic safety concept based on "load" and "resistance" for the conventional part of the building, the "load" is now the maximum link deformation under the earthquake effect (modified by the Hydes in the link) and the "resistance" is the link displacement corresponding to the elastic limit of the SHS. Both can be expressed by their probability density functions, with the overlapping area representing failure (similar representation like in Fig.5). The load PDF is time dependent, but stabilises after a very short time into the earthquake for a well designed Hyde system. It also dominates the failure probability. This justifies the use of nominal values for the permissible link displacement and link forces in this calculations. The approximate assessment of the safety by calculating STDs and using an index |3 is required by the computational effort. New advanced Monte Carlo Methods may allow a more accurate safety estimate in the near future [4]. The next question is: How does the probability of failure of the Hyde System influence the safety of the building? To discuss this in the context of our example, let us assume friction devices have been used. There is a certain probability that those devices may get stuck with time or loose there pre-stressing. Apart from those two extreme conditions, changes in the devices may cause a change in frictional force, up or down. This will increase the variance of the Hyde limit force and raise the probability of failure for the PHS (overload on the PHS). Let us assume that an inspection cycle of x years has been introduced that fully verifies the working condition of the devices at that time (for some friction devices, this cycle may be as long as the expected life of a building). Additionally, the PHS may have one or several serious flaws (including the device connections) that may cause premature failure. From this, we have to look at three basic failure states of the control system: (1) "link stuck", (2) "link loose" and (3) "PHS weak".

"PHS weak" will occur when the strength of the PHS drops below the link limit force. The Hyde system then behaves linearly until it breaks at a certain force level without activating the Hydes. Primary system strength and link limit force can be represented by probability density functions (PDFs) at the end of the last inspection cycle in the lifetime of the building, where the variance in link limit force is largest and the PDF of the resistance of the primary system may have shifted to lower values due to structural deterioration. Because primary systems are conventional structures (rc-walls, steel trusses etc.) their strength PDFs are known. The PDF of

134 the link limit force is a function of the number of devices and their quality. This will lead to a probability that the control system fails (area common to both PDFs, Fig.5) A "stuck link" might damage the primary system severely or break the device(s). The Hyde system will again not be able to activate the Hydes, behave linearly and break, now at a much higher force than in the case of a weak PHS. This case is therefore included in the PDF approach mentioned above: It represents the high end of the link limit force PDF whereas the case of a weak PHS represents the low end of the primary system resistance PDF. i k

/ / /

weak PHS

^

link force PDF

\ I

failure probability

\

/

/

V - " PHS resistance PDF

stuck link

force

Figure 5. Failure probability of control system in a structure with Hyde System.

The failure of the Hyde System will not always cause the collapse of the conventional structure. Above a certain linear resistance of the primary system, the conventional structure will not fail although the control system may. This limit can be calculated using an elastic model for the primary system with brittle link failure. A "loose" link leaves the control system in tact but will have such a low limit force that the displacements in the conventional structure increase to levels that cause collapse there (soft first storey collapse in the building of Fig.3). A non activated control system in this force region is inconsequential to the failure probability of the structure because it will fail in any case. To assess the safety of the building considering the failure of the control system, two failure modes occur now that require two different simulation models: A model for a working control system covers also the case of "link loose" but another model is needed using a linear link restoring force with a brittle failure limit to cover the cases "link stuck" and "PHS weak". With both models the STDs of link displacements can be calculated for various link limit forces. This will provide two curves (Fig. 6). By plotting the PDFs of Fig. 5 on

135 the level of the permissible STD, the confidence that the building will have the required safety level in case of an event (system confidence Cs) can be expressed by C s =l-[p(F 1 ) + p(Fh-F1)] with p(Fi) and p(Fh-F!) as indicated in Fig. 6: pCFh-FO is the joint area of both PDFs bound by F) and Fh. p(Fi) is the area under the link force PDF up to F,. Both areas do not overlap. A required system confidence can now be defined in conjunction with the occurence probability of the relevant event and the required survival probability, suitably at the end of the building's life (end of last inspection cycle). The required value for this confidence may be defined in a code. Depending on the event (earthquake, wind etc.), this value should vary. It may also vary with the use of a building.

link displ. STD

link force

A

PHS resistance PDF

link force Figure 6. Illustration of control system confidence for a Hyde system.

As with other buildings, life cycle cost considerations may enter the definition of a target value for the system confidence. That way the definition can be treated as an opitmization problem. A difficult question to answer in this approach is still the cost attached to failure, e.g. the cost of human life, which has to enter here. In some countries, the cost for a human life is based on the insurance costs (life insurance) and/or production value of an individual. The social status of the occupants of a building enters here which usually drops with the age of a building and its state of maintenance. Such an approach leads to a safety that highly depends on the social status of the occupants and therefore is morally questionable. A minimum

136

acceptable safety level should be required for all buildings. Additional safety and, in the context of structural control, additional system confidence may be based on cost optimization, if the owner so wishes. As can bee seen from Fig.6, the variations of the link forces and the PHS have a significant influence on the confidence level. Thus, an improved quality of the control system (decrease in variations of link force and PHS) will increase the system confidence. With low control quality, only a shift to the right will provide additional confidence but will require larger forces and make the structure more expensive. Because such a shift may not have much of an effect on p(Fh-Fi), a large value here can only be reduced efficiently by improved control quality. This example shows that when dealing with structural control systems, only simulation models capable of estimating the response under various system conditions (including failure modes) will provide an answer to the system's probability of survival. A "system confidence" can be estimated (or required) based on the quality of the control system and the required safety level for the event.

3

Unforeseen Modes of Failure

With new technology, there may be unforeseen modes of failure. Because the main issues of this chapter have been discussed in [5], only the essence of it is reported here. Unforeseen failures may be divided into "forseeable" and "unforeseeable" ones [5]. Two types of unforeseen failures may occur: Those that could have been foreseen, but were not a part of the design team's knowledge and those that were not part of the technical knowledge of the time. Both types of failures can be illustrated by historic examples. An example for a foreseeable failure is the Titanic disaster. With the engineering knowledge of the time, one could have noticed that the section walls were not high enough to prevent the water from overflowing once the ship developed a certain tilt. Those section walls were a new technological achievement but the designer did not develop its full potential because he didn't include such an "exotic" failure mode in his design considerations. It is actually quite possible that, in a first draft, these walls went all the way up but where later reduced in height because of economic or other reasons, with no anticipated failure mode available to prevent that. An example for an unforeseeable failure is the collapse of the Tacoma Narrows bridge. Here, a previously unknown wind induced excitation by vortex shedding combined with the detrimental effect of close bending and torsional frequencies

137

caused a resonance effect that eventually destroyed the bridge. This type of excitation was first observed in this bridge and it took several years of research to fully understand it. A way to improve the safety against foreseeable failures is the incorporation of external expert knowledge. Here, it is important to register the help of experts outside the pertinent field, but with some background knowledge of it. In structural control, two additional engineering disciplines interact with structural engineering: mechanical and electric & electronics engineering. Therefore, in designing a structural control system, one should require engineers from those fields to be part of the design team and have a separate, independent team check all safety aspects of the design and not only its code conformity. Such a "dual" team would certainly want to perform various fault tree analyses which are typically not considered by structural engineers. This will shed some light on possible failure modes that otherwise go undetected. Regular design approaches, like the incorporation of backup systems (e.g. for electronic components) will then allow to provide adequate safety against these failures by minimizing the risk of neglecting "exotic" failure modes. Unforeseeable failures are another matter since they are the result of effects that are not part of the current knowledge. Even the most sophisticated analyses or rigorous testing will not reveal them since those methods are all based on current knowledge. Even scientific study programs are only of limited value in structural engineering: Here, each project has its unique design requirements. There is almost no way to reproduce actual situations in a laboratory or computer model and full scale prototype testing is practically out of the question. Thus, only real life experience will reveal such unforeseeable failures and that experience, with time, will eventually close this safety gap. This experience means possible structural failure and possible loss of life. It is the risk a society takes when new technology is applied. The level of acceptable risk will differ from application to application, even within the same type of technology. An example is transportation technology with different risk perceptions for cars, rail based transportation or air planes. The acceptance of risk in building structures is usually very low: In the perception of society, a building must be safe and sound for a century under all kinds of loading conditions. But there are exceptions. In a catastrophic situation, like hurricanes and earthquakes, nature is perceived as the villain. That's why they are called "natural disasters" and because nature today is perceived as a force that cannot be conquered or cheated upon, the acceptance of risks involved with this type of "loading" is much higher, even in buildings where collapses under such conditions are usually accepted by society. Applications of new technology in

138

buildings to reduce the effects of natural disasters therefore can be based on a much higher risk acceptance level which translates into much lower required safety levels. This perception of society can be used with advantage to foster the application of structural control technology by applying them at first to catastrophic load cases. Let us take passive control systems as example. Hysteretic device systems or base isolation definitely will improve the behavior of most buildings under earthquakes. This has been shown time and again through the application of current knowledge and even recent earthquakes like Northridge [6]. Although some structures with passive systems may collapse in the next strong earthquake, it is safe to say though that most buildings using this type of technology will fare much better than any conventional structure around them and the acceptance of this technology within society will increase with future earthquakes or hurricanes, if enough of these structures are around to prove their advantages in a statistical manner. The unforeseeable failures, which will occur with certainty, will close the inevitable safety gap, but will not distract society from applying such a basically advantageous technology. It is therefore a logical requirement that the safety margin in codes for such systems should not be higher than for conventional systems. That way, many more applications will be possible which is required to produce a statistical mass that, under the next hurricane or earthquake, will produce a representative picture of the advantages of this new technology and provide the necessary experience through unforeseen failures. Restricting its application by excessive requirements on safety might just produce a few sample structures (as is the case today). A failure in one of them then carries an enormous statistical bias which might have a dramatic effect on society's perception of the whole technology and even may prevent its application for a long time to come. Structural control systems are more and more governed by code requirements that are often based on fear of applying new technology, rather than rational safety requirements. Base Isolation has suffered this fate already. It is therefore very important now for the structural control community to commit itself to the development of rational safety concepts for structures with control.

4

Conclusions Drawn for a Safety Concept

Current safety concepts in codes are not sufficient to cover buildings with structural control although the important modes of failure are still defined by the conventional part of the structure. An adequate safety concept must consider the load

139 modification capability of the control system which strongly influences the design of the structure, if an economic advantage is to be gained from the control system. To assess this capability, a simulation model is required for the structure rather than the usually crude design models that are sufficient for the verification of conventional structures. With the current lack of modelling guidelines, those simulation models should be verified for each building to ensure an acceptable model accuracy. The safety of the structure with working control system can then be verified by evaluating the standard deviations of important variables of the conventional part of the structure, like storey drifts or beam end rotations using the verified simulation model. Efficient Monte Carlo methods are available for these calculations, if a time history analysis must be performed (e.g. if strong non-linearities are present). Additionally, the possible failure modes of the control system and their effect on the response of the conventional structure must be assessed. Often, this requires additional simulation models to calculate the response under those control failure conditions. Usually, not all control system failures lead to structural failure. A control system confidence can be defined based on the failure probability of the control system bounded by the limit states for failed and working control, plus the failure probability for a working control system (Fig. 6). The level of required control system confidence may be defined in codes. Life cycle cost optimization may be used in this context but including the cost of human life raises serious moral questions. A minimum acceptable level of confidence should therefore be defined by separate reasoning. Because structural control is a new technology, unforeseen failures may arise. They can be separated in foreseeable and unforeseeable ones. The foreseeable ones can be dealt with by including outside expert knowledge in the design team and have the design approach checked by another team. Unforeseeable failures can only bee detected by experience. This experience may be hindered by excessive requirements on the safety for known failure modes, which does not prevent the unforeseeable ones. Therefore, there is no reason to require a higher level of safety from a structure with control than is required from a conventional structure! Unfortunately, this has not been generally recognised and the wrong approach has been used in modern codes (see Base Isolation). This can only be avoided in the future, if the structural control community commits itself rigorously to the

140

development of a comprehensive safety concept for these exciting and valuable structures.

References 1. 2.

3.

4.

5.

6.

U.E. Dorka; Hysteretic device systems for earthquake protection of buildings. 5'h US nat. conf. on earthq. eng. (5th NCEE), Chicago, 111, 1994. U.E. Dorka, V. Bayer; Distribution of seismic links in Hysteretic Device Systems. 12th World conf. on earthq. eng., (12th WCEE) Auckland, New Zealand, 2000. U.E. Dorka, A. Ji, E. Flygare; A hysteretic device system for earthquake retrofit of large panel buildings. 11th European conf. on earthq. eng. (11 th ECEE), Paris, France, 1998. V. Bayer; Ch. Bucher, U.E. Dorka; First passage reliability of bridges by spectral importance sampling. Proceedings EURODYN'99, Prag, Tchech Rep., 1999. U.E. Dorka; New technologies and codes: Or how to deal with the "unforeseen". 8' int. conf. on appl. statistics and probability. (ICASP8), Sydney, Australia, 1999. J.F. Hall, W.T. Holmes, P. Somers (Ed.); Northridge earthquake reconnaissance report, Vol. 1&2, Earthquake Spectra^ Vol. 11, Suppl. C, April 1995 & January 1996.

SEMI-ACTIVE CONTROL OF 3-D LINEAR AND HYSTERETIC STRUCTURES FOR SEISMIC APPLICATIONS

SAMIEL-BORGI Associate Professor, Ecole Polytechnique de Tunisie, BP 743, La Marsa 2078, Tunisia E-mail: sami. elborgi@ept. rnu. tn CHOKRIZAMMALI Graduate Student, Ecole Polytechnique de Tunisie, BP 743, La Marsa 2078, Tunisia E-mail: [email protected] PANOS TSOPELAS Assistant Professor, The Catholic University of America, Washington DC 20064, USA E-mail: [email protected] A number of studies have been conducted so far on active or hybrid control of hysteretic structures using various linear and nonlinear control algorithms. However, most research work on the use of semi-active control systems has been limited to linear structures modeled as 1-D shear-type representation (one degree of freedom per floor). The structures used in this study are modeled with a 3-D shear type representation (three degrees of freedom per floor: two translations and one torsional rotation), and can behave either in a linear elastic or in a hysteretic manner. The purpose of this paper is to examine the effectiveness of semi-active variable viscous dampers ( W ) in reducing the seismic response of such structures. The control algorithms considered is one based on the Sliding Mode Control (SMC) algorithm. The analysis results of a linear and a hysteretic, single-story 3-D structures indicate that W dampers can be effective in reducing the displacement and acceleration responses of both linear and hysteretic structures.

1

Introduction

Semi-active control devices combine the features of active and passive control to reduce the response of structures to various dynamic loadings. The main purpose of this paper is to examine the effectiveness of semi-active variable viscous ( W ) dampers in reducing the response of 3-D structures subjected to relatively strong earthquakes. Several investigators have developed algorithms for selecting the appropriate damping parameters of these devices during the structure's response to an excitation. The algorithms included a clipped optimal control algorithm [7], a bang-bang algorithm [3], a Linear Quadratic Regulator (LQR) algorithm [6,7], a Sliding Mode Control (SMC) algorithm [9,11], a generalized LQR algorithm with a penalty on the acceleration response [8], a displacement-acceleration domain algorithm [8] and a fuzzy logic controller [6].

141

142

Under relatively strong earthquake excitations, structural members might experience yielding and the response will become non-linear hysteretic. To date, numerous studies have been conducted on active or hybrid (active/passive) control of hysteretic structures modeled with a 1-D shear-type representation using a wide range of linear and nonlinear control algorithms [10,11]. However, most research work on the use of semi-active control systems has been limited to the same type of structural model accounting only for linear elastic behavior [8,9]. On the other hand, few researchers considered the control of 3-D structures with linear behavior only [1,4,5] except for [6] who studied base-isolated structures with a hysteretic behavior for the base and a linear elastic behavior for the super-structure. In this paper, the structure is modeled with a 3-D shear-type representation and can behave either in a linear elastic or in a hysteretic manner. The algorithm for selecting the damping properties of W dampers presented here in is the SMC algorithm, which is formulated based on full-state feedback. The equations of motion are formulated in the state-space and in the drift (inter-story) coordinate system. A linear and a hysteretic, single-story structure subjected to the El Centro earthquake applied along the F-direction are analyzed using the SMC algorithm. 2

Equations of Motion of Controlled Structure

Consider an n-story structure modeled as a 3-D shear-type representation equipped with m W Dampers, placed each in the X or y-direction, and subjected to the two horizontal components of an earthquake ground excitation ag = {x ,yg). Each story is described by three degrees of freedom as shown in Figure 1: two horizontal translations and one torsional rotation. This structural model was adopted from [6]. If the behavior of the structure is hysteretic, its motion is described by the following system of differential equations defined in the physical coordinate system: MX + CX + KelX + Kin V = DU + Eag

(1)

X = (*[ y\ 9] ••• x„ y„ 6„f a 3n-vector with x}, yj and 0, being the relative interstory displacement of the j * story in the X, Y and 0-direction, U is an m-vector representing the control forces generated by the W dampers, M and C are respectively the mass and damping matrices of size (3n x 3n), D is a (3n x m) matrix defining the locations of the control forces, Ket and K,„ are, respectively, the elastic and the inelastic stiffness matrices of size (3n x 3n), E is a (3n x 2) mass matrix, representing the influence of the earthquake excitation, whose elements are zero except: £(3/ +1,1) = -MXM and £(3/ + 2,2) = -MyM for i=0,1,... ,n-1. All elements of M, C, Kei and K,„ are zero except:M(i,j) = M, for j
143

Kel(i,i + l) = -Kfil,

and

Kin(i,i + l) = -K£1

for i= l,2,..,n-l. The matrices

Mh C,, Kf and K'f are (3 x 3) matrices verifying: M*

0

0

0

M?

0

0

0

/?

AY,=

cf

o

(l-af^Dj

0

-{\-a*)fC*R?D>}

0

(l-«(K,^

{l-afJKfRfD^

K'" =

cf «f

-afKfRf a?K?R? afKf

0

0

Kf

Q-

-CfRf CfR? C?

-afKfRf

afKf afKfRf

in which Mf and A// are the masses of the 1th story in the X and F-direction and /f is its inertia moment, Kf, Kf and AT,9 arerespectively the elastic stiffnesses of the 1th story in the X, Y and 0-direction, af, af and af are the ratios of the postyielding to pre-yielding stiffness in the X, Y and 0-direction respectively, Dyj, Dyyi and DBy! are the yield deformations in the X, Y and 0-direction, Rf and Rf are the eccentricities of the i* story, from the center of mass CM to the center of rigidity CR, in the Xand 7-direction (Figure 1). Z

4 Y

Figure 1. Model of three dimensional 1-story structure

Appearing

also

in

equation

(1)

is

the

evolutionary

3n- vector

T

P = |Vf • - ( •

Vf

Vf

vXn v>

representing the non linear hysteretic behavior of

the structure where each of its components vf , vf and vf is modeled by the BoucWen model [12] as follows:

144

vf -faYUi,

-P,\x^f

P _1 - r , i , | v , f

(2)

in which Ah fa, ji and «/ are dimensionless quantities that define the scale, the shape and the smoothness of the hysteresis loop. Using the state-space representation, equation (1) becomes: Z=^Z)+BU+H%

(3)

where

W

o B=

Y VV9nxl

3

X

0 H-V &) = M~lDs9nxm -M-x(ck+KelX+KinV) M~'EJ9nx2

/9«xl

Semi-Active Control Algorithm

The SMC algorithm used in this study is similar to the one developed by [11] for active control. This algorithm is based on two steps, the first being the sliding surface design using an LQR algorithm and the second being the controller design using the Lyapunov method. The design of the sliding surface S = PZ = 0 consists of obtaining the sliding matrix P through the ininimization of the following '/ performance index: J = \[ZTQZ]dt in which Q of size (6n x 6n) is a positive o semi-definite weighting matrix subject to the state equation of motion (3). The purpose of the controllers design is to drive the response trajectory into the sliding surface S - 0. The following Lyapunov function is considered: L - 0.5STS. Based on Lyapunov's theorem, the sufficient condition for the sliding mode to be stable is given by: L = S S < 0 . Using the state equation of motion (3), we obtain: L = XT \[J - UJ where U is the control force and X and U are given by: X = STPB and U = -[PB^1 P(AZ + B"V + Hag). Using the control law proposed by [11] U = U-8XTin which 5 is called the sliding margin matrix and is user input, we obtain finally the expression of the control force regulated by both the state response and the earthquake excitation: U = GlZ + G2ag (4) where Gx and G2 are gain matrices.

145

For a semi-active variable viscous damper located either in the X or F-direction, its damping coefficient at time t can be computed as follows:

C' = — orC' = — with C ' e [ C U , C U ]

(5)

x y in which x or y is the relative velocity between the ends of the damper placed either in the X or F direction; C'^

and C ^ are the minimum and maximum

damping coefficients of the damper. 4 4.1

Results and Discussion Linear Elastic Structure

A single story linear structure shown in Figure 1 and adopted from [2] is considered to study the 3-D response of a variable damping system. The lateral force resisting system consists of three frames (see Figure 2) which result in Kx =1168960 N/m, Ky =1095900 N/m, and Ke =11103328 Nm/rad. The floor is orthogonal with b=9.144m, and d=6.096m, and has the following mass properties Mx = My =27188 Kg, if =273806 Kg.m2 and a damping ratio of 5% for the three modes of vibration. The aforementioned semi-active SMC control algorithm was implemented to control two variable viscous devices located respectively at the location of frame A along the F-direction and at the center of mass along the Xdirection.

Frame B Frame A X

^ Frame C

Figure 2. Plan view of three unnensional 1-story structure

The 1940 El Centro S00E component scaled to 0.3g PGA was used in the analysis along the ^-direction and passing through the center of mass. Because of the structure's asymmetry in the y-direction (RX=0A51 m, and Ry=Q), any excitation in the y-direction will induce a combined translational and rotational response.

146

The semi-active SMC algorithm was implemented considering a matrix Q = diagonal [I 1 1 1 1 1] and 8 = 500 N.kg.m/s. The effects of the Variable Viscous Dampers controlled using the aforementioned SMC algorithm are compared against the responses of a bare (no dampers) structure and the responses of a structure with passive dampers with damping constants equal to C ^ and C ^ . Table 1 compares the peak drift and acceleration responses, along the Indirection of the Center of Mass, and translational displacement and translational acceleration of point P of the plan view (translational displacement = rotation x distance between the center of mass and point P). The comparison is done for a structure without W dampers and one with VV dampers controlled with SMC algorithm. Because the earthquake excitation is applied along the y-direction, the bare and the controlled structure does not undergo any translational response along the Xdirection. Therefore, only the response quantities along the Y and ^-direction are indicated in Table 1. The structure was analyzed using the SMC algorithm with no constraint on the devices (active control case) to achieve a full compensation state. As shown in Table 1, the structure moves as a rigid body with zero inter-story displacement along the Y and 0-direction with an absolute acceleration in the Indirection equal to that of the ground. It is worth mentioning that the 0 absolute acceleration is equal to zero because the ground excitation contains only translational components. Semi-active control using W dampers results in a response comparable to that using active control, considering that the larger semiactive displacements are accompanied by substantially reduced control forces. 4.2

Non-L inear Hysteretic Structure

The structure previously used was modified to experience nonlinear hysteretic behavior. The yield displacement of the stiffness elements in both directions was considered to be 1% of the total story height, that is Dyi=3.6 cm. The yield force was considered to be 14.6% of the structural weight, where the post to pre-yielding stiffness ration was 1% (almost elasto-plastic behavior). The Bouc-Wen parameters of the structure are: A=l, (3=7=0.5 and n=95 for the three degrees of freedom. Looking at the Table 1 it can be deduced that the controlled structure shows better performance when compared to the bare structure in all cases (that is expected). When the responses are compared to the passively controlled structure with C ^ both the displacements and accelerations in both directions were reduced. When the structure was passively controlled with C ^ x the structure never yielded and experienced elastic behavior at the expense of higher accelerations. The structure controlled with SMC was allowed controlled yielding, as a result the

147 displacements were slightly more than the displacements of the structure with C'n but the acceleration response was reduced. Table 1. Maximum response quantities of the Bare and Controlled 1-story Asymmetric Structure (El Centro applied in Y direction)

Bare Structure

Hysteretic

Linear

y

5

e

Drift 8.29 11.47 (cm) Acceleration 334 426 (cm/s2) Control Force 0 — (kN) Drift 10.44 3.95 (cm) Acceleration 196 147 (cm/s2) Control Force 0 — (kN)

Passive C •

y

0

Passive C y

e

6.67 8.23 2.58 2.68

Active SMC

Semi-active SMC

y

9

y

0

0

0

3.31

3.5

274

338

214

112

294

0

188

148

0

...

0

...

80

...

45

...

8.74

3.8

3.11 1.94

0

0

4.29 2.39

203

144

217

79

294

0

183

97

0

—

0

...

80

...

42

—

Conclusions

A 3-D building modeled as shear-type structure was considered to study the effect of semi-active variable viscous dampers, placed along the X and ^-direction, in the translational and rotational response. A semi-active algorithm based on Sliding Mode Control was developed and implemented in a computer code. A single story asymmetric structure was excited using S00E El Centro 1940 acceleration record. The bare (no W dampers) structure experienced substantial rotational response. The introduction of the W dampers controlled by SMC algorithm, mitigated the rotational response while it substantially reduced the translational responses of both displacement and acceleration. A parametric study was also performed to validate the efficiency of the semi-active system when compared to the passive one. Two cases where considered, in the first the structure had damping equal to the minimum damping coefficient of the W damper, and in the second the damping was equal to the maximum. The presented results showed the versatility and potential of the semi-active considered semi-active Variable Viscous Damper.

148

6

Acknowledgements

The first author is grateful for the partial funding provided by the EC's INCO-MED project CHIME to attend this conference. References 1. Arfiadi, Y. and Hadi, M.N.S. Passive and active control of three-dimensional buildings. 29, (2000) pp. 377-396. 2. Chopra, A.K., Dynamics of structures: theory and applications to earthquake engineering. (Prentice Hall, 1996). 3. Feng, Q. and Shinozuka, M., Control of seismic response of bridge structures using variable dampers. J. Intelligent Material Systems and Structures. 4, (1993) pp. 117-122. 4. Fur, L.S., Yang, H.T.Y. and Ankiredi, S. Vibration control of tall buildings under seismic and wind loads. ASCE Journal of Structural Engineering. 122, (1996) pp. 948-957. 5. Kobori, T., Koshika, N., Yamada, K. and Ikeda, Y. Seismic response controlled structures with active mass driver system. Part I: Design. Earthquake Engineering and Structural Dynamics. 20, (1991) pp. 135-149. 6. Nagarajaiah, S., Semi-active control of base isolated structures subjected to near field earthquakes, Proceedings of First World Conference on Structural Control, Los Angeles, California, USA (1994). 7. Sack, R. L., Kuo, C. C , Wu, H. C , Liu, L. and Patten, W. N., Seismic motion control via semi-active hydraulic actuators. Proc. U.S. 5th National Conference Earthquake Engineering. (1994) pp. 311-320. 8. Sadek, F. and Mohraz, B. Semiactive control algorithms for structures with variable dampers. ASCE Journal of Engineering Mechanics. 124, (1998) pp. 981-990. 9. Symans, M. D and Constantinou, M.C. Development and experimental study of semi-active fluid damping devices for seismic protection of structures. Report No. NCEER-95-0011, State University of New York at Buffalo, Buffalo, New York, (1995). 10. Yang, J.N., Li, Z. and Vongchavalitkul, S. A generalization of optimal control theory: Linear and nonlinear structures. Report No. NCEER-92-0026, State University of New York at Buffalo, Buffalo, New York, (1992). 11. Yang, J.N., Wu, J.C. and Agrawal, A.K. Sliding mode control for nonlinear and hysteretic structures. ASCE Journal of Engineering Mechanics. 121, (1995) pp. 1330-1339. 12. Wen, Y.-K. Method for random vibration of hysteretic systems. ASCE Journal of Engineering Mechanics. 102, (1976) pp. 249-263

REPORT ON 1999 KOCAELI AND DUZCE (TURKEY) EARTHQUAKES MUSTAFA ERDIK Bogazici University, Dept. of Earthquake Engineering, 81220 Cengelkoy .Istanbul, E-mail: [email protected]

Turkey

This paper presents a summary of the main lessons learned from the Kokaeli and Duzce earthquakes occurred in 1999. Some retrofitting aspects are also included.

1

Introduction

On August 17, 1999 a magnitude MW 7.4 earthquake struck the Kocaeli and Sakarya provinces in northwestern Turkey, a densely populated region in the industrial heartland of Turkey. The earthquake nucleated at a depth of about 15km at about 10km east of the town of Golciik. It is associated with a 120km rupture involving four distinct fault segments on the northernmost strand of the western extension of the 1300 km-long North Anatolian fault system. Predominantly rightlateral strike slip offsets were in the range of 3 to 4 m over a significant length of the fault.. The earthquake region has been identified as a seismic gap with stress concentrations indicative of a large impending earthquake. The August 17 earthquake is considered to be the largest event to have devastated a modern, industrialized area since the 1923 Tokyo earthquake. Another segment at the eastern end of the fault break has ruptured on November 12 producing the MW=7.2 Duzce earthquake. The region affected by the earthquake is both geographically extensive and economically dynamic. It forms the industrial heartland of Turkey. The four districts most severely affected (Kocaeli, Sakarya, Bolu and Yalova) contribute over 7 per cent of the country's GDP and 14 per cent of industrial value added. Per capita income is almost double the national average. Though containing only 4 per cent of the nation's population, the region contributes over 16 per cent of budget revenues. The immediately surrounding districts (of Bursa, Eskisehir, and Istanbul) have been mainly affected indirectly by their close economic linkages with the former area, e.g., industries and small businesses supplying services or material inputs to each other's production processes. They also are subject to a shared seismic risk and so face magnified uncertainty for the future as a fall-out of the recent events. Taking all seven cities together, the wider earthquake region accounts for 35 per cent of national GDP and almost half of the nation's industrial output. Building losses are reported to amount to about US$5 billions. Damage to lifelines is estimated to be in the order of US$1 billion. Industrial facilities and small business losses are respectively about US$2 and US$1 billion. If we assume that the indirect socioeconomic losses will be about as much as the direct physical losses the total loss

149

150

figure will be in the vicinity of 16 Billion US$ (about 7% of GDP of Turkey). Most of the industrial losses will be covered by the insurance. Most of the residential losses will be borne by the government since under the current disaster law the state serves as the free insurer of households. 2

Seisrao-Tectonics

August 17, 1999 (MW 7.4) Kocaeli and November 12, 1999 (MW=7.2) Duzce earthquakes are consequences of the motion a wedge of continental crust, known as the Anatolian Block, being squeezed between the Arabian and the Eurasian plate. This motion is accommodated by two major strike-slip faults: the North and East Anatolian faults (Figure 1). The August 17 Kocaeli and November 12, 1999 Duzce earthquakes were both associated with the North Anatolian fault. This major fault is predominantly a single right-lateral strike-slip fault with a differential slip rate of 10-20 mm/yr. The faulting on this mega tectonic entity has segmental character with a characteristic earthquake in the Mw=7+ range. The last earthquake sequence began with the 1939 Erzincan earthquake, followed by earthquakes in 1942, 1943, 1944, 1951, 1957, 1967, and finally the 1999 earthquakes (Figure 2). The Duzce earthquake is associated with the so-called Duzce fault, which forms a morphological boundary at the south of the Duzce Plain with and extends 70 km between Akyazi and Kaynasli. At Adapazari and Bolu, Duzce Fault joint to the North Anatolian Fault System.

Figure 1. Regional Tectonic Map (http//www.ipgp jussieu.fr)

The historical seismicity of the region during the last two millennia is well studied (Ambraseys and Finkel, 1991, 1995 and Parsons et. al, 20(D). In this century, starting with 1939 the North Anatolian Fault Zone had a generally

151

westward migrating sequence of earthquakes, which, for long, has indicated the potential for the Kocaeli and Duzce earthquakes (Toksoz et al, 1979 and Barka and Kadinsky-Cade, 1998). The recent seismicity of the region is provided in Figure 3. = ?0G

-SOU

-S00

-m

-300

-230

-10D

0

3.D0

100

33S

m

Figure 2. Miration of Earthquakes on the North Anatolian Fault in this century and distribution of fault offsets. The deficit in Marmara Sea is indicated (http//wwwipgp.jussieu.fr)

3.

Surface Faulting

The August 17, 1999, Kocaeli earthquake produced right-lateral onshore surface slips along an east-west trending zone of right-stepping fault strands over a distance of about 120km. The slip was typically 2.5 to 4.5 m, reaching a maximum of approximately 5 m at a location about 30 km to the east of the epicenter. Followed or formed parallel sets of faults oblique to the trend of faulting. The surface expression of rupture consisted of tension cracks and fissures with limited positive relief along a 10-20m zone. Duzce Earthquake produced a surface fault rupture of approximately 40 km on the so-called Duzce Fault between the eastern terminus of the Koceli Earthquake rapture at Eften Lake and Bolu Tunnels at Elmalik. The maximum right-lateral offsets were measured to be about 4 m. The rupture has also a vertical component ranging between 10 to 150cm. 4

Source Process

USGS Rapid Moment Tensor Solution provides the following parameters for the two events:

152

17.08.1999 Koeaeli Earthquake: Epicenter; 40.639 29.830, mb=6.3, MS=7.8, Seismic Moment: Mo=l.4* 10**20 Nms Mw=7.4 11.12.1999 Duzce Earthquake: Epicenter: 40.768 31.148, mb=6.5. MS=7.3, Seismic Moment: Mo=4.5*10**19 Nm, Mw=7.1 ^ '"

I.

'"-''•%"•

•'

„ ' - . . • '

..

..•..."

•' O-j

v.*

-o

1 m^n&imsiw*** *"*-y

°

^: 1

' x0 j

%?^s

Figure 3. Recent Seismicity of the Region

Source time functions for these earthquakes provided by University of Michigan indicate essentially single triangular slips with maximum moment rates of

153

respectively 0.18*10**20 Nm/s and 0.08*10**20 Nm/s for the Kocaeli and Duzce events. The associated durations are reported to be 14s and 10.5s. The seismic moment of the Kocaeli earthquake can be easily verified by the field data. Using the observed fault length of 120km5 width of 15km, average displacement of 2.5m5 and a shear modulus of 32GPa we can obtain a static moment of 1.4 x 10exp20 Nm. Taking an average fault rapture area of 120 .km x 15 km, the average stress drop can be found to be about average stress drop = 2.5 x Mo / S**1.5=6Mpa.

Figure 4. Epicenter, fault fupture and fault slip distribution associated with the Kocaeli Earthquake (Slip distribution from Yagi and Kikuchi,: http://www.eic.eri.u~tokyo.ac.jp/yuji/trk2)

Seismic imaging of the Kocaeli earthquake rupture done by Bouchon et al. (2000) indicates almost pure lateral strike-slip rapture that runs west at a velocity of about 3km/s and towards east at a very high velocity of 4.7km/s for a distance of about 40km before dropping to about 3.1km/s at the easternmost segment. The largest slip 7m occurs between 25 to 45km east of the epicenter. West of the epicenter the slip is large between distances -of 10 to 30km. The rise time is generally between 2 to 4s. According to Delouis et. al (2000), the pure strike-slip rapture in Kocaeli earthquake is dominated by the bilateral braking of a central asperity located between Karamursel (29.7E) and Arifiye (30.3E). Slip lasts 45 to 50 s but most of the energy is released in 15s. Rupture velocity to the west is 3km/s.

154

Figure S. Epicenter, fault fuptuie and fault slip distribution associated with the Duzce Earthquake (Slip distribution from Yagi and Kikuchi,: http://www.eic.eri.u-tokyo.ac.jp/yuji/trk2)

Rupture velocity to the east is faster but there is no evidence for or against supershear rapture. Yagi and Kikuchi (1999) characterize the rapture process in Kocaeli earthquake by an asymmetric bilateral rupture propagation and smooth slip (Figure 4). It consists of two major fault segments, a rupture propagating to the west and a second rupture propagating to the east. The maximum dislocation and the maximum dislocation velocity are 6.3 m and 2.7 m/s, respectively, both found at the former segment. The total source duration is 20 s. The average dislocation is about 4 m. The extent of the coseismic rupture suggests that a considerable part of the anticipated seismic gap remains unruptured. It is inferred that the rupture first propagated along the western fault segment, and then it triggered another rupture on the eastern fault segment. The maximum ground accelerations measured in this earthquake are rather small, only half of the value observed in various large earthquakes, while the maximum ground velocities are comparable to those observed in large earthquakes. The smoothness of rupture propagation is responsible for the comparable ground velocity but small acceleration in this earthquake.

155

Yagif Y. and M. Kikuchi (1999) have found out that in the Duzce earthquake, the rapture propagated 10 km to the East and 20 km to the West (Figure 5). Average dislocation over the raptured segment is about 2.7 m. The source duration is 12 s. Using the observed fault length of 30km, width of 15km, average displacement of 2.7m and shear modulus of 32GPa we obtain a static moment of 3.9 x 10expl9 Nm. Taking an average fault rupture area of 30 km x 15 km, the average stress drop associated with the Duzce event can be found to be about 2.5 x Mo / S**1.5 =12 Mpa, S

Distribution Of Intensities and Sea Wave

The maximum MSK intensity of the Kocaeli earthquake was X, essentially assigned on the basis of fault rupture and excessive ground deformations. Figure 6 provides an Isoseismal map of the earthquake prepared by Earthquake Research Division of General Directorate of Disaster Affairs.

Figure 6. Isoseismal Map of Koceli Earthquake (http://www.deprem.gov.tr/)

In Kocaeli earthquake large sea waves were reported in Izmit Bay. Run-up heights ranged up to 2.5m along the shores of the middle basin of the Gulf of Izmit between Hereke and Degirmendere after a general depression. The cause of this phenomenon Is argued to be near shore tectonic subsidence and submarine sediment slumping. Figure 7 pictures a ferryboat carried onshore by a strong seismic wave.

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Figure 7. Ferry Boat in Izmit Gulf thrown to shore due to strong wave action 6 Strong Ground Motion The strong motion stations operated by the General Directorate of Disaster Affairs, the Kandilli Observatory and Earthquake Research Institute of Bogazici University and Istanbul Technical University have produced at least 27 strong' motion records for the Kocaeli earthquake within 200 km of the fault. Kocaeli earthquake has generated six motions within 20 km of the fault (Sakarya, Yarimca, Izmit, Duzce, Arcelik, and Gebze), adding significantly to the near-field database of ground motions for Mw >= 7.0 strike-slip earthquakes. The strong motion data pertaining to Kocaeli and Duzce earthquakes can be downloaded from Earthquake Research Division of General Directorate of Disaster Affairs (http://www.deprem.gov.tr/) and the Department of Earthquake Engineering of Bogazici University (http://www.koeri.boun.edu.tr/earthqk/earthqk.html). The peak ground accelerations recorded at the near fault stations in both earthquakes are provided in Figures 8 and 9. The two stations closest to the fault rapture are Sakarya (3.3 km) and Yarimca (4.4 km). Sakarya is founded on stiff soil, while Yarimca is founded on soft soil. Of these, the largest peak ground acceleration was about 0.4g at Sakarya. All of the attenuation relationships over predict peak accelerations observed in Kocaeli earthquake at distances less than about 20 km. However the peak velocities is in the order of what has been observed in previous earthquakes of similar nature. It should be noted that the attenuation relationships rely heavily on extrapolation from larger distances and smaller magnitude earthquakes to define ground motion predictions in the distance and magnitude range and may not yield

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correct values in the near field for large magnitude events. Other reasons for low accelerations may be the smoothness of rapture and the relatively low stress drop in the Kocaeli earthquake. At distances greater than 20 km, the acceleration data from the Kocaeli earthquake are generally bound by the plus and minus two standard deviation predictions. As it has been observed in almost all past earthquakes, the ground motion amplitudes are larger for the soil sites (Yarimca, Diizce) than for the rock sites (Gebze, Izmit, Sakarya)

Figure 8. Peak horizontal ground accelerations recorded in the Kocaeli earthquake

Figure 9. Peak horizontal ground accelerations recorded in the Duzce earthquake

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The Duzce (DZC) record is the only record closer than 20 km that falls above the median prediction. This record was affected by rupture directivity. The Ambarli (ATS) site recorded unusually large accelerations (above the plus two standard deviation prediction for each attenuation relationship), possibly due to strong focusing and site effects.

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In Kocaeli earthquake the fault ruptured from Golcuk first to the west approximately 40 km then rupturing approximately 80 km to the east. Forward directivity may be observed both to the east and west of the fault. The western segment of the August 17 fault ruptured from east to west in the Izmit Bay for an unknown distance. As indicated in the source rupture models developed for the earthquake, the directivity effects may have contributed to damage in Yalova. And Cinarcik. Forward directivity can be observed both to the east and west of the fault. Sakarya and Yarimca records display strong velocity pulses and a static displacement of 2.0 m and 1.5 m, respectively, in the E-W component (Figure 10). The N-S component of the Yarimca (YPT) record also displays a significant static offset (1.2 m), indicating some movement to the north. Yarimca record is rather

159 complex compared to others and clearly indicates an early aftershock with high frequency vibrations originating very close to the main shock epicenter. The complexity of the waveform at YPT may also indicate the influence of the local geology at the site. At Arcelik (ARC) the waveform is simple. The largest motion is in fault normal direction with the peak amplitude directed towards south. At Sakarya record (SKR) the time difference between the s- and p-wave arrivals is only 1.8s. This may be taken as an indication that the rupture might have propagated at a supershear velocity of 4.7km/s between the source and the SKR station. Figure 11 provides a comparison of response spectra of several records with the code-based spectrum. ftsevco-^cnixowias rerspONsg RSCCTW. rem tMLi**>*i*u. owfccraoN

Figure 11. 5% damped linear response spectra for fault normal components of YPT, IZT, SKR and DZC records obtained during Kocaeli Earthquake and comparison with the code-based spectrum.

During the Kocaeli earthquake the Diizce (DZC) station was in the forward directivity direction of the eastern segment of the fault and as expected, the fault normal motion is dominant. The acceleration response spectra for the DZC motion exceed of the UBC design spectrum at periods less than 0.5 s and greater than 3.0 s. At longer periods the fault normal component is above the fault parallel component, as expected for forward directivity situations. Dtizce earthquake generated two strong motion records in the near field from the stations operated by the General Directorate of Disaster Affairs. A mobile array installed in the Golyaka region (western terminus of the rupture) installed by Lamont-Doherty Observatory and French research team also recorded several accelerograms. The peak acceleration levels on these accelerograms are in the vicinity of 0.8g (Figure 9). The peak accelerations recorded in Duzce earthquake are more in line with the available attenuation relationships. The stress drop associated with this event is also at least

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twice higher than that of the Kocaeli earthquake. In the November 12 Duzce earthquake Bolu was in the forward directivity of the ruptured segment of the fault. This is evidenced by the short duration of the strong motion at Bolu compared to Duzce. Duzce station recorded two near field strong motions during these two earthquakes. A comparison of their acceleration spectra indicates similarity for frequencies higher than 2Hz. In mid frequency ranges, the November 12 record has larger spectral accelerations. This may be a manifestation of different source characteristics. It should be noted that these results do not provide very strong evidence for the directivity phenomena as described in Somerville et al (1997), This may be due to very sparse sampling if the ground motion and the rather unfavorable location of the stations for observation of directivity effects. During the Duzce earthquake the closest strong motion stations to the fault rupture were Dilzce, Adapazari, Bolu and Mudurnu. These stations were operated by General Directorate of Disaster Affairs. The peak ground accelerations were 0.51g at Duzce, 0.81g at Bolu, 0.02g at Adapazari and 0.12g at Mudurnu. The high intensity ground motion obtained in Bolu can be a manifestation of forward directivity, sudden stopping phase of rupture and/or site response. The long duration and the long period energy content seen in Duzce record may be indicative of basin response and softening of soil media. 7

Geotechnical Effects And Site Response

Along the southwestern shore of the Gulf of Izmit large scale ground subsidence has occurred due to combination of vertical tectonic motion associated with pull-apart structures and land sliding. Many buildings located near the surface fault were torn apart by the fault rupture and collapsed, although there were similar buildings near the fault with no apparent damage. In Adapazari, located over young riverbed sediments with soft and liquefiable silts and sands, hundreds of buildings sank, as much as 1.5m, or tilted due to shear failure of the foundation media and liquefaction (Figure 12). Surface manifestations of liquefaction in Adapazari and Sapanca included sand boils and lateral spreading. Buildings punched down into the soil softened by the shaking and high numbers of oscillation cycles, which lifted up the sidewalks due to the injection of soil material (Figure 13). However the softened and/or liquefied soil media also acted as an isolator dissipating the energy at the foundation level and avoiding shaking damage to the buildings. In Duzce earthquake no surface indication of liquefaction was reported in Duzce nor Kaynasli However, several building settlements observed in Duzce, similar to thoses in Adapazari in Kocaeli Earthquake, indicates that some total or partial liquefaction might have taken place below the thick silty-clayey layer (Aydin, 2000).

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Figure 12. Overturned binding in Adapa/ari due to woakened/liqucfiod foundation

Figure 13. Building in Adapazari that sank into the ground and the displaced soil heaved

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Only limited slope failure, mostly in the form of road embankment failures was observed in both events The only major landslide took place on west bound lane of E-5 highway at Bakacak in Duzce earthquake which disrupted the traffic for several days until a bypass road was constructed (Figure 14) . The landslide occurred on the natural slope and in the highly weathered parts of the rock.

Figure 14. Landslide on E5 Highway in Duzce Earthquake

In the eastern part of Gdlctik, a broad regional subsidence occufred affecting the Ford Factory under construction Mid several urban settlements (Figure 15). The subsidence is believed to be the result of a graben-like action associated with a local pull-apart tectonic structure. The subsidence caused a 4-km-long section of the coast near Gdlcttk to submerge about 3 m. Avcilar, to the west of Istanbul, exhibited relatively high rates of building damage indicating the influence particular geological conditions, also evidenced by strong motion records with higher peak accelerations than in surrounding areas. Site effects at Avcilar were estimated using S waves from both type of records (Ozel etal, 2000). The results show that the amplifying frequency band is, in general, lower than 4 Hz and the geology of the area is capable of amplifying fee motions by a factor of 5-10. In this frequency band, there is a good agreement between the spectral ratios from the two main shocks and their aftershocks. Kudo et. al (2000) has shown that the large and long duration of strong motion records at Ambarli (ATS) are closely related to the low velocity (Vs~200m/s) of surface layers. The S-

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wa¥e velocity structure at Avcilar Is similar to the lowland Ambarli (ATS) and the stong ground motion at Avcilar during the mainshock is estimated to be similar to that at ATS.

Figure 15. Subsidence at Golcuk along the southern shore of the Izmit Bay

Site effects in Adapazari and Golcuk areas were studied by Kudo et al. (2000) on the basis of amy observations of microtremors and aftershocks. Results indicate that jpmmd motions in downtown Adapazari (extensively damaged area) were significantly different from those of SKR. SKR is located on very hard soil. Similarly, aftershock records also 'indicate a large difference of strong motions between a hillside and Izmit Bay area in and around Golcuk. 8

Building Damage And Casualties

The two earthquakes caused considerable damage to residential and commercial buildings, public facilities and infrastructures with substantial casualties in an area of 20km by 200km (Figure 16 and 17). In Kocaeli earthquake the majority of the building collapses occurred in towns located on the southern shorelines of the Sea

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Figure 16. A general view of building damage in Golcuk

Figure 17. A general view of bilding damage in Duzce

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of Marmara and in Adapazari. A western suburb of Istanbul, Avcilar, also suffered significant building damage despite its distance of about 100km from source zone. Damage is concentrated in Duzce and Kaynasli in the Duzce earthquake. The Duzce earthquake epicenter was located about 6km south of Duzce, where most of the buildings, already moderately and lightly damaged by Kocaeli earthquake, Have collapsed. The damaged buildings in Duzce also included several post-Kocaeli earthquake strengthened buldings.

Figure 18. A "pancake" type collapse in Kocaeli Earthquake

The number of condemned buildings after the earthquakes amounted 23,400. About 16,400 of these were heavily damaged and collapsed buildings during the earthquakes, which encompasses around 93,000 housing units and 15,000 small business units. Another 220 000 housing units and 21,000 small business units have experienced lesser degrees of damage. As much as 120,000 families were left in need of homes after the earthquake. The number totally collapsed buildings (pancake collapse) is estimated to be in the range of 3,000-3,500 (Figure 18). The pervasive building collapses in the two earthquakes caused substantial number of casualties. There were 18,373 accounted deaths and 48,901 hospitalized injuries, of which about 40% will be left permanently disabled. Altogether up to 600 000 people were left in need of homes after the earthquake. About 95% of these losses were associated with the Kocaeli earthquake. In past urban earthquakes in Turkey almost 50% of all medium-rise R/Cframebuildings were damaged beyond repair in

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Intensity IX+ regions. This ratio is at least 4 times higher than what was observed in 1995 Kobe and 12 times higher than 1994 Northridge earthquakes. The general vulnerability relationship for mid-rise R/C frame buildings in Turkey is provided in Figure 19, where damages grades are indicated from Dl (slight) to D5 (collapse) following the EMS (European Macroseismic Scale) terminology.

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Post earthquake fire was limited to a number of ignitions in collapsed buildings. However, these were confined to the source and mostly affected the building contents, due to the non-flammable nature of the commonly used building materials. However, a serious fire occurred at the Tupras refinery. In contradiction to other earthquakes in developing countries, most of the people affected in these earthquakes were the upper middle class living in multi-story residential apartment blocks that compromise on the quality of construction. The building development system in Turkey was conducive to poor construction. The chronic high rate of inflation associated with high real interest rates was the main impediment to the development of the mortgage (hence insurance) market, largescale housing development schemes and to the industrialization of housing construction. The high rate of industrialization and urbanization created the everpresent need for inexpensive housing. The sheer number of housing units being built was beyond the capability of municipalities to regulate and supervise. The amount of bureaucratic red tape and the limited accountability of municipal officers created disincentives for proper control. Finally, the government's legal obligation to replace or repair damaged housing after an earthquake provided discouragement for insurance and implicit encouragement and rewards for inexpensive housing with poor earthquake performance. The Marmara Region has been exemplary in very

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rapid growth in the last twenty years, due to rapid industrialization. This industrialization and the attendant jobs have attracted migrant population, leading to excessive demand for housing. Much of demand has been met by construction of five to six story reinforced concrete buildings by local builders with inadequate engineering, faulty construction practices and often without inspection by local municipalities. Stemming from the poor earthquake performance of the buildings in Turkey, the death rate in earthquakes has been at least an order of magnitude higher than those of Japan and California. In the past urban earthquakes the number of buildings damaged beyond repair were approximately equal to the number of deaths. In Golcuk, a small town near the epicenter, about 7% of the population lost their lives The predominant structural system used for buildings in Turkey consists of reinforced concrete frames with a symmetric floor plan and with unreinforced masonry infill walls. Typically hollow clay tiles are used with inadequate mortar at the joints. Although not intended, these walls form the first line of resistance against the earthquake forces and, in many cases, control the lateral drift. Once the infill walls fail, the lateral resistance is to be provided by the reinforced concrete frames alone, with usually have low concrete quality, inadequate reinforcement and poor detailing. Extensive inelastic action at the critical regions has caused varying degrees of building damage that, in extreme cases, lead to formation of hinge mechanisms and pancake-type collapses. It should be of interest to analyze the recorded ground motion to assess whether the design basis ground motion levels foreseen in the earthquake resistant design codes has been exceeded. It is believed that almost 90% of the mid-rise buildings in the earthquake-affected area were built during the last 30 years. Thus their design were supposed to follow partly the 1961 and mostly the 1975 issue of the Turkish Earthquake Code. According to the 1961 issue of the code the lateral force coefficient applicable to the region was 0.10 for reinforced concrete framed structures up to 40 m high. This coefficient was 0.15 at maximum in the 1975 issue. Elastoplastic nonlinear response spectra of the near-fault ground motions recorded in the Kocaeli and Duzce earthquakes indicate that the spectral accelerations were in the range of 0.25-0.35g for ductility ratios between 3 and 5 and for periods that encompasses the fundamental vibration periods of mid-rise buildings (Figure 20). Since would be difficult, even for those buildings that are in conformity with the 1975 code, to supply adequate capacity for this demand, the main reason behind the good earthquake performance of some structures can be the over-strength supplied by the infill walls. It should be noted that these are very general statements since it is known that the ground motion has very high spatial variability in these period ranges and the difference of damage in seemingly identical might, at least partially, be a reflection of this variability. The answer to question should wait for the installation of dense strong motion networks in urban areas. Leaving the foundation problems and failure due to being located on the fault rupture aside, poor earthquake performance of most buildings is essentially due to

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Figure 20, Elasto-plastic response spectra of YPT NS component for different ductilities (after Prof.. N.Aydinoglu)

Figure 21. Damage at TUVESASrailcar factory (steel building) in Adapazari

169 the noncompliance with the earthquake resistant design codes. The contrasting performance between similar buildings that survived and those that failed provides evidence that conformity with the design code and good construction practices can limit damages during strong earthquakes. The damage to reinforced concrete buildings can be attributed to one or more of the following reasons: •

•

• • •

Poor building material quality: The strength of the concrete was in general well below the values specified in the building codes. The use of smooth reinforcing bars (as opposed to the deformed bars) was also common. Soft stories: Soft stories increased deformation demands, P-Delta effects and forced the first-story columns to dissipate the all the energy. This effect has caused a large portion of the building collapses. Although, there were many cases where the first story collapsed while the upper stories remained relatively undamaged. Strong beams and weak columns: Deep beams used with flexible columns have contributed to the early failure of columns. Poor detailing: Insufficient anchorage, splice lengths and confinement have severely limited the ductile response of the reinforced concrete frames. Short Columns: In many cases improperly designed infill walls limited the height of the columns, leading to shear failures.

Although relative few in the region, steel buildings fared much better than the non-ductile RC frames. Steel buildings in a large industrial automotive plant under construction (Ford Otosan), was undamaged except due to strains caused by ground settlement and a fault trace intersection. A poorly designed and relatively old steel structure (Railcar Factory) has received heavy damage and partial collapse (Figure 21). Typical causes for failures in steel structures were: inadequacy of anchor bolts at column bases and failure of brace connections. Although most of the better-built pre-fabricated buildings of the industrial facilities survived the earthquakes intact, there were many collapses of pre-cast reinforced concrete buildings due to failure of beam to column connections. A portion of these collapses was observed in incomplete structures that lack the exterior walls. 1

Hospitals And Schools

The performance of public hospital and school buildings has been on the average much better than the general building stock. The main reason behind this is the 50% increase in earthquake design loads for these buildings (i.e. importance factor=1.5) and simple symmetric structural layout with no soft stories. The performance of private hospitals and schools were similar to that of the general building stock.

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Out of the 47 public and private hospitals in the affected region, 12 (26%) were damaged beyond repair. 28 health centers were totally destroyed while 20 others were heavily damaged. About 50% of 550 pharmacies in the area have received various levels of damage. In the earthquake affected region 43 schools were destroyed and 381 schools damaged. A total of 22 elementary schools and 21 secondary schools were damaged beyond repair. Another 267 basic education schools and 114 secondary schools have received minor to moderate damage. 2

Lifeline And Infrastructure Damage And Losses

Heavy damage was sustained in the energy, transport, and communications sectors. Oil and gas production facilities suffered extensive damage, highlighted by the fire damage to the Tiipras oil refinery. Modest oil and gas pipeline damage was sustained to municipal distribution systems. Telecommunications damage included ruptured transmission lines, station damages, buildings and network facilities. Office buildings, water pipes and supplies, wastewater treatment, sewerage systems and other structures accounted for additional damage to municipal infrastructure. Damage to the transport infrastructure included 60 km. of the Ankara-Istanbul highway, the railroad and numerous harbors. The public finance need for the repair of infrastructure has been estimated (State Planning Organization) to be about 3 Million USD for the energy transmission, 70 Million USD for the energy distribution, 250 Million USD for the highway system, 40 Million USD for the railway system, 24 Million USD for the ports and 75 Million USD for the telecommunication. A brief treatment of the damage sustained by different sectors is given below. 2.1

Highways

The highway system performed well considering the scale of the fault rupture and the significant near fault ground motion. In Koceli earthquake damage was restricted to isolated bridge collapses at fault crossing locations in the region southeast of Adapazari. The Arifiye overpass totally collapsed due to excessive tectonic displacements. The Duzce earthquake caused damage in Bolu crossing involving an geometric misalignment in an important viaduct and progressive collapse of a tunnel. In Duzce earthquake the E-5 highway was damaged in Kaynasli due to extensional cracking and buckling of road surface in the vicinity of fault crossing. Due to strong shaking a number of trucks were overturned on the E5 highway near Duzce. During 17.8.1999 Kocaeli earthquake most of the highway damage was restricted to the section between "Izmit Dogu" and "Akyazi" crossings on the TEM (Trans European Motorway-E80). These crossings are marked "11" and "14" on Figure 22 and the damaged section is highlighted. In this section the road goes

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Figure 22. General view of highway and viaduct damages in KoceM and Duzce Earthquakes

parallel to the fault rapture at a less than 3km distance. The damage was in the form of surface ruptures (both tension and compression cracking) and settlement of roadway fills. Settlements ranging between 10 to 50cm were observed (Figure 23).

Figure 23. Damage to road surface on ITEM Highway in KocaeM Earthquake

The most common types of damage to bridges and overpasses were displacements of girders at seating, shear key failures, and cover concrete spalling of deck around abutments. Several overpasses and viaducts on TEM'sustained damage varying from limited shifting of girders from their seats (Mustafa Inan Viaduct), failure of shear keys and damage of elastomeric bearings (Sakarya River Bridge and D310 Overpass) to total collapse (Arifiye Overpass - D650). Location of these viaducts and bridges are shown in Figure 22. Sakarya River Bridge is located about 2km to the north of the fault. Most girders in the north lane are shifted off their seats as much as 0.5m as a result of the failure of shear keys. Most of the elastomeric bearing pads were dislocated and become dysfunctional. The fault rupture passes under the Arifiye Overpass with a right-lateral offset of 1.5m (Figure 24). The fault rapture passed between the northern abutment and the adjacent pier at

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an angle of about 65 degrees with the bridge axis. As a result of this tectonic movement in excess of the seat width the girders were unseated in a consecutive manner and fell from, their supports..

Figure 24. Collapse of the Arifiye overpass on TEM Highway in Kocaeli Earthquake.

A section of the Trans-European Motorway (TEM) between Bolu and Dtizce is under construction. The motorway follows-the northern side of the Dizce basin from GUmttsova to the Asarsuyu portal of the Bolu Tunnels. Bolu Viaducts #1 and #2 (under construction), Bolu Bridge and Bolu Tunnel (under construction), located in the last segment of the TEM to be completed, were strongly affected by the earthquake. Bolu viaducts 1 and 2 carry a 6 km long section of the motorway with a maximum height of 49 m, span of 39m and a width of 17.5m. The piers are supported by 12 1.8m diameter piles. Bolu Viaduct #1, 2.3km long with dual 59 spans, was located directly on the fault rupture. The fault crossed the viaduct at Pier#46 at an angle of 20-30 degrees with the viaduct axis, with a right lateral offset of 2.5m, causing substantial shifts between the superstructure and the piers (Figure 25). Some piers rotated (about the vertical axis) by 13 degrees (Figure 26). Almost all the sliding elements at girder seats and the energy dissipating devices between spans became damaged or useless. Bolu Tunnels, under construction, consists of two 3.4 km long three-lane tubes with an average diameter of 16m. The tunnel portals are at Elmalik on the Bolu side and Asarsuyu Valley on the Dtizce side. The structurally incomplete sections, crossing thick bands of highly plastic clay fault gouge sandwiched between rock units with only temporary shotcrete lining, have collapsed during the earthquake.

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Figure 25. Aerial view of the Bolu 1 Viaduct. The faultraptureis indicated by the red line.

: '$:; Figure 26. Movement between the piers and the girders of Bolu 1 Viaduct

2.2 • Railroads At the fault crossing near Arifiye, the tracks of the main railroad between Ankara and Istanbul were damaged. The tracks were distorted to an "S" shape by the fault offset at the Tepetarla station damaging about 200m section of the railroad. At

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another locations, extensive ground deformations (near Kurtkoy) and tension caused misalignment (Figure 22).

Figure 27. Bucking of the railroad track near Sapance in Koceeli Earthquake

2.3

Telecommunications

Telephone communication was temporarily lost due to damage to the main fiber optic cable at the fault crossing to the east of Izmit and damage to equipment and batteries in the central telecommunication facilities. The usual telephone congestion occurred due to overloaded lines with extensive private calls. Typical damage to tie regional telecommunications systems experienced in previous earthquakes was also experienced in Kocaeli and Duzce earthquakes. Many batteries toppled from racks, broken and need to be replaced. A number of trunk connections, local loops and cross bars were damaged due to ground shaking and/or falling structures. 2A

Drinking and Waster Water

The earthquake-affected region has a modern water system with steel transmission lines and water treatment plants. Izmit Water Project, the main source of water in the Kocaeli district, received only minor damage. Damage to some water treatment plants were easily repaired with minimum interruption of service. The 80km long water pipeline between Golcuk and Yalova and elevated water tanks were damaged at a number of locations. Water supply within the cities (especially Golcuk,

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Adapazari and Sapanca) was cut off for a long period of time due extensive failures in the distribution pipes due to fault rupture and liquefaction. Izmit wastewater treatment plant was closed after the earthquake due to damage to the mechanical equipment. The intercepting sewer pipes between Golcuk were heavily damaged. The salinity of the raw wastewater in the Tuzla Wastewater Treatment Plant increased after the earthquake to the infiltration of seawater to the system through damages in the collector pipes laid below the sea level. In Duzce earthquake the sewage systems in Duzce and Kaynasli were heavily damaged due to ground deformations. 2.5

Dams

State Water Works (DSI) has reported no damage dams and reservoirs. Yuvacik Dam, a 40m high rockfill dam, experienced only very minor settlements although it is located only 4km away from the fault rupture. Gokce Dam (61m high) near Yalova experienced limited longitudinal cracking at the crest. Other dams in the earthquake effected region (Hasanlar near Duzce, Omerli and Darlik near Istanbul, and Kirazdere near Izmit) performed very well with no damage. The nearest dams to the Duzce earthquake epicenter are Hasanlar dam and Golkoy dam. Hasanlar dam, a 72.8m high rockfill dam, is at 12 km from the epicenter while Golkoy dam, a 24.5m high earth-fill dam, is located at about 21km from the epicenter. No damage has been reported for at these dams. 2.6

Electricity

The electricity in Turkey is produced by TEAS (also independent power plants and industrial power plants) and distributed to main transformation stations operated by TEAS. The distribution from these main transformation stations, the electricity is distributed to the cities and industrial facilities by TED AS. These are state owned companies. Medium voltage (MV) and low voltage (LV) electric power distribution facilities owned by TEDAS and affiliated distribution companies. No damage was reported in power plants owned by TEAS and other independent and industrial power plants in Kocaeli and Duzce earthquakes. The power transmission facilities affected by the earthquake are located in eight provinces (Sakarya, Kocaeli, Bolu, Yalova, Bursa, Eskisehir, Bilecik and Istanbul). The damages which occurred in High voltage (HV) transmission substations (Adapazari No.2, Izmit No.l and Kentsa) include breakage of transformer bushings, breakage of surge arresters, damage of disconnections, movement of transformers and damages to substation buildings. This damage causied power blackout in northwestern Turkey within minutes of the earthquake. The electricity was generally restored to most areas within several days. On the basis of information provided by TEDAS (Electricity Distribution Authority), about 14 (7% of total inventory) of MV/MV type and 800 (7% of total

176 inventory) of MV/LV type Distribution Transformers in the affected urban areas have received heavy damage. About 850km (35% of the total) MV type and about 1300km (20% of the total) underground distribution cables in the affected region were damaged. Damage to overhead lines were much less. However, 1050 (7% of the total) MV type towers and 3000 (5% of the total) LV type towers were replaced. 2J

Ports

Most of the ports and jetties privately operated by industrial facilities in Izmit Bay sustained damage (Figure 28). Extensive damage was observed at Golcuk Navy Base due to fault crossings (Figure 29). Damage included failure of piers, mechanical equipment, piping and the collapse of cranes. The government owned Derince general cargo and grain port,, which handles some 2 million tons of cargo annually, suffered heavy damage to docks, cranes and warehouses, including cracks and severe subsidence. Deince Port, which is of the concrete caisson type with shorefront length of about 1.5 km, shifted away from the wharf up to 0.7m horizontally and 1m vertically due to liquefaction-induced deformations, settlements and lateral spreading (Figure 30). Several rail mounted portal cranes and some old steel warehouses were damaged. A substantial number of the jetties at the industrial facilities were also damaged. These include PetMm facilities, Tupras Oil Refinery, Petrol Ofisi, Shell Oil, Trans Turk, Seka Paper Mill and UM Shipyard.

Figure 28. Location of affected ports and jetties in Izmit Gulf in the the Kocaeli Earthquake

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Figure 29. Arial view of the No vy Base in Golcuk. The fault rapture is indicated by red line.

Figure 30. Damage at Derince Port in KoeaeM Earthquake

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2.8

Airports

The new terminal building at Ataturk Airport under construction in Istanbul experienced minor structural problems but the Airport remained fully functional. The control tower of a military airport near Izmit received heavy damage. 2.9

Natural Gas and Oil Pipelines

The government owned Botas (Petroleum Pipeline Corporation) which covers all oil and gas imports and major distribution pipelines, reported no damage on any of their installations. The Russia-Turkey natural gas pipeline in the region crosses the Izmit Bay at about 30 km west of Izmit and the natural gas pipeline connections to industry and power plants in the affected area was operational after the Kocaeli earthquake. In Izmit (IGSAS) municipal gas distribution system (only urban gas system in the affected area, excepting Istanbul) no damage is reported to the main distribution network. IGSAS reports that about 15% of service boxes (out of a total of 21,000) damaged due to collapsing houses. Some damage to service boxes in Istanbul (especially in Avcilar District) was also reported. 3

Damage To Industry And Losses

The epicentral area can be considered as the home of Turkey's heavy industry, including petrochemical plants and car manufacturers. The major industries are automobile, petrochemicals, manufacturing and repair of motor (and railway) vehicles, basic metals, production and weaving of synthetic fibers and yarns, paint and lacquer production, tire factories, paper mills, steel pipes, pharmaceutical, sugar, cement, power plants and tourism. Many foreign companies have affiliates nearby in the region, including Goodyear, Pirelli, Ford, Honda, Hyundai, Toyota, Isuzu, Renault, FIAT, Ford, Bridgestone, Pepsi Co, Castrol, Dow Chemical, Shell Co., British Petroleum, Mannesmann, Bridgestone, DuPont, Akza Nobel, Phillips, Lafarge and Bayer. Damage to industry was more extensive than those in other earthquakes with similar ground motion levels. The damage encompassed cooling tower collapses, damaged cranes; collapse of steel, reinforced concrete framed and prefabricated structures, damage to jetties, and extensive equipment failures. The extent of damage to industry depended on, distance to fault, site conditions, quality of construction, anchorage conditions of machinery and robustness and redundancy of fire fighting facilities. Losses due to extensive business interruption were substantial as compared to the physical damage. The Kocaeli Earthquake provides a unique opportunity to investigate the performance of industrial facilities subjected to substantial strong ground shaking under near-fault conditions.

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3.1

Petrochemical Industry

An extensive concentration of state-owned petrochemical complexes is located within 5km of the fault, including Tupras, Petkim and Igsas. The heaviest damage occurred at the Tupras facility, the largest refinery in the region producing about twelve million tons per year. The refinery was working at about 90 percent of its design capacity and can be considered a modern and efficient plant. The earthquake caused significant structural damages to the refinery itself and associated tank farm with crude oil and product jetties. The consequent fire in the refinery and tank farm caused extensive additional damage (Figure 31). Fire started in one of the Naphtha tanks continued for three days endangering the safety of the whole region. Six tanks of varying sizes in the tank farm of 112 tanks were damaged due to ground shaking and fire (Figure 32). There were damage to cooling towers and the port area. Collapse of a 150m high heater stack on the boiler and crude oil processing unit caused significant damage and started a second fire. The total damage is estimated to be around US$350 million.

Figiire31 A helicopter view of the fire in Tupras petrochemical complex.

The Petkim petrochemical facility had limited damage, which includes settlement at the port and the collapse of a cooling tower. No damage to the equipment in this facility is reported. The fresh water for the Tupras and Petkim complexes, as well as for several other industries in the region (e.g. Seka paper factory), is supplied from Sapance Lake via 30km long pipelines. Fault rapture and soil failure caused extensive damage to pump stations and pipelines at about 20 locations. The failure of the water supply caused problems in controlling the fire at Tupras. Igsas fertilizer plant has experienced extensive damage in the administration building. Ammonia processing and packing units and the port

180

facilities were partially damaged. At Aksa chemical industries located in Yalova region there was damage in port facilities and storage tanks. All of these facilities also experienced extensive losses business interruption.

Figure 32. Post-earthquake fire damaged tanks in Tupras petrochemical complex

3.2

Automotive Industry

There are numerous car and tire factories in the region. The Hyundai factory experienced significant nonstructural damage. The Toyota car factory had fault ruptures in its parking lot. There was no structural damage to the steel framed building. Nonstructural damage included collapsed storage racks, transformers and cars on the assembly line. Some automatic machinery in the production lines of these factories suffered from alignment problems. Ford Otosan car factory, under construction during the earthquake, has experienced significant terrain subsidence and some structural damage. Pirelli Tires, Brisa Tire and Kordsa tire steel belt and cord company had extensive damage and business interruption. 3.3

Other Industry

Other industrial facilities include cement plants, steel mills, paper mills, and food processing plants, textile and pharmaceutical factories. TUVASAS railway wagon Production Company, Adapazari sugar factory and Asil Celik steel production company has all received extensive structural damage. In TUVASAS a large maintenance building and several small buildings collapsed due to lack of bracing in steel structures. In the sugar factory a stack and an elevator pipe failed and fell into the sugar-processing facility, partly damaging the facility with extensive damage to the equipment inside. Examples of specific damage include collapse of two cranes at the Mannesmann Boru pipe factory; roof collapse, transformer damage, and silo collapses at the SEKA paper mill; collapse of a steel frame structure and movement of bioreactor vessels at the Pakmaya food processing plant;

181

storage rack collapse, toxic releases from mixing chemicals, and damaged piping at the Toprak pharmaceutical firm; and collapse of liquid oxygen tank support structures at the Habas medical gas facility. Kudos textile factory in Adapazari, Cak textile factory in Akyazi (Duzce) and Ak-Al textile factory in Yalova had extensive damage due to the collapse of the pre-fabricated reinforced concrete factory buildings. Some tanks in Aksa chemical installation in Yalova experienced damage, which was associated with leakage of chemicals. Food processing plants that have experienced heavy damage include Pepsi Co-Uzay Gida (Izmit) and Merko Gida (Yalova). In Duzce earthquake Siiperlit pipe factory, Akisik appliances factory, Sarsilmaz firearm factories in Duzce and Anlas Anadolu tire factory in Kaynasli were heavily damaged. There wren limited damage to the industry in Bolu (Filiz Macaroni Factory and Kelebek Furniture Factory). Private and public sector estimates of the damage to the industry as a whole range from $1.1 to $4.5 billion. The value-added loss in manufacturing is estimated by at $600 to 700 million. The added value loss stemming from the damage to industry is estimated to be about 700 Million USD (SPO) which may result in a 1.6% decline in the growth of the production sector in Turkey. Other sources put this loss figure as much as into the 2 Billion USD range. For example, according to Kocaeli Chamber of Industry, 214 enterprises (about 19% of all enterprises in the province) reported significant damage amounting to a total of US$2.5 billion in capital losses. Many major facilities are known to face extensive business interruptions, however the biggest loss will be the loss of qualified manpower. Most of the industrial losses will be covered by the insurance. Payments of claims are estimated to have amounted to about 600-800 million USD. State Planning Organization estimates an $880 million total loss just for the 19 affected stateowned enterprises in the region. A total of 15 percent capital loss for has been reported for the major state owned enterprise located in the region, (mainly in TUPRAS, TUVASAS, IGSAS, PETKIM, SEKA and Asil Qelik). The State planning Organization estimates that the loss of business in these industries may have amounted to 632 Million USD. The tourism industry (based in Yalova) has been virtually destroyed and tourists may not return for many years, so that a fundamental restructuring will be needed.

4

Economic And Business Losses

Estimates of total wealth and income losses range from $5 to $14 billion. Estimates for the loss of physical capital accounts range between 4 to 10 Billion USD. Housing sectors accounts for roughly 40%. Average total loss (physical and socioeconomic) may be in the range of 16 to 20 Billion USD, about 7-9% of the nation's GDP. According to World Bank (2000) the damage (wealth loss) significantly exceeds the direct physical damages of the earthquake. The increase arises from the following principal sources: (1) reduced tax revenues from the region due to the

182

negative output shock, (2) losses from a tax payment deferral announced by the Government, (3) credit subsidies for loan refinancing and new loans to small and medium enterprises which sustained damage in the region, (4) postponed non-tax revenues from public enterprise privatization, and (5) emergency assistance to the population, cost of temporary housing and compensation for loss of life and disability. State Planning Organization estimates that the earthquake will bring a load of about 6.2 Billion USD on the public finance. About 3.5 Billion USD of this amount will be needed for post-earthquake housing construction. The special earthquake taxes and paid military service scheme introduced by the government have generated about 3 Billion USD in one year after the earthquakes. Foreign finances (World Bank, European Union and others) contributed another 2.5 Billion USD. The decline in GDP during 1999 (-%5) stopped in the first half of 2000 and an increase of (%5) realized on year basis (State Planning Organization, Aug., 2000 report). The improvement in the consolidated budget revenues during the first half of 2000 was significantly assisted by the additional taxes, amounting to 3 Billion USD, due to earthquake disaster. Damage to large enterprises have been moderate and mostly covered by the insurance (rather reinsurance) sector. However, human capital losses sustained by industry have been more serious, but harder to estimate. Besides temporary disruptions to labor supply due to deaths, injuries, and demotivation, large enterprises in the region are concerned about possible out-migration of qualified employees. Micro and small enterprises (retail shops, craftsman and artisan workshops, and small service units) were the hardest hit by the earthquake, losing most of their working capital and premises and key family workers. While the total capital stock and value added of the micro and small enterprises might be relatively limited, their large number could bring their total loss to significant levels. World Bank (1999) estimates that about 6,000 small shops (employing less than 5 persons) were severely damaged by the earthquake. The total number of small enterprises (employing 5-10 persons) damaged by the earthquake was estimated to reach 1500. Insurance coverage for small and micro these enterprises are very limited; they are undercapitalized and have limited access to funding. About 20,000 small businesses have terminated their operation leaving behind about 140,000 jobless people. Job losses could be as much as 45% of the pre-earthquake labor force in the earthquakeaffected region. Job losses especially for the self-employed may recover in the near future with government credit incentives, debt rescheduling and assistance for rebuilding. Several source have reported small business loses to be in the order of 1 Billion USD. The loss of capacity in small and micro enterprises has additional adverse socio-economic effects due to loss of unemployment, production and economic linkages with larger firms.

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5

Earthquake Insurance

It is reported that about 620,000 earthquake policies are in force in Turkey with a total insured sum of about 102 billion USD. The gross retention of Turkish insurance companies is around US$24 billion. About 5% of these policies were in the earthquake-affected area with more than 7 billion USD portfolio. The total insured losses are reported to be around US$0.6 billion as reported by Munich-Re. Since the vast majority of this is reinsured internationally, the payment by the domestic insurance companies is around US$25 million. The information gathered on the differences between the damaged and undamaged structures and the observational vulnerability relationships will help insurers to gain valuable insight on the catastrophe modeling and evaluate portfolios and underwriting financial risk. The insurance premia in the affected region have significantly increased after the earthquake. Through a World Bank project a national mandatory earthquake insurance plan has been initiated. The main reason behind this scheme is to relive the government from the burden of replacing earthquake-damaged housing. On December 17, 1999 a government decree to start a national scale mandatory earthquake insurance scheme for housing units along with cancellation of the legal government obligation for the post-earthquake housing was announced. A government-sponsored insurance pool "Turkish Catastrophic Insurance Pool (TCIP)" is now being put in place, which will transfer the national risk into world-wide risk-sharing pools, managed by international reinsurance companies and backed by substantial capital resources. Insurance coverage for each housing unit will have a coverage limit of about US$30,000 per house. For the additional value usual private insurance coverage will be permitted. Although the new scheme is expected to be operational by 28 September 2000, the mode of operation has yet to be decided. The government hopes that in the future, the TCEP can contribute to the control of construction through differentiation of premia on the basis of earthquake vulnerability. Several opponents to the plan express that it would be impossible to find adequate reinsurance capacity, the TCIP will not be anything different that a property tax and the government would have been much better to insure itself while retaining the existing scheme of post-earthquake housing assistance.

References This paper is mostly based on the online material available in the web page of the Bogazici University Department of Earthquake Engineering: http://www.koeri.boun.edu.tr/earthqk/earthqk.html. The following list of references is provided to provide further information to the reader. Not all entities are referenced in the paper. Some references are Internet - Online web addresses.

