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CISM COURSES AND LECTURES
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The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences.
INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES COURSES AND LECTURES - No. 520
NEW TRENDS IN VIBRATION BASED STRUCTURAL HEALTH MONITORING
EDITED BY ARNAUD DERAEMAEKER UNIVERSITE LIBRE DE BRUXELLES, BRUXELLES, BELGIUM KEITH WORDEN UNIVERSITY OF SHEFFIELD, SHEFFIELD, GREAT BRITAIN
SpringerWienNewYork
This volume contains 149 illustrations
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © 2010 by CISM, Udine Printed in Italy SPIN 80021260
All contributions have been typeset by the authors.
ISBN 978-3-7091-0398-2 SpringerWienNewYork
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An Introduction to Structural Health Monitoring
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An Introduction to Structural Health Monitoring
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4EBOB >OB PL J>KV QVMBP LC PBKPLOP LK QEB J>OHBQ QE>Q FQ FP KLQ MLPPF?IB QL DFSB > @LJMOBEBKPFSB IFPQ LC QEBJ 4EB DL>I LC QEFP PB@QFLK FP QL FKQOLAR@B QEB JLPQ @LJJLK QVMBP LC PBKPLOP >P TBII >P PELT QEB KBT QOBKAP FK QEFP >OB> %%'-'30.'5'34 #V C>O QEB JLPQ @LJJLK PBKPLO CLO JB>PROFKD SF?O> QFLKP FP QEB >@@BIBOLJBQBO 4EB ?>PF@ TLOHFKD MOFK@FMIB LC PR@E > ABSF@B FP MOBPBKQBA FK 'FDROB > *Q @LKPFPQP LC > JLSFKD J>PP LK > PMOFKD >KA A>PEMLQ >QQ>@EBA QL > JLSFKD PLIFA 4EB >@@BIBO>QFLK LC QEB JLSFKD PLIFA OBPRIQP FK > AFBOBKQF>I JLSBJBKQ . ?BQTBBK QEB J>PP >KA QEB PLIFA 4EB DLSBOKFKD BNR>QFLK FP DFSBK ?V . Z .= $.
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*K QEB COBNRBK@V ALJ>FK . .Z0 FP DFSBK ?V . .Z0
2 2 #
>KA CLO COBNRBK@FBP LKB E