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16. EERI (1999), The Izmit (Kocaeli), Turkey Earthquake of August 17, 1999, EERI Special Earthquake Report-Learning From Earthquakes-October 1999, Also available online: http://www.eeri.org/Reconn/Turkey0899/Turkey0899.html 17. ERD (Online), August 17th Kocaeli Earthquake, Earthquake Research Division of the General directorate of Disaster Affairs, Availabe: http://www.deprem.gov.tr/ 18. EQE (Online), August 17, 1999 Izmit, Turkey Earthquake and M7.2 Duzce, Turkey Earthquake November 12, 1999, EQE Inc. San Francisco, Available: http://www.eqe.com/revamp/turkey3.htm 19. GEES (Online), Kocaeli, Turkey, Earthquake of August 17, 1999 and The November 12, 1999, Turkey, Earthquake, Geotechnical earthquake Engineering Server, University of Southern California, Available: http ://geoinfo .use. edu/gees/ 20. Ghasemi (1999), Ghasemi, Hamid, James D. Cooper, Roy Imbsen, Hasan Piskin, Fulya Inal, and Azmi Tiras, Summary Report of The 1999 Duzce Earthquake Investigation By The FHWA Reconnaissance Team on November 30 and December 2, 1999, Publication No. FHWA-RD-00-146. 21. ITU-IAHS (1999), Proceedings of the International Conference on Kocaeli Earthquake 17 August 1999, Istanbul Technical University, Istanbul, 1999 22. Kocaeli Earthquake (Online), Bogazici University, Department of Earthquake Engineering, Available: http://www.koeri.boun.edu.tr/earthqk/earthqk.html 23. Krinitzsky, E.L., R.S.Olsen, M.R.Chowdhury (2000), Effects on Dams of the 17 August 1999 Kocaeli (Izmit) Earthquake in Turkey, WES, USACE, Vicksburg. Mississippi, USA 24. Kudo, K., T.Kanno, H.Okada, O.Ozel, M. Erdik, M. Takahashi, T. Sasatani, S. Higashi and K. Yoshida (2000), Site Specific Issues on Strong Ground Motion during the Kocaeli, Turkey Earthquake of August 17, 1999, as Inferred from Array Observations of Microtremors and Aftershocks, Submitted to BSSA 25. Le Seisme d'Izmit (Online), ITnstitut de Physique du Globe de Paris, available: http//www.ipgp.jussieu.fr 26. MCEER (2000), The Marmara, Turkey Earthquake of August 17, 1999: Reconnaissance Report, Ed by C. Scawthorn, The Multidisciplinary Center for Earthquake Engineering Research, Universty of Buffalo, NY, "USA 27. Milli Reasurans (2000), Deprem'99, Istanbul 28. Mucciarelli et. al (Online), 1999 Kocaeli Earthquake, Turkey, Earthquake, Available: http://www.pz.cnr.it/imaaa/turchia/ 29. ODTU (2000), Marmara ve Duzce Depremleri Muhendislik Raporu, ODTUDeprem Muhendisligi Arastirma Merkezi, Ankara, Nisan 2000. 30. OECD (2000), Bibbee, Alexandra, Rauf Gonenc, Scott Jacobs, Josef Konvitz And Robert Price, Economic Effects Of The 1999 Turkish Earthquakes: An Interim Report, Organization For Economic Co-Operation And DevelopmentEconomics Department, ECO/WKP(2000)20

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Ozel,0., E. Cranswick, M.Meremonte, M.Erdik and E.Safak (2000), Site Effects in Avcilar, West of Istanbul, Turkey from Strong and Weak Motion Data, Submiited to BSSA Special Volume. Parsons, T., S.Toda, S.Stein, A.Barka and J.H.Dietrich (2000), Heightened Odds of a Large Earthquake Near Istanbul: an Interaction Based Probability Calculation, Science, 288. Rathje, E., I.M. Idriss, A.Ansal, P Somerville and M.Erdik (2000), Strong Ground Motions and Site Effects, Submitted to Earthquake Spectra. RMS (1999), Event Report, Kocaeli, Turkey Earthquake, San Francisco Safak, E. and M.Erdik (Coordinators) (2000), Recorded Main Shock and Aftershock Motions, Submitted to Earthquake Spectra. SCEC (Online), Turkey, Izmit Earthquake, Southern California Earthquake Center, Availabe: http://www.scec.org/worldwide/turkey.html SPO (2000), State Planning Organization - Uzun Vadeli Strateji Ve Sekizinci Be? Yillik Kalkinma Plani, Ankara Toksoz, M.N., Shakal, A.F. and Michael, A.J. (1979), Space-Time Migration of Earthquakes along the North Anatolian Fault Zone and Seismic Gaps, Pageoph, Vol. 117, pp. 1258-1270. USGS (2000), Implications for Earthquake Risk Reduction in the United States from Kocaeli, Turkey, Earthquake of August 17, 1999, USGS Circular 1193, US Department of Interior, USA World Bank (1999) Turkey, Marmara Earthquake Assessment, September 14, 1999, Turkey Country Office, The World Bank World Bank (1999), Project Appraisal Document on a Proposed Loan in the Amount of US$505 Million to the Republic of Turkey for a Marmara Earthquake Emergency Reconstruction Project, Nov. 1, 1999, Report No: 19844-TU Yagi, Y. and M. Kikuchi (1999), Preliminary Results of Rupture Process for The November 12, 1999 Turkey Earthquake, Earthquake Research Institute, The University of Tokyo. Yagi, Y. and M. Kikuchi (1999), Source Rupture Process of the Kocaeli, Turkey, Earthquake of August 17, 1999, Obtained by Joint Inversion of Nearfield Data and Teleseismic Data, Earthquake Research Institute, The University of Tokyo. Yagi, Y. and Kikuchi, M. (Online), The 1999 Turkey Earthquake, ERI, University of Tokyo Japan, Available: http://www.eic.eri.utokyo. ac .j p/y uj i/trk2

HEALTH MONITORING AND OPTIMUM MAINTENANCE PROGRAMS F O R S T R U C T U R E S IN S E I S M I C Z O N E S LUIS ESTEVA AND ERNESTO HEREDIA-ZAVONI Instituto de Ingenieria,

Universidad National Autonoma de Mexico, Apartado Postal Coyoacdn 04510, Mexico, D.F., MEXICO

70-472,

E-mail: esteva(a),merlin. iineen. unam. mx The problem of health monitoring for structural systems built on sites with significant seismic hazard levels is formulated as one of determining cumulative damage levels for the purpose of making repair and maintenance decisions that are optimum within a life-cycle framework. An integrated review is presented of previous work by the authors on three fundamental issues that are relevant for the problem at hand. These issues are the quantitative models of damage, the theoretical methods to determine its value at a given instant on the basis of experimental measurements, and the implications of damage accumulation on the evolution of the functions that measure the vulnerability of the system. A Markov process model is adopted to represent the process of damage accumulation as a consequence of the occurrence of seismic events and repair and maintenance actions.

1

Introduction

The inelastic response of a structural system to moderate or high intensity seismic excitations is the result of local strains larger than the elastic limit at some members or critical sections. The occurrence of these strains may give place to residual deformations and stiffness reductions that could affect the response of the system to future excitations, ordinarily increasing its vulnerability to them. For this reason, such change in the structural properties is often denoted as damage. Its quantitative evaluation and the assessment of its consequences on the expected behavior of the system, when subjected to new excitations, are essential tools for making decisions related to maintenance or repair actions. In the formulation proposed here, these decisions are made in accordance with a minimum expected cost analysis within a life-cycle framework. The costs involved are the initial construction costs and the expected present values of future expenditures and losses: maintenance, repair, damage and failure consequences. A decision model covering these concepts for building frames with energy-dissipating devices has been presented by Esteva et al [5]. Decisions concerning repair of the frame and/or replacement of the devices after an earthquake are made on the basis of damage estimates derived from visual inspection, complemented by theoretical evaluations of structural response based on the information available about the seismic event. In this paper the attention is focused on three fundamental issues: the quantitative models of damage, the theoretical and experimental methods to determine its value at a given instant, and the implications of damage on the 187

188

evolution of the vulnerability function of a system. Due to the wide scope of the concepts presented, and to the many tools yet to be developed, the material that follows places its attention on general criteria and potential solutions, together with detailed presentations of recent work. 2

Damage accumulation, damage indicators and system reliability

The damage accumulated on a structural member or system subjected to alternating load/deformation cycles can be quantitatively described in terms of the numbers of such cycles experienced by that member or system, normalized with respect to some measure of their deformation capacities. Damage indicators of this type are directly determined from the corresponding response time-histories. Some examples of these are that proposed by Miner [10] to measure safety with respect to fatigue failure or that due to Park and Ang [12], which expresses damage as a weighted superposition of the maximum deformation amplitude and the strain energy dissipated through hysteretic behavior. Other descriptions of damage center their attention on the evolution of the mechanical properties of structural elements as derived from response histories. For an individual structural member, a well-known example of an indicator of this type is the percentage reduction of its low-deformation tangent stiffness with respect to its value in the undamaged state. For a structural system, the stiffness reduction is normally measured by the elongation of its fundamental period of vibration in the linear range of behavior. A third approach to the quantitative description of damage is concerned with its consequences on the evolution of the cyclic load-deformation (or stress-strain) properties of a system, or of the members that constitute it. Attention is then focused on the expected future behavior, rather than on past response history. A number of constitutive-function models for structural elements subjected to cyclic excitations are available in the literature. They all predict the evolution of the cyclic response properties of those elements on the basis of the previous history of damage accumulation. The model originally proposed by Wang and Shah [13], and later modified by Esteva et al [5], is used here to represent the cyclic moment-curvature functions at the end of a reinforced concrete member. That model considers one such member subjected to a sequence of load-deformation cycles with different random amplitudes. The maximum value reached by the curvature in a given direction (positive or negative) will evolve with time. If the member is reloaded in a given direction, making its curvature reach the maximum value experienced in that direction during previous loading cycles, the bending moment developed for such curvature value will be smaller than that corresponding to the undamaged, monotonically loaded member (Fig.l). The ratio of the acting bending moment for the damaged member to that associated with the undamaged conditions is the reduction factor D, given by Eq. 1:

189

(1)

D = 1.0-exp(- Y D m )

In this equation, Dm is the fatigue index given by the following equation: m

(2)

D

A

=v^-

Here, m is the number of deformation cycles, Ao is the deformation at failure under monotonic load, Aj is the deformation amplitude of the j-th cycle and y is a constant parameter that can be taken equal to 0.602, according to the experimental evidence presented by Wang and Shah [13]. If the deformation grows beyond its maximum value during previous cycles, the load-deflection function will tend to join the envelope function for the undamaged condition, as shown in Figure 1.

Moment

c rotation,®

Figure 1. Stiffness-degrading functions for plastic-hinge rotation

190

Heredia-Zavoni et al [9] have proposed a model to describe the influence of the damage accumulated on a multistory frame on the residual mechanical properties of that frame. According to it, the secant stiffness associated with the shear-distortion curve for a given story or for the system as a whole is described by the ratio Kj of the secant stiffness of the i-th deformation cycle, K(Aj,Dj), to the initial stiffness, Ko, for the undamaged condition:

,3,

Ki=B|^>=C„(D,,

'A.v 1+a J J

Here, D ; is the value given by Eq. 2 for m = i; C0(Dj) = 1- Djq, a = (A0Ko)/F0 - 1, F 0 is the force developed by the undamaged system for a deformation equal to A0 and n, q are parameters that determine the rates of stiffness reduction that result as a consequence of deformation amplitude and cyclic response, respectively. If the structure is linearly elastic, a = 0 [9]. This model predicts that the normalized secant stiffness decreases for increasing cumulative damage Di and for larger displacement ratios, A/A0. For the purpose of measuring the seismic reliability of a system, use will be made here of a criterion proposed by Esteva and Ruiz [4], on the basis of the wellknown P safety index originally proposed by Cornell [1]. The criterion proposed by the former authors deals with the case of a multistory building frame with uncertainly known mechanical properties, subjected to a random earthquake ground motion acceleration time history. This excitation is represented as a non-stationary stochastic process with evolutionary amplitudes and frequency-content. If ASi is the peak value of the deformation demand on the i-th story of the frame produced by its seismic response and ARi is the corresponding deformation capacity, then the reliability level can be measured by (3, given by the following equation: (4) P =

- ^ a(lnZ)

In this equation, Z is equal to the ratio ASi/ARi observed at that story where it reaches its maximum value; E(-) and a(-) stand for expected value and standard deviation, respectively. These statistical parameters can be estimated by Monte Carlo simulation. Let us now consider the case of a structural system built with elements with mechanical properties that deteriorate under the action of cyclic deformations. As time goes on, the mechanical properties of those elements may change, reflecting the damage produced by the response of the system to the excitations acting on it. For the i-th member of that system, this damage will be reflected in the reduction of

191

its stiffness (K;), its strength (R,) and its deformation capacity (A Ri ). For the system as a whole, this conducts to a reduction in the effective lateral stiffness of the system, as well as in its shear strength and deformation capacity [6]. The ultimate consequence of this is a reduction in the expected system reliability levels for future excitations [3]. An important objective of this paper is to show how the information about the evolution of the mechanical properties of a system, or of portions of it, can be used to assess the state of accumulated damage and its consequences on the expected reliability levels for future seismic excitations. This implies expressing damage on the structural members in terms of its influence on the residual mechanical properties of the system that will determine its expected behavior for future earthquakes of given intensities. 3

A Markov process model for damage accumulation and reliability evolution

Consider first a simple system, where all damage accumulates at the same critical section. If the modified Wang and Shah model [13] proposed by Esteva et al [6] is adopted, the damage level for the system at a given instant (during an earthquake or between earthquakes) can be described by the current value of the damage index given by Eq. 2. The damage accumulated at the end of the j-th earthquake is a random variable with a probability density function (pdf) that depends on the ground motion intensity, Vj, and on the value dj of the damage index Dj at the start of the ground motion. If the form of this pdf is known, it will be completely determined by a vector AD(yJ dj) of parameters that depends on dj. The damage index at the end of this earthquake will be denoted by Dj', which will be assumed to remain constant until the start of the next earthquake: Dj+] = Dj'. Therefore, the pdf of the latter variable, conditional to Dj = dj, can be calculated as (5) fDj.(d|dJ) = Jf Dj .(d|y,d ] )f Yj (y)dy, where the first term under the integral sign represents the pdf of Dj' conditional to an earthquake intensity equal to y and the second term is the pdf of t n e intensity of the j-th earthquake. According to the stochastic process model adopted to represent seismic hazard, this pdf may depend on the previous seismic history or be independent from it. In any of these cases, the marginal pdf of the state of damage in the system at the end of the j-th earthquake will be determined by the state of damage at the start of that earthquake and by the pdf of the intensity Yj. The latter pdf can be either independent of the previous seismic history or determined by a description of the current state of the seismic hazard that is expressed in a form independent from that history. Thus, the pdf of Dj' will be completely determined

192

from the states of damage and seismic hazard at the end of the j-th earthquake. This will permit representing the accumulation of damage on the system as a Markovian stochastic process. These ideas have been applied by Diaz and Esteva [3] to the study of the timedependent process of damage accumulation and reliability evolution of building frames. They have also been employed for the study of optimum design criteria and maintenance strategies for structural frames with hysteretic energy-dissipating devices [5]. Because of the complexity of the probability transition matrices involved, extensive use has been made of Monte Carlo simulation. One of the cases studied corresponds to a two-bay, five-story frame system with hysteretic energy dissipating devices. The system was supposed to be built at a site in Mexico City where seismic hazard was represented as a Poisson process characterized by the function relating seismic intensity with rate of exceedance per year. The state of damage at the end of an earthquake was measured by the maximum value attained by the ratio D = (KQ - K ) / K O at any story. Here, Ko is the tangent initial story stiffness for the undamaged system and K is the secant stiffness value for the story deformation cycle having the largest amplitude during the earthquake. Searching for a life-cycle optimum solution, several options were explored regarding the seismic design coefficient c and the threshold values of D adopted as a condition for repair of the main frame and for replacement of the energy dissipating devices (Drc and Drd, respectively). Values of a negative utility function U, calculated as the sum of initial construction cost, C0, and expected present values of future expenditures, were obtained for each option. The resulting values of U, normalized with respect to the initial construction cost for the main frame designed for gravitational loads only, are depicted in Figure 2. The first section corresponds to the plain conventional frame, while the other three sections contain energy dissipating devices that contribute 75 percent of the lateral strength and stiffness of each story. It can be observed that the negative utility function is sensitive to both the seismic design coefficient and the repair and replacement strategies. The latter were less significant for other cases studied, including ten- and fifteen-story systems.

193

U/G

NoEDD

DUf02

Du=04

DnrP.6

1.020

1.015

•c=0.05 •e=0.10 A c=0.15

1.010

1.005

1.000* 0.0

04

°' 8 0.0

04

08

0.0

04

08

0.0

04

°8

Dk

Figure 2. Utility values for 5-story systems In order to avoid the significant amount of computational work required to make optimum post-earthquake repair decisions in accordance with the life-cycle approach described above, it may prove convenient to resort to a simplified method to estimate the expected present value of the consequences of possible failure events. One possibility would be to consider one single "equivalent" earthquake with an adequately chosen intensity. A discussion of this problem is left for future studies.

4

Damage assessment and reliability updating

Diaz and Esteva [3] conducted some exploratory studies about the influence of damage accumulation on the reduction of the reliability index P for an earthquake of a specified intensity. For this purpose, they considered a two-bay ten-story

194

reinforced concrete frame that had been designed in accordance with the Mexico City seismic design regulations of 1987. The system was subjected to a family of artificial acceleration records with statistical properties similar to those of the EW component of the SCT, Mexico City record obtained during the destructive earthquake of September 19, 1985. The uncertainties about the mechanical properties of the structural system and the gravitational loads acting on it were accounted for by Monte Carlo simulation. The well-known model due to Takeda was used to represent the moment-curvature behavior of the critical sections at the ends of beams and columns. For the initially undamaged system, P was equal to 2.02. At the end of the earthquake, the damage index (Ko- K)/Ko was equal to 0.18. A second sample of earthquakes was then assumed to represent a second event, with the same intensity as the first one, applied to the damaged system. The value of P for the system with initial damage conditions was estimated as 1.39. Since the assumptions made to estimate the story deformation capacities were conservative, these two values are supposed to underestimate P; however, a significant difference between them would still remain if less conservative assumptions were adopted. Under usual conditions, the residual damage after a severe earthquake can be estimated on the basis of the information derived from visual inspection and from approximate evaluations of structural response and performance during that event. This information can be significantly enhanced with instrumental records of the response of the system during the earthquake or during forced or ambient vibration experiments. An approach to this problem has been presented by Heredia-Zavoni et al [9]. According to it, Equation 3 is used to represent the consequences of damage on the evolution of the amplitude-dependent effective secant stiffness of a hysteretic system with deteriorating strength and stiffness. Damage is measured by the variables presented in Equations 1 and 2. A method based on bayesian statistical analysis is developed for updating the probability density functions of parameters n and q that appear in Equation 3, as well as of the residual damage D at the end of the earthquake. The application of this method to a single story system is summarized in the following paragraphs. Suppose that a record is obtained of the response of the system to an earthquake ground motion. A set of L observed values of A; and K; can be obtained from that record, and the corresponding values of D; can be calculated, using Equation 2. If the values of n and q are assumed, then it will be possible to apply Equation 3 for each pair of values (Ai; Dj), to obtain K[' = Ki(Ai; Dj), as well as the ratio X[ = KJ'/KJ, provided Ko, Fo and A0 are known. These variables can be estimated from an analytical model of the system based on the most likely values of its mechanical properties. The values of x( are considered as realizations of a random variable £ that accounts for the model error. Under the assumption that the damage-function model in Equation 3 is not skewed, the expected value of \ is assumed to be zero, while its variance a 2 is handled as uncertain. The bayesian probability density function of the latter is taken as the conjugate distribution of a normally distributed variable with known mean and uncertain variance [2]:

195

(6)

f

(s;a^d,n',q') = - ^ - s - ( " + V p , s , s > 0 ° i ' -i T(a) Dn

Here, a and P are functions of d, n' and q'. They determine the mean and variance of a2. If the joint prior bayesian probability density function of (D,n,q) before counting with the recorded response information is fDn?q(d,n',q'), then the joint posterior distribution of those variables is given by Equation 7, where R is the vector of values Xj, a' = a + L/2, and P' = P + (1/2)EXJ 2 [9].

(7)

f

(d p,

r)

BTCa")

1

^ - 'q1 "(prr(a)(a t )- fp - (d,n,,q ' )

The posterior probability density function of D can be obtained by integration of the first member in Equation 7 with respect to n' and q'. For illustrative purposes, this criterion is applied in [9] to a single-story frame with a force-displacement curve as shown in Figure 3, obtained from a static nonlinear analysis. The modified Wang and Shah model [6] was used to represent the cyclic moment-curvature function for the cross sections at the ends of the beam, while a perfectly elasto-plastic function was assumed for the columns. The system was first subjected to the EW component of the acceleration time history recorded at the SCT site in Mexico City during the earthquake of 19 September 1985. The prior probability density function of D, n and q was established under the assumption that they are statistically independent. Parameters n and q were taken as lognormally distributed with means equal to 1.0 and 0.5, respectively, and a variation coefficient equal to 0.3 for both of them. The initial value of D was taken as uniformly distributed between 0 and 1.0. a and P were taken equal to 4 and 0.3, respectively, independently of D, n and q. This corresponds to an expected value of a 2 equal to 0.1, with a variation coefficient equal to 0.15. The prior distribution of D before the earthquake is shown in Figure 4, together with the posterior distribution of its value after that event. The latter was then taken as the distribution of the state of damage before the system is subjected to a new ground acceleration time history, now assumed to be equal to that of the first event multiplied by a scale factor of 1.1. The prior and posterior density functions of D for the second event are shown in Figure 5. The influence of damage accumulation is easily noted, observing that the expected value of D increased from 0.04 after the first earthquake to about 0.6 after the second one, with a value of the intensity only 10 percent larger. Finally, Figure 6 shows the probability density function of D after the second earthquake when the information resulting from the response record for the first event is ignored. A larger expected value is obtained now for D, which probably reflects the higher values assigned to this variable in its prior (uniform) probability density function.

196 ouu

250 ^

200 -

I

150 I UU

50 0 -

i

0.01

0.02

0.03

0.04

A(m) Figure 3. Force-displacement curve obtained from a static nonlinear analysis

40 35 30

Pnctorinr

j

—-P rior

^20 *• 15 10 5 0

I

0

0.2

0.4

. 0.6

0.8

Figure 4. Prior and posterior distribution of cumulative damage due to SCT

197

— Posterior - - - • Prior

~2

\ * -—

0

0.2

0.4

d

0.6

0.8

Figure 5. Poterior distribution of damage D due to the seismic event, using as prior distributions those obtained after the first one

4-

— Posterior — Prior

'"•* o

£2 100

0.2

0.4

, 0.6

0.8

d Figure 6. Prior and posterior damage distribution after the second seismic event, when no updating is done after the first one

198 5.

Optimal instrumentation for health monitoring

The uncertainties about the mechanical properties of a structural system, its current state of damage, as well as those related with analytical modeling, can be reduced on the basis of information from instrumental response records to actual excitations. When making decisions about the instrumentation of a structure, one faces the problem of selecting the optimal locations of a reduced number of sensors that should provide sufficient and high-quality information about the structure from recording its response. A criterion for optimal sensor location for system identification of linear structural systems was recently proposed by Heredia-Zavoni and Esteva [7]. According to it, optimal locations of a given number of sensors are selected so that the posterior uncertainties of the system parameters to be identified, as measured by a Bayesian loss function, are minimized given the information obtained from the recordings. The criterion has also been extended to systems on flexible base so that the soil-structure interaction effects could be taken into account [8]. Use of this criterion has shown that, for the purpose of identifying the lateral stiffness of MDOF shear buildings, optimum solutions include at least one accelerometer at the top floor. For reasonably long and low-noise records, a large amount of prior uncertainty on the lateral stiffness can be reduced by means of an accelerometer located at the top floor. Recent efforts have been undertaken to address the problem of monitoring inelastic structures, for the purpose of making decisions on optimal maintenance policies [11]. Issues involved in such decision making process are the optimum number and location of response recording instruments, the optimal damage threshold for repair, the updating of time-variant probability distributions of damage, the probabilistic assessment of life-cycle damage evolution, and the modeling of repair and failure costs. It is proposed that decisions be made in accordance with a minimum life-cycle expected cost analysis. In this framework, response records obtained during an earthquake are used to update the probability distributions of damage and of the non-linear parameters in the damage-function model according to the bayesian formulation presented above. Given the updated state of knowledge of the structure, probability distributions of damage, f (x), for a future k-th earthquake of given intensity "a " are computed as follows:

<8>

f

* « = ) w , <x I x°> fDS ( x ° } dx°+W(x 1 0 ) p [ D " * d *] 0

where f

k k (x

| x o ) is the probability density function of damage at the end of the

event given an initial level of damage D0- In Equation (8), d* is a damage threshold for repair such that:

199

(9) W

D'" 1 w D" = \ ° |0

if D k " 1 d*

If Cd(x) denotes damage cost associated with repairs, economic losses, injuries and human life losses, then the expected cost due to the k-th future earthquake can be evaluated as follows, a

(10)

max °°

k

E [C'J = J Jc d (x)f D k | a (x)f A (a)dxda "mill 0

where fA(a) is the probability density function of earthquake intensities. The expected present cost is then given by (11)

Ek[Cd] = jEk[C'Jexp(-Ytk)fTk|Tk5T(tk)dtk 0

and fT iT
6

Concluding remarks

A criterion has been presented to use damage levels derived from dynamic response measurements of a structural system to estimate the residual values of the mechanical properties of that system that determine its cyclic response curves for future excitations. A decision framework for optimal repair and maintenance policies has been formulated under the assumption that damage accumulates in accordance with a Markov stochastic process. Practical implementation of these concepts requires the development of computational tools to describe damage accumulation in multi-degree-of -freedom systems, as well as of its consequences on the vulnerability of those systems for future events.

200

References 1. 2. 3.

4. 5.

6.

7.

8.

9.

10. 11.

12.

13.

Cornell, C. A., A probability based structural code. Journal of the American Concrete Institute 66, 12 (1969). Degroot, M. H., Probability and Statistics, Addison Wesley (1988). Diaz, O. and Esteva, L., Seismic damage indexes in decisions related to structural safety. Proc.7,h IFIP WG 7.5 Working Conference on Reliability and Optimization of Structural Systems, Boulder, CO. (1996). Esteva, L. and Ruiz, S. E., Seismic failure rates of multistory frames. ASCE Journal of Structural Engineering 115, 2 (1989) pp. 268-284. Esteva, L., Diaz-Lopez, O. and Garcia-Perez, J., Life cycle optimization of structures with seismic energy-dissipating devices. Case Studies in Optimal Design and Maintenance Planning of Civil Infrastructure Systems, American Society of Civil Engineers. Edited by D. Frangopol. Esteva, L., Diaz-Lopez, O., Garcia-Perez, J. and Perez-Gomez, D., Reduction of stiffness and deformation capacity in the evaluation of seismic reliability of structural systems. To be presented at 9lh IFIP WG 7.5 Working Conference on Reliability and Optimization of Structural Systems, Ann Arbor, MI (2000). Heredia-Zavoni, E. and Esteva, L., Optimal instrumentation of uncertain structural systems subjected to earthquake ground motions. Earthquake Engineering and Structural Dynamics 4 (1998) pp. 343-362. Heredia-Zavoni, E., Montes-Iturrizaga, R. and Esteva, L., Optimal instrumentation of systems on flexible base for system identification. Earthquake Engineering and Structural Dynamics 28 (1999) pp. 1471-1482. Heredia-Zavoni, E., Zeballos, A. and Esteva, L., Theoretical models and recorded response in the estimation of cumulative seismic damage on nonlinear structures. Earthquake Engineering and Structural Dynamics. To be published (2000). Miner, M. A., Cumulative damage in fatigue. Journal of Applied Mechanics 12, 1(1945) pp. A159-164. Montes-Iturrizaga, R., Criteria for optimal instrumentation of buildings, PhD Thesis, School of Engineering, National University of Mexico (2000, in Spanish). Park, Y.-J. and Ang, A. H.-S., Mechanistic seismic damage model for reinforced concrete. ASCE Journal of the Structural Division 110 (1984) pp. 722-739. Wang, M. L. and Shah, S. P., Reinforced concrete hysteresis model based on the damage concept. Earthquake Engineering and Structural Dynamics 15 (1987) pp. 993-1003.

FUZZY CHIP CONTROLLER IMPLEMENTATION L. FARAVELLI University ofPavia Dept. of Structural Mechanics Via Ferrata 1, 27100 Pavia, Italy E-mail: [email protected] R. ROSSI University of Pavia Dept. of Electronics Via Ferrata 1, 27100 Pavia, Italy E-mail: [email protected]

This paper presents a control scheme which deploys a fuzzy chip controller. The controller drives an actuator on a test structure. The results of laboratory tests are reported to show its effectiveness. The possibility of implementing concurrently working controllers is discussed. The controller is designed in order to avoid future incompatibility with the fuzzy-chips industrial production.

1

Introduction

In the literature Fuzzy Logic theory [1] [2] has widely been proposed for the active control of structural systems [3] [4] [5]. It easily allows the resolution of imprecise or uncertain information and, in particular, can handle structural non-linearity. The fuzzy controller possesses inherent robustness due to the fact that its implementation is based on linguistic synthesis. Therefore, its behaviour is not affected by the choice of a specific mathematical model. Another main advantage is that the control action can be designed as a bounded function of the state variables. This provides an appropriate model for the actual behaviour of the actuators. Indeed, there are not special difficulties in implementing the controller required by structural applications into a software tool [6], but the slow reaction time offered by this approach prevents one from making a laboratory test feasible. This suggested the idea of looking for an integrated fuzzy chip [7] [8] and its development environment, so as to implement the controller in a hardware form. Also, it was deemed desirable to be able to perform real-time simulations of both the controller and the controlled system. Thus, an electronic emulation circuit for a multi-degreeof-freedom (MDOF) specimen frame was designed and built [9] [10]. Working in this analogue field, the controller can be designed, tested and tuned. The specimen frame is a three-story structure actively controlled by an active mass damper (AMD) located on the top. The structure has the possibility of adding braces at each level so as to assign the desired number of degrees of freedom. In this paper, the system is set up to work in its three-degree-of-freedom configuration.

201

202

#

Figure 1: Input-output model for a feedback controlled system.

The frame is mounted on a shaking table, which simulates ground motion by means of a hydraulic piston controlled by a personal computer. The active mass damper used is a position-controlled DC motor engaged on a rack which allows a 30 cm free run limited by safety springs [11]. By moving the motor, whose mass is about 1.7 kg, a control force proportional to the second time derivative of the AMD input is generated. For this reason, the correct approach is to design the fuzzy controller output (Figure 1) as a signal displacement. No problems appear as long as the AMD is driven by a control signal representing a force. It can be easily pursued by the analogue modular electronic circuit discussed in Refs. [9] and [10] . But the actual AMD is controlled by a position input signal. This inhibits the use of such a modular electronic circuit. To address this issue, an AMD electronic emulator was built and connected to the system emulator. This new circuit has a position as actuator input signal, thus allowing the designer to carry out the design of the fuzzy controller on a fully emulated structure. Unfortunately, some critical difficulties are introduced, possibly related to the phase of the motor frequency response. For this reason, it was decided to resort to a different kind of system emulator. Yet, this emulator should continue to work in real time and should be accurate enough to enable us to do a first design of the fuzzy controller. Hence, starting from a system identification carried out in a previous work [11], a software tool capable of performing both the required real-time emulation and the analogue/digital interface between the fuzzy controller chip and the personal computer was developed. Next, after a first design and tuning of the fuzzy project, the real frame can be connected to the real fuzzy controller in order to verify proper operation and to perform the final fine tuning work, as some non-ideal effects, such as non-linearity and hysteresis, along with some inaccuracies introduced by parameter identification and real-time simulation, were neglected. In this paper, the MDOF system laboratory testing is summarised together with a screening of potential developments.

203 2

MDOF theory

Let a physical system (Figure 2) be given, together with the specifications of its desired behaviour. A non-linear dynamic system is governed by a set of differential equations. In the design of an active controller, the goal is the reduction of the structural response in terms of accelerations, velocities and displacements. This must be pursued under the limitation of both the number of measured signals and the control force level (limited by the features of the actuators and by the required amount of energy).

\

I Figure. 2: The three-degree-of-freedom frame investigated in this paper.

The design of a fuzzy controller is greatly helped by emulating the behaviour of the structural system by means of real-time simulations. This approach allows the performance of the system under design to be evaluated and optimised with no need for hazardous and time-consuming laboratory tests on full-scale or scaled real structures. The idea that an electronic circuit behaving like the real structure could be used to speed up the design of the fuzzy controller was discussed in previous papers [9] [10] [12]. The equivalent circuit should be as simple as possible, to allow easy implementation and flexible use. An electronic circuit which emulates the original SDOF structural system was conceived and implemented on a board [9]. Also, an electronic circuit for the three-degree-of-freedom case was designed and built. Since the equations describing the behaviour of the structure are quite straightforward, no particular problems were encountered. What required special care was the emulation of the actuator: an active mass damper. The general MDOF linear theory which lies underneath these circuits will be developed in this section according to the features that governed its implementation. A linear model seems an appropriate approximation (Figure 3), as the purpose of the controller is to minimise the structural response. Let x, be the absolute position of the i-th story of the frame and x0 the absolute position of the shaking table, which simulates ground motion during an earthquake. The following set of equations can be written for a three-story frame:

204 m3x3 + c 3 2 (i 3 - i 2 ) + £32(^3 ~ xi) - ^3 m

2*2 + c 2l(*2 ~ x0 + ^ 3 ^ 2

_

*i) + ^21(^2 _ ; c l ) +

m

i*i + cio(-*i - * o ) + cn(*\ ~xi)

+ £23(^2-*,) = F 2

(1) +

*io(*i ~*o) +

+ M * i - xi) = F\

where the kg coefficients {ky = &,-,-) represent the stiffness of the columns, the ciV coefficients (cy- = c/,) account for their damping and F, denotes the control force at each story. As described in a Ref. [9], this mathematical model can be implemented as a modular electronic circuit by letting: v

i =

x

i

(2)

I O.: = V:

and x, = AV„ -BV2i

(3)

-CV-ii a, = DVA,

( a n d a c = DVAG)

a

F

17*

3rd Story —Tlv X

~i

f 3

2nd Story

f

k

J

1st Story

"J1

*

Figure 3: Block diagram of the three-degree-offreedom electronic emulator.

205 where A, B, C and D can be chosen to properly scale the circuit voltages. It can be shown that, after rearranging terms, the final model for the electronic circuit can be written as

'l!

ST,

V2i=^-

(4)

ST2

Va = -auV2i +

-a2iVll+aiiVii+{a4iV2M1+a5iVhl+1)+

{a6lV2^i+0!1yu^yasV4G

Where the a parameters have constant values. This set of equations leads to the well-known Kerwin-Huelsman-Newcomb (KHN) biquad loop [13], which can be implemented with four operational amplifiers. The basic building blocks used are: the integrator, the inverting amplifier and the noninverting amplifier. It should be pointed out that the voltages corresponding to all three mechanical variables (i.e., displacement, velocity and acceleration) are made available by this circuit. If three blocks like the one described above are properly connected to each other, then the resulting circuit emulates the three-story frame to an outstanding degree of accuracy. What is still missing is the emulation of the active mass damper, which is basically a device that converts a displacement signal to a control force driving the frame. In fact, the input signal of the AMD is a voltage that represents the desired displacement of the motor mass; the dynamic response of the motor is used to produce a force, which is directly applied to the top story of the frame. First of all, a mathematical model of the AMD is needed. To obtain it, a parameter identification was carried out for a third-order linear model. A third-order model was chosen, as it seemed to be a reasonable compromise between accuracy and complexity. The resulting system model can be expressed as follows:

(

z=Az+B

(5)

y = Cz

where u represents the displacement signal, which is meant to be directly taken from the fuzzy controller, jc3 is the absolute acceleration of the top story and y is the control force that the AMD delivers to the top story of the frame. As mentioned above, the circuit that emulates the frame requires a force as input, while the fuzzy controller is supposed to deliver the displacement of the AMD. This circuit block acts as an interface between the frame emulator and the fuzzy controller. The elements of the matrices are reported below:

206 -1.855 105.1 -17.34 -104.7 -121.1 93.13 16.87 92.81 -96.98 2.245 8.515 " 1.008 61.83 1.355 -31.39^ -8.806 61.84 -31.42] In Figure 4 the frequency responses of the AMD are shown.

'"\ ^'-'''

\ , 'W

. /' / I

TF:Command to Acceleration

W ^ ^ - M V A

TF:Ground Ace to Acceleration

r i

vj

j

1II

II

1 i 1-

i

Figure 4: Transfer functions of the AMD.

Next, this third-order linear model was directly implemented as an electronic circuit using the same set of basic building blocks as before. Then it was plugged into the

207 emulator of the three-story frame. The resulting system has one input and three outputs. The input is the voltage signal that the fuzzy controller would send to the AMD, while the outputs represent the accelerations of the three-stories in the same scale that is adopted in the accelerometers in use. R,

I—vwv\—I c

_ l l_

Figure 5: Damped integrator used to obtain a relative velocities from the absolute acceleration measured by an accelerometer.

It is thus clear that this system can be perfectly interchanged with the real laboratory structure. From the fuzzy controller perspective, the two systems are completely equivalent.

3

Some implementation details

Two special aspects should be mentioned. The first one is related to the use of accelerometers as sensors for signal acquisition. Since the fuzzy controller is fed with two story velocities relative to ground, these velocities have to be estimated. Probably, the most accurate way to perform this estimate is by implementing a Kalman filter, however it does not seem to be the easiest technique. Also, a standard Kalman filter would require a PC or a digital signal processor, which is in contrast with the ultimate goal of this research goal of realizing a standalone controller. Thus, it was concerted to resort to a much simpler damped integrator configuration, which requires only two operational amplifiers and a few passive electronic components. If the ground acceleration is referred to as aG, the i-th story acceleration as a,, the ground velocity as vc and the i-th story velocity as v„ the fuzzy controller should be fed with v2 - vG and v3 - vG. To carry out this task, a very simple electronic damped integrator is adopted. It performs a pure integration of the signal a - aG in the frequency band ranging from 0.5 Hz to 25 Hz. The circuit schematic of the integrator is illustrated in Figure 5 [14 ].

208 Figure 6 shows the fuzzy sets that make up the fuzzy controller [15]. The values reported on the universe of discourse axis are normalised in the range 0 to 255, as the fuzzy chip data bus is 8-bit wide.

M

NE

ZE

PO

PL

\]

1

\l

\\

\1

\\

M

* i;

ZE

NE

NE

NL

/I

.1 L

PO

ZE

NE

XN

I'O

l'I

PO

PO

ZE

PO

l'I

M'L

PL

XPL

PO

ZE

AA4J

-*Figure 6: The fuzzy sets that make up the fuzzy controller.

The equivalent electronic system was first used as controlled system and the results are shown in Fig. 7.

Story 3 - Velocity

I'muh

Ui U-

l| '

1ft1! Will

11

\i MM 1 1

- I

I'lli 11 i

\i \l \n ini i

I

-0.06 -0.08 -

1 !l

i t J f U.i J

Figure 7: Controller behaviour on the electronic emulator.

209 Although the results obtained on the electronic emulator seem good, it must be pointed out that there is incompatibility between the emulated system and the real structure. As a matter of fact, some parameters in the controller loop have to be changed. This seems to be due to some inaccuracies in the phase of the AMD electronic model adopted. Figure 8 shows the performance of the fuzzy project described above when used to control the three-story frame studied in [11]. The seismic ground excitation, produced by the shaking table, fed to the emulated structure is a 1.2 Hz sine wave, close to the frequency where the resonance peak of the structure is located. Story 3 - Velocity (V)

100 Time (sec)

120

Figure 8: Controller behaviour on the real frame

Figure 9 shows a possible improvement over the previous fuzzy controller. In this new case, the negative and positive fuzzy sets no longer overlap. Moreover, some slight modifications are introduced into the fuzzy rules to enhance the control action.

\L NE ZE PO PL

XL /I \E \P I'O \P

NE \l ZE PO PL PO

ZE

I'O

PL

\\

\l

\.\

NE ZE PO XP

NL NE ZE PO

NE XN PO ZE

:

i~\

A

Figure 9: The fuzzy sets that make up the improved fuzzy controller.

<•' I

210 The improvement over the previous case is remarkable: the difference between the controlled case and the uncontrolled one is now significant (Fig. 10). Story 3 - Velocity (V)

0

20

40

60

80 100 Time (sec)

120

140

160

180

Figure 10: Controller behaviour on the real structure (improved).

4

Concurrently working controllers

When dealing with active controllers, the most general configuration for an engineering system makes use of a single controller block that processes a set of feedback variables and produces a control output, as in Figure 1. As opposed to classic control theory, fuzzy control theory does not provide the designer with a mathematical framework that allows him to simultaneously optimise the design of the controller and ensure its stability. Thus, partitioning the controller block into simpler parts can give the designer a deeper physical insight into the whole system operation. For this reason, when controlling a multi-degree-of-freedom structure, it may prove convenient to split the controller into multiple controller blocks, each driving a single actuator. Also, co-operation among the blocks is a very important issue. Each controller block should be aware of how all the others are working, as failure to do so may result in a worse performance or even instability.

211 v System • Fuzzy Controller

( R S Z ^

Fuzzy Controller

s. RS232 y

*

PC

M

PC

4—

I

fc P

w

Figure 11: Implementation configuration.

of

a dual

fuzzy

controller

Communication between any two blocks can be implemented either in direct (i.e. by physically interconnecting them) or indirect form (i.e. by providing them with the same amount of information about the system motion). Fig. 11 shows a possible implementation for such a controller. The system is controlled by two identical fuzzy chips, each connected to a single actuator. Both chips receive the velocities of the second and the third story, though differently weighted. Each of them evaluates the control action to be introduced in the system to drive the actuators. The PCs serve as an interface between the system, which is analogue in nature, and the fuzzy chips, which communicate with the external world via two digital ports. Also, they are used to store all the data into disk files, thus allowing the designer to make plots and to compare the effectiveness of different fuzzy projects.

Industrial production evolution All this work was carried out by using the W.A.R.P. 2.0 fuzzy processor. This chip is shipped with an application development board, which allows the fuzzy chip to be easily programmed via the standard PC serial port and used in a controlling loop. However, the interface between this chip and the real world is entirely digital, thus requiring additional hardware to perform analogue-to-digital and digital-to-analogue conversions. In this work, an Advantech board controlled by a PC was used to carry out conversions between the analogue world and the digital one. Later on during the ongoing research activity, ST Microelectronics released a new version of its fuzzy processor: the ST52T301 DuaLogic© Micro Controller Unit. A major enhancement over its predecessor is the introduction of a set of peripherals and also of a standard instruction set in addition to the fuzzy logic core. It includes a multiplexed four-channel analogue-to-digital converter, a PWM digital-to-analogue converter and a standard serial UART interface. Its main drawback is the absence of a test board: it is only shipped with a programming board to download the machine code into the on-chip EPROM. Since

212 no testing boards are provided, to use this chip it is necessary to design a dedicated board. This is the only reason why in this work an earlier version of the fuzzy processor was used. Future work will involve the development of a standalone fuzzy controller board based on the latest release of the fuzzy processor. In this way, a PC will no longer be required to accomplish data acquisition and conversion of the digital fuzzy controller output. Also, it will be possible to deploy the fuzzy logic controller directly on the structure to be controlled without any additional circuitry.

6

Conclusions

In this paper, a new design method is used to design a fuzzy controller for earthquake engineering applications. Development and testing are carried out on a real-time emulation system. Subsequently, the fuzzy controller is adopted for the real test structure. Attention is now focused on implementing the best way for producing standalone, concurrently-working controllers to be used on multiple devices located in the same building.

Acknowledgement This research was supported by grant ARS-99-50 from the Italian Space Agency (ASI). The support of the Italian Ministry of University and Scientific and Technological Research (MURST) within the COFIN'98 project co-ordinated a national level by Prof. F. Casciati, of the University of Pavia, is also acknowledged.

References 1.

Passino K.M. and Yurkovich S., Fuzzy Control, Addison Wesley Longman Inc (1998).

2.

Jang J.S.R., Sun C.T. and Mizutani E., Neuro-Fuzzy Prentice Hall Inc.( 1997).

3.

Casciati F., Faravelli L. and Yao T., Control of Nonlinear Structures Using the Fuzzy Control Approach. Nonlinear Dynamics, 11,(1996), pp. 171-187.

4.

Casciati F. and Yao T., Comparison of Strategies for the Active Control of Civil Structures, Proceedings of V world Conference on Structural Control, IASC, Los Angeles, Vol.1, WA1-3 (1995).

5.

Faravelli L. and Yao T., Use of Adaptive Network in Fuzzy Control of Civil Structures, Microcomputers in Civil Engineering, 11 (1), (1996), pp. 67-76.

and Soft

Computing,

213 6. Battaini M., Casciati F. and Faravelli L., Fuzzy Control of Structural Vibration. An Active Mass System Driven by a Fuzzy Controller, Earthquake Engineering and Structural Dynamics, 27, (1998), pp. 1267-1276. 7.

Casciati F., Faravelli L. and Giorgi F., Laboratory Validation of a Fuzzy-Chip Controller, Proceedings ofEUFIT'97, Aachen (1997).

8. Casciati F. and Giorgi F., Fuzzy Controller Implementation. Proceedings of 2nd International Workshop on Structural Control. IASC, Hong Kong, (1996), pp. 119-125. 9. Casciati F., Faravelli L. and Torelli G., A Fuzzy Chip Controller for NonLinear Vibrations. Nonlinear dynamics 20, (1999), pp. 85-98. 10. Casciati F., Faravelli L. Speeding up the design process of a fuzzy logic controller for civil engineering applications IASTED International Conference Arttificial Intelligence and Soft Computing (1999), pp. 216-220 11. Battaini M., 1994, Sistemi strutturali controllati: progettazione e affidabilitd (in Italian), Ph.D. Thesis., Dept. of Structural Mechanics, University of Pavia. 12. Casciati F., Faravelli L. Fuzzy chip control of MDOF structural systems Proceedings of the European Control Conference ECC (1999) 13. Sedra A.S. and Smith K.C. , 1991, Microelectronic Circuits, Third Edition, Saunders College Publishing, Philadelphia. 14. STMicroelectronics, 1996, Fuzzystudio" 2.0 User Manual.

HEALTH MONITORING OF CIVIL STRUCTURES USING SPATIAL INFORMATION OBTAINED FROM AMBIENT VIBRATION YOZO FUJINO

fujino @ bridge, t. u-tokyo. ac.jp MASATO ABE

masato @ bridge, t. u-tokyo. ac.jp Department of Civil Engineering, The University of Tokyo Hongo 7-3-1, Bunkyo, Tokyo, 113-8656, Japan

In order to detect local damage in structures using vibration measurement, identification of modal shapes of high vibration modes is very important. In this report, the effectiveness of spatial measurement of civil structures under ambient vibration is emphasized. In the first place, spatially-dense array measurement of ambient vibration of a suspension bridge subject to wind is explained and effect of wind on modal information is discussed. Next, spatial vibration measurement method using Laser Doppler Vibrometer is presented and its validity to identify the damage using modal information including mode shapes is demonstrated.

1. Introduction Health monitoring of degrading civil structures is an urgent and important issue in the world. Especially, quantitative methods, which can detect local damage in structures is highly desired to develop. Among many direct and indirect methods for health monitoring, vibrationbased method has been studied from various points of view for many years. In the vibration-based monitoring, the change of modal frequencies/damping and mode shapes due to local damage is considered as one of the indices that can identify the damage quantitatively. Particularly, change of shape of high modes possesses the possibility of detection of damage, because they are sensitive to local damage. Use of ambient vibration is suitable to health monitoring of civil structures because it does not require any additional exciting forces and the data can be easily obtainable. To identify the modal shapes, spatial vibration measurement is needed. In this study, in the first part, application of RD(Random Decrement) method together with Ibrahim time domain method to ambient vibration data of Hakucho suspension bridge in Hokkaido is explained. It will be shown that up to 19-th vertical bending mode can be identified with high accuracy. Dependency of the modal properties on the wind velocity, i.e. amplitude of girder response was shown from the data. Cause of this dependency was analyzed by inverse analysis of nonproportional damped system and it is indicated that the wind-induced motiondependent aerodynamic forces and the forces associated with the bearings at the 215

216

pylons are closely related to this dependency. In the second place, usefulness of Laser Doppler Vibrometer for ambient vibration measurement is discussed. The vibrometer can measure the motion of many points of an object by changing the laser beam direction. Non-stationary and random components in measured ambient vibration are eliminated by stacking technique. In this way, it is shown that mode shapes of high modes can be identified with high accuracy Then, the modal frequencies and mode shapes measured before damage and after damage are compared and the location and extent of stiffness change which will indicate the degree of damage in the structure are inversely obtained. The method is demonstrated by an experiment using an steel plate with added mass.

2. Analysis of ambient vibration measured in a suspension bridge 2.1 Outline of the bridge and measurement The outline of the "Hakucho Bridge" is shown in (Figure 1). Hakucho Bridge is suspension bridge with a 720 m span and two symmetric side spans with 330 m and the total length is 1380 m. Each span is discontinuous and the center span is simply supported at the attachment tower. The bridge is located at the entrance of Muroran Gulf in Hokkaido Prefecture, which is a windy and seismically active area in northern part of Japan. It has been monitored by densely distributed ambient vibration measurement system with 40 measurement points. Only nineteen stations of accelerometers are shown in (Figure 2) were used in this study to measure the vertical motion of the girder. Because of these densely distributed measurement stations, reliable identification up to higher vibration modes are expected. Anemometer is installed at the center of the span to measure wind velocity and direction. In this study, continuously measured ambient vibration data over 100 hours in June 1998 is analyzed.

2.2 Random Decrement Vibration Signature (RD) Identification of the dynamic parameters of structures is normally associated with the case of excitation as well as the response. Normally, in this case the loads are unknown, and thus, the modal identification has to be carried out based on the responses only. Real examples can be found in Ventura and Horyna (41 and in Andersen et al.[51.

217

2.2.1 Theory Although the excitation source cannot be identified and measurement of the input force is not available for ambient vibration, the random signature is the same as the free vibration response of the liner system to a set of specified initial condition, Vandiver et al. The time history of ambient vibration response can be decomposed into three parts (Figure 3): l)Free vibration response with initial acceleration a 0 . 2)Free vibration response with initial acceleration equal to zero. 3)Forced oscillation response with initial acceleration equal to zero. This procedure can be explained by the following equations:

x(T) = -Yzi(T) x(T) = -ftZ1(T)

(1) + -^Z2(T)

+ -fiZ3(T)

(2)

When the excitation is random white noise, the second and the third parts are expected to be cancelled by summing many time responses that starts from a0 (Figure 4). X(T) = Z,(T)

(3)

2.2.2 Results By using the Random Decrement Signature technique the large noise in the ambient vibration measurements can be reduced or eliminated. By decreasing the initial acceleration ( a 0 ) the number of sample (n) increased and the free vibration improved. In this study the initial acceleration is used equal to 0.8 of the mean square root (rms) of the measurement acceleration and the number of sample is around 10000. Figure 5 shows the effect of a 0 on the noise reduction. In figure 5 then a 0 changes as 0.285, 0.18, 0.12, 0.09 ( c m / s e c 2 ) the corresponding number of summing samples will be change as 50, 1000, 5000, 10000 (sample) respectively. So to change the ambient response to free response, which can used to identify the dynamic parameters of the structure with high accuracy, the number of samples should equal to 5000 (sample) at least.

218

2 3 Structural Identification Physical and analytical understanding of such response is depending upon the knowledge of a bridge's natural frequencies, damping, and mode shapes of vibration. Presently those techniques used in vibration tests [7] can be classified as frequency domain method. Vibration parameters data is extractedfromfrequency response information obtained directly from sine wave testing or from Fourier analysis of random or transient test results.

Figure 1: Hokocho Bridge

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222

Figure 8: The comparison of the natural frequencies In this paper, time domain technique is used to identify the dynamic properties of Hakucho Bridge. This technique can be used without any assumptions for the exciting force, the structure damping and/or the space between the natural frequencies.

2.3.1 Ibrahim Time Domain Method (ITD) Free response with multi degree of freedom system that obtained in the previous step is supposed to be a liner sum of free vibration response of each mode. Ibrahim time domain method is used to determine the natural frequencies, damping ratios, and mode shapes. The system is assumed to be described by the following equation during its free response:

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223

Where[X] = [JC, (t})],

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[A] = [exp((-£>, + iQ), <Jl-tf)tj)]. The dimension of each matrix is, [X]: n x L, [\|/]: n x 2N, and [A]: 2N x L, where n is the number of measurement points, and L is the total number of time steps. The response with delay time of At is expressed as,

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(7)

Which can be discretized to,

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(8)

An n x n square matrix [A] to transform from the original time history to the lagged time history is defined as,

[Aim=m

(9)

Using this relationship, the modal properties can be obtained by solving the following eigenvalue problem:

[A]{Wt} = exp((-£>, + ia), VW?)AO{^} (10) The matrix [A] is derived by pre-multiplying both sides of equation (6) by [A] to obtain,

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(11)

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(12)

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(13)

Because all the modes are identified simultaneously by solving the eigenvalue problem of equation (10), this method can easily be applied for multi mode structures with closely spaced natural frequencies, such as suspension bridges.

224

2.3.2 Identify the Higher frequencies Modes

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By direct application of ITD only the first few modes of low frequency can be identified with high accuracy, however the higher modes can only be identified with less accuracy [81. To use the dynamic properties in health monitoring of structures, the higher modal parameters should be identified with high accuracy. In this study the following two different methods are used to identify the high frequency modes accurately: 1. By filtering the low frequency components. 2. By increasing the number of measurements (Time Shift Method). Filtering the Low Frequency Components Outline of the scheme used in this method is shown in (figure 6). The high frequency mode shapes are identified beginning from the ambient vibration data. The following procedure is used in this step: i) Transform the time domain response to frequency domain response by using the Fast Fourier Transform (FFT). ii) Filtering the first part, which contain some of low frequency modes by using high pass filter. iii) Return the response again to time domain by using the Inverse of Fast Fourier Transform (IFFT). iv) Identify the high frequency mode shapes by using Ibrahim time domain method. Repeat these steps until identify all the higher mode shapes. Time Shift Method By using equation (5), which will be rewritten in equation (14), at any instant of time (t), 2N conjugate modes are identified. But only the first few modes can be identified with high accuracy.

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229 modes extended to 61 mode. By this procedure the first 19 mode can identify with very high accuracy.

2.3.3 Results In this study all the mode shapes of Hakucho Bridge were identified. The results of the two methods are excellent comparing with each other and comparing with the results of the finite element method and also with forced vibration results. Figure 7 shows the 10th, 15th, and 19th mode shapes of Hakucho Bridge as examples of the higher modes. Figure 8 shows the comparison of the natural frequencies of all the 19th modes. Both the two methods give excellent results comparing with the finite element method and the forced vibration test.

2.4 Effect of Wind Speed More than 100 hours measurement data in June 1998 were analyze in this study. The wend speed changed from about 4 to 13 (m/s) and the mean square root of the acceleration response also changed from 0 to 2.5 (gal) as shown in figure 9. For this range of acceleration response the dynamic properties of Hakucho Bridge are affected as shown in figures 10,11,12, and 13.Figure 10 shows that the natural frequency decreases if the wind speed increase and this behavior is the same for the low frequency and the high frequency modes. Figure 11 shows that the damping ratio increases if the wind speed increase and this behavior is the same for the low frequency and the high frequency modes. But for the very high wind speed this behavior is not so clear because of the high noise in the data measurements. Figure 12 shows that the mode shapes depend on the amplitude level but this effect is only notified in the higher modes and near the tower. Figure 13 shows that the mode phases delay if the wind speed increases until certain limit and after that they advance again.

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231

3 Identification of mode shapes by spatial measurement using Laser Doppler Vlbrometer 3.1 Laser Doppler Vibrometer . Laser Doppler Vibrometer (LDV) is an optical measurement device that is able to detect velocity of moving objective using the difference of frequencies between irradiation and reflection laser (Fig. 14). The features are shown as following; and concrete characteristics are shown in Table. 1. At first, LDV is able to measure vibration by non-contact method. There is no surface processing such as attachment of reflection tape. Second, it possesses extremely high resolution, and capable to measure in wide frequency range. Therefore, it is able to accurately measure until high frequency vibration component of the spatially large civil structures, which are difficult to set sensors, under ambient vibration. Third, LDV can measure spatially many points by controlling irradiation angle of laser beam by rotating two reflection mirrors in the sensor head.

Fig. 14. Laser Doppler Vibrometer Table 1. Characteristics of LDV He-Ne Laser Laser type 633nm Wave length 2mw / 3 A Laser output / class 100m Possible measurement distance 0.D Dm/sec Resolution 0 ~ 35kHz Measurement frequency range Laser irradiation Range -15 - 15°

232

3.2 Spatial Vibration Measurement using LDV Spatial vibration measurement system that is able to measure vibration at designated points in selected range is constructed by controlling irradiation angle of laser beam automatically (Fig. 15) [6, 7]. In identification of mode shape, measured vibration results are needed high accuracy as a matter of course. However speckle noise, which is circled in Fig. 16, is often contained in recorded time history, when optical measurement device is used. Minute response spectrum cannot be measured by containing much speckle noise, which causes the decrease of identification accuracy. Therefore the decrease countermeasures of speckle noise are carried out by both hardware and software side. The content of speckle noise is entirely different by microscopic change of irradiation point of laser beam. So, changing the irradiation angle per 0.01 degree around the first measurement point each repetitive measurement, concentrated contain of speckle noise for a particularly point is prevented. Next, the standard deviation of the measured vibration results is calculated, and the response that has constant time larger than the standard deviation is considered as speckle noise. Then, in the case that contained less than five speckle noise in one measured vibration results, the extraordinary values are recalculated by the front and the rear data, and in the case that contained more than five speckle noise, the measured vibration results were eliminated when the averaging of the spectrum was carried out.

Controller

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Fig. 15. Spatial vibration measurement system

233

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Fig. 16. Speckle noise Identification Method of Mode Shape without Knowledge of Input Excitation The measured vibration results using LDV can not be measured all points at the same time. Furthermore ambient vibration that is used as input is random vibration, which possesses non-stationary, so usually mode shapes can not be identified. Then following averaging methods are carried out. At first, the effect of non-stationary in measured ambient vibration is dispersed by getting shorter of the measurement time for one point and sweeping the area of interested. Next, temporary averaging that random components is stacked the time histories recorded repeatedly is carried out. In these way, stationary vibration components are extracted from ambient vibration without knowledge of input excitation, and then mode shape is identified by counting peak amplitudes of spectrum. Experimental Verification The identification of mode shape for a steel plate (385x300x2 [mm]), which was fixed at one side, was demonstrated experimentally. With respect to measurement condition, measurement points were arranged as 20 points along vertical direction and 15 points along horizontal direction, and total 300 points were set. Measurement time was 2048 [sec] per point considering the step size of frequency and the length of measurement time.

234

Sampling frequency was decided as 2000[Hz] from objective modal frequency. Then, the measured vibration results were recorded into the a personal computer through an AD converter. On the other hand, the change of measurement point was controlled by the personal computer through a DA converter. In this measurement, the maximum irradiation angle was 4 degrees. Based on this measurement condition, measured velocity amplitude spectrum was averaged by 300 times repetitive measurement. The 5 times standard deviation per each measured vibration result was employed to judge speckle noise. Fig. 17 shows the comparison of averaged velocity amplitude spectrums between 1 and 300 times repetitive measurement. From this figure, noise level was suppressed by the averaging process, and the peak of high frequency vibration component was stuck out clearly. The identified 6th and 14th mode shapes, which were changed in repetitive number [10,100,300], and theoretical analysis results of the plate by RayleighRitz method [8] are shown in Fig. 18. The mode shapes were normalized that maximum value became 1, and the absolute values were plotted. It is clear that the identified mode shapes are closely to the theoretical results, as the number of repetitive measurement is increased. Therefore it can be considered that nonstationary and random component in measured ambient vibration are eliminated by 300 times repetitive measurement. Table.2 shows the comparison between identified modal frequencies and theoretical ones. From this table, 10 mode shapes until 16th mode were identified in this vibration measurement. Moreover, in Fig. 17, many peaks except for vibration components are stuck out. These are caused by vibration component of LDV, electric noise and so on. For example, these peaks are extracted and plotted in Fig. 19. This shape is not obviously different from mode shape of the plate. Therefore mode shapes and the other noise components can be distinguished visually using this proposed method.

235

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236

Fig. 18. Comparison of identified mode shapes and theoretical ones: (a) Repetitive number: 1; (b) Repetitive number: 300; (c) Theoretical mode shapes (6th mode; above, 14th mode; bellow)

Mode order 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Table 2. Identified Modal Frequencies Theoretical Value [Hz] Identified Value [Hz] 10.74 12.07 34.18 76.01 66.41 121.0 112.8 137.2 135.0 192.4 212.7 234.5 233.9 260.9 336.7 391.6 384.8 371.1 417.7 432.5 465.6 580.1 599.5 606.0 666.5 686.4

237

Fig. 19. Vibration shape due to noise

3.3 Damage Detection on the Change of Mode Identification Method of Change of Mass and Stiffness Caused by Damage The effect of structural damage comes out as the change of mass and stiffness of structures. So the quantitative knowledge of mass and stiffness decrease is needed to evaluate damage degradation. Hence, the damage detection method based on the change of mode shape before/after damage is suggested. The merit of this method is that information of material characteristics, geometrical shape and boundary condition is not needed if modal frequencies, mode shapes before/after damage and mass density are obtained. That is, the damage detection can be carried out by identified modal frequencies and mode shapes before/after damage using the spatial vibration measurement method, if mass density is obtained. The theoretical procedure is shown as follow. At first, it is considered that negative mass and stiffness are added to the objective structure by damage. Considering that the structure before damage, additional mass and stiffness are separated, total kinetic energy : T and potential energy : Vare shown in the following equation [9].

Z

Z

i=l

£ ,=1

± 7=1

7=1

£ ;=i

*• y=i

In these equations, i is mode order, N is total mode number. Mt, Kt, CO,- and qt show modal mass, modal stiffness, modal frequency and modal displacement

238

ofrthmode, respectively. On the other side, j is the number of additional mass and stiffness, J is total number of those. mp kt and «j show jth additional mass, stiffness and the displacement at point j respectively. Further q,it means first derivative of q and u with respect to time. However, the amount of J numbers of restrict conditions, which are shown as following equation, have to be considered at each additional location j of mass and stiffness. jr<J>,.OX.-",. = 0

(.7=1,

,J) (20)

1=1

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(2D

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(22)

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l

XJ = 0

Hence, qi='qie"a, Equations(22),(23),(24),

uJ=uJe"a,

(24) Aj =Aje"a are

-0}2M^ +0)i2Miqi - X X ^ ( ; ) = 0 -co2mjZj + kjZj + Ij = 0 E^,O')^,-Z7=0

(23) substituted

into

(25) (26) (27)

i=i

were given. Next equations are derived as z is eliminated by solving equations given by Equations(25),(26),(27).

239

+ 7=1

(28)

i=l

•or % + X ^ E ^ ^ K O " ) =0 7 =1

i=l

Therefore, the calculation of modal frequencies and mode shapes of the structure after damage is come back solving eigen problem given by following equation [10]. A-COd

B v = {0}

(29)

A and B are matrices(/VxAO, the components for each matrix are shown by following Equations(30), (31). And CO is equal to CO, v is the N order vector}^ •••g„}' . mn

tnn

m

m

^^ j=i

j

m ^ •/ /

n

^J'

(30)

Bmn-SmnMm+^m^mU)^nU) ;'=i

(m = l,

,N, n = 1,

,N)

(31) In the above equations, S is the Dirac's delta function. Therefore, ith modal frequency after damage is given by CO ,-, mode shapes O, after damage is obtained by

(32) So, unknown parameters, which were needed to calculate mode shape after damage, are only additional mass, stiffness and location, if the distributed mass of structures and mode shapes before damage are obtained. rrij and kj are identified by minimizing the following evaluation function(33), that is the difference between the mode shape : W and modal frequency : E7 after damage measured by spatial vibration measurement and ones obtained analytically is minimized.

£=S

£[¥,.(*)-<&"i(Jfc)l 2 4=1

$>di(k)

\m,-a)di}2

+•

CO

P is the total number of measurement points.

(33)

240

Identification Experiment of Additional Mass The experiment to identify location and size of damage was demonstrated by adding a mass to the plate used in the previous section. A magnet was employed as an additional mass. The additional location and size are shown in Fig.20(a). The spatial vibration measurement were carried out both plates before/after adding mass, the additional location and size were identified by the suggested method. In this case, kj in Equation(30) could be ignored, because identification object was only the change of mass. In the same figure, identification result is shown. However it is able to verify little error with respect to both location and size. Especially, identification result about additional mass size was obtained as 300[g], for exact value was 376[g]. This reason was caused by that non-symmetry mode shapes before additional mass could not be measured. Therefore, it was considered the mode shapes after additional mass as before condition, another mass, which possesses different mass size, was added. The identification result are shown in Fig.20(b), it is able to verify that identification accuracy of additional location and size are increasing.

(a)

(b)

O : Designed AW : Identified

Fig.20. Identification results: (a) easel (designed: 376[g],identified:300[g]); (b) case2(designed: 118[g], identified: 150[g])

4. Conclusions Feasibility of health monitoring of long span suspension bridge by ambient vibration measurement is studied using actual measurement data. To utilize ambient vibration measurement data, the random decrement vibration analysis technique is used to reduce the noise in the data by stacking many samples at the same initial acceleration. Ibrahim time domain method is used to identify the modal properties from ambient vibration with high accuracy even the high frequency modes. This

241

study also shows the variation of natural frequencies, damping ratios, mode shapes, and mode phases due to change in wind velocity, which can be used efficiently in health monitoring of the bridge. The results indicate that the ambient vibration measurement can provide reliable information of dynamic properties, which has the potential to be applied to health monitoring. In the second part of the paper, spatial vibration measurement method was constructed by controlling automatically irradiation angle of laser beam of LDV. Identification method of high order mode shapes was constructed without knowledge of excitation by eliminating non-stationary and random component measured ambient vibration with repetitive vibration measurement. Damage detection method that was possible to identify local damage directly using only spatial vibration measurement results was suggested.

242

References 1.

Abe, M., Structural Monitoring of Civil Structures using Vibration Measurement -Current Practice and Future-, LNAI 1454 Artificial Intelligence in Structural Engineering (1998) pp.1-18

2.

Andersen, P, R. Brincker, B. Peeters, G. De Roeck, L. Hermans and Kramer, Comparison of System Identification Methods Using Ambient Bridge Test Data, Proc. of the If International Modal Analysis Conference, Kissimee, Florida, (1999)

3.

Caughey, T. K. and Stumpf, H. J., Transient Response of a Dynamic System under Random Excitation, Journal of Applied Mechanics (1961) pp. 563-566,

4.

Doebling, S.W., Farrar, C.R., Prime, M.B., Shevitz, D.W., Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in Their Vibration Characteristics, A Literature Review, LA13070-MS (1996)

5.

Dowell, E.H., On Some General Properties of Combined Dynamics Systems, ASME Journal of Applied Mechanics, Vol.46 (1979) pp.206-209

6.

Farrar, C.R., Duffey, T.A., Cornwell, P.J., Dowbling, S.W., Excitation Methods for Bridge Structures, Proceedings of 17 International Modal Analysis Conference (1999) pp. 1056-1062

7.

Flannelly, William G., Joseph H. McGravy and Alex Berman, A Theory of Identification of the Parameters in the Equation of Motion of A Structure Through Dynamic Testing, Symposium on Structural Dynamic, University of Technology, Loughborough, England, March 1970.

8.

Ibrahim, S.R. and Mikulcik, E.C., A Time Domain Modal Vibration Test Technique, The Shock and Vibration Bulletin, Bulletin 43, Part 4 (1973)

9.

Ibrahim, S.R., Random Decrement Technique for Modal Identification of Structures, The AIAA Journal of Spacecraft and Rockets, Vol. 14, No. 11 (1977)

10. Kajimura, T., Construction of Structural Monitoring Method for Ambient Vibration Testing, B.S. Thesis, Department of Civil Engineering, University of Tokyo (1999)

243

11. Kaito, K., Abe, M., Fujino, Y. and Yoda, H., Measurement of Mode Shape using Laser Doppler Vibrometer and Application to the Damage Detection, Proceedings of 2nd Structural Diagnosis Symposium (1999) pp. 157-162 (in Japanese) 12. Kaito, K., Abe, M., Fujino, Y. and Tariq, M.T.A., Performance Evaluation of a Base-Isolated Bridge using Complex Modal Analysis, Proceedings of 17 International Modal Analysis Conference (1999) pp.1749-1755 13. Leissa, A.W., Vibration of Plates, NASA Special Publication (1969)

SP-160

14. Salawu, O.S., Detection of Structural Damage through Changes in Frequency, A Review, Engineering Structures, Vol.19, No.9 (1997) pp.718-723 15. J.K. Vandiver, A.B. Dunwoody, R.B. Campbell, and M.F. cook, A Mathematical Basis for the Random Decrement Vibration Signature Analysis Technique, Journal of Mechanical Design, Vol. 104 (1982) pp. 307-313 16. Ventura, Carlos E. and Tomas Horyna, Structural Assessment by Modal Analysis in Western Canada, Proc. of the 15th International Modal Analysis Conference, Orland, Florida, Orland (1997) 17. Yoda, H., Abe, M., Fujino, Y. and Kaito, K., Experimental Modal Analysis using Laser Doppler Vibrometer, Proceedings of 54th Annual Conference ofJSCE (1999) (in Japanese)

A D A P T I V E C O N T R O L OF M D O F S T R U C T U R E S T H R O U G H NON-COLLOCATED SENSOR/ACTUATOR PAIR V. GATTULLI AND F. ROMEO Dipartimento di Ingegneria delle Strutture, Acque e Terreno, Universita di L'Aquila, Monteluco di Roio 67040 L'Aquila Italy E-mail: [email protected], [email protected] An adaptive control procedure is applied to structural systems equipped with noncollocated actuator/sensor pairs. The dual goal of vibration suppression and damage detection is pursued using full-state feedback in a model reference adaptive control algorithm with a tracking error based parameter estimator. Suitable outputs are designed resorting to a parameterized linear function of the state variables guaranteeing the system overall stability. The inherent lack of information of collocated schemes is resolved in non-collocated schemes where the complete set of mechanical parameters of discrete structural models is shown to be identifiable. Control and on-line identification effectiveness are eventually presented in a shear-type structural model with either initial uncertain or time-degrading physical parameters.

1

Introduction

Vibration suppression and health monitoring of flexible structures are themes that have been recently effectively dealt with by introducing integrated mechanical and electronic components whose design relies on both control and identification algorithms. As a matter of fact, a structural system equipped with sensors and actuators may be designed in order to enable both the identification of the relevant structural parameters and the reduction of the oscillations during a dynamical event. In most of the investigations the two aspects have been treated separately according to the primary objective of the on-line strategy. On-line identification procedures, initially developed in the context of system theory (Isermann et al. x ) , have recently received attention for applications to linear and nonlinear MDOF structural systems (Ghanem and Shinozuka 8 ) . Most of these procedures rely upon prediction error based estimators; stability proof, parameter boundedness, smallness condition for the estimation error and speed of adaptation delineate the differences in the available methodologies (Ioannou and Datta 3 ) . Recently, some specific studies in the structural context have been carried out for time dependent degrading structures (Lin et al. 4 ) and for nonlinear chain-like MDOF hysteretic systems (Smyth et al. 6 ) . In both cases a least-squares based procedure has been implemented. Good

245

246 accuracy in the stiffness degradation estimate is obtained in the former, while the use of forgetting factors and the effects of both persistent excitation and under- or over-parameterization are some of the results obtained in the latter. Adaptive control procedures for structural systems have been investigated with the main goal of bringing some state variable combinations of an uncertain dynamical system to track a desired behavior relying on on-line adjustment of control parameters. The use of these methodologies has been proposed in different engineering applications (Poh and Baz n , Ghanem et al. 2 , Gattulli and Ghanem 5 , Gattulli and Romeo 7 ) . Recently, in Ray and Tian 12 , an initial step towards a dual use of feedback control for both vibration suppression and damage detection has been undertaken. Indeed, closed-loop control is shown to be apt to modify the system dynamics placing the modal frequencies so that the observability of parameter variations is increased. Proceeding along a parallel line, an integrated procedure based on a model reference adaptive control approach has been also proposed in Gattulli and Romeo 13 for both robust control of oscillations and damage detection of linear structural systems. In this work control canonical forms are recalled as a mean to separate from the assignable dynamics the internal dynamics unaffected by the control input. By doing so, allowable sets of input/output pairs corresponding to non-collocated schemes can be easily singled out. On this basis, performances of the on-line identification have been tested in different situations. Indeed, a shear-type 3-dof model under persistent excitation is presented showing that the complete set of the stiffness and damping parameters are identifiable in presence of an initial error and during a damageinduced smooth time-degradation of the parameters. 2

Governing Relations

It is assumed that structural oscillations induced by dynamic loads are described by a linear discrete model with nq lagrangian degrees-of-freedom. A set of nq linear ODEs of the form Mq + Cq + Kq = Eu + Fw

(1)

represents the governing relations of the dynamical motion. The vector q describes the nq displacements of a discrete set of points of the structural system from a reference configuration, the vector u contains the m control actions and the vector w represents the nq components of the dynamic loads. The (nq x nq) mass, damping and stiffness matrices, are represented by M , C and K respectively. The allocation matrices for the control and the external

247 actions are expressed by the matrices E (n 9 x m) and F (n ? x » , ) , respectively. The equations of motion (1) can be rewritten in the state space fo|:m as x = Ax + Bu + Hw

(2)

where x = (q, q ) is the n = 2nq dimensional state vector. A vector y representing the p < n outputs, can be obtained by a linear combination of the state variables through the following observation equation, y = Cx

(3)

where C is the (p x n) observation matrix. In particular, the state space matrix A and the allocation matrices B and H are given by

A=

(-M^K-M^c)

; B=

(-M^EJ

; H=

(-M^FJ

(4)

MRAC procedures aim to lead the actual system to follow a desired reference system. Complete matching between actual and reference outputs can be pursued when their number is equal to the number of inputs (Ih et al. 9 ). Noncollocated input-output pairs can be properly selected using control canonical forms (Gattulli and Romeo 1 3 ) . Indeed, these representations highlight both the relation between input and output and the existence of internal dynamics not affected by the control input. 2.1

Model reference

Despite the imperfect knowledge about the parameters of the chosen model for the structural system, the present procedure aims to devise a controller which will steer the system to track a desired reference response. A reference dynamical system is used to generate such desired response through the following representation xd = Adxd + Hdwd

(5)

yd = CdXd p

where the vector yd € K denotes the desired trajectories. 2.2

Sliding mode control

The control algorithm is based on the convergence of the output actual state y(t) to the desired target state yd(t). Therefore, defining e(t) = y(t) - yd(t), the combined scalar s(t) is defined as s = (e + Ae) where the positive parameters A, representing the relative weights, is used to fine-tune the controller.

248 Obviously, for s(i) being identically zero, the tracking error e(t) goes exponentially to zero. This observation justifies the design of a control algorithm that keeps s(t) at or near zero. This goal is achieved sliding along the line s(t) + kc s(t) = 0

(6)

where the weighting parameter kc defines the convergence rate. Therefore the control law is designed such that equation (6) is satisfied in the closed loop form of (2)(Gattulli and Romeo 1 3 ) . Thus, by resorting to the control canonical form of the system (2), an asymptotic tracking of the reference output can be achieved through the control law , u = 1/&2 (yd — Ae — kcs — c A 2 x — /i2w)

(7)

where the state space vector x and the external force vector w are the fullstate feedback and feedforward terms respectively. 3

Tracking Error Based On-Line Identification Procedure

In the above analysis, it has been assumed that the values of the parameters a; entering the mass, damping and stiffness matrices were known and time invariant. Introducing uncertainties in these coefficients will not permit, in general, the synthesis of (6). Thus, assuming that only estimates of these coefficients are available, some conditions on updating these estimates will prove necessary for the stable operation of the controlled system. 3.1

Parameters

estimator

Due to the chosen reference model based control algorithm both prediction error and tracking error constitute possible sources of parameters information and even a combination of the two errors can be used. The on-line identification procedure here considered is based on tracking error. Denoting parameter estimates by dj and the external force vector estimation by w, a control law with the actual quantities replaced by their estimates is used at this stage, yielding u = l / 6 2 (yd - Ae - kcs - c A 2 x - / i 2 w j

(8)

From (8) it follows that the estimates of the parameters enter nonlinearly in the feedback control law. Nevertheless, by selecting the output in terms of displacements, a linear function of stiffnesses and dampings estimates can be still assured provided that the masses are known. In this case, the unknown parameters can be introduced through the (1 x n) vector

249

?1

,

p|

„ , , .. ..

.. ,.,,..

I

I

..,;.,...;

,

I

i

• , .. ., ,

L

*; Figure 1. a) MDOF actively controlled structural system, b) Uncontrolled displacements under white noise excitation; actual model (dashed line), reference model (solid line).

eT = (cii, (ai, a,2, £3, ..., an), where a,i = en — Oj are the parameters er:. The following equation governs the dynamics of the combined output -T 9 X + /l2W

s(t) + kcs

(9)

where w is a vector of colored noises modeling errors between the estimate of the external excitations and its actual value and possible errors in the measurements of the output variables or even in the dynamical model itself. The convergence of s(t) to zero, in this case, is not unconditional, and depends on the values of aj. A Lyapunov function argument guarantees that a sufficient condition for the asymptotic decay of s(t) can be ensured by imposing the following adaptation law to the uncertain parameters, 0

-sf

Jx

(10)

Due to the relevance of the initial combined tracking error s, a variable gain vector 7 has been introduced in the procedure. The variable gain vector avoids large initial chattering of the estimated parameters. Asymptotic convergence of the motion of MIMO systems can be guaranteed in the presence of the above control as shown in Gattulli and Romeo 13 . 4

Applications

The numerical investigations presented in this section refer to linear shear-type structural models. Through a linear transformation applied to the original state space equations, an output selection criterion assuring the system overall stability gives rise to the following expression (Gattulli and Romeo 13 ) for the

250 3-DOF model output combination, y = (6 + l)a;i + Sx2 + ax3

(11)

The adaptive control scheme is implemented for both vibration suppression and damage detection of the 3-DOF system sketched in Fig. la. The selected values for the actual and reference model parameters are reported in Table 1. Table 1: 3-dof model parameters

d.o.f. 1 2 3

4-1

m (kNs2/m) 0.9823-0.9823 0.9823-0.9823 0.9823-0.9823

Actual Model-Reference Model k c t (kN/m) (kNs/m) 0.4677- 25.00 0.001-0.03 1965.0-1965.0 0.005-0.05 0.1837-0.500 1946.0-1946.0 0.005- 0.05 1184.1-1184.1 0.3879-0.500

Vibration suppression and on-line identification through model reference control

The results reported in this section aim at validating the procedure for vibration suppression and on-line identification purposes for a non-collocated scheme (a = 1.0 and 8 = 2.0, in (11))- Aiming at reducing structural oscillations, a reference model characterized by high modal dampings has been selected (see Table 1). Thus, the control action permits the output tracking by increasing the actual structural damping values by one order of magnitude. The significant differences in the level of oscillations between actual and reference model under white noise excitation are shown for a selected time interval in Fig. l b .

H/VWA/^' - L i I l I. 600

598

t

600

Figure 2. Floors' displacement time histories: actual model (solid line), reference model (dotted line).

251

0

200

400

t

600

0

200

400

(

600

Figure 3. On-line identification in presence of initial stiffness a) and damping b) errors.

As shown in Fig. 2, the strategy is successful in terms of displacement reduction through accurate output tracking. The system is excited by a white noise signal applied at the first mass level and the shown time interval indicates a satisfactory matching for all the three floors displacement (Figs. 2a, 2b, 2c). Furthermore, assuming the masses to be known, the selected output allows for a complete identification of the structural parameters because all the floor state variables do appear in the control law (7) thanks to the chosen noncollocated scheme. The performance of the on-line identification is reported in Fig. 3 for a 25% initial error in all the parameters. The values of the gains can be tuned to regulate both the initial chattering and the velocity of convergence of the parameter estimation. In particular, Fig 3. shows that using a variable gain as mentioned in Section 3 the chattering has been minimized.

4-2

Damage detection and simultaneous corrective control action

In this section the ability of the procedure in detecting damage occurring in the structural system is exploited. It is generally recognized that damage in structures appears as degradation of system characteristics, such as stiffness and/or damping (Lin et al. 4 ) . In particular, structures are apt to suffer damage caused by different events such as strong environmental loads, sudden impacts and degradation due to longtime exposure. Assuming the damage model as a smooth time-variations in the stiffness and damping coefficients, the procedure on-line identification effectiveness can be exploited to detect and track these structural changes. Assuming a good knowledge of the system initial mechanical parameters, a reference model close to the actual one can be designed. Thus, the initial small control action compensates only the small

252 differences between actual and reference model. When damage begins to affect the mechanical properties of the structure, the procedure detects on-line both the reduction of stiffness and the increase of damping and simultaneously compensates such degradation through the control. Indeed, the actual system is forced to behave as the reference model that represents its initial undamaged conditions. A numerical experiment has been carried out to demonstrate the performance of the procedure. The reference model has been selected with a 2% lower estimate of the mechanical parameters. Therefore, the parameters in Table 1 referred to the reference model take, in this case, the following values: fi = 0.457, fci = 1925.7,^2 ='0.18, k2 = 1907, & = 0.375 and k3 = 1160. The masses are left unchanged. The time dependent behavior of the stiffness and damping parameters is governed by the following expressions, h(t) = k0ii - 0.25k 0 : i t 2 /t}

; a(t) = c0li + 0.25c Oii < 2 /*/

(12)

where a smooth time variation during the time interval tf — t0, with t0 = O.Osec and tf = 300sec, is assumed. fc0,i and c0j, with i = 1,2,3, represent the initial stiffness and damping parameters of the three floors. The model reference tracking is shown in Fig. 4 in terms of floor displacements. The shear-type model is excited by a white noise acting on all the three masses. In Fig. 5 the estimated time-dependent behavior of the parameters is shown. As far as the stiffness parameters, Fig. 5a shows that apart from a slightly different path followed by the first two floors variations, a good accuracy is obtained throughout the duration of the simulation. For the third floor case, a short interval of stiffness underestimation occurs in a time interval centered around the final instant of the parameter variation. The final error between the estimate and the actual parameter values is lower than 1% for all the floors. In Fig. 5b the damping parameter estimation is shown. Although the estimated smooth increase of the parameters does not last exactly as the actual variation time (0 — 300 sec) a satisfactory final estimate is obtained.

t

600

598

f

600

598

t

Figure 4. Floors' displacement time histories: actual model (solid line), reference model (dotted line).

253

0

200

400

t

600

0

200

400

t

600

Figure 5. On-line identification in presence of smooth stiffness a) and damping b) variations.

The error in this case is about 11% for the third floor while is lower than 5% for the remaining floors. 5

Conclusions

A model reference adaptive control procedure in which the full-state feedback is employed to address a dual goal, vibration suppression and damage detection, has been presented. The procedure is used in this paper enabling both reference model tracking and parameters identification for non-collocated control schemes. In the former, by tracking a reference output of an arbitrary model with desired damping characteristics; in the latter, by detecting on-line simulated damage-induced mechanical parameters variations. Applications to shear-type models have been considered showing that a linear combination of the complete state variables guarantees exact output reference tracking. Assuming the masses to be known, non-collocated schemes are shown to allow on-line estimation of all the relevant mechanical parameters of the discrete dynamical model of the structure. The possibility of relying solely on acceleration measurements and to tackle the nonlinear parameters dependence in the control law represent the main issues among those deserving further investigation. References 1. R. Isermann, U. Baur, W. Bamberger, P. Kneppo and H. Siebert, Automatic 10, 81 (1974). 2. R. Ghanem and M. Shinozuka, J. Engrg. Mech., ASCE 1 2 1 , 255 (1995).

254 3. M. Ioannou and A. Datta Proc. IEEE 79, 1736 (1991). 4. C.C. Lin, T.T. Soong and H.G. Natke, J. Engrg. Mech., ASCE 116, 2258 (1990). 5. V. Gattulli and R. Ghanem, Int. J. of Non-Linear Mech., 34, 853 (1999). 6. A.W. Smyth, S.F. Masri, A.G. Chassiakos and T.K. Caughey, J. Engrg. Mech., ASCE 125, 133 (1999). 7. V. Gattulli and F. Romeo, J. of Struct. Control 6, 187 (1999). 8. R. Ghanem, M. Bujakov, K. Torikoshi, H. Itoh, T. Inazukam, H. Hiei and T. Watanabe, J. Engrg. Mech., ASCE 123, 1161 (1997). 9. C.H. Ih, D.S. Bayard, A. Ahmed and S.J. Wang, AIAA J. Guidance Control and Dyn. 16, 9 (1993). 10. C.H. Ih, D.S. Bayard, A. Ahmed and S.J. Wang, AIAA J. Guidance Control and Dyn. 16, 14 (1993). 11. S. Poh and A. Baz, J. of Fluids Struct, 10, 615 (1996) . 12. L.R. Ray and L. Tian, J. Sound Vib. 227, 615 (1999). 13. V. Gattulli and F. Romeo, J. Engrg. Mech., ASCE 126, 730 (2000).

DESIGNING AND TESTING DEVICES FOR SEMI-ACTIVE STRUCTURAL CONTROL

H. GAVIN, M. DOBOSSY AND J. LAMBERTON Department of Civil and Environmental Engineering Duke University, Box 90287 Durham, NC 27708-0287 E-mail: hpgavin(a).duke. edu The suppression and control of structural respon se to strong earthquakes requires devices which can generate high forces, rapidly, and with very little (or no) required external power. Within the last ten years, devices utilizing the controllable properties of electro-rheological (ER) and magneto-rheological (MR) materials have been studied for this application. In addition, devices with controllable ori" ces have also been studied. This paper describes device design methods, and the results of device tests for each of these three types of control devices. Conclusions are made regarding the suitability of these devices for this application and the amount of electrical power required to operate each of the devices.

1 Introduction Devices with controllable damping properties have received considerable attention recently for earthquake vibration control applications [1,2,3]. The appeal of using these devices for this application is that the energy to generate the control forces comes from the structure itself, and that large external power supplies need not be relied upon. Three similar types of devices have emerged in this context: electrorheological (ER) devices [2,3,6], magnetorheological (MR) devices [4,7,8], and controllable hydraulic devices [5]. ER and MR devices make use of particle suspensions which change from a viscous fluid to a soft, yieldable, solid upon application of an electric (ER) or magnetic (MR) field. These devices feature few or no moving parts and, ideally, low power consumption. The yield stresses induced by the external fields are low compared to common structural stresses, and the devices need to be designed carefully in order to generate large forces. The third type of device is based on commercial hydrualic components, and features a doubleended cylinder and a network of controllable by-pass valves. Such valved devices also consume only a few watts of electrical power to regulate kilowatts of mechanical power.

255

256

This paper describes some recent experiences in designing, constructing, testing, and modeling representative devices from each of these three categories. The piston bore is the same for each device each device can operate on a few watts of power, and each device can regulate peak forces on the 5 kN level.

2

M R Devices

The MR device designed in this research is a piston in a cylinder filled with MR fluid. The MR fluid contains carbonyl iron particles of 5-micron diameter, suspended in a water or oil dispersant. When a magnetic field passes through the fluid, the iron particles align, creating a micro-structure which must be yielded before the material will flow. The piston is wrapped in magnet wire to create an inductor within the device. When current is run through the wire, a magnetic field is created which is guided through the center of the piston, the MR fluid and the cylinder walls. The yield stress of the MR material increases substantially where it is exposed to the magnetic field. This change in material properties is sufficient to generate significant changes in damping forces (factor of 10) in well-designed devices. 2.1

Design Parameters

A commercial hydraulic cylinder was modified for this device; several geometric properties such as the diameter of the cylinder, and its length were fixed. The diameter of the outer wall, Dw, was 1.82 in., the thickness of the wall, tw, was 0.14 in., and the diameter of the piston rod, Dr was 0.625 in. The selected design parameters were the gap thickness, tg, magnetic field, Bg, number of turns in the coil, TV, the core diameter, Dc, and the pole length, Lp. Note that most of these paramters directly influence the behavior of the magnetic circuit, and by choosing the parameters intelligently, MR devices with fast response times and low power requirements can be designed. At high magnetic fields the magnetic permeability decreases with field strength. To balance the power requirements of the device and the flux density in the MR material, it is advantagous to design the magnetic circuit in such a way that under operating conditions all of the components are below their saturation fields. An additional benefit of operating at lower flux densities is that remnant magnetizatoin of the magnetic circuit and MR material is diminished. Hence, the maximum flux density in the core and walls was set at 1.5 tesla.

257

2.2

Design Equations

The device force is proportional to the pressure drop across the MR piston. the difference in pressure Ap need to be considered. The shear stress r in the MR material is related to the shear rate 7 and the magnetic flux density in the gap, Bg, T = Ty(Bg)sgni

+ r)i

(1)

where, for the MR materials used in this study, 105B3/2,

Ty(Bg) = 15 +

where TV is in Pa and Bg is in Tesla. The pressure drop across the piston, Ap, has a viscous component, A p ^ , and a component related to the magnetic field, Ap«Apw + 2.1^,

(2)

tg

where AP

»

~

ir(Dp

+

tg)tg

W

At low fields, the relationship between flux density, B, and magnetic field strength, H, can be modeled as being linear, B = fiH. For stronger fields, however, this linear relationship is not accurate, and a different model must be used. For our device, the following B — H relationship was used. IT J}

1 1

H = —\—h —( Jb

2s /x0

U

^)(exp(arcsinh(s(5 —Jh)))—exp(arcsinh(—sJb))) (4) Jb

where Hc is the threshold field of the material calculated, s is the "sharpness" of the B-H knee for the given material, UQ is the permeability of free space, and Jb is the saturation flux density of the material. Using these expressions, and given a set of values for the design parameters the total magnetic and fluidic behavior of the device can be calculated. A set of parameters was chosen to minimize J = | + /3iR.

(5)

The final design used consists of 4 spools in series with three layers of windings. The core diameter is 26.0 mm, while the pole diameter is 37.0 mm. The end poles are 4.5 mm wide, while the poles inside are twice as wide, at 9 mm.

258

2.3

Test Results

Figure 1 illustrates preliminary data from the MR device. The target 4 kN was almost reached using a diluted MR material. The pinching of the forcedisplacement hysteresis loop is caused by a flow constriction between the cylinder and the accumulator. This problem has since been remedied. For™ VI. Dhptacwnort lor MR Dlvir*

F e r n v( Vtbcty tor M3 0»V(CB

Or*ri«csrranl. 0 (cm)

Vakjdly, V (err.*)

Figure 1. Force-Displacement and Force Velocity hysteresis of t h e M R device tested.

3

Hydraulic Damper

A controllable-valve damper of similar geometry to the MR damper was designed" and tested, as shown in figure 2. The hydraulic circuit contains four valves: a manual needle (viscous) valve, two manual pressure relief valves, and an electric solenoid valve. By adjusting the pressure relief valves, the maximum force in the device can be selected from 1 kN to 25 kN. The device easily reaches the 4 kN target force and the dynamic range, P, (ratio of onto-off forces) is greater than 10. The device behavior is consistent and can be modeled by an algegraic expression of the form: / = /o tanh(cf/iio + v/vo) + kd + cv

(6)

Note that the behavior of the hydraulic device with pressure relief valves is qualitatively similar to the MR device. The response time of the solenoid valve is on the order of 20 to 30 milliseconds, as shown in figure 3. "Simulation Technologies, 2423 South Alston Ave., Durham, NC 27713

259 Force vs. Displacement For Open and Closed Device

-

2

-

1

0

1

2

3

Force vs. Velocity For Open and Closed Device

4

- 4 0 - 3 0 - 2 0

-10

Displacement, D (cm)

0

10

20

30

40

Velocity, v (cm/s)

Figure 2. Force-displacement and force-velocity hysteresis of the valved hydraulic device

Fwn vi Thna lor Swtdttig. On itata. m ! ON S
r

Figure 3. Transient behavior of the hydraulic valve device.

4

Electrical Power Considerations for E R and M R Devices

ER devices are electrically capacitive and require high voltages; MR devices are electrically inductive and require moderate currents. To rapidly apply power (charge) to an ER device, it is advantageous to temporarily send more current than the leakage current to the devices. (The leakage current is the voltage (i.e. 5 kV) times pCh/r], where p is the current density.) To rapidly apply power (current) to an MR device, one should overdrive the device's voltage. Removing power (charge) from ER devices is a simple matter of shorting the high-voltage electrodes of the device to ground, through a power resistor. (RC is small because C is small.) To safely dissipate the current in an MR device, a resistor in parallel with a zener are placed in parallel with the coil. When the MR switch is closed only a small current passes through the parallel resistors. However, when the switch opens, the current through the resistors changes direction, and all the current in the coil passes through the resistor and dissipates rapidly. (L/R is small because R is large.)

260

The analysis of the power requirements for an ER device is more straight forward than for an MR device. The design of the magnetic circuit entails multiple varialbes, as outlined above, which allows the designer to optimize various electro-magnetic attributes of the MR device, such as power. The net surface area of the electrodes in an ER device that achieves a dynamic range of P at mechanical power Pm, with a material yield stress Ty and viscosity 77 and a gap size h is approximately A = 2.7(P-l)^r

(7)

The capcitance of the device is C = eA/h, and the steady state current is pA, where e is the permittivity of the ER material and p is the current density. If the device is switched on and off with a period T, then the average electrical power requirement Pe is _ CV2 ~ AT

p e

+

Viuc_ 12

CV

{iP -

IDC)T

(8)

where V is the power supply voltage and ip is the peak current output by the power supply. Using these expressions and proprties for a particular ER material it is possible to relate the electrical power, Pe, required to regulate a given amount of mechanical power, Pm. As an example, the device/material combination described in table 1 will result in ER and MR devices with the efficiencies shown in figure 5. The ER and MR materials used in this example are commercially available. Note that in ER devices increasing power supply current and increasing gap reduces the charging response times. Any water absorption of the ER material will result in a significant rise in the current density. Should the current density reach about 1 Amp/m 2 , the electromechanical efficiency of the device would be seriously compromised.

5

Acknowledgements

This material is based on work supported by the National Science Foundation under Award No. CMS-9624949 and by Enidine Corporation. The authors are grateful to Professor Pradeep Phule for providing samples of MR materials and to Nippon Shokubai Corporation for providing samples of ER materials for this research. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the sponsors.

261 Table 1. Electro-mechanical efficiency for E R and MR devices Material Current Draw Viscosity (at 0 kV), 77 Yield Stress, r v Dynamic Range, Fon/FQu Plow Gap, h Electrical Field limited by: Response Time Power Supply Current, t m a x Power Supply Voltage, V m a x

M R F - 2 4 0 B S a t 1 Tesla 150 k A - t u r n s / m 0.5 Pa-sec 80kPa 10 ( a t 5 0 c m / s e c ) 0.8 — 2.8 mm L = 0.015 — 0.5 Henry magnetic saturation 0.1 — 12 ms 4.9 Amp

TX-ER8 at 4 k V / m m 0.13 A m p / s q . m 0.035 Pa-sec 5kPa 10 ( a t 5 0 c m / s e c ) 1.6 mm C = 0.001 — 0.050 IJ.F dielectric break-down 0.1 — 10 ms 0.3 Amp (peak) 0.001 — 0.250 Amp (continuous) 6400 Volt

Power Supply

200 Volt (peak) 4 — 24 Volt (continuous)

Power Supply 0-200 Volt 0-5 Amp 100k

*>^& 100k

OverDrive

0.1 H

100k

-

ON 1 1

OFF

1

\

1

T

1 f 1

1

\

1 1

r

1

\

RC or UR

Figure 4. Electrical circuits for rapid operation of E R and MR devices.

6

References 1. S.J. Dyke, B.F. Spencer, M.K. Sain MK, et al. An experimental study of MR dampers for seismic protection. Smart Materials and Structures, 7(5) pp. 693-703, 1998. 2. H.P. Gavin, R.D. Hanson, F.E. Filisko, Electrorheological dampers, Analysis and design. J. Applied Mech., 63(3) pp. 669-675 1996.

0

20

40 60 controllable mechancial power (kW)

60

100

Figure 5. Electrical power requirements for switching E R and M R devices.

3. H.P. Gavin, Design method for high-force electrorheological dampers. Smart Materials and Structures, 7(5) pp. 664-673, 1998. 4. W.H. Li, G.Z. Yao, G. Chen, S.H. Yeo, F.F. Yap. Testing and steady state modeling of a linear MR damper under sinusoidal loading. Smart Materials and Structures, 9(1) pp. 95-102, 2000. 5. W.N. Patten, C. Mo, J. Kuehn, J. Lee. A primer on design of semiactive vibration absorbers (SAVA). J. Engineering Mechanics, 124(1) pp. 61-68 1998. 6. N.D. Sims, D.J. Peel, R. Stanway, A.R. Johnson, W.A. Bullough. The electrorheological long-stroke damper: A new modelling technique with experimental validation. J. Sound and Vibration, 229(2) pp. 207-227, 2000. 7. N.M. Wereley, L. Pang, G.M Kamath. Idealized hysteresis modeling of electrorheological and magnetorheological dampers. J. Intelligent Material Systems and Structures, 9(8) pp. 642-649, 1998. 8. N.M. Wereley, L. Pang, Nondimensional analysis of semi-active electrorheological and magnetorheological dampers using approximate parallel plate models. Smart Materials and Structures, 7(5) pp. 732-743, 1998.

COST ACTION F3 "STRUCTURAL DYNAMICS" 1997-2001 PRESENTATION AND SOME PRELIMINARY RESULTS

J-C. GOLINVAL Universite de Liege, LTAS - Vibrations et Identification des 1 Chemin des Chevreuils, 4000 Liege Belgium E-mail: [email protected]

Structures,

P. ARGOUL Laboratoire Central des Ponts et Chaussees Marne la Vallee 2, Allee Kepler, 77 420 Champs-sur-Marne France E-mail: [email protected] The COST Action F3 "Structural Dynamics" was initiated in 1997 by Professor Jean-Claude Golinval. The main objective of this COST Action is to increase the knowledge required for improving the structural design, the mechanical reliability, and the safety of structures in linear and non-linear dynamics. This research Action is supported by the European Community and is divided into three working groups dealing with the following issues: WG1: "Finite Element Model Updating Methods"; WG2: "Health Monitoring and Damage Detection"; and WG3: "Identification of Non-linear Systems". This paper presents the objectives of the COST Action F3, the organization of the Action, the members of the management committee, and the scientific program of each working group in more detail. Finally, preliminary results of the COST Action are presented.

1

Introduction

The COST (Co-operation in the field of Scientific and Technical Research) Action "F3" Structural Dynamics was initiated in 1997 by Jean-Claude Golinval, Professor at the University of Liege in Belgium. Supported by the European Community., this research Action started on the 25th of June, 1997, and will end the 24th of June, 2001. Its purpose was to develop in Europe collaboration, to intensify and to coordinate research in the fields of structural testing, dynamic analysis, and model updating. The idea was to allow European research institutions working on similar problems in parallel to exchange information with others and let them be aware of similar research programs. The COST framework seemed to be an efficient and simple way of gathering a database and diffusing information among many European partners. At the very beginning of the Action, the 25th of June, 1997, six European countries (Belgium, Denmark, Italy, Netherlands, Portugal, and United Kingdom) signed the Memorendum of Understanding (MoU). The last six months of

263

264

1997 were devoted to the definition of coherent objectives between different partners. On the 26th of June, 1998, seven more European countries (Austria, Finland, France, Germany, Greece, Spain, and Switzerland) signed the MoU; thus thirteen signatory countries in total. Jean-Claude Golinval was elected the chairperson and Michael Link, Professor at the University of Kassel, the vicechairperson. This paper is divided into two parts. The first one is devoted to a brief presentation of the COST Action F3 including the objectives and organization. The second part deals with the scientific program of the three working groups with the description of the benchmarks, the short term scientific missions and the preliminary results. 2

2.1

Presentation of the COST Action F3

Objectives

Regarding the increasing complexity of mechanical structures due to the increasing demands on safety, load-carrying capacity, weight reduction, construction or equipment performance and service life, the mathematical and numerical models used for computer simulations become increasingly important. Despite the high level of sophistication of today's computational tools in structural analysis, the analytical and numerical results often reveal considerable discrepancies when compared with the experimental ones. For example, whenever non-linearities (e.g. damping effects that are not decoupled by the modal basis of the undamped equivalent system) are suspected, traditional modal analysis techniques collapse because their underlying mathematics are restricted essentially to the linear domain. Structural dynamic test data is therefore used for correlating with analytical predictions and for updating the analytical models when the deviations are not acceptable. The problem is then of test-analysis reconciliation (model updating, health monitoring, etc.) that depends upon the type of structure and the type of structural modification involved. In various situations, a local identification of the dynamics of a component may be extracted from the modal test of the structure. Therefore, the problem becomes that of "modal subtracting" the behavior of the studied components from that of the whole system. A few attempts in this direction have been developed but a thorough investigation has not yet been proposed. This problem has numerous industrial applications; for example, the inspection of bolted joints in metallic structures as well as the control of joints in pipe networks. In other cases, for instance, when structural changes originate from localized damage, the problem must be investigated from a non-linear point of view. For example, untightening of bolted joints may determine particular vibrational patterns of the type "vibration with contact,'' due to joint free play.

265

The objective of this COST Action is to develop and validate procedures to allow engineers to enhance structural safety, maintainability and performance using vibration measurements, structural modeling and data processing algorithms. The key concept involves utilizing changes in the "vibration signature" to locate and estimate the extent of damage and/or model errors. Although the problems of model correlation, damage detection and non-linearities identification require different mathematical solutions, they all draw heavily on System Identification (SI) methodology. This methodology seeks to determine the best fit mathematical model directly from experimental data. 2.2

Organization of the COST Action

The COST Action is managed by a management committee (MC) consisting of a chairperson, a vice-chairperson, plus two representatives of each of the thirteen signatory countries. Its goal is to implement, to supervise and co-ordinate the COST Action. Scheduled to meet once or twice per year, there have been six meetings of the MC to date. This research Action is divided into three working groups dealing with the following issues: (WG1) Finite Element Model Updating Methods; (WG2) Health Monitoring and Damage Detection; and (WG3) Identification of Non-linear Systems. The co-ordinators are, respectively, Dr. M. Friswell and Prof. M. Link for WG1, Prof. M. Link and Dr. K. Worden for WG2, and Dr. P. Argoul and Dr. F. Thouverez for WG3. One main idea for the three working groups is to work on common benchmarks in order to compare results and methods. One (or two) workshop/conference(s) is(are) organized each year in the framework of the COST Action F3. The past conferences were: 1. International Seminar on Modal Analysis (1SMA 23) at the Katholieke Universiteit Leuven (Belgium) on 10-12th September, 1998 (cf. www.mech.kuleuven.ac.be/pma/events/isma/isma23conf/isma23.html); 2. Identification in Engineering Systems at the University of Swansea (Wales) on 29th-31th March, 1999 (cf. www.swan.ac.uk/mecheng/ies99): 3. European COST F3 Conference on System Identification & Structural Health Monitoring at Universidad Politecnica de Madrid (Spain) on 6th-9th June, 2000 (cf. www.dmpa.upm.es/SHM). The two conferences to come are: 1. International Seminar on Modal Analysis (ISMA 25) at the Katholieke Universiteit Leuven (Belgium) on 13-15th September, 2000 (cf. www.mech.kuleuven.ac.be/pma/events/isma/isma25conf/isma25conf.html); 2. International Conference on Structural System Identification at the University of Kassel (Germany) on 5-7 September, 2001 that will be the final conference. Several Short-Term Scientific Missions (STSM) have been made since the beginning of the COST Action. The aim of a STSM is to contribute to the realization of the scientific objectives of a COST Action. These missions will strengthen the existing networks by allowing scientists to go to a laboratory in

266

another COST country to learn a new technique or to make measurements using instruments and/or methods not available in their own laboratory. During the period 1998-1999, ten scientific missions were made covering the subjects dealt within the WG's. They are briefly described in the following part. 3

Scientific program of the COST Action F3

The program of each working group is first briefly recalled. To focus even more on the participants' common interests, several benchmarks (Bm) have been defined within each WG, thereby allowing them to compare their different scientific approaches. The data of nine benchmarks are now available, one for WGl called Bmll, four for WG2 called, respectively, Bm21, Bm22. Bm23. Bm24 and also four for WG3 that are called, respectively, Bm31, Bm32. Bm33, Bm34. For each working group, the benchmarks are described below (for more details see the website of the COST F3 Action: www.ulg.ac.be/ltas-vis/costf3/costf3.html). Moreover, it appears that one or two benchmarks have been studied more intensively by two or more participants from two different countries. Thus, these Bms will be presented in more detail in the following. For WGl, this is Bmll; for WG2 these are Bm21. and Bm22; and for WG3, these are Bjn_32, and Bm33. For the other benchmarks, the following remarks are given: • Bm23 is the Z24 Swiss concrete bridge (SIMCES project). The bridge was tested under artificial production of progressive damage due to traffic excitation. Three data sets are available: a) undamaged, b) damaged by a 95 mm pier settlement, c) damaged by concrete spalling. Since the original traffic excitation data sets measured and made available by the EMPA in Switzerland, are extremely large, Prof. R. Brincker from Aalborg University has volunteered to provide a smaller subset of the data as to facilitate the process. • Bm24 is a small building model with two decks and four columns (similar to the JRC-Ispra lab case, but with quadratic plates). The loading is in random (unknown) pulses, so it is close to real ambient loading. With three measurements on each deck, one can find the movements of the plates assuming rigid body motions, and time series with 10000 data points in each. The modeling is very simple, so that additional experiments can easily be performed, and the amount of data is rather limited. Three cases are provided : a) undamaged, b) damaged by one localized stiffness reduction, c) introduction of an additional mass. Some additional tests may also be performed by Prof. R. Brincker. • The layout for Bm31 consists of a steel beam hinged at the end with two masses. This model is intended to reproduce the vertical motion of a beam subjected to vertical acceleration at the ends (for example, a bridge deck subjected to the vertical component of an earthquake).

267

•

The layout for Bm34 is composed -of three linear plates representing the base, die wing, and the aileron. The non-linear junction element" connecting the wing and the aileron is made of two Paulstra flexible coupling rubbers that are working mainly in torsion stress. Finally, some preliminary results are presented (the list is not exhaustive, for more detail see the proceedings of the past COST conferences previously mentioned). 3.1

Working Group 1 "Finite Element Model Updating Methods'*

3.1.1 Program The main feature- of the program of WG1 is to complete a study on generating a validatedfiniteelement model using computational model updating.

Figure 1. Benchmark 11: *The GARTEUR SM-AG 19 structure".

3.1.2 Description of the benchmarks Two benchmarks have been defined; Bmll: 'The'GARTEUR SM-AG 19 structure" (and Bml2: 'The NASA 8-bay truss", whose data are not yet available). Benchmark WG1 Bmll - GARTEUR SM-AG 19 structure. The structure shown in figure 1 was built previously for a benchmark study on experimental modal analysis conducted by the Garteur group. It schematically simulates the dynamic behavior of a glider structure. Experimental frequency response functions and modal data were made available from previous studies by

268

DLR (German Aerospace Establishment) and by the University of Manchester (Aerospace Engineering Division). The test structure shown is described in detail in the report of ref. [6], including the geometry, the material data and the measurement plan. Refs. [2]-[7] describe the experimental benchmark results whereas ref. [3] provides the starting point for the model validation benchmark. 3.1.3

Preliminary results

Several research groups from Belgium, France, Germany and United Kingdom are currently working on the benchmark Bmll. They have meshed the GARTEUR structure with their own finite element model using either beam or shell elements. The modal data proposed by DLR is used to correct these FE models using different updating procedures and the results will be published in the near future. 3.2

Working group 2 "Health Monitoring and Damage Detection "

3.2.1

Program

The main feature of the program of WG2 is to assess the damage localization and me level of damage inside the structure by using a mathematical model. 3.2.2

Description of the benchmarks

Four benchmarks have been kept; Bm21: "KULeuven's beam structure" proposed by Ing. B. Peeters from Belgium; Bm22 : "Steel frame structure" proposed by Dr. J. Molina and tested at JRC-Ispra in Italy; Bm23: "SIMCES concrete bridge case: the Z24 Swiss bridge" tested at EMPA in Switzerland; Bm24: "Two deck laboratory building model" proposed by Prof. R. Brincker from Germany. Benchmark WG2 Bm21 - KULeuven's beam structure The beam is 6 m long with a rectangular cross section (250 x 200 mm2) (cf. Fig. 2). It is somewhat unusual for a reinforced concrete (RC) beam that the height is smaller than the width; this is done so the eigenfrequencies are not too high. There are six 16 mm diameter reinforcement bars, equally distributed over the tension and compression side, corresponding to a reinforcement ratio of about 1.4%. Shear reinforcement consists of 8mm diameter vertical stirrups every 200 mm (cf. Fig. 2). It is known that the static Young's modulus of concrete differs from the dynamic one. The first longitudinal eigenfrequency of a cylinder (h = 300 mm, N = 150 mm) made of the same concrete and at the same time as the beam was measured to determine the dynamic modulus (Edyn = 35 000 MPa). A total beam mass of m = 750 kg results in a density of the reinforced concrete of p = 2500 kg/m3.

269

Figure 2. Benchmark 21 : "The KULeuven's beam structure".

Benchmark WG2 Bm22 - "Steel frame structure"

Figure 3. Benchmark 22 : 'The steelframestructure".

The structure is a two-story frame of main dimensions 8m x 3m x 9m as depicted in Fig. 3. Each story is made up of corrugated sheets supporting a concrete slab and are connected by welded vertical and horizontal steel girders. The columns consist of HE300B, the storeys of EPE400 on the long side and EPE300 on the short side. Bracings are made of L60x30x5 profiles. The structure was tested pseudodynamically and cyclically along its longitudinal direction by means of two 500kN

270

displacement-controlled hydraulic actuators at each floor. At the end of this damaging test, major cracks appeared at some of the beam-column joints (cf. Fig. 4).

Figure 4. Cracks

3.2.3

Preliminary results

Generally, the damage identification procedure is carried out in the following three main steps: (1) updating of the initial finite element- model by means of the measurement data of the undamaged-structure in order to obtain'a reliable reference model; (2) damage localization from the changes in the measured dynamic behavior, including parameter selection and (3) calculation of the extent of damage. Some preliminary results are presented below for benchmark Bm23, the Z24 Bridge in Switzerland and for benchmark Bm22. the steel frame structure. The goal for the benchmark Bm23 was to be able to detect die precise time and type of damage by performing forced and ambient vibration tests on the bridge. The date was then processed in order to detect the damage done to the bridge. Since the excitation of the bridge was not known (it was due to wind, traffic* etc.). the use of the stochastic subspace technique for determining the model order.from only the output data was. proposed (cf. [13]). This technique was based on the discrete time state-space formulation. During ambient testing, the process noise vector is the only excitation. The system identification therefore consists of the estimation of the system and the output matrices from measurements by using robust numerical techniques such as QR factorization, singular value decomposition and leastsquares. Once these matrices are found, one can then find the modal parameters easily. In {13]/the stabilization diagram was used to select the optimal model order. This was done by determining the stabilization of the model, which was calculated to be the weighted sum -of the stabilization degree of poles in the model, giving a higher weight to poles- that had more stable modal parameters. The stability of the poles were, in ton, determined by a set of criteria: 1% deviation for frequency, 10% for damping ratio and 5% for natural mode. Damage detection was done by comparing the model of the bridge at any given time to the models at previous times. Since this detection depends upon prior.knowledge,

271 it was necessary to collect some initial data, during a period where it is known that there is no damage to the structure, from which to base the comparisons. The final detection process was only somewhat automatic, for a human was needed to visually view the results and look for deviations in the modal parameters. It was found that the best signal of damage was the instability of frequency and mode shape; the damping ratio was found to be an unuseful indicator of damage due to its great variability. In addition, not all modes were ideal for detection; (modes 2 and 5 for the pier settlement of 40 mm were too scattered to be reliable, for example). It was thus found that one could detect the precise time of damage to model structure using a modal analysis followed by a visual inspection of the data. Moreover, one parameter not considered in this study was the effect of temperature on the modal parameters. Although many studies can show that temperature variation may cause a higher variation in natural frequencies that structural damage, it was assumed that all of the difference in modal parameters was due to damages in structure. This is a subject of future investigation. For the benchmark Bm22. an attempt to identify the location and extent of damage to the steel frame induced by seismic loads is discussed in [9]. First, an FE program was used to make a numerical model of the frame before any damage was done. The mean of the MAC values, which indicates the mode shape deviation, was 99.24% (3rd torsion mode not included). The eigenfrequency deviations, however, were quite high (average around 8.41 Hz, again not including 3rd torsion mode). In order to improve on this result, an extended least-squares technique was done that minimized an objective function that contained the differences in the eigenfrequencies and mode shapes. The result was a great decrease in eigenfrequency deviation, down to 0.04 Hz (not including the 3rd torsion mode). In order to investigate modeling damage done to the structure, a set of 63 parameters that were assumed to cover all possible damage cases, was chosen. After investigating the sensitivities of the modal data to changes in these parameters, a subset of the most important parameters was taken. The physical structure was then damaged, and data was recorded as to how these parameters changed. In order to see if the location of the damage could be predicted, the same perturbation in the parameters was made in the undamaged model. Stiffness reductions of about 90% were predicted by the numerical model in the three locations of cracks in the physical model. These results were not satisfactory, however, for the solution oscillated. One possible reason for this was that too many parameters were used, resulting in a complex calculation that did not lead to accurate results. The number of parameters was therefore reduced, resulting in a reduction in the average eigenfrequency error and MAC value to 0.57% and 93.4%, respectively. It should be noted, however, that a small deviation in regularization parameters leads to other results. Thus, it seems that the identified parameters and the models used can relatively accurately predict the location and extent of the damage done to the physical structure in question. Further investigation

272

needs to be done with more sensors and modes so that the number of local minima that appear when searching for the parameter values decreases. C-P. Fritzen et al. [8] have developed with MATLAB-Toolbox "Mafem", a 1476 DOF finite element model of the Bm22 structure, consisting in 104 four-node shell and 172 two-nodes beam elements. A model updating was performed minimizing the objective function considering the MAC-values and the eigen frequencies of the first ten modes. The unknown parameters vector is made of the Young's moduli and the shear moduli of both steel and concrete, as well as the bracing's moment of inertia and the stiffnesses of the grounded springs. An inverse sensitivity problem with parameter subset selection is formulated for the damage detection, localization and quantification. The equations predicted four cracks, however during the experiment only 3 of these actually occurred. To improve the results, the number of sensors must be increased and they must be placed in more optimal locations. ARMAV models technique for system identification and damage detection has been applied to benchmark Bm22 in [5]. A procedure based on multi-layer perceptrons is also proposed in [21] to assess the damage in Bm22. 3.3 3.3.1

Working group 3 "Identification of Non-linear Systems" Program

Researchers in structural dynamics have long recognized the importance of diagnosing and modeling non-linearity. The last twenty years have witnessed a shift in emphasis from SDOF to MDOF nonlinear structural dynamics (cf. [20]). The main feature of the program of WG3 is to work on a benchmark test based on two linear sub-structures connected by a localized non-linear component in order to compare different non-linear identification procedures on the same data. 3.3.2

Descriptionofthe benchmarks

Four benchmarks have been kept; Bm31: "Two-degree-of-freedom non linear system for seismic applications" proposed by Prof. O. Bursi from Italy; Bm32: "Flexible mounts" proposed by Dr. J. Linjama and Dr. M. Juntunen from Finland; Bm33: "Beam with a non-linear (NL) component" proposed by Dr. F. Thouverez from France; and Bm34: "Structural scale model of a wing and an aileron" proposed by Dr. Ph. Fargette from France. Bm32 and Bm34 concern isolated non-linearities where the test is carried out on the single non-linear component. Bm31 and Bm33 relate to a global non-linear behavior where linear sub-structures are connected by non-linearities.

273

Benchmark WG3 Bm32 : "Flexible mounts" The purpose of this test is to have a standard experimental procedure that gives practical information of the dynamic properties of resilient mounts (mounts, viscoelastic materials, etc.). The tested mounts are helical wire rope isolators. The system is made of the non-linear element between two masses (cf. figure 5) and is excited by an electrodynamic shaker. The bottom mass is driven by the shaker while the top mass is left free. The accelerations of the top and bottom masses were then measured to determine the acceleration transmissibility defined as the frequency response function between the measured acceleration of the two masses (cf. [14]). From this, conclusions about the non-linearity of the element in question have been made in [10].

Figure 5. Benchmark 32 : 'Theflexiblemounts".

It was found that as the excitation level increases, the dynamic stiffness (related to the acceleration transmissibility decreases and the loss factor (related to the energy lost in the system) increases. In addition, it was noted that the accuracy of the results decreased as the frequency of the excitations increased. Since the results were

274

relatively accurate, it was concluded that the described setup was a good starting pointfromwhich one could examine the non-linearities of various test objects. Benchmark WG3 Bm33 : "Beam with a non-linear component" The goal of this test is to analyze the efficiency of nonlinear identification methods on a simple case. This experimentation involves a clamped beam with a local non-linearity on its extremity.

Figure 6. Benchmark 33 : " The beam structure with a non-linear component ".

Figure 7. Benchmark 33 : " NL components of the Benchmark 33".

A thin beam, excited in large deflection, realizes the nonlinear component. The beam is composed of three parts (Part A: main beam, Part B: junction element & Part C: NL component) the characteristics of which are given in "Table 1. The structure has been excited harmonically near the right clamping using five different excitation force levels (2, 3, 5, 9 and U N ) . Four acceleration pick-ups had been used to measure the response. Afrequencyrange between 8 and 500 Hz has been measured and three resonances can be found around 25 Hz, 135 Hz and 400 Hz.

275 Table 1. Caption for Table.

3.3.3

rt-

VI Eft

i-*- i-*-

CW

o ct n

Material Part A PartB PartC

Length 593mm 40mm 57mm

Thickness 14mm 20mm 0.5mm

Width 14mm 30mm 30mm

Preliminary results

Some non-linear identification procedures have been tested within the framework of WG3. One of the "classical" methods for the analysis of the frequency response distortions is the harmonic balance. The equation of motion is linearized following the basic idea of the harmonic balance method (the approximated response to a harmonic excitation is assumed to be harmonic with the fundamental angular acceleration). In [17], the studied nonlinear terms are local cubic springs and cubic dampers. In order to determine the mechanical non linear parameters, a weighted least squares minimization was done on an objective function that included the difference between the experimental and theoretical data. Three different residuals were used in this minimization: the difference in the real portion, in the imaginary portion and in the magnitude of the displacement response. This method was then tested on a simulated 5 degree-of-freedom system with five masses connected to each other and ground through non-linear springs and dampers. The values of the parameters were identified exactly using the algorithm described. However, the results were not as good when applied to the data of benchmark Bm33. Although a good model of the shape of the displacement amplitude versus frequency was calculated, the characteristic jump frequency (where the displacement amplitude suddenly decreases) could not be modeled well. Due to the non-linearity in the system, the value of the parameters varies with each data set, making it therefore unreliable. Thus, the proposed algorithm was found to be reasonable in describing the nonlinear properties of a structure in the frequency domain. More research needs to be done, however, in more accurately modeling non-linearities, so that practical applications are better modeled by the algorithm. A recent development which shows promise for the analysis of MDOF systems is the "reverse path" class of algorithms, which are frequency-domain identification algorithms for a wide class of parametric models. The originator of the approach was Bendat, specifically for SDOF systems [4], then Rice and Fitzpatrick [19]. The idea is that, given a system with localized non-linear springs and dampers, one can separate the non-linear terms from the linear ones in order to make an accurate model. In the motion equations, the non-linear terms are assumed to be separated from the linear ones in the form of non-linear vectors that have a coefficient matrix. The limitation of this model is that the type and locations of the non-linearities must be known in order to solve for the coefficient matrix. It should be noted, however,

276

that this is a common problem for many of the currently known identification procedures of non-linear systems. The reverse path method allows to estimate the coefficient matrix. This is done by taking the Fourier transform of the motion equations, thereby separating the force excitation vector into components due to the linear effects of the displacement vector and the non-linear effects present in the nonlinear vectors. The next step is to write the relationships between the power spectral densities of the displacements, forces, and non-linear vectors, in which appear several terms: (1) the cross spectral density matrices between the force vector and the displacement vector, and between the force vector and the non-linear vectors; (2) the matrix containing all of the possible cross spectral density matrices between the displacement vector and all the nonlinear vectors; and (3) a row vector containing the unknown coefficients. This method requires that excitations be applied at every response location, which is not practical in real experiments for two reasons. First, real experiments often have a fewer number of excitations as response locations. Second, the non-linearities in the system are sometimes away from the locations of applied excitation. In either case, the reverse path method fails. These problems are overcome with the conditioned reverse path method (CRP). A hierarchy of uncorrected frequency domain response components is constructed and then run through a series of matrix calculations involving their cross spectral density matrices similar in form but not in detail to the RP method. The ultimate goal is to separate the part of the response uncorrelated from the force from that part that is correlated, and to discover the linear relationship in the correlated portion. This solves both problems mentioned above. The CRP method was then tested on benchmark Bm32 (cf. [16]). The Fourier transform of the acceleration, instead of the displacement, is used. Error due to numerical integration is thus not introduced; an advantage of the CRP method which allows the use of accelerations instead of displacements. It was found that the CRP method produced a very stable peak frequency of around 108 Hz for the studied system, while the linear estimation had a left shift of about 26 Hz. The CRP method seems to be relatively good at detecting and quantifying non-linearities in multi-degree-of-freedom systems. Further research must be done to make the calculation more robust and to reduce analyst interaction. The Proper Orthogonal Decomposition (POD) is a method used to reduce the complexity of a model by selecting only a few functions that can be used to accurately represent the entire system. This is done by finding the coherent structures in the experimental data, which are merely those functions that contain the maximum possible energy content of the measured signal. These coherent structures would therefore maximize the ratio of the square of the inner product between themselves and the time-varying portion of the given data set and the inner product of the function with itself. This is because each coherent structure would capture as much of the energy in the signal as possible. The coherent structures are therefore determined by solving the eigenvalue problem that directly comes from this

277

property. A physical interpretation of the proper orthogonal modes (POM) is given in [11] using the singular value decomposition. It is shown that the Proper Orthogonal Modes (POM; the modes determined by the SVD) converge under certain conditions to the normal modes of the system as the number of samples goes to infinity. A physical model was studied using the above POD algorithm. Experiments with a clamped beam connected to a nonlinear spring at one end were performed. The errors computed with first POM and then with normal modes taken as basis functions were compared. It was found that the error associated with the POM was always lower than that with the normal modes. Thus, it was found that the POD algorithm is an effective way of reducing the model size when studying nonlinear systems. Further study must be done in order to determine better reduction algorithms for damped systems. During the STSM, two other techniques were studied and compared : the restoring force surface technique and the identification technique using the wavelet transform (cf. [1]) in order to process the free oscillations of mechanical nonlinear systems. 3.4

Short Term Scientific Missions

Within WGl, three missions: (1) K. Bohle from Siegen, Germany to Liege, Belgium and (2) R. Pascual Jimenez from Liege, Belgium, to Ispra, Italy. Their aim was to compare and to apply computational procedures for updating respectively the benchmarks Bmll and Bm22 presented below. During the mission of R. Pascual, the tests on the undamaged structure were performed, and the extracted model data were compared to the finite element model results. It consisted of preliminary work to identify the location and the magnitude of the damage. (3) D. Simon from Liege, Belgium to Lyon, France studied during his mission the use of high resolution optical field measurements for damage location and model updating. Within WG2, two missions : (4) S. Diaz-Carrillo from Madrid, Spain to Swansea, UK spent his mission in developing a special finite element which analyzes the effects of a composite patch repair that was applied to a concrete beam. The analytical results have been compared to the existing experimental ones. (5) J.L. Zapico (from Gijon, Spain, to Sheffield, UK) learned the neural networks techniques used at the University of Sheffield for damage detection and identification in order to design a compact procedure to detect damage of the benchmark Bm22. Within WG3, five missions were made. The mission of (6) O. Bursi from Trento, Italy to Champs, France was devoted to improve modeling and identification techniques for damage assessment and prediction in particular to the establishment of a continuous hysteretic non-linear model. The application under study is the assembly of metallic or composite beams under pseudo-dynamic testing. The mission of (7) S. Marchesiello from Turino, Italy to Manchester, UK was aimed at identifying the parameters representing the non-linear effects (local or distributed) of

278

systems submitted to known excitations by means of "Reverse Path" method. This technique allows to estimate the frequency response functions. During his mission, (8) G. Kerschen from Liege, Belgium to Sheffield, UK exchanged information on the restoring force surface technique used in Liege and in Sheffield. The identification technique was applied to the case of an experimental beam with and without clearance that allowed him to draw conclusions about the accuracy and efficiency of the technique. (9) F. Conti from Rome, Italy, to Champs, France worked on the processing of free vibrations of nonlinear dissipative systems by means of the wavelet transform. From the wavelet transform, the amplitude and the instantaneous frequency of each component of the signal are extracted and the parameters governing the non-linear behavior can be then estimated. (10) The mission of V. Lenaerts from Liege, Belgium, to Turino, Italy was aimed at comparing two different identification techniques: the wavelet transform technique used by F. Conti and the restoring force technique used by G. Kerschen. These techniques were applied to an experimental set-up; the results were compared and some conclusions about their efficiency were made. 4

Acknowledgements

The authors would like to thank Mr. Afsheen Afshar and Mr. Jim McQuade of Princeton University for their significant help with the preparation and translation of this paper. References 1. Argoul, P., Hans, S., Conti, F., and Boutin, C , Time-frequency analysis of free oscillations of mechanical structures. Application to the identification of the mechanical behavior of buildings under shocks, European COST F3 Conference on System Identification & Structural Health Monitoring, (ETSI Aeronauticos, Madrid, June 2000), pp. 283-292. 2. Balmes, E., Garteur Group on Ground Vibration Testing Results from the Tests of a Single Structure by 12 Laboratories in Europe, IMAC (1997). 3. Balmes, E., Predicted Variability and Differences between Tests of a Single Structure, IMAC (1998). 4. Bendat, J.S., Nonlinear Systems Techniques and Applications, (WileyInterscience, 1998). 5. Bodeux, J.B. and Golinval, J.C., Armav model technique for system identification and damage detection, European COST F3 Conference on System Identification & Structural Health Monitoring, (ETSI Aeronauticos, Madrid, June 2000), pp. 303-312.

279 6. Degener, M. and Hermes, M., Ground Vibration Test and Finite Element Analysis of the GARTEUR SM-AG19 Testbed, Deutsche Forschungsanstalt fiir Luft-und Raumfahrt e.V. Institut fiir Aeroelastik (23200), (October 1996). 7. Degener, M., Ground Vibration Results from the tests of an Aircraft Model Performed as Part of an European Round Robin Exercise, CEAS International Forum on Aeroelasticity and Structural Dynamics, Rome, (1997). 8. Fritzen, C.P., Bohle, K., and Stepping., A., Damage detection in structures with multiple cracks using computational models, European COST F3 Conference on System Identification & Structural Health Monitoring, (ETSI Aeronauticos, Madrid, June 2000), pp. 191-200. 9. Gorl, E., and Link, M., Identification of damage parameters of a full scale steel structure damaged by seismic loading, European COST F3 Conference on System Identification & Structural Health Monitoring, (ETSI Aeronauticos, Madrid, June 2000), pp. 397-405. 10. Juntunen, M. and Linjama, J., A test method for estimation of dynamic properties of isolators, European COST F3 Conference on System Identification & Structural Health Monitoring, (ETSI Aeronauticos, Madrid, June 2000), pp. 815-829. 11. Kerschen, G., Lenaerts, V., and Golinval, J.C., Proper orthogonal decomposition and model reduction of nonlinear systems, European COST F3 Conference on System Identification & Structural Health Monitoring, (ETSI Aeronauticos, Madrid, June 2000), pp. 451-460. 12. Keye, S., Prediction of modal and frequency response data from a validated finite element model, 2nd International Conference on Identification in Engineering Systems, (Swansea, March 1999), Edts Friswell, Mottershead & Lees, pp. 122-134. 13. Kullaa, J., Monitoring simulation and damage detection of the Z24 bridge, European COST F3 Conference on System Identification & Structural Health Monitoring, (ETSI Aeronauticos, Madrid, June 2000), pp. 353-362. 14. Linjama, J., and Juntunen, M., Estimation of dynamic properties of resilient mounts, 2 International Conference on Identification in Engineering Systems, (Swansea, March 1999), Edts Friswell, Mottershead & Lees, pp. 74-83. 15. Link, M., and Graetsch, Th., Assessment of model updating results in the presence of model structure and parametrisation errors, 2nd International Conference on Identification in Engineering Systems, (Swansea, March 1999), Edts Friswell, Mottershead & Lees, pp. 48-62. 16. Marchesiello, S., Garibaldi, L., Wright, J.R., and Cooper., J.E., Applications of the conditioned reverse path method to multi-degree-of-freedom non-linear systems, European COST F3 Conference on System Identification & Structural Health Monitoring, (ETSI Aeronauticos, Madrid, June 2000), pp. 429-438. 17. Meyer, S., Weiland, M., and Link, M., Identification of local stiffness and damping non-linearities, European COST F3 Conference on System

280

18.

19.

20.

21.

Identification & Structural Health Monitoring, (ETSI Aeronauticos, Madrid, June 2000), pp. 439-450. Peeters, B., De Roeck, G., Hermans, L., Wauters, T., Kramer C. and De Smet, C , Comparison of system identification methods using operational data of a bridge test, ISMA 23, International Conference on Noise and Vibration Engineering, (K.U. Leuven, Belgium, September 1998), pp. 923-930. Rice, HJ. and Fitzpatrick, J. A., A generalised method for spectral analysis of nonlinear systems, Mechanical Systems and Signal Processing, (1988), 2, pp. 195-207. Worden, K., Non linearity in structural dynamics : The last ten years, European COST F3 Conference on System Identification & Structural Health Monitoring, (ETSI Aeronauticos, Madrid, June 2000), pp. 29-51. Zapico, J.L., Worden, K., and Molina, F.J., Structural Damage assessment using neural networks, European COST F3 Conference on System Identification & Structural Health Monitoring, (ETSI Aeronauticos, Madrid, June 2000), pp. 387-396.

ELASTIC SHEAR FRAMES WITH TUNED LIQUID COLUMN DAMPERS A CONTROLLED STUDY OF SMALL-SCALE MODELS ANDREAS HRUSKA Institute of Steel Structures, Technical University of Vienna Karlsplatz 13/213, A-1040 Vienna E-mail: [email protected] AL DORFMANN Institute of Structural Engineering, University of Applied Peter Jordan Street. 82, A-1190 Vienna E-mail: [email protected]. ac. at

Sciences

Tuned liquid column dampers (TLCD) are passive energy absorbing devices to control vibrations of structures. The objectives of this paper are to study the influence of TLCD's on the dynamic response of elastic shear frames. Small-scale model experiments and analysis of the TLCD modeled as a SDOF oscillator are undertaken. The influence of excitation frequency, liquid column length and container geometry on the optimal performance of the damping device are investigated. Free vibration tests and frequency sweeps are performed to determine the optimal tuning ratio and corresponding geometry of the TLCD.

1

Introduction

Undesirable vibrations occur frequently in high-rise and/or long span lightweight structures in general characterized by low intrinsic damping mechanism. These vibrations even though in general do not affect the primary load carrying capacity of the structure itself, do interfere with comfort and quality of life of occupants. In recent years the passive energy dissipating device known as tuned liquid column damper (TLCD) has been employed successfully in practice to control vibrations under different dynamic excitations. Originally the concept was developed for vibration control of long-period structures subjected to wind load, but has recently been extended to earthquake engineering applications as well [21,12,19]. Tuned liquid column dampers are passive vibration devices rigidly connected to the primary structure and capable of dissipating energy through oscillations of the liquid column in a U-shaped tube of rectangular or circular cross section. With proper and accurate tuning of the primary and secondary structure, the out-of-phase response of the small mass in the TLCD exerts an inertia force to the primary structure capable to counteract external excitations. The damping force resisting these excitations is a combination of various sources: The gravitational restoring force acts on the displaced liquid whereby vibration energy is absorbed through viscous interaction between the liquid in motion and the rigid container. Additional energy dissipation is introduced by the hydrodynamic head loss resulting from the 281

282

flow separation of the liquid between horizontal and vertical column, from the passage through a Bernoulli-type orifice as well as by internal viscosity in the liquid itself. From the above listed sources, the orifice damping is considered the most significant one. Obviously, for a successful vibration control, the TLCD must be designed to have the correct natural frequency, optimum level of damping (optimum coefficient of head loss or the corresponding orifice opening ratio) correct geometry and mass ratio. In this study accurately controlled small-scale experiments are performed to determine the parameters, which significantly influence the non-linear damping characteristics of the device. For this purpose, a single degree of freedom aluminum frame structure with flexible columns and rigid floors is build and subjected to free vibration and frequency-sweep experiments. Thereby the influence of the total liquid column length, the geometry of the TLCD (in this case defined as the ratio of vertical to horizontal column length), as well as the excitation frequency on the behavior of the damping device is analyzed and recorded. 2

Mathematical Model

A U-shaped tuned liquid column damper composed of liquid mass and rigid container is schematically shown in Figure 1. It is assumed that the container is infinitely rigid and that the excitations are in lateral direction only. Further, it is assumed that damping sources such as viscous interactions, flow separation and internal viscosity in the fluid are small and thus neglectable. Finally, it is assumed that the motion of the liquid mass is given by a small displacement response and is described by a single coordinate y(t). Then, the analytical equation describing the motion of liquid oscillation in an U-shaped TLCD is given by a second-order, nonlinear differential equation in which the non-linearity is introduced by the velocity dependent damping coefficient, Sakai et al.[13] and Saokaetal.[14], pALy(t)

+ ±pAZ\y(t)\y(t)

+ 2pAgy(t)

= -pABx(t)

(i)

In equation (1), p is the mass density of the liquid, L the total length of the liquid column, B the length of the horizontal column, A the uniform cross-sectional area of the device, £ the coefficient of head loss governed by the opening ratio of the orifice. The horizontal motion of the damping device which coincides with the motion of the primary structure is indicated as x(t). In the above equation the first term on the left hand side is the inertia force resisting the motion with a corresponding liquid mass equal to p A L . The damping term is given by the coefficient of head loss £,, the average flow velocity y(t) multiplied by the uniform cross-sectional area A and by the fluid density p. The average flow velocity depends on the loading intensity and the absolute value is to

283

maintain the directional sense of the damping force. The dependents of the damping parameter from the loading intensity imply that for passive systems the best performance can only be achieved for one specific loading intensity, [3, 4]. The head loss coefficient £ depends on the orifice opening ratio and needs to be determined experimentally for a specific TLCD geometry, Sakai et al.[13], Fried and Idelchik [5], Blevins [2]. Active and semi-active control algorithms have been introduced recently to keep damping independent of the loading intensity and therefore at a permanent optimal value by adjusting the head loss coefficient £ [6, 19, 21]. The third and last term on the left hand side determines the restoring gravitational force of the liquid mass 2pAgy(t), considering that the head difference of the two free surfaces is 2 y(t) and g is the gravitational acceleration. The right hand side of the equation describes the reaction force when the rigid container is suddenly subjected to the accelerationx(t), see Figure 1. The constant horizontal portion of the liquid mass generates a reaction force equal to-pABx(t) which act opposite to the direction of motion. This term implies however that the horizontal portion of the TLCD is always filled with fluid. The nonlinear equation of motion contains the velocity dependent damping coefficient and can only be solved numerically. However, to obtained an approximate solution, equivalent linearization techniques are used as well where the velocity dependent damping coefficient is replaced by an equivalent linearized damping parameter ceq, Sakai et al. [13], Iwan and Yang [10], Balendra et al. [1], Swaroop et al. [15], Chang and Hsuy [3], Kwok et al. [11], Xu et al. [20]. The linearized system is then given by pALy(t)

+ ceqy(t) + 2pAgy(t) x

= -pABx\t)

i B ,

Figure 1: Experimental Setup and System Geometry

(2)

284

Selecting the linearized damping parameter ceq by minimizing the mean square of the error between the original damping force in the non-linear expression (1) and the linearized term in equation (2) given above, gives

IT

C

(3)

=\\—PA%ay

eq

where ay is the standard deviation of the liquid mass velocity y(t). To solve for the equivalent damping in equation (3), an iteration procedure is necessary since ceq depends on cry and that quantity is not known in advance. Finally, the natural frequency coj and the natural period Td of the TLCD is given by Td

(OA

=2n.

(4)

(T

2g Combining the primary SDOF structure with a secondary oscillator such as a TLCD can best be described as an energy sharing process, see Figure 1. First, the total input energy is shared between the two systems and at the same time the TLCD dissipates part of that energy by the induced motion of the liquid mass. For a SDOF structure with mass m0, damping coefficient cB and stiffness constant k0 subjected to the ground acceleration x the coupled equations can be written as

3

m0 +pAL

pAB

pAB

pAL

0

K

o

0

IpAg

m0+pAL\

pAB J

(5)

Experimental Investigation

A small-scale SDOF frame structure was designed to experimentally determine and evaluate the influence of the total liquid column length L, the influence of the horizontal column length B and the effect of the excitation frequency on the damping characteristics of the device [9]. The SDOF structure made of aluminum had a total participating mass equal to 2.517 kg, a column length of l=0.381m and an eigenfrequency f0 of 1.37 Hz, which was verified by performing free vibration tests. Figure 1 shows the most significant dimensions, the top floor where the TLCD is mounted and the first floor that will be subjected to an external excitation xg during the forced vibration tests. The U-shaped TLCD with a constant circular cross-section of 0.032m in diameter was rigidly connected to the SDOF structure as shown in Figure 1. Based on results from experiments performed by Hitchcock et al. [7, 8], optimum vibration mitigation for a given mass ratio and liquid damping ratio are to be expected for a

285

natural frequency ratio of 0.98. Thus, by using equation (4) and a frequency ratio of one, a total liquid column length L of 0.265 m should provide near optimal performance. During the experimental investigation the total column length L was incrementally increased from an initial value of 0.13 m up to 0.37 m, which corresponds using Equation (4) to a change in natural frequency of the TLCD from 1.955 Hz to 1.159 Hz, see Table 1. Secondly, to evaluate the influence of the horizontal column length on the optimum performance, four different models (Model 1A, IB, 1C and ID) were selected with values B equal to 0.13m, 0.16m, 0.19m and 0.23m. Equations (5) shows that the length B influences the transfer of energy from the primary to the secondary structure but not the natural frequency of the TLCD. To maintain constant mass in all cases, small supplementary masses were added to balance the variation in liquid mass and/or mass of the damper. Table 1. Eigenfrequencies of the TLCD L[cml f[Hzj

fo/f L[cm]

HH4 fo/f

3.1

13.0 1,955 0.70

15,0 1,820 0,75

17,0 1,710 0,80

19,0 1,617 0,85

21,0 1,538 0,89

23,0 1,470 0,93

24,0 1,439 0,95

25,0 1,410 0,97

26,0 1.383 0,99

27,0 1,357 1,01

27,5 1,344 1,02

. 28,0. 1,332 1,03

29,0' 1,309 1,05

31,0 1,266 1,08

33,0 1,227 1,12

37,0 1,159 1,18

Free Vibration Experiments

During this sequence of tests, the floor level of the shear frame structure was not allowed to move, while the upper level with the attached TLCD was subjected to a free vibration motion to evaluate the influence of the TLCD geometry on the damping of the structure. Our base line case consists of the frame structure with no secondary energy dissipation activated. To maintain a constant mass condition throughout all tests, a supplementary mass was added in place of the TLCD. The free decay of the structure during the first 60 seconds is shown in Figure 2 on a semi-logarithmic scale, where the low damping characteristic of the frame structure is evident, which corresponds to a damping of 0.24%. To evaluate the length change of the horizontal column four different TLCD models are used (Model 1A, IB, 1C and ID) for which B assumes values of 0.13m, 0.16m, 0.19m and 0.23m, respectively. In all four cases the total liquid length L is kept constant and equal to 0.27m. From equation (4), the natural frequency of the TLCD corresponding to a value L of 0.27m is 1.356 Hz, thus close to the eigenfrequency of the primary structure.

286 10m/s2

AIJ AI A11A11 l l i U I M j i m i •iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiTiiiiTiiiiiiiiiiiiiiiiiiiiiriiiiiiiiiiiiiiiiiiTiiiiiiniriiiiiini

0,1

0.0-MM Figure 2: Free Vibration Test without TLCD (semi-logarithmic scale) 10. m/s2

0,1

nffi ,llll| Ah

0,0

10

20

30

40

50

s 60

40

50

s 60

Figure 3: Free Vibration Test Model 1C (semi-logarithmic scale) 10 m/s2

0,1

0,0

10

20

30

Figure 4 : Free Vibration Test Model ID (semi-logarithmic scale)

287

A horizontal length of 0.13m and a vertical column length of 0.07m characterize model 1 A. The acceleration versus time response shows a high damping during the first 10 seconds of the free vibration. During the first 15 seconds, the damping is large, but nonlinear. For the remainder of the time, the damping reduces to a lower, but constant value. After 45 seconds, the amplitude reduces to zero. Next, Model IB and 1C are used to apply additional damping to the structure. A horizontal column length of 0.15m and a vertical column height of 0.06m characterize model IB. Similarly, Model 1C has a value B equal to 0.19m and a vertical column height of 0.04m. Comparing the acceleration response shown in Figure 2 and Figure 3, an increase in damping is noticed. In fact, for Model 1C the total duration of the free vibration motion reduces to 34.5. Finally, in Model ID the horizontal column length increases to 0.23m, which leaves only 0.02m of total vertical liquid height for each of the two columns. For this last case, the assumption of small displacement response in Equations (2) and (5) is not satisfied any longer. Further, the coupling termp AB in Equation (5) is assumed to have constant mass; in other words, the horizontal portion of the TLCD is always filled with liquid. Thus, if during motion the horizontal column is not filled at all times, the coupling between the primary and secondary structure weakens and the effectiveness of the TLCD reduces. However, the damping in the TLCD increases at the same time due to an increase in the hydrodynamic head loss resulting from additional flow separation at the vertical-horizontal column interaction reducing the duration of the free vibration motion to 18 seconds (see Figure 4). To evaluate the influence of the total liquid length L, Model 1A with a constant horizontal column length of 0.13m is used. The value for L is increased from an initial value of 0.13m up to 0.33m in increments of 0.02m. The eigenfrequencies of TLCD's corresponding to each value of I are given in Table 1. It is shown that a total length L of 0.27m does provide the optimal damping response. Using Equation (4), the value L of 0.27m corresponds to a natural frequency ration between primary and secondary structure of 0.99. 3.2

Unidirectional Frequency-Sweep Response

Similar to the free vibration response in the previous section, unidirectional frequency-sweeps are performed to determine the natural frequency ratio necessary to provide optimum vibration mitigation. The frequency ratio is the ratio between load frequency and natural frequency of the primary structure. The SDOF frame structure with eigenfrequency of 1.37 Hz is combined with a TLCD and subjected to frequency ratios starting from 0.7 up to 1.3. The dynamic amplification factor is the ratio of the dynamic amplitude of load acceleration in the bottom floor to the dynamic amplitude of acceleration in the top floor.

288

To best determine the frequency ratio required to provide optimal damping characteristics, Model 1A is used with a total liquid length L equal to 0.25m, 0.27m, 0.275m and 0.28m. The dynamic amplification factor of the structure without any secondary damping device shown in Figure 5 is representative for a linear-elastic SDOF system with the highest value corresponding to a forcing frequency equal to the eigenfrequency of the structure, causing resonance. Also the time response of the system is shown for a frequency ratio of 1 and >1. Using a TLCD with a total liquid length L of 0.25m produces a response spectrum where the dynamic amplification factor has a local maximum of 18.3% of the original structure without TLCD. This is a local maximum recorded at a frequency ratio of 0.974. An additional local maximum is seen to exist at a frequency ratio of 1.076 equal to 7% of the original value. Since the two local maximums are different in value and the larger one lies at a frequency ratio less then one, the natural frequency of the TLCD must be lowered (see Figure 6). Therefore, by increasing the total liquid length L to 0.27m an improvement is expected. The first local maximum occurs now at a frequency ratio of 0.949 equal to 13.3% of the original value. The second local maximum equal to only 10.3% lies at a frequency ratio of 1.058. The liquid length is now increased to 0.275m and the first local maximum reduces further to 12.2%, while the second maximum increases to 11.3%, always of the original undamped response. Thus, the optimal value for L is very close to 0.275m. The last experiment is performed using L equal to 0.28m.

Excitation Frequency [Hz]

Figure 5: Frequency Sweep - Shear Frame without TLCD

289 As expected, the first local maximum is now lower then the second one, 10.35% compared to 12.7%. Using an interpolation procedure of these results, the optimum liquid length L is found to be equal to 0.276m, corresponding to a natural frequency of the TLCD equal to 1.34 Hz. Thus, the frequency ratio to provide optimum vibration mitigation is equal to 0.979. This result corresponds with the findings of 0.98 in Hitchcock et al. [8].

0.70

0,80

0.90

1.00

1.10

1,20

1,30

1.40

1,30

1,40

F r e q u e n c y R a t i o : Excitation F r e q u e n c y / E i g e n f r e q u e n c y

Figure 6: Frequency Sweeps - Variation of the Liquid Column Length L - Model 1A

0,70

0,80

0,90 1,00 1,10 1,20 F r e q u e n c y Ratio: Excitation F r e q u e n c y / E i g e n f r e q u e n c y

Figure 7: Frequency Sweeps Models 1A-1B-1C

290

0,70

0.80

0,90

1.00

1.10

1,20

1.30

1.40

Frequency Ratio: Excitation Frequency / Eigenfrequency

Figure 8: Frequency Sweeps Models 1C-1D

The final investigation focused on determining the best value for B using a constant liquid length L of 0.275m. Model 1A, IB, IC and ID are used for frequency sweeps and the results shown in Figure 7 and Figure 8. It is interesting to note that the two local maximums are now approximately equal for Model 1A, IB and IC. In other words, the optimal liquid length L does not change for different geometry, see Figure 7. It is to be further noted, that increasing the length of the horizontal column does increase the damping characteristics of the TLCD. Thus, Model IC with a total liquid length L of 0.275m does provide the best damping from all models analyzed. The maximum value of the dynamic amplification factor reduces to only 9.3% of the original response (100%). Comparing the results of Model ID with the results from the previous three models, it shows that increasing the horizontal column length to 0.23m does not improve the response any further. For a total column length of 0.275m, only 0.0225m of fluid are in each vertical column when the TLCD is at rest. During motion, the horizontal column is not continuously filled with water, introducing large additional damping due to sloshing in the curved part of the tube, shifting the eigenfrequency of the TLCD. Thus the coupling between the primary and secondary structure weakens due to the shifted frequency ratio and the effectiveness of the TLCD is reduced. Even though the damping of Model ID is increased as determined during the free vibration tests, for the frequency sweep in Figure 8, the calibration of the TLCD is found to be not optimum.

291 4

Conclusions

Results from free vibration tests and unidirectional frequency sweeps are summarized in this paper with the objective to determine the optimal total liquid length L and to evaluate the influence of the horizontal column length B on the damping characteristics of a small scale TLCD. It is found that the results are best when a frequency ratio of natural frequency of the TLCD to the eigenfrequency of the SDOF structure is equal to 0.979. Further, the horizontal column length is important and in general the damping does increase with an increase of B. However, if the geometry of the TLCD is such that during motion the horizontal column is not filled with liquid at all times, the coupling between the two structures reduces the energy transfer between the primary and secondary system and effectiveness of the TLCD is reduced. References 1.

Balendra T., Wang CM. and Cheong H.F., Effectiveness of tuned liquid column dampers for vibration control of towers. Engineering Structures, 17(9), pp.668-675. 2. Blevins R.D., Applied fluid dynamics handbook. Van NostrandReinhold, 1984. 3. Chang C.C. and Hsu C.T., Control performance of liquid column vibration absorbers. Engineering Structures. 1998, 20(7), 580-6. 4. Chang C.C, Hsu CT. and Swei S.S., Control of buildings using single and multiple tuned liquid column dampers. Structural Engineering and Mechanics. 1998, 6(1), pp.77-94. 5. Fried E. and Idelchik I., Flow Resitance: A design guide for engineers. Hemisphere Publishing Co. 1989. 6. Haroun M.A., Pires J.A. and Won A.Y.J., Suppression if environmentallyinduced vibration in tall buildings by hybrid liquid column dampers. The Structural Design of Tall Buildings 1996, 5, pp.45-54. 7. Hitchcock P.A., Kwok K.C.S., Watkins R.D. and Samali B., Characteristics of liquid column vibration absorbers (LVCA) - I. Engineering Structures, Elsevier Science, Vol. 19, No. 2, 1997,pp.l26-134. 8. Hitchcock P.A., Kwok K.C.S., Watkins R.D. and Samali B., Characteristics of liquid column vibration absorbers (LVCA) - II. Engineering Structures, Elsevier Science, Vol. 19, No. 2, 1997, pp.135-144. 9. Hruska A., Elastic Shear Frames with Tuned Liquid Column Dampers, M.Sc. Thesis, Technical University of Vienna, 2000. 10. Iwan W.D. and Yang I.M., Application of statistical linearization techniques to nonlinear multi-degree of freedom systems. J. Applied Meek, 39, pp.545-550, 1972.

292 11. Kwok K.C.S., Xu Y.L. and Samali B., Control of wind-induced vibrations of tall structures by optimized tuned liquid column dampers. Cheung Y.K., Lee J.H.W. and Leung A.Y.T. (eds), Computational Mechanics, Balkema, Rotterdam, 1991, pp.249-254. 12. Sadek F., Mohraz B and Lew H.S., Single and multiple-tuned liquid column dampers for seismic applications. Earthquake Engineering and Structural Dyanamics, 27, 1998, pp. 439-463. 13. Sakai F., Takaeda S. And Tamaki T., Tuned liquid column dampers-new type device for suppression of building vibrations. Proc. Int. Conf. on Highrise Buildings, Vol 2 , Nanjing, China, 1989, pp. 926-931. 14. Saoka Y., Tamaki T., Sakai F. and Takaeda S., A proposal for suppression of structural vibrations by tuned liquid column dampers. Proc. 43rd Ann. Conf., JSCE, 1988 (in Japanese). 15. Swaroop K.Y., Kareem, A. and Kantor, C.J., Semi-Active Control Strategies for Tuned Liquid Column Dampers to Reduce Wind and Seismic Response of Structures. 2nd World Conference on Structural Control, Kyoto 1998 16. 2nd World Conference on Structural Control, Kyoto 1998 17. Tuned Liquid Column Dampers to Reduce Wind and Seismic Response of Structures" 18. 2nd World Conference on Structural Control, Kyoto 1998 19. Won A.YJ., Tuned Liquid Column Dampers and Hybrid Liquid Column Dampers to suppress earthquake-induced motions in flexible structures. Ph.D. Dissertation, University of California Irvine, 1994. 20. Xu Y.L., Samali B. and Kwok K.C.S., Control of along-wind response of structures by mass and liquid dampers. J. Eng. Mech. ASCE. 1992, 118, pp.2039. 21. Yalla K.S., Kareem A. and Kantor D.J., Semi-active control strategies for tuned liquid column dampers to reduce wind and seismic response of structures. 2" World Conference on Structural Control. Kyoto 1998.

DEVELOPMENT OF A TESTING SYSTEM FOR DYNAMIC CHARACTERIZATION OF ENERGY DISSIPATING DEVICES

HIROKAZU IEMURA, A. IGARASHI AND H. TANAKA Dept. Civil Engineering Systems, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan E-mail: [email protected], [email protected] The objective of this research is to develop a system which allows an economical and accurate loading of dampers and energy dissipating devices to characterize the dynamic properties and performance of those devices under the loading condition when it is installed to structures subjected to strong earthquakes. The concept of the test is an elastically supported main mass system and a mass-driver device (shaker) installed on the main mass system. This system forms a SDOF system, which is dynamically excited with the massdriver system either with sinusoidal or seismic input. The proposed method is shown to be an effective test procedure and it has great advantages over the conventional testing method by verification test using an oil damper specimen to demonstrate the capability of the test system.

1

Introduction

Recent findings and investigation on the damage of civil engineering structures due to strong earthquakes revealed the essential need of the concept of seismic isolation and structural control, especially with added damping mechanisms by means of energy dissipating devices in order to achieve the acceptable earthquake performance of the structure. For this reason, various dampers and energy dissipating devices have been developed for the actual application to buildings and large-scale structures. However, verification of such devices with conventional loading equipments, typically with hydraulic systems, requires a high level of capacities to the hydraulic system with significantly large strokes and velocities. The objective of this research is to develop a system which allows an economical and accurate loading of dampers and energy dissipating devices to characterize the dynamic properties and performance of those devices under the loading condition when it is installed to structures subjected to strong earthquakes. 2

Method and Experimental System

The concept of the testing system consists of a RC floor system supported by roller bearings and an elastomeric bearing to provide elastic restoring force and a massdriver device (shaker) installed on the floor system. Mass of the RC floor combined

293

294 with the elastic restoring force-forms a SDOF system, which is dynamically excited with the mass-driver system.

Shaker

Figure 1. Concept of the test system

Figure 2. Side view of the test system

The shaker, which consists of an auxiliary mass and a mass driving mechanism (an electric motor connected to the mass with a ball screw shaft), is controlled so that the dynamic response to the designated ground motion is induced at the floor system. Inertia force generated by the vibratory motion of the floor is' transmitted to the damper specimen. There are several advantages in this, method; the loading time history for the energy dissipating device reflects the boundary condition (i.e. displacement, velocity and acceleration) to the device when it is installed in the main

295 structure under earthquake excitation, including the dynamic interaction between the device and the structure in the real time scale.

*.& ^m<m^ y Figure 3. Mass Driver System for the excitation of the test system

Tables 1 and 2 show the specification of the main floor mass system, and that of the mass driver system, respectively. Table 1. Specification of the test system.

Main Mass Weight Dimensions

26.9tf 7.0m X 4.0m X 3.0m

Table 2. Specification of the mass driver system

Auxiliary Mass Weight Maximum Stroke Maximum Driving Force

2.0tf

"

1

±50cm 15.7kN

Loading capacity of this system is theoretically evaluated considering stroke limit of the mass driver system as well as fundamental design parameters such as the mass of the mass driver and the main floor system, maximum driving force of the mass driver, and the equivalent damping of the device.

296

"0

0.477

1 0832

frequency[Hz]

Figure 4. Loading capacity of the test system

3

Verification Test

Theoretical evaluation shows that effective loading tests can be performed with die proposed test concept. In order to check the capacity of the testing system used with earthquake record inputs, numerical simulation of the test process, including the stroke limiting algorithm and driving force restriction is conducted, and it is shown that the loading condition is acceptably accurate.

3.1

Test Specimen

The energy dissipation device model used as the test specimen is an oil damper intended for the use of seismic response reduction of building structure, shown in Figure 5. The damper is designed to generate nonlinear viscous damping force in accordance with the characteristics shown in Figure 6.

297

Figure 5. Oil clamper specimen

Velocity Peine]

Figure 6. Design characteristics of the oil damper specimen Table 3. Specification of the oil damper

Damping Coefficients 1 Maximum Stroke 3.2

Ci=100, C2=29.4 [kN/(m/sec)]

±5cm

Sinusoidal Loading Test

Figures 7 and 8 show the results of sinusoidal loading tests, in which the damper is subjected to sinusoidal loadings with various frequencies and amplitudes. For the test cases in which the velocity amplitude of the loading is +/- 3cm/sec (Figure 7), the behavior of the damper is expected to be linear, and for the case +/- 6 cm/sec (Figure 8), the yielding takes place in the velocity-damping force relationship. The test results indicate that the energy dissipation performance is as expected, except that hysteresis loops are observed in the velocity-damping force relationships, presumably caused by associated mechanical phenomena such as friction and backlash as well as damper stiffness.

298 Damping force-Disp.(0.5Hz lOgal)

*

0

Damping force-Vel.(0.5Hz 10gal)

£

0

-5 -2 Damping fon#tfep'!fe.5Hz 60gal>

£

0

-5

^ 0

-0.2

0

0.2

-5

0

Disp. [cm]

Vel.Ckine]

Figure 7. Sinusoidal loading test results for linear region (top: 0.5Hz, lOgal; bottom: 3.5Hz, 55gal) Damping force-Disp

Damping force-Vel.

f. o

-10

0 DampVreOMP&l-Vel.

•2 0

0

2 - 1 0

0

disp. [cm] vel.fcine] Figure 8. Sinusoidal loading test results for nonlinear region (top: 0.57Hz, 15gal; bottom: 1.5Hz, 50gal)

299

3.3

Seismic Loading Test

Seismic loading tests are conducted by controlling the mass driver so that the response of the main mass system simulates that of the structural system excited by earthquake ground motion. Figure 9 shows a typical set of seismic loading test results, in which JMA Kobe record NS component (scaled to 50gal maximum acceleration) from the 1995 Hyogo-ken Nanbu earthquake is used as the input. In spite of slight difference between the design and the actual damper response, especially in the force - velocity relationship, the response reduction effect of the device is well predicted.

Damping force-Disp.

Damping force-Velocity

Exp Sim

•6 0

•2

0

s 1,me History o Displacement

disD.fcml

' !

A ?! 1 \ IK

IK

vellkinel

S^w-~^/^-4^~~/>**s^^

i "

i

i

Time History of Vel.

Figure 9. Seismic input loading test results (Kobe record NS, 50 gal max. ace.)

300 4

Conclusions

The proposed method is shown to be an effective test procedure and it has great advantages over the conventional testing methods. One of the clear advantages is that the method is economical and effective in testing real size energy disspating devices. Also, the loading time history for the energy dissipating device reflects the boundary condition (i.e. displacement, velocity and acceleration) to the device when it is installed in the main structure under earthquake excitation, including the dynamic interaction between the device and the structure in the real time scale. Construction of an actual example of the proposed test system has been completed. This system has been accepted as the Japanese patent. Experiments of different types of dampers with the constructed system are now being carried out. Following the passive devices, semi-active and active dampers will be tested.

5

Acknowledgements

The research described in this paper is supported by Japan Society for the Promotion of Science. References 1. 2.

Soong, T. T. and Dargush, G. F., Passive Energy Dissipation Systems in Structural Engineering (Wiley, Chichester, 1997). lemura H., Igarashi A. and Toyooka, A., Study on simulation of earthquake response of structure using excitor, J. Structural Engineering 45A, (Japan Society of Civil Engineers, 1999), pp. 719-726 (in Japanese).

PERFORMANCE OF VARIABLE-DAMPING SYSTEMS: THEORETICAL ANALYSIS AND SIMULATION J.A. INAUDI National University of Cordoba, Argentina Email: [email protected]

Abstract The dynamic performance of structures with variable-damping actuators subjected to broad-band excitation is analyzed herein through numerical simulation of simple models. A comparison of the response of structures with passive, active and semiactive controllers is developed to evaluate the efficacy of semi-active damping devices for vibration reduction. It is demonstrated that semi-active dampers can achieve better performance than passive dampers and comparable to fully active systems in the case of lightly-damped frame structures. Using random vibration concepts, the relative efficiency of the realization of clipped linear optimal controller using semi-active dampers is evaluated in conventional structures, structures with tuned mass dampers and in interacting structures. New algorithms for variable friction and electro-rheological (ER) actuators are presented aiming at deformation reduction and acceleration reduction. The use of semi-active ER dampers as enhanced passive dissipaters that require deformation feedback and no state estimation is considered to be the most promising and less complex alternative in active control systems in the near future.

1 Introduction Most research on active control systems for structural engineering published since 1980 has dealt with variations on control theory concepts developed in other engineering fields. Linear quadratic optimal control has been the control strategy considered in most published research. The linearity of this controller and phase margin theoretically provided by this technique are the main reasons for its choice. However, the physical realization of such controller in civil engineering structures such as buildings or bridges subjected to earthquake loading implies the use of actuators connected to power sources capable of delivering tremendous power. This requirement typically makes this active control scheme unfeasible because of technological or cost constraints. One exception is the active mass damper system used for wind-induced vibration reduction in tall buildings where the power requirements are much smaller. In fact, more than twenty active mass dampers have been installed in buildings intended for occupancy in Japan during the last two decades. Generally speaking, passive control systems (energy dissipater or reinforcement) that can achieve a desired performance for a given structure will be

301

302 preferred over an active system on the basis of technological simplicity, cost, reliability and maintenance requirements. Semi-active control systems originally proposed in 1974 for suspension of automobiles [1] have been studied since 1980 in the context of civil engineering structures [2,3,4,5]. They constitute a promising alternative for structural vibration reduction because these systems deliver significant power and require negligible external power during operation. A semi-active system consists of an essentially passive device whose mechanical characteristics can be modified in real time using very little power (compared with that delivered by the device) to provide control forces. Recent experimental research on magneto-rheological (MR) fluid actuators in the context of earthquake engineering has shown significant potential of these devices for vibration reduction. Today, MR dampers (MRD) are commercially available under the name of MagneShock™ for automobiles suspension. MRD capable of applying dissipative forces of 20 metric tons have been built and tested for building applications [7]. The dynamic performance of structures with MRD has been investigated experimentally and through numerical simulation [5]. The objective of the research reported herein is to analyze the dynamic performance of structures with variable-damping actuators. Both variable viscous dampers and variable-resistance dampers are considered in the study and compared with the performance achieved through passive damping and fully active systems.

2 Passive and fully active controllers Although several types of energy dissipating mechanisms have been proposed and applied to vibration reduction, viscous fluid and friction dampers are the damping mechanisms used for benchmark analysis herein. The structural models considered are assumed to remain linear during vibration with the effect of supplemental linear or nonlinear components provided by passive dampers and/or actuators. The following differential equations govern the dynamics of the models: My(t) + Cy + Ky{t) + ^LTd / , (t) + £ / £ «,(0 = Lww(t) ,=i

(l)

>=i

M,C,K are the mass, damping and stiffness matrices of the structure, fjft) is a vector of forces in supplemental dampers, u(t) is a vector of forces applied by the actuators, and wft) is the excitation signal. Lj and Lu are transformations relating the degrees of freedom yft) of the structure to the deformations in the dampers Ad(t) and the relative displacement of the actuator Auft), respectively.

303 2.1 Passive damping and LQR controller Generally speaking, better deformation and acceleration reductions can be achieved using passive dampers when the dampers can be positioned within the whole controlled structure. Architectural constraints however, may determine that only a reduced number of devices can be installed and this may impose limits in the reachable performance. It has been proved that linear hysteretic damping is superior than linear viscous damping in the sense of larger deformation reduction for the same maximum force level [4]. It is also known that and increase in energy dissipation in a structure can produce an increase in floor accelerations for large damping ratios, especially in the case of multi-story lightly-damped long-period structures with supplemental dampers installed in a single level. Root mean square (rms) inter-story drift constitutes a simple index for evaluating damage potential a structural system. Let the inter-story drifts be defined as D = LDy(t) (2) Consider a structural model with supplemental linear viscous damping provided by viscous dampers located in a single level of the structural system subjected to broad-band excitation. Let the excitation signal be modeled as a zero-mean whitenoise signal with E[w(t)w(t+T)J=WS(T). The selection of the damping constant c of the dampers can be done by minimizing the trace of the drift covariance matrix with respect to c: PDD=E[DDT] (3) As an example for a benchmark analysis, consider the steel frame structure in Fig. 1 subjected to broad band excitation with supplemental dampers located in the lower level. The lateral displacements yj (?) / = 1,2,...,6 of each floor of the steel-frame are taken as degrees of freedom of the structure. The natural frequencies of the structure are 4.5, 12.5, 21.5, 31.4, 41.1, and 51.5 rad/s. The damping of the structure without dissipaters is modeled as a classical damping matrix C with modal damping ratios of 1% of critical. Figure 2 shows in thick line the square root of the trace of the drift covariance matrix divided by the white-noise excitation intensity, ^] trace (PDD) / W , as a function of c, the damping parameter of the dampers located at the first level of this structure. The circular symbol in the graph shows the optimum damping parameter obtained using this criterion. Although an increase of c above the optimum value produces a reduction in the lower level drift, it produces an increase in the rms inter-story drifts of the upper levels.

304

-+-

-I

[email protected] 1

W24x84

•y6(t) W14x99

W24x; 4

*

W24xl

y,(.t)

* y4(0

W27x: 4

W14xl32 [email protected]

W27x 02

W14xl93

Actuator or damper ^

* y2(0

W30) 116

533.4cm

fa

%

^

J3S

Figure 1. Steel frame structure used for benchmark.

Assuming an actuator is installed in the lower level of the structure, full-state feedback is feasible and a powerful actuator is available for design, let us obtain the achievable performance using a linear quadratic optimal control (LQR) with performance index T = E[J x (t)Qx{t) + ru2 (t)dt]

(4)

where £[.]= expectation operator, and the dynamics of the state of the system x(t) is given by (5) x(t) = Ax(t) + Buu{t) + B w(t) withx(0 = LK0

A=

O -M~XK

y(t)Y, I -M'XC

B =

O

B =

O -M'lL.

(6)

and w(t) = white noise signal of intensity W, E[w(t)w(t+T)J=WS(r). Matrix Q in Eq. (4) is selected so as to penalize the sum of the squared inter-story drifts, L'DLD O

fi = o

o

(7)

305

The optimal controller is u(i) = -Gx(t) = -r~'BTuPx{t) where matrix P is the solution of the corresponding Riccati equation.

(8)

Figure 2 shows in thin line, the performance ^trace(PDD)/W achieved as a function of the parameter r of the LQR controller. Figure 3 shows in thick line, the performance for varying c as a function of the normalized rms viscous damper force (fc,) and in thin line, the same performance measure for varying r as a function of the normalized rms actuator force. As Figs. 2 and 3 show, active control can in principle render better performance of the structural system than passive damping in frame structures. However, the marginal improvement is not always that significant and the associated cost may be prohibitive in terms of necessary technology for achieving the force-levels in medium or strong earthquakes.

Iog10(r)

log10(c/[Ns/cm])

Figure 2. Performance of frame subjected to random excitation

log10(RMS(u)/sqrt(W)), log10(RMS(fc)/sqrt(W))

Figure 3. Force requirement of LQR and viscous damping.

As an example, let us compute the response of the steel-frame structure (Fig. 1) subjected to the registered ground acceleration of the El Centra (Imperial Valley, 1940) with no added damping (BF), with optimum viscous damping (VD), with LQR control (r~12, see circular symbol in Fig. 2), and with optimum viscous and LQR control. The results in Table 1 show significant and comparable drift reductions achieved by passive damping, LQR controller and combination of both. It is not surprising that the maximum force in the actuator reaches between 13% and 20% of the building

306 weight, loads that can easily make the physical realization of both active controllers unfeasible for earthquake applications. Table 1. Peak responses of 6-story steel frame subjected to the El Centro signal. Controller

BF VD LQR LQR + VD

Peak force/ trace(Mg) 0 0.148 0.192 0.132

Drift 1 (cm)

Drift 2 (cm)

Drift 3 (cm)

Drift 4 (cm)

Drift 5 (cm)

Drift 6 (cm)

4.47 2.17 2.50 2.39

2.65 1.92 1.43 1.54

3.23 2.62 2.08 2.18

3.62 2.51 2.22 2.19

4.06 2.66 2.81 2.69

3.06. 1.97 2.32 2.11

2.2 Liapunov bounded controller As an alternative to reduce force requirements in an active controller, bounded non linear controllers can be designed using Liapunov techniques. Consider a stable linear system (damped structure) described by Eq. (7). Let the control force be bounded

I "(0 l< «„a,

(9)

Taking the following Liapunov function [4] t u(t)

A(t) = x(tf

Px(t) + 2aj j g~l (-^—)dsdt 0 0

(10)

Mmax

with g(z) monotonically increasing, anti-symmetric and bounded, g(z)=-g(-z) and \g(z)\ < 1 for all z, a Liupunov controller can be designed by minimizing the time derivative of the Liapunov function along the solution of the system with respect to u(t). This yields the following bounded controller u(t) = -umaxg(a-,BTPx(t)) For a stable controller, P is selected as the solution of the Liapunov equation for any positive definite matrix Q. r ATP + PA = -Q

(11)

(12)

To illustrate that this nonlinear controller can achieve deformation reductions comparable to those of an LQR controller but with significantly smaller maximum force requirements, the response of the frame structure with LQR controller and nonlinear Liapunov controller is computed for the El Centro signal. The nonlinear controller is designed as N(t) =

^-tan-" (arxBrPx(f)) n

(13)

307

Q is taken as a block diagonal matrix with LTDLD and the identity matrix / in the diagonal, and umm is taken as a fraction of the building weight. The results are presented in Table 2. NLC 0.05 means umax = 0.05trace(Mg)

where g is the

acceleration of gravity. Table 2. Peak responses of steel-frame subjected to El Centro. Controller

Peak force/ trace (Mg) 0.192 LQR NLC 0.05 0.0470 NLC 0.10 0.0939 NLCE0.10 0.0864 FD 0.03 0.03

Drift 1 (cm)

Drift 2 (cm)

2.50 2.54 2.51 2.54 2.72

1.43 1.65 1.67 1.63 1.99

Drift 3 (cm)

Drift 4 (cm)

Drift 5 (cm)

Drift 6 (cm)

2.08 2.26 2.56 2.28 2.51

2.23 2.62 2.79 2.51 2.64

2.82 3.10 2.97 2.88 2.85

2.32 2.31 2.51 2.36 2.26

The results corresponding to NLCE 0.10 correspond to a particular selection of Q that yields the mechanical energy of the structure. For comparison, the response of the structure with optimum level of friction damping (FD) is also presented in Table 2. For this structure and an excitation model given by the El Centro signal, the optimum yield force in the friction dampers is around 3% of the building weight. As these results indicate, nonlinear controllers with maximum force requirements of 5% of the weight of the structure can render drift reductions comparable to those achieved by LQR with maximum forces of about 20% of the weight. It is worth noting that the nonlinear controllers have not been optimized with respect to a. It is also worth mentioning that friction dampers (FD) can provide performance levels similar to those achieved by nonlinear controllers. 3 Semi-active dampers Two alternative controller designs of semi-active systems are considered in this section: (i) semi-active damper as an actuator for realizing an LQR controller, and (ii) improved hysteresis is SAD through collocated controller design. 3.1 LQR realized through semi-active damper Consider a semi-active viscous damper with controllable viscous constant c(t) (in fact the semi-active viscous damper may show nonlinear dynamic behavior and internal dynamics due to compressibility of the fluid). Consider an LQR controller

308 designed for the structure with optimal control force given by Eq. (10). A feasible implementation of this controller using SAD is c(t) = u(t)/A(t)

if

c(0=0

if

u(t)A(t)<0

(14)

u(t)A(t)>0

Table 3 compares the maximum drifts and maximum force requirements of this controller (SA LQR) compared with the corresponding LQR controller for the same simulated earthquake. The results show that clipped optimal control performs as well as the fully active LQR strategy with comparable maximum force levels. While still it may be technologically unfeasible to provide 20% of the building weight with variable dampers, it is by far more feasible than hydraulic actuators realizing an LQR controller. Table 3. Comparison of LQR and clipped LQR controller (SAD LQR) performance

Controller Peakforce/ trace(Mg) 0.192 LQR SALQR 0.233

Drift 1 (cm) 2.51 2.46

Drift 2 (cm) 1.43 1.47

Drift 3 (cm) 2.08 2.10

Drift 4 (cm) 2.23 2.23

Drift 5 (cm) 2.82 2.80

Drift 6 (cm) 2.32 1.91

3.1.1 Can semi-active dampers realize an LQR controller with accuracy ? The ability of SAD to follow an LQR controller can be explained from a probabilistic perspective. A semi-active damper can apply the same control force as the LQR when sgn(GxA) > 0, that is when the LQR control force dissipates energy, u(t) A(t) < 0. It seems appropriate then to analyze the probability of this event for the closed-loop structure controlled with LQR and subjected to a stationary broadband process. Given a structure with LQR controller subjected to stationary Gaussian white noise process, the probability of interest can be computed by transforming to independent unit-variance variables the zero-mean joint Normal random variables u(t) and A(t) with covariance matrix

PIZ=E[[u(t)

A(t)]T[u(t)

A(f)]] =

E[u(t)A(t)] E[u(t)A(t)]

„2

(15)

which can be computed relating z(t)=[u(t) A(t) ]T to the state of the system x(t) and computing the stationary covariance matrix P^ ofx(t). Let's define z(t)=Lzx(t), then P22=LZPXXLTZ

(16)

309 Let O be the orthogonal eigenvector matrix, <J? O = / , and A be the diagonal matrix with the eigenvalues of P K , then A^r r 77 = A 2 0 z = [v(

1 v2Jz

(17)

is a random vector with zero-mean unit-variance Gaussian independent random components. The probability P[u(t)A(t) > 0] can be computed easily in the transformed domain (see Fig. 4) by computing the angle 6 between vectors v, and v,: 0 = cos~'(-

v,||

ii

(18)

and computing the probability as an angle ratio: P[u(t)A(t)<0] = —

(19)

n This probability approaches / as the correlation coefficient between A(t) and Gx(t) goes to 1. To illustrate that in fact LQR controllers designed for deformation reduction of lightly-damped conventional structures apply dissipative control forces in the structure, let us compute in simple structural models, the stationary state covariance matrix of the structure, the trace of the inter-story-drift covariance matrix, the correlation coefficient between kit) and Gx(t), and the probability given in Eq. (19). For simplicity, let us consider first a two-story building model with a controller in the lower level. The masses of both levels and the stiffness of both levels are assumed equal. The modal damping ratios of the uncontrolled structure are assumed as 1% . The LQR controller is designed to reduce inter-story drifts (see Eqs. 4 and 7) for a range of values of r.

Gx(t)A(t)>0

r) = A2Tz

zi=Gx

Figure 4. Computation of probability in transformed space f]i,T]2.

310 Figure 5 shows in thick line the achieved drift reduction J(r) = -JtraceiP^ ) normalized with respect to the uncontrolled structure J(0), the correlation coefficient and the probability of dissipative control force as a function of the parameter r. For values of r that provide significant marginal drift reductions, the correlation coefficient is larger than 0.95 and the probability of a dissipative control force is larger than 90%. This behavior of an LQR controller will repeat in lightlydamped structures with low and medium level controllers. These high probabilities explain why a clipped LQR controller realized by means of a variable viscous or ER damper can yield performances comparable to LQR controllers in conventional structures. To illustrate a type of structure in which the LQR controller is not dissipative, let us consider two SDOF structures, a main structure and an auxiliary structure coupled by an actuator. The controller is aimed at vibration reduction of the main structural system using the auxiliary structure as a reaction frame. Let the main structure be lightly damped (1% of critical damping), let both structures have the same mass, let the auxiliary structure be damped with 10% critical damping, and let it have a natural frequency three times larger than the main structure. Defining an LQR performance index with a diagonal matrix Q, with coefficients in the diagonal: 1 for the deformation of the main structure and 0.01 for the auxiliary structure, and a range of values of r, the rms deformation of the main structure, J(r)=a , normalized by the rms deformation of the uncontrolled structure, J(0), is computed for the system subjected to white noise support acceleration. Figure 6 shows the results obtained. Not only we see low values of probability of dissipative LQR forces but we also see negative correlation coefficients between A(t) and Gx(t) for strong controllers; this means that a strong LQR controller aimed at energy transfer inputs energy to the system in the mean, something a variable damper cannot do at all. The LQR controller then plays the role of energy transfer rather than energy dissipation in this case. In this type of vibration reduction situation, a clipped LQR controller would perform poorly compared with the corresponding linear LQR controller because with high probability the semi-active damper would not be able to follow the LQR control signal. An even more interesting example of energy transfer can be obtained in a lightlydamped structure with a damped optimum tuned mass damper (TMD) whose performance is to be enhanced by an actuator connecting the TMD to the structure. Again, the LQR controller can yield very low probabilities of dissipative control forces (see Fig. 7) and consequently, can not be realized successfully with a variable damper.

311

• &

1

;orrel
Ilea

m0-4

I

/

^

I

Prob[Gxd/dt(A)>o/7

/ /

/ /

Prob[Gxd/dt(A)>0)

J(r)/J(0)

/

Correlation / Coefficient /

/j(*0(0)

y

/


./

•

Correlation Coefficient

^ ^ logtO(r)

Iog10(r)

Figure 5. Probability of dissipative LQR control force in conventional structure.

Figure 6. Probability of dissipative LQR force in interacting structures.

mm ^Z Prob[Gxd/dt(A)>0}

! :

: Correlation Coefficient

— / /

:

Iog10(r)

Figure 7. Probability of dissipative LQR control force in structure with TMD.

These simple results illustrate that in the case of active mass dampers, active controllers can yield significantly better performance than that attainable by passive damping (see J(r)/J(0) in Fig. 7), dynamical systems in which energy transfer prevails over energy dissipation. Although a clipped LQR strategy is not a suitable strategy for vibration reduction in these cases, semi-active dampers can be successfully used in interacting structures using other controllers [8,9].

312

3.2 Variable-friction dampers Several control algorithms have been proposed for variable friction dampers and variable yield-stress fluid dampers (MR dampers). Only work developed by the author on this topic is presented here. Collocated controllers aimed at enhancing the hysteresis loops of the device are presented [9, 10, 11, 12].

3.2.1 Modulated homogeneous friction Modulated homogeneous friction (MHF) [10], a control algorithm for variablefriction dampers or MR actuators, is a collocated dynamic feedback law that uses the deformation of the damper A(f) as the only feedback signal for the control of the yield force of the device: Fy(t) = kd\P[Mt)] (20) where Fy(t) = yield force of the device, kd = positive gain coefficient with units of stiffness and P[A(t)] = prior-local-peak operator, value of the closest prior local maximum or local minimum of the deformation signal. When operated with the proposed control law (Eq. 33), the force in the semi-active damper is given by /[A(0] = kd | P[A(0] | sgn(A(0) (21) The dynamic behavior of structures with MHF actuator has been analyzed in detail elsewhere [10]. Results obtained for benchmarking this controller with LQR are shown in Table 8. The results shown illustrate the high efficiency of the controller in reducing inter-story drifts with relatively low levels of peak force. 3.2.2 Amplitude-modulatedfriction (AMF) In the case of MHF (Eq. 21), the capacity of the friction device was selected to be linear in | H[A(t)] | so as to maintain homogeneity of degree one in the deformationforce relation. Although from an analysis point of view this is a convenient feature that permits very accurate linearization techniques and simplified analysis of the controlled structure [10], from a performance perspective nonlinear relationships between capacity and amplitude of vibration of the type: Fy(t) = h(\P[A(t)\) (22) offer better performance when the yield force capacity of the semi-active damper is limited. In Eq. (22) h(.) is a positive monotonically increasing function for positive

313 argument. For example, if the actuator force is to be bounded by a maximum value F0, the following is a convenient control law: Fy(t)=^tan-l(b\P[A(t)\) y n

< 23 )

With b a positive constant that controls the variation of capacity of the friction device with the amplitude of vibration. Table 4 compares the drift reductions and peak force requirements of MHF and AMF with those achieved using an LQR controller. MHF 0.062 indicates the assumed value of kd I K{\,\) = 0.062, AMF 0.05 indicates that F0 ltrace{Mg) = 0.05. As in the case of passive friction, an increase in the yield capacity may turn out to be deleterious, producing an increase in the inter-story drifts of the higher levels. Since the device is operated as an enhanced friction damper, the distribution of the variable-resistance dampers over the height of the building is recommended. Table 4. Performance of structure with MHF. Controller LQR MHF 0.062 AMF 0.05 AMF 0.10

Peakforce/ Trace(Mg) 0.192 0.034 0.049 0.097

Drift 1 (cm) 2.51 2.51 2.60 2.39

Drift 2 (cm) 1.43 1.79 1.94 2.09

Drift 3 (cm) 2.08 2.37 2.58 2.62

Drift 4 (cm) 2.23 2.50 2.54 2.38

Drift 5 (cm) 2.82 2.98 2.83 2.83

Drift 6 (cm) 2.32 2.28 2.00 2.32

3.2.3 A new modulated homogeneous friction (MMF) controller The following aspects motivated the development of the MHF controller presented above: (i) simplicity of the controller, (ii) homogeneity of degree one so as to ease the design, and (iii) rectangular hysteresis loops to maintain the efficiency of passive friction dampers that maximize the energy dissipation per cycle for a given maximum force applied to the structure. Another motivation in the creation of this controller was to keep in the semi-active damper, a rate-independent behavior following the fact that linear hysteretic damping offers better performance than linear viscous damping in terms of deformation reduction and maximum accelerations in the controlled structure [4]. Although a rectangular hysteresis loop shows maximum efficiency in terms of energy dissipation per cycle for a given maximum force in the damper, it is not

314 necessarily the most efficient shape in terms of maximum base shear. The reason is that it is the sum of the elastic force and the dissipative forces what produces the maximum shear on the foundation of the structure. It is apparent that for a SDOF structure with dampers that provide rectangular hysteresis (such as dry friction), the maximum shear will coincide in time with the maximum contribution of elastic forces to the base shear which in turn coincides with peaks of the deformation signal. Thus, a new MHF controller is proposed that reduces the damper force as a function of the current deformation, so as to reduce the maximum total force transmitted to the adjacent floors of the structure in the vicinity of local peaks of the deformation signal. The proposed new MHF algorithm is

Fy (t) = kd | P[A(t) 11 (1 - y I - j ^ - 1 ) I // P[A(0] * 0, | P[A(0 |>| A(/) | L WJ Fy(t) = 0 ifP{A(t)]=0, or | P[A(t) \<\ A(01

(24)

where kd is the gain parameter of the controller with stiffness units; y is a dimensionless hysteresis-shape factor; 0
Figure 8. Hysteresis loops of MHF controller at constant deformation amplitude.

Table 5 demonstrates the efficacy of the new controller in reducing simultaneously deformations and absolute accelerations (base shear divided by mass) in a singledegree of freedom model of a structure subjected to ground acceleration. The

315 structure has a natural frequency co = nradl s , and the SAD are characterized by

kd = pmco1. Applied in base-isolated multi-degree of freedom systems, the modified MHF controller yields also lower base shears. However, the system excites high frequency modes producing higher floor accelerations than those obtained with the original MHF controller. Table 5. Performance of SDOF structure with MHF subjected to the El Centra signal. Max(/7m) (cm/s2)

P

Max(£») (cm)

No control

-

31.9

(cm/s2) 315

MHF

0.15 0.30 0.45 0.48

14.6 11.4 12.6 12.3

165 133 129 128

21.6 33.7 55.9 57.7

MHF

0.30 0.60 0.90 0.95

14.2 12.5 10.7 10.9

141 124 105 107

41.8 73.6 89.9 101

7

=1

Max(g)

-

4 Conclusions Bounded nonlinear controllers for fully active systems have been proposed as an alternative for LQR; they offer satisfactory performance in terms of deformation reduction (provided it is adequately tuned for a given ground motion intensity) and significantly smaller force requirements than LQR controllers. It has been demonstrated that LQR controllers do not yield significantly better performance than passive dampers in the case of lightly damped conventional structures subjected to broad band excitation. On the other hand, a fully active system can provide energy transfer which plays a significant role in vibration reduction in the case of interacting structures and structures with TMD. It is precisely in these cases where active systems outperform passive damping systems which are limited in the capacity of energy transfer. This fact, combined with the significantly lower force requirements of active controllers in TMD applications, makes the hybrid mass damper a very suitable strategy for wind-induced vibrations in building and bridge structures.

316 Three strategies for semi-active dampers have been studied. Using probabilistic arguments it has been demonstrated that semi-active dampers can realize LQR controllers with excellent performance in the case of lightly-damped conventional structures, and for its very low power requirements should be preferred in these types of applications. Semi-active dampers offer also promising alternatives for efficient damping mechanisms; especially in the case of enhanced dissipaters that require deformation feedback and no state estimation, which implies a minimum level of complexity and, at the same time, ample flexibility for design. Further analysis and experimental verification is considered appropriate for the validation of the numerical predictions of the dynamical behavior of structures with MHF dampers.

References 1. D. Karnopp, M. J. Crosby and R.A. Harwood, Journal of Engineering for Industry, Vol 96, pp. 619-626 (1974). 2. D. Hrovat, P. Barak, and M. Rabins, Journal of Engineering Mechanics Vol. 109, No. 3., pp. 691-705 (1983). 3. Kobori et al., Device and method for protecting a building against earthquake tremors, U.S. Patent 4,922,667 (1990) 4. J. A. Inaudi, Ph.D. Dissertation, University of California at Berkeley, (1993). 5. S. J. Dyke and B. F. Spencer, Proc. Intelligent Information Systems, pp. 580-584, H. Adeli, editor, IEEE Computer Society, Los Alamitos, California, (1997) 6. N. Kurata et al, Earthq. Engineering and Structural Dynamics, Vol. 29, 629-645, (2000). 7. G. Yang, J. C. Ramallo, B.F. Spencer, J.D. Carlson, and M. K. Sain, Proc. 14th ASCE Conf. Eng. Mechanics, Austin, TX, (2000) 8. J. C. Hayen and W.D. Iwan, Proc. First World Conference on Structural Control, Vol. 1, pp. WA2-23-WA2-32, ( 1994). 9. J. A. Inaudi and J. Hayen, Proc. Post Smirt Seminar on Seismic isolation,Passive Energy Dissipation and Control of Vibrations ofStructures, Santiago, Chile, (1995). 10. J. A. Inaudi, Earthquake Engineering and Structural Dynamics, Vol. 26, pp. 361-376, (1997). 11. J. A. Inaudi and J. M. Kelly, Nonlinear homogeneous dynamical systems. Report Ne UCB/EERC-93/11, University of California at Berkeley, (1995). 12. H. Kurino and T. Kobori, Proc. 2 Worl Conf. Str. Control, Vol. 1, pp. 407-416, (1999).

A BENCHMARK PROBLEM FOR STRUCTURAL HEALTH MONITORING AND DAMAGE DETECTION E.A. JOHNSON University of Southern California, Los Angeles, CA 90089 E-mail: JohnsonE@usc. edv H.F. LAM and L.S. KATAFYGIOTIS Hong Kong University of Science and Tech., Clear Water Bay, Kowloon, Hong Kong E-mail: [email protected], [email protected]' J.L. BECK California Institute of Technology, Pasadena, CA 91125 E-mail: jimheck@caltech. edu

Structural health monitoring (SHM) is a promising field with widespread application in civil engineering. However, many SHM studies apply different methods to different structures, often making side-by-side comparison of the methods difficult. This paper details the first phase in a benchmark SHM problem organized under the auspices of the IASC-ASCE Structural Health Monitoring Task Group. The scale-model structure adopted for use in this benchmark problem is described. Then, two analytical models based on the structure — one a 12DOF shear-building model, the other a 120DOF model, both finite-element based — are given. The damage patterns to be identified are listed as well as the types and number of sensors, magnitude of sensor information, and so forth. More details are available on the Task Group web site at wusceel.cive.wustl.edu/asce.shm/ .

1

Introduction

Structural health monitoring (SHM) systems seek to monitor the state of a structure's "health" — that is, the level of damage or deterioration within a structure. SHM has application for all types of structures. For civil engineering purposes, detecting the damage caused by an earthquake or monitoring the long-term deterioration due to the environment and human use (and abuse) can provide vital information on structural safety. Recent seismic disasters, including those in the past year in Turkey and Taiwan, demonstrated yet again the damage caused by earthquakes that occur in or near urban areas. The Hector Mine earthquake in the California desert in the Fall of 1999, though far from major population centers, served to remind us again of the continued need to be prepared for future seismic events. The level of structural damage caused by an earthquake is sometimes immediately obvious (e.g., a building that has toppled over), but damage is often hidden within a structure, such as damaged joints embedded behind walls or encased in concrete. Such damage is difficult and expensive to discover by visual inspection, but may still pose a risk to the health and integrity of the structure. SHM systems may prove invaluable in future urban earthquakes by giv317

318 ing quick assessments of the damage level of a structure shortly after the quake itself. Not only does this give a building owner knowledge of what and where damage may have occurred, but also whether immediate evacuation of the occupants/contents of the structure is necessary. Currently, acquisition of sensor information is not a crucial issue. Several recent workshops and symposia on SHM and Damage Detection (e.g., [1]) have demonstrated significant developments in sensor technologies for a variety of monitoring purposes. However, these meetings also generated general agreement that the critical problem now is not the acquisition of information, but rather the algorithms to process the vast wealth of information and provide useful and simple measures of a structure's current health status. There have been numerous studies by researchers around the world applying various SHM techniques (the interested reader is directed to the review article by Doebling et al. [2]). A difficulty, however, is that the various studies apply different methods to different structures, rendering side-by-side comparison difficult. A benchmark study, where participants apply a number of monitoring techniques to a common structure with common objectives, provides a platform for consistent evaluation of the proposed SHM methods. One such recent benchmark study was initiated at the 15' International Modal Analysis Conference (IMAC XV) and is detailed in Black and Ventura [3]. This study was a "blind test" in that the participants were provided with forced vibration response data of a scale-model steel frame structure in undamaged and damaged (certain elements removed from the frame) states but with no knowledge of the level or location(s) of damage. The task, then, was to identify where the damage had occurred. The blind test is, of course, a realistic measure of the performance of different SHM methods. However, it makes it difficult for researchers to understand the advantages and disadvantages of the methods, particularly the sensitivity to various aspects of the problem, such as full/limited sensor information, the effects of noise, and so forth. In the end, only one paper was actually submitted to the next IMAC conference directly addressing this blind test [4]. Presumably, researchers were a bit leery of the completely blind nature of the study. At the 1996 International Workshop on Structural Control [5], a plan was formed to create task groups to study the problem of structural health monitoring. Three task groups — one per region (Europe, Asia, US) — were to be formed. The US task group solidified in 1999 jointly under the auspices of the US Panel of the International Association for Structural Control (IASC) and the Dynamics committee of the ASCE Engineering Mechanics Division, with Prof. James L. Beck (Caltech) as chair. This joint IASC-ASCE task group met first in June 1999 at the 13th ASCE Engineering Mechanics Conference at Johns Hopkins University, and has two subsequent meetings (Caltech, August 1999; USC, February 2000). The task group is charged with studying the efficacy of various structural health monitoring methods. The IASC-ASCE SHM Task Group is developing a series of benchmark SHM problems, beginning with a relatively simple problem and proceeding on to more realistic (but more difficult) problems. This paper details the first phase of this study, based on simulation of a test structure that forms the cornerstone of the work, including the motivation for the structural model as well as the data generation mecha-

319

eisms. Subsequent papers in this same session apply several SHM methods to this common benchmark problem. Later work • will involve analysis of experimental data from the test structure. 2

The Benchmark Structure

The Task Group decided'that the use of simulated data from an analyticalstructural model based on an existingstructure would allow for future comparisons with data taken on the actual structure. Starting with simulated data allows participants to better understand the sensitivities of their methods to various aspects of the WM¥en$ur&'; problem, such as difference between the identification model and the true Figure 1. Steel-frame-scale "structure. model, incomplete sensor information, and the presence of noise in measurement signals. Since the earlier "blind test** study was based on data from a scale-model structure, the Task Group chose to use an analytical model based on the same structure. The structure (Black and Ventura, 1998), shown in Fig. 1, is a 4-story, 2-bay by 2-bay steel-frame scale-model, structure in the Earthquake Engineering Research Laboratory at the University of British Columbia (UBC). It has a 2.5 m x 2.5 m plan and is 3.6 m tall. The members are hot rolled grade 300W steel (nominal yield stress 300 MPa (42.6 kpsi)). The sections are unusual, designed for a scale model, with properties as given in Table 1. There is one floor slab per bay per floor: four 800 kg slabs at the first level, four 600 kg slabs at each of the second and third levels, and, on the fourth floor, either four 400 kg slabs or three 400 kg and one< 550 kg to create some asymmetry (discussed further below). Table 1. Properties of structural members. Property

Columns

Floor Beams

1 section type 1 cross-sectional area A [m2] 1 moment of inertia (strong direction) Iy [m ]

B100x9 1.133X1CT3 1.97X10"6

S75xll 1.43xl(T3 1.22x10*

(moment of inertia (weak direction) Iz [m ] | St. Venant torsion constant J [m ] hfoung^sModulus £ [Pa] § Mass per unit length p [kg/m]

.664x10*

.249x10*

8.01X10"9 2xl0n 8.89

38.2xl0~ 9 2xlO n 11.0

Braces

1

L25x25x3 J 0.141xl0~3 1

~~

0 0

I 1

0

j

i

2xlQn

r

l.n

i

320

Two finite element models based on this structure were developed to generate the simulated data. The first is a 12DOF shear-building model that constrains all motion except two horizontal translations and one rotation per floor. The second is a 120DOF model that only requires floor nodes to have the same horizontal translation and in-plane rotation. The columns and floor beams are modeled as Euler-Bernoulli beams in both finite element models. The The w; are excitations. The y,-,- are accelerometer meabraces are bars with no surements (the jilc and yi(i in the x-direction are omitted bending stiffness. A diafor clarity). The braces andfloorbeam drawn with dashed gram of the analytical lines are ones damaged in damage patterns (m)-(v). model is shown in Fig. 2. The finite element models, by removing the stiffness of various elements, can simulate damage to the structure. Five damage patterns are defined for the structure: (0 all of the first floor braces removed, (ii) all of the first and third floor braces removed, (Hi) one brace removed in first story (drawn as dashed line in Fig. 2), (iv) one brace removed in each of the first and third stories (drawn as dashed line in Fig. 2), and (v) as the previous damage pattern but with the floor beam from (2.5m, 0, 0.9m) to (2.5m, 1.25m, 0.9m) partially unscrewed from the column at (2.5m, 0, 0.9m) (consequently, the beam-column connection there can only transmit forces and cannot sustain any bending moments). 3

12DOF Shear-Building Model

The structure is assumed to act as a shear building in the 12DOF model, with 3DOFs/ floor (translation in the x- and ^-directions, and rotation 8 about the center column). A MATLAB® based finite element analysis code* is used to compute mass M, damping C d , and stiffness K matrices. The model has story stiffnesses as shown in Table 3. The natural frequencies are given in Table 2 for the undamaged case and

t The codes and data are available on the Task Group web site: wusceel.cive.wustl.edu/asce.shm/.

321 Table 2. Natural frequencies [Hz] of analytical models. Modes with weak direction dominant motion are shaded.

Damage Pattern (ii)

Damage Pattern (i)

Undamaged

st

12DOF 9.41 y 11.79 * 16.53 0 25.60? 32.07* 38.85? 45.17 0 48.37 ? 48.68* 60.60* 68.64 0 85.51 0

no 1 story braces 12DOF 120DOF 6.24? 4.91? 9.91 * 6.61 * 11.84 0 8.82 0 21.58? 18.38? 28.99* 21.06* 37.56? 32.56 6 38.75 G 33.98 ? 47.57 * 38.09 * 48.19? 45.80? 60.45 * 54.68 * 66.46 0 58.110 85.20 0 78.80 0

120DOF 8.20 y 8.53* 13.95 0 22.54? 24.24* 35.58? 39.05 0 39.73 * 46.12? 55.16* 60.75 0 79.46 0

no 1st, 3 story braces 12DOF 5.83? 9.52* 11.13 0 14.93? 24.98* 28.78 0 36.28? 41.65? 47.06* 54.76* 64.86 0 74.27 0

120DOF 4.36? 5.77* 7.74 0 10.26? 15.22* 18.32 0 33.80? 37.47? 37.83* 47.81* 58.01 0 66.38 0

Table 3. Horizontal story stiffnesses.

Stry

X-dir. (strong) [MN/m] undmgd

dmgd(i')

"T" 106.6

58.4 106.6 106.6 106.6

2 3 4

106.6 106.6 106.6

9.41Hz

y-dir. (weak) [MN/m]

dmgd(ii') undmgd

58.4 106.6 58.4 106.6

67.9 67.9 67.9 67.9

dmgd(i')

rotation [MN-m]

dmgd(i'i) undmgd

19.7 67.9 67.9 67.9

19.7 67.9 19.7 67.9

232.0 232.0 232.0 232.0

11.79 Hz

Figure 3. First 3 mode shapes of the 12DOF model.

dmgd(i)

dmgd(i'i)

81.3 232.0 232.0 232.0

81.3 232.0 81.3 232.0

16.53 Hz

322

damage patterns (i) and (ii). The mode shapes of the first three modes are shown in Fig. 3. 4

120DOF Model

ASCL B o r

Most structures are not as simple as engineers often model them, which leads to the presence of model error. To include model error effects in this benchmark study, a more complex 120DOF model was constructed using finite elements. This model is used to simulate the response measurements, while the model used in the identification analyses remains the (simpler) 12DOF shear-building model. The 120DOF model constrains the horizontal translation and rotation (about the ..

t

. ,

r .

,

, ^

x

.

^

Rob. w DA] ,

^ ^

F;;^

'; €mE v-%w^.}^mm^h....^. **jfe**** ; - ™ „ <™mt , M I ^ ; « .- > *«__«^^ "' m£ 3: n#$ iwmmhl MM^I ', %A$%4:Vim$ l^mrmmubad^tod ~™^^ [.... ^ j j j y 0 F im^^^^l h^m^ *>^___^ „. . 1onr ,^ c ^ TTT . _ Figured 120DOFGUI start,

vertical axis) of the nodes in each floor to be the same. The horizontal slab panels are assumed to contribute only towards the inplane stiffness making the floor behave as rigid with respect to in-plane motions only. The remaining out-of-plane degrees of freedom (namely, vertical motion and pitching/ rolling of the floor) are active. The resulting natural frequencies, given in Table 2 for undamaged and damage patterns (i) and (ii), are lower than those of the 12DOF case due to fewer constraints. The horizontal story stiffnesses are the same as in Table 3. The data generation program for the 120DOF model (with the option of running the 12DOF code as well) is available on the Task Group web site. These codes present a graphical user interface (GUI) that allows the user to pick which case to run (see Fig. 4), what damage pattern to use, and even to select a user-defined damage pattern. 5

Simulation Cases

The finite element models (either the 12 or 120 DOF models) give a structural model in terms of active degrees of freedom q, related to physical degrees of freedom by x = Tq . The equation of motion is Mq + C d q + Kq = T T f where f is a vector of forces applied to the physical degrees of freedom. Sixteen accelerometers, two each in the x- and j-directions per floor, return noisy sensor measurements: y - Cq + Df + v where v is a sensor noise vector, the elements of which are Gaussian pulse processes with RMS 10% of the RMS of the roof acceleration. The matrix of simulation cases of this benchmark problem on which the Task Group is currently working is shown in Table 4. Figure 2 depicts the scenario for the first two simulation cases, which is a one-dimensional analysis in the weak (y) direction. The excitations are applied one per floor, and are modeled as filtered Gaussian white noise (Gaussian white noise processes passed through a 6 th order low-pass Butterworth filter with a 100 Hz cutoff.) The data generation uses a discrete-time inte-

323 Table 4. Simulation case matrix of current Task Group work.

Ca ses Description

1

2

(lD+noise) (+ model error) (weak dir.)

X

4

5

6

(roof excit)

(3D)

(+ model error)

(+ limited sensors)

X

X X

X

X

X

X

X X

X X

X

X

X

X

X

X

X X

X X

X X

a b

a b

b

b

b

X

X

X

X

X

X

X

X

X

X X X X

X X X X

c

X X X X

Data generation model: 1. Floors rigid (USC 12DOF) 2. Floors rigid in-plane (HKUST 120DOF) Mass Distribution: 1. Symmetric (four 400kg masses on roof) 2. Asymmetric (three 400kg, one 550 kg) Excitation: 1. "Ambient" 2. Shaker diagonal on roof ID Model: linear 12DOF shear building ID Data: 4 sensors/floor w/10% RMS noise 1. Known input 2. Unknown input 3. Unknown input; sensors on 2 ,4 floors Damage Patterns: remove the following i. all braces in 1 st story ii. all braces in 1 st and 3 stories Hi. one brace in 1 st story iv. one brace in each of 1 st and 3 stories v. as iv, and loosen floor beam at 1 st level

3

gration at IkHz and provides the sensor measurements at IkHz; participants in the study may use a lower sampling rate (to reduce computational effort, for example). Subsequent cases add additional realism. Case 3 replaces the "ambient" excitation with a shaker on the roof (assumed to excite at the top of the center column in a direction ± ( i - j ) , where i and j are unit vectors in the x- and v-directions, respectively). Although the structure is excited in two directions, only the v-direction is to be analyzed for Case 3. Cases 4—6 introduce asymmetry by replacing one of the 400 kg floor slabs on the roof (the one with hatched shading in Fig. 2) with a 550 kg slab, and are analyzed with 3-D motion of the floors. Case 4 reverts to the 12DOF data generation model, but case 5 brings model error back into the picture. Case 6 decreases the number of sensors by 50% and introduces damage pattern (v). 6

Conclusions

The first phase of a benchmark problem in structural health monitoring has been detailed. The IASC-ASCE Task Group on Structural Health Monitoring is currently studying this phase. The remainder of the papers in this session apply various SHM

324

methods to this phase of the benchmark problem. A session is also planned for the 3IWSC in Paris this summer. The Task Group would appreciate any comments or suggestions on this work. More details on this study, as well as the current and future efforts of the Task Group, are available on the web at wusceel.cive.wustl.edu/ asce.shm/ 7

Acknowledgements

The authors wish to thank the other members of the IASC-ASCE SHM Task Group for their assistance, suggestions, and cooperation in the development of this benchmark problem; particularly: Dionisio Bernal (vice-chair, Northeastern Univ.), Raimondo Betti (Columbia Univ.), Joel P. Conte (UCLA), Shirley J. Dyke (Wash. Univ. St. Louis), Sami F. Masri (Univ. of Southern California), Andrew Smyth (Columbia Univ.), and Carlos E. Ventura (Univ. of British Columbia). Thanks especially to Prof. Ventura for the photograph of the UBC frame, and to Prof. Conte for assistance in calibrating the finite element models described herein. References 1. Chang, F.-K. (1999). Structural Health Monitoring, Proceedings of the 2 nd International Workshop on Structural Health Monitoring, Stanford University, September 8-10, 1999, Technomic Publishing Co., Lancaster, PA. 2. Doebling, S.W., C.R. Farrar, M.B. Prime, and D.W. Shevitz (1996). "Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in their Vibration Characteristics: A Literature Review." Los Alamos National Laboratory Report, LA-13070-MS (http://www.lanl.gov/projects/ncsd/pubs/lit_review.pdf). 3. Black, C.J., and C.E. Ventura (1998). "Blind Test on Damage Detection of a Steel Frame Structure." 16th International Modal Analysis Conference (IMAC XVI), Santa Barbara, California, February 2-5, 1998. Proceedings, 623-629. 4. Park, S., N. Stubbs and R.W. Bolton (1998). "Damage Detection on a Steel Frame Using Simulated Modal Data." 16th International Modal Analysis Conference (IMAC XVI), Santa Barbara, California, February 2-5, 1998. Proceedings, 612-622. 5. Chen, J.C., ed. (1996). Proceedings of the Second International Workshop on Structural Control: Next Generation of Intelligent Structures, Hong Kong, December 18-21, 1996. Available on the web pages of the US Panel on Structural Control Research http://cwis.usc.edu/dept/civil_eng/structural/welcome.html.

COMUNITY RESEARCH ACTIVITES ON COSTRUCTIONS COMPETITIVE AND SUSTAINABLE GROWTH RTD PROGRAMME

G. KATALAGARIANAKIS European Commission, Directorate General RTD Research, Technology and Development E-mail: georgios. [email protected] The construction sector is of prime significance in the economic activity of the European Union Industry. It is highly fragmented, labour intensive sector presenting continuous opportunities for development and use of advanced technologies, materials and processes. Structural Control is a challenging subject for the sector on which technology developers and users are spending considerable efforts. The Framework programme of the European Union is trying to help resolve some of these challenges at European level and supports in consequence all stakeholders in their collaborative and joint research efforts.

1

The Construction Sector

Total construction activity within the European Union is estimated at about 750 billion Euro (for 1996) with about one third of it talcing place in Germany and with the activity in the UK, FR, IT and ES ranging from 9,1 to 12,4% of that amount. Total direct employment is estimated at 8.8 million persons, about a quarter of which are self-employed. Adding about 0.8 million jobs in design and engineering and 2.5 million in the construction products sectors, a total of 12.1 million jobs are directly related to construction. Indirect employment is estimated at 14.3 million people giving a total of 26.4 million. Construction activity is therefore responsible for about 10-12% of GNP or 25% of all manufacturing. The sector is extremely fragmented. There are more than 2 million enterprises the vast majority (93%) of which employ less than 10 persons (97% employ less than 20), though they count for 43,5% of total employment and for 34,2% of total turnover. Big enterprises with more than 500 employees are about 700 (about 0,03%) counting for 10.4% of employment and 15.8% of turnover. The EU has about 45 large contractors with an annual turnover in excess of 1 billion EURO (1992 prices). The EU does not have very large contractors such as Fluoz Daniel, Bechtel or Shimizu. This situation accounts for some slower progress in regarding concepts, processes and technologies. In particular, the increase, in the use of IT, is less spectacular than in the USA and Japan. In addition, the relatively low building replacement rate (2%) in connection with a strong public requirement to preserve and maintain cultural heritage result in substantial maintenance and refurbishment activity which is highly labour intensive 325

326

involving traditional building techniques. However, technological progress is now felt in the construction industry in several ways. Construction remains a large consumer of building materials that integrates considerable amount of technological evolution. It uses machines and equipment that integrate latest advances in mechanical engineering. Better knowledge of environmental aspects allows for improved control of in-door environment, use of new materials for minimal environmental impact and correct practices in demolition and recycling operations.

2

European RTD Activities

2.1

European Union Research

It should be noted that RTD work in the European Union is taking place on several levels. There is the clearly private research, which is done by the enterprises concerned, with their own means or by subcontracting the research work. In these cases the sources of information are the enterprises themselves or the scientific publications. Work is also done on a national level by building research institutes, academia and industry supported by government and/or industry. It is recognised that single companies or individual Member States cannot resolve their problems alone because of the highly international and even global character of industry and trade. A major objective of the Community research policy is therefore to achieve a leveraging effect on selected topics, even though the Community funding only represents 4% of total EU public research funding as well as 4% of the European Union budget (about 3000 millions ECU per year). Today all efforts have to be directed towards a sustainable growth, necessary condition for preservation and creation of employment. This sustainable growth has obviously to be supported by innovation and research efforts, in particular keeping in mind the interests and the role of SMEs which represent more than 99% of the European enterprises. The EU research policy is above all to stimulate integrated approaches with a high European added value in fields where the single national efforts are not sufficient. The Fifth FWP (1998-2002) is mainly organised around four Thematic Programmes and three Horizontal Programmes.

327

Tablel THE FIFTH FRAMEWORK PROGRAMME (1998-2002) Funding (Meuro) Thematic Programmes Quality of life and management of living resources

2413

User-friendly information society

3600

Competitive and sustainable growth

2705

Energy, environment and sustainable development

2125

Horizontal Programmes International role of Community research

475

Innovation & encouragement of SME participation

363

Human research potential /socio-economic knowledge base

1280

Joint research centre (non nuclear part) + Euratom

1999

Total

14960

Construction related technologies are addressed by several specific programmes like in "Environment" for urban aspects, "Energy" for energy saving, "Information Society" for IT development. Construction as a sector and the technologies normally useful to it or having an output to it are included in the same degree as for any other sector in Programme 3 "Growth" and its Key action 1 "Innovative Products, Processes and Organisation". The problem solving approach characterising this Framework programme needs, however, in addition to a reduced number of research objectives to maintain concentration on few relevant priorities. Concentration of resources and efforts are achieved through calls for proposals targeted on RTD priorities. Those priorities under Key Action 1 are referred to as Targeted Research Actions (TRA). Participants to the calls might submit proposals for the development and deployment of critical technologies (addressing all or part of the RTD objectives described above) as well as groups of projects (clusters) or single large proposals, with the objective to integrate and validate such technologies around strategic objectives. However proposers should ensure themselves that these objectives correspond to the priorities defined for each call.

328 2.2

Activities currently in hand

Structural control in construction has been attracting the attention of the industry and the research institutes resulting in several projects running in this domain. These projects were selected as best responding to the requirement for precompetitive industrial research leading to high economic, social and environmental benefits through innovation, technical excellence and solid strategic planning for bringing the results into industrial practice. In the following some information is given on examples of new projects or running ones. Further information on these projects can be obtained at http://www.cordis.lu or at the given project WebPages. SMART STRUCTURES: Integrated Monitoring System for Durability Assessment of Concrete Structures This project aims at developing an integrated modular monitoring system for new and existing concrete structures and will be combined with enhanced deterioration models. A number of new inexpensive probes for monitoring existing structures will be developed to cover the parameters which influence or represent the most relevant deterioration mechanisms: Chloride induced corrosion, carbonation of concrete, freeze-thaw damage, alkali-aggregated reaction, mechanical damage. The consortium is co-ordinated by RAMB0LL, Denmark and comprises technology leaders in their field and big owners of large structures. (http://www.ramboll.dk/smart). ACE: Active Control in Civil Engineering The technical objectives of this project are to improve the understanding of the induced vibrations of cable-supported structures, improve an appropriate software package capable of analysing the behaviour of cable-supported structures, develop an active system to control induced vibrations of cable-supported structures, develop the appropriate actuators and validate the active control system with high scale mock-ups and measurements of existing structures. The deliverables of this project will make it possible for the various industrial involved in cable-supported structures to understand and predict the behaviour of the structures when exposed to wind induced vibrations, live load induced vibrations and seismic induced vibrations. MILLENIUM: Monitoring of large civil engineering structures for improved maintenance The primary objective of this project is to develop and demonstrate an on-line strain measurement system with the capability of meeting the required specification for life prediction and maintenance control of large civil engineering structures surviving for the lifetime of the structure for up to 100 year. The base technology for the instrumentation is optical fibre distributed sensing, which when compared

329 with alternative candidate technologies, offers the optimum solution to meet the required specification. SIMCES: System Identification to Monitor Civil Engineering Structures The main objective of this project was to prepare for the development of a methodology for vibration monitoring of civil engineering structures by integration of the following research activities: 1. establishment of an optimum dynamic testing procedure in order to obtain high quality experimental data 2. application to civil engineering structures of adapted time and frequency domain system identification methods to extract the required dynamic information from the data 3. development of FE programs to model the dynamic behaviour of damaged structures 4. updating based on models derived from operational data 5. use of damage patterns as parameters in the updating process of the finite element model 6. development of a method to incorporate information from vibration monitoring into techniques revising safety and reliability 7. proof of feasibility by full scale 8. long duration tests and progressive failure tests of representative structures (e.g. bridges). The project was successfully ended and new projects are now starting for bringing this technology to industrial use. http://venus.kulnet.kuleuven.ac.be/bwm/Z24/partners.html REEDS: Optimisation of Energy Dissipation Devices Rolling Systems an Hydraulic Couplers for Reducing Seismic Risk to Structures and Industrial Facilities The main objectives are to optimise the design manufacture and performance of the types of device mentioned to fabricate prototypes and to evaluate the benefits of the devices to design of safe structures. Structure mock-ups in particular civil buildings sections, chemical or other industrial plant (liquefied natural gas tank and curved pipeline segments) and equipment (in particular HV electrical switch-gear) protected by the most appropriate type of device were tested under seismic loads and the performance of the devices assessed. Comparison with predictions of structural response using a theoretical model of the particular device enables the adequacy of those models for structural design purposes to be evaluated. The above are just examples of actions bringing together research teams from several European Union member countries and from countries associated with the programme. The target is to promote the collaboration across borders, between researchers and industry, responding to the needs of the end-user and the citizen. For increased synergy between projects networking activities have also been set-up.

330

EFCT: Targeted Research Action on "Environmentally Friendly Construction Technologies" This Thematic Network, was established on the initiative of the European Commission (EC DG XII) under the Fourth Framework Programme and within the context of the Research and Technical Development Programme on Industrial and Materials Technologies (BRITE/EURAM III). The general idea behind the action is to secure added value to EC funded research projects by helping participants in complementary projects, covering different technologies of the programme, to co-ordinate their activities around a specific objective. In particular this TRA aims to : 1. Provide a European forum for the development, dissemination and exchange of scientific and technological knowledge, and of ideas relating to all aspects of construction 2.

Accelerate dissemination and exploitation of research results

3.

Improve the synergy and co-ordination of research being carried out in EC programmes

4.

Inform RTD programme planners of the research needs and priorities of tomorrow.

The TRA Network brings together representatives from a large number of enterprises, institutions and universities from all over Europe, linked together by the involvement in the construction industry and their participation in ongoing research projects under the various EC RTD Programmes, such as Brite/Euram, CRAFT, SMT (Standards, Measurement & Testing), Environment, TMR (Training and Mobility of Researchers), ECSC Steel Research.(http://www.tra-efct.com/). The European Research Area and the 6' Framework Programme The Council of the European Union in its meeting of June 15th 2000, emphasised the "significant role played by research and development in generating economic growth, employment and social cohesion". This new policy aims at the creation of a frontier-free area for research where scientific resources are used more to create jobs and increase Europe's competitiveness. Special attention will be given to the networking of centres of excellence, to the development of a European approach to large research infrastructures as well as to the establishment of an open method for benchmarking of national research policies. This will be combined with measures to promote spin-offs from research such as action on patents and easier access to risk capital. The problems of fragmentation and lack of collaboration between public and industrial research in Europe are to be addressed through better co-ordination, progressive opening of national research programmes and by encouraging the mobility of researchers. Other targets, like the very high-speed transeuropean

331 network and the international co-operation, are complementing this policy. http://europa.eu.int/comm/research/area.html 3

Conclusion

Considerable progress has been made in past years to improve the productivity and quality of the construction industry. However, the requirements for construction processes including assessment and upgrading of existing structures are still increasing at high rates and this trend is bound to continue in coming years when developing countries will also be reaching the global market place. Strong interdisciplinary socio-economic and technology research actions involving the major stakeholders (such as producers, suppliers, software and logistics companies, legislative bodies, and others) will be essential to maintain competitiveness of the European enterprises. Investment in technology advancements is only really possible with co-operation between the various interests in a project. With almost 15 000 million Euro for four years and its new targeted approach, the European Union's Fifth RTD Framework Programme promises to be a powerful instrument helping to catalyse the necessary changes. Future research policy of the European Union will have voluntary co-ordination of research as one of its prime objectives. For the construction industry this is expected to have significant benefits as most of the research work is done by academia, private interests, public or semi-public research centres at national or local level. Big projects in infrastructure and housing usually become an incentive for considerable progress in technology, transfer of technology from other sectors and integration of knowledge into industrial practices. The target is to obtain maximum society benefit at minimum consumption of resources. The construction sector can benefit from these developments and it is advisable for all stakeholders to be informed about developments and participate in the debate for the shaping and the fine-tuning of this future policy's actions and instruments.

OUTLINE OF SAFETY EVALUATION OF STRUCTURAL RESPONSECONTROL BUILDINGS AND SMART STRUCTURAL SYSTEMS AS FUTURE TRENDS

KITAGAWA YOSHIKAZU Professor, Keio University,3-14-1 Hiyoshi, Yokohama 223-8522, Japan E-mail: kitagawa @ sd. keio. ac.jp

TAMAIHIROYUKI Research Associate, Hiroshima University, 1-4-1 Kagamiyama, Higashi-hiroshima 739-6527, Japan For buildings structures, there are many unknown variables, such as the structure type, material, site condition, and the temporal deterioration of the structural performance. For controlling the structural vibrations during earthquakes, the response time of the control system must be sufficiently short to minimize the time between sensing an external disturbance and operating the actuators of a control system. It is difficult, however, to design control algorithms that can handle arbitrary scenarios for controlling large, complicated response-control systems, which are necessary for buildings that are built in unpredictable environments. Under this situation , we first looked at the classifications of the control principles behind structural response-control systems, and also reviewed the required performance of control systems. We then introduce the guideline for safety evaluation of structural response-control buildings. To demonstrate how piezoelectric materials can be incorporated into smart material systems, we made vibration tests with scaled cantilevered beam and portal frame. The results of vibration tests confirmed the validity of the control effect of the response-control systems and demonstrated the possibility to clarify the characteristics and performance of piezoelectric materials for use actuators, sensors, and dampers in a smart material systems. Finally we speculated on the general concept and the prospects of using smart material systems in building designs as future trends.

1.

Introduction

Japan is subjected to frequent seismic activity due to its location within three major earthquake zones: the Pacific Ocean side, which produces large earthquakes; the Japan Sea side, which produces medium-sized earthquakes; and the inland areas, which produces shallow, medium-sized earthquakes. Protection against earthquakes is therefore required in building construction. In addition to designing buildings with proper structural resistance, it is also important to maintain the safety and functionality of buildings, as well as the living comfort of the residents during

333

334 earthquakes and strong winds. Designing a building to be a response-control structure is the most effective way to economically meet this societal demands. For building structures, there are many unknown variables such as the type of structure, material, site condition, and the temporal change of the structural performance. For controlling the structural vibrations during earthquakes, the response time of the control system must be sufficiently short to minimize the between sensing an external disturbance and operating the actuators of a control system. It is difficult, however, to design control algorithms that can handle arbitrary scenarios for controlling large, complicated response-control systems, which are necessary for buildings that are built in unpredictable. As the complexity of the control systems increases, the possibility of providing accurate, comprehensive information decreases, thus degrading the responsiveness, reliability, safety, and robustness of the systems. To overcome these problems, the development of active response-control systems is needed. In this paper, we first present the control principles for structural response-control systems and their required performance. We then introduce the guideline for safety evaluation of structural response-control buildings. We then describe how the innate performance of piezoelectric materials, which we call a smart material, can be used to make actuators, sensors, and dampers. We then describe vibration tests and results for evaluating the performance of scaled cantilevered beam and portal frame that use smart materials. Finally, we speculate on the general concept and the prospect of using smart materials and related systems. 2.

Control Principles and Required Performance of Control Systems.

Currently, the most commonly used response-control method in structures is feedback control, which feeds back j £ , % , and % to the control systems. Classical control principles are used to obtain vibration control at the design stage of the control systems, such as shifting the natural frequency of the structure for the predominant frequency of the external disturbance or increasing the damping factor. On the other hand, modern control principles are used to feed back information to the control system with controllability and sensing ability. However, if these problems are solved, dynamic characteristics of the control system can be easily changed. Control principles may be classified into the following four groups: (1) Self-organizing structural control, in which the optimum configuration of a control system is determined by the control system itself. (2) Adaptive control, in which an evaluation function and the parameters to be optimized are determined adaptively in a given structure.

335 (3) Optimum control, in which the operational quantities are determined so as to optimize a given evaluation function. (4) Direct control, in which the operational quantities are directly determined by matching the process variables with their target values. These classifications are based on two factors: the degree of complexity of the system and the degree of uncertainty in the information. In the design of a structural response-control system, it is important to identify the dynamic characteristics of the structure that are to be controlled. It is also necessary to include fail-safe mechanisms to improve the reliability of the entire system. Therefore, it is desirable to develop fail-safe systems that have adaptive control, in which the control parameters can be adjusted in response to environmental effects. In buildings structure, it is generally difficult to construct systems because of the large number of unknown variables, such as the type of structure, materials, and site conditions, and the temporal rate of deterioration of structural performance. To control the vibration of a structure subjected to earthquakes, a fast response time of the control system is critical. The response sequence includes sensing the external disturbance, conveying the signal to the control circuit, and putting the actuators into operation. There are, however, many uncertainties in the input signals to a control system, such as the direction of the input ground motion and location of the sensors. Pwmwtsn SyjteraRHpiinnKiiB AdipUbleComrotTkiay N o * RgOfTQtttt

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WiiRMfoQatmoi

Quick RO^OMC

» HahttsRi^nw

Tasitxwri.ii^iantil, ffDConiiDl

Figure 1: Relationship between adaptive control theory and response control system requirements

336 Safety

Habatbiliry |

Economy }-—» control Capacity]

1

Target Response

M c i e d Excitation

TaijaCoiuol Variable

Response Equation Structural Identification

Fuzzy Rule

Marimiang Decision

Optuid Control Variable

Senior

Earthquake Motion

Actuator

>| Structure |

Sensor

>|ltiuaural Response

F i g u r e 2 : Flowchart o f a fuzzy optimal control s y s t e m

To deal with these uncertainties, optimum control systems that incorporate fuzzy logic or neural networks must be used. Figure 1 shows an example of the relationship between response-control system requirements and control principles for structural safety evaluation of a response-control structure, and Fig. 2 shows a flowchart of a control system that uses fuzzy optimal control, as an example [4,2] .This systems uses fuzzy theory to make real-time predictions of earthquake ground motion and obtain the response function from a combination of real-time structural identification, a target response that satisfies the living comfort and safety of the residents, and target control variables determined for economy and technology. From this information, the fuzzy control method determines the optimum response. 3.

Guideline for Safety Evaluation of Structural Response-Control Buildings

Structural response-control technology for practical use in buildings is developed mainly by private companies aiming to improve the living comfort against strong winds or moderate earthquakes. Structural engineers, however, have not yet reached a consensus on the design philosophy and safety of structural response-control buildings, and a general social consensus of this type of new building is not yet to be developed. Under this situations, it is desirable that safety evaluation procedures of structural response-control buildings are established to not restrict but promote the development of this technology. The Structural Response-control Research Committee (chaired by Prof. Inoue, University of Osaka) was established in

337 Building Center of Japan, and reported as the "Guideline and Commentary for Safety Evaluation of Structural Response-Control Buildings"in 1993 [3]. This guideline mainly consists of three chapters; general, safety evaluation of structural, and safety evaluation of response-control devices. Chapter 1 consists of scope, definitions, classification of structural responsecontrol buildings in safety evaluation, and safety evaluation of structural responsecontrol buildings, Chapter 2 consists of outline of buildings and ground conditions, design principles and safety evaluation contents, setting of design conditions, design of structures, detail design at response-control devices location, earthquake and wind response analysis of structural response-control buildings, and effects to structures in unusual condition of active control devices, and Chapter 3 consists of composition and specifications of response-control devices, control design of active control devices, operation program of active control devices, performance validation and durability of response-control devices, maintenance inspection of response-control devices, and environmental safety.

Start

^ P a s s i v e Control"^

Yes

Out of Application of Guidline

JNo

/'Relaxation of

\ ^sVes

-Design Conditions

No

Operation limit of Active Devices

L-l

Figure 3:Flowchart of classification of structural response control building

338 Figure 3 shows a flowchart of classification. Structural response-control buildings are classified based on the relaxation of design conditions of structure and the operation limit of active control device as shown in Table 1. Safety of a structural response-control building is evaluated for the structure and the response-control device. Necessary evaluation items are determined according to the classification in Table 1. are shown in Table 2. The items that are not shown in this guideline shall be followed by the Building Standard Low of Japan, the related specifications, and recommendations. Operation limit of Active Devices Relaxation of Design Conditions

Level 0 Earthquake Motions or Wind Loading L-Q

Level 1 Earthquake Motions or Wind Loading L-l

Level 2 Earthquake Motions or Wind Loading L-2

Not Relaxed R-l

A

B

C

Relaxed R-2

D

E

F

Notes: 1) Relaxation of design conditions means that some design conditions of a structural response-control building arc relaxed considering the effects of response-control device in comparison with an ordinary building. 2) Operation limit Of active control devices means a level of upper limit of earthquake ground motions or wind loading at which an active control device operates effectively. Table 1 Classification of structural response-control buildings

Class of Responsecontrol Buildings A B C D E F

Evaluation Items (1) Outline of Building to be Evaluated

Remarks (To understand outline of a building to be evaluated)

1, Outline of Ground 0 0 0 0 0 0 a. Site 0 0 0 2 2 2 b. Conditions around site (topography, environment) 0 0 0 2 2 2 c. Subsoil conditions 2. Outline of Building 0 0 0 0 0 0 a. Use 0 0 0 0 0 0 b. Scale and shape 0 0 0 2 2 2 c. Structure (structural type, foundation) 2 2 2 2 2 2 3. Outline of Response-control Device a. Type of system b. Size and shape of device c. Setting location 4. Desip Principles 2 2 2 2 2 2 a. Goal of response-control

Active, Hybrid

living comfort, Function, Earthquake and wind resistance

2 2 2 2 2 2 b. Criteria for earthquake and wind resistance c. Target performance of earthquake and 1 1 1 1 1 1 wind resistance 2 2 2 3 3 3 d. Operation limit of active control device 0 0 0 3 3 3 e. Relaxation of desip conditions Relaxed or not, Relaxed contents (2) Safety Evaluation of Structure 5. Design Conditions of Structure 0 0 0 0 0 0 a. Materials 0 0 0 3 3 3 b, Design loads (permanent load, seismic load, wind load, others) 0 0 0 3 3 3 c. Story drift limitation 0 0 0 3 3 3 d. Structural specifications

(To confirm that a structure is designed appropriately considering earthquake and wind response of response-control building)

6. Design of Structure 0 0 0 0 0 0 a. Design for permanent load 0 0 0 0 0 0 b. Design for temporary load 0 1 1 0 3 3 c. Ultimate limit state 7, Detail Desip at Response-control 2 2 2 2 2 2 Device Location

Supporting structure, equipment, others

Class of Responsecontrol Buildings A B C D E F 0 0 0 0

2 2 2 1

3 3 3 2

2 2 2 2

3 3 3 3

3 3 3 3

Evaluation Ileitis 8. Response for Earthquake Ground Motions a. Input earthquake ground motions b. Analytical method c. Mathematical model d. Evaluation of seismic safety

9. Response for Wind Loading 0 2 3 2 3 3 a. Wind loading 0 2 3 2 3 3 b. Analytical method 0 2 3 2 3 3 c. Analytical model 0 1 2 2 3 3 d. Evaluation of wind safely

1 2

10. Effect to Structure in Unusual Condition of Active Control Device 3 1 3 3 a. Necessity of consideration on unusual condition

1 1 1 1 3 3 b. Safety of structure at power failure 1 2 3 1 3 3 c. Safety of structure in excitation 1 1 1 1

1 1 d. Emergency interruption mechanism

(3}Safeiy Evaluation of Response-control Device 2 2 3 2 3 3 11. Composition and Specifications of Response-control Device a. System Composition b. Components and specifications (Sensing system, Control system, Drive system) 2 2 3 2 3 3 12. Control Design of Active Control Device a. Sensing of quantity of state b. Signal processing c. Control theory d. Driving program

Remarks

Locality, Level 1, Level 2 Time history response analysis Structure, Response-control device Criteria for earthquake resistance, Safety margin Level 1, level 2 Time history response analysis, Frequency response analysis Structure, Response-control device Criteria for wind resistance, Safety margin

Reliability on normal operation, Simultaneous effects of earthquake and wind Out of operation, Impulsive force Exciting force, Simultaneous effects of earthquake and wind, Operation limit Reliability of emergency interruption mechanism, Effect of sudden stop on structure (To confirm that a responsecontrol device is in normal operation) Block diagram, Backup system Size, Weight, Input and output, Accuracy, Capacity, Computing performance, Environmental conditions

341 Class of ResponseEvaluation items control Building A B C D E F 1 2 3 1 3 3 13. Operation Program of Active Control Device a. Period, conditions and method of operation

2 2 3 2 2 2 3 2 12

3 2

12

3 2

Remarks

Program of stan and stop

14. Performance Validation and Durability of Response-control Device 3 3 a. Fabrication and product inspection Quality and standards of device procedures material 3 3 b. Operation test and performance test Operation of device, Performance of response-control building 3 3 c. Durability Environmental conditions, durable year, and durability of sensor, CPU, driving device, power source, and others 3 3 15. Maintenance Inspection of Responsecontrol Device a. Type and contents of inspection Measuring system, CPU, Control software, Driving device, and Power source b. Maintenance organization Monitoring of response-control system, Diagnosis method, and c. Performance monitoring Restoration design and manual Control design considering malfunction d. Countermeasures of malfunction

2 2 3 2 2 3 2 2 3 2 3 3

16. Environmental Safety a. Active factors

Influence of device on circumstances fafluence of circumstances on device

b. Passive factors 1 1 1 1 1 1

(4) Others

2 2 2 2 2 2 17. Others Materials related to Item 14 a. Construction 18. Reference Documents Notes: a. Performance validation test data 1) "0" denotes that evaluation equivalent to ordinary building is necessary. "3" denotes that detailed evaluation as response-control building is necessary. "2" denotes that evaluation as response-control building is necessary. " 1 " denotes that evaluation as response-control building is not necessary exceptforspecial cases. 2) Earthquake and wind response analysis isfora structural response-control building including the structure and response-control device. Degree of investigation for each item is different according to a balance between the potential performance of response-control device and the lateral load-carrying capacity of structure. Table 2: Safety evaluation items for structural

342 4.

Vibration Tests on Piezoelectric Materials

To develop a comprehensive smart material systems, it is necessary to focus on either the innate characteristics of material itself or on a combination of computational and mechanical technology that combines a sensors, actuators, data processing, and expression. As a controllable materials in a smart material systems, piezoelectric, magnet-strictive, magnet-rheological-fluid (MRF), electrorheological-fluid (ERF), and shape-memory alloys (SMA) materials, which have been tried to use in aeronautical engineering, are considered to develop the optimum applications in controlling large-sized and complicated building structures. To demonstrate how the innate performance of piezoelectric materials can be incorporated into a smart material systems, we made vibration tests of cantilevered beam and of a portal frame [4] 4.1 Vibration Tests To demonstrate the applicability of piezoceramic materials for sensing, actuating and damping, we made three types of vibration tests, Figures 4 and 5 show the cantilevered beam and detail of the bimorp used for the vibration tests, Figs.6 (a) and (b) show the sensing and actuating systems, respectively. A bimorph, consisting of a steel plate and two piezoceramics plates, was installed in the fixed end of the beam. The material and electrical properties of the piezoceramic are shown in Table 1. The portal frame and the systems used for the damping verification tests are shown in Figs.7 and 8, respectively. Bimorph similar to that installed in the beam where installed in the end of the portal frame columns. For the bimorphs installed in the portal frame columns, however, an adjustable resistor was used to shunt the piezoceramic electrodes. In all tests, the strain,e, was measured in the vicinity of the fixed end. Also, in the sensing verification tests, the strain of the piezoceramic sensors in the bimorph, e was also measured. The output from the piezoceramic sensors was calibrated by using the amplitude of strain measured in a vibration tests with a beam vibrating at its natural frequency, / , of 6.0 Hz.

343

m.

ft

ru L^

Fb-65x5

7.4 Strain Gage

Shim / Strain Gage Bimorph

\

2L-150x150x10-^

Piezocerar ics

U 1 IU 1„ fi.» 1

"

Shaking T a b l e "

Figure 5: Detail of bimorph

Figure 4: Cantilevered beam specimen (Type A speciment)

lead Ziicotitanete Ceramics (PbZrCVPbTiO}) Young's Modulus Posson's Ratio

hi V

035

hfk

2000

h h

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C

120(nF),(=4x30nF)

Relative Dielectric Constant Xlp8.854xlO-l2(F/m) Piezoelectric Constant Electro-mechanical Coupling Cofficiem Static Capacitance

5.8x10'* (N/ar1)

035

(Bimorph has 4 PiezocraiRks) Table 3 Mechanical and electrical properties of piezoceramic used in bimorph

344 Speotnm

r

'

Strain Me(er

f

>

Specimen

f

Computer A for sating

r~i

• StnmCtga ^

Oscilloscope

J

Strain Meter

Computer A for rasing

|

• SmuiOage

Osciucscope

*—

f

L.

r

DC Amplifier

i

/ l

L

Input (Shaking Title)

_.. ,, uuiu,

Computer B far input

e a : Strain Gage

\— i—1

• •

: Piezoceramics

- Piezoceramics V )

i — >

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input (Shaldnn Table)

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F i g u r e s 6 (a) & (b): Systems for evaluating sensing function and evaluating actuating function

r^

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-

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il

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F i g u r e 7: Portal frame specimen

F i g u r e 8: System for evaluating damping

(Type B specimen)

function

In all of the tests the excitation was done with a shaking table. For the sensing verification tests the excitation forms were sinusoidal excitation with, f, of 6.0 Hz, and ll.OHz, and for the actuating and damping verification tests, excitation was four sinusoidal cycles at the system's natural frequency, / , of 6.0 Hz and 12.8Hz. In actuating verification testes, an AC voltage of 250V, and an inverse phase of 6.09Hz was applied to the piezoelectric materials. The damping ratio, h, in each test was calculated from vibration data measured for free vibrations, by using a least-square method based on the following equation:

345 |ea| = anexp{-/i~-r}

W

Where | e l is the strain amplitude, / is time, a is the amplitude at ?=0, and T, is the natural period. 4.2 Optimum resistor in piezoceramic damper Under the steady-state vibrations, the equivalent damping ratio added by the piezoceramic damper, ft , is obtained as follows[5,6] fc-=2A 2 v Where,

"

(l-*?l)+p p = R-c{l-kll)-2n-f

(2)

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346 4.3 Results and discussion (a):(f=6.0Hz)

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347 Figures 9 (a) and (b) show results for sensing tests, Figs. 10 (a) and (b) show results for actuating tests, and Figs. 11 (a) and (b) show results for damping tests. The temporal strain response of the piezoelectric materials are shown in Fig.9 (a) for/=6.0Hz and in Fig.9 (b) for/=11.0Hz. Figures 10 (a) and (b) show the temporal vibration of strain in the vicinity of the fixed end with and without actuation, respectively. In Fig. 10, £ is normalized by the strain, £a measured when the top of displacement of the specimen reaches. l.O(cm) and t is normalized by the natural period, ;/T, . Figure 11 shows R/R m , vs h, where Row is calculated from Eq.(5) and h is calculated from Eq. (1) The result shown in Fig.ll (a) correspond to R/R0IU was varied from 0 to 10 and the results shown in Fig.ll (b) correspond to R/Rou, varied from 0 to 2. In Figs. 11 (a) and (b), the relationships between R/Rou; and h^ + hinh calculated from Eq.(2) are also plotted. Where, the inherit damping ratio, hinh , is identified as the experimental observation when the resistance is to be 110(k£2). From these results, we clarified that 1) The amplitude and phase of strain measured with the piezoceramic sensor depended on the frequency of excitation. 2) The piezoceramic actuator was able to control the vibration at 1.5 times its inherit damping ratio. 3) The optimum resistance of the piezoceramic damper that maximized the damping ratio was accurately predicted by Eq (5). 4) When the damping was attached over only 10% of the column, the piezoceramic damper increased the damping ratio by 30% compared with its inherit damping ratio.

5.

Prospects for Smart Material Systems as Future Trends

A smart material is one that not only adds intelligent function, but one that also functions as a sensor, data processor, actuator, and expression for external disturbances. That is, smart materials add an aspect of artificial life. This is different from intelligent materials, which only respond according to a single set of inputoutput (non-evolving) response characteristics. Recently many research studies are being made on artificial life, focusing on evolution, shape formation, learning, distributed parallel biological processing, immunity, and self-remodeling [7,8]. As one of the basic mathematical functions of artificial life, genetic algorithms based on the principle of biological evolution (i.e., selection, crossover, and mutation) are the models for the evolution process. Among the possible processing functions, evolution is the most useful method for optimization, because the system responds

348 according to simple internal principles and through interactions with outside sensors, and not by external instructions. Thus, self-organization can independently form the system order. Also, self-formation is the mapping from a genetic type to an expressing type, and has the important role of enhancing the robustness of the system adaptability. In designing and controlling large-sized, complicated response-control systems for buildings that are in uncertain and changing environments, it is impossible to provide control algorithms and data that can handle every control scenario. As the complexity of the control system increases, the possibility of providing accurate, comprehensive information decreases, thus degrading the responsiveness, reliability, safety, and robustness of the system. To avoid this, the development of smart material systems that use them is needed. Figure 12 shows the overview of smart material systems that use them, as modification to reference [9]. External Diitwbance | .,— •„,„ jv f

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r Evolution, Learning, Monitoring and Repairing, Shape Fomiatian, Immunity, Self-Remodeling, and Distrib. uted Parallel Processing Figure 12: Overview of smart material systems (added to 9) Figure 13 shows the technical development of building structures from the late 20th century to the first half of 21 st century. Currently, earthquake disaster countermeasures for buildings are seismic design and response-control devices, such as actuators and sensors. Monitoring is also a must for maintaining and controlling such response-control devices. In the future, incorporating genetic algorithms into response-control systems will make the self-organization of systems and their organic optimization economically possible (i.e., economization). Fuzzy theory and neural networks are examples of artificial intelligence. It is possible to merge the characteristics of each of these algorithms by adopting genetic algorithms for selecting or improving the rules of fuzzy theory or neural networks. Consequently, introducing smart material systems into buildings is practicable only

349 when coupled with the development of smart materials. Structural interpretation of the aspects of artificial life (i.e., evaluation, shape formation, learning, distributed parallel processing, immunity, and self-remodeling) will coincide with the development of technology related to each aspect. Incorporating smart material systems into buildings (i.e., smartization) is the future of earthquake countermeasures; the ultimate goal of engineers is to design a buildings that behave like a human being.

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6.

Concluding Remarks

In this paper, we first summarize the control principles behind structural responsecontrol systems, and also reviewed the required performance of control systems. To demonstrate how piezoelectric materials can be incorporated into smart material systems, we made vibration tests with scaled cantilevered beam and portal frame. The results of vibration tests confirmed the validity of the control effect of the response-control systems and demonstrated the possibility to clarify the characteristics and performance of piezoelectric materials for use as actuators, sensors, and dampers in a smart material systems. Finally we speculated on the general concept and the prospects of using smart material systems in future building designs. The performance of structural response-control systems depends on the control devices, which have been developed mainly from a practical-use viewpoint.

350 When we reach a consensus on the requirements of future structural control systems, incorporation of smart materials into these systems will proceed. When that occurs, it will be important to develop reliable smart material technology and methods for evaluating the vulnerability of each component of structural responsecontrol systems. References

1.

2.

3. 4. 5.

6. 7. 8. 9.

BRI Technical Report,"R&D to achieve active response-control structurescooperative study between public organization and private company",MOC (1992, 1993, and 1994). Fujitani, H., Midorikawa, M., Iiba, M., Kitagawa, Y. et a\."Seismic response control tests and simulated by fuzzy optimal logic building structure", Engineering structures, vol.20, No.3. (1998). Report of project on R/D to achieve structural response-control of building structures, MOC, Government of Japan, (1993, in Japanese). Kitagawa, Y., Tamai, H., and Takeshita, M. "Smart structural systems of exposed to external, disturbances-concept and technology'', 12 WCEE (2000), CD-ROM Hagood, N.W., Flotow, A. Von "Damping of structural vibrations with piezoelectric materials and passive electrical networks", J. Sound and vibration, vol.146, No.2,(1991),pp.243-268. Hagood, N.W., Crawley, E.F "Approximate frequency domain analysis for linear damped space structures", AIAA Journal, vol. 28. (1990), pp.1963-1961. Labgton, C. Artificial Life, (1989), Santa Fe. Kitano, K.,"Artificial life and combination of evolution, generation and learning", Mathematics Science vol. 353. (1992) Report on "Leading Research R&D of Smart Structure Systems", NEDO-PR-95011, (1996).

THE MOST RECENT APPLICATIONS OF SEISMIC ISOLATION AND PASSIVE ENERGY DISSIPATION

ALESSANDRO MARTELLI Chairman, Working Group on Seismic Isolation (GLIS) of the Italian National Association for Earthquake Engineering; ENEA, Bologna, Italy E-mail martelli @ bologna, enea. it MASSIMO FORNI Technical Secretary, GLIS; ENEA, Bologna, Italy E-mail forni@bologna. enea. it Summarized in this paper is the state-of-the-art on seismic protection through innovative antiseismic techniques, namely seismic isolation (SI), passive energy dissipation (ED) and active control (AC), based on the information collected at the Post-SMiRT Conference Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control of Vibrations of Structures held at Cheju (Korea) in August 1999 and on even more recent information which became available to the authors. Reported is information on the most recent applications of such techniques, together with the progress of R&D activities at word-wide level, availability of design rules and the related issues and needs for further activity. With regard to the latter, somewhat more detailed information is reported for European and especially, Italian applications.

1. Introduction Modern society is being more and more characterized by a strong interaction among the large systems by which it is formed: the physical, human and infra-structural systems. Seismic risk results from the interaction among seismic hazard, vulnerability of structures and social-economical effects. In the past, an earthquake mainly caused collapse of buildings and fatalities. Nowadays, a seismic event may also endanger the social-economical stability of large areas, due to the complexity of technologically advanced societies. For instance, the Great Hanshin-Awaji earthquake of 1995, which struck Kobe (where one of the most important ports of the world is located) is the first case in the history of a seismic event that occurred in a highly industrialized urban area, by producing enormous damage to the building, road and in particular, productive systems. The earthquake which struck Izmit in Turkey on August 17, 1999, caused the fire of the biggest Turkish petrochemical plant, by leading to very difficult fuel supply and heavy pollution. A scenery similar to those mentioned above might take place in many other areas in the world, from California to Italy: in California, for instance, in case of a strong earthquake closer to San Francisco and Silicon Valley, 351

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with the respect to the 1989 Loma Prieta event; in Italy, for instance, in case of events like that which struck the now highly industrialized area around Po River in 1117, or that which destroyed South-East Sicily (where a huge number of petrochemical plants and components is now located) in 1693. In addition, it is worthwhile mentioning that recent earthquakes showed a fully unexpected violence, like for instance, that which struck again Turkey, with epicenter near Kaynasly (Bolu Mountains), on November 12, 1999. Since ground acceleration was much larger than the design value, this caused severe damage even to some very important modern structures, like a viaduct of the new IstanbulAnkara freeway, being erected using the most modern anti-seismic technologies, which was extremely close to the epicenter [1]: in fact, the maximum displacement allowed by the horizontal fail-safe system (stoppers) was largely exceeded (another viaduct behaved very well, although it displaced twice the design value, but this was still allowed by the stoppers). The aforesaid remarks demonstrate, without any doubt, the increased degree of complexity of modern society, and thus, the need for an integrated management of the territory, able to make development and safety compatible. This implies that more and more numerous shall be the structures for which design shall not be limited to prevent their collapse, but shall require the absolute integrity and full operability after the earthquake. The feature of absolute integrity is also indispensable to protect investment, taking into account that the value of contents of more and more buildings is much larger than that of the structural members, as well as to avoid spending the enormous amounts of money during both the emergency phase and reconstruction which were necessary after the recent earthquakes. For the above-mentioned reasons, a wide extension of the use of innovative anti-seismic techniques, such as seismic isolation (SI) and passive energy dissipation (ED), which aim at ensuring the full integrity and operability of structures, is necessary for both new constructions and retrofit of existing buildings [2]. In fact, SI and ED technologies are now fully mature for such an use, as demonstrated by the results of very numerous research projects and also, by the excellent behavior of seismically isolated buildings in both the Great HanshinAwaji earthquake and the Northridge earthquake which struck the Los Angeles area the year before [2]. This conclusion has been confirmed in all the recent Conferences on seismic engineering, in particular at the 1999 International Post-SMiRT Conference Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control of Vibrations of Structures [3]. 2.

Recent applications

The invited lectures and contributed papers presented at the Cheju Seminar and the

353

extensive discussion both following their presentation and during the Closing Panel, demonstrated that not only SI, but also several ED systems are already fully mature for wide-ranging applications. They also showed that, at last, the benefits of such systems have been well understood in several countries and that they are now being more and more used. The aforesaid benefits had already been very well understood by Japanese after the 1995 Kobe earthquake and to a certain extent, by Californians after those of Loma Prieta (1989) and Northridge (1994). Even before, this had occurred in New Zealand, where there are still new applications of SI to both new and existing ancient constructions, in spite of the limited population; more recently, it also occurred in other countries, like the P.R. China, Russian Federation (especially after the Sakhalin earthquake in 1994) and Italy (after the earthquake that struck Umbria and Marche Regions in 1997, by severely damaging famous frescos of Cimabue and Giotto in the "San Francesco Basilica Superiore" at Assisi). It is also worthwhile citing again that, according to the information provided at the Cheju Seminar, SI and ED are now considered of great interest also for areas characterized by low or moderate seismicity [3]. 2.1 Applications in Japan In Japan the number of buildings provided with innovative anti-seismic systems is still considerably increasing, in spite of the need for still asking for a specific approval for each design including these techniques [3]. The number of licenses began to drastically increase in September 1995, some months after Kobe earthquake (60 new applications) and the annual number reached 207 in 1996, while the overall number during the 10 previous years was 79; such a dramatic increase ended in 1997, when a probably steady progress began (the new licenses were 135 in 1997 and 131 in 1998). In this country, the use of SI was recently extended from new constructions to retrofit of existing buildings (e.g. Le Courboisier Museum at Tokyo), as well as to many new or existing bridges and viaducts (in some cases, at least in Kobe, becoming compulsory for the latter). SI is having many variations in application objects, application methods of rubber bearings and kinds of devices. The variations include SI of tall buildings of about 100 m height, SI of artificial grounds for multiple buildings, and application of non-rubber type SI devices. SI is finding new applications which include wooden houses, masterpieces in museums, automatic storage systems of warehouses, etc.: for wooden houses, nonrubber type SI systems using ball/rubber bearings or sliding bearings to support the superstructure have been developed and began to be used; for masterpieces in museums, various types of SI systems have been developed and used for the containing showcases; for automatic storage systems of warehouses, a new type of SI floor has been developed and used.

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It is also noted that SI is beginning to be used for very important public buildings and facilities, such as, for instance, the new official residence of the Japanese Prime Minister. 2.2 Applications in the USA In the USA (especially in California), new constructions of important isolated strategic buildings, including emergency control centers (e.g. those at San Francisco and Long Beach) are going on and retrofit of even large public buildings using SI (e.g. the San Francisco City Hall and San Bernardino Medical Center) is progressing [3]. Most applications make use of rubber bearings, namely High Damping Rubber Bearings (HDRBs) or Lead Rubber Bearings ( LRBs). However, the extent of the aforesaid progress is much less than in Japan. In fact, although the first US seismically isolated building was completed in 1985, in 1999 there were in this country only 25 applications to new constructions and 22 retrofits of existing buildings: this is due to very complex and conservative regulations. Conversely, SI is now being widely used in the USA for highway bridges, for which it is governed by a simple and not overly conservative code. 2.3 Applications in New Zealand There were 10 isolated buildings in New Zealand in 1999 (in addition to several applications to bridges and viaducts), four of which being retrofits of ancient constructions (those of the Old Bank of New Zealand and Wellington Museums were completed in 1999) [3]. Most applications make use of LRBs, in some cases in conjunction with teflon sliders. 2.4 Applications in Other Non-European Countries As regards other non-European countries, in the P.R. China there were already 160 buildings isolated by means of rubber bearings in 1999 [3]; the total numbers of Chinese isolated buildings and bridges & viaducts reached 230 and 20, respectively, in May 2000 [4]. In Taiwan 10 bridges had been supported by LRBs, in addition to others being erected using viscoelastic devices (VEDs) and elastic-plastic (EP) dampers [3]. It is also worthwhile noting that the number of seismically isolated bridges using LRBs was approaching 30 in Korea in 1999, in spite of its low and moderate seismicity [3]: the main reason is that the use of SI is generally accepted in Korea as an alternative way to reduce the additional construction costs caused by the seismic design requirements recently adopted in this country. With regard to important new applications of ED systems to bridges and viaducts, to be cited are also those to: - three new viaducts of the Istanbul-Ankara freeway in the Bolu Mountains (Turkey), two of which completed and one under construction, which have been

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provided with 'multidirectional EP devices (Figure 1): as previously mentioned and explained in [1], two of these viaducts behaved in an excellent way in the earthquake of November 12,1999; - the Bangabundhu Bridge over the Jamuna River in Bangladesh, with hysteretic devices [5, 6]; - 26 important railway viaducts in Venezuela, again with hysteretic devices [5, 6]; - 5 bridges along the North-South Route in Chile, with VEDs [5, 6]. In Chile, the new hospital of the Catholic University has been isolated with HDRBs [5, 6]. 2 J Applications in Western Europe As regards Europe, to the knowledge of the authors, most new applications of the innovative anti-seismic techniques (in progress or under design or planned) concern Italy, where there were already over 30 applications of such techniques in 1998 [2], 2.5.1 Applications in Italy. In Italy to be cited are the following recent / new applications to [3, 5, 6]: - The "San Francesco Basilica Superiore" at Assisi (Umbria), which had been severely damaged by 1997 earthquake: in October 1999, it was equipped with Shape Memory Alloy (SMA) devices and innovative shock transmitters (the latter developed in the EC-funded REEDS Project, in the framework of the restoration of the Basilica (see Figure 2 and [7]). - The "San Giorgio in Trignano" Bell Tower at San Martino in Rio (Reggio Emilia, Emilia-Romagna), which had been severely damaged by the Reggio Emilia and Modena earthquake of 1996: in November 1999, it was also retrofitted using SMA devices, in the framework of the EC-funded ISTECH Project (see'Figure 3). - The San Feliciano Cathedral at Foligno, damaged by the 1997 quake, being retrofitted using SMA devices. /--CONTINUOUS SLAB

Figure la. Viaduct N. i of the Istanbul-Ankara Figure l b . Detail of the pier top of the Viaduct of freeway provided with EP devices. Figure la.

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Figure 2 a. SMA devices installed on the ''San Figure 2 b. Shock transmitters installed between Francesco Basilica Superiore" at Assisi (PG). nave and transept of the "Basilica Superiore".

- The "La Vista" and "Domiziano Viola" schools at Potenza (Basilicata), which were retrofitted in 1999 using dissipative braces (see Figure 4). - The "Gentile Fermi" school at Fabriano (Marche), a reinforced concrete building constructed in the years s50s, being one of the few examples of rationalist architecture in the town, which had been also heavily damaged by the 1997 earthquake: it is being retrofitted using VEDs (see Figure 5). - An apartment building, under construction with HDRBs at Rapolla (Potenza, Basilicata) close to a twin conventionally founded building (see Figure 6); this application is similar to the twin isolated and non-isolated buildings already existing at Squillace (Catanzaro, Calabria) [2]. - The "Rione Traiano" Civic Center at Soccavo (Naples, Campania), a very large consfruction erected with conventional foundations before the 1980 CampanoLucano (Irpinia) earthquake, when the area was not considered as seismic: this is being retrofitted using approximately 500 HDRBs. - A new hospital at Frosinone (Lazio), which has been designed using HDRBs. - Several buildings of the new Emergency Management Center for Central Italy at Foligno (Perugia, Umbria), being designed using various innovative anti-seismic systems (see Figure 7). - The new hospital at Perugia and some apartment buildings at Citti di Castello (Umbria), being isolated with HDRBs.

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Figure 3. Application of SMA devices on the Sail Giorgio in Trignano (RE) bell-tower.

- Two new buildings at the Navy Base of Augusta (Siracusa, Sicily), to be probably isolated using HDRBs, similar to those already existing at such a Base [2]. - An electric substation at Laino (Calabria), to be isolated by the Italian Electricity Board (ENEL) with wire ropes, based on the results of an extensive numerical and experimental study (this will be the first electric equipment in Italy to be provided with a SI system). - Several viaducts of the Salerno-Reggio Calabria freeway (Campania, Basilicata and Calabria), for which retrofits using ED systems are being designed. - A bronze statue of Germanicus Emperor, located in a museum at Perugia (Umbria), which was provided with a multistage SI system using HDRBs (this will be the second Italian application of SI of this kind, following that to the famous Bronzes of Riace at the Reggio Calabria Museum [2]).

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Figure 4. Dissipalive braces installed on the "La Vista" and "Domiziano" schools (Potenza).

Figure 5 a. The 'Gentile Fermi' school at Fabriano damaged by the 1997 Umbria&Marehe earthquake. Cut of the walls for the introduction of the breaces supporting the viscoelastic devices (Figure 5 b).

Figure 5 b. Viescoelastic device (REEDS Project) similar to those installed on the Fabriano school.

359

Figure 6. Isolated under construction and already erected conventional buildings at Rapolla (PZ); [IDRB during the installation phase.

Figure 7. Sketch of one of the buildings of the Center of the new Emergency Management Center of Central Italy, Foligno, Umbria, which will be seisrnically isolated using HDRBs.

In addition, SI might be adopted in Italy for other buildings or structures; in particular, based on the already promising results of an ongoing study funded by the National Group for the Defense from Chemical, Industrial and Ecological Risks of the National Research Council (CNR), it may be adopted for Liquefied Natural Gas (LNG) tanks, such as an existing spherical butane storage tank located in a highly seismic Italian site, as a possible pilot application in Italy for chemical plants (Figure 8) [8].

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Figure S. Sketch and Finite Element Model of the IMG tank selected as possible pilot application.

Finally, the possibility of reconstructing ancient villages in Marche and Umbria Regions using the original masonry materials and to make it feasible, SI is being considered in Italy: to this aim, under consideration are the village of Mevale di Visso in Marche Region (which was almost fully destroyed by the Marche and Umbria earthquakes of 1997-98, after being severely damaged by previous earthquakes) and villages around Nocera Umbra in Umbria Region (which were also severely damaged by the 1997-98 earthquakes). Data concerning the Italian applications are available on Internet at the GLIS address: http://192,107,65.2/glis. It is noted that some applications, in particular those of the new Emergency Management Center at Foligno and (if confirmed) that to the reconstruction of Mevale di Visso, will take advantage of collaborations recently established (or being established) between ENEA and Italian Regions for carrying out pilot applications on buildings, by joining the use of innovative anti-seismic systems with the energetic-environmental quality [5, 6, 9]. 2.5.2 Applications in Other Western European Countries. With regard to other Western European countries, new / recent important applications known to the authors are to [3]: - Two storage tanks of Lonza Company for hazardous chemical materials, which were retrofitted at Visp (Switzerland) using HDRBs. - Bridges in France, including a "TGV" fast train bridge at Marseille, which were provided with VEDs. - A French building at La Martinica to be provided with VEDs in conjunction with cables. - The 4 km long Santarem cable-stayed bridge over Tagus river, isolated using

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HDRBs (Portugal). - The "21th April" suspension bridge over the Tagus river (Portugal), which was upgraded using viscous dampers (VDs). - The new "Vasco de Gama" Tagus crossing (Portugal), which was provided with shock transmitters, VDs and elastic-plastic (EP) devices. - Some small bridges in Greece, provided with HDRBs. 2.6 Applications in the Former USSR Countries Some new building applications of SI were also carried out in the former USSR countries (where the total number reached 306 in 1999 [3]: these were performed in Russia, Armenia and Uzbekistan and made use of HDRBs (the previous applications mostly made use of so-called "low cost isolators"). To be cited among the aforesaid recent applications of HDRBs is the retrofit of the bank of Irkutsk-City (Russia), where isolators manufactured in the P.R. China were installed. 3.

State-of-the-art on R&D

The papers presented at the Cheju Seminar also showed that most necessary R&D activity has already been completed, not only for SI, but also for most types of ED systems (further work remaining necessary for very new devices such as electromagnetic dissipators [3]. With regard to studies performed in the European Union on SI and ED systems, those previously mentioned, concerning the REEDS and ISTECH Projects for the optimization of hysteretic, viscous and viscoelastic dampers and shock transmitters, as well as the development of innovative rolling SI systems and SMA devices, had been just completed at the time of the Seminar and confirmed the excellent behavior of such devices [3]. To be cited is also the present availability, of test equipment - not only in Japan, but also in the USA (for instance, that of Caltrans at San Diego) - capable of qualifying full or at least, large scale devices, as necessary to correctly estimating safety margins: in fact, such tests, if performed on small scale devices, may be not very satisfactory even for rubber bearings (for instance because bonding conditions could be different from those of the real scale device) and are certainly not adequate for VDs, because they cannot correctly describe fluid heating conditions [3]. Regarding future studies and application of SI and ED systems, issues which were stressed were the importance of: - extending retrofit using the innovative anti-seismic techniques; - improving studies concerning innovative systems applicable to cultural heritage; - improving knowledge and develop systems for vertical isolation; - promoting more applications to hospitals and chemical plants and components;

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- widely extending application from strategic to apartment buildings; - performing adequate monitoring; - improving knowledge on seismic input, in particular for near-field earthquakes (how correct is this point was confirmed later by the aforesaid earthquakes in Turkey); - improving studies concerning some reliability and uncertainty issues which have not been yet fully analyzed (including scale effects for qualification tests of SI and ED devices, the behavior of such devices at earthquake levels exceeding the design value, and failure modes, at extremely violent beyond design earthquakes, of structures provided with the anti-seismic systems); - considering other sources of vibrations which may damage or weaken structures, for instance, traffic. Finally, with regard to non-passive control systems (active, semi-active and hybrid systems), the papers presented by the experts at this topic stressed that also their development is further progressing well. Thus, it was decided that the attention devoted at Cheju to this topic has to be kept also at the next Seminar. 4.

Design guidelines development

The only still remaining problems for a wide-ranging application of SI and ED systems that were stressed at the Cheju Seminar concern the design rules for structures provided with such systems [3]. In general, the situation did not improve much with respect to the previous Post-SMiRT Conference Seminar held at Taormina in 1997 [10], especially because such rules are still different in the different countries, frequently still penalize the use of SI with respect to the conventional design and their application still requires heavy approval processes. The only important improvement is that there are now, at least, design guidelines available in most countries (including Italy, where they were only very recently published by the Ministry of Construction). An interesting recommendation made in the Closing Panel of the Cheju Seminar was to try to find the way to develop international design guidelines for structures provided with the innovative anti-seismic systems. Among others, these international guidelines should explain such systems correctly and leave official codes out of consideration. They would not have any legal value, but may be useful, because they would be based on knowledge and experience of real experts. This guidelines' development might be part of the activities of the International Earthquake Research Center that had been proposed at the main SMiRT Conference, held at Seoul (Korea) the week before that of Cheju Seminar. The problem to allow for these activities is to find the necessary funding. In the aforesaid Closing Panel, it was also proposed the guidelines of all countries represented in the Seminar to be translated in English and published in an

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appropriate volume at the next venue, and that, at such a venue, there shall be papers on applications, each containing sufficiently detailed reference to the codes used in the related country. With regard to non-passive control systems, it was stressed at Cheju that the development of these techniques suffer from the fact that they are not considered at all by design rules [3]. 5.

Conclusions

Based on information collected at the International Post-SMiRT Conference Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control of Vibrations of Structures, held at Cheju (Korea) in 1999 and more recent information that became available later to the authors, the state-of-the-art on the applications of SI and ED systems has been shortly reported and some remarks on the progress of R&D activities at word-wide level and design guidelines development have been made. It has been stressed that SI and ED technologies, which aim at ensuring the full integrity and operability of structures, are fully mature, as demonstrated by both the results of very numerous research projects and the excellent behavior of seismically isolated buildings and viaducts in violent earthquakes. It has been shown that, consequently, a wide extension of the use of these techniques is in progress, for both new constructions and retrofit of existing buildings. References 1. Marioni, A., The Effects of Recent Earthquakes on the Base Isolated Bridges of the Istanbul Ankara Motorway near Bolu. Proceedings, IASS Symposium on Bridging Large Spans - From Antiquity to Present, Istanbul, Turkey, (2000) pp. 261-270. 2. Martelli, A., and Forni, M., Seismic Isolation of Civil Buildings in Europe. Progress in Structural Engineering and Materials, Construction Research Communications Ltd., London, 1 (3), (1998) pp. 286-294. 3. Koh, H.M., and Martelli, A., Preface - Overview and Summary of the International Post-SMiRT Conference Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control of Vibrations of Structures. Seismic Isolation, Passive Energy Dissipation and Active Control of Vibrations of Structures - Proceedings of the Post-SMiRT Conference Seminar, Cheju, Korea, August 23-25, 1999, Seoul, Korea, (2000). 4. Zhou, F.L., Recent Development on Isolation and Energy Dissipation Used in New Seismic Design or Retrofit for Structures in China. Proceedings, IASS Symposium on Bridging Large Spans - From Antiquity to Present, Istanbul,

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Turkey, (2000) pp. 230-240. 5. Martelli, A., and Forni, M., State-of-the-Art on Seismic Protection through Innovative Techniques. Proceedings, IASS Symposium on Bridging Large Spans - From Antiquity to Present, Istanbul, Turkey, (2000) pp. 251-260. 6. Martelli, A., and Forni, M., State-of-the-Art on Recent Applications and Research Needs, Session on Base Isolation System. Proceedings, Final Workshop on "Protezione Sismica dell'Edilizia Esitente e di Nuova Edificazione attraverso Sistemi Innovativi; Programma MURST PRIN 97, Naples, Italy (2000). 7. Castellano M.G., and Martelli, A.,The Influence of Shape Memory Alloy Ties on the Seismic Behaviour of Historical Masonry Buildings. Proceedings, IASS Symposium on Bridging Large Spans - From Antiquity to Present, Istanbul, Turkey, (2000) pp. 271-280. 8. Forni, M., Martelli, A., Poggianti, A., Spadoni, B., Pugliese, A., Sano, T, Ciampi, V. and Foraboschi, F.P., Development of Innovative Anti-seismic Passive Systems for the Protection of Industrial Structures and Components. Proceedings, Second European Conference on Structural Control, Champs-surMarne, France (2000). 9. Martelli, A., Forni, M., Bettinali, F., Bonacina, G., Bergamo, G., Castellano, M.G., Medeot, R., Marioni, A., Sano, T., and Pugliese, A., New Activities Performed in Italy on Innovative Anti-Seismic Techniques for Civil and Industrial Structures. Proceedings, 1999 ASME-Pressure Vessel and Piping Conference, Boston, Massachusetts, USA, PVP-Vol. 387, ASME, New York, (1999) pp. 311-326. 10. GLIS, Seismic Isolation, Passive Energy Dissipation and Active Control of Seismic Vibrations of Structures - Proceedings of the International Post-SMiRT Conference Seminar, Taormina, Italy, August 25 to 27, 1997. A. Martelli and M. Forni eds., Bologna, Italy (1998).

THE STATE OF THE ART IN STRUCTURAL CONTROL IN ARMENIA AND PROPOSAL ON APPLICATION OF THE DYNAMIC DAMPERS FOR SEISMICALLY ISOLATED BUILDINGS

MIKAYEL G. MELKUMYAN Earthquake Engineering Center of the National Survey for Seismic Protection under the Government of Armenia, Davidashen -IVMassiv, Yerevan, 375054, Armenia E-mail: [email protected] In recent years in Armenia the introduction of seismic isolation into the practice of new construction as well as of seismic protection of existing buildings has started. In 1992 EEC of NSSP has launched active works searching for new solutions which could strengthen buildings and structures against the attacks of the underground element. New technologies, using seismic isolation systems for upgrading the earthquake resistance of existing buildings were developed in EEC, which have already attracted international professional attention. They allow upgrading the earthquake resistance of existing buildings without interruption of their functioning. Along with that seismic isolation systems were developed and designed for the construction of different new buildings. The paper presents the state of the art in structural control in Armenia [1, 2, 3, 4] and devoted to the description of the structural concepts, which can provide significant seismic safety for existing and newly constructed buildings.

1

The first attempt to design building with seismic isolation

The study of the experience accumulated in the field of seismic isolation worldwide became the basis for the first attempt to design a seismic isolation system. An experimental (pilot) project of a 4-story R/C frame building with seismic isolation was developed [5]. The number of bearings in the isolation system was 22. Vibration period of the building with base isolation was taken 1.1 sec as it was planed to test this building in the resonance regime using special vibration machine. With the bigger period of the considered building it is impossible to realize the test, as the excitation force on the vibrator shafts will decrease significantly. The design displacement of isolation system was 35 mm. The laminated rubber bearings (LRB) were designed using different approaches [6, 7, 8]. Their comparison shows a substantial disparity of the values of elasticity characteristics. However, taking into account the lack of results of our own experimental studies, the technique given in [7] was chosen. Parameters of the LRBs are presented below in Table 1. After the designing was over EEC together with the "NATRIT" plant manufactured in autumn 1993 the first in Armenia LRB using cold fastening technique. The free vibrations of the LRB were recorded when constant vertical load was applied. The damping of the LRB was equal to about 3% and the period of vibrations - 1.2 sec. Then under the horizontal force the bearing was gradually brought to failure. Force - displacement relationships in the form of hysteresis loops were obtained. The performance of the bearing up to horizontal displacement of 55 365

366

mm was elastic. With further increase of horizontal displacement cracks occurred in the lower layers of the bearing due to deterioration of rubber-metal bonding. Test proves that Armenia is able to produce seismic isolation structures and apply them to solve the main task of seismic risk reduction. Table 1. Parameters of laminated rubber bearings

2

Name of parameter

Symbol of unit

Value

Overall height Overall diameter Number of rubber layers Thickness of rubber layer Number of steel layers Thickness of steel layer Diameter of steel layer Thickness of rubber cover layer (side) Thickness of endplates Diameter of two endplates Shear stiffness Vertical load

mm mm

158.7 368.0 19.0 4.8 18.0 1.5 360.0 4.0 20.0 510.0 0.049 220.0

mm mm mm mm mm mm kN/mm kN

First application of seismic isolation in Armenia

In 1995 the first real application of seismic isolation system in the record of earthquake engineering in Armenia was realized on a one-story bathhouse. The project was developed in cooperation with Engineering Research Center of the American University of Armenia. It has been introduced in Giumri, Vanadzor and Spitak. Each of bathhouse rests on 21 seismic isolation bearing [9]. Design displacement of bearings was 10 cm. Totally "NATRIT" plant has manufactured 193 bearings with the parameters listed in Table 2. A question may arise of whether it was reasonable to apply seismic isolation system at a simple one-story building. Our opinion is that to ensure successful evolution of this new earthquake engineering line one should proceed from simple to complicated tasks gaining new experience with each step. On the other hand the design envisions placing 20 ton capacity tanks for cold and hot water in attic space of the bathhouses. This will adversely affect capability of the buildings to withstand reliably seismic impacts. However, the seismic isolation nullifies such a negative effect of water tanks.

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Table 2. Parameters of bearings for bathhouse Name of parameter

Symbol of unit

Value

Overall height Overall diameter Number of rubber layers Thickness of rubber layer Number of steel layers Thickness of steel layer Diameter of steel layer Thickness of rubber cover layer (side) Thickness of endplates Diameter of two endplates Shear stiffness Vertical load

mm mm

206.0 200.0 20.0 7.0 19.0 2.0 190.0 5.0 14.0 330.0 0.15 75.0

mm mm mm mm mm mm kN/mm kN

Four bearings have been tested at EEC. The natural vibration period and damping factor were measured. Vibration period in the horizontal direction of the bearings was equal to 1.13 sec, while logarithmic decrement was 0.31 that corresponds to 5% of critical damping. The LRBs were tested through exposition to reversal static horizontal forces. Two LRBs were tested simultaneously. Vertical load of 150 kN, simulating the weight of the building on two bearings, was applied to the upper frame of the test machine. Test of LRBs under reversal horizontal loads revealed their satisfactory behavior within the range of design displacement values. In total, 4 cycles of deforming were realized. At each following cycle the displacement was increased by 2 cm. Upon achieving a displacement of 8 cm the specimens were deformed in single direction by increasing the horizontal load up to the failure. The force - displacement relationship was obtained. As it demonstrates, approaching the design value of displacements, performance of LRB changes to clearly defined nonlinear stage. At this stage of deforming an increase in bearing stiffness is observed. Failure occurred under 14 cm displacement of the specimens. As the specimen failed, both its glue and rubber layers partly ruptured. Such type of failure is evidence to the fact that for the given rubber type the best strength of rubber-tometal bonding was really achieved. The outcome of the testing appears to be encouraging. Being this time manufactured using "hot fastening" technology, the LRBs have been collapsing only when horizontal deformation appreciably exceeded design values.

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3

Control of seismic forces at upgrading the earthquake resistance of existing 9-story R/C frame building

The 9-story R/C buildings are designed as prefabricated framed systems, the horizontal stiffness of which is provided in the longitudinal direction by the frames with strong beams and in the transverse direction by the frames with weak beams and shear walls [10]. These buildings were heavily damaged during the 1988 Spitak earthquake. The project on upgrading seismic resistance of a 9-story building by means of Additional Isolated Upper Floor (AIUF) method [11] pioneered in applying seismic isolation structures to the top part of the building instead of its base and was implemented in 1995. The considered building has the square plan with the distance between columns 6x6 m. There are 16 columns in the plan of the building. All columns are passing through the slab of the ninth floor on the height of 1.0 m into the space of the attic floor. The assembling of AIUF over the 9-story building starts after dismantling of the attic floor. The connection of AIUF to the building was designed by means of rubber bearings. In this project the high damping rubber bearings (HDRBs) were used. The bearings were designed in collaboration with Tun Abdul Razak Research Center (TARRC) to give a horizontal displacement of 13 cm. All 16 columns on the top of the building were taken into steel jackets with the height of 1.0 m so that the horizontal parts of each jacket in the size of 414x414 mm represented steel plates with the thickness of 25 mm, to which recess rings were bolted. The steel jackets of all 16 columns were connected to each other by means of steel trusses. Thus a rigid structure is created to transfer the forces from AIUF to the building. To implement the project 16 bearings were manufactured by Min Rubber Products Sdn. Bhd., Beranang, Selangor, Malaysia. Parameters of the HDRBs are presented below in Table 3. After installation of all HDRBs the structures of AIUF were assembled above them. The AIUF represents a steel frame structure with the same number of columns in plan as in the building. The base of each column is a steel plate bolted to the upper recess rings of HDRBs. All steel columns of AIUF also were connected to each other by means of steel trusses. On the level of upper belts of trusses a R/C slab is designed using precast panels. In essence, the additional floor itself also represents the rigid structure, which during the earthquakes, being supported by HDRBs, practically has no deformations. Under the earthquake impact AIUF, acting as vibration damper, reduces stressdeformed state of the building and increases its earthquake resistance in average by a factor of 1.6 [11]. The reduction of shear forces horizontal displacements in the building with AIUF takes place because of increase of the period of vibration of the whole system (building plus AIUF). Then a new type of second mode of vibration appears and becomes prevailing and as a result AIUF oscillates in anti-phase related to the building.

369

Table 3. Parameters of bearings for AIUF Name of parameter

Symbol of unit

Value

Overall height Overall diameter Number of rubber layers Thickness of rubber layer Number of reinforcing layers Thickness of reinforcing layer Diameter of reinforcing layer Thickness of rubber cover layer (side) Thickness of endplates Diameter of two endplates Thickness of end cover layer Shear stiffness Vertical load

mm mm

196.0 380.0 14.0 9.0 13.0 2.0 360.0 10.0 20.0 376.0 2.0 0.81 820.0

mm mm mm mm mm mm mm kN/mm kN

It is worth noting that the isolated upper floor allows not only upgrading earthquake resistance of a building, but enlarging its useful space as well. The most distinctive feature of the new earthquake resistance upgrading method, however, is that there is no need to re-settle residents from the building during construction works. In present time the upgrading of earthquake resistance of two buildings by means of AIUF is already accomplished in the city of Vanadzor.

The use of high damping rubber isolators for retrofitting of existing 5-story stone building Buildings of this type also have been erected in all regions of Armenia. They have the bearing walls located mainly in transverse direction. The horizontal stiffness in the longitudinal direction is provided partly by the R/C frames with strong beams and columns, made inside the body of walls, and by longitudinal walls at the edge parts of the buildings. The most vulnerable zones in these buildings are the edge parts where the direction of bearing walls had been changed. It is in these very zones that intensive plastic deformations resulting in failure of the buildings have been developed due to the weak connections between longitudinal and transverse wall [12]. The developed by EEC in 1994 structural concept aims to retrofit an existing building by means of seismic isolators using simple working technology. This is a unique pioneering seismic isolation project introduced in 1996 for an existing 5-

370

story stone building. The idea is to supply this building with seismic isolation by gradually cutting the building from its foundation. It was supposed to install the isolators at the level of foundation upper edge by creating continuous upper and lower R/C beams along all bearing walls of the building. After removing parts of walls between seismic isolators the building appears separated from its foundation and linked to it only through seismic isolators. It is very important that openings in walls are made with single-spacing, i.e., two adjacent openings should not be made simultaneously; parts of walls existing between seismic isolators should be cut off beginning from the middle of building in plan. The operation is made without resettlement of the dwellers. The world practice has had no similar precedent in retrofitting of apartment buildings. To implement the project two types of bearings were used [13]. The seismic isolators were designed in collaboration with TARRC to give a horizontal displacement of 13 cm. Min Rubber Products Sdn. Bhd., Sime Engineering Rubber Products Sdn. Bhd. and MRPRA have manufactured all together 60 HDRBs (see Table 3) in Malaysia and UK. In present time the retrofitting of one building by means of base isolation is already accomplished also in the city of Vanadzor.

5

Implementation of base isolation in construction of new four story apartment building

In 1996 for the first time in Armenia a seismic isolation system was designed for the construction of a new apartment building in the center of the old Spitak - the city that was destroyed during the Earthquake of December 7, 1988. The structure of the building represents a system with monolithic bearing walls and prefabricated slabs. Thirty-nine HDRBs manufactured in Malaysia by Min Rubber Products Sdn. Bhd. were used for this building (see Table 3). Two unique tests were carried out in 1997, when construction of the building was almost completed [4]. The first one was the trial of the technology of replacement of seismic isolators. During the construction a dummy isolator, made from the steel pipe, was installed in certain positions instead of a rubber bearing. Two jacks with the capacity of lOOt were used to lift the building at each location by about 0.5 mm. After that the dummy isolator was taken out and installation of the real seismic isolator started. The latter was gradually brought into its design position with the recess rings placed around it. Finally the two rings were bolted to the upper and lower steel plates. The trial confirms that replacement of the isolators, should this ever be necessary, can be accomplished in a quick and simple operation. In order to carry out the second test, a special loading system by which a horizontal static or dynamic force could be applied to the building at the level of the upper beams of the isolation system was designed and constructed near the building. Four cycles of loading and unloading were performed during the static tests up to a maximum displacement of 20% of the design value. It was revealed that the initial

371

stiffness (at 0.2 cm displacement) of the isolation system is more than 10 times higher than its expected stiffness at the design displacement; the ability of the system to provide an intrinsic restraint against wind loading is confirmed. The nonlinear behavior of the isolation system is close to that observed in tests on rubber samples. At a deformation equal to about 20% of the design value the observed secant stiffness of the overall isolation system correlates well with the stiffness expected at that deformation from the design calculations and the quasistatic test results on individual isolators [13]. The dynamic tests were carried out by releasing the isolation system at the displacement of 0.2 cm. The experimental value of the period of vibrations is virtually identical with the value calculated on the basis of initial stiffness of the isolation system and actual weight of the building. The displacements and accelerations at the third floor and the roof are respectively 1.03 and 1.06 times those at the first floor, figures agreeing well with the design analysis. The damping of the isolation system is equal to 8.8% of critical damping at small displacements (<0.2cm).

6

Structural concept and design of the dynamic damper for seismically isolated buildings

It is well known that the isolation of buildings from ground motion by means of different types of rubber bearings is now more and more applied in earthquake prone countries. By reducing the transmitted seismic forces, base isolation protects the contents and secondary structural features as well as the main structure. At the implementation of base isolation special attention should be given to horizontal displacements of the whole isolation system and to the restriction of these displacements. Because of this, different types of dampers were designed and implemented to reduce and control the horizontal displacement [14]. Generally, such dampers are complicated devices and their manufacturing and installation require high precision, which usually increases the cost of the isolation system. A new type of damper which is called Dynamic Damper (DD) is suggested for restriction of displacements. The idea is to create a mechanical system, which will be hanged to the superstructure on the level of isolation system and will damp the vibrations during the earthquakes. For connection of DD to superstructure laminated rubber bearing are used. The stiffness and the mass of DD should be chosen so, that the period of vibration of DD be equal to the period of vibration of the isolated building. Such a damper will allow to not only decrease the horizontal displacements but also to simplify the isolation system itself by using isolators with the cheaper and simpler rubber compound. DD increases the overturning resistance of the isolated building as well. Earthquake response analysis of isolated 4-story building with and without DD has shown that by implementing DD the horizontal displacements of the isolation

372

system as well as total shear forces can be reduced by about 27%. The magnitude of reduction of horizontal displacements depends on the parameters of DD.

7

Conclusions

For the first time in Armenia seismic isolation was designed and introduced into the practice of earthquake engineering by EEC of NSSP in 1993. The first application of base isolation system for a simple structure presenting one-story bathhouse was realized in 1995. Conventional earthquake resistance upgrading techniques to be applied for existing buildings are not acceptable in Armenia, as far as they require re-settlement of residents. Two unique and effective non-conventional seismic protection methods on increasing the earthquake resistance of existing buildings were developed and introduced into construction practice in 1995-1996. First - by means of an AIUF and second - by means of seismic isolation. Based on those methods the structural concepts with the use of HDRBs, which can provide the significant seismic safety for the existing vulnerable apartment buildings without re-settlement of the dwellers, are described. In 1996-1997 for the first time in Armenia a seismic isolation system was designed for the construction of a new four-story apartment building. This full-scale building was tested and it was revealed that the observed characteristics of the overall isolation system correlate well with those expected from the design calculations. The non-linear behavior of the isolation system is close to that observed in tests on rubber samples. A new type of damper which is called Dynamic Damper (DD) is suggested for restriction of displacements of isolation systems. The structural concept of DD is described. Earthquake response analysis of isolated 4-story building with and without DD has shown that by implementing DD the horizontal displacements of the isolation system as well as total shear forces can be reduced by about 27%.

References 1. Melkumian M. G. The use of high damping rubber isolators to upgrade earthquake resistance of existing buildings in Armenia. Proceedings of the International Post-SMiRT Conference Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control of Seismic Vibrations of Structures, Taormina, Sicily, Italy (1997) pp.861-867. 2. Melkumian M. G. Non conventional approaches for retrofitting of existing apartment buildings against future strong earthquakes. Proceedings of The World Urban-Earthquake Conference in Fukui, Japan (1998) pp.178-182.

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3. Melkumian M. G. Development of laminated rubber bearings and their implementation in Armenia. Optimization and Control in Civil and Structural Engineering. Edited by B.H.V. Topping and B. Kumar (CIVIL-COMP PRESS, Edinburg, 1999) pp.239-244. 4. Melkumian M. G. et. al. Testing of a full-scale base isolated four-story apartment building in the city of Spitak, Armenia. Proceedings of the 12-th World Conference on Earthquake Engineering, Auckland, New Zealand (2000) paper No. 0131. 5. Melkumian M. G. et. al. Research and development of laminated rubber bearings for seismic isolation of buildings in Armenia. Proc. International Conference on Continental Collision Zone Earthquakes and Seismic Hazard Reduction, Yerevan-Sevan, Armenia (IASPEI/TDNDR, 1994) pp. 228-231. 6. Coladant Ch. Base isolation and seismic bearing. Civil engineering structures and industrial facilities (1991). 7. Derham C. & Thomas A. The design of seismic isolation bearings. Report of UCB/EERC. Edited by J.Kelly (1981). 8. Kelly J. Base isolation and energy dissipation. Code design - SEAONC and UBC(1991). 9. Melkumian M. G. et. al., Design, manufacturing, testing and first application of seismic isolation bearings in Armenia. Proc. 4-th International Conference on Civil Engineering, Tehran, I.R.Iran, vol. 1 (1997) pp. 306-312. 10. Inoue T. et. al. Earthquake response analyses of precast R/C buildings damaged due to Armenia Spitak earthquake. Bulletin of Earthquake Resistant Structure research center (Institute of Industrial Science, University of Tokyo, No. 24, 1991) pp. 57-64. 11. Melkumian M. G. Dynamic tests of 9-story R/C full-scale building with an additional isolated upper floor acting as a vibration damper. Proc. Third European Conference on Structural Dynamics, EURODYN96, Florence, Italy, Vol. 2 (1996) pp. 577-560. 12. Melkumian M. G. Base isolation retrofit project in Armenia. Proc. Workshop on Use of Natural Rubber Based Bearings for Earthquake Protection of Small Buildings, Jakarta, Indonesia (1994). 13. Fuller K.N.G. et. al. Design and testing of high damping rubber earthquake bearings for retrofit project in Armenia. Abstracts of The Second International Conference on Earthquake Hazard and Seismic Risk Reduction, Yerevan, Armenia (1998) p.214. 14. R. Ivan Skinner, William H. Robinson & Graeme H. McVerry. An introduction to seismic isolation. John Wiley & Sons, Inc. (1993) 354 p.

EARTHQUAKE PROTECTION OF BRIDGES USING SLIDING ISOLATION SYSTEM AND MR DAMPERS

SATISH NAGARAJAIAH Associate professor Dept. of Civil Engineering, Rice University, Houston, TX 77005 E-mail [email protected] SANJAY SAHASRABUDHE Graduate Research Assistant Dept. of Civil Engineering, Rice University, Houston, TX 77005 IYER, R IT Engineer, 12 Technologies, Inc., Irving, TX 75039 Response of sliding isolated bridges with smart dampers in near fault earthquake ground motions is evaluated in this study. The smart damper used is a Magnetorheological (MR) damper. A 1:20 scale single span sliding isolated bridge model with four sliding bearings and a MR damper is studied. New Lyapunov based controller is developed and implemented in real time. Several near fault ground motions recorded in the Northridge earthquake are used in the testing. Shake table test results of the scaled sliding isolated bridge model with MR damper are presented to demonstrate the effectiveness of the dampers. It is shown that the smart MR dampers can reduce displacements and forces in the piers further than the passive dampers. While these displacement reductions can be achieved by increasing the passive damping further, it can only be done at the expense of greater forces in the piers.

Introduction In semi-active systems the control forces are developed due to the variation of damping of the system, and not due to direct application of control force; hence, these systems need nominal power. This is a distinct advantage when compared to fully active structural control systems, which require considerable amount of power to generate the control forces that are applied directly to the structure. Semi-active Magnetorheological dampers have been tested in fixed base structures; the test results indicate that such semi-active or smart dampers can reduce the response further compared to passive dampers (Spencer et al. 1997, Dyke et al. 1998). Response of bridges with variable dampers has been studied by Feng et al. (1990) and Patten et al. 1999. Response of bridges with elastomeric isolation systems has been studied by Kawashima et al. 1994, Symans et al. 1997, and Yang et al. 1995. The advantage of smart dampers in sliding isolated bridges needs to be evaluated.

375

376 Sliding isolation bearings, between the bridge deck and piers, reduce the deck response and the forces transmitted to the piers (Nagarajaiah et al. 1993). Earthquake ground motions in the near fault situations are often characterized by high velocity pulses, which place extreme seismic demand on the isolation systems, resulting in large bearing displacement. The technique used in such near fault situations is to provide additional damping—in addition to the energy dissipation capacity in the isolators—in the form of passive dampers. An alternative technique in such cases is to use smart dampers that provide variable damping. The response of base isolated structures, with elastomeric isolation systems and smart dampers, in near source ground motion, has been studied by Nagarajaiah (1994), Markis (1997), and Spencer et al. (1999). The studies revealed that smart dampers enhance the performance of base isolated structures. In this study the response of sliding isolated bridge with smart dampers under near fault earthquake ground motions is evaluated. 1.83 m 12.485 kN Deck 0.23 m 0.127 m Restoring Springs /

MR Damper

0.957 m

wm

Deck Beam "W4xl3 Sliding Bearing Load Cell

- 0.535 kN Pier S 2-1/2x2-1/2x1/4

0.6 m

Shake Table

jjfWr- Ug 1.52 m

Fig.l. 1:20 Scale Sliding Isolated Bridge Model with MR Damper

1:20 Scale Sliding Isolated Bridge Model with MR Dampers A single span bridge model (1:20) was designed and built based on artificial mass simulation. Weight of the deck was 12.36 kN and mat of each pier was 0.53 kN. The bridge had a clear span of 1.83 m, width of 0.89 m, and height of 0.96 m. The bridge was designed to have a natural period of 0.55 sec in the isolated case and 0.1 sec in the nonisolated condition in the longitudinal direction. In the isolated condition, the deck was free to slide relative to the pier cap. In me non-isolated condition, the deck was restrained from sliding, by means of an angle welded between deck and pier caps. System

377 identification of the bridge model was conducted for non-isolated and isolated deck conditions, with ground excitation as a white noise signal of 0 - 50 Hz frequency range and a sine sweep signal from 0 - 5 0 Hz, respectively. The fundamental periods were determined to be 0.13 sec for the non-isolated case and 0.57 sec for the isolated case (Iyer 1999). The model is shown in Fig. 1. The bridge model had sliding isolation bearings, consisting of Teflon-stainless steel interface, shown in Fig.l. The coefficient of friction varied with velocity, from 0.04 at low velocity to 0.07 at high velocity. The sliding bearings were supported by tri-axial load cells, which measured the forces transmitted from the bridge deck to the piers. Springs with a total stiffness of 1632 N/cm were connected between the left/right pier and the deck. Magnetorheological damper was connected between the left pier and the deck as shown in Fig. 1. The input voltage to the MR damper varied from 1 volt to 4 volt based on a Lyapunov controller. The variation of damper force with change in applied voltage is clearly evident from the force-displacement loops for sinusoidal excitation of 1 Hz shown in Fig. 2. A load cell of capacity 4.45 kN was used to measure the force in the MR damper. The total force in the sliding isolation system is composed of the frictional force in the sliding isolation system, the MR damper force, and the spring force. Lyapunov Based Controller The following newly developed Lyapunov based controller (Nagarajaiah et al. 2000) was used to control the Magnetorheological damper

C« =

Q™ c m»

< 0 P,(Ptx,„+P2*,„)•*/mt P, (P,*,. + P2*lm )A, lmt > 0

where C(t) = time varying damping coefficient of the damper, Cm;,, = minimum damping coefficient for zero volts, C,,,, = maximum damping coefficient for 4 volts, x la = absolute deck displacement, X[ = relative deck displacement, m ^ mass of the bridge, and p] and p 2 are constants. Test Program Shake table tests were performed on the bridge model in the isolated and non-isolated condition. These tests included MR damper off—constant zero volts—low damping, MR damper on—constant four volts—high damping, and controlled cases where the voltage is switched between one and four volts. Fifteen tests were performed for five earthquakes: 1) El-Centro SO0E Earthquake (May 18, 1940), peak table acceleration: 0.74 g. 2) Newhall Channel 1 90 Deg. (Jan. 17, 1994), peak table acceleration: 1.4 g.

378 3) Newhall Channel 3 360 Deg. (Jan. 17, 1994), peak table acceleration: 0.9 g. 4) Sylmar Channel 1 90 Deg. (Jan. 17, 1994), peak table acceleration: 0.98 g. 5) Sylmar Channel 3 360 Deg. (Jan. 17, 1994), peak table acceleration: 0.78 g. The records were time scaled by a factor of 4.47 to satisfy similitude requirements. The peak accelerations were scaled from the original recorded values. The Newhall and Sylmar earthquakes are near fault ground motions. The bridge model was instrumented with LVDT's, accelerometers, and load cells to measure response quantities. Data acquisition and real time control was performed using MATLAB/SIMULINK/dSPACE digital signal processing system. Results Experimental results for near source ground motion Newhall 90 are presented in detail. The bridge response to Newhall 90 in the non-isolated condition is presented in Fig. 3. The peak table acceleration was reduced to 0.5g to prevent yielding of the piers. The deck-table relative displacement or pier displacement time history is presented in Fig. 3(a). The total force-displacement response (total force at the deck level normalized by the weight of the deck) is shown in Fig. 3(b). The response is essentially elastic, since the table acceleration is restricted to 0.5 g, as compared to 1.4 g in me isolated case. The total force in the non-isolated case reached 0.5W. The pier drift normalized with respect to pier height is ~ 0.005. The response of the bridge to Newhall 90, in the isolated condition, in three cases with low damping (0 volts), high damping (4 volts), and smart damping (1 to 4 volts), is presented in Fig. 4 and Fig. 5. The peak table acceleration was 1.4 g, which is nearly

2r

1.5

1

^V <]>

0.6

a o

u. U
f


a

-1 -1.5-

-2

Relative Displacement: Deck - Pier (cm) Fig.2. Force Displacement Behavior of MR Dampers with Varying Voltage

379 three times that of the non-isolated case. The deck-table displacement in the passive low damping (0 volts) case is increased to 1.8 cm as shown in Fig. 4(b), as compared to 0.35 cm in the non-isolated case. However, the left pier-table relative displacement is reduced to 0.15 cm as shown in Fig. 4(c). This is due to the reduction in the total force in the isolation system to 0.27 W in Fig. 5(a), as compared to a total force of 0.5 W in the nonisolated condition. The piers would yield in the non-isolated case if subjected to the level excitation of the isolated case, 1.4g. The effect of sliding isolation system with low damping is thus to reduce the total force, at the expense of larger bearing displacement. In the passive high damping (4 volts) case, shown in Figs. 4 and 5, the deck-left pier displacement is further reduced to 1 cm, as compared to 1.72 cm in the low damping case. However, the total force is increased to 0.29 W as compared 0.27 W in the low damping case. It is obvious from Fig. 5 (b) that the energy dissipation has increased significantly in the high damping case. In the controlled case with smart damping, shown in Figs. 4 and 5, the deck-left pier displacement is further reduced to 0.75 cm and the total force is also reduced to 0.268 W. It is worth noting that with less energy dissipated—but more efficiently dissipated—in the controlled case the response reduction is superior to that of the high damping case, revealing the potential of smart damping. The newly developed Lyapunov controller is effective; however, even better control algorithms may be possible and deserve investigation. A nonlinear analytical model has been developed for the sliding isolated bridge and the smart damper. In Fig. 5 the simulated force-displacement loops are also shown; the agreement between experimental and simulated results is good. Figs. 6 and 7 show a comparison of peak values of relative deck-table displacement and peak force/weight in three different earthquakes, El Centro, Sylmar 90 and Newhall 90, with increasing peak table acceleration. It is evident from Figs. 6 that the controlled case with smart damper leads to least displacement response in all three cases; the reduction being more in the case of strong near source ground motions Sylmar 90 and Newhall 90. The peak force, shown in Fig. 7, in the controlled case is nearly the same as the low damping case. It is clearly evident that the controlled case with smart damper, with the same or lower level of peak force then the low damping case, can reduce the displacement further then the high damping case. Hence, both displacement and force are reduced in the controlled case with smart damper, demonstrating the advantages of smart dampers. It is also evident that the developed Lyapunov controller is effective in all three-ground motions with different characteristics.

380 Conclusion Response of a sliding isolated bridge with smart damper, subjected to near source ground motions, has been experimentally and analytically investigated. A new Lyapunov controller has been developed and implemented in a shake-table study. In bridges subjected to near source ground motion it is clearly evident that the sliding isolation system with passive low damping (zero volt) reduces the shear force, effectively, but with increased bearing displacement, which can be problematic. Introducing passive high damping (4 volt case) reduces the bearing displacement, at the expense of higher shear force at the isolation level. The semi-active case or controlled case with smart damping reduces both the displacement and force effectively, indicating the advantage of smart damping and efficient energy dissipation. While the displacement reductions can be achieved by increasing the passive damping further, it can only be done at the expense of greater forces in the piers. It is also evident that the control strategy is effective regardless of the nature of the earthquake motion. Acknowledgments Funding for this project provided by the National Science Foundation Grant (CMS9733962 / 9996290), with Dr. S. C. Liu as the Program director, and the Mid-America Transportation Center is gratefully acknowledged. References 1. Dyke, S. J., Spencer, B.F., Sain, M. K., and Carlson, J. D. (1998). "An experimental study of MR dampers for seismic protection," Smart Materials and Structures, Vol. 7, 693-703. 2. Feng, Q., and Shinozuka, M. (1990). "Use of a variable damper for hybrid control of bridge response under earthquake," Proc. U. S. Nat. Workshop on Struc. Control, USC Pub. CE-9013. 3. Kawashima, K., and Unjoh, S. (1994). "Seismic response control of bridges by variable dampers," J. of Struct. Eng., ASCE, Vol., 2583-2601. 4. Makris, N. (1997)."Rigidity-plasticity-viscosity: can electrorheological dampers protect base isolated structures from near-source ground motion" Earthq. Eng. Struct. Dyn., 26, 571-591. 5. MATLAB: The Math Works, Inc. Natick, Massachusetts (1994). 6. Nagarajaiah, S., Sahasrabudhe, S., and Iyer, R. (2000). "Semi-active Control of Sliding Isolated Bridges with Magnetorheological Dampers subjected to near source earthquakes" Structural Research at Rice Report 52, Dept. of Civil Eng., Rice University, Houston, TX. 7. Nagarajaiah, S., Riley, M. A., and Reinhorn, A. M., (1993). "Control of sliding isolated bridges with absolute acceleration feedback," J. of Eng. Mech., ASCE, Vol. 119, No. 11,2317-2332.

381

8. Nagarajaiah, S., (1994). "Fuzzy controller for structures with hybrid isolation system," Proc. First World Conference on Structural Control, USC, CA, TA2-67-76 (1994). 9. Patten, W. N., Sun, J., Li, G., Kuehn, J., and Song, G. (1999). "Field test of an intelligent stiffener for bridges at the 1-35 Walnut Creek Bridge," Earthquake Eng. Struct. Dyn., Vol. 28, 109-126. 10. Spencer, B.F., Dyke, S. J., Sain, M. K., and Carlson, J. D., (1997)."Phenomenological model for Magnetorheological dampers," J. of Eng. Mech., ASCE, Vol. 123 (3), 230238. 11. Spencer, B. F., Johnson, E.A., and Ramallo, J.C. (1999). "Smart isolation for seismic control," Proc. Int. Symp. on Motion and Vibration Control, Japan, 169-174. 12. Symans, M.D., and Kelly, S.W. (1999). "Fuzzy Logic Control of a Seismically Isolated Bridge Structure," Int. J. on Earthquake Engineering and Structural Dynamics, Vol. 28, No. 1, pp. 37-60. 13 Yang, J.N., Wu, J.C, and Agrawal, A.K., (1995). "Sliding Mode Control for Nonlinear and Hysteretic Structures", J. of Eng. Mech., ASCE, Vol. 121, No. 12, pp. 1330-1339. 14 Yang, J. N., Wu, J. C , Kawashima, K., and Unjoh, S., (1995). "Hybrid control of seismic excited bridge structures," Earthquake Eng. Struct. Dyn., Vol. 24, 1437-1451.

Newhall 90 Earthquake

Fig. 3. Measured Response of Bridge Model in Non-isolated Condition

382 Newhall 90 Earthquake 0.0 V -.-4.0 V - Control ' ~

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. Simulation - Experimental

0 -0.2 -0.4

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Fig. 5. Measured and Simulated Response of Sliding Isolated Bridge Model with MR Damper in Passive Low (0 v), Passive High (4 v), & Controlled Cases (0 to 4 v)

383 E2.5 JJ,

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R E C E N T D E V E L O P M E N T S IN SMART S T R U C T U R E S R E S E A R C H IN INDIA S. N A R A Y A N A N Professor, Department of Applied Mechanics Indian Institute of Technology, Chennai 600 036, INDIA Email : [email protected] V. B A L A M U R U G A N Combat

Scientist, Mechanical Systems Laboratory Vehicles R& D Establishment, Chennai 600 054, Email : [email protected]

INDIA

Several academic institutions and research laboratories and organisations are engaged in research in the area of smart structures, active vibration control in India. These include the Indian Institutes of Technology, Indian Institute of Science, National Aerospace Laboratory, Indian Space Research Organisation, Vikam Sarabhai Space Centre, Defence Research and Development Organisation etc. Mainly the research activities focus on the use of smart materials as actuators and sensors in vibration control. Some effort is also devoted to the development and characterisation of smart materials. Finite element modelling of composite laminates embedded with piezoelectric films and ceramics, magneto-strictive materials for structures and integrity analysis have been developed. Constitutive modeling of shape memory alloys, vibration control using active constrained layer damping treatment, evaluation of optimal control schemes using feed forward and feedback techniques, optimal location of actuator and sensors are some of the specific research areas undertaken. Active vibration control schemes have been devised and implemented on basic structural configurations like beams, plates and shells. Application areas include helicopter vibration control, flutter control, shape memory alloy as active vibration absorber, smart underwater anechoic linings from rubber matrix composites, active suspensions for vehicular vibration control and active noise control. This paper will highlight some of these activities in some detail.

1

Introduction

Significant progress has been made on various fronts in the field of the smart structures technology in the last two decades. This highly multi-disciplinary technology have been extensively explored by the researchers for possible applications in various fields. The holding of SPIE '96 symposium on smart materials, structures and MEMS in December '96 in Bangalore created a wave of enthusiasm from the researchers in India to explore the field of smart technology. Several research programmes are on the anvil in many of the Indian academic and research institutions. A society called Institute of Smart

385

386 Structures and Systems (ISSS) has been formed in 1999 which will serve as a common forum for sharing the information among the researchers. The benefits of exploiting the smart structures technology have been perhaps most widely recognized by aerospace engineers and it is no wonder that several practical application programmes are currently being undertaken in this sector world-wide for sorting out problems in utilization of this technology. The structures panel of Aeronautical Research and Development Board and DRDO of India are funding many research activities in this technology to various Research and academic institutions. A smart or intelligent structure involves distributed actuators and sensors, and one or more microprocessors that analyze the response from the sensors and use distributed-parameter control theory to command the actuators to apply localised strains. A smart structure has the capability to respond to changing external environment (such as loads, temperature and shape change) as well as to changing internal environment (such as damage or failure). Smart structure applications are wide ranging from active shape control, vibration and noise control, improved damping, improved aeroelastic stability, to change stress distribution and damage assessment. The developments of these structures offer great potential for use in advanced aerospace, hydrospace, nuclear and automotive structural applications. Many types of actuators and sensors are being considered, such as fibre optics, electro-rheological fluids, piezoelectric materials, shape memory alloys, electrostrictive materials, magnetostrictive materials etc. Development of distributed parameter control algorithms, mathematical modelling of smart systems etc. are receiving increasing attention. An international conference on Smart materials, structures and systems has been held in India in conjunction with the Ninth national seminar on aerospace structures (NASAS) during 7-10 July 1999. Majority of this paper highlights the contributions made in this conference. 2

Activities in the development of sensors and actuators

The remotely piloted low subsonic propeller driven air vehicle Nishant has been designed and developed for aerial survey and reconnaissance purpose. Its range and endurance are very critical and hence every effort is taken to shed the weight as much as possible. Introduction of smart concepts provide new opportunities for weight reduction. It uses at present 2 actuators for its two ailerons which are required to be actuated upto ±5 during the flight envelope. The hinge moment required is of the order of 0.030 Kgf-m/deg. The existing electro-mechanical actuator with control linkages weigh around 2 Kgs. It is

387

proposed to replace this system by piezoelectric bimorph of 40 layers clamped at one end and inserted into a fork extended from the aileron 30 . The force at the tip of the piezo-bimorph cantilever is estimated to be 4.9 Kgf maximum with a corresponding displacement of 2.6 mm that will result in ±5 rotation of the aileron. The required bimorph measuring 25 mm width and 220mm length weighs 115gm only. The total smart system is estimated to weigh not more than 500 gms. The same concept is being considered to other control surfaces as well. In the same vehicle a concept of smart Gimbal using piezoceramics is being studied 30 . Applications of smart concepts for structural health monitoring of ageing aircraft and helicopters are also being considered. The challenge really lies in developing these integrated smart system embedded in the structures to the required airworthiness standards. Ferroelectric thin films are being considered for application in numerous electronic and electro-optic devices ranging from non-volatile memories to large-scale electro-optic applications 15 and in the field of integrated microelectronics 2 5 . These thin films were deposited with techniques such as sol-gel 15 and pulsed laser ablation microelectronics 2 5 . Glasses containing ferroelectric crystallites are promising materials for application in polar and non-linear optical devices 34 . The characterization study of PVDF for its device potential in their electrical parameter like dielectric constant, loss of conductivity both ac and dc, pyro- and piezo- coefficients and their thermoelectric energy conversion capability and the thermal expansion has been successfully done 4 2 . Lead magnesium niobate relaxor ferroelectric materials can be used as excellent moisture sensor in both low (order of lppm) as well as high (order of 1000 ppm) moisture content ambients u . Extensive R&D work has been carried out on monolithic PZT ceramics and piezocomposite materials suitable for the fabrication of smart transducers 3 1 . Characterization of ferrites as gas sensor materials3 have been carried out by Gopal Reddy et al 16 . IR sensors have been developed using MEMS technology by Jain 19 . A vibration sensor has been made by fabrication of a seismic mass supported by four thin silicon hinges. Movement of the seismic mass in the presence of vibration is monitored to sense and control vibrations. A capacitance type miniature accelerometer has been designed using finite element technique 2 1 . Trends in standardization of interfaces for smart transducers have been provided by Subramani 3 9 . A simple method to distinguish between the effects of strain and temperature in sensor application has been proposed and demonstrated using a chirped fibre Bragg grating 23 . Experimental studies on devices fabrication, test and

388

evaluation of pyroelectric detectors are carried out in which the devices are packaged using lithium tantalate (LiTa03) pyroelectric sensors having the required metallization and black absorber coatings and hybrid micro circuit package technique 10 . 3

Activities in the smart structures development

Krishnamurty 24 have studied feasibility of using magnetostrictive materials for vibration control, improvement in pointing accuracy of air borne antennae and sensing damages in laminates. He modelled these problems using a laminated composite thin walled beams containing a magnetostrictive layer. A finite element model incorporating the viscoelastic effects of the adhesives for the analysis of adhesively bonded smart structures have been proposed by Ajay Gandhe et al. 13 . In this the piezoactuator and the substrate (beam) have been modelled as linear elastic materials and the adhesive as linear viscoelastic material using three parameter Kelvin model. Hemalatha et al. 18 have given a general theory for smart laminated composite thin-walled beams of arbitrary cross-section. They have also demonstrated feasibility of vibration suppression using magnetostrictive layers embedded in the structure. Static and dynamic analysis of piezothermoelastic composite laminates have been studied by Ganapathi et al. 12 . They have studied the influence of various parameters on the structural behaviour of the plates. Roy Mahapatra and Gopalakrishnan 32 have studied the composite beam with embedded smart layers using spectrally formulated finite element. The problem which is formulated in the transformed frequency domain, characterizes, the mass distribution exactly through the use of exact solution to the wave equation as the kernel function for element formulation. Vibration control capability has been demonstrated using these elements. The smart control and material technology have created a new paradigm in the design of members against instability failures. The state of the art of control of buckling of struts is reviewed and a generalized approach to active control of instability failure of struts has been provided by Kalyanaraman 2 0 . A schematic of active control of buckling modes is given in Fig. 1. The steps involved in buckling control are, 1. Calculate the number of half sine waves, N, into which the strut be forced to buckle. 2. Provide N sensors and actuators on each of the two extreme fibre surfaces of the strut, equally spaced along the length of the strut such that they would be at the crest of the N half waves. The material of the sensor

389

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Senstrs/AauattE '

Sw ~ NSncwaves = L

^

Figure 1. Schematic of active control of buckling modes

and actuator would depend upon the rate of loading, size of the member, etc. Usually electrical faster loading and lower actuator forces and SMA actuators would be appropriate in the case of slower loading and larger actuator force requirement. 3. At any load P obtain the strain values from all sensors. 4. Evaluate the average axial strain, corresponding to the axial deformation. 5. For various trial values of the desired curvature at the crest of all the N half sine waves, calculate the RMS value of the actuator strain to be applied and choose that value which minimizes the RMS value. 6. Calculate the strains to be applied to all the actuators. 7. While these actuators are controlled, continuously monitor and repeat the steps 1-6. It has been shown theoretically that the buckling failure of a strut can be avoided and failure governed by material strength can be achieved by using smart structures concepts using smart sensors and actuators. Active damping in a smart cylindrical shell using piezoelectric sensors/actuators has been studied by Saravanan 33 . A three noded isoparametric, semianalytical finite element is developed and used to model the cylindrical shell. A first order shear deformation theory is considered for the displacements and a layerwise theory is considered for the electric potential. Rubberlike materials in various geometries are used for lining hard surfaces for reducing their reflectivities in underwater acoustics. Reinforcement of such viscoelastic matrices having high Poisson's ratio, with short high modulus fibres can make the materials smart 2 7 . Shear mode oscillations are generated through micromechanical interactions of the fibre-matrix interfaces, when stimulated by dynamic acoustic waves. Very low volume fraction of short fibres dispersed in the rubber in a planar random orientation are sufficient to cause mode conversion and resultant echo reduction at the lined

390

surface. A theoretical model based on shear lag analysis has been developed for simulating echo reduction performance of such composites by Narayandas and Nair 27 . The use of SMA as actuators is an area of great interest. One of the most widely expoited use of SMA are those in which an external constraint prevents the SMA from refusing to its original shape on heating. This phenomena is commonly referred to as constrained recovery forces. Keeping this end objective in mind, the embeddment of SMA in carbon/epoxy composites has been studied by Ramesh Sundaram et al. 40 . Suresh et al. 41 have investigated the flexural behavior of smart composite panels subjeted to electromechanical loads. An eight noded isoparametric finite element with usual five mechanical and two electrical degrees of freedom has been developed. The effect of various laminate parameters and actuators is investigated. 4

Activities in active vibration control

Raja and Rajagopal 29 have offered a generalized piezothermoelastic finite element formulation of a laminated beam with embedded piezoelectric materials as distributed actuators/sensors. Electromechanical and electrothermal couplings are incorporated using the linear equations of piezothermoelasticity. Inclusion of temperature and electric potential as state variables along with mechanical displacement permit a unified representation of multifield coupling in finite element formulation. A two noded 3D beam element is derived using first order shear deformable displacement theory to model direct and coupled effects. Eigen structure assignment technique using output feedback is employed in the controller design which is subsequently adopted to actively control the first three modes of a cantilever PZT/steel/PZT beam. The control spillover effect is minimize d by optimally selecting the actuators/sensors location and optimizing the damping factors of the desired closed-loop eigenvalues. Venkataraman 43 reviewed the vibration prediction and reduction in helicopters and described the active control methodology and their relative merits. Balamurugan and Naryanan 1 ' 2 ' 3 ' 4 ' 5 ' 6 ' 7 ' 8 ' 9 have developed piezolaminated beam, plate and shell finite elements and studied active vibration control of piezolaminated smart beams, plates and shells. They have used classical control laws like, direct proportional feedback, constant gain negative velocity feedback and Lyapunov feedback based on output feedback and modern control law, Linear Quadratic Regulator (LQR) scheme which is based on state feedback. A composite shell structure is then considered with thin PZT piezoceramic

391 layers embedded on top and bottom surfaces. A C° continuous, shear flexible, nine-noded quadrilateral shell element derived based on field consistency principle has been used and has been developed to include the stiffness, mass and electromechanical coupling effects of the piezoelectric sensor and actuator layers. The linear constitutive equations coupling elastic field and electric field in piezoelectric medium is expressed by the direct and converse piezoelectric equations. A doubly curved shell is considered. Assuming small deformation and considering the effect of shear deformation, the total strain could be expressed as, {e} = < /* > + <

6

> where, {ep} are midplane (membrane)

strains , {e&} are bending strains and {e s } are shear strains. In general the electrical field E is expressed as, E = {Ex Ev EZ}T = —{,x ,y ,z}TThis element has five elastic degrees-of-freedom u°,v°,w,6x,8y per node and one electrical degree-of- freedom per piezoelectric layer, i.e., electric potential <j> is assumed to be constant over an element and varying linearly through the thickness of the piezoelectric layer. The element electrical energy is, We = | / v [jE]T[D]dV^, where Vp is the volume of the piezoelectric layer in an element. The equation of motion for an element is given by,

WeuuW} + \KUW}

+ [K^]{<} = {F?}

[KluW} + [KUW) = {Feq}

(1) (2)

where, [M^u] is the element mass matrix and [K£u] is the elastic element stiffness matrix obtained from the kinetic energy and strain energy functional. [•^|J = [Kt]T a r e t h e elastic-electric coupling stiffness matrices and [K^] is the electric stiffness matrix, {F£} is the applied mechanical force and {F^} is the applied electrical charge. When equation (2) is applied to sensors, the sensed voltage is given by, {s} = -[^^[K^tf,}. Combining (1) and (2) and assembling the elemental equation, the global equation of motion can be written as,

[Muu}{6} + [Cuu]{6} + [Kuu] - [Ku^WK^]

[K$u] {6} = {Fs} - [Kua}

(3) where {<pa} is the actuator voltage vector and [Cuu] is the internal structural damping. Using normal mode transformation and introducing state space variables {£} = <

>, the system dynamics can be written in state space

392

form as ,

{i} = [A]{0 + [B]{M + [B]{ud} and

{y} = [[0] [Co][*]]{0 = [(?„]{£}

(4) where {77} are the modal coordinates, [A] is the system matrix, [B] is the control matrix and [B] is the disturbance matrix. {ud} is the disturbance input vector and {a} is the control input and {y} is the output vector. A cantilevered laminated composite plate (Rx = Ry = Rxy = oo) with both the upper and lower surfaces symmetrically bonded with piezoceramic is considered and active vibration control performance have been studied using classical control laws like constant gain negative velocity feedback 2 . The active control performance when the plate is subjected to random loading which is a band limited white noise of power spectral density lxlO -6 TV 2 /(rad/sec) in the frequency range of 0 to 1000 rad/sec is also considered. The uncontrolled and controlled responses at the free end of the plate are shown in Figs. 2 and 3 respectively. It can be noted that there is a reduction in mean square response (MSR) in the controlled case. LQR optimal control theory is also used by

3uo 200 lOO

-100 -200 -300

Figure 2. Uncontrolled tip response of the piezolaminated smart plate to the random loading (MSR = 1.03956e - 8)

Balamurugan and Narayanan 4 to determine the active control gains. The cost function is given by, J = f£°({y}T[Q]{y} + {(i>a}T[R]{<j)a})dt, where, [Q] and [R] are the semi-positive-definite and positive-definite weighting matrices on the outputs and control inputs , respectively. In this case, larger (relatively) elements in [Q] mean that more vibration suppression ability from the controller is demanded, while larger [R] elements mean one's interest is in limiting the control effort (voltage). Assuming full state feedback, the control

393

Figure 3. Uncontrolled tip response of the piezolaminated smart plate to the random loading (MSR = 2.25384e - 8)

law is given by, {a} = -[Gc]{£} = -[^{BfiP}^}control gain and [P] satisfies the Riccati equation,

Where, [Ge] is the

[Af[P] + [P}[A] - [P}[B}[R}-l[Bf[P] + [C0]T[Q}[C0] = 0

(5)

The closed loop system dynamics is given by, {£} = ([A] - [B][Ge]){0 + [B]{ud} = [Aa]{t} + {B]{ud}

(6)

Figure 4. Semicircular piezolaminated smart shell with one end fixed

A semicircular steel shell embedded with a PZT piezoceramic layers on the top and a bottom surface is considered 3(Fig. 4). One end of the shell is fixed and the other end is free. It is 150mm wide and 6mm thick with the inner radius of 300mm. The thickness of the PZT layers are 0.25mm.

394

The material properties of PZT are, Ea = Es = 63xl0 9 N/m 2 , pa = ps = 7600 kg/m3, va = vs = 0.3, d 3 i = d32) = - 1 . 7 9 x l 0 - 1 0 m / l / , ( c n = e22 = e 33 = 1.650xl0~ 8 F/m. An initial structural damping is assumed to be 0.2%. An impact line load of 666.7 N/m is applied to the free end of the shell

-hoop displacement -radial displacement

I°" = - o.:

ft"

1.5 T i m e (sec)

Figure 5. Controlled tip response with 20% actuator coverage along the hoop direction from the fixed end

-hoop displacement -radial displacement

1 .5 rime (sec)

Figure 6. Controlled tip response with 40% actuator coverage along the hoop direction from the fixed end

along the hoop direction for 1 millisecond and tip responses with and without control are evaluated. The distributed vibration control of the shell with different lengths of actuators is investigated. SISO LQR scheme is used (with Q = 10 10 and R = 1). Figs. 5 and 6 show the tip responses and actuator voltages for 20% and 40% coverage of the actuators. Fig. 7 summarises the

395

damping ratios for the first two transverse modes. It shows that the controlled

40 eo E x t e n t of A c t u a t o r c o v s r a f l e (%)

Figure 7. Damping ratio vs extent of actuator coverage along the hoop direction from the fixed end

damping ratio increases rather quickly as the extent of actuator coverage increases (from fixed end) upto 40% coverage and afterwards levels off at 70% coverage. It can also be observed that the second mode damping ratio initially increases upto 20% coverage and then decreases upto 40% coverage. This is due to the control spillover to the second mode. But as the extent of actuator coverage increases, the second mode damping ratio also increases and levels off at 80% coverage. The active control performance of the shell when subjected to a band limited white noise of power spectral density 10~ 2 N2/(rad/sec) in the frequency range of 0 to 2500 rad/sec is considered. The variation of the root mean square (RMS) response, with the extent of actuator coverage is indicated in Fig. 8. It can be observed that we could get optimal vibration control performance with optimal cost using 60% actuator coverage. Balamurugan and Narayanan 6-7 have studied the active vibration control performance in beams using enhanced active constrained layer damping initially proposed by Liao and Wang 2 6 . Two mechanisms of control operate in ACLD treatments passive and active actions. The passive action is due to shear deformation in the constrained viscoelastic layer and the active action arising from the bending moments developed by the constraining active layer. Liao and Wang 26 have designed EACLD by introducing edge elements connecting the piezoelectric active cover sheet with the host structure to improve actuator authority. A cantilever beam with partially treated EACLD (Fig. 9) is considered7 and the vibration control performance has been studied for different parametric combinations. A beam finite element has been formulated based on Timoshenko's beam theory. The edge elements are modeled as

396

20

30 40 50 60 70 Extent of actuator coverage (%)

100

Figure 8. RMS response of actuator coverage along the hoop direction from the fixed end

daip

•£

Figure 9. Cantilever beam with partially treated EACLD treatment

equivalent springs mounted at the boundaries of the piezoelectric layer , connecting them with the host structure. The Golla-Hughes-Mctavish (GHM) is employed for the damping characteristics modal of the viscoelastic layer 26 . The GHM model represents the material modulus function as a series of mini-

397 oscillator terms in Laplace domain, sG(s) = K, 1

s 2 + 2C,rCjrs

+ £<*>• s

2

+ 2C,rCjrs + w 2 .

(7)

The factor n corresponds to the equilibrium value of the shear modulus. The GHM parameters K and a are related to the shear modulus and loss factor of viscoelastic materials. The models of PCLD, ACLD and purely active systems can also be obtained as a special case of EACLD model with appropriate assumptions. LQft optimal control theory is used to determine the active control gains. An EACLD treated cantilever beam of the dimension 300mm x 15mm x 3mm is considered with the viscoelastic layer and piezoelectric cover sheet of 100mm x 15mm at 30mm from the fixed end.

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1000 rad/sec

1.0

Table 1: Systems parameters Table 1 gives the other system parameters. An impact load of 1.0N is applied at the free end of the cantilever beam for 1 millisecond duration. Fig. 10 shows the vibration control performance for PCLD, ACLD, purely active and EACLD systems. The EACLD treatment with sufficient edge element stiffness, outperforms the PCLD, ACLD and purely active systems. This is due to increase in the active action authority. In order to study the effect of the edge elements in EACLD treatment, three aspects such as active action authority, passive damping ability and hybrid (combined) active-passive action ability are considered. To establish vibration control performance and control effort indices, the system is assumed to be subjected to a white noise external disturbance with zero mean. The system response consists of a state vector with zero mean and a variance given by

398

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Time (sec)

0.1 0:2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Time (sec)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (sec)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (sec)

Figure 10. Vibration control peformance of purely active, ACLD and EACLD (with the value of edge elements to be 103 and 108 N/m, Q = 10 10 , R = 1

the solution [Pt] of the Lyapunov equation, [A][Pi] + [Pi][A]T + {B}Ud{B}T = 0, where [Pt] = E[{q(t)}{q(t)}T]. The output co-variance matrix can be written as, E[yyT] = [C0][Pi][C0]T. In this study, a random disturbance with intensity 2.5 x 10~5N2/(rad/sec) is applied to the beam at the free end and the output {y} is chosen to reflect the beam tip displacement. The standard deviations of the output vibration amplitude and required voltage are defined as aw and av respectively. An index which represents the active-passive hybrid action quantitatively is defined as, Iap = "^p""" x 100. Here, (
399 the effectiveness of the hybrid actions.

Rjrely active case

/

1.E+O0

1.E-(02

1.E404

1.E-406

Kx

1.&OB

1.E+10

1.E+12

k-,(NM

Figure 11. (Iap/
Fig. 11 indicates that the keq at which Iap/<JV value of EACLD is larger than that of a purely active case could be denned as kcr. If the keq more than kcr is provided in EACLD design, it will outperform the purely active and passive designs. Figs. 12 and 13 show that the values of Iavjav for a wide range of K and a for ACLD and EACLD with keq > 10 8 . It can be noted that the EACLD designs outperform the purely active design for the entire K - a range as keq is larger than maximum kcr. Vibration control of smart aerospace structure which simulates satellite with solar panels and helicopter rotors is done using piezoelectric actuators. The LQR control is applied to find feedback gains and simulate active vibration control 14 . Active vibration control of aerospace structures using smart concept is o ne of the potential areas of application, the successful implementation o f which requires design, development of instrumentation electronics, digital signal processing technology, computers, control system, robust control law, structure with built-in sensors and actuators coupled with good analytical and system identification studies. Some of these issues and requirements have been studied by Shankar et al. 34 - 35 . The control system based on the Least Mean Square (LMS) algorithm has been developed for active control application 36 . The adaptive algorithm can simultaneously perform system identification and control. Active vibration control of beam has been demonstrated using vir-

400

logKCN/m1)

Figure 12. (/ a p /cr v ) versus K VS O: (ACLD de- Figure 13. {lap/'^u) sign space) design space)

Jx^

versus K vs o: (EACLD

tual instrumentation software 17 . System is fitted with piezoelectric sensors and actuators. The displacement and velocity feedback gains are adjusted optimally according to the frequency of vibration. The study is also extended to active vibration control of a beam with a piezoelectric patch. Feedback from computer is given to piezoelectric patch, which applies counter force to control the vibration. Kandagal and Kartik Venkataraman 22 have investigated the performance of piezoceramic as actuator elements to control classical bending-torsion flutter. A typical airfoil section analysis is used to provide an understanding of the fundamental mechanism involved in flutter control. The control action is through single-input single-output control. The results demonstrated the effect of distributed surface bonded piezoceramic actuators on flutter control. Srikanth Phai and Kartik Venkataraman 38 have studied the vibration damping properties of an electro rheological fluid sandwiched between flexible aluminum face sheets. The ER fluid is treated as a viscoelastic material sandwiched between two elastic layers. The partial differential equations describing the dynamics of the sandwich beam are solved for a cantilever beam by modal analysis. The damping effect of ER fluid has been demonstrated by simulating a sandwich beam cantilevered at one end. The ER fluid is found to dampen the vibrations in higher modes quickly with open loop control.

401

5

Summary and conclusions

In this paper, some of the recent activities carried out in India, on the smart structures technology and their application to active vibration control, are highlighted. The research activity in this area is given prim e importance in the academic and research institutions and laboratories in the country. References 1. Balamurugan, V. and Narayanan, S., Active vibration control of smart beams using distributed piezoelectric sensors/actuators, Proceedings of the National Seminar on Aerospace & Related Mechanisms, DRDL, Hyderabad during June 25 & 26, (1999). 2. Balamurugan, V. and Narayanan, S., Vibration control of laminated composite plates using piezoelectric active devices,Proceedings of the International Conference on Smart Materials Structures and Systems, IISc, Bangalore during July 7-10, (1999). 3. Balamurugan, V. and Narayanan, S., Vibration control of shells using distributed piezoelectric sensors and actuators,Proceedings of the 51st Annual general body meeting of Aeronautical Society of India & seminar on Advances in Aerospace Technologies, (SAAT-2000), January 21 & 22, (2000). 4. Balamurugan, V. and Narayanan, S. Active vibration control of smart shells using distributed piezoelectric sensors and actuators, Smart Materials and Structures, (in press), (2000). 5. Balamurugan, V. and Narayanan, S. Finite element formulation and active vibration control study on beams using active constrained layer damping treatment (SCLD), Jl. of Sound and Vibration, (under review), (2000). 6. Balamurugan, V. and Narayanan, S., Finite element formulation and vibration control study on beams using enhanced active constrained layer damping treatment (EACLD), Jl. of Aeronautical Society of India, (in press), (2000). 7. Balamurugan, V. and Narayanan, S., Study on active-passive hybrid damping in beams with enhanced active constrained layer treatment, Bit Smart Materials and Structures (under review), (2000). 8. Balamurugan, V. and Narayanan, S., Shell finite element for smart piezoelectric composite plate/shell structures and its application to vibration control, Finite Elements in Analysis and Design, (under review), (2000). 9. Balamurugan, V. and Narayanan, S., Active vibration control study on

402

10.

11.

12.

13.

14.

15.

16.

17.

18.

piezolaminated smart beams using finite element method, Defence Science Journal, (under review), (2000). Dhanunjaya, D., Nagendra, C.L., Shanbhogue H.G., and Thutupalli, G.K.M., Performance Evaluation of Pyroelectric Detectors for Space Application, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 268-273, (1999). Dipika Saha, Saha, M., Sengupta, K., Sen, A., and Maiti, H.S., Lead Magnesium Niobate Relaxor Ferroelectric Materials as a Moisture Sensor, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 103-107, (1999). Ganapathi, M., Giri, S.N. and Sambandam, C D . , Static and Dynamic Analysis of Piezothermoelastic Composite Laminates, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 331-336, (1999) . Gandhe, A., Seshu, P., Mujumdar, P.M. and Seth, B., Viscoelastic Analysis of Induced Strain Actuators, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 319-324 (1999). Giri, N.P., Pradeep, S. and Rao, Y.V.K.S., Selection of Optiaml Location of Piezo Electric Actuators and Vibration Control of Smart Aerospace Elements,Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 424-429, (1999). Goel, T.C., Tripathi, A.K. and Chariar Vijayaraghavan, M., Ferroelectric Thin Films : Ceramics and Composites, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 65-72, (1999). Gopal Reddy, C.V., Manorama, S.V. and Rao, V.J., Preparation and Characterisation of Ferrites as Gas Sensor Materials, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 146-151, (1999). Harpreet Singh, Singh, S.P. and Agarwal, V.P., Active Vibration Control of a Beam Using Virtual Instrumentation Software,Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 443-448, (1999). Hemalatha, E., Krishna Murthy, A.V. and Nagabhushanam, J., A General Theory for Smart Laminated Composite Thin-walled Beams,Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 325-330,

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(1999). 19. Jain, V.K. and Jalwania, C.R., Developments of IR Sensor Using MEMS Technology, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 190-198, (1999). 20. Kalyanaraman, V., Smart Control of Instability of Struts,Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 343-348, (1999). 21. Kamesh, J.V., Sivakumar, V., Mangalgiri, P.D. and Upadhya, A.R., Design of Capacitance-Type Minature Accelerometer,Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 229-233, (1999). 22. Kandagal, S.B. and Kartik Venkataraman, Flutter Control Using Distributed Piezoceramic Actuators and Sensors,Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 455-459, (1999). 23. Kiran Kumar, T., Shodhan Shetty, K., Srinivas, T. and Selvarajan, A., Dual Fibre Bragg Grating for Simultaneous Detection of Strain and Temperature for Sensor Application,Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 263-267, (1999). 24. Krishna Murthy, A.V., Smart Structural Concepts For Aerospace Applications Using Magnetostrictive Materials, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 303-310, (1999). 25. Krupanidhi, S.B., Integrated Antiferroelectric Pervoskite for MicroElectro Mechanical Applications, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 88-93, (1999). 26. Liao, W.H. and Wang, K.W., Characteristics of Enhanced Active Constrained Layer Damping Treatments with Edge Elements, Part 1 and 2, ASME Jl. Of Vibration and Acoustics, 120, pp 886-900, (1998). 27. Narayandas, J. and Nair, N.G., Smart Underwater Anechoic Linings From Short Fiber Rubber Matrix Composites, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 355-360, (1999). 28. Naryanan, S., Vibration Control of Beams Using Enhanced Active Constrained Layer Damping Treatment, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 385-392, (1999).

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29. Raja, S., and Rajagopal, P., Finite Element Modelling and Active Vibration Control of Laminated Piezoelectric Composite Beam, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 417-423, (1999). 30. Rajaiah, K., Smart Structures : Some Issues and Potential Aeronautical Application, C.V. Joga Rao Memorial Lectme,Proceedings of International Conference on Smart Materials, Structues and Systems, 7-10 July, 1999, Bangalore, India, pp 3-12, (1999). 31. Ramji Lai, Recent Developments of PZT Ceramics and Piezoelectric Composites at NMRL for Smart Transducers,Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 145, (1999). 32. Roy Mahapatra, D. and Gopalakrishnan, S., Spectrally Formulated Finite Element for Elementary Composite Beam with Embedded Smart Layers, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 337-342, (1999). 33. Saravanan, C , Ganesan, N. and Ramamurti, V., Analysis of Active Damping in Laminated Smart Cylindrical Shells of Revolution Using the Semianalytical Finite Element Method, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 349-354, (1999). 34. Shankar, M.V. and Varma, K.B.R., Multifunctional Glass Nanocomposites of Layer-Structured Ferroelectrics, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 94-95, (1999). 35. Shankar, V., Rajagopal, P., Shashikala, P., Nagaraja, B.V. and Vijayakumar, P.S., Design and Development of Instrumentation for Active Vibration Control of Smart Aerospace Structures, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 430-436, (1999). 36. Shashikala, P., Rajagopal, P., Shankar, V., Anitha, C M . and Shameer, A.V., Adaptive Vibration Control Using and LMS-Based Control Algorithm and Smart Actuators/Sensors, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 437-442, (1999). 37. Sivakumar, M.S. and Chenchiah, I.V., A Constitutive Model for SMAs Considering Twinning Transformations, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 127-133, (1999). 38. Srikanth Phai, A. and Kartik Venkataraman, Vibration Control Using

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39.

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and Electro-Rheological Fluid Sandwich Beam, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 460-465, (1999). Subramaniam, C, Trends in Standardization of Interfaces for Smart Transducers, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 234238, (1999). Sundaram, R., Subha Rao, M., Satish Babu, K., Raghavendra, B.S. Dinakar, D.S. and Diddarth, Studies Related to Embedment of SMA Wires in Composite Laminates,Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 361-367, (1999). Suresh, R., Gajbir Singh and Venkateswar Rao, G., An Investigation of Flexural Behaviour of Smart Composite Panels Subjected to ElectroMechanical Loads,Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 368-372, (1999). Tiwary, H.V., Sensor Characterisation of Ferroelectric Polymer Polyvinylidene Fluoride Fims as Smart Materials, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 99-102, (1999). Venkatesan, C , Evolution of Active Vibration Control Schemes in Helicopters, Proceedings of International Conference on Smart Materials, Structures and Systems, 7-10 July, 1999, Bangalore, India, pp 393-402, (1999).

SEMIACTTVE STRUCTURAL CONTROL STRATEGY FOR BUILDINGS AGAINST SEVERE EARTHQUAKES AKIRANISHITANI

Department ofArchitecture, Waseda University, Okubo, Shinjuku, Tokyo 169-8555 JAPAN E-mail: akira@nstn. arch, waseda. ac.jp This paper discusses semiactive control strategy accounting for the feasibility in case of severe earthquake. First of all, a brief overview of the current state of active-controlled buildings in Japan is presented, with main focus on the semiactive structural control strategy. The significance and necessity for semiactive control of structures are discussed from the viewpoint of severe earthquake resistance strategy. Following the general discussion, the current practical applications of semiactive control to actual buildings are demonstrated. Then, one of the author's recent attempts is presented, which is semiactive control utilizing variable-friction damper systems. In this variable-friction damper, only the slip-force level in the bilinear hysteresis loop is controlled on the basis of a relatively simple algorithm. The effectiveness of this system is demonstrated through theoretical simurations and simple experiment.

1

Introduction

Japan has had a long history of severe earthquake damages of buildings and civil infrastructures. Among the Japanese structural engineers community, therefore, one of the major concerns has been how to make earthquake-resistant structures. For the last decade, the seismic design of structures has been changing its basic concept along with the rapid development of structural control. Perhaps it will be more usual in the future to integrate a variety of control concept in the design. The recent rapid development of information science and computer technology is changing the traditional concept of almost every engineering product. Such a change will expectedly bring forth a variety of long-time dreams in the near future. Computer-control of seismic or wind response reduction for civil structures is one of these dreams. The strategy of constructing active-controlled structures is one of the most challenging research issues in structural engineering. Such structures would not be established without a variety of modern technologies, such as computer, sensor, monitoring, control technologies, etc. In this paper, a brief overview of the current state or state-of-the-art of active control structures is given in the first place, with the very quick looking-over of its historical background. Following that, semiactive control strategy is discussed in regard to the future direction of active-control structures, especially with focus on the strategy against severe earthquake excitation.

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408

2

Current State of Active Structural Control

As repeatedly mentioned in the author's previous papers [8,9], the conceptual philosophy of automatic control strategy for structures is not a totally new idea. The ideas of integrating the automatic control concept or installing a mechanical control device into the seismic structural design were proposed, more than thirty years ago in Japan, by Kobori [3], Kobori and Minai [5,6], and Katsuta et al. [2]. However, the technological environment at those times was not ready for bringing such control-based ideas into practical application. In 1972, in the United States, Yao [15] presented the concept of structural control as more realistic scheme integrating modern control engineering into the stage for anti-earthquake or anti-wind response reduction. Inspired by his paper, a number of researchers in civil engineering field, especially in the United States, published papers aiming at the establishment of active control design philosophy. Then, the world's first active control building, the Kyobashi Seiwa building, was produced in Tokyo in 1989. Following the birth of the Seiwa building, there are now more than 30 buildings in Japan that have implemented a variety of active, hybrid or semiactive control systems (Table 1). However, most of these active control systems are mainly aimed at the response reduction to strong wind or quite moderate earthquake excitation, not to severe seismic excitation. But, of course, the ultimate purpose originally intended for active-control scheme is to enhance the seismic safety of structures in particular against strong earthquake. In view of this, the current state of active control technology has not yet reached its full potential. In looking over the development of active control scheme of structures, the 1995 Hyogoken-Nanbu or Kobe earthquake was a kind of turning point. Table 1 tabulates the active control buildings in Japan, presenting the names, the dates of completion, the locations, the story numbers, the heights and the types of control systems. This table does not include any structures for experimental use. Only the real-used buildings are listed. It is recognized in Table 1 that up to 1995 the number of active control buildings had rapidly increased since the first active control building was born in 1989. It appears that engineers might have been in a little rush to construct active control structures. However, after 1995, especially for a couple of years after 1995, the increase of active-controlled buildings was apparently slowed down. Most of the controlled buildings constructed before the Kobe earthquake were designed to intentionally stop working in case of severe earthquake. Actually, some of the active control buildings in the Osaka area were reported, not necessarily officially, to have stopped the operation at the time of the Kobe earthquake. In some sense, such information might have made building owners lose their interests in making their buildings actively-controlled. Despite that, it seems that the active control strategy for the enhancement of structural safety will play more important role in the future stage, along with more integration of computer-based control technology in every aspect of our life. So it would be quite reasonable to expect such technologies to be fully

409 utilized also for the enhancement of seismic safety. However, in order to achieve reliable active control systems that could ensure the safety for strong earthquake, not a few problems must be solved. They are, for instance, how to make systems with less reliance on external power, or how to increase the reliability and robustness of active control systems, etc. 3

3.1

Semiactive Control Strategies

Overview ofApplications of Semiactive Control

In view of the above discussion, active control should be reconsidered from the point of feasibility view against large earthquake. The most frequently used active-control system is the HMD type, in particular the active tuned mass damper (ATMD) type. ATMD is the dynamic vibration absorber that is installed in a building as TMD and is driven so as to transfer more of the energy of vibration from main structural system. In conducting the operation of ATMD, both a large amount of power and a large stroke seem to be needed to counteract a severe earthquake excitation. The direct use of those systems thus does not appear to be very much fitted to the final target of active control at the present level of technology. In view of this, some other scheme with less energy and better performance would be wanted. In this respect, semiactive control will expectedly play a significant role in the near future stage. Although a widely accepted definition of semiactive control has not been established yet, semiactive control is considered herein the one in which power supply is needed only at appropriate points of time during the control operation. According to the author's investigation, there are three buildings with semiactive control systems implemented. They are the Building #21 in the Kajima Research Institute [4], the Kajima Shizuoka Building [7], and the new building in Keio University School of Science and Technology. All of those systems are expected to work in case of quite large earthquake. The Building #21 employs an active variable stiffness (AVS) system. By conducting the full-on or full-off control of the effectiveness of six braces, two in each story of the three-story building, the most appropriate stiffness for earthquake excitation is selected based on the measurement and theoretical prediction of ground shaking so as to avoid resonance vibration. Quite recently, the Kajima Shizuoka Building has employed a semi-active damping system. This five-story building installs eight semiactive hydraulic dampers on the both sides of the first to fourth floors. The control computer provides the building with the optimal control force in terms of the damping force. Through the computer simulations, the system has been demonstrated to work greatly even during a large earthquake. Another recent application of semiactive control is found in the new building in the Keio School of

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Science and Technology. This building was recently completed and integrates semiactive control dampers into the base isolation system. 3.2

Semiactive Control with Variable-Friction Dampers

Following the presentation of a very brief view of the practical applications of semiactive structural control, one of the author's recent attempts to produce a methodology for semiactive control of buildings is presented. It is variable-friction or variable slip-force level damper system. The basic concept for this damper system is to have a hysteresis damping effect in any seismic input excitation [10]. In this system, only the slip-force level is controlled in a bilinear elasto-plastic type of hysteresis loop of the damper. Some computer simulation results as well as a simple experimental result will be given to demonstrate the basic concept and assess the effectiveness of the system. For this type of damper, the slip-force level is of great significance. A high slip-force level would not provide any hysteresis loops for small or moderate earthquake excitation. A low level of slip-force, on the other hand, would provide the damper with too large deformation in the event of large seismic excitation. Therefore, it would be effective having the slip-force level variable so that the damper would work regardless of the magnitude of seismic excitation. The employed algorithm is rather simple, yet effective. Suppose this variablefriction damper is implemented in a single degree of freedom (SDOF) model representing a one-story building. It is known that, for a stationary sinusoidal input excitation, the bilinear hysteresis with the ductility factor of two should spend most effectively the input energy [14]. The ductility factor of two can be obtained in the case of sinusoidal excitation by employing the algorithm that the slip starts at the time of peak response velocity. This algorithm also works even if the amplitude of sinusoidal excitation changes from cycle to cycle. With such an excitation, Figure 1 shows the simulated hysteresis loop of the damper. The targeted hysteresis has been obtained. This result is given by the model of its natural frequency 2.3 sec without any damper, which is subjected to the sinusoidal input excitation frequency 2.0 Hz. For the case of the excitation based on a real earthquake record, Figures 2 and 3 depict the theoretical and experimental hysteresis loops of the damper, respectively. The SDOF model is excited by the EW component of the 1972 Taft earthquake with PGA=0.15 m/sec2. The experimental building model having the experimental device for the variable-friction damper is shown in Figure 4. This device produces the damper's force by clamping a horizontal plate connected to a pair of vertical plate elements hanging from the upper floor. The vertical elements provide the damper's initial horizontal stiffness to the structure as long as the horizontal plate is clamped tightly. The clamping condition is controlled by an air compressor. The results in Figures 2 and 3 demonstrate how the employed algorithm works for actual seismic excitation.

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3.3

Applications of Variable-Friction Dampers to Multi-Story Building

To assess the effectiveness of the presented control system for high-rise buildings, the response analysis is conducted assuming a 20-story building model with the dampers installed. The model building for the analysis is represented by the equivalent-shear structural model with 20DOF accounting for the effect of the bending deformation of the building as well [13]. The natural periods of vibration of the model building are 1.9 sec, 0.63 sec, and 0.36 sec, respectively, for the first, second, and third modes. It is assumed that the variable friction dampers are installed on every floor and the building is subject to the seismic excitation of the NS component of the El Centro earthquake with PGA of 200 cm/sec2. It is also assumed that the total mass of the building is about 2.0 x 107 kg, the structural damping is proportional to the stiffness matrix so as to have 1% damping ratio for the first mode, and the initial stiffness of each damper is set equal to the stiffness of each story. Each damper is controlled so that the slip should start as soon as the peak inter-story velocity response is observed. The maximum response displacement of each story relative to the base is presented in Figure 5, and the maximum absolute acceleration response of each story is shown in Figure 6. In both figures, the controlled and uncontrolled responses are compared, with the solid and dotted lines for the controlled and uncontrolled responses, respectively. Figure 7 compares the time histories of the controlled and uncontrolled accelerations of the top floor. Figures 8, 9 and 10 depict the simulated hysteresis loops of the dampers installed in the twentieth, tenth, and first stories, respectively. Of course, the presented results will be changed depending on the ratio of the initial stiffness of each damper to the stiffness of each story of the building. To evaluate the damping effect resulting from the variable-friction damper control, system identification is conducted utilizing the response data of the twentieth and tenth stories and the input excitation earthquake acceleration data. In conducting the identification, the identified system is treated as an equivalent-linear single-input-double-output system and the ARX model [1] is employed. The transfer function fitted to this reduced degree-of-freedom system is obtained from the ARX model [11]. The poles of the obtained transfer function provide the resulting natural frequencies and the resulting damping ratios. Since the main purpose of this identification is, however, to evaluate the resulting first modal damping ratio, the ARX model uses the input and output data which have passed through the low-pass filter. As a result, the first modal frequency for the equivalent linear system is found 0.75Hz (the period is 1.3 sec) and the damping ratio for the first mode is 10%. Figure 11 compares the response time histories for the twentieth story. Figure 11(a) gives the result of the identified linear system model, while Figure 11(b) presents the low-pass-filtered controlled-response. These two seem exactly the same. The identified linear model perfectly describes the behavior of the controlled structure. This fact indicates that the variable-friction damper makes the structure behave like a linear system although the damper provides the nonlinear effect to the structure. This implies that the presented control strategy will be

412

effective regardless of the magnitude of seismic excitation. More detailed discussions with respect to this control strategy are presented in the 2000 American Control Conference 2000 [10]. 4

Concluding Remarks and Future Direction

Enthusiastic efforts have been devoted to the research and development of active structural control. Now there have been in Japan more than 30 real buildings with active control systems. Although most of such systems are not aimed at the enhancement of building safety during a severe earthquake, a few of them are expected to work effectively even against large earthquake. They employ semiactive control strategy with less reliance on external power. In this paper, together with a brief overview of such semiactive systems already implemented in real buildings, the semiactive control strategy utilizing variable-friction dampers has been presented. It has been demonstrated that this system will work effectively with a simple control algorithm. In structural control field, more and more semi active-control schemes will be expectedly integrated for the purpose of the enhancing the safety against severe earthquake. In ten to fifteen years, active control including semiactive control will change the traditional images of buildings, along with more sophisticated advances of computer technology. 5

Acknowledgements

The research for semiactive control strategy with variable-friction dampers is supported by the JSPS Research for the Future Program (96R15701). References 1. Choi, B.,ARMA Model Identification, (Springer-Verlag 1992). 2. Katsuta, K. et al., Jidoseigyo niyoru menshinho no kenkyu 1, 2 (Base isolation technique associated with automatic control 1 and 2), Trans. Architectural Institute of Japan 102 (1964) pp. 10-24 (in Japanese). 3. Kobori, T., Quake resistant and nonlinear problems of the structural vibrations to violent earthquake, J. Kyoto University Disaster Prevention Laboratory; 5th Anniversary Edition (1956) pp. 116-124 (in Japanese). 4. Kobori, T. et al., Seismic response controlled structure with active variable stiffness system, Earthquake Engineering and Structural Dynamics 22 (1993) pp.925-941

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5. Kobori, T. and Minai, R., Analytical study on active seismic response control: Seismic-response-controlled structure 1., Trans. Architectural Institute of Japan 66 (1960) pp.257-260 (in Japanese). 6. Kobori, T. and Minai, R., Condition for active seismic response control: Seismic-response-controlled structure 2., Trans. Architectural Institute of Japan 66 (1960) pp.253-256 (in Japanese). 7. Kurata, N., et al., Actual seismic response controlled building with semi-active damper system, Earthquake Engineering and Structural Dynamics 28 (1999) pp. 1427-1447 8. Nishitani, A., Application of active structural control in Japan, Progress in Structural Engineering and Materials 1(3) (1998) pp.301-307. 9. Nishitani, A., Application of Active, hybrid, and semi-active structural control in Japan, Proc. the International Post-SMiRT Conference Seminar: Seismic Isolation, Passive Energy Dissipation and Active Control of Vibrations of Structures (Cheju, Korea, 1999) pp.461-466. 10. Nishitani, A., Nitta, Y., Itoh, A., and Ikeda, Y., Semiactive variable-friction damper control with simple algorithm, Proc. the 2000 American Control Conference (Chicago, 2000) CD-ROM No.503. 11. Nishitani, A. and Yamada, S., H-infinity control system re-design based on structural system identification with AMD providing input excitation, J. Structural and Construction Engineering AIJ 516 (1999) pp.65-71 (in Japanese). 12. Tajimi, H., Introduction to Structural Dynamics, (Corona, Tokyo, 1965) (in Japanese). 13. Osaki, Y., Kenchiku Shindo Riron (Vibration Theory for Architectural Structures), (Shokokusha, Tokyo, 1956) (in Japanese). 14. Tajimi, H., Introduction to Structural Dynamics, (Corona, Tokyo, 1965) (in Japanese). 15. Yao, JTP, Concept of structural control, J. Structural Division ASCE 98(ST7) (1972) pp.1567-1574

414 Table 1. Active/semiactive control buildings in Japan Name

Completion Date Tokyo 1989 Tokyo 1990

Building use office

Tokyo Osaka

1992 1992

Kansai Airport Control Tower Osaka ORC200 Ando Nishikicho Bldg.

Osaka Osaka Tokyo

Yokohama Landmark Tower Long Term Credit Bank Porte Kanazawa Shinjuku Park Tower

Yokohama Tokyo

RIHGA Royal Hotel MHI Yokohama Bldg.

Hiroshima Yokohama Tokyo

1992 1992 1993 1993 1993 1994 1994 1994 1994 1994

office 11 34 hotel, office theater 7 control tower 50 hotel, office 14 office 70 hotel, office 21 office 29 hotel, office 52 hotel, office 35 hotel 34 office 24 hotel, office 46 hotel, office

Kyobashi Seiwa Bldg. Kajima Research Institute No.21 Bldg Sendagaya INTES Applause Tower

Hikarigaoka J City Bldg. Hamamatsu ACT City

City

Kanazawa Tokyo

HERBIS Osaka Nisseki Yokohama Bldg.

Hamamatsu 1994 Tokyo 1994 Miyazaki 1994 Osaka 1995 Osaka 1995 Osaka 1995 Tokyo 1995 Chiba 1995 1997 Osaka Yokohama 1997

Itoyama Tower

Tokyo

Riverside Sumida Hotel Ocean 45 Osaka World Trade Center Dowa Kasai Phoenix Tower Rinku Gate Tower Bldg. Hirobe Miyake Bldg. Plaza Ichihara

1997

Stories

laboratory

11 3

Type

12

AMD AVS

44 161

AMD AMD

86 200 54 296 129 121 232 150 152 100 212 134 154 252 144 255 30 61 189

HMD HMD HMD HMD HMD HMD HMD HMD HMD HMD HMD AMD HMD HMD HMD HMD HMD HMD AMD HMD

18

89

HMD HMD HMD HMD HMD

residential hotel

33 43

office office hotel, office

52 28 56 9 12 40 30

hotel, office office office,

Height (m) 33

residential OTIS Elevator Tower Odakyu Southern Tower Bunka Fukuso Gakuin

Chiba Tokyo Tokyo

1998 1998 1998

laboratory hotel, office school

39 36 20

154 151 93

Oita Oasis Plaza 21 Kajima Shizuoka Bldg.

Oita

1998 1998

hotel, office office office

20 5

101 19

32

145

Shinagawa Inter City Bldg.

Shizuoka Tokyo

New bldg. Keio Univ.

Yokohamai 2000

1998

school

AVD HMD ABI

415

uncontrolled controlled

-5 0 5 Displacement (xKT'm)

figure 1.

-15

Theoretical hysteresis of clamper (sinusoidal excitation)

-10

-5 0 5 Displacement (x1CT3 m)

10

0.1 Displacement (m)

flgureS Maximum displacements

15

1

Figure 2. Theoretical hysteresis of damper 40

0,2

2 3 Acceleration (m/sec2)

4

r

Figure 6. Maximum absolute accelerations

Displacement (*W"S m)

Figure 3. Experimental hysteresis of damper

Figure 7. Absolute acceleration response of top floor

/CEzz / -15

figure 4. Photograph of experimental model

-10

/

r -5 " ~ ~0" ~ ,5 Displacement (s 10~3 rn)

10

figure 8. Hysteresis of damper in 20th story

416

- 5 - 4 - 3 - 2 - 1 0 1 , 2 Displacement (xKT'm)

3

10 Time (sec)

4

Response from identified linear model

Figure 9. Hysteresis of damper in 10th story

]• (b) - 5 - 4 - 3 - 2 - 1 0 1 , 2 Displacement («10~m)

3

4

Figure 10. Hysteresis of damper in 1st story

Low-pass filtered controlled response Figure 11 Comparison of responses

PRESERVATION OF MEDITERRANEAN HISTORICAL MONUMENTS USING INNOVATIVE SEISMIC TECHNIQUES

ASHRAF OSMAN Associate Professor, Faculty of Engineering, Cairo University, Giza, Egypt AHMED SALEH Assistant Professor, Faculty of Engineering, Cairo University, Giza, Egypt ADEL EL-ATTAR Associate Professor, Faculty of Engineering, Cairo University, Giza, Egypt E-mail: [email protected] This paper addresses the seismic risk potential of cultural and historical sites in the Mediterranean area. It defines the problem of seismic protection of such sites, illustrates the current state of the art protection and retrofitting techniques, and proposes an innovative protection technique based on base isolation and semi-active devices. The paper is part of project CHIME (Conservation of Historical Mediterranean Sites by Innovative SeismicProtection Techniques), co-sponsored by the European Commission, and five concerned Mediterranean countries (Italy, Greece, Egypt, Tunisia, and Cyprus).

1

Introduction

The Mediterranean area is probably one of the richest areas in the world in terms of cultural and historical heritage. The area was the birthplace of a diversity of civilizations including; the Ancient Egyptian, the Greek, the Roman, the Phoenician, and the Arab-Islamic civilizations. As a result, there exists an invaluable wealth of cultural and historical sites in this area. Unfortunately, a number of these sites are located in seismically active areas, and many of them have already suffered various degrees of damage during past earthquakes. It is the responsibility of the concerned Mediterranean countries to take appropriate measures to protect and preserve their cultural heritage from potentially future earthquakes. 2

Problem Statement

Current seismic design philosophy of structures is based on the development of a ductile structure that can undergo large post-elastic deformation and dissipate a significant part of the input seismic energy E;. This approach implies the acceptance of some degree of damage during strong ground motion. The degree of damage is typically classified as; (a) non-structural damage during minor earthquakes, (b) minor structural damage during moderate earthquakes, and (c) preventing structure 417

418

collapse during major earthquakes. However, this approach can not be directly applied to historical buildings, as most of them are mainly made of massive stones (granite or lime stones for the case of Egypt) interconnected through a weak (if any) mortar-like material (Figure 1). Such type of structures possesses very little (or even zero) ductility, but have high stiffness, resulting in attracting high seismic forces during strong ground motion. This fact was clearly observed during the inspection of damaged historical buildings after the October 12th 1992 Dahshur earthquake in Egypt as will be discussed in the following sections of this paper. Traditional seismic repair and/or retrofitting techniques for buildings include the addition of steel and/or concreteframesto increase their strength and to some extent their ductility. A major draw back of such techniques is that they are usually apparent, a quality that may significantly reduce the historical value of the building. An. alternative technique is to reduce the forces acting on the structure using some innovative control devices. To implement these new techniques, a joint project was initiated under the name CHIME (Conservation of Historical Mediterranean Sites by Innovative Seismic Protection Techniques). The project is co-sponsored by the European Commission and five concerned Mediterranean countries, namely Italy, Greece, Egypt, Tunisia, and Cyprus. In the following sections, examples of historical sites in Egypt with high seismic risk and/or that have already been damaged during past earthquakes will be introduced and the traditional repair techniquestypicallyused for such cases will be discussed.

Figure 1. Entrance to Ramsis II (1298-1235 BC) Temple.

419

3

Current Seismic Repair and Protection Techniques Used in Egypt

In this section, attention will be paid to two types of historical monuments that were reported to experience significant damage during past earthquakes in Egypt namely; (a) Islamic minarets, and (b) Ancient Egyptian monuments. Traditional techniques used for repairing and/or retrofitting these monuments will be briefly introduced wherever appropriate. 3.1 Islamic Minarets Minarets are the most prominent external feature of Islamic religious buildings (mosques). They are basically elevated structures intended for use of "Mu'adhin" to summon people for prayer. Lanterns were often attached to the top of the minaret in the Islamic holly month of Ramadan to announce-by their extinction-that time has become to start the day's fasting. The history of Islamic minarets goes back to 641 AD when the first minaret of Amr Ibn Al-As mosque was constructed. In addition to their historic value, minarets have a great spiritual value to the Moslem society [1]. Earlier models of Cairene minarets had a rectangular shaft, with a domed structure on top. In the next stage of development, the rectangular base of the dome became octagonal. Finally the classical minaret consisting of three parts, each with a different cross section, the first square, the second octagonal and the third circular evolved. These developments reflected the influence of the architectural style of the cities that ruled the Islamic Empire over the years. From a seismic point of view, two distinguished minaret styles are of interest, namely the "Mamluk" style and the "Ottoman" style. The Mamluk style is characterized by their irregular distribution of mass and stiffness, as during this era, architectural requirements overweighed structural knowledge (Figure 2.a). On the other hand, the Ottoman style, which was designed by engineers who developed good earthquake engineering experience by observing damage to minarets in their home country (Turkey), were slender with almost uniform mass and stiffness distribution (Figure 2.b). It is not surprising that most damaged minarets during the October 12th 1992 Dahshur earthquake had a Mamluk style [2,3]. 3.1.1

Minaret of Umm Al-Sultan Sha'ban

(a) Historical background: This minaret forms apart of the school and mosque (Madrasa) of Umm As-Sultan Sha'ban which is located in old Cairo (Figure 3). The Madrasa was built in 1368 A.D during the Mamluk period. It consists of a central square open courtyard (Sahan), surrounded by four perpendicular halls (Iwans). The minaret is surrounded from the southern side with a mausoleum and from the northern side with a group of rooms. Originally, the minaret consisted of three segments however, as shown in Figure 3, the top segment was lost at the beginning of this century [1].

420

E

n

(a) Manjaa Al-Yusiifi Minaret (Marnluk Style)

fb) At-Husayri Shrine Mtiwret (Ottoman Style)

Figure 2. "Mamluk" Style and "Ottoman" Style Minarets. Currently, the minaret height is about 39 m above street level. It has a massive square cross-section above the roof level of the Madrasa (on which the minaret rests) followed by an octagonal cross-section. The transition between the two crosssections is carried out using pyramids set at the corners of the square base.

421

Figure 3. Minaret of Umm Al-Sultan Sha'ban (b) Structural Condition: Structurally, the minaret has a solid base, which extends 4.0 to 6.0 meters below ground level. The base was constructed by connecting a series of stone walls together to form a closed square space, which in turn, wasfilledwith rubble stones mixed with mortar. This solid base extends up to the roof level of the Madrasa. At the foundation level, the exterior walls that form the base are connected to the walls of the Madrasa. From the roof level, the minaret shaft is formed from multiple leaf layered walls consisting of two layers of dressed lime stones forming the outer and inner surfaces of the wall and bounding between them a less heterogeneous filling material formed from random boulders mixed with lime mortar. Within the minaret

422

shaft andfromthe roof of the Madrasa extends a stone helical stair up to the minaret top [1]. After the October 12th Dahshur earthquake, the minaret and the surrounding area were thoroughly inspected to assess their structural condition, and to investigate the possibility of restoring the missing part of it. In general, the stones forming the top segment of the minaret, which extendedfromthe Madrasa roof to the top of the minaret, showed slight signs of deterioration that were attributed mainly to the environmental conditions and aging process. Minor cracks were spotted within the minaret body (Figure 4). However, these cracks are not expected to affect the structural integrity of the minaret. On the other hand, severe damage and excessive cracking were found in the screed and clay blocks forming the roof, a sign of a relative movement between the minaret and the Madrasa (pounding). Furthermore, by examining the connection between the minaret body and the Madrasa parapet along the northern facade, a clear separation between the two elements was detected. It was concluded that those relatively weak walls were not able to force the minaret to vibrate with the Madrasa as one entity during recent earthquakes [4].

Figure 4. Wall Bulging and Cracking at Minaret Base.

423

When the vertical alignment of the minaret was assessed, it wasfoundthat the minaret is tilted by 00° 28f 27" from the vertical direction resulting in a top displacement of 176 mm (height/220)fromits original position [4]. (c) Analysis of the incomplete minaret: To identify the levels of the stresses within the incomplete minaret, the structure was modeled using the non-linear finite element computer program COSMOS/M (Figure 5). The model simulated the minaret, including all changes in its cross section and the walls connected to it, including all openings and recesses in it. The Madrasa roof was not included in the model as it is aflexiblewooden one, which is separated from the minaret at many locations, consequently, can not act as a rigid diaphragm. The effect of the soil was considered in the analysis by modeling the soil layers under the minaret as a one meter thick layer of solid elements having a modulus of elasticity equal to 42000 KN/m^[4].

(a) Model

(b) Stress distribution

(c) First Mode

Figure 5. Finite Element Model of the Incomplete Minaret The minaret was analyzed for the case of (a) vertical gravity load, and (b) horizontal forces caused by wind or earthquakes. A lateral force equivalent to 10% of the dead load of the minaret was applied in combination with the gravity dead loads in both principal horizontal directions of the minaret. Dynamic analysis was also performed to identify the minaret dynamic characteristics.

424

Analysis results for the vertical gravity load case indicated a stress level in the minaret body of 1.02 MPa (compression) and 0.20 MPa (tension). These stresses were well below the allowable compressive stresses of limestone (4 MPa compression, and 0.4 MPa tension). However, maximum stress on soil was 0.52 MPa which was higher than the allowable values (0.45 MPa). The situation is further aggravated if the walls connected to the minaret were neglected. Obviously, these walls distributed a part of the minaret load to a larger area. Dynamic analysis indicated that the minaret is a relatively flexible structure with long natural periods (T, = 2.85 sec). Consequently, earthquakes with low frequency contents are expected to have a destructive effect on this minaret. Available geotechnical data indicates that the minaret is founded over stiff sandy layer very close to the base rock at that site. Consequently, the earthquakes hitting this minaret are expected to have a high frequency contents (due to the absence of any local site effect which may filter out the coming earthquake and change its frequency content), resulting in relatively small seismic forces acting on the minaret. To investigate the behavior of the minaret under the action of seismic forces, the model was subjected to lateral loads equivalent to 10% of the minaret self weight in two perpendicular directions (X, Y), combined with its dead loads. As the load was applied in X-direction, the top of the minaret displaced about 4.5 mm in X-direction and 2.3 mm in Y-direction, resulting in total movement of 5.07 mm. displacement, while for loads applied in Y-direction, the recorded total displacement was 6.24 mm. Vertical stress levels were within the allowable limits, with the exception of the tensile stresses at the connection between the minaret body and the walls of the Madrasa block under the action of the lateral loads in Xdirection. However, these tensile stresses were within the strength of the construction materials (0.8 to 1.0 MPa). Horizontal tensile stresses between the minaret and the wall were found to exceed the construction material strength. Overstressed regions in tension matched exactly the location of cracks recorded during site inspection [4]. (d) Analysis of the restored minaret Similar analysis was performed for the restored minaret, with the missing segment completed (Figure 6). Analytical results indicated that vertical stresses remained within the allowable limits, but horizontal tensile stresses at the minaret-wall junction well exceeded these limits. Vertical stresses on soil reached a maximum value of 0.58 MPa, with the walls contribution neglected.

425

K. W^

(a) Model

(b) Stress distribution

(c) First Mode

Figure 6. Finite Element Model of the Restored Minaret (e) Remedy solution In order to restore the missing part of the minaret and to protect the minaret and the rest of the structure during future earthquakes the following remedy solutions were proposed;

1- Separate the minaret totallyfromadjacent walls using an appropriate seismic gap. This will require developing a newframingsystem to support the walls instead of the minaret body. 2- Use micropiles at the minaret base to alleviate the high soil stresses. This will typically be associated with enlarging the minaret foundation using mechanically prestressed dowel bars (Figure 7). 3- New columns carrying the new minaret top part shall be carefully designed to resist the expected lateral loads and to secure the new minaret tip (bassala). 4- Damaged and worn out stones in the minaret and/or die wall shall be replaced with new ones of the same material.

426

Figure 7. Use of Micro-piles (at arrow locations) to Support Isolated Minaret.

3.1.2 Minaret of Northern Shaykhu Mosque (a) Historical background The northern 'Shaykhu5 mosque was built in 1349 AD by Amir Shaykhu. Six years later, he built another mosque across the Saliba street in old Cairo with an identical minaret to create a symmetric view. Both minarets had the architectural features of the Mamluk style. Almond shaped bulbs (Bassala) resting on narrow necks crowned both minarets [1]. (b) Damage experienced during recent earthquakes The northern Shaykhu mosque was seriously damaged during the October 12th 1992 Dahshur earthquake. The top bulbs (Bassala)- totally collapsed and fall in pieces as. shown- in Figure 8.a. Furthermore, walls underneath the minaret had large cracks and bulged out as shown in Figure 8.b [5]. (c) Restoration and protection The top part of the minaret was • reconstructed using natural -stones similar to the original ones (limestone). The tip bulb (Bassala)- was restored using the original stones, where specially configured shear keys were used to secure it in place (Figure 9). Bulged, worn out and deteriorated wall stones were replaced by similar ones of the- same material (Figure 10).

427

(a) Minaret Tip (Bassaia) Failure

(b) Wall Cracking and Bulging

Figure 8. Failure Experienced by Northern Shaykhu Mosque During October 12 Dahshur Earthquake

Figure 9. Restoration of Northern Shaykhu Mosque Minaret.

428

Figure 10. Restoration of Northern Shaykhu Mosque Walls.

3.2 Ancient Egyptian Monuments Ancient Egyptian monuments are typically made of large stones (basically Granite and/or Limestone blocks), that were broughtfromthe southern'part of the country for Ms purpose. With their relatively low aspect ratio (height/width) and heavy weight, these stocky columns, walls, and statues survived over thousands of years till now. However, some signs of distress were reported after the October 12th Dahshur earthquake [2]. These sijps rangedfromsome loose stones fallingfromthe Giza Pyramids to minor cracks in the Sphinx neck. Historically, it is obvious that several monuments Mid temples collapsed due to seismic activity at some point of time. The only reported case is the Immense Mortuary temple, built by

429 "Amenhoteb" 14 centuries BC (Figure 11). The temple was reported to collapse during the 27 BC earthquake. Currently the only left part of this temple is the Mamnon colossi (to be introduced in the following sections).

Figure 11. View of the Original Immense Mortuary (14 00 BC), Luxor - Egypt.

4

Project CHIME

Project CHIME (Conservation of Historical Mediterranean Sites by Innovative Seismic Protection Techniques) is a joint project co-sponsored by the European Commission and five concerned Mediterranean countries, namely Italy, .Greece, Egypt, Tunisia and Cyprus. The project addresses the potential use of appropriate seismic protective systems in the preservation and protection of Mediteiranean historical buildings existing in earthquake-prone areas. 4.1

Motivation

Modem seismic retrofit techniques applied to existing structures, such as the addition of moment resisting steel frames or reinforced concrete shear walls, waste

430

the historical value of ancient buildings as they are aesthetically apparent. Base isolation, which basically consists of placing isolators and/or dampers at the foundation level of the building, where they are not apparent. This type of protective systems introduces flexibility and damping at the base of the structure, resulting in reducing the force and drift level of the building during strong ground motion, and in turn reduces the level of damage to the building. As an alternative, small size devices could be distributed across the monument to dissipate energy. These devices can eventually made intelligent (semi-active control), provided that their properties are the result of a suitable control process. 4.2 Innovation Features The energy balance equation of a structure at time tf after which a forced system goes back to rest is given by [6];

Ep(tf) + Ed(tf) = Ei(tf) Where Ep is the energy plastically dissipated through hysteretic cycles, Ed is the energy dissipated through viscous phenomena and £, is the input energy. The value of Ep can be increased by improving the local ductility of the structure, while Ed can be increased by adding dampers to the structure. Finally, Et can be reduced by reduced by changing the dynamic characteristics of the structure. Based on the above energy balance equation, base isolators will decrease Eh while damped base isolators will have the effect of decreasing £, and increasing Ed. Base isolators can be classified to (a) rubber bearings, (b) sliding systems, (c) sand back systems, and (d) impermeabilized covers. Moreover, damped base isolators are categorized as (a) lead-rubber bearings and (b) friction bearings. High damping rubber bearings (HDRB) have been used worldwide for seismic protection of various types of structures in Italy, United States, and Japan [7,8]. Due to their popularity and low cost, they form a justified priority for seismic protection of Mediterranean historical buildings. The coupling of the HDRB with semi-active control devices also will be a major contribution of this project. 4.3

Project Work Plan

The work plan was broken according to the following logical arrangement

431

1- Identifying case studies: candidate sites in each country will be screened, and required engineering data are gathered. 2- Hazard vulnerability analysis: Ambient or forced vibration tests are performed to obtain the modal signature (frequencies, mode shapes, damping ratios), and mathematical models are calibrated. 3- Seismic protection devices: Seismic protection using passive and/or semi-active devices is experimentally investigated, and mathematical models are refined. 4- Evaluation of technical/economical benefits. 4.4 Investigation Sites in Egypt 4.4.1 Manjaq Al-Yusufi Minaret Manjaq Al-Yusufi minaret was built in 1349 AD during the Mamluk period (Figure 12). The minaret is 26.0 meters high and consists of square base 3.8 meters wide, carrying an octagonal shaft. The minaret cap (Mabkharah) is carried on eight columns, which is a common feature of this minaret style. The minaret stands alone, and it probably represents all what is left of Manjaq mosque. Its staircase that starts from the ground level indicates that the minaret wasfree-standingat the time of its construction. I'.

Figure 12.

Manjaq Al-Yusufi Minaret, Mamluk Style (1349 AD).

432

The minaret was selected as the first investigation site for two basic reasons, first, it belongs to the Mamluk style, which was reported to experience most damage during recent earthquakes in Egypt, second, its free-standing feature, which simplifies modeling, measurements, and experimental model testing. Preliminary survey of the minaret is shown in Figure 13, where the variation of the minaret cross section over its height can be clearly seen.

Figure 13. Preliminary Survey of Manjaq Al-Yusufi Minaret.

Preliminary dynamic analysis of the minaret was performed using a threedimensional finite element model. Properties used in the analysis were; (a) Young's modulus of 2000 KN/cm2 for stone, and 1500 KN/cm2 for double walls with rubble masonry fill in between, (b) Poisson's ratio of 0.2, (c) unit weight of 20 KN/m3, and (d) proportional damping of 5%. First four modes of vibration are shown in Figure

433

14, where it can be seen that the first, second and fourth modes were bending ones, with a relatively short period of 0.234 seconds for the fundamental mode.

MODE1 (T=0.23sec)

MODE 2 (T=0.11 sec)

MODE 3 (T=0.10sec)

MODE 4 (T=0.06 sec)

Figure 14. Mode Shapes of Manjaq Al-Yusufi Minaret. 4.4.2

Mamnon Colossi

The Mamnon colossi are the famous statues of Amenhotep (18th Dynasty), which form the last remains of the Immense Mortuary temple, located on the west bank of the river Nile, Luxor, Egypt (Figure 15). They were built 14 centuries BC, and were reported to collapse during the 27 BC earthquake. The statues were restored two centuries later. The two statues were selected as the second investigation site. Preliminary geometrical survey of the site was carried out. Determination of material properties and soil conditions are on going.

5

Summary

Seismic risk potential of cultural and historical sites in the Mediterranean area is addressed. Examples, representing the current state of the art repair and protection techniques in Egypt were introduced. Innovative seismic protection techniques using passive in addition to semi-active devices have been proposed through project CHIME (Conservation of Historical Mediterranean Sites by Innovative SeismicProtection Techniques), co-sponsored by the European Commission, and five concerned Mediterranean countries (Italy, Greece, Egypt, Tunisia, and Cyprus).

434

Figure 15. Mamnon Colossi at Luxor, Egypt (14 Centuries BC).

References 1. Abouseif, D.B., "The Minarets of Egypt9, The American University in Cairo Press, 2nd print, 1987. 2. Sykora, D., Look, D., Corci, G. and Karaesman, E., "Reconnaissance of Damage to Historic Monuments in Cairo, Egypt Following the October 12, 1992 Dahshur Earthquake", National Center for Earthquake Engineering Research, NCEER-93-0015." 3. Mourad, S. and Osman, A., "Seismic Risk Appraisal for Islamic Minarets", Proceedings, First Cairo Symposium on Earthquake Engineering, 3-5 December 1994. 4. Osman, A. and Hassan A., "Umm Al-Sultan Sha'ban Minaret: A Structural Study", An Internal Report, Center for Conservation and Preservation of Islamic Architectural Heritage, Cairo, Egypt, August 1999. 5. Abdel-Gawad, A. and Mourad, S., "On the Structural Stability and Repair of Historical Monuments", Proceedings, First Cairo Symposium on Earthquake Engineering, 3-5 December 1994. 6. Caciati, F. Mid Lagorio, H.J., "Urban. Renewal Aspects and Technological Devices, in. Infrastructure Rehabilitation", Proceedings, First European Conference on Structural Control, pp. 173-182, Barcelona, Spain, 1996.

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7. Buckle, H.G., "Future Directions in Seismic Base Isolation, Passive Energy Dissipation and Active Control", Proceedings, ATC 171 Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control, Vol. 1, pp. 307-318, 1993. 8. Arnold, C , "Seismic Design: Now Comes Base Isolation", Architecture, pp. 64-67, March 1987.

SIMPLE CONTROLLER D E S I G N FOR N O N L I N E A R S T R U C T U R A L SYSTEM U S I N G R O B U S T P E R F O R M A N C E PROPERTY WONSUK PARK Department of Civil Engineering, Seoul National University, Kwanak-Gu, 151-742 Seoul, Korea E-mail: [email protected]

Shinrim-Dong,

HYUN-MOO KOH E-mail: [email protected] DONG-HO HA E-mail: [email protected] This paper presents an application of robust H2 control design method to nonlinear structural control system. Nonlinearity of the system is treated as uncertainty instead of complex nonlinear models. By using suggested method, an effective controller for nonlinear structural control system can be designed without developing nonlinear models. To design the robust controller, the method combines the Popov stability analysis and worst-case H2 performance bounds of Lur'e system and an iterative optimization method based on linear matrix inequality (LMI) approach is used. Numerical results show high robust performance of the proposed method in contrast with the case of a nominal LQG controller.

1

Introduction

Need for nonlinear control method is increasing recently to design more effective structural control system. For example, hybrid control system consists of energy dissipative damping devices and active or variable components. Nonlinearity such as the typical hysteretic behavior of damping devices should be reflected in the controller design. Semi-active control devices such as magnetorheological dampers and variable orifice dampers also show nonlinear behavior. Under severe condition like strong earthquake, nonlinearity due to the yield of structural members should be considered. In general, the use of precise nonlinear models of the system and appropriate nonlinear controllers is effective to achieve the full performance of the nonlinear control system. However, developing such nonlinear model and controller is complicated. This paper presents an application of robust Hi control design method to nonlinear structural control system. Nonlinearity of the system is treated as uncertainty instead of complex nonlinear models. By doing this, wide range of nonlinear

437

438

structural control problem can be described by a linear system subject to nonlinear uncertainty. Thus, an effective controller for nonlinear structural control system can be designed easily without developing nonlinear models at the cost of negligible relative performance degradation. A numerical example illustrates robust performance and efficiency of the proposed controller for a simple hysteretic nonlinear system.

2

Controller Design

The basic idea is that it may be possible to describe a nonlinear dynamic system as a linear system with nonlinear uncertainty block. Although this is basically a linearization method, the range of controller operation can be wider than that of pure linearization method by adjusting the size of nonlinear uncertainty block. To design a controller for this system, several robust control methods can be used. Among the recent research results for robust control problem, robust Hi control method 2 has many favorable features for vibration control applications. While Hoc and // are typical examples of robust control problem, -ffoo norm itself is not very satisfactory as a disturbance rejection criterion. Optimal -ffoo control yields allpass closed-loop transfer functions, which would exhibit very poor performance under the broadband disturbance. Frequency-weighting method is necessary to alleviate this problem, but weight selection becomes a largely ad hoc procedure. This difficulty arises mainly because .ffoo norm is the peak frequency response specification, which is not suitable for a measure of the response to broadband excitation. In contrast, H2 norm is the rms value of the frequency response, which is appropriate to vibration control applications. In this paper, parametric robust H2 control design method is used. The method combines the Popov stability analysis and worst-case H2 performance bounds of Lur'e system. Controller synthesis uses an iterative optimization method based on linear matrix inequality (LMI) approach.

2.1

System modeling

A linear time invariant system subject to sector bounded nonlinear uncertainty, a Lur'e system, is considered to design a controller for nonlinear sys-

439 Force

Force

Figure 1. Sector-bounded nonlinearity and stiffness variation

tem. A Lur'e system is described by

x = Ax + Bpp + Bww + q = Cqx + Dqpp + Dqww z — Czx + Dzpp + Dzww y = Cyx + DyPp + Dyww

Buu + Dquu + Dzuu + Dyuu,

p = <j>(q)

(1)

where x : (n x 1) is the state, u : (nu x 1) is the control input, w : (nw x 1) is the disturbance input, y : (ny x 1) is the measured output, z : (nz x 1) is the performance output, q : (np x 1) and p : (n p x 1) are the input/output of the nonlinear uncertainty 4>. The nonlinear perturbation <> / is assumed to satisfy the sector bound [0,1]; that is, € $ where $:={: (np x np), 4>{q) = [i(qi), • • -,(f>np(qnp)]T

and 0 < i(a)/cr < 1, Vz = 1 , . . . , n p }

In this modeling and following controller design, nonlinear uncertainty <j> represents a memoryless nonlinear function. This nonlinear model can describe a system subject to a parametric uncertainty when functions 0 when t —> oo), sector bound nonlinearity can effectively represent it (Fig. 1(a)). If k has hysteresis feature, the nonlinearity cannot be represented in regions outside the sector bounds (Fig. 1(b)). However, if the system is stable and the region is relatively small, it can be expected that a controller based on this (f> function may be good enough for hysteresis nonlinearity.

440

2.2

Controller design procedure

The controller design problem is to find a strictly proper full-order LTI controller that minimizes the upper bound of the worst-case H2 performance of the closed-loop Lur'e system. The controller is xc = Acxc + Bcy,

u = Ccxc

(2)

where xc : (n x 1) is the controller state and Ac, Bc, and Cc are constant matrices of appropriate size. The closed-loop system of the Lur'e system (Eq.(l)) and the LTI controller (Eq.(2)) have dynamics x = Ax + Bpp + Bww q = Cgx + DqPp + Dqww z = Czx + Dzpp + Dzww,

p = (j>{q)

(3)

where, A 'A

Bp

Bw

cg

Uqp

Uqw

cz

Dzp

BCCy

LJzw.

BUGC J±C +

BP

Bw

tjcL)yU\yC

=

cq

Uqu^c

Dqp

•Lsqw

cz

DZUCC

Dzp

Uzw

and x = [xT xj] . The upper bound of the worst-case H2 performance of the closed-loop Lur'e system (Eq.(3)) is computed by solving the following optimization problem: minimize tr B^ \P + C^ACq Bv subject to ATP + PA + CTZCZ PBp + ATCJA + CjT BTP + KCqA + TCq KCqBp + BjCfA - 2T

<0

P > 0, A > 0, T > 0

(4)

To design a controller, the algorithm proposed by Banjerdpongchai and How1 is applied. This algorithm uses the procedure of alternating between three different LMI problems for solving non-convex optimization problems.

441 fm2) < /

K2 : Nonlinear

mh —> z*==xl

C*y /

Force

u

K l : Linear

vl

••

>1

V >'

Displacement

//

K2 : Bilinear

Figure 2. Two-degree-of-freedom system

3

Numerical example

Among the nonlinear control problems in structural control systems, one of the main concern is hysteretic nonlinearity. To investigate efficiency of the proposed method for hysteretic nonlinear system, a numerical example of a two-degree-of-freedom system subject to ground motion is considered. Stiffness between mass 1 and ground is linear and, nonlinearity of the stiffness between mass 1 and 2 is introduced by bilinear hysteresis model (Fig. 2). The system parameters are mi = m? = 1, £i = £2 = 0.01, fci = 4.7T2 and ka,nominal = fctt = 4 x 7r2. Control force is applied to 7712, and the velocity of mi is measured. To apply robust Hi control method, nonlinearity of ki is approximated as £2(2;) = kiynom{nai ~ &{%)-> where a > 0 is a relative uncertainty size, and <j>(x) is a [0,1] sector bounded nonlinear uncertainty. Several controllers are designed and investigated for various design parameters such as secondary stiffness kb, yield displacement A and relative uncertainty size a. The ratios of post yield stiffness to primary stiffness kf,/ka are 0.2 ~ 0.9, those of a are 0 ~ 0.14, and A values are 0.03 ~ 0.15, which were determined from the response of nominal linear system. Kobe earthquake record (JMA Kobe, NS 1995) was used as input ground motion. In the controller design, the design parameters are two constant values, the relative uncertainty size and the relative size of control force. Because control force parameter can be fixed to a value from nominal LQG controller design, the only parameter of concern is the relative uncertainty size, a. This feature makes controller design process simple and easy. An optimal or sub-optimal performance of vibration control is achieved directly from the solution of robust H2 control problem. No further tuning of weighting functions and parameters is needed. Figure 3 shows robust performance anlalysis for the nominal linear system, in which fe2 is linear but has parametric uncertainty. Robust performance is shown clearly in this comparison. As fc2 decreases, the results show a drop of

442

,

I

1

1

1

0.6

0.65

0.7

0.75

B

1

1

•

•

1

O.B

0.B5

0.9

0.95

1

Vs..™™.,

Figure 3. Comparison of robust performances

the performance of the closed-loop system, that is, H2 norm increases. As a increases, robustness improves at the cost of nominal performance degradation. Analysis results of the nonlinear model are represented in Figures 4 ~ 6. When the nonlinearity is weak (kb/ka = 0.9), responses with nominal LQG controller and proposed robust controller (er = 0.10) are almost identical as shown in Figure 3. This is because the system's behavior is nearly linear. As nonlinearity of k^ increases (kb/ka — 0.6), responses become quite different (Fig. 5). The proposed robust controller works effectively in contrast with the unstable response of nominal LQG controller. If strong nonlinearity prevails (kb/ka = 0.2), both controllers show almost same performance (Fig. 6). It is because hysteretic energy dissipation dominates and contribution of control force is relatively small. These results can be summarized as shown in Figure 7. Three regions are clearly shown with the level of nonlinearity. In weak nonlinear region (kb/ka > 0.7), both nominal LQG and proposed robust controllers are satisfactory. Nominal LQG controller outperforms proposed robust controllers. In the region of 0.3 < h/ka < 0.7, results show that nominal LQG controller is inadequate and proposed robust controllers operate successfully. Note that energy dissipation effect increases as the value of kb/ka decreases, that is, nonlinearity grows. In the region of kb/ka < 0.3, energy dissipation of hysteretic behavior prevails over the effect of control system. Both controllers have very small influence on the stability of the system in strong nonlinearity region. Similar results were obtained in the case of variation of yield displacement A.

443 V K . ^ 9 . ^ 0 03 I

\

I

\ /.. _J ! A _ !! :! // ! ! I /

LOO 1

1

!

;

i 02

04

06

OB

Figure 4. Responses of weak nonlinear system (kb/ka = 0.9) K9I\

/ K , =0.6, 4=0 03

06 A 0 03

«.

1

o—i. J

03 02 01 0 -0.1

•0 2

|

_jlf «' . 1 *

j

„

1

f

i

i

/

f

-03

1

>

Figure 5. Responses of moderate nonlinear system (fcj,/fc0 — 0.6) K,'K,-0 2. = 003

K /K =02. a=003 i

|—

i

LQG

1

nf-hf

i

^

i

^•jfTpp

•*-f•••

Figure 6. Responses of strong nonlinear system (fcj,/fc0 = 0.2)

4

Conclusions

Simple controller design method for nonlinear system was presented. In this design, a nonlinear dynamic system is described as a linear system with nonlinear uncertainty block. Complex nonlinear model can be avoided by treating

444

Figure 7. Performance variation according to nonlinearity

nonlinearity as uncertainty. Robust H2 control was used for controller design. Nonlinear uncertainty is represented by a sector bounded memoryless nonlinear function. Unlike a typical H^ control for robust control problem, optimal vibration control performance is automatically achieved through a solution of the worst-case H2 norm minimization problem. This feature makes the controller design procedure simple and easy. A numerical example of two-degree-of-freedom system subject to ground motion was considered. Hysteretic behavior of stiffness was introduced to investigate the effectiveness of the proposed controller. The numerical analysis result shows that the suggested controller has extremely high robustness compared to the nominal LQG controller when treating nonlinear system. The robustness of this controller is quite promising with the broad variation of nonlinearity, besides, the nominal LQG controller loses its robustness with the increase of nonlinearity. Although sector bounded memoryless nonlinearity does not include some important nonlinearity like the hysteretic behavior, numerical simulation results show that the proposed method can be effective even for vibration control of a hysteretic structural system. References 1. Banjerdpongchai, D. and How, J. P., Parametric Robust H2 Control Design Using Iterative Linear Matrix Inequalities Synthesis, Journal of Guidance, Control, and Dynamics, Vol. 23, No. 138, (2000). 2. Stoorvogel, A. A., The Robust H2 Control Problem: A Worst Case Design, IEEE Trans, on Automatic Control, Vol. AC-38, 1358, (1993).

P E R S P E C T I V E OF APPLICATION OF A C T I V E D A M P I N G OF CABLE S T R U C T U R E S ANDRE PREUMONT & FREDERIC BOSSENS Active S t r u c t u r e s L a b o r a t o r y , U L B - C P 165 Av F.D. Roosevelt 50, B-1050 Brussels, Belgium E-mail: [email protected], http://www.ulb.ac.be/scmero This paper proposes a strategy for the active damping of cable structures, using active tendons. The first part of the paper summarizes the theoretical background: the control law is first briefly presented and the main results of an approximate linear theory which allows to predict the closed-loop poles with a root-locus technique are mentioned. The second part of the paper reports on experimental results obtained with a truss structure representative of future space applications.

1

Introduction

The current design of future large space structures relies heavily on the use of trusses. As an example, Fig.l shows a schematic view of a future interferometric mission such as NASA "Terrestrial Planet Finder" or ESA "DARWINIRSI". In this concept of spacecraft, a main truss supports a set of indepen-

Independent pointing telescopes

Laser metrology

Laser metrology

NNW^N^WVN^WKm

Large truss

delay line

Beam

combiner

\A/

, V V, Attitude Control

Figure 1. Schematic view of a future interferometric mission

dently pointing telescopes. The relative position of the telescopes is monitored by a sophisticated metrology and the optical paths between the individual telescopes and the beam combiner are accurately controlled with optical delay lines controlled by a wave front sensor. Typically the distance between the telescopes could be 50 m or more, and the order of magnitude of the error allowed on the optical path length is a few nanometers ; the pointing error on the individual telescopes would be as low as a few nanoradians (i.e. one order of magnitude better than the Hubble space telescope). Clearly, such

445

446

stringent geometrical requirements could not be achieved with a precision monolithic structure, but rather by active means as suggested in Fig.l. The main requirement on the supporting truss would therefore not be precision but stability, the accuracy of the optical path being taken care of by the wide band vibration isolation/steering control system of individual telescopes and the optical delay lines. Geometric stability includes thermal stability, vibration damping and prestressing the gaps in deployable structures (which is a critical issue for deployable trusses). In addition to the geometric requirements mentioned above, this spacecraft would be sent in deep space (perhaps as far as the orbit of Jupiter) to ensure maximum sensitivity; this makes the weight issue particularly important. In summary, the supporting truss should possess the two conflicting features of minimum weight and geometric stability. This paper can be regarded as an attempt to achieve that. The use of cables to achieve lightweight spacecrafts is not new; it can be found in Herman Oberth's early books on astronautics; tension truss structures have already been used for large deployable mesh antennas. The use of guy cables is probably the most efficient way to stiffen a structure, in terms of weight. In addition, if the structure is deployable and if the guy cables have been properly designed, they may be used to prestress the structure to eliminate the geometric uncertainty due to the gaps. Several strategies have been proposed for the active tendon control of space structures, as well as for the in-plane and out-of-plane cable vibrations 1,2 j all of them use non-collocated actuator/sensor configurations. These strategies use different control algorithms for the various vibration modes, and they have been found to be prone to instability when the interaction between the cable and the structure is large. An alternative strategy has been proposed by the present authors 3 ' 4 , which is based on a displacement actuator (active tendon) collocated with a force sensor; this approach does not rely on a model of the system and enjoys guaranteed stability properties (assuming perfect actuator and sensor dynamics). The claim of this paper is that actively controlled cable reinforced trusses may help to meet the above objectives of minimum weight and geometric stability. This paper is divided in two parts: the first one summarizes the most important theoretical results which have been published earlier 5 ' 3 . Section 2 explains the control algorithm used to control cable structures and section 3 summarizes the main results of an approximate linear theory which allows to predict the closed-loop poles and provides design guidelines for the selection of the active cables. The second part of the paper reports experimental results. Section 4 examines a free floating truss, somewhat similar to the JPL-MPI testbed 6 .

447

2

Active damping of cable structures Cable

(a)

Structure

"V

•—^,'M

1L

VWvl

Active tendon^ 20

(b)

without contn

Structure

ith control -20

O -40

-60 •f,.>„

10

f,„......15 Frequency (Hz)

25

Figure 2. Active damping of cable structures.

The active damping of linear structures is much simplified if one uses collocated actuator-sensor pairs 5 ; for nonlinear systems, this configuration is still quite attractive, because there exist control laws that are guaranteed to remove energy from the structure. The direct velocity feedback is an example of such "energy absorbing" control. When using a displacement actuator (active tendon) and a force sensor, the (positive) Integral Force Feedback

u = gjTdt

(1)

(refer to Fig.2.a for notations) also belongs to this class, because the power flow from the control system is W = —Tit = —gT2. This control law applies to nonlinear structures; all the states that are controllable and observable are asymptotically stable for any value of g (infinite gain margin). However, the amount of damping that can be introduced in a cable without sag is very low, because the tendon control appears only as a parametric excitation 7 . The foregoing theoretical results have been confirmed experimentally with a laboratory scale cable structure similar to that represented schematically in Fig.2.a, where the active tendon consisted of a piezoelectric actuator 3 . Figure

448

2.b shows the experimental frequency response between a force applied to the structure and its acceleration; also shown in the figure is the free response of the structure with and without control. We see that the control system brings a substantial amount of damping to the system, without destabilizing the cable (theoretically, the control system does indeed bring a small amount of damping to the cable, which depends on the sag); this behaviour is maintained at the parametric resonance, when the natural frequency of the structure is twice that of the cable. The foregoing approach can readily be extended to the decentralized control of a structure with several active cables, each tendon working for itself with a local feedback following Equ.(l). This statement was verified experimentally on a T-shaped structure controlled with two cables 7 , and is further confirmed by this study. Next section describes an approximate linear theory to predict the performance of the control system and provides design guidelines to select the active cables. 3

Closed-loop poles

If we assume that (i) the dynamics of the active cables can be neglected and that their interaction with the structure is restricted to the tension in the cables and (ii) the mode shapes are identical with and without the active cables, it is possible to develop an approximate linear theory of the closed-loop system. For a decentralized feedback control law u=

9

-K~xT

(2) s where T is the local force measurement, u is the active tendon displacement, Kc is the stiffness of the active cable {K^T represents the elastic extension of the active cable) and g is the control gain (the same for all control elements), the following results have been established in earlier studies 3 : 1. If we assume no structural damping, the open-loop zeros are ±juit where uii are the natural frequencies of the structure where the active cables have been removed. 2. The open-loop poles are i j f i j where f2; are the natural frequencies of the structure including the active cables. 3. As g goes from 0 to oo, the closed-loop poles follow the root locus corresponding to the open-loop transfer function G(S)

~ 9s(s* + W

(3)

449 natural frequency with the active cables

4s 2 +n,- 2 )

Re(,)

max .H

U

®i 2(0 i

active cables removed

Figure 3. Root locus of the closed-loop poles.

(only the upper part of the root-locus is shown in Fig.3, because it is symmetrical with respect to the real axis). Thus, the closed-loop poles go from the open-loop poles at ±jOj for g = 0 to the open-loop zeros at ±ju>i for g —> oo. 4. The depth of the loop in the left half plane depends on the frequency difference Cli — u>i and the maximum damping, for g = fij i/f2j/w,, is fii — u)i 2u>i

(4)

5. For small gains, the modal damping ratio resulting from the active tendon control is given by

fc«

9vi

(5)

where V{ = (fi? — w?)/Of is the modal fraction of strain energy in the active cables. Equations (4) and (5) can be used very conveniently in the design of actively controlled cable structures. The foregoing results are based on the assumption that the dynamics of the active cables can be neglected and that the passive ones behave linearly 3 .

450

4

Scale model of the JPL-MPI test bed

The structure considered in this experimental study is the free floating truss of Fig.4. The geometry is representative of a scale model of the JPL-MicroPrecision-Interferometer 6 . The JPL-MPI structure is a large trihedral passive truss with a size of about 9 m. The possibility of using three active Kevlar cables of 2mm diameter connecting the tips of the three trusses was considered in a previous study 4; using the root locus theory of section 3, a damping ratio between 14 % and 21 % was predicted in the first three global flexible modes. The aim of this experiment is to substantiate this claim. During the tests, the free-floating condition is simulated by hanging the structure from the ceiling of the lab with soft springs. Each of the three trusses constituting the structure is provided with an aluminum plate supporting a piezoelectric active tendon described in a previous paper 4 . In this study, two different types of

Figure 4. Free floating truss with active tendons.

cables have been used: a fairly soft cable of 1mm diameter of polyethylene (EA « 4000i¥) and a stiffer one of synthetic fiber "Dynema55 (EA « 18000JV); in both cases, the tension in the cables was chosen in order to set the first cable mode at 400rad/sec or more, far above the first five flexible modes for which active damping is sought. Table 2 (inset into Fig.4) gives the measured natural frequencies Ui (without cables) and 0« (with cables), for the two sets of cables. Figure 5 compares the experimental closed-loop poles obtained for increasing gain g of the control with the root locus prediction of Equ.(3). The closedloop poles have been obtained from frequency response functions with the MATLAB Frequency Domain Identification Toolbox. The results are con-

451

-10

-5 Real axis

-15

-10 Real axis

Figure 5. Experimental poles vs. root-locus prediction for the flexible modes of the free floating truss, (a) EA = 4000JV (b) EA = 18000iV.

sistent with the analytical predictions, although a larger scatter is observed with stiffer cables. A strange behaviour is observed in Fig.5(b): the closedloop poles corresponding to mode 5 follow loops joining ± j n 5 to ±ju>i\ also, the loop starting at j£ti goes upwards rather than downwards. We do not have any explanation for this behaviour which may be related to the fact that the approximate model leading to the root locus predictions assumes that the mode shapes are identical with and without the active cables. Note, however, that the experimental results tend to exceed the root locus predictions. Figure 6 compares typical frequency response functions with and without control. 5

Conclusion

This study proposes a strategy for active damping of cable structures with active tendons. The decentralized control architecture has excellent robustness properties with respect to actuator and sensor failure; the control law is simple, has guaranteed stability properties, and can easily be implemented in an analog manner. An approximate linear theory has been developed, which gives simple guidelines for designing the structure and predicting the closed-loop poles. Experimental results have been presented; they confirm the efficacy of the proposed approach. Acknowledgement This study was partly supported by the Inter University Attraction Pole IUAP IV-24 on Intelligent Mechatronics Systems. The authors wish to thank Bob

452

100 120 140 160 Frequency (rad/sec)

180

200

Figure 6. Typical frequency response functions with and without control (EA = 4000Af).

Laskin for providing the modal data of the JPL-MPI structure, and Ben Wada for stimulating discussions on the future of adaptive structures in space. References 1. Y. Fujino and T. Susumpow. An experimental study on active control of planar cable vibration by axial support motion. Earthquake Engineering and Structural Dynamics, 23:1283-1297,1994. 2. J. C. Chen. Response of large space structures with stiffness control. AIAA, J. Spacecraft, 21(5):463-467, Sept-Oct 1984. 3. A. Preumont and Y. Achkire. Active damping of structures with guy cables. AIAA, J. of Guidance, Control, and Dynamics, 20(2):320-326, March-April 1997. 4. A. Preumont, Y. Achkire, and F. Bossens. Active tendon control of large trusses. AIAA Journal, 38(3):493-498, March 2000. 5. A. Preumont. Vibration Control of Active Structures : An Introduction. Kluwer Academic Publishers, 1997. 6. G. W. Neat, A. Abramovici, J. M. Melody, R. J. Calvet, N. M. Nerheim, and J. F. O'Brien. Control technology readiness for spaceborne optical interferometer missions. Proceedings SMACS-2, Toulouse, 1:13-32,1997. 7. Y. Achkire. Active Tendon Control of Cable-Stayed Bridges. Ph.D. dissertation, Active Structures Laboratory, Universite Libre de Bruxelles, Belgium, May 1997.

STRUCTURAL CONTROL OF A ROTATING SPACECRAFT WITH ELASTIC SPIKE ANTENNAS USING THE MAGNETOHYDRODYNAMIC CONTROL SYSTEM BORIS RABINOVICH Space Research Institute, Russian Academy of Sciences, 84132 Profsoyuznaya Str., Moscow, 117810 Russia, http://www.iki.rssi.ru/people/br-cw.htm, E-mail: [email protected]

An unstable rotating spacecraft (SC) with a flexible spike antenna located along the rotation axis is considered. The Auroral Probe of the INTER- BALL project is a typical example of such object.. It is shown that MHD elements may be efficiently used for the control system of the spacecraft. In particular, it is demonstrated that it is possible to stabilize the undisturbed rotation of the SC without reducing its angular velocity. It is important that tbe considered control system has no hinges and does not need any special fuel storage.

1. Introduction The problem considered here is that of structural control of a rotating spacecraft (SC) with elastic elements of a spike antenna type. The main problem of this object is the dynamic instability of the system. A typical example of such SC is the Auroral Probe (AP) of the INTERBALL project. This rotating SC is equipped with nine spike antennas. The overall size of the probe with the antennas is close to 20 m. Flexible rigidity of such antennas is very low, and the natural frequencies of the system are comparable with the angular velocity of the spinning SC. Such SC must be stabilized relative to any direction in the inertial frame (e.g., the direction to the Sun). This single-axis attitude control is typical for most of spacecraft. Stability of the undisturbed rigid-body motion of the SC is provided by rotation around its longitudinal axis. Rotation of a rigid body about the axis of maximum moment of inertia is highly stable. However, the elasticity of the antenna can greatly diminish the stability of the undisturbed body motion. In particular, such effects have occurred at the Auroral Probe [1]. We consider the regions of stability and instability for this system using a relatively simple model of a rotating rigid body with a single one-dimensional flexible element which is aligned along the spacecraft longitudinal axis. As it follows from this model, the spacecraft rotation is unstable when its angular rotation velocity is greater than the fundamental frequency of the flexible element oscillations [1]. The two methods commonly used to solve this problem are either to reinforce rigidity of the antenna or to reduce the angular rotation velocity of the spacecraft.

453

454

The first method is too difficult in its structural realization, while the second method makes the SC more sensitive to gravitational disturbances. We therefore propose to use a special magnetohydrodynamic (MHD) device for the additional attitude control of the spacecraft. This method was recently developed by the author to provide the dynamic stability for liquid fuel rocket carriers (RC) [2]. This MHD device has a cylindrical cavity completely filled with liquid of high electrical conductivity (e.g., mercury), so that the magnetic Reynolds number of a disturbed motion of the liquid is sufficiently high. A solenoid mounted around the cavity is generating the magnetic field under control. The ponderomotive forces arise from the magnetic field induced by the controlling current. This idea was used for development of the control system aimed to stabilize the rotating SC with the flexible antenna mentioned above. Two MHD elements of semi-tore configuration are assumed to be located in two orthogonal planes which intersect the longitudinal axis of the SC. The mathematical model of such system is described in the next section. The relatively simple control law is based on measuring acceleration components in both orthogonal planes. The following methods have been used for the mathematical analysis of the stability problem: (a) analytic study of a simplified model, (b) development of stability regions, (e) numerical realization of a root locus method, (d) mathematical simulation using the Runge-Kutta method. 2.

Stability of a SC with a flexible element located along its axis of rotation

Let us consider the stability of a rotating SC of the AP type using the following mathematical model. The equations of the disturbed motion are

(i)

§ - i (A/ -1) e + MO + D (c + 21 c - o = °;

using the generalized coordinates

(2)

6 = 62+183; C =

V

s — q-ip; e=

d?;

UJ = U2+ii^3 =6 + i6; c=

d7;

T = Uot

'

455

and main parameters (3)

Aw = er2 - 1; J = J2 = J3; z0 = a +1;

J

J

w0

The notation used is as following: G j (j = 2,3) are the orientation angles of the SC relative to an inertial frame; (»j (j = 2,3) are the angular velocity components in the reference frame of the SC; pj, qj (j = 1, 2) are transversal displacements relative to the SC of the flexible mass element; m, 1 are the attached mass and length of the flexible element; a is the distance between the connection point of the element and the center of mass of the SC; w0 is angular velocity of SC rotation about the longitudinal axis; coc, is the normal oscillation frequency of the flexible element.

Figure 1: Stability and instability regions for the rotating SC of the AP Type

456

Figure 2: Root loci for &b=const=0.0523 s"' and the variable parameter a>c (solid thick line corresponds to exact and thin line to approximate solution) This mathematical model yields the following stability condition [1]: det ~^0^

A/ -1

-D Aw

= AJ Aw - D > 0. ^092-

~e#t

Figure 3: Mathematical simulation of nutation of a gyro-stable SC of the AP type ('&>o=const=0.0523 s"' and , coc =0.06 s"1): (a) s is the vector locus corresponding to the mass m displacement by the strains of the flexible element; (b) a is the vector locus corresponding to the angular velocity components of the SC

457

Figure 4: Mathematical simulation of the nutation of the gyro-unstable Se of the AP type (o0= const = 0.0523 s"1 and coc = 0.03 s"1): (a) s is a vector locus corresponding to the mass m displacement due to a strain from the flexible element; (b) ft) is a vector locus corresponding to the angular velocity components of the SC. The respective stability regions and root loci of the characteristic equation corresponding to the mathematical model (1) with the AP parameters are presented in Figures 1 and 2. We see in Figure 2 that the third A.3 root is responsible for the unstability of the SC and coc, = 0.05432 s"1 marks the boundary of the domain of stability. The mathematical simulation of nutation of a gyro-stable SC of the AP type (ft)c =0.06 s"1) is presented in Figure 3. The same plot for a gyro-unstable SC (ft>c,=0.03 s" ) is shown in Figure 4. 3 Structural control of the SC by the MHD elements Let us consider a simplified mathematical model of the MHD element, which may be presented in non-dimensional coordinates as follows [2, 3]:

f + 7r f + al r = -k \ S(T) dr, o where r is a relative non-dimensional displacement of the electro-conductive liquid inside the element, r is the non-dimensional time, yr is the damping coefficient, an is the natural frequency of the liquid proportional to the permanent current f in the coil, k is the constant depending on the parameters of the MHD element, &= SV/V is voltage normalized with its mean value V°.

458

Figure 5: Root loci for the SC of the AP type with MHD elements and accelerometers in the control loop (a0 = 2, at= 3) for coo = const = 0.0523 s"' and a variable parameter coc, (solid thick line marks exact and thin line approximate solutions) We consider two MHD elements located in the two main planes of the SC, which have the same coefficients yr, ar, as for the flexible element y, a, . Using the notation ph qh for displacements of the attached mass of the element and p2, q2 for liquid displacements inside the MHD elements, while taking into account the control law r

/ = -Jfc f(ag - iav) dr = 2 [ao 0 + <*i (6 - i6) - i C], o we obtain the following mathematical model of a SC with MHD control. The equations of the disturbed motion are §-i(AI-l)6

+ Aid + 2D (C + 2 it - C) = 0;

C + ( 2 i + 7 K + AwC + 0 + 2 z 0 - 0 = 000 + 0! ( 0 - i 0 ) , which can be compared with model (1).

459 The generalized coordinates are the same as in (2), where P=O(PI+P2);

9 = 0 ( 9 1 + 92),

and the main parameters are the same in (3)

I

1

^-2-J

-J

1

I

1——

1—-0J0&-J

1

Figure 6: Stabilization of the gyro-stable SC of the AP type with MHD elements and accelerometers. The mathematical simulation for a>0 = const = 0.0523s"1 and co = 0.06 s" (a0 = 2, ai = 3): (a) 5 is a vector locus corresponding to the mass m displacement by the strains of the flexible element; (b) ft) is a vector locus corresponding to the angular velocity components of the SC. Using this model we have solved the same problem as in the case of the gyrostabilized SC without the additional control. Some results are presented in Figures 5-7 (compare with the respective results for the previous model shown in Figures 24). Figure 5 shows the new version of the root loci estimated while considering the additional control based on two accelerometers and two MHD elements for one of the above combinations of the control law constants a0, ah

460

Figure 7: Stabilization of the gyro-unstable SC of the AP type with MHD elements and accelerometers. The mathematical simulation for a>0 = const = 0.0523 s"1, co = 0.03 s~' (a„ = 2, ai = 3): (a) s is a vector locus corresponding to the mass m displacement by the strains of the flexible element; (b) (a is a vector locus corresponding to the angular components of the SC. Figures 6 and 7 demonstrate the results of the mathematical simulation of gyrostable or gyro-unstable Se nutation with a MHD control system. These examples illustrate the possibility to stabilize the steady-state rotation of the Se without any constraint on its angular velocity. 4. Summary The use of flexible elements with relatively low normal frequencies, which are located along the rotation axis of the gyro-stabilized SC, may lead to instability of steady-state rotation about, the axis with a maximum moment of inertia. The logarithmic increment of oscillations in nutation is proportional to a the oscillation decrement of the flexible element and to a difference between the SC angular velocity and the normal frequency of this element. A possible solution to the stability problem is to use the additional control system with MHD elements, accelerometers, and/or angular velocity sensors. Acknowledgments. The author is grateful to Alexey Grishin for his help in calculations and graphical presentation of the results, to Josef Cherniawsky for constructive comments and careful editing of the text and to Victoria Prokhorenko for producing an electronic version of the paper. This work was supported by the Russian Foundation on Basic Research (Grant 00-001-00244).

461

References 1. L.V. Dokuchaev, and B.I. Rabinovich. Analysis of Perturbed Motion Near the Stability Boundary of a Spacecraft of the INTERBALL Auroral Probe Type . Cosmic Research, (37), pp. 554, 562, 1999. 2. B.I. Rabinovich., V.G. Lebedev, and A.I. Mytaxev. Vortex Processes and Solid Body Dynamics: The Dynamic Problems of Spacecraft and Magnetic Levitation Systems Kluwer Academic Pubi., Dordrecht, 1994. 3. B.I Rabinovich. Vortex Fields in Dynamics of Spacecraft, Maglev, and Magnetohydrodynamic Systems: Theory and Experiment J. Tech. Phys., (40), pp307, 314, 1999.

ACTIVITIES OF THE EUROPEAN LABORATORY FOR STRUCTURAL ASSESSMENT IN THE FIELD OF STRUCTURAL CONTROL FOR CIVIL BUILDINGS, BRIDGES AND ARCHITECTURAL HERITAGE V. RENDA, G. MAGONETTE, J. MOLINA, D. TIRELLI AND F. MARAZZI European Commission, Joint Research Centre, TP 480, 1-21020 Ispra (VA) E-mail: [email protected]

Activities relevant to structural control have been performed at the European Laboratory for Structural Assessment (ELSA) and focused on seismic protection of civil and architectural heritage structures obtained by using base isolation and energy dissipation systems. Steel and concrete frames and bridge columns have been tested to assess and validate base isolation and energy dissipation devices. Relevant tests have been done also for protection systems applicable to architectural heritage structures in order to contribute to the development and validation of technologies, techniques and tools for the vulnerability assessment and retrofitting techniques for these very important structures having specific characteristics. In the framework of an international Consortium partially funded by the EC-DG-Research (ISTECH project), innovative retrofitting techniques have been developed and tested using Shape Memory Alloys (SMAs) for the realisation of intrinsic dissipation devices.

1

Introduction

The European Laboratory for Structural Assessment (ELSA) of the Joint Research Centre (JRC) is specifically equipped with up-to-date means for carrying out Pseudo-dynamic (PsD) tests to reproduce the behaviour of large scale structures subjected to earthquake loading. The ELSA laboratory is at present engaged in international consortia to optimise and test innovative anti-seismic devices based on passive vibration control. PsD testing is, by virtue of the expanded time scale of the tests with respect to real seismic events, normally restricted to materials assumed to behave in a rate-independent manner. As regards to seismic isolation and energy dissipation based on rubber bearings and devices, although the strain rate effect cannot be taken into account at the experimental stage, it can be taken into account in the numerical part of the method. A standard procedure for the PsD testing of large-scale models of structures protected by base-isolation and energy dissipation devices has been developed and validated at the ELSA laboratory. Comparison with shaking table tests and dynamic snap-back showed the effectiveness of this experimental technique also for structures equipped with devices based on moderately strain rate dependent materials. Some experimental PsD tests performed at ELSA are described in the following for cases of civil (steel and concrete frames) and architectural (masonry walls) structures protected against earthquakes by base isolation and energy dissipation systems. 463

464 2 2.1

Base isolation Objectives of the activities

The main aim of this activity was to validate a standard procedure to test base isolated structures by the PsD method [1]. This was done in collaboration with the Italian Working Group on Seismic Isolation (GLIS) chaired by the national research centre ENEA and includes the national electricity board EMEL, the industrial research centre ISMES and the manufacturer of isolators ALGA. Based on the validated procedure, a large series of tests have been performed for full/large scale models of both civil and architectural base isolated structures. 2.2

Description of the Mock-up

In the framework of this collaboration it was decided to test at the ELS A laboratory a scaled structure (provided by ENEL), isolated by means of high damping rubber bearings (HDRBs), which had been tested on the Shaking Table of ISMES. The mock-up, named MISS (Model of Isolated Steel Structure), is a 5-storey steel frame with an interstorey height is 0.9-m composed of 2-bays for a total length of 3.3-m in one direction and 1-bay of 2.1-m in the orthogonal direction. This structure supports up to 20 concrete masses, each weighting 1300 kg (Figure 1).

Figure 1: Thr WIS 2 :~.-yc\.--

465

As known the rubber bearings are devices sensitive to strain rate; the procedure for PsD testing set up and validated by JRC consists mainly of characterisation tests of the isolator for different strain rates to assess the stiffness increment to the difference in time-scale between dynamic and PsD tests. This increment leads to a correction factor (about 19% this case) of the shear force measured at the top of the isolator during the PsD tests.

This experimental activity aimed to validate the PsD method to test base isolated structures and to perform a wide investigation on the effectiveness of these devices for seismic protection. The procedure has been validated both comparing results from Shaking Table with PsD tests and Dynamic Snap-Backs with PsD simulations. 2.3

PsD seismic test results

On the shaking table of ISMES, several synthetic and natural base acceleration time-histories had been applied to the MISS mock-up. The Tolmezzo NS -6dB record was selected and used for the PsD experimental campaign because it was the only one for which mono-axial responses of the structure in the non-isolated and isolated configurations were available.

466

As expected the results for the isolated structure (Figure 2) showed a large displacement at the top of the isolation system and small interstorey drift on the frame. Comparing the results for the non-isolated with the isolated case, the maximum interstorey drift drops from 10-mm to about 2-mm while the maximum shear force decrease from 80-kN to 25-kN. Many other tests performed at ELSA also on other structures of civil and architectural heritage interest showed the effectiveness of base isolation as earthquake protection system in all cases but for signals having a response spectrum with acceleration peaks at low frequency (1-Hz and less). In this case the frequency interaction between earthquake and structure must be assessed with care. 3 3.1

Energy dissipation systems Framework of the activity

This activity has been performed in collaboration with an international Consortium in the framework of a European project, named "REEDS", partially funded by the EC through the Brite-EuRam Programme [2]. It has been set up to focus the efforts of manufacturers, developers and end-users of anti-seismic devices towards identifying methods to augment the options currently available and therefore greatly increase the possibility that economic seismic protection can be provided to any particular structure, plant or equipment. 3.2

Description of the Mock-up

A two-storey mock-up of a reinforced concrete office building was designed for pseudo-dynamic (PsD) testing to be performed at the ELSA laboratory. The mockup (10m long, 4m wide and 5.2m high) represents a portion of the building scaled by 2/3 in dimension and consists of two bays of 5m in the direction of testing and of one bay across its width (Figure 3). Eight energy dissipation devices were placed in each bay along the longitudinal facades and were supported by steel K-bracings. The connections of the steel bracing with the reinforced concrete frame have been made by means of anchor bolts to simulate a real retrofitting situation. A particular attention has been devoted to the instrumentation of the mockup, to measure the relative rotation between beam and column at the joints, and to measure the deformation of the antiseismic devices. The JRC has designed and instrumented the steel bracing in order to measure the shear force developed by devices. This measurement was necessary to compensate the strain rate effect induced by the PsD method according with the procedure mentioned in the paragraph related to seismic isolation.

467

3.3

PsD seismic test results

The tests performed at JRC-Ispra showed a relevant reduction of displacements and highlighted the effectiveness of the devices for earthquake engineering applications. Frame structures, which are quite common in seismic areas of Europe, the technical study has proved that reinforced concrete frame buildings designed initially for non-seismic areas may be up-graded, by incorporating viscoelastic dampers to respond elastically to earthquakes specified in European Seismic Code EuroCode 8. The devices can indeed provide an alternative protection strategy for such buildings. The dampers raise the stiffness between floors, the increase itself contributing to the reduction in the response. However, the inherent damping of the devices reduces the response much further. The PsD tests carried out at ELSA on the large-scale civil building have shown that when the structure is installed with

468

the devices it responds elastically to earthquakes twice the magnitude of that for the bare structure. The second storey displacements of the PsD tests on bare and protected frame are shown in Figure 4. The efficiency of the energy dissipation devices is demonstrated by a reduction of the displacements of the frame by more than a factor of four, keeping thus the ductility demands on the RC members below unity, as shown by the hysteresis loops of the RC frame.

1 3 4 5 8 ? I 9 10 Figure 4: 2ndfloordisplacement bare and protectedframe(mm)

Protection of architectural heritage with shape memory alloy devices 4.1

Objectives and material properties

The activity refers to the contribution of the Joint Research Centre (JRC) of the European Commission (EC) to the project ISTECH (Innovative Stability Techniques for the European Cultural Heritage) funded by EC/DG-XII through the Environment and Climate Programme. The project investigated the possibility to use the Shape Memory Alloys (SMAs) for the realisation of mechanical and seismic protection systems for cultural heritage structures based on devices having intrinsically energy dissipation capabilities. SMAs materials are characterised . by super-elasticity allowing energy dissipation through a phase change from Austenite to Martensite and vice-versa. This

469

stress-strain cycling does not produce any material damage and is always performed in traction, allowing the use of cables for the realisation of the devices. The most relevant tasks of JRC were oriented towards two specific line of research. The first leaded to a large experimental campaign for the mechanical characterisation of a wide range of samples of SMAs materials (mainly based on NiTi). The second consisted in performing seismic tests on full-scale models of masonry walls for the validation of a retrofitting technique based on SMAs devices. 4.2

Characterisation of SMAs

Most of SMA's are binary alloys, most frequently composed by an association of Nickel and Titanium. They change their crystalline arrangement as they are cooled down or heated up, as well as in the presence of a stress field. The crystalline geometry is ordered cubic, but after phase transformation from austenite to martensite the crystal, under stress, bends. The result is a large elastic deformation of the sample with reversibility when returning in the austenite phase. This property of no-degrading the crystal structure when the alloy is under stress is the so-called super-elastic behaviour of the material. In addition, the path followed by the material in the stress-strain curve shows a flat level of stress in the loading phase, whereas another plateau appears at a lower stress level, during the unloading phase. The hysteretic diagram shows that the SMAs are intrinsically dissipation materials under loading/unloading traction cycles. The characterisation tests have been performed with the apparatus shown in Figure 5 and are composed of a series of increasing strain cycles, conducted at a constant strain rate for sequences of increasing strain [3]. From this type of tests it is possible to define, until which strain its is convenient to use the material (Figure 6). Stabilisation tests, consisting of a2a: ISTECH:Charactefizationtest(a) :DeltaT=o.ls. twenty cycles, showed the 70014 ! degradation of the v 1~ 1 /~J f " ' material only during the first t I - _ h £ i / cycles followed by a nearly stable state. A large 1 series of tests have fM, Material A2 been conducted to study the :J °0 frequency dependence of the Figure 6: Results of characterization tests material behaviour 600

500

I

400

300

200

100 /

"P

A IL/

1

' '*,

-- • , . . ; . ,

2

3

4

Strain (%]

1

-

5

8

7

.

8

470

for frequencies higher than 1 Hz. The main effects observed' have been the inclination of both plateau, and a hardening of the material with the frequency leading to a reduction of energy dissipation capability. These results showed unfavourable frequency dependence for the purpose of applying SMAs devices for the protection of architectural heritage in seismic areas. During all the tests the temperature has been measured with a thermocouple in contact with the perimeter of the wire by conductive glue, at the middle of the sample. The measurement of the temperature allowed correlating the influence of the strain rate to the temperature variation on the samples and defining a method for the improvement of the dynamic behaviour of SMAs. 4.3

Experimental tests on full scale masonry walls

The aim of the task was the validation of the effectiveness of the system for the protection of and monuments buildings historical against the effects of earthquakes and other loads leading to instability. The activity has been focused on the behaviour of masonry shear walls under the effects of in-plane seismic loads. The tests have been performed on three full scale masonry shear walls; the first for assessing the numerical models and the two others to compare the behaviour of the unprotected wall with the protected one [4]. Multiple SMA Figure 7: Masonry wall with crossbracing wires are grouped in singles devices in order to have the adequate total section for the development of effective reaction forces. FIP Industriale provided JRC with the devices and has developed the best

471

mechanical solution. Finite-elements 1STECHW Up0174 analyses has been conducted to determine correct values of lengths and section areas of the super-elastic wires to avoid deformations / exceeding the maximum value of the super-elastic strain. The University of Rome, in close Figure 8: Energy dissipation collaboration with (GREEN: bare wall; BLUE: protected wall; RED: SMAs JRC, participated to devices) this numerical study. JRC has provided to FIP the basic parameters for the design of the devices. The cross bracing system has been positioned symmetrically on the external surfaces of the Model. This solution allows an easier anchoring of the elements, even after the completion of the model, and the possibility to inspect the devices during the tests. From the architectural point of view, a more attractive solution could be the insertion of the elements into the wall. For the purpose of the tests it is more relevant to have a full control of the devices and the possibility of maintenance and intervention. The crossbracing system must be strongly fixed to the wall in order to transmit adequately the counterbalancing forces when an earthquake occurs. Problems are in the fragility of the masonry that does not allow a simple fixing of the SMA devices. This solution provides a good distribution of the crossbracing system on the wall avoiding in this way dangerous stress concentration. The steel bars of the crossbracing system are fixed to a steel beam anchored to the reinforced concrete basement. Load cells and strain gages provide the necessary information on the behaviour of the devices during the tests.

J

4.4

Tests performed and main results

At first a cyclic test has been done for displacements until 12 mm that strongly damaged the model. The damage consisted mainly in opening of cracks in the three lower panels starting from the central one. Those results are fully consistent with the expected ones; in fact a horizontal tendon were put up to the openings and calibrated in such a way to avoid cracks generation at the top of the model. A second bare wall, including the horizontal tendon, was tested for a reference earthquake and for different amplitudes assessed from numerical analyses.

472

The first signal used in the PsD testing had amplitude of 70% on the reference value; the results showed a linear behaviour of the wall and no damage was visible. The second test was run with amplitude of 200% of the reference and showed some crack distribution mainly in the central panel. This test has been repeated once again and some more degradation has been observed also in the two lateral panels. Finally one more test has been performed for 300% of the reference value and the experience was stopped at half of the transient due to big cracks appeared in the three feet of the wall and a strong degradation of the restoring force. Finally a third wall has been equipped with the cross bracing including the SMAs devices; it is shown in Figure 7. The tests on this wall have been repeated with the same sequence that for the bare one. Until 300% of the reference signal some dissipation of energy has been measured but no crack opening has been seen at a visual inspection. It has been decided to go to 400% of the reference signal and some crack appeared in the central panel of the model but not on the lateral one. Finally a final earthquake was simulated for 500% of the reference value. Big cracks appeared both on the central and lateral foot. For safety reasons it has been decided to stop the test at half of the transient also if the forcedisplacement curves showed a good shape and the SMAs devices were working correctly. The results showed in Figure 8 clarified that the SMAs devices contributed to the energy dissipation for about 30% of the total showing a good effectiveness in the improvement of earthquake resistance of the structure. References 1. Renda V., Verzeletti G., Magonette G., Tirelli D. and Papa L., Validation of the pseudo-dynamic method to test large-scale models of base isolated structures. 14th SMiRT International Conference, August 18-22, 1997, Lyon. 2. Taucer F., Magonette G., Marazzi F., Molina J., Verzeletti G. and Renda V., PsD tests on the seismic retrofit of a large scale RC civil building with energy dissipation devices. Proceedings of the ASSISI-99 International Workshop on Seismic Performance of Built Heritage in Small Historic Centres, April 22-24, 1999, Assisi, Italy. 3. Tirelli D., Renda V. and Bono F., Characterisation and fit to seismic protection of shape memory alloys. Proceedings of the 4th European Conference on structural dynamics, EURODYN '99, Prague.Czech Republic, 7-9 June 1999 4. Bono F., Tirelli D., Verzeletti G., Molina J. and Renda V., Shape Memory Alloy crossbracing of brick masonry walls: Cyclic tests of a large-scale model and numerical analyses. Proceedings of MONUMENT-98 workshop on seismic performance of monuments, Lisbon, Portugal, November 12-14, 1998

O P T I M A L D E S I G N O F D A M P E R S A N D STIFFENERS IN S T R U C T U R E S USING ACTIVE CONTROL APPROACHES

A.M. REINHORN University at Buffalo, Buffalo, New York, 14260, USA e-mail: reinhorn@buffalo. edu N. GLUCK, J GLUCK & R. LEVY Technion-Israeli

Institute of Technology,

Technion City, Haifa, 32000,

Israel

A suggested method for design of supplemental dampers in multistory structures is presented. Active optimal control theory is adapted to design linear passive viscous or viscoelastic devices dependent on their deformation and velocity (best represented by Kelvin model). The theory using a linear quadratic regulator (LQR) is used to exemplify the procedure. The design is aimed at minimizing a performance cost function, which produces a most suitable minimal configuration of devices while maximizing their effect. The method is fully effective using full-state static feedback. Since the active feedback action require a linear combination of all states and passive devices cannot supply it, the paper introduces a methodology to eliminate the off-diagonal interactions between states using various engineering ways. The paper shows the development for velocity feedback only, for the sake of simplicity. However, the full-state formulation can be manipulated similarly to obtain a combined position-velocity feedback design. The paper shows a numerical implementation of the design methodology for a structural model prepared for further experimental considerations.

1

Introduction

Active control theory provides a suitable framework for design of control systems in which forces are introduced in structures to reduce the unwanted effects of vibrations. The control theories assume that each force-generating device has the capability to process information from all observable sensors simultaneously and generate compatible forces. This control can be obtained using either active or semi-active operating systems. Passive devices [7],[3] produce forces depending either on their elongation or internal velocity, or both, dictated by the structure movement. The parameters that govern such behavior are fixed by design. For example, viscoelastic type damping devices develop forces, which can be approximated by: F d = k d x ( t ) + C d x(t)

(1)

473

474

in which kj and cd are constant parameters for unique frequency input. The optimal linear control approach is used in this paper to determine the constant coefficients for the damping devices. Inaudi et al. [8] used a stochastic linearization along with a similar optimization procedure to determine initial design values for damping devices. The design process developed in this paper is deterministic and can be used for structures using damping braces, which can be easily implemented in new construction or in rehabilitation and retrofit [7],[5],[4],[10]. The procedure can be used with some approximation for design of other force delivery devices with passive characteristics such as friction or hysteretic devices [3]. The process is illustrated by a design example for a small model structure. 2

Optimal Control Theory

For a frame structure braced by devices that control it's vibration the equation of motion may be written as:

(2)

Mx(t) + Cx(t) + Kx(t) = Ef(t) + Du(t)

in which, matrices M,C,K characterize mass, structural damping and stiffness related to the deformations x(t) at various degrees of freedom. The brace forces are included in the system as control forces u(t) at locations indicated by matrix D designed to reduce the response due to excitation forces, f(t) at locations indicated by E. The equation of motion can be easily compacted to a state space formulation:

z(t) = Az(t) + Bu(t) + Hf (t)

(3)

where, z(t) = { x(t), x(t) }T, and the parameter matrices for the system, A, for the control location, B, and for force operation, H, are: A=

1

0

B=

0

ivrt

H=

0

rVrt

Assuming that the control forces are of linear form, for sake of simplicity: u ( t ) = G z ( t ) = [G J G * ] z ( t ) = G x x ( t ) + G

xx(t)

(4)

in which, the gain matrix, G includes the constant coefficients, Gx, Gif for the structural control devices. The gain matrix G is obtained from the minimization of a performance index (Gluck, Reinhorn, Gluck, and Levy, 1996) as: G = -1/2R_1BTP in which, P is the solution of Ricatti equation:

(5)

475

A T P + PA - 1/2PBR _ 1 B T P + 2Q = 0

(6)

The control forces are obtained therefore: (7a)

u(t)=Gxx(t)+Gix(t) or explicitly: 8ll,x

§ln,:

§12,x

Sll.x

§12,x

oln,x

Onl,x

&n2,x

tonn,x

+ onl,x

on2,x

onn,x

X

(7b) If passive diagonal braces in a structure (see Fig. 1) supply the control forces, then these forces are dependent on their constant stiffness and damping coefficient as follows: (8a)

u (t) = Kxx(t) + Cix(t) or explicitly:

u, * u2 • = *

Kj+K^ fCj

«2 Ao

I /(o

\

-K -K

-K K_

<. > +

q+c 2 ~C2

V

-c 2 c2 +c3 -c 3

x2 ~Cn

X

n,

~Cn

C

n _

A. (8b)

The coefficients of the passive formulations, ky, Cy, in Eq. (8) are derived from the gain coefficients gy>x, gy k _ in Eq.(7) using several approximations which are described below. For simplicity of further derivations Eqs. (7) and (8) can be transformed using story-drift formulation (see Fig. 1) obtained from the linear transformations for deformations x(t) and for the diagonal braces forces v(t):

476

© k.

/

x*-t

© k,

) *M

— d,-

i (B) ®

©

-id,

k, ••

(c) Loading

Damping Brace

(a) Structural Frame

(b) Structu ral Deformation

Figure 1: Structural Frame with Diagonal Damping Braces

800mm 178.0 ka

120mm

/

\i' 200.4 kg J

120mm L

V

«i

r

m /

Brace

200.4 kg ' J

*.

d,

—• •-»

r 120mm

d,

mptr P'SPS

Structural

/

/—m

Figure 2: Model Structure for Numerical Example

477

v(t) = T T u(t)

x(t) = Td(t)

(9)

where T is a matrix of units on the upper right triangle and the rest zeros (Gluck et al, 1996) and where v(t) are the control forces in terms of story drifts and drift velocities obtained from Eq. (7) are given as: v(t)=G d d(t)+Gjd(t)

(10)

Gd=TTGxT;Gd=TTGxT

(11)

in which:

Using the same transformation the brace forces of Eq. (8) can be written as: v*(t)=Kdd(t)+Cdd(t)

(12)

in which: K d = T T K x T = diag(Aki) and where,

C d = T T C i T = diag(Ac i )

(13)

Akj, Ac ; are supplemental stiffness properties and damping from each

brace in the structure at level i . To determine the individual components of matrices K<j and Cd in Eq. (13), a least squares approach is considered. Since the stiffness Kj and damping C d can be assumed independent, the least squares will be applied separately for Kj and Cd. Applying the least square approximation to the difference between the formulations of Eqs. (10) and (12) using the notation of Eqs. (11) and (13) results in explicit form:

ddk(t)

I S [g^d^-Dc^Cofdt =0 o

(14)

J

Only the damping coefficients of Cd are determined in Eq 14. However, the same types of formulations can be applied to determine the coefficients of K^.: T

T

Ac

* = J"5Xi,a d^dt/jXodt 0

j

o

T

T

Akk = jXgk.d dj(t)dt/}dk(t)dt 0

where, T is the total time for the event considered.

J

o

(15)

478

The above coefficients can be determined using further simplifications as outlined in the following: Response spectrum approach - "Peakfit":Assume that in the time interval T, the velocity can be obtained from a modal spectrum approach using the square root of sum of squares (SRSS) superposition: d

ji =

SMS*)

2

1/2

dK =

ZMs*)

5

1/2

(16)

where, d^ cL; are the displacement and velocity (resp.) in mode i at degree of freedom (d.o.f.) j , (foj the story differential mass normalized shapes, P; is the participation factor ( = S m j ( t ) j i ) ' a n d Svi, Sdi the spectral velocity and j

displacements of mode i. Damping and stiffness can be calculated as follows:

Sgkj,d S f e P i ^ ) 2

Eg*. E(pA)3 Ak,

Ack=-

_

J

(17)

EMA)

X(9 H P,S„) J

2

Single mode approach: In applications involving building structures in earthquakes, most often only one mode of vibration is relevant. If mode i is retained in Eq. (17), i.e., i = m, then: -4^°kj,dTJn

Acv

<\> km

I 8kj.dC

k

A k k ^ E g k j ^ jm

(18)

where, (|)jm =<|)jm / <()]„„ is the modal shape normalized to unit at degree-of-freedom k. In this case the damping and stiffness coefficients are not anymore dependent on the history of the event. Truncation approach: If only a single gain factor is considered, i.e., the one corresponding to the degree-of-freedom k. In such case, j = k in formulation of Eq. (18) and:

A c k = g kk,d

Akk=g kk,d

(19)

This simplified formulation can be obtained directly from Eq. (10), "truncating" all the off-diagonal terms of matrix G j .

479 3

Implementation of passive viscous or viscoelastic dampers

As indicated above, the optimal solution given by Eq. (10) can be implemented only by active means, which can provide the combination of information from all degrees-of-freedom through the gain matrix, G, which is fully populated [9]. However, using passive braces with viscous, viscoelastic, added damping and stiffness [11], or friction dampers, which can be modeled by Eq. (12) [10], the structure can be protected close to the optimum as derived above. For example, fluid viscous or viscoelastic dampers can be modeled using an equivalent Kelvin model: f d (t) = k(0)) d(t) + C(C0) d(t)

(20)

in which, the storage stiffness, k(to) , and the damping coefficient, c (CO) , (derived from the loss stiffness divided by the circular frequency, CO), can be well approximated as constants in narrow frequency bands of structural response [10]. To determine the desired optimal, or near optimal, coefficients k<. and ce, expressions from Eqs. (17), (18), or (19) can be used (similarly for k as for c). 4

Numerical examples

To illustrate the procedures outlined above and the performance of optimally, or near optimally designed dampers, a 1:5 scale three-story model structure made of two flexible shear frames with rigid floors is considered (see Fig. 2). An artificial mass simulation was used to retain a frequency scaling in a constant accelerated field [1]. The complete mass, stiffness and structural damping of the structure without dampers, as obtained from structural identification are:

~ 200.40 M=

0 200.40

symm

178.00 [kg

" 238,932 -119,466 K=

238,932 symm

0 0 0.0 -119,466 119,466 [N/m]

(21a)

480

26499

-7&09 -1608' 24689

c= symm

-9215

(21b)

16202 [N-se
The natural frequencies of the structure are 1.78 Hz, 4.96 Hz, and 7.05 Hz in the first three modes, respectively. Fluid viscous dampers [2] were considered in this study. These dampers can be constructed as linear or nonlinear functions of velocity. In this study, the configuration studied by Constantinou et al., (1992) was considered. These are dampers which can be represented by a linear relation within the expected range of operations (Eq. (1)), without stiffening characteristics (kd= 0). The optimal design of dampers was developed using the procedure outlined above for weighting matrices, R and Q (in Eq. (6)): R = 10"p I3x3.

Q = I6x6

(22)

in which, Inxn indicate a unit diagonal matrix of size n x n, and p is a variable parameter used to adjust the solution's weights toward the practical range. The optimal solution was obtained by solving the algebraic Ricatti equation (Eq. (6)) using MATLAB™ package [6]. The gain matrices were obtained from a parametric analysis, varying p in Eq. (22) between 2 and 9. By increasing the parameter p, the demand for damping increases and the response decreases. Therefore increasing p one can increase the size of dampers up to the limit of "shelf availability. The results are listed in Table 1 using the form:

1 G = g0

'12

'23

"21 '31

The gain matrix G

'13

(23)

'33

(Eq. (10)) in Table 1 was obtained by direct solution of the d

Ricatti equation with the matrices A and B transformed into coordinates suitable with the transformation in Eq. (9). The results obtained for these matrices are different than those from the transformation in Eq. (11), due to the different influence of weighting matrices, R and Q. The results obtained for the G ; (Eq. (10)) are most representative to the solution, therefore, are used further to determine the damper sizes as follows:

481

go ni

n2

N I

J

3.0

N-sec/m — — —

2.31 1.35 1.68 0.82

N-sec/m — — —

2.20 1.40 1.89 0.84

N-sec/m — — —

3.87 2.73 4.26 3.21

I max

ni

n2

h i

P

j

imax

go ni

2 ?6;; 1J

4.0 G,,Eq.(ll) 21.28 1.26 1.54 0.66 G ,Eq.(ll) 20.79 1.40 1.89 0.84 G ,Eq.(10) 32.81 2.63 4.09 3.04

5.0

6.0

156.16 1.09 1.26 0.32

778.78 1.02 1.09 0.11

151.00 1.40 1.88 0.83

702.90 1.39 1.87 0.82

196.83 2.35 3.62 2.59

847.90 2.13 3.23 2.22

max

Table 1 - Variation of gain matrices for the 3-story building (notation in Eq. (23))

It can be noted that off-diagonal terms, \£J, in the gain matrix G^ shown in Table 1 are substantially different than zero. However, the damping matrix [Cd, Eq. (13)] for the damping braces in Fig. 2 takes a diagonal form. Therefore, the damping coefficients Ac k need to be determined according to the procedure outlined in the previous sections: (i) by "truncation" using Eq. (19); (ii) by "single mode approach"; or (iii) by "engineering" round off of the solution determined in (ii) such that will fit "off-the-shelf devices. It can be noted that off-diagonal terms, 6"^ , in the gain matrix G j shown in Table 1 are substantially different than zero. However, the damping matrix [Cd, Eq. (13)] for the damping braces in Fig. 2 takes a diagonal form. Therefore, the damping coefficients Ac k need to be determined according to the procedure outlined in the previous sections: (i) by "truncation" using Eq. (19); (ii) by "single mode approach"; or (iii) by "engineering" round off of the solution determined in (ii) such that will fit "off-the-shelf devices. The results for p=6 leading to acceptable size dampers, are listed in Table 2. The results are presented using a notation similar to Eq. (23) in which g0 is replaced by Ac d for the damping matrix Cd. The optimal gain matrix is listed in column (6) of Table 2 for comparison. If the design is done by truncation large dampers are required for the higher stories of the structure. For the single mode approach the design leads to larger size dampers

482

overall, but all of same approximate size. The engineering round off leads to identical dampers that can be found "off-the-shelf."

"Truncation Ac d or g0 ni

?2

taL

N-sec/m — — -

847.9 2.13 3.23 0.00

Estimation Method Single"Engineering" Mode Round Off "Estimator" 4,600.0 4,935.0 1.00 0.95 1.00 0.93 0.00 0.00

Gain Matrix 847.9 2.13 3.23 2.22

Table 2 - Properties for dampers in structure in Fig. 2 (notation in Eq. (21))

The design obtained above was evaluated using several earthquake excitations. The structure was subjected to (i) El Centro N-S 1940 accelogram with peak ground acceleration, (PGA) of 0.34 g; (ii) Mexico City SCT 1985 accelerogram (PGA 0.20g); (iii) Hachinohe 1968 accelogram (PGA 0.20g). The displacements at the third and first floors of the structure are shown in Fig. 3. The peak response is shown in Table 3. The structure without dampers has the largest response ("uncontrolled"), while the response using the design based on single-mode approach (estimator) is almost identical to that for the exact optimal solution (which can be obtained only by active means). The design using the "truncation" approach produces also substantial reduction, but not as efficient as the single mode ("estimator") approaches. The engineering round-off selection has the same performance as the single-mode approach. The single-mode approach used the first mode of the structure, which is dominant in earthquake response in tall structures. If there is uncertainty of which modes might be dominant, then the response spectrum design ("peak fit") can be used as outlined in the previous section.

483

Uncontrolled Optimal Design Control) "Estimator" Design "Truncation" Design Uncontrolled Optimal Design Control) "Estimator" Design "Truncation" Design Uncontrolled Optimal Design Control) "Estimator" Design "Truncation" Design

Displacement [mm] El Centra 1940 22.5 (Active 9.2

Velocity [m/s]

Acceleration [m/s2]

0.25 0.10

3.10 1.55

9.3 13.5 Mexico 1985 18.0 10.1 (Active

0.10 0.15

1.52 2.11

0.13 0.06

1.52 0.48

10.1 12.0 Hachinohe 1968 59.1 25.2 (Active

0.06 0.07

0.50 0.60

0.63 0.24

7.52 3.05

0.24 0.32

3.06 4.20

25.0 32.2

Table 3 - Peak Response of Top Floor Subjected to Ground Motions

5

Remarks and conclusions

The paper presents a method of design of supplemental passive damping devices based on optimal linear control theory. Other control schemes can be also applied if the gain matrices are properly handled as shown in here. The design presented can be used to size viscous, viscoelastic or added damping and stiffness devices (ADAS) dampers, (with some additional approximations), if their location was established. It can also help to optimize their location, if an iterative process is followed adjusting the terms in the optimization weighting matrices Q and R and the coefficients in the location matrix B. The design considered herein is based on the control gains, which can be implemented only by an active system. However, the comparison in the numerical example shows that same equivalent effect can be obtained using passive devices only. The above remark is valid for structures dominated by a single mode of vibration. If more modes are contributing to the response, a single passive damper cannot provide the same effect. In such a case a fully active system is more efficient. The design solution for the passive devices is always stable, as provided implicitly by the formulation based on the Riccati equation. The design using

484

passive devices is free of time delays (implicitly avoided by all the reactive passive systems) and is reliable in its operations. The procedure outlined in the paper can also be used to size also friction dampers for which the reaction force is dependent on an adjustable normal force [6].

FIRST STORY DRIFT - ELCENTRO

1 2 . oo l O . oo

g

o a. o oo :::"|^ffi:u oo oo oo oo oo — oo

w

1S40

OfjWrVMr'aGiMilafV";^^^-"' otftflrnatfor~"cliB>slon""-----"

ytMueeunmumi""--"'-"

::!§!jtgig!^ TIME

[XK]

FIRST STORY DRIFT - MEXICO 6.00 4.00 2.00

— --• —

o.oo -2.00

y-

-4.00 -O.OO

— -••

1985

5 Uncontroltocl.

!

ir

18 20 22 T I M E fi a FIRST STORY DRIFT - HACHINOHE I

OO l O . OO O OO - I O . OO - 2 0 . OO -30 00

•^^•^=4/

' "l

1S68

—1

Sites

«• :: :• ):*•

•'""?

t'*

' e r t l m a t o n o y n g Q p | .y—-—

1

t

i

•

T I M E fa

Figure 3: Structural Response at First Story for Various Ground Motions

6

Acknowledgments

This research was supported by the Technion-Israel Institute of Technology and in part by US National Center for Earthquake Engineering Research grant # MCEER 98-4.1, which in turn is supported by the US National Science Foundation Master Contract BCS-90-25010.

485

References 1. Bracci, J.M., Reinhorn, A.M. and Mander, J.B., (1993), "Seismic Resistance of Reinforced Concrete Frame Structures Designed for Gravity Loads: Part I: Design and Properties of a One-Third Scale Model Structure," Tech. Rep.NCEER-93-0027, National Center of Earthquake Engineering Research, SUNY/Buffalo. 2. Constantinou, M.C. and Symans, M.D., (1992), "Experimental and Analytical Investigation of Seismic Response of Structures with Supplemental Fluid Viscous Dampers", Tech. Rep.NCEER-93-0032, National Center of Earthquake Engineering Research, SUNY/Buffalo. 3. Constantinou, M.C. (1994a), "Principles of Friction, Viscoelastic, Yielding Steel and Fluid Viscous Dampers: Properties and Design," Passive and Active Structural Vibration Control in Engineering (Soong, T.T. and Constantinou, M.C. eds.), Springer-Verlag, Wien, New York, 209-240. 4. Constantinou, M.C. (1994b), "Passive Energy Dissipation Development in U.S.," Passive and Active Structural Vibration Control in Engineering (Soong, T.T. and Constantinou, M.C. eds.), Springer-Verlag, Wien, New York, 255-270. 5. Fierro, E.A. and Perry, C.L. "San Francisco Retrofit Design Using Added Damping and Stiffness (ADAS) Elements", Proc. of Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control, Applied Technology Council, ATC 17-1, 2, 593-604. 6. Gluck, N., Reinhorn, A.M., Gluck, J., And Levy, R. (1996) "Design of Supplemental Dampers for Control of Structures," J. of Struct. Engrg., ASCE, 122 (12), 1394-1399. 7. Hanson, R.D., Aiken, I.D., Nims, D.K., Richter, P.J. and Bachman, R.E., (1993), "State-of-the-Art and State of the Practice in Seismic Energy Dissipation", Proc. of Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control, Applied Technology Council, ATC 17-1, 2, 449-472. 8. Inaudi, J.A., Kelly, J.M. and T.C.W.S., To "Statistical Linearization Method in the Preliminary Design of Structures with Energy Dissipation Devices", Proc. of Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control, Applied Technology Council, ATC 17-1,2, 509-520. 9. Reinhorn, A.M., Soong T.T., Riley, M.A., Lin R.C., Aizawa, S., and Higashino, M., (1993), "Full Scale Implementation of Active Control, Part II: Installation and Performance", J. of Struct. Engrg, ASCE, 119 (6), 1935-1960. 10. Reinhorn, A.M., Li, C. and Constantinou, M.C, (1995), "Experimental and Analytical Investigation of Seismic Response of Structures with Supplemental Damping: Part I Fluid Viscous Damping Devices", Tech. Rep.NCEER-93-0001, National Center of Earthquake Engineering Research, SUNY/Buffalo. 11. Ribakov, Y. and Gluck J., (1999), Optimal Design of ADAS Damped MDOF Structures", Earthquake Spectra, EERI, 15(2), 317-330 12. Soong, T.T., (1990), "Active Structural Control: Theory and Practice", Longman Scientific & Technical.

O N A STABILITY-BASED A P P R O A C H FOR R O B U S T A C T I V E , SEMIACTIVE A N D H Y B R I D S T R U C T U R A L CONTROL J. RODELLAR Department of Applied Mathematics III, School of Civil Engineering, Technical University of Catalunya, Campus Nord, C-2, 08034-Barcelona, Spain E-mail: [email protected] The constructive use of Lyapunov stability offers an approach to control of dynamic systems with uncertainties. This paper gives an outline of the basic background and describes applications to some problems of active control of structures like buildings and cable-stayed bridges.

1

Introduction

Most of the methods available for control of dynamic systems are based on the combination of a mathematical model of the control loop plus a feedback control strategy. One of the relevant issues in this combination is the presence of uncertainties in the model. This is a real important issue to deal with, since control systems are designed to achieve some desired behaviour for the system and the system is usually seen as the model. A broad spectrum of approaches have been proposed in the literature for the control of uncertain systems, which are generically referred to as robust control methods. By nature, civil engineering structures are parameter distributed systems with large dimensions. The process of dynamic modelling is prone to introduce uncertainties in aspects such like: discretization to obtain finite dimensional models, order reduction, selection or identification of parameters (stiffness, damping, etc.), non-linear elements, sensor/actuator dynamics, couplings and interactions, as well as lack of knowledge of the environmental excitations. As the importance of these modelling uncertainties has been more emphasized, active control community has paid attention to robust control methods. One of the directions to robust control is stated in terms of constructive use of Lyapunov stability techniques. 1 The objective is to design a control law (linear, non-linear or combinations) that guarantees a form of stability of the controlled system for any realization of the uncertainties (deterministic) that belongs to a prescribed class. In this paper some basic background on this approach is outlined and applications to some problems of active control of civil engineering structures are briefly described.

487

488

2

Conceptual control objective

Consider a general class of uncertain systems described by the following differential equation: x = F{t,x(t),u(t),S(t,x)),

x(t0)=x0

(1)

n

where t G if? is the time variable, x(t) G R is the state and u(t) G Rm is the control input. All the uncertainty in the system is deterministic and represented by S(t,x). In general, it may represent a number of unknown parameters or disturbance inputs which may be constant or time varying. It may also describe nonlinear elements which are difficult to model accurately. S is unknown and the only information on it is that it belongs to certain set A. Definition: A compact set K C Rn system (1) if and only if:

is a global uniform attractor for the

1. existence and continuation of solutions: for every (io,£o) £ R x Rn, the system (1) has a solution, and every solution can be extended into a solution on [to, oo); 2. uniform boundedness of solutions: for each r > 0 there exists R > 0 such that ||a;(£)|| < R for all t > to on every solution x(-) of (1) with 11aroiI < r\ 3. uniform stability of K: for each e > 0 there exists S > 0 such that d(x(t),IC) < e for all t > t0 on every solution x(-) of (1) with d(x0, K.) < 5; 4. global uniform attractivity of /C: for each r > 0 and fi > 0 there exists T > 0 such that d(x(t),K.) < /J for all t > t0 +T on every solution x(-) of (1) with ||a;o|| < r, where d(x,K.) = min||a; — k\\ defines the Euclidean distance of £ G Rn from K.. The essential control objective is to choose a feedback control law u(t)=q(t,x(t))

(2)

such that the closed loop system x = F(t,x(t),q(t,x(t)),S(t,x)),

x(t0) = x0

(3)

has a global uniform attractor (containing the origin) for any realization of the uncertainty S C A. The design of this class of controllers is made through the constructive use of Lyapunov stability theory. Roughly speaking, the design guidelines go

489

through the definition of a positive Lyapunov candidate function V(t, x) and the construction of an appropriate feedback control ensuring that the time derivative of V for the controlled system is negative outside a compact set K that can be explicitly given. Theoretical background can be found, for instance, in Corless and Leitmann. 1 Reviews with extensive bibliography exist 2 3 where different classes of controllers are described for a variety of realizations of dynamic models of the form (1) and different structural conditions for the uncertainties. 3 3.1

Applications to structural control Active control of base isolated structures

Consider a base isolated building as illustrated in Figure 1, subject to horizontal seismic ground motion. Combinations of passive isolators and active feedback controllers in a hybrid scheme have been proposed with interest in the last years. In an early work by Kelly et al. 4 a hybrid scheme was proposed in which the structural model was formulated in terms of absolute motion (with respect to an inertial frame). The use of absolute coordinates makes the seismic disturbance enter only at the base level through the displacement and the velocity of the ground motion. This makes natural to add an active controller to apply a control force at the base only. Since the active force reacts to the absolute motion, it is conceptually able to supply an additional resistant scheme not attainable by purely passive isolators. The Lyapunov stability approach was used to derive a control law robust against unknown earthquake excitation, assuming knowledge of a bound. 4 Following the above scheme, Rodellar et al. 5 considered the whole system decomposed into two coupled subsystems, namely the structure (E r ) and the base isolation (S c ) described by the model Sr : Sc :

Mqr + Cqr + Kqr = CJqc + KJqc

m0qc + (c0 + JTCJ)qc

+ {k0 +

(4)

JTKJ)qc

-JTCqr - JTKqr - c0d - k0d + fN{qc,qc,d,d) =u (5) where qr £ Rn represents the horizontal inertial displacements of the floors and M, C and K are the mass, damping and stiffness matrices. The base isolation is modelled as a single degree of freedom system with absolute displacement qc £ R and mass, damping and stiffness m 0 , qo and fco. fw represents a non-linear component in the isolator. The term — c^d — k^d is the

490

I

i

nth floor

, jJ

1

—!

|

L 1st floor

I

'/

I

BASE

|

|

FOUNDATION

d(t),

z

•>

d(t)

Figure 1. Base isolated building.

excitation force on the base due to the seismic ground motion with inertial displacement d(t). J € Rn represents the rigid body motion and is a unit vector when the structure is a shear building. The terms associated with J represent the linear coupling between the structure and the base isolation, u is a single active control force applied on the base. A linear controller stabilizing the whole system was designed 5 assuming uncertainties in the coupling terms and in the excitation. Considering additional uncertainties in the mass, damping and stiffness parameters and the presence of the non-linear element f^ in the isolator, non-linear adaptive strategies were developed and numerically tested, 6 showing good performance to reduce the absolute base motion and the inter-story drifts. In a similar vein, sliding mode controllers, which are very close to the controllers derived via the Lyapunov stability approach, have been derived for active control of base isolated structures with satisfactory performance. 7 8 3.2

Active control of cable-stayed bridges

Cable stayed bridges are very prone to vibrations induced by external loads due to earthquakes, wind and traffic. The introduction of control forces via the active modification of the tensions at selected tendons has been proposed as a mean of reducing such vibrations. A recent work 9 has studied the use of a finite element model combined with optimal control techniques. The use of Lyapunov stability techniques for active control of cable stayed bridges has been proposed by Magana et al.10 n and first analyzed for simple lumped mass

491

and finite element models in a decentralized control setting. As an illustration, consider the bridge model of Figure 2, which essentially is composed by a deck segment with two end supports and 12 stay cables.

Figure 2. Cable stayed bridge.

The bridge is excited by the vertical component of a seismic ground acceleration which travels from left to right. A finite element model is built to represent the dynamics of the bridge. 18 equal length, two-node, two degree of freedom (vertical and angular displacements) per node are used for the bridge deck. The vertical displacements of the towers are neglected. The control strategy adopted here uses a subset of the stay cables as active tendons to supply control forces. In this study only vertical deflection dof's are considered. The objective is to design a decentralized scheme in which each individual active tendon is driven by a controller that uses local vertical displacement and velocity feedback only. Thus the overall model is decomposed into a set of interconnected subsystems. The one corresponding to dof i and attached cable cn is described by 38

muTi{t) + kuri{t) + ^2 kiiri{t)

= &*a(*) + fdi(t)

- an(t)un(t)

(6)

3= 1

with fdi(t) = AnEn[sin6n(t)

- sin0 p n ],

an(t) =

A E

sin9n(t)

where n(t) is the vertical displacement at time t, ma and ku are elements of the mass and stiffness matrices, 6j accounts for the influence of the seismic vertical acceleration a; An and En are the cross-sectional area and the Young modulus of the cable, respectively, 6n is the time varying angle between the cable and the local horizontal and 6pn is the same angle at prestressed cable

492

condition; l0n is the unstressed length of cable c„ and un is the cable elongation produced by the nth actuator as control signal. In this work the local control law is chosen with the form un(t) = gnfi(t) + vn(t)

(7)

where gn is a linear velocity feedback gain (chosen to introduce a prescribed damping) and vn is a non-linear additional control signal. The design of vn is accomplished by using Lyapunov stability approach for control of uncertain systems. Consider the subsystem (6), neglecting the coupling terms, but with the presence of a(t) and fdi(t) as unknown disturbances with known bound Si such that \bi
for \ia(t)\ > en otherwise

(8)

ensures the existence of a neighborhood of the origin for the decoupled subsystem which is a global uniform attractor. Here Hi(t) = —a„imin[Pni2ri(^) + Pn22"ri(t)]6i, where pn\2 and p„22 are components of the 2 x 2 real, symmetric and positive definitive matrix Pn solution of the Lyapunov equation F^Pn + PnFi = —Qn for a given symmetric and positive definite matrix Qn, with Fi being the subsystem state matrix including the linear velocity feedback control:

n=( L \

Jn..

* a

n,min9n

en is a positive parameter judiciously chosen. More details on the formulation can be found elsewhere.11 Numerical results are available showing the efficiency of this control strategy. 12 Figure 3 illustrates these results for the midspan bridge, where uncontrolled vertical displacement is compared with the one with active control for both the case when only linear velocity feedback control is used and when also the non-linear control (8) is in operation. 3.3

Semiactive control

Something between passive and active control, semiactive control has been proposed as an appealing alternative. In a semiactive control system, on-line adjustment of the damping and/or stiffness of adaptable devices are done according to feedback signals and control commands. In general, a semiactive controller can act in a desirable fashion in both a passive and a feedback control mode, with its performance generally enhanced in this mode. Early use

493

I

1

Figure 3. Midspan vertical displacement. ear/nonlinear control (solid line).

No control (•••); linear control (—•—); lin-

of Lyapunov stability techniques for semiactive control is reported by Leitmann and Reithmeier. 13 Recently,14 this approach has been used to develop a semiactive control strategy to reduce the absolute motion and the inter-story drift motion of a building structure with base isolation by adjusting only the damping and stiffness of the base and the first floor. We may recall Figure 1 for an illustration. Consider the same system decomposition as in (4,5), but now, instead of having an external active control force u, we consider that stiffness and damping parameters of the base and the first floor can be adjusted by control signals within intervals h(t) G [K,k+],

Ci(t)

e [c-,cf],

i = 0,1.

By using Lyapunov stability arguments, assuming bounded uncertainty in the seismic excitation, a simple bang/bang law is obtained to adjust these parameters such that the whole structure/base system has a global uniform attractor ball. 14 Figure 4 illustrates the efficiency of this semiactive control law to reduce the absolute base motion as compared with the case with pure base isolation. Inter-story drifts are also significantly reduced. 14 Acknowledgments The support of the CICYT (national Spanish research agency) under Project TAP99-1079 is appreciated.

494 pure Dasfl Isolation

semiactlve control

Figure 4. Absolute base displacement.

References 1. M. Corless and G. Leitmann, IEEE Trans. Automat. Control, AC-26, 1139 (1981). 2. G. Leitmann, ASME J. Dyn. Sys., Measur. Control, 115, 373 (1993). 3. M. Corless, ASME J. Dyn. Sys., Measur. Control, 115, 362 (1993). 4. J.M. Kelly, G. Leitmann and A.G. Soldatos, J. Opt. Theory Appl., 53, 159 (1987). 5. J. Rodellar, G. Leitmann and E.P. Ryan, Int. J. Control, 58, 445 (1993). 6. A.H. Barbat, J. Rodellar, E.R Ryan and N. Molinares, ASCE J. Engr. Mech., 121, 676 (1995). 7. N. Luo, J. Rodellar and M. de la Sen, Earthquake Engr. and Structural Dynamics, 27, 301 (1998). 8. N. Luo, J. Rodellar, M. de la Sen and J. Vehi, J. Franklin Inst., to appear (2000). 9. A.G. Schemmann and H A . Smith, Earthquake Engr. and Structural Dynamics, 27, 81 (1998). 10. M.E. Magana, P. Volz and T. Miller, ASME J. Vibrations and Acoustics, 119, 523 (1997). 11. M.E. Magana and J. Rodellar, J. Structural Control, 5, 45 (1998). 12. C. Monroy, J. Rodellar and M.E. Magana, Proc. 2nd European Conference on Structural Control, Paris (2000). 13. G. Leitmann and E. Reithmeier, Dynamics and Control, 3, 7 (1993). 14. N. Luo, J. Rodellar and J. Vehi, Proc. 2nd European Conference on Structural Control, Paris (2000).

CIVIL STRUCTURES IN THE NEW MILLENNIUM MIXING ART, NATURE, AND SYSTEM SCIENCE

ROBERT E SKELTON UCSD bobskelton @ ucsd. edu My training in control came from an electrical engineering perspective, but to solve structural control problems in industry, modeling issues demanded most of my time. This prompted a degree in structural dynamics. This combination of the two disciplines flavors the point of view on everything I have to say here. What I learned about the intersection of the dynamics and control disciplines was more important than anything I learned about either discipline. While, in isolation, each discipline is relatively mature, their intersection is still in its infancy. I believe that the future of control lies at the intersection of disciplines, hence, this paper is about those intersections.

1

Introduction

The structural control community has an extraordinary opportunity and responsibility to contribute toward the merging of the disciplines structure design and control design. I begin this paper with this charge to caution against an overeagerness of civil engineers to simply add control to an existing structure design. While indeed there are useful applications of such thinking in retro-fitting, this is not our grand challenge. This paper points out the lack of a system design procedure as the greatest deficiency of current systems and control science. If developed, such a system design procedure would allow more efficient use of materials, more costeffective design, and survivability of larger earthquakes and wind disturbances. It might be said that physics paved the way for technology in the first half of the 20th century, and engineering paved the way in the second half. As we ask "What will drive and enable new civil engineering technology as we round the corner of the new millennium?", we must begin with the fact that Engineering has produced sophisticated component technologies without instructions how to put them together. We have multidisciplinary problems searching for an interdisciplinary theory. So, I believe that methodologies for analyzing and synthesizing interdisciplinary systems will be the enabler of technology in the next few decades. I believe that the next grand challenge is to give the soul of control a body, to enlarge the tools of control theory to embrace the much more general problem of system design. By system design we refer to the task of determining the design requirements of the multiple components that make up the system, given only the requirements of the overall system. Traditional control theory assumes that all other components (except the control component) have already been designed.

495

496

One may ask whether the integration of two disciplines should start at die state of the art of either discipline. In structural control problems of the future, should control begin after the structure is designed? Of course this is the tradition, but this isolation of the disciplines is not the way to obtain the best system performance. Hence, the future in structural control will depend upon our ability to integrate the issues of structure and control design at fundamental levels. This is the nature of the task of we call design. Design remains a dirty word at the university. It is not viewed as a scholarly activity, because a scientific method to do it is lacking. Herein, I dare to use the dirty word design; Design of Systems, Design of System Models, and Design of Structures, pausing along the way for some inspiration from art and nature. How can one identify the performance-limiting technology in a design? In a modern design problem we wish to guess the performance- limiting technology in a system, see Fig 1. Perhaps we could get better performance by improving the manufacturing precision of selected components. If so, which components? Maybe we need a better model of the system components. If so, which components?

Pin theToil on the Performcnce- Limiting T echnology in e saf| Structure! Control:

Figure 1

Or, maybe we're limited by computational precision, or, maybe by the algorithm selected for signal processing or control. Or, maybe we need better sensors, or a different distribution of the sensor or actuator locations. Or, maybe, more money in the component technologies would be wasted because we are already at the limits of

497 physics. Oddly enough, a systems theory is not available that even allows one to answer these simply questions. We just don't know where to spend our money to get the most cost-effective system design. Neither can we look to the universities to provide immediate answers to these questions. Universities teach component technology. They draw narrow boundaries around subjects for tractability, leading to uncoordinated decisions about system design. For example, Control is a component technology, which assumes all other components are already specified. We might typically say, " if these are the components you want to manufacture, this is how to manufacture it". We typically say, "if this is the component you want to model, this is how you model it". We typically say, "if you have already decided how you want to distribute sensors and information, and if all other components are already designed, this is how to control it". We haven't learned how to take Michael Faraday's advice: "begin with the whole, then construct the parts". Given all the parts, we know how to use existing theory to predict the response, but we don't know how to invert that process: " Given the system response requirements, how do we determine the design requirements of each component"? Indeed, this is our definition of design: determining component requirements from system requirements. Synergism is a popular concept, but when is the whole less than the sum of the parts? In system design, the answer is usually. In the absence of a necessity theory, we over design the components, dealing with what is sufficient, rather than what is necessary. However, contrary to popular opinion, the best system is not constructed from the best parts. We can waste money on components that are not necessary, or by making a component too precise. There is often more to be gained by unifying two disciplines than by improving the technology of either discipline. Unfortunately, funding agencies seek the best component technology, leaving very little national efforts focused on system design. Yet, the best system performance (defined to include cost) cannot be achieved simply by inserting the best component technologies. Some examples make the point in the next section.

498

Figure 2; Finite Precision Computing

2

Integrating Signal Processing and Control Design:

Suppose, in the computational component of the system, depicted in Fig 2 as the "ODE solver", we want to build a simulation or a controller in a digital computer with fixed point arithmetic, with beta bits in thefractionalpart of the wordlength, and with a uniformly distributed white noise model for roundoff. The error in computing the state is e. Tfixesthe coordinates we choose for the calculations. G is the transfer function from input to output, and of course, it is independent of the realization. However, the effect of roundoff error, e, is realization dependent. Thus, here is a class of problems that cannot be studied with input/output methods. There is no clue from the component technology, physics, how to choose the basis functions for modeling so that computational errors are small. It is clearly a waste of resources to model the physics more precisely than the computational error. Hence, an important question for all modeling problems designed for computer computations is "just how large can the roundoff error be, anyway? Can't we just solve the problem with double precision, if necessary?" It has been shown by Liu and Skelton that the variance of the roundoff error is unbounded over T, regardless of the wordlength. That is, one can compute in an arbitrarily bad set of coordinates. Hence, one can spend a lot of money getting good component models that are worthless is a system of interconnected components. This example shows that how one models one component of the system can affect the error dynamics of another component. This illustrates the general principle that the Design and Modeling of components should not be independent decisions.

499

Mullis and Roberts, Williamson, and others have shown the optimal realization for digital computation, to minimize the roundoff, subject to a scaling constraint, as shown in Fig 3. From a component technology viewpoint, one can model the system first, and then compute the optimal realization, T. However, since T depends on the choice of the model, and the model may contain free parameters, such as a controller to be designed, the systems approach would be to jointly choose the model and the realization. Following this procedure one can design LQG controllers that are optimal for the specificfinite-precisioncomputing environment, as shown in Williamson 87, Liu, Grigoriadis,SMton 88. There is no separation principle in this case, but two Riccati equations appear with a coupling term that disappears as the.number of bits in the wordlength go to infinity. This theory yields controllers that are tailored to fee computational environment, and the classical seperation principle results as a special case when the computation is with infinite precision. This result has been applied in a redesign of the controller for the Hubble Space Telescope [Grigoriadis and Skelton].

No Que cfoout Basis! From Physio

}

(Mullis/Roberts 76) (Williamson 86) Oiu/GrigaicdSiSkeltcn 88) (Gevers 92, Bamfeh 94)

* Component technology: Design (AjpQ, thanT •System tCKtinology: Design (MAT)Jointly Control: CtauptatfARE(£T FignreS: Unified Signal

RrocessingCoiilrci

The original HST controller was designed assuming infinite precision computing. A redesign, using the above procedure, is accomplished in the references of Fig 4, using the fact that the a/d and d/a converters are 16 bits and the control computer is 24 bits. The simulation result yields 2 orders of magnitude improvement in pointing efficiency (ratio of pointing variance to control variance). This is a no cost solution, in the sense that the control complexity is not increased. Telemetry can send up new

BOO

coefficients within the existing algorithm. Furthermore, using the new control design technology can give the same performance with 4 bits as the existing controller can achieve with 24 bits. This is perhaps not a significant contribution to either Signal Processing or Control disciplines, but the extraordinary improvement is due to Integration of the disciplines.

tobl#$|X)CQ.X4tascope

Figure 4

3

Integrating Plant and Control Design:

Such efficiencies are to be found by unifying other disciplines. Consider integrating plant and controller design. We have suggestions already of two extreme positions, designing control after plant design, and the HST project suggestion of designing the control before plant design. What about designing the control during plant design? Suppose the free parameters in the plant appear affinely in the plant matrices, with some practical bounds on the parameters. Consider the following algorithm, summarized in Fig 5. First, fix the plant parameter and minimize the control energy subject to a performance constraint. This is a convex problem, but perhaps we will not like this controller. It may be beating up on the structure and using too much control energy, but the performance is guaranteed.

501

min E uTu T

update

Y Exx =X Ntain E uTu Y

E yyT
Convex, given X

Picnf p, Control K

Pi - Pi - Pi

Guarantee PsrformaiiccY

Compute E xxT = X where CXCT
Convex, given Y

"~5£ > / - - ^

x = A(p)x + B
( A B ) S M + I R M .

'

'

FigureS; Optimal Mix of Plant/Control Design [Grigoriadis, Zhu, Skelton, 1992] Next, reduce the control energy further my enlarging the domain over which the optimization takes place, over both the plant and control parameters. Normally this is a nonconvex problem, but we add just the right constraint to make the problem convex. We match the state covariance from the previous step. Matching covariance X also guarantees the performance bound accomplished in the previous step. Thus, the dual role of this constraint is to make this problem convex and to preserve the performance guarantees of the previous step. With a new plant parameter repeat the first step. This algorithm monotonically reduces the control required to guarantee a specific output covariance bound. Notice that if not much performance is requested (if Y is large), then the algorithm reduces the control energy to zero, because performance is achievable with plant parameters alone. This method is therefore useful for plant design, having nothing to do with control. An Example from civil engineering follows in Fig 6. Let's ask what is the optimal distribution of mass, damping, stiffness, and control energy in a 5 story structure? Oversimplified for clarity, the motion is in the plane. For any L2 earthquake bounded by a given number we wish to keep the stress at critical points in the building below a specified bound. For large performance bounds, the active control is zero, and the optimal distribution of mass and damping and stiffness is shown in the Fig 6 (where the width of the bar chart at the 3rd floor

502

indicates the amount of mass at the 3 rd floor). Control Theory has been used to design the structure without the need for control. Demanding better performance leads to the indicated distribution of mass and stiffness and damping and control energy. Since disturbances were introduced only at the base, it is clear that the stiffness at the base is reduced, putting the building on virtual roller skates. (Of course, if we introduce more realistic disturbances such as wind at the top of the building, the stiffness at the base would not go to zero). Note that the most control energy is applied were the mass is smallest.

0:ii!,ri>i,C}

Stiffness

5 storii

I

f:.. j Stiffness

!

ikes* iwass-j \

H

Damping

r

•-& -tftore '• ! Performance

' I

Control

I""

"" !

j|

L2< 1 earthquake

More Actuators j

il _J

Figure 6: Optimal Mass/Damprng/Sttfrness/CoBtrol [Lu, Skelton, Computer Aided Civil Infrastructure Engr, vol 13, 1998]

In over a dozen practical examples, a fairly general trend emerges. Adding actuators reduces the mass of the structure, as shown in the next Fig 7. One might use a lot of structure and few actuators, or less structure and more actuators, or little or no structure, leaving control to do it all. What is the optimal mix of the disciplines, structure and control? The trends are shown in the Fig 7. Using more actuators reduces mass, up to a point. Using more actuators also reduces the total energy required to control to a given precision, up to a point. This is a win-win situation, since both control energy and mass reduce-up to a point. After this point, then adding actuators requires more control energy to achieve the same performance. Hence, there is an optimal number of actuators, but little help from theory is available to find this number. My favorite method for selecting actuators follows in the next section.

503

less structure, moreactudors

1 _—• • * '

_

O p t i m d Number Actuators

; "

•

•Less energy, more robust j »More complex controller 'Avoidinginteger progrcm.

less structure, moreactuctors

Figure 7: Optimal Mix of Physics/Information, Structures/Control

4

The Economic Design Problem

Assume that the variance of a noise is proportional to the variance of the signal to which it is added, as in Fig 8. This is realistic in practice, since a milliwatt amplifier has less noise than a megawatt amplifier. Let's call Sigma Inverse G the Signalto-Noise-Ratio (SNR). Now assume that the price of a component is proportional to its precision, as measured by its SNR. The system design objective is to minimize the sum of the component costs, subject to a performance constraint. This is not a convex problem, but a convergent algorithm is available. Suppose the algorithm converges to the result that sensor 1 requires much more precision than sensor 2. We now know where to spend money, making sensor 1 reliable, because performance is critical to this sensor. Sensor 2 might be taken off the shelf, or even deleted. Once a component is thrown away, the design cycle must be repeated. This is an example of a system design problem, where the system level performance is specified first, then the component precisions are determined. The importance of the economic design problem is the ability to determine how to distribute precision among components throughout the sysytem.

5G4 W = er Z

w noise

Finite Signal~f©-No!$e ratio EWjWk=WSjk

If

(T

>>

,

a

z

EzzT = Z

, then delef© sensor 2, or QfMhe-tholf

Figure 8: Tie Economic Design Problem [Lu, Skelton, Int. J. Contrail, 1999, vol 72, no 9,799-814]

5

The Critical Challenge: System Modeling

The point of this section is that good component models do not imply good models for system design purposes. Indeed, the critical challenge in finding a system design methodology is to find a system modeling methodology. Component models are usually considered good if the output error is zero, but for any model, M in Fig 9, there is always some input to excite unmodeled dynamics, making the open-loop error, e, large. It is therefore clear that modeling decisions for a component ought to be influenced by inputs from neighboring components that dynamically interact with this component. For example, the basis functions chosen to model the displacement in a structure ought to be influenced by the inputs. Even though there exist natural basis functions from physics to match stated boundary conditions to make e small, these are not the most appropriate basis functions for other inputs, such as control. Recall also from Mullis & Roberts that the optimal basis for a physical component depends on the disturbances in the computational component.

'505

Flipuret; CcMEtpcmcaitMaic&ig [Hu/Skelton, Computers and Structures, 1985]

6

No Good Modeling Theory

Let's discuss 3 models of a plant, in Fig 10. P is the exact model from physics, a damped 2nd order system. M and N are erroneous models. In fact, both models have unbounded errors relative to the exact model, P.

Figure 1©: Is System Modeling Just Physics, Physics? Or can Mother Nature be fooled?

506

M is an undamped 2nd order system and N is a first order system. Now suppose the models are to be used for control design to minimize some specific objective function, shown in the Fig 10. For this particular objective function, all 3 models, P,M,N, yield the same controller. Note that these models are arbitrarily far apart, by open loop criteria, but entirely equivalent by a closed loop criteria. Hence, the same controller can be optimal for many different models of the plant besides the exact model from physics. In fact, there might exist a better model for System Design than the Actual model from physics. The first order model would be simpler and yet yields the same controller. This point needs emphasis. Not only is the exact model inferior, assuming that it could be available, but searching for the exact model is more costly. Hence, modeling for system design is not just physics, physics, physics of the components, to make the open loop error smaller. Yet bounding this open loop error is the focus of robust control. These examples show that bounding the open loop error is neither necessary nor sufficient for a good control design. The conclusion is that "An Ounce of Model Improvement is worth a Ton of Robust Control". System Modeling is a discipline. It seems to require more than just Component Technology, and more than what each discipline (including controls) already knows.

Minimize

J (j£fiy* + uTkRuk)

Subject to xk+1 = Axk+Buk

,

yk=Cxk

Theorem Optimal Controller Requires Only CA'B . i = 0,1.2 A' - I l Only E rrors in CA B Affect Control Performance •Any QMC from data yields the optimal control *Nhy compute Markov Parameters, Use Data Directly

Figure 11: Control Models : How Much Info is Really Necessary? [Shi, Skelton, DATA-BASED CONTROL, '94], [Furuta, '93], [Dceda, '99]

How much information about the plant do we really need to compute the optimal control? If we use the separation principle in the finite time LQG problem in Fig 11, we need the entire state space model. Yet, in this problem only the first N Markov

507

parameters are needed to compute the exact optimal control. Modeling from first principles, physics, focuses on modeling A and B and C, over-parametrizing the model by a large margin. In a 1000th order system, there are more than a million parameters in A, B, C. It is only a special combination of these parameters that is important to controlled performance. The use of a separation principle seems to utilize much more information about a model than is really necessary. Note that any model obtained from data that matches the first N Markov parameters will produce the exact optimal control for the finite horizon optimal control problem, regardless what other properties the model possesses.

Does there exist any linear model to ¥• -'• he inputMrtput data? t Actud y Plant IFF R~MHT>® _Junear = Model % EykH$k > Hi - Eyk+imk R=

MCQ

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Jul. Q

Many MocWs E quivalent to th© One F rom P hys Ics Figure 12: Data Equivalent Models [Skelton, Zhu, Qmarkov COVER, 1991]

There are several identification methods which can preserve the first N Markov parameters. Since Markov parameters can be obtained from data, one can eliminate the step that computes the markov parameters and compute the optimal control directly from data. See [Furuta, Ikeda, Favoreel]. To illustrate how many models might be equivalent to a given set of data, Suppose we compute the first q auto-correlations and the first q cross-correlations, from the real data, (which of course evolves from a nonlinear system) and ask "does there exist any linear model that can match these 2q pieces of data exactly"? The answer is none if the matrix R-HH in Fig 12 has a negative eigenvalue, and an infinite number otherwise. (Note that only one of these models is the exact model

508

derived from physics). There is a Q Markov COVER algorithm (matches the first Q covariance parameters and the first Q Markov parameters) to generate all models that can match this data. Note from the previous "data-based" control theorem, that any of these infinite number of models (Q Markov COVERS) will yield the exact optimal control for an LQG problem with horizon equal to Q. These examples have shown that good component models do not imply good system models. The controller and the model are compatible, or not, as a pair, and neither the controller nor the model have any significance in isolation of each other. All the investment we've made into modeling the minutia of component technologies may have little value in the discipline of System modeling. Whether you are given a controller and are designing a model, or given a model designing a controller, it's an iterative process. Obviously control design should occur during, and not after modeling. We should abandon the classical approach of designing and modeling the plant before control design. But this is not going to happen until more systems design theories are in place. The primary conclusion thus far is that we don't know how to design systems because we don't know how to model the interacting components that make up the system.

7

A New Paradigm for Structural Control

The second part of the paper focuses on the integration of just two disciplines, structures and control. But first, some inspiration. In 1992 I visited the KrollerMuller Museum in Holland, where I saw a piece of art by Kenneth Snelson that changed the way I think about my job, see Fig 13. For 30 years, I had been trying to integrate structures and control design by bending and torturing classical continua with control forces to make them do something they didn't naturally want to do. Here in the museum was a pretensioned structure with global bending, but no individual member bends. I could see the equilibrium could be easily rearranged to take on any preassigned shape, and that the shape could be held constant while changing stiffness. Yet, in his writings, Kenneth Snelson felt the structure had no practical value. I was so impressed by his art that I set out to prove the artist wrong, that his artform indeed preceded a valuable function. Buckminister Fuller coined the word tensegrity to classify this structure with discontinuous compressive members, and a continuous set of members in tension.

509

instead of •Forcing Continue •Adding Acfuctort to adParadgpfss: I # a n s , P l o l « t Stutfs

UseTenscgrityllll •No Joints •NoLoadRwerscIs •No Friction •No Member Bending € as y to Changs E qMlMxIum Figure 13: Inspiration From Art

Some Lessons From Nature It has been known since the middle of the twentieth century that the theory of continua can't explain the strength of materials. We must pay attention to the microstracture of materials. The integration the structures and control discipline should begin by looking for a new paradigm, looking for ways to integrate the choices of material architecture and control architecture. We look now to Natural systems to find suggestions. The continuum model of a cell as a liquid-filled membrane cannot describe the mechanical properties of cells. The cytoskeleton of a cell contains lots of mechanical structure, shown in Fig 14. The Harvard.Biologist Don Ingber claims that the mechanical properties of cells is consistent with the mechanical architecture found in Kenneth Snelson* s tensegrity structure. Hence, in a strange twist of fate, a biologist and an artist both declare tensegrity as the architecture of life.

510

Figure 14

Another lesson of strength from geometry comes from carbon nanotubes, a single molecule 1.4 nanometers in diameter and arbitrarily long, pictured in Fig 15. Carbon fibers are ropes of nanotubes in bundles 10-20 nanometers thick . A Fullerene is a closed convex cage molecule containing only hexagonal faces along the walls and pentagonal faces on the tube ends. We can explain different nanotube properties in the following way. Imagine a 1 atom thick sheet of grapherie, where the local topology is composed of hexagons formed by the atomic structure. Now close the sides about a vertical line to form a tube. This gives the structure at the top of Fig 16. Now, close the sheet about a different axis across the sheet to get yet another tube (second from top in Fig 16) with completely different electrical and mechanical properties. The conclusion is that the rales of closure relative to the local topology dictate both the electrical and mechanical properties of the final structure. We will try to mink this concept for man-made structures.

511

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Figure 15

Another lessonfrom-naturecomes from nature's strongest natural fiber, the spider fiber. The amino acids emitted by the spider take on twoforms,one is a hard, rigid form (beta-pleated sheets) that can take compressive loads. [Jelinski, Turmonia]These compressive units are not connected. The other amino acid forms are soft stands that take up the strain. Fuller's definition of tensegrity-required discontinuous compressive members,and continuous tensile members. By that definition, the spiderfiberis a tensegrity structure.

512

Figure 16: Buckyballs and Fullerenes

We observe that the common property among Fullerenes, spider fibers, cell cytoskeletons, and Snelson's artform is: strength from a tensegrity material topology. Now we use these observations to introduce new man-made materials. What follows is an attempt to mimic at the large scale what nature is doing at the nanoscale. 8

Tensegrity Definitions

We say N points in a 3D space form a tensegrity geometry if the points are stabilizable by axially-loaded connections. Tensile members are required to stabilize such a system. To show that any 4 points in a plane form a tensegrity geometry, consider Fig 17. Three tension and three compressive members will stabilize the first configuration. The 4 points of the second configuration can be stabilized by 2 compressive and 4 tension members, but the same 4 points can also be connected in an unstable way, as the last arrangement shows. Tension in either of the two strings would collapse this structure about a diagonal axis. Class 2 and Class 1 in Fig 17 denote continuous and discontinuous arrangement of compressive members.

513

A Tensegrity Geometry is a set of points that can be stabilized in space using only axially-loaded elements Class 1: Discontinuous Compressive Members Class 2: Continuous Compressive Members

Tensegrity System C3T3, Class 2

Tensegrity System

3D: No Tensegrity

C2T4, Class 1

Figure 17: Tensegrity Systems

The set of points in the Fig 18, together with closure rules to from a tube, form a tensegrity geometry. Given that compressive members cannot stabilize in 3D (less than three allowed at each point), there exist tensions to stabilize this configuration with axially-loaded connections. See Fig 19 for a solution. There is a closure rule (as in Fullerenes) so that after closure this topology is stabilized by some choice of tensions. The black lines are tendons and the blue lines are compressive members, and they are not in the same plane. The goal of this research is to develop theory and software that assigns both the local topology and the closure rules so that after closure the structure has a specified shape and a specified set of mechanical, or electrical, or thermal properties. In the symmetric example shown here, there are only 3 parameters that characterize the entire structure. One of these parameters is constrained by the stable equilibrium requirement, so there are only 2 free parameters. The significance of this simple parametrization cannot be overstated. In classical plates and shells the number of parameters required to characterize the structure is very large. For the symmetric case shown in Fig 19, the equilibrium can be analyzed in Fig 20 by summing all the forces to 0, where t is the vector of tensions in all tendons throughout the structure. The matrix F in the Fig 20 contains only geometric parameters, while the tendons can only support positive tension. There exists a tension vector t that will stabilize this geometry only if the geometrical parameters are constrained so that F has a right nullspace. Then one parameter can be solved in terms of the other 2. In the space of these 3 parameters,

514

this constraint yields a hyperplane on which all solutions must lie. This hyperplane contains all tensegrity geometries associated with this symmetric topology.

Figure 19: A Tensegrity System

A more specific example appears in Fig 21, where the three geometric parameters that characterize the structure are two angles to fix the attitude of one bar and h represents the overlap of one stage of three bars with another stage of three bars. In this symmetric structure all bars are fixed in terms of these three numbers. These three numbers are not arbitrary, but must give the matrix F a nullspace.

515

( h , a ,8 )

F (h,a r IF F

,S)t

= Stable equilibrium

= 0,

• t> 0

I =o

2 tan 6

}

T ens egrity Geometry (Skelton. Helton. Adhlkorl. 1998). (Sultan£ kelton. 1998)

cos

(- ifr+

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•Pugh. 1976 •Pelligrino. Calladine. 1986 •Motro, 1986 •Furuya 1992 •Coughlin, Stamenovic, 1997

3 L * sin

* ,J

* kelton, 1993 - 1999 •S Ultan. S kelton 1996,1997. 1998. 1999 •Oppenheim, 1998 •Williamson, S kelton. 1999 •Helton, Skelton 1999

Figure 20: Tensegrity Geometry

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Figure 21: Shell Class Tensegrity Structures

516

This yields the two-dimensional surface in the three dimensional space of the geometric parameters. To control the shape of the tensegrity structure we must move from one point on the "tensegrity surface" in Fig 21 to another. Moving along the tensegrity surface, the shape of the structure can be changed. Along a path on this surface, should the control power suddenly be turned off at some time, then the structure will maintain its current shape, since it is already at an equilibrium. The advantage of tensegrity applications to shape control is that shape can be changed without significantly modifying stiffness of the structure, and without applying significant control power. Traditionally, when one separates structure and control design, one builds a continuum structure (beam, plate, shell, etc.) and then adds control actuators to bend and stretch and push the structure out of its equilibrium. This requires work, and leads to high power controllers. In the tensegrity paradigm the structure and the control are cooperating to modify the equilibrium, so that very little control power is needed to accomplish the shape change. One can move from one tensegrity geometry to another without changing the potential energy, and one can turn off the tendon controls anywhere along the way and the structure will hold that shape in a stable equilibrium. Control energy is not required to hold the new shape.

•Design Control After Structure •TwistthejJ«fcTureagdnst it's equilibrium. This requires work (7 deg limit, 20 deg desired)

•New Paradigm: Unify or mar©fundamental level •Change shape by changing the equilibrium Figure 22: Controlling (Torturing) Structures

517

In DARPA's Smart wing program, an F16 wing is twisted with a torque tube, controlled by nichol-titanium (see Fig 22). This requires work, to twist against the equilibrium, and power limitations restrict deflections to 7 degrees. 20 degrees is desired. A host of practical applications would be enabled if one could change the equilibrium so that energy is not required to hold the new position. The Tensegrity Paradigm has this capability. 9

Mass Efficiency of Tensegrity Structures

Suppose that strength and stiffness to mass ratio is important. Designing for a given compressive load, we replace each bar in a tensegrity by yet another tensegrity structure, without decreasing its compressive strength.

m, = bm 0 b

_fl-£ 0 (tan 2 c?)

<j = Tensile

yj

strength

mR = (2 cos

1

2

3

4

5

6

Figure 23: Minimal Mass Tensegrity Structures

One can repeat this self-similar process i times, and write a formula for the mass, as in Fig 23. The mass of the bars decrease toward zero as the number of self-similar operations go to infinity [skelton helton]. The mass of the tendons increase with the iterations, so the minimal mass occurs after a relatively small number of iterations, 6, for this specific example (length to diameter ratio of original bar =25), yielding a mass 30% of the original bar mass, while preserving the strength. To a first order approximation, the compressive stiffness of the structure is the tensile stiffness of the shortest string, which can be easily controlled.

518

• All Members Axially Loaded

,

.,

- Global bending without member bending

• All Members Um-Directionally Loaded (Pretension) - No reversal of load direction (no friction, hysteresis)

• Structural Efficiency

'";

°

- Strength to mass very high - Inspired by Art and Biological forms

• Easy to Integrate Structure/Control - More accurate models (hence more precise control) - A structural member also serves as sensor, actuator - Actuator/Sensor architecture easily optimized

r,

- Change shape with little work (one equilibrium to another) Figure 24: Advantages of The Tensegrity Paradigm

Fig 24 shows some advantages of the new paradigm for structural control: No torques are applied to any members. Without bending, the members can be more accurately modeled, and hence more accurately controlled. Pretension is chosen so that loads in members never reverse their direction, avoiding friction, hysteresis and a host of nonlinearities that plague control problems. Large changes in shape are possible, including deployable structures. Integrating control and structure design is easy , since each member can serve multiple functions. A given member can simultaneously serve several functions. It can be a load-carrying member of the structure, and a sensor, and an actuator.Our lab is testing the fundamental concepts. Both tendon and strut controlled structures are being tested. With the tendoncontrolled structure, actuators do not have to be placed on the structure itself, but on the base, as in Fig25. Many biological systems employ this feature, such as the human arm, which uses tendon control with many actuators at the base of the arm, and in the shoulder. The potential applications of controlled tensegrity structures include deployable space structures, as shown in the deployable heat shield in Fig 26, under development for NASA/AMES.

519

Figure 25: Two-Stage Tensegrity: Tendon- Control

10 Conclusions Universities and funding agencies should give the soul of control a body, by enlarging the concepts of control theory and the concepts of structure design, to embrace the must more noble task of system design. The fundamental challenge is to create theories of system modeling. It will necessarily be an iterative process. System design theory will never fully replace the systems engineer, who must tune to get a final design of all components. However, the value of such a theory is to reduce the number of iterations required to achieve a final design, and to enable products to achieve performance or efficiencies or lower' costs that were not possible to achieve using the traditional isolated component technology approaches. Naturally, communication problems will haunt us during the transition to a system way of putting disciplines together. Part of the problem is the lack of language to describe the system concepts. The word system has been used to means too many things to be a sufficient descriptor of the methodology that is to follow. To those that say "We already have a procedure for systems engineering and design. We've been doing it for years", the data from the examples in this paper will suggest what is missing. Existing design codes deal with what is sufficient, rather than what is necessary. They are locked into the classical thinking of component technology, where the structure is designed first and the control is added later. These codes never consider the question whether dramatic improvements in performance are

520

possible by combining the structure and control resources as a joint pool of resources to be used to solve a jointly optimized problem.

Figure 26: Deployable Tensegrity Heat Shield

As the engineering community searches for the knowledge to put systems together, we offer here more imagination than science; a new paradigm for the unification of structure and control design. As a start, the tensegrity paradigm will require a unified approach to the design of material architecture, information architecture, and feedback control design. The tensegrity paradigm allows one to control shape and stiffness of a structure with very little control effort. Much more research is required to know the full capabilities of this paradigm, but the stiffness to mass efficiency is higher than any material found by this investigator. The structural control community has an extraordinary opportunity and responsibility to contribute toward the merging of the disciplines structure design and control design. Civil engineers should be cautioned against an over-eagerness to view their responsibility as simply adding control technology to an existing structure design. While indeed there are useful applications of such thinking in retro-fitting, this is not our grand challenge. A combination, (at fundamental levels), of civil engineering and control science is the challenge. The contribution of a system design procedure would allow more efficient use of materials, more costeffective design, and survivability of larger earthquakes and wind disturbances.

PARAMETRIC AND NONPARAMETRIC ADAPTIVE IDENTIFICATION OF NONLINEAR STRUCTURAL SYSTEMS

ANDREW W. SMYTH Columbia University, Department of Civil Engineering & Engineering Mechanics, New York, NY 10027-6699, USA E-mail: smyth @ civil. Columbia, edu SAMI F. MASRI University of Southern California, Department of Civil Engineering, Los Angeles, CA 90089-2531, USA E-mail: [email protected] ELIAS KOSMATOPOULOS University of Southern California, Department of Electrical Engineering, Los Angeles, CA 90089-2531, USA E-mail: ikosmato @ rcf-fs. use. edu ANASTASSIOS CHASSIAKOS California State University, Long Beach, Department of Engineering Technology, Long Beach, USA E-mail: [email protected] Adaptive estimation procedures have recently gained significant attention by the research community to perform real-time identification of nonlinear hysteretic structural systems under arbitrary dynamic excitations. This paper presents an overview of some of the authors' previous work in this area, and also discusses some of the new issues being tackled with regard to this class of problems. The trade-offs between parametric based modeling and nonparametric modeling of nonlinear hysteretic dynamic system behavior are discussed. A new neural network based identification procedure is introduced. Both simulation and experimental results of the performance of the parametric and nonparametric methods are presented.

1

Introduction

Developing robust adaptive control strategies for real-world civil structures has been a topic of recent interest (1st World Conference on Structural Control (1WCSC), 1994; Housner et al.l; 2WCSC, 1998). The motivation for exploring adaptive techniques comes from the acknowledgement that since structures behave in unexpected forms and non-linearly when excited by strong-ground motions, the implementation of conventional fixed controller strategies may prove to be naive. Often the governing response properties only exhibit themselves for the first time when subjected to strong shaking. As a result of this, control strategies should incorporate flexible

521

522

adaptive identification schemes which can quickly capture and emulate the essential response signature of a structural system and react accordingly. Of course, another key feature of adaptive techniques is that they can model time-varying behavior, for example, structural deterioration is often observed during the course of strong ground excitation. Adaptive identification schemes can be employed in either the form of a parametric or nonparametric model. Parametric adaptive identification schemes have been investigated in the context of strong nonstationary excitations (Smyth et al.6, Sato and Qi 5 ). This work is however limited by the parametric model to identifying certain classes of nonlinearities. In this paper, the parametric modeling will be reviewed, and motivation will be presented for moving to nonparametric techniques in the context of active control. The authors then apply an adaptive artificial neural network identification technique, which can cope with a much broader family of unknown nonlinear response behaviors. 2

Problem Formulation

The fundamental problem which will be considered here is the prediction of the restoring force of a nonlinear hysteretic structural element, and the estimation of either a nonparametric or parametric model which describes the element's dynamic behavior. For the nonlinear single-degree-of-freedom (SDOF) system shown in Fig. 1, the equation of motion can be expressed as mx(t)+r{x(t),x(t))=u(t)

(1)

where x(t) is the displacement of mass m, r(x(t),x(t)) is the nonlinear restoring force and u(t) is the system's external excitation. The identification problem may be formulated in several ways depending upon which parameters are known. For example, it will be shown that if the mass of this system is considered unknown a priori, it can still be identified as one of the system parameters. The nonlinear hysteretic restoring force r can be modeled by the following differential equation (Wen, 1980) r = (1/r?) [Ax - u(P\x\\r\n-1r

- 7z|r| n )]

(2)

This Bouc-Wen model was chosen for its ability to capture, in a continuous function, a range of shapes of hysteretic loops which resemble the properties of a wide class of real nonlinear hysteretic systems (Vinogradov and Pivovarov4). The shape of the hysteretic loop is governed by the combination of the parameters rj, A, u, /?, 7

523

r (x, x)

Figure 1. Model of hysteretic system.

and n, and it can be made to assume a wide range of qualitative features spanning the range from purely polynomial-like nonlinearity to a fully elastoplastic system. 2.1

Parametric Modeling

The parametric modeling of the nonlinear element can be made quite flexible by incorporating additional terms into the model. For example (Smyth et al.6), the Bouc-Wen model may be complemented by a linear damping parameter c and a cubic term parameter d. In the SDOF Mass Known case (i.e., it is assumed that the value of m is available) the variable of interest r could be related to an auxiliary variable z by z = r = u — mx z = kx + ex + dx3

(3)

- [ (l/V)[v(J3\x\\r\n-1r--yx\r\n)]dt Jo The signal to be predicted z in Eq. (3) can be rewritten in a more generic form as a linear combination of the product of the unknown parameter clusters (in vector 0) and the corresponding nonlinear observed signal combinations (in vector ): z = 0T

2.2

(4)

Nonparametric Modeling

An alternative parameterization whose parameters do not have any physical meaning is also explored. The nonparametric model used in this study is the Volterra/Wiener

524

Neural Network (VWNN) (Kosmatopoulos2) which is linear-in-the-weights, and can hence be written just like Eq. (4). Such a parameterization requires very little a priori information about the system properties, and will potentially require fewer measurement quantities to be available. These are two very significant advantages over physical model based identification techniques, because the system may not behave within the class of models initially assumed. The VWNN model allows the system nonlinearities to be extremely general and completely unknown at the outset. When the system becomes more complex than the SDOF system shown in Fig. 1, with many interconnected elements, such as the general system shown in Fig. 2, parametric modeling approaches to this problem have proven to require more signals to be measurable than is realistic in civil applications. In the case of nonparametric identification, the internodal restoring forces are not estimated because of insufficient sensor information, and therefore, the internodal elements parameters remain unknown. Rather, the resultant force which each node experiences due to the elements to which it may be connected is estimated.

Figure 2. General structural system, with discrete response measurement locations. The system can experience force excitation, and multiple support motions.

2.3 Adaptive Laws The adaptive law which tracks the measured restoring force is driven by the error between the predicted force and the measured force at the previous time-step. The

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Figure 3. Adaptive identification of structural steel sub-assembly undergoing cyclic testing, (a) Phase plane plot of restoring force prediction vs. exact measured force; (b) evolution of the estimated parameters.

authors have found that both least-squares based, and gradient projection algorithms obtain very good performance in the context of civil structural elements. Recently, additional effort has been made to refine the rate of adaptation in optimal ways (Lin et al.3), without a priori information about the level of excitation or type of excitation, and the corresponding response. 3

Applications

Several applications are presented in the context of civil structural identification during strong excitations. The tracking of a least-squares based adaptive law, using the parametric Bouc-Wen model, is shown in Fig. 3 for actual experimental data from a cyclic test of a steel beam-column connection. The time-variation of the system's stiffness can be clearly seen in the progressive decrease in the identified 6Q parameter. In addition to the experimental results from this SDOF system, the methodology is also applied to the simulated response of multi-degree-of-freedom systems. The limitations of the parametric approach can be shown for system identification purposes, when either the model is phenomenalogically different from the assumed class of model, or when insufficient measurements are available. The adaptive neural network modeling technique can be applied to nonlinear systems with increased complexity in the inter-connections of the nonlinear elements. In this paper the VWNN approach is applied to a simulated 3DOF chain-like system, which is a simplistic representation of a three story building. The interstory elements are hysteretic. Fig. 4 shows the real-time adaptation of the algorithm to yield accurate estimates of the interstory element restoring forces. In this case the network was not trained at all

526 Time-history of Restoring Forces and their Estimates

40

45

Figure 4. Time History of actual (solid curve) and estimated (dashed curve) restoring forces when adaptation is on.

before the simulated event, therefore the model is completely unknown a priori. Despite this, the network adapts within a few cycles. References 1. Housner, G.W., Bergman, L.A., Caughey, T.K., Chassiakos, A.G., Claus, R.O., Masri, S.F., Skelton, R.E., Soong, T.T., Spencer, B.F., and Yao, J.T.P., (1997),"Structural Control: Past, Present and Future," ASCE Journal of Engineering Mechanics, (Special Issue), Vol 123, No 9, Sept 1997, pp 897-971. 2. Kosmatopoulos E.B. (1999), "Neural controllers for output feedback control," IEEE Transactions on Automatic Control. 3. Lin, J.-W., Betti, R., Smyth, A.W., and Longman, R.W., "On-Line Identification of Nonlinear Hysteretic Structural Systems using a Variable Trace Approach," ASCE Jo. of Engineering Mechanics, [submitted in February, 2000].

527

4. Vinogradov, 0. and Pivovarov, I., (1986), "Vibrations of a System with NonLinear Hysteresis," Jnl Sound and Vibration, vol 111,No l,pp 145-152. 5. Sato, T. and Qi, K., (1998), "Adaptive HQO filter: its applications to structural identification," J. Eng. Mech., ASCE. 6. Smyth, A.W., Masri, S.F. & Chassiakos, A.G., (1999), "On-Line Parametric Identification of MDOF Non-Linear Hysteretic Systems/ViSCis Journal of Engineering Mechanics, , February.

THE ATHENS (GREECE) EARTHQUAKE OF SEPTEMBER 7,1999 C. A. SYRMAKEZIS AND A.A. SOPHOCLEOUS Institute of Structural Analysis and Aseismic Research National Technical University of Athens Zografou Campus, Athens, GR-15773 E-mail: [email protected]

GREECE

On September 7 1999, at 14.56 local time, a strong earthquake occurred 18 kilometres NorthWest of the town of Athens center. The earthquake was of magnitude Ms =5.9 and the coordinates of the epicentre were located to 38.12N-23.64E, at the area of Parnitha mount. This earthquake was a suprising one since no seismic activity was recorded in this region the last 200 years. According to strong-motion recordings, the range of significant frequencies is approximately 1.5-10Hz while the range of the horizontal peak ground accelations is bettween 0.04 to 0.36g. The most heavily damaged areas lies within a radius of 15Km from the epicentre. The consequences of the earthquake were rather hard: 143 people died and more than 700 injured. The structural damage perspective of the earthquake was also drastic since 2700 buildings were destroyed or left with inrepairable damage and 35000 buildings experienced repairable damage.

1

Introduction

After a quiescent period of 200 years, a damaging earthquake of magnitude Ms =5.9 occurred in the area of Parnitha mount, in the north-east of the town of Athens on September 7, 1999, at 14.56 local time, just 20 days after the devastating earthquake in North-Western Turkey. More than 1000 aftershocks were recorded in the first five days. The area affected by the Athens earthquake is densely inhabited. The earthquake caused 143 deaths and injured more than 700 people. Out of 37700 household in the affected region, sheltering a population of 100000, 2700 buildings were destroyed or left with inrepairable damage and 35000 buildings experienced repairable damage. Lifeline systems exhibited a very well behaviour during the earthquake. Concerning transportation, almost no damage were observed to bridges or to the road and rail network. Only a permanent oversetting of few centimeters of the deck of a bridge and a damage of a road near the epicenter were reported. The communication system failed for a short period time. Underground pipelines exhibited an excellent performance. Latest estimates put the cost of the earthquake at 200 billion drachmas (630million US dollars). This cost covers the first urgent measures, the temporary sheltering, the reconstruction and repairing of buildings and the assistance to the industries.

529

530

2

Seisin©tectonic and geology of Athens

The seismic history of Athens starts in the 5th century BC when the first witness appears for an earthquake event in the north Euboea Gulf. Subsequent earthquakes have been occured, the stronger of which are: Ms =6.4, Ms =6.7 and Ms =6.7 on April 26 and 27, 1894 and February 24, 1981, respectively. On figure 1 the epicentres of historical earthquakes around the city of Athens, greater than Ms =6.0, are shown. Thetownof Athens is located in an area surrounded by mountains made up of massive limestone and dolomites overlied by softer schists. Recent deposit along Kifissos and Ilissos river mainly of low clay and clayey sands, axe also noted. On figure 1 fault lines are also depicted [1].

•»

**•*•**

/

*«o

•..: r:

* *ra

*i e*a

Figure 1. Past earthquake events and fault Hnes of the general region.

3

The earthquake event

The earthquake was of magnitude Ms =5.9 and the coordinates of the epicentre were located to 38.12N-23.64E, at the area of Parnitha mount, about 18Km from the centre of the town (Fig. 2).

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The magnitude of the main shock and the distribution of the aftershocks defines a seismic volume of 12-15 kilometres diameter. The seismic moment was calculated to 7xl0 17 Nm (National observatory of Athens, MEDNET, USGS, HARVARD). The macroseismic intensity of the earthquake reached IX of Mercali scale. Main shock was followed by a more than 1000 aftershocks during the first 5 days. The main aftershocks occurred on September 7 and 8, with magnitude of Ms= 4.7. Figure 3 shows the distribution of aftershocks for the first seven days [2]. Strong motion reccordings were available in the wider Athens area at epicentral distances of 10-20Km. The location of the main stations are shown on figure 3. According to strong-motion recordings, the range of significant frequencies is approximately 1.5-10Hz while the range of the horizontal peak ground accelations is bettween 0.04 to 0.36g. Table 1 presents the recorded data of the three stations shown on figure 4.

Figure 2. The epicentre of the main shock.

532

E z

Sep 7 to S©p14(mornirtg) Steo 4 Hours

Figure 3. Distribution of aftershocks for the first seven days.

Figure 4. The location of recording stations.

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Table l. Recorded data of the three stations. Station Epicentral Distance (Km) 2 17 3

16

4

16

Max Acceleration Max Acceleration (L)/Period (T)/Period 0,139g 0,15sec 0,29g 0,12sec 0,14g 0,14sec

0,19g 0,15sec 0,35g 0,25sec 0,12g 0,12sec

Max Acceleration (V)/Period 0,llg 0,08sec 0,19g 0,07sec 0,06g 0,06sec

Taking into account the recordings of the three stations, elastic response spectra were developed [3]. These spectra are depicted on figure 5. On the same figure the elastic response spectrum of the Greek Aseismic Code (NEAK) is also presented for soil conditions of type B (medium soils). In the first Greek seismic code (1959), three seismic factors were adopted for the area of Athens, 4%,6% and 8%, for firm, medium and soft soils respectively. In 1995, the new seismic code (NEAK) was introduced. This code refers to a three-part spectrum as it is indicated on figure 5. It is obvious that the recorded accelarations were several times greater, for both the buildings designed either according to the old (1959) or even to the new seismic code (1995). This is valid especially in the range of periods 0.1g-0.4g, i.e for the two to five story builgings, which are the majority of the affected buildings. Concerning the level of accelerations recorded it is interesting to point out that for Athens new seismic code (NEAK) prescribes a peak ground acceleration 0.16g with a return period 50 years. If 0.25g ground acceleration is accepted for this earthquake event, return period Tm and ground acceleration ym can be correlated according to the following relation [4]: logym= 0,266 logTm+1,579 Following this formula, a return period of 839 years is obtained. This fact clearly shows the extreme character of the seismic event of September 7, 1999. 4

Structural damage

According to the damage survey conducted in the affected area by the Ministry of the Environment and Public Works for 60812 buildings, 4682 of them were destroyed or left with irreparable damage (8%), 38165 experienced repairable damage (62%) and 17965 appeared with almost no damage (30%) (Fig. 6).

534 1(00

(cm/sec )

1

:

1

1

,

1

Spectral acceleration Sa for the earthquake in Athens (7/9/1999) - 3 accelerometers Horizontal, Sa, Spectra at KEDE Horizontal, Sa, Spectra at Halandri Horizontal, Sa, Spectra by GYS Horizontal, Sa, Spectra for design by NEAK (ground type B)

Figure 5. Elastic response spectra.

30%

INREPARABLE

REPAIRABLE

SLIGHTLY DAMAGED BUILDINGS

Figure 6. Damage distribution among the buildings inspected.

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Most of the damage occurred in an area of about 15Km from the epicentre. The macroseismic intensity of the earthquake reached IX of Mercali scale as it is shown on figure 7 [5]. The majority of the collapsed buildings were low to mid-rise apartment houses, and commercial/industrial buildings. On figure 8 earthquake spectra as well as rough building classification according to their period is shown [5]. According to this figure greater values of accelerations appear in the period range of 0.1s to 0.4s corresponding to two-to-five story buildings. Concerning the collapsed and heavily damaged buildings it must be mentioned that the majority of them were design and constructed according to the old seismic code (1959) where no capacity criteria, confinement and minimum shear wall requirements were included. On figure 9 and 10 damaged poorly reinforced joint areas are shown. The lack of stirrups is also obvious. On the other hand, buildings designed and constructed according to the new code (1995) were heavily damaged if short columns or soft story without shear walls existed. Short column effect was common failure mechanism for many industrial buildings. In this case damage was the result of shear appeared as total deterioration of the concrete in this part of the column. Figures 11 and 12 show two characteristic failures of this type. Soft ground story failure was faced in the cases of apartment buildings since this type of construction is very common in Greece. The main difference between buildings with a soft ground story designed with the old and new code is the requirement for shear walls in the second case, and this is the reason of extended damage for buildings of the first case. This type of failure appears first as joint failure leading the system to a mechanism. As a consequence, large horizontal displacements and failure occurred. Figures 13 and 14 present such types of failures. Due to the increased values of the vertical acceleration component structures designed and constructed without beams, i.e. flat slab system, without any special measures failed due to penetration of the slabs by the columns. An interesting case is shown on figure 14 where the ground floor of a five-story building was destroyed due to penetration of the slabs while the above levels remains unaffected. Finally masonry structures were also affected and damaged. Most of them were very old adobe and stone masonry structures. Partial collapse of external bearing walls or failure of corners were the common types of damages appeared (Fig. 15).

536

® Epicenter Horizontal projection of the fault "**' Direction of seismic i. ~, - waves * Position of \ acceloiiseters I

Figure 7. Hie fault of Pamitha and the damages by MercaH scale Spectral acceleration (g)

Period (sec) Figure 8. Damage distribution among the buildings inspected, spectra.

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Figure 9. Joint failure-lack of both bending and shear reinforcement.

"i

Figure 10. Joint failure-lack of stirrups.

538

Figure 11. Damage to short columns of an indusMal building.

Figure 12. Damagetoshort columns of an industeial building.

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Figure 13. Soft story failure of a four stoiy building.

Figure 14. Soft story failure leading the systemtoa mechanism.

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Figure 15 Failure of afivestory building due to the flat slab penetration.

Figure 16. Failure of comers in a case of adobe masonry structure.

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References 1. Abraseys N. N. and Jackson, J. A., Seismicity and Strain in the Gulf of Corinth (Greece) since 1964. Journal of Earthquake Engineering 1 (3) (1997) pp. 433^74. 2. Kalogeras I. and Staurakakis G., Initial results of the analysis of the Athens earthquake accelerogramms (in Greek). Technical Chamber of Greece Report 2068 (1999) pp. 76-82. 3. Penelis G., et all. The Athens earthquake, assessment of the response of old and new buildings (in Greek). Technical Chamber of Greece Report 2081 (1999) pp. 100-114. 4. Papazachos V. and Papazachou C , The earthquakes of Greece. Thessaloniki 1997. 5. Protonotarios G., Report on Athens earthquake on September 7, 1999. Eleutherotupia 2/11 (1999).

CONTROLLING M O D E L I N G ERROR IMPACT IN S T R U C T U R A L PARAMETER ESTIMATION

SARA WADIA-FASCETTI 1 AND SAYGIN OZGU 2 Department

of Civil and Environmental Engineering, Northeastern Massachusetts, 02115 USA E-Mail: [email protected]; [email protected]

University,

Boston,

MASOUD SANAYEI 1 Department of Civil and Environmental Engineering, Tufts University, Massachusetts, 02155 USA E-Mail: [email protected]

Medford,

Structural parameter estimation algorithms identify changes in structural parameters (such as axial rigidity and bending rigidity) by adjusting the parameters that define an a priori finite element model to reconcile measured structural response with a set of measured test data. Two common challenges when applied to field test data are measurement noise and modeling error. Modeling error, a bias error, which is represented as uncertainty in the parameters of a finite element model of the structure, is the most significant challenge and can curtail capability of parameter estimation to capture the physical behavior of the structure. A weighted parameter estimation procedure is reformulated to control the impact of the modeling error. It is shown that the effect of modeling error on the final parameter estimates can be reduced using a set of loads, set of measurements, and an estimate of the modeling error location. In many cases the effect of modeling error on the final parameter estimates is eliminated completely or significantly reduced.

1

Introduction

Structural parameter estimation, a sub-field of structural identification, is a tool enabling the prediction of structural stiffness and mass parameters for finite element model (FEM) updating. The estimation is performed by adjusting the parameters of an analytical FEM in a systematic approach to reproduce measured data (static or dynamic). Parametric changes in a baseline FEM identified using a parameter estimation tool can be related to physical changes in a structure leading to an assessment of the overall health of a structure for use in condition assessment. The effect of measurement error, which can be represented by a statistical dispersion about a zero mean response, on parameter estimation and structural identification is well understood [1,4,8]. While it is well accepted that parameter estimation is stable within prescribed limits of measurement error on each sensor, modeling error presents a different type of problem. Unlike measurement error, modeling error is a bias error that is not referenced to a zero mean. The potential 1 2

Associate Professor Graduate Student

543

544

bias in the modeling error presents a greater challenge to the application of parameter estimation. Without properly acknowledging modeling error the parameter estimation procedure can incorrectly estimate the unknown parameters by reconciling an incorrect or shifted baseline model to the nondestructive test data. This paper presents a methodology to identify and control the potential contamination that modeling error can have on the resulting parameter estimates. Conditions are presented that identify cases in which parameter estimates are uncoupled from modeling error. A weighting procedure is proposed to reduce the effect of modeling error. The methodology is demonstrated on an example. 2

Parameter Estimation Including Modeling Error

Parameter estimation, at the element level, is used to identify the implicit crosssectional properties in the stiffness and mass matrices of a structural FEM such as axial rigidity (EA), bending rigidity (EI), and torsional rigidity (GJ). A typical parameter estimation procedure considers two types of parameters: those that are known and those that are unknown. The known parameters are assumed to be accurate while the unknown parameters are to be estimated. Modeling error in FEM parameters that are considered known introduces a third type of parameter that is uncertain. In general, structural parameter estimation consists of a finite element module to assemble structural mass and stiffness matrices, a routine to assemble an error function, and an optimization routine to minimize the error function. Error function formulation must consider the inability to measure responses at all degrees of freedom [6, 7] and compare "analytically" predicted data to "measured" data. The error function matrix E considered in this study is a static displacement-based function shown in Eqn. 1 where measured forces are compared to analytically computed forces. [E(p,e)]={[Kj-[Kj[Kbb)-l[Kbj)[ua]

+[**][*J'1 &]-&.]

0)

where a and b denote degrees of freedom in which responses are measured and not measured, p is a vector of unknown parameters, e is modeling error on a vector of parameters, Fa and Fb are known applied forces, and Ua represents measured displacements. The scalar objective function J in (2) is defined as the square of the Frobenius norm of the residual error matrix in (1) and is minimized by updating the unknown stiffness parameters through a nonlinear least squares routine.

/(P)=£2X2 i

(2)

i

where i and j denote the row and column location in E. When there is no modeling error or measurement error and as the updated parameter estimates approach the true value of the unknown parameters / will

545

approach zero within an acceptable tolerance limit. This implies that a global minimum has been found on the surface of the objective function, /. In the case of modeling error, J is no longer guaranteed to equal zero at the global minimum and in many situations the global minimum will move away from the actual results due to the modeling error. It is also important to note that there is a potential lack of uniqueness in the unknown or free set of parameters. The reader is referred to Hjelmstad [3] for an in depth discussion of uniqueness in parameter estimation. There are a number of criteria in addition to uniqueness that are necessary to ensure that the unknown parameters can be estimated. For example, the structural elements with the unknown parameters must be significantly stressed by the excitations and be observable by the sensors. Practical cases can limit the availability of excitation sources and measurement scenarios. The modeling error alters the shape of the J surface. However, it is possible that the least squares search, which is dependent on the sensitivity matrix of the residual error matrix, is independent of the modeling error in the system. This situation can be identified with the second partial derivative [6] of the error function with respect to the unknown parameters, p, and the modeling error, e. d[S(p)}

d2[E(p,ej]

de

d{p)Tde

(3)

where S is the sensitivity matrix and e is the modeling error present in one or several known parameters of the FEM. 3

Controlling the Effect of Modeling Error in Parameter Estimation

Modeling error, due to uncertainties in stiffness properties of structures, enters into the error function during parameter estimation and results in a decrease in quality of estimated parameters and possibly divergence of the solution technique. Due to the complex topology of the error function in Eqn. 1 and the algebraically nonlinear relationship between loads, measurements, and modeling error, a set of measurements that leads to a null value for Eqn. 3 is not the usual case. Error function weighting, motivated by Total Least Squares [2], artificially modifies (through weight factors) the numerical values of entries in an error function such that favored data have greater influence in the least squares estimation leading to better estimations. Error function weighting is of the form: [E*(p,e)]=[E(p,e)].*[w]

(4)

where E*(p,e) denotes the weighted error function (matrix), and W denotes the weighting matrix [5]. The operator '.*' denotes entry by entry multiplication of E and W. Weighting is implemented on the error function prior to the minimization. The weights change the shape of the objective function surface based on the user's estimate of the modeling error location. Since the least squares optimization technique minimizes the Frobenius norm of the error matrix, weighting an entry of

546

the error function by a large number will increase the effect of that entry, and will also increase the norm of the error function, J. Therefore, the non-weighted entries or entries weighted with a relatively smaller number than others will have little contribution to J. The error function is weighted with the matrix, W, defined by Eqn. (5). w. -

max - ^

._.

_Lid

5

<>

de

Weight factors that consider modeling error in the system will lead to better estimations. Entries in E not affected or slightly affected by modeling error can be assigned greater weights, where entries highly affected by modeling error can be assigned smaller weights. The partial derivative of the error matrix with respect to modeling error, dE/de, evaluated numerically and using initial guesses for the unknown parameters, gives the relationship between each element in the error matrix and the anticipated modeling error. An entry in the partial derivative matrix that is zero indicates that that entry is not affected by the modeling error and should be assigned the greatest weight. If an entry is large compared to the others, then that particular entry is highly contaminated and should receive a smaller weight. 4

Estimating the Influence of Modeling Error

Three analytical tests are presented to determine (1) if parameter estimates are uncoupled from modeling error; (2) in the case they are not, if error function weighting can uncouple the modeling error from the estimated parameters; and (3) in the case that modeling error can not be uncoupled from the estimation process, an index is presented to assess the potential improvement in the parameter estimate with error function weighting [5]. In all three cases, it is necessary to know the location of the modeling error. Situations where the modeling error location is known and these parameters must be considered as uncertain rather than unknown can occur if there aren't sufficient sensors to obtain measurements near the location of modeling error. These three tests are as follows. 4.1

Test 1: Modeling Error(s) Relationship to Estimated Parameters

The first step is to determine if the modeling error can be uncoupled from the unknown parameters for the given parameter estimation problem. If the norm of Eqn. 3 is zero, then modeling error will not interfere with the solution. Otherwise, error function weighting should be considered. 4.2

Test 2: Error Function Weighting

Test 2 determines if it is possible to obtain parameter estimates uncoupled from modeling error with error function weighting. The test is performed on E(p,e) prior

547

to weighting. The first derivative of the error function with respect to modeling error, dE/de, is found numerically. If the resulting derivative is a full matrix, then it is not possible to obtain parameter estimates uncoupled from the modeling error, even with error function weighting. If there are any zero entries in the resulting derivative matrix, then it may be possible to uncouple the modeling error from the parameter estimates. A comparison must be made between dE/de and *EA . for each unknown parameter, pt, to determine if there are entries in E that are independent of modeling error and in which pt is observable. Such a case is defined as a value point (VP). Thus, a VP is assigned for each zero entry in s%e that corresponds to a nonzero entry in ^EA .. The comparison is continued for each unknown parameter (UP). To ensure that there is sufficient data that is not contaminated by modeling error, an entry identified as a VP can not be applied as a VP for a another UP. In summary, error function weighting will yield error free parameter estimates if the following conditions are met: • The location of modeling error(s) are known. • The total number of assigned value points is greater than or equal to the total number of unknown parameters in the error function (#VP > #UP). • At least one VP is assigned for each UP. 4.3

Test 3: Improvement Measure with Error Function Weighting

The objective of Test 3 is to quantify the increase in quality of the final parameter estimates upon error function weighting. Unlike the previous tests, Test 3 requires that parameter estimation is implemented four times to evaluate P;, which is the potential percent increase in quality with weighting, for parameter i. Eqn. 6 defines Pi where 82i and 8n are defined for each unknown parameter i as illustrated in Figure 1. The interval [a, b] is the expected modeling error range in percentage of the expected true value. The range does not have to be around 0 and the values of a and b can be negative or positive. estimation error

Estimates without weighting

(

>li

.

f ^

a

Estima :es with weighting

1'

4=

X

>

*100

% modeling error

Figure 1. Schematic description of parameter estimate improvement with error function weighting.

(6)

548

5

Example

Two parameter estimation cases are considered for the example structure shown in Figure 2. The example plane frame is a two story two bay rigid frame comprising of 10 2-D frame elements and 9 nodes. The supports at the base of each of the three columns are assumed to be perfectly rigid with all degrees-of-freedom restrained. 11

L.4 ik

a

13 ft. 0 2

Li ,& 13 ft.

E

a

t7

^1*10 12

18

M

s

^Li

rj

E

15

S

nhr 30ft

14

CASE MDOF FDOF Modeling error, e Unknown parameters, pf

1 7-9,13-18 1,4,13,16

2 3, 6, 9, 12, 15, 18 1,4,7,10,13,16

I9,110

I i , I2, Is

I.,I 2

Itf' ^9» 110

T777T

30 ft.

-A

Figure 2. Example steel structure. Columns are W14x61 and girders are W18x76. In case 1, there are 2 unknown parameters with 9 measurement locations and 4 load cases. Application of Test 1 fails yielding a nonzero value for the norm of Eqn. 3. In Test 2, the partial derivative of the error function with respect to modeling error contains many zero entries suggesting that a number of potential VPs exist. The corresponding partial derivative of the error function with respect to each unknown parameter yields full matrices making it possible to identify many different VP pairs. Thus, there is sufficient data to estimate the two unknown parameters and the final estimates will be uncoupled from modeling error. Therefore, it is not necessary to continue to Test 3. Figure 3 shows that the weighting procedure uncouples the modeling error from the estimated parameters, /; and I2. In case 2, there are 3 unknown parameters with 6 different measurement and load locations. Test 1 yields a nonzero value for the norm of Eqn. 3. Test 2 yields a full nonzero partial derivative matrix of the error function with respect to modeling error. Thus, it is impossible to uncouple the modeling error from the estimated parameters. Test 3 is applied to estimate the potential reduction in error with weighting. The test is based on an estimated range of modeling error between 50% and 50% of the actual value for I9 and l10. The resulting estimates with and without weighting are shown in Table 1 with p for each estimated parameter. Figure 4 illustrates the full range of error for each estimated parameter with and without weighting. It is worth noting that while all three parameter estimates improved with weighting, I6 and //o experienced the most improvement as evidenced by the ft parameter.

549

-100

-50 0 50 00 % Modeling Error in I9 and lie

-100

-50 0 50 % Modeling Error in I9 and lie

Figure 3. Error in parameter estimates for Case 1 with error function weighting ('0') and without error function weighting ('x').

Table 1. Selected simulation results for case 2.

Unknown Parameter 16

U Iio

% estimation error without error function weighting -50% 50% -29.81 % -54.59 % -44.83 %

% estimation error with error function weighting -50% 50%

12.02 % 46.04 % 35.49 %

1.71 % -32.17 % 5.65 %

% improvement with weighting

0.14% 31.93% -3.51 %

5n

52i

A

41.83 100.63 80.33

1.71 64.10 9.16

95.92 % 36.30 % 88.60 %

B 100

1 50

;

^

^

-50 0 50 % Modeling Error in Ii, I2, and Is

i-100

IP' -50 0 50 % Modeling Error in Ii, Ij, and Ij

a.

I

0

uj -50 S*

I-100

-50 0 50 % Modeling Error in li, I2, and I5

Figure 4. Error in parameter estimates for Case 2 with error function weighting ('0') and without error function weighting (V).

6

Conclusions

An approach to reduce the impact of modeling error in parameter estimation is presented. If the location of modeling error is known, it is possible to uncouple or reduce the effect of modeling error on final parameter estimates. The uncoupling is performed through error function weighting where the entries in the error function that are the most contaminated by modeling error are given the lowest importance. Three tests are proposed to evaluate the potential quality of the final parameter estimates in the presence of modeling error. The first two tests are implemented without performing parameter estimation. The third test requires 4 selective parameter estimation simulations around the expected range of modeling error.

550

The approach presented in this paper, which utilizes a static stiffness-based error function, is general and can be applied to any other error function used in parameter estimation. It is worth noting that error functions considering a structural mass or damping matrix will introduce significantly more modeling error into the system. It is possible, however to obtain flexibilities from modal test data and to perform parameter estimation using a flexibility-based error function. In the case of the flexibility-based error function, while it is possible to improve the results, it will be impossible to uncouple the modeling error from the parameter estimation due to inversion of the stiffness matrix. There are a number of issues that remain to be discussed. These include: evaluating a set of measurements in which uniqueness is guaranteed, integration of modeling error with measurement error, and application to in-service structures. 7

Acknowledgements

NSF grant numbers CMS-9622515, CMS-9702656, and CMS-9622067 support the work presented in this paper. This support is gratefully appreciated. Contributions made by graduate students Dr. B. Arya (Tufts), E. Santini (Tufts), and B. Gunes (Northeastern) in previous studies related to modeling error is appreciated. References 1. Beck, J. L. and Katafygiotis, L. S. Updating models and their uncertainties. I: Bayesian statistical framework, Journal of Engineering Mechanics. 120(4) (1998) pp. 455-461. 2. Golub, G. H., Van Loan, C. F. Matrix Computations. 2nd edition, John Hopkins University Press, Baltimore, USA. (1989) pp. 576-577. 3. Hjelmstad, K. D. On the uniqueness of modal parameter estimation, Journal of Sound and Vibration. 192(2) (1996) pp. 581-598 4. Hjelmstad, K. D. and Shin, S. Damage Detection and Assessment of Structures from Static Response, Journal of Engineering Mechanics. 123(6) (1997) pp. 568-576. 5. Ozgu, S. Improving Structural Parameter Estimation Results Considering Modeling Error. A Masters Thesis, Department of Civil & Environmental Engineering, Northeastern University, Boston, MA, (2000). 6. Sanayei, M., Wadia-Fascetti, S., Arya, B., Santini, E. Signifance of Modeling Error in Structural Parameter Estimation, Journal of Computer-Aided Infrastructure Engineering 16(1) (2001). 7. Sanayei, M. Onipede, O., Babu, S. R. Selection of Noisy Measurement Locations for Error Reduction in Static Parameter Identification, AIAA Journal, 30(9) (1992) pp. 2299-2309.

ACTIVE CONTROL REQUIREMENTS IN RAILWAY PROJECTS

DR. HELMUT WENZEL Vienna Consulting Engineers Vienna, Austria E-mail: vce @ atnet. at For attenuating noise and vibrations in buildings nearby railway tunnels new developments for mass-spring-systems are presented. After a short introduction into the dynamic background of such systems the special static and dynamic characteristics of the used components and materials are described. The Modelling of continuous floating track slab systems and the comparison of the calculated results with measurements is shown for a mass-spring-system in a tunnel of the Austrian Westbahn railway. These evaluations lead to design criteria and indications for computation models of future mass-spring-systems based on the new continuous construction concept.

1.

Introduction

Due to their high transport capacity and their effective use of energy with lowest damage to the environment railways are one of the most important means of transportation for the future. In spite of the advantages of railways in comparison with other transport systems, as for example motor cars the acceptance of new railway lines is very low, especially by potential neighbours. One of the most important reasons for that is the fear of irritations by noise and vibrations induced by modern high speed trains. Especially these problems occur in densely populated areas as in towns where railway routes are in tunnels with low overburden very close to residential buildings. Because of that it is nowadays very difficult to realise new railway lines or improve the capacity of existing ones in densely populated urban areas. Due to maintenance reasons ballastless permanent ways become more and more important, especially for tunnel lines. With regard to load carrying capability and to long-time stability of the track these solid roadways show a lot of advantages. Nevertheless the most important disadvantages of most kinds of permanent ways are the increasing noise and vibration emissions caused by using such superstructures. To reduce noise and in particular vibration emissions modifications of solid roadways in form of mass-spring-systems have been developed in the last years. With such systems the emissions can be reduced far below the level of ballasted track systems even with sub-ballast mats.

551

552 2.

Theoretic Background

The principle of mass-spring-systems is based on the response amplification factor of a dynamic system and can be explained in a very simple way by a linear singledegree-of-freedom system (Fig. la and lb). Fig. 2 shows that vibration attenuating effects occur for frequencies higher than // v2, where// stands for the natural frequency of the system. Furthermore, it can be seen that the inner damping capability of the system does not considerably influence the vibration attenuating capacity of the mass-spring-system especially not for higher frequency excitations.

P(t)

m (wheel, rail, sleepers, trough )

F(t)

1_ Figure la: Mass-spring-system

Figure lb: Dynamic Magnification factor of a SDOF system

553

[dB]

i\ PC ym, \VJ ,

m,

m2

\ ...-- „---J —

4

m1 < m2 < m3 < m4 1 80

1

1

1

120

frequency [Hz] a) Variation of mass m A

LE [dB] V-v

-*,

\

A \ \ ,*,"* *> k,>k2>k3>

I 0

40

80

I

k4

I

120

frequency [Hz] b) Variation of spring-stiffness k A

>- E

[dB]

20

"C, 10

Jp':

0 -10

c, ,, -i"ij?

<

;r,

-20

c,
-30

I -40

80

I

I

120

frequency [Hz] c) Variation of damping c

Figure 2: Effectiveness of mass-spring-systems

554 On the other hand the inner damping factor has a dominant effect on the amplification of excitations with frequencies nearby the natural frequency of the system. These basic principles of the physics of a dynamic system can be transformed into possible variation parameters for realisation of a vibration mitigating construction. Reduced to a single-degree-of-freedom system consisting of a vibrating mass m, a spring k and a damper c, the effects to the insertion loss performance by varying these three elements are shown in Fig. 2 assuming linearity of the vibrating system. The insertion loss ALE is defined as the difference of the noise and vibration level induced by trains on conventional ballast bed track systems and on mass-springsystems. According to the effectiveness (Fig. 2) of mass-spring-systems (MSS) the following division into three groups is commonly used: light-weight MSS with m < 4 t / m , / ; > 15 Hz medium-weight MSS with m < 8 t/m,// > 10 Hz heavy-weight MSS with m > 8 t/m,// < 10 Hz. These theoretical thoughts can be summarised by the statement "elasticity in modern railway superstructures reduces noise and vibrations".

3.

Real Construction

3.1 General To put the shown principle into practice different construction philosophies have been developed during the last 25 years All these systems consist of a more or less heavy sprung mass on which the rails are mounted (Fig. 3). The bearings can be either real steel springs or made of artificial or natural elastic materials. The dynamic performance of a mass-spring-system depends very much on the material used for the bearings - the differences occur especially due to non-linear effects of the different materials. The mass consisting of reinforced concrete with a rail carrying system mounted can be either a chain of short elements connected by hinges or a jointless slab with several hundreds of metres length. In the first case a single-degree-of-freedom (SDOF) model seems to be an appropriate simplification, whereas for the second case - the jointless system - more detailed investigations on a multi-degree-offreedom (MDOF) model are necessary

555

concrete trough rail carrying elements

base (e.g.: t u n n e l bottom floor)

bearings (springs)

Figure 3: Cross-section of a real mass-spring-system

3.2 Elastic elements- Bearings As mentioned before the dynamic behaviour of mass-spring-systems is dominantly influenced by the bearing material. For applications different groups of requirements for the elastic elements have to be defined. The first group can be summarised under the headline "vibration requirements" the dynamic characteristics of the bearing material are needed for the design. The most important quantity is the stiffness, the frequency and amplitude of excitation, and the inner damping. Furthermore, changes of the dynamic behaviour of the materials over time should be considered. Additionally, "mechanical requirements" can be defined. Long-time stability of the elastic elements has to be ensured for the relevant applied load combinations. Important for the serviceability of the bearings, are the load carrying capability, the fatigue behaviour, the deformations due to pressure and the long time settlements. A third group of requirements must be defined to ensure the "integrity of the elastic elements" under site conditions. The material has to be stable not only against water but also against chemicals like diluted alkalis and acids, and against commonly used types of oil and fat. To reduce the risk of installation mistakes, the bearings should be easy to manage on site. "Classic" steel springs show a linear behaviour between load and deflection through the whole dynamic exciting frequency range. Furthermore the stiffness of this kind of bearings does not depend on the load level. Steel springs have a distinctive

556

natural frequency which would lead to a collapse of the insertion loss of the whole mass-spring-system in this frequency-range due to resonance effects. Therefore an additional damping element must be part of each steel spring unit.

Figure 4: Steel spring bearing(Gerb) Fig. 4 shows a typical steel spring bearing which is used for heavy-weight massspring-systems with natural frequencies down to 5 Hz. The most important disadvantages of these bearings are the high initial investment costs and the maintenance problems due to fatigue and corrosion. Furthermore, the handling on site makes high-qualified labour necessary. In contrast to the steel springs, bearings made of natural or artificial rubber-like materials show a more or less extensive non-linear stress-deformation diagram. Fig. 5 shows the stress-strain relationship for chloroprene (CR) rubber and a cellular polyurethane (PUR) elastomer for different excitation frequencies. In general all rubber-like materials show the same tendency - for higher excitation frequencies these materials react with an increasing stiffness. Between the static and the dynamic stiffness (e.g. excitation frequency about 40 Hz) there is a factor of about 1.50 up to 2.50 depending on the kind of material used.

557

PUR-bearing mat:

- • — static — • - dynamic 5 Hz - * - dynamic 40 Hz

A V St

1h.

^ H 0,1

f

S,C

0,2

0,3

0,4

pressure [N/mm2] CR-bearing mat:

- • - static — • - dynamic 5 Hz - * ~ dynamic 40 Hz

0.1

0.2

0.3

0.4

0.5

pressure [N/mm2]

Figure 5: Non-linearity of CR-bearings and PUR-bearings

558

The higher the quality of the bearing material the lower the factor k<jyn : kstat. PURbearings make it possible to limit the increase of stiffness due to dynamic loading by a factor of 1.30 and for natural rubber this factor reaches values down to 1.05. Using such advanced materials high efficient mass-spring-systems with natural frequencies about 7 Hz are possible. In summary, one can say that the most important parameter which describes the quality of a bearing made of natural or artificial rubber is the quotient between the static kstat and the dynamic stiffness kdyn. The static stiffness is responsible for the deflection of the mass-spring-system under dead and live loads, whereas the dynamic stiffness is the key-parameter for the insertion loss. 3.3

Mass

In general the sprung mass, consisting of a reinforced concrete trough or slab, the rail carrying system (sleepers in a ballast bed or any kind of solid roadway) and the rails, is a mass-spring system itself. Most kinds of rail fastening systems contain an elastic layer (rail pads, baseplate pads) which make a defined deflection of the rail possible. Other kinds of solid roadways include sleeper pads which have the same function as elastic rail fasteners. Anyway, for the further reflections these elasticities will be neglected - the mass is assumed as a rigid element. The estimation models for the insertion loss of a mass-spring-system are based on the dynamic parameters under permanent loads and the not sprung masses of the sets of wheels of the trains. For constructions with short concrete mass elements uncoupled or coupled by shear bolts the bending stiffness does not considerably influence the dynamic parameters of the system. Therefore such systems have been used in the past due to their close relationship to idealised SDOF-systems. Furthermore the fear of unclear bearing conditions and of the consequences of restraint forces and deformations due to shrinkage and temperature changes lead to such constructions. At least for medium- and heavy-weight MSS it is necessary to couple the single elements to reach a continuous deflection curve. In some cases for light-weight systems the bending stiffness of the tracks themselves is sufficient to reach a continuous deflection curve. To reduce the initial investment costs and to limit the maintenance expenditure for mass-spring-systems, VCE developed a new type of MSS based on a continuous design philosophy which does not need expensive coupling elements any more. A continuous concrete mass-slab shows a non-linear load-deflection behaviour itself, depending on the live load intensity and the stiffness of the mass under permanent loads. For modelling the non-linearity of the reinforced concrete beam according to EUROCODE 2 the stiffness Beff of the reinforced concrete mass is used. If the bending moment due to permanent and live loads is smaller than the cracking moment linearity can be assumed. Nevertheless for a correct prediction of the

559 damping characteristic it is necessary to take the load history as well as other longtime effects into consideration. This means that the mass has to be modelled with the not cracked and the cracked stiffness as well, which leads to parameter studies with different boundary conditions. 4.

Practical Experiences

4.1

Mass-Spring-System Romerbergtunnel

For the first time the new concept of a jointless mass-spring-system was put into practice in the Romerbergtunnel near Schwanenstadt in Upper Austria. The Romerbergtunnel with a total length of 710 m represents a section of the development programme of the Austrian Westbahn railway. It partly runs situated under existing buildings of a residential area with low overburden. After having finished the inner tunnel lining, VibroScan® tests were made by Prof. Steinhauser which showed that preventive measures for noise and vibration mitigation were necessary. To reach the limits for good noise and vibration protection in residential areas according to ON S 9012 a medium-weight mass-spring-system had to be realised. The result of the prediction model based on linearity for both main construction elements, bearings and reinforced concrete trough, was, that a natural frequency of about 13 Hz and a mass of 6 tons per metre would be sufficient. Knowing these parameters, a jointless system was developed and put into practice (Fig. 6).

Figure 6: Cross-section MSS Romerbergtunnel

560

The system has a total length of 348 metres, 192 metres are supported on single bearings and the remaining parts of the system lie on a continuous bearing layer. For the horizontal stabilisation of the floating reinforced concrete trough shear keys with vertical elastic bearings were developed. At both ends of the MSS instead of rail expansion joint constructions a continuous connection between the MSS and the conventional ballast bed superstructure was designed, together with the exchangeable bearings and the continuous transition to the ballast bed the jointless MSS has two big advantages compared with other systems: the construction costs are very low and the expenditure for maintenance works is limited to a low level, too. The static design concept of the MSS Romerbergtunnel is based on the new "semi-probabilistic" Austrian codes. So in the ultimate limit state partial safety factors have been used for the different loads and for the resistant values of the materials. The serviceability limit state (deflections, crack width) was calculated using the same finite element model as for the ultimate limit state but without any amplification factor for the loads. The deformations were limited to three criteria: maximum deflection due to live loads below 10 mm, length of deflection line versus maximum deflection over 2,500 and maximum inclination of the deflection line below 0.3 %. Additional special investigations were necessary for long-time effects due to temperature, creep and shrinkage. Because of the tunnel situation it was decided to reduce the range of temperature values according to the Austrian codes down to ±10 Kelvin. The horizontal deformations of the single bearings and of the continuous bearing layers due to temperature and shrinkage are limited to tan y ^ 0.70. The dynamic characteristic of the MSS Romerbergtunnel - the natural frequencies and the mode shapes - was determined by modal analysis of the MDOF-system. Therefore, the dynamic stiffness of the bearings was taken into account as well as different stiffness conditions of the mass. During the construction of and after finishing the MSS in the Romerbergtunnel a lot of different measurement programmes have been carried out. The targets of these investigations are to gain knowledge of the static and dynamic behaviour of the MSS under real conditions. The measurements can be split into four groups: -dynamic characteristic and insertion loss -temperature and long-time displacements -deflections of the MSS due to live loads -rail stresses and rail deformations Because of the importance of the damping capability of the MSS, for the dynamic characteristic and the real insertion loss a lot of different tests and measurements were done. After finishing the trough construction, VibroScan tests were made to be sure that all components of the system work correctly. These tests showed that the prediction model for the vibration propagation through the soil and for the

561

insertion loss of the MSS was accurate. Ambient vibration measurements and evaluations with the dynamic measurement and testing system BRIMOS developed by VCE showed, that the natural frequencies and mode shapes fit very well to the calculated ones for the not cracked MSS and the 40 Hz bearing stiffness. Fig. 7 shows a comparison of two measurement results of the VibroScan tests and the predicted insertion loss. The comparison shows that up to 32 Hz the measured results are identical with the calculated ones, for higher frequencies the calculated insertion loss is higher than the real one. The reason for that is not an insufficient prediction model, but the fact that the VibroScan® tests were made on the pure concrete trough without the mass of the rails and the rail carrying elements. Nevertheless the spectral analysis (FFT) of the VibroScan® sweeps and the BRIMOS results fit very well together. Both investigations led to a highest effective vertical natural frequency of about 11.8 Hz for the single bearing section. The absolute values of the noise and vibration level are responsible for the effects on the neighbours of railway lines. After finishing the whole system, including also the rails and additional equipment, a lot of noise and vibration measurements were done in the buildings nearby the Romerbergtunnel. All these investigations showed that the limits for good noise and vibration protection according to the Austrian codes are reached. Beside the dynamic parameters the static behaviour of the MSS due to live loads is of special interest. Especially the real deflections and displacements of the concrete trough are responsible for the safe operation of the whole system. Therefore several load tests with electric locomotives were done before starting with the regular traffic on the MSS.

m J1

measurements

<

calculation

32

64

frequency [Hz]

Figure 7: Insertion loss of MSS Romerbergtunnel

562

4.2

Mass-Spring-System Zammer Tunnel

Based on the good experiences with a jointless mass-spring-system in the Romerbergtunnel the Austrian railway company OBB decided to use a similar vibration attenuating system in the Zammer Tunnel in the Tyrol. The Zammer Tunnel with a total length of 2.3 km is situated in a very sensitive area in the river Inn valley near Landeck. Once more VibroScan® tests by Prof. Steinhauser lead to the input values for design. This time in the most sensitive part of the tunnel a heavy-weight mass-spring-system with a natural frequency of 7.5 Hz and a sprung mass of 10 t/m was necessary. In other parts of the tunnel systems with natural frequencies from 10 to 24 Hz and masses from 10 t/m to 4 t/m had to be designed - in some insensitive parts conventional solid roadways were possible. Based on the design parameters developed for the Romerbergtunnel, VCE created a modular jointless mass-spring-system. The lengths of the conventional solid roadway is incorporated with the lengths of mass-spring-systems. Thus, the final system is one continuous system without any joints. Even between the different systems no joints were arranged. This concept led to a continuous superstructure with a lot of advantages for the construction process and also for the regular operation of the railway line. A major advantage is that maintenance costs are reduced to a minimum due to the fact that no moveable elements are part of the system, and because of the continuous transition to the ballast bed at both portals of the tunnel. For the springs of the MSS Sylomer® and Sylodyn® bearings were used once more. The newest developments made it possible to reach a natural frequency of the MSS of 10 Hz by use of full surface bearings.

563 Cross-Section 2-2;

Cross-Section 1-1

continuous bearing layer (spring)

precast element concrete trough (mass)

^ concrete trough (mass)

r* 1

0^%

[*••

continuous continuous bearing layer

_ .

,_,

transition area '

.ingle bearing. 7.5 Hz

„ , JT^fSIK,

permanent way J " 1 " " " " *"«!>

10 Hz transition area

"fm ballast bed

Figure 8: Cross-sections and part of the longitudinal section MSS Zammer Tunnel

The system in the Zammer Tunnel was erected in 1998 and regular operation started in spring 1999. Extensive measurements similar to those in the Rbmerbergtunnel proved the structural integrity of the superstructure, the correct dynamic tuning of the different MSS and the predictions of the insertion losses.

5.

Future Prospects

The importance of noise and vibration reduction motivated the Austrian railway companies OBB, HL-AG and BEG to establish a research programme. These research and development works started in 1999 and are going to run over two years. Experts of different sciences - dynamics, railway engineering, tunnelling, bridge engineering, concrete design - work together to develop optimised railway superstructures for the future based on the investigations made until now. Conclusion The static and dynamic performance of mass-spring-systems based on a continuous floating reinforced concrete track slab on elastic bearings can be estimated accurately by using simple linear-elastic finite element models. Non-linear effects of the bearing materials and the reinforced concrete mass can be taken into

564

consideration by using different linear-elastic parameters for the calculation of the static and dynamic characteristic of the system. For computation of the internal forces and the deformations due to dead and live loads the static stiffness of the bearing materials has to be used, for the calculation of the dynamic parameters - natural frequencies and mode shapes - the dynamic stiffness has to be used. Also the dynamic stiffness is the correct input parameter for the estimation of the insertion loss. The change of the stiffness of the mass due to cracking does not considerably influence the insertion loss. Even simple SDOF models lead to sufficient accurate natural frequencies for prediction of noise and vibration propagation. Together with simple construction concepts using precast elements jointless massspring-systems provide the possibility to reduce noise and vibration emissions of railway lines very effectively without leading to an excessive increase of the erection and maintenance costs. Due to the importance of noise and vibration reduction measures an international research group installed by the Austrian railway companies is working on further improvements. References 1. 2.

3.

4.

5.

6.

7.

CLOUGH, R.W., PENZIEN, J., Dynamics of Structures, Second International Edition, McGraw-Hill, 1993. PICHLER, D., MECHTLER, R., and PLANK, R., "Entwicklung eines neuartigen Masse-Feder-Systems zur Vibrationsverminderung bei Eisenbahntunnels", Bauingenieur 72, Springer-VDI-Verlag, 1997, pp. 515521. PICHLER, D., HUBER, P., "Reduction Measures for Tunnel Lines", Report for RENVIB II Phase 1 to ERRI, Vienna Consulting Engineers and Rutishauser Ingenieurburo, 1997. PICHLER, D., "Concrete based floating track slab systems - modelling and reality", Proceedings of the EURO-C 1998 Conference on Computational Modelling of Concrete Structures, Badgastein, Austria, 31 March - 3 April 1998, A. A. Balkema, Rotterdam, Brookfield, 1998, pp. 665-671. PICHLER, D., ZINDLER, R., "Development of artificial elastomers and application to vibration attenuating measures for modern railway superstructures", Proceedings of the First European Conference on Constitutive Models for Rubber, Vienna, Austria, 9-10 September 1999, A. A. Balkema, Rotterdam, Brookfield, 1999, pp. 257-266. STEINHAUSER, P., Romerbergtunnel - Ergebnisse der VibroScan Untersuchung zur immissionsmafiigen Abstimmung des Oberbaus, Report to HL-AG, Vienna, 1996. STEINHAUSER, P., Romerbergtunnel - Ergebnisse der VibroScan Untersuchung auf dem Masse-Feder-System, Report to HL-AG, Vienna, 1997.

565

STEINHAUSER, P., Romerbergtunnel Ergebnisse der Erschiitterungsimmissionsmessungen des Bahnverkehrs auf dem MasseFeder-System, Report to HL-AG, Vienna, 1997. STEINHAUSER, P., Zammer Tunnel — Ergebnisse der VibroScan Untersuchungen aufder Betonsohle, Report to OBB, Vienna, 1996. WENZEL, H., PICHLER, D., and RUTISHAUSER, R., "Reduktion von Larm und Vibrationen durch Masse-Feder-Systeme fur Hochleistungseisenbahnen", Oral presentation at the D-A-CH-Meeting in Zurich, SIA-Dokumentation D 0145, 1997, pp. 123-132.

SEMI-ACTIVE BASE ISOLATION CONTROL OF A BUILDING USING VARIABLE OIL DAMPER

K. YOSHIDA AND T. FUJIO Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522,

Japan

E-mail: yoshida@sd. keio. ac.jp

Recently semi-active control methods have been proposed and received much attention. In semiactive base isolation, coefficient of viscous damping or spring constant are changed effectively according to the state of control object. And the system using semi-active damper is classified into a bilinear system which belongs to nonlinear systems. In this paper, the optimal control theory is applied to the bilinear system using the feedforward information of disturbance and the bilinear optimal control law is derived. Then the method is applied to the 10-DOF structure vibration isolation using Maxwell model for a semi-active oil damper. The numerical analysis shows that the method has high control performance in a wide frequency range and it is effective for the vibration base isolation of building structures.

1

Introduction

The need of vibration isolation has been spreading in civil engineering, mechanical engineering and so on. Particularly, in the civil engineering, passive vibration isolation (or base isolation) using rubber bearing has rapidly been applied to various real structures in Japan since the Kobe earthquake occurred in 1995. In the vibration isolation, passive control methods have already been studied and applied broadly. In the theory of vibration isolation, however, the limitation of passive elements is well known. In other words, passive element can reduce the resonant transmissibility, while it raises the transmissibility in the higher frequency range. From the viewpoint, in the field of automobiles, the skyhook damper which can be basically realized by active control methodology and this was put into practice. In the recent decade, active vibration control systems have been put into practice and the number of buildings in which active vibration absorber is installed exceeded 20 in the last year. However, their limitation is indicated, since active control systems require much power for large earthquake and strong wind. Therefore, semi-active control method, which is a method to control parameters of control device such as spring stiffness or coefficient of viscous damping, has recently received more attention than active control methodology which needs much power. Semi-active is char567

568

Figure 1. Base isolation building with semiactive varaibale damper

Figure 2, Analytical model

Freauencv [Hzl

Figure 3. Step response of ssemi-active damper

Figure 4. Frequency characteristics of .disturbance

acteristic of less power than active control and higher performance than passive control. Especially, variable dampers have already been put into practice in thefieldof automobiles and a skyhook damper was approximately realized by using variable damper. Since the suppression of actuator power is an important issue for active structural control, in this study, new semi-active control methods for vibration base isolation are presented by applying disturbance accommodation control theory and the bilinear optimal control theory. One of the authors proposed the feedforward control of an active dynamic vibration absorber and improved the performance of active control by applying such feedforward augmented control [6], pointed out that importance of how to choose coordinates and weighting functions in vibration control [1] and then proposed the feedforward control of base isolation [2]. In other words, in the vibration isolation control, it is important to include the information of disturbance into control algorithm, which is known in the control theory as the principle of internal model. Therefore, in this study, the two control theories are applied to the generalized plant which includes disturbance information, so that the obtained control theory is applied to semiactive control of base isolation for a real building as shown in Fig. 1.

569

2

Controller Design Method

2.1

Modelling

As shown in Fig. 2, we consider the semi-active control problem of the base isolation of a 10-DOF structure model in which variable damper is installed between the base and the first story of structure and its compression property is regarded as a Maxwell model. This control object is represented as a bilinear model in the following: x,(t) = Asxs{t) + *,{*,(*) - x0(.t)}u(t) + D,m where x,(t) = [x0(t) *,« ••• jr10(r) j,(r) ••• x10(t)]T, u(t) = c~\t), andx, cs and £ denote respectively the state vector, the damping coefficient of variable damper and the vector of acceleration disturbance. The step response characteristics of semi-active damper shown in Fig. 3 is taken into consideration in the numerical analysis. 2.2

Accommodation of disturbance

In order to accommodate the information of disturbance, an augmented state system is introduced by including the state equation of fictitious disturbance system. The frequency range of the disturbance is supposed by determining the upper limit frequency of disturbance as shown in Figure 4, since the disturbance has uncertainty. Therefore, the spectral density of disturbance is assumed to be flat at this range. That is, the transfer function of the filter to generate disturbance from a white noise is assumed as follows: Z(s) W(s)

co:

s2 + 2Cd0)ds + coy

The disturbance filter is represented by the following state equation. where

**(0 = [z(0

z(Of. 4*,=

0

l

-co:

*>*=[0 a>l]T

By combining the above state equations, we obtain the following augmented state system which includes the dynamics of control object and the disturbance. x(t) = Ax{t) + B{xi(t) where X(t) •-

*.(0 **(0

, A=

A 0

*0(0}K(0

+ Dw(t),

DsCdls ,B = [B 0]\D = [0 D f S s A

«s .

andCdil=[Q

l],

570

2.3 Design of controller First, we design a Kalman filter for the above-mentioned augmented system. The observed values are the acceleration of ground, the relative displacement between the ground and the base of building and the acceleration of building roof. In this case, the output equation of the system is written by where y(t) = [z xy

y(t) = Cx(t), xw + 'if. The Kalman filter is represented by

x(t) = (A - KC)x(t) + Ky(t) + B{x,(t) - xQ{t)}u(t), K = PCTVK 0 = AP + PAT- PCTVlCP{t) + W. Secondly, we design a controller for the augmented bilinear system, The following criterion function is used, in which the objective function is the kinetic energy of the roof. /(H) = l i m i E{QxT(t)CrpqCpx(t) + uT(t){Xl(t) - x0(t)}T r{x,(t) - xQ(t)}u(t)]dt}, where Cp = [0lx20 1 1 0]. According to the bilinear optimal control [7], the optimal control law is derived as follows: u°(t) = -

*

BTPx(t)

r{Xl(t)-x0(t)} where P satisfies the following Riccati's equation. 0 = PA + ATP - PBrlBTP

+ CTpqCp

In this study, the semi-active force is supposed to be realized by variable dampers. The damping coefficients should be positive, and remain within a certain range for practical use. Therefore, the damping coefficients of semi-active dampers are limited by the following inequality. 0
By supposing that the control force generated by the semi-active dampers under the above constraint is as close as possible to the control force of active control, the damping coefficient is expressed as follows: cL (u(t)cH)

571

3

Numerical Calculation

In order to investigate the effectiveness of the semi-active control using variable dampers for base isolation control, numerical calculations were carried out. The control characteristics of the proposed semi-active base isolation control are examined in both the time and frequency domains. Since the semi-active control is essentially nonlinear, the vibration transmissibility under semi-active control is obtained as a ratio in the frequency range of spectral densities of input and output which is white noise. The specifications of the 10-DOF structure model and passive and semi-active dampers are shown in Table 1, 2 and 3, in which the specifications of rubber bearing with lead plug is included. Then the passive 1 case means that the damping ratio of 5% is a priori realized by the damping of the rubber bearing, the passive 2 case means the case Table 1 Specification of the structure model Layer

Mass

Spring Constant Coefficient of Viscous Damping [tlcm] [ t 1 kine]

10

2499.9

1020.0

8.71

9

2066.4

1180.0

8.48

8

2037.1

1410.0

10.15

7

2036.9

1600.0

10.55

6

2050.0

1850.0

11.05

5

2033.1

1840.0

11.15

4

1826.4

2020.0

13.34

3

2490.6

2820.0

19.71

2

3438.2

2320.0

12.94

1

4981.4

68.2

1.84

Table 2 Specification of the hysteresis model Spring constant [tlcm]

K

136.40

K

13.64

Yield strength [t]

Q,

600

Table 3 Specification of passive and semi-active dampers Coefficient of Viscous Damping [tlkine] Passive damper Semi-active damper

0.85 max

15.00

min

0.85

C

572 F, Slopt^-'

a Slope/

Ik. 0

Slept/

Stop*/

*i

/*. /

-a

&W

h,

J

& Figure 5.

Bilinear properly of rubber bearing with lead plug

Non Isolation Passive 1 (NRB) Passive 2 (NRB+POD) Skyhook Bilinear Opt.

Figure 6. Vibration Transmissibility

using rubber bearing and ordinary oil damper where the damping ratio is much higher than the passive 1 and the passive 3 means the case using the rubber bearing with lead plug of which property is shown in Fig. 5. And the semi-active control means the case where variable viscous damper between the base and the first story is installed and the skyhook case means the skyhook control using the same scheme as the semi-active control. The frequency range assumed to be less than 7 Hz. Numerical calculations were carried out for the case that the absolute velocity is adopted as an objective function as Q=cTc, R=r, C = [0liao 1 1 0] Figure 6 shows the numerical results of the vibration transmissibility for passive cases and semi-active case based on the bilinear optimal control. In the case of passive dampers, the performance at the high frequency range is affected, while the semi-active damper is effective at the whole frequency range. Figure 7 shows the time

573 1

Passive 2 (NRB+POD) Passive 3 (LRB)

~

1

Jk§^

w

5

raf*V*

10

15 20 Time[s] (a) Passive 3 (LRB)

25

-20 0 20 40 Displacement [cm] Figure 8. Hysteresis of LRB for Kobe earthquake

30

Passive 2 (NRB+POD) Skyhook

10

15 20 Time [s] (b) Skyhook 1

1

—

10 Time[s] (a) Skyhook

Passive 2 (NRB+POD) Bilinear Opt.

— "

H

110 i

J nil!'! i

i

i

i

!

!

1

i

!

10

15 20 Time [s]

25

10 Time [s]

(b) Bilinear Opt.

(c) Bilinear Opt. Figure 7. Time histories of X 0 + Z earthquake

30

V'ffli r' :j I

y y li yiilTl J

|

Command Output

for KoDe

Figure 9. Time histories of damping coefficient for Kobe earthquake

15

574 120 100

100 80 •-60 40 20

Q I! Passive 1 Passive 2 Passive 3 Skyhook Bilinear (NRB)(NRB +POD)(LRB) Opt.

•

.,

!

Passive 1 Passive 2 Passive 3 Skyhook Bilinear (NRB)(NRB +POD) (LRB) Opt.

(a) Maximum

(b) r.m.s.

Figure 10. Ratio of maximum response and r.m.s. of Xl0 + Z for Kobe earthquake Table 4 Response ratio of r.m.s. of x10 + z f° r various earthquakes [%] Kobe

Northridge

El Centra

Hachinohe

Taft

Non Isolation

563.8

1104.0

529.1

467.7

1015.2

Passive 1 (NRB)

76.1

108.3

71.9

89.8

102.0

Passive 2 (NRB+POD)

100.0

100.0

100.0

100.0

100.0

Passive 3 (LRB)

58.6

51.0

81.4

107.1

118.3

Skyhook

63.3

78.6

73.7

92.0

77.5

Bilinear Opt.

56.0

74.2

72.4

88.5

72.0

history of the top floor acceleration under Kobe earthquake. Figure 8 shows the hysteresis response of the rubber bearing with lead plug. From these figures the effectiveness of semi-active damper was shown. Figure 9 shows time histories of damping coefficient of semi-active damper for Kobe earthquakes. It is seen from this figure that the change of the bilinear optimal control is smoother than the skyhook control. Figure 10 shows the ratio of maximum response and r.m.s. of xm + z for Kobe earthquake. The optimal bilinear control shows the best performance in the comparison. Table 4 shows the response ratio of r.m.s. of xm + z for various earthquakes, Kobe, Northridge, El Centro, Hachinohe and Taft. On the whole, the bilinear optimal control shows the best performance. 4

Conclusions

In this study, the optimal bilinear control theory is applied to the semi-active base isolation control of real building. The following conclusions were obtained from the results of numerical analysis.

575

(1) The semi-active base isolation control shows not only good reduction performance of resonant first mode, but also better performance in higher modes than the passive dampers and the skyhook semi-active base isolation system. (2) The bilinear optimal control of semi-active control shows smoother change of damping coefficient and better performance than the sky hook semi-active control. References 1. Kang, S. and Yoshida, K., Criterion Function and Their Control Characteristics for Active Vibration Control, Proc. Int. Conf. on Motion and Vibration Control (1992), pp.291-296. 2. Kang, S. and Yoshida, K., Vibration Isolation Control with Feedforward Link using H" Control Theory, Proc. JSME Int. Conf. on Advanced Mechatronics (1993),pp.645-649. 3. Kang, S., Yoshida, K. and Hara, S., Frequency-Shaped Optimal Control with a Feedforward Link on Magnetically Levitated Vibration Isolation System, Simulation and Design of Applied Electromagnetic Systems (1994), pp. 615-618. 4. Karnopp, D., Active and Semi-Active Vibration Isolation, Trans. oftheASME 117 (1995), pp.177-185. 5. Shimizu, M. Sampei and M. Koga, Vibration Control of the Multi-Degree-ofFreedom Structure Using a Nonlinear i/„ Output Feedback Controller, Proc. Int. Conf. on Motion and Vibration Control (1998), pp.497-500. 6. Yoshida, K., Shimogo, T. and Nishimura, H., Optimal Control of Random Vibration by the Use of an Active Dynamic Vibration Absorber (Experimental Considerations on the Effect of the Control with Feedforward Link), JSME Int. J., Ser. Ill, 31-2 (1988), pp.387-394. 7. Yoshida, K. and Fujio, T., Semi-active base isolation for a building structure, Int. J. Computer Applications in Technology 13 (2000), pp.52-58.

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Author index

Anh Dong Nauyen Argoul Pierre Aris Sophocleons Asano Koichiro Auperin Michel Balamuragan V. Baratta Alessandro Beck James L. Bossens Frederic Bourquin Frederic Casas Rius Joan Ramon Casciati Fabio Chassiakos Anastassios Chu S. Y. Collet Manuel Corbi Ottavia De Luca Antonello De Stefano Alessandro Del Grosso Andrea Dorfmann Luis Dorka Uwe E. Dumoulin Claude Dyke Shirley El-Attar Adel El-Borgi Sami Erdik Mustafa Esteva Luis Faravelli Lucia Forni Massimo Fujino Yozo Fujio T. Gattulli Vincenzo Gavin Henri P. Gluck N. GluckJ. Golival J. C.

Heredia Zavoni E. Hruska Andreas Iemura Hirokazu Igarashi A. Inaudi Jose Iyer R. Johnson Erik A. Katalagarianakis G. Katafygiotis L.S. Kitagawa Yoshikazu Koh Hyun Moo Kosmatopoulos E. Lam H. F. Lamberton J. Levi R. Magonette Georges Marazzi Francesco Martelli Alessandro Masato Abe Masri Sami F. Mele E. Melkumyan Michael Nagarajaiah Satish Nakagawa Hajime Narayanan S. Nishitani Akira Osman Ashraf Ozgu Saygin Park Wonsuk Preumont Andre Rabinovich Boris Ratier L. Reinhorn Andrei Renda Vito Rodellar Jose Romeo F.

27 263 529 39 49 385 59 317 445 73 85 3 521 93 73 59 119 19 107 281 127 49 15 417 141 149 187 201 351 215 567 245 255 473 473 263 589

187 281 293 293 301 375 317 325 317 333 437 521 317 255 473 463 463 351 215 521 119 365 375 39 385 407 417 543 437 445 453 73 93,473 463 487 245

590

Rossi Roberto Sahasrabudhe S. Saleh Ahmed Sanayei Masaud Skelton Robert Smyth Andrew Soong Tsu T. Syrmakezis Costas Tamai Hiroyuki Tanaka H. Tirelli D. Tsopelas Panos Wadia-Fascetti Sara Wenzel Helmut Yoshida Kazuo Zammali Chokri

201 375 417 543 495 521 93 529 333 293 463 141 543 551 567 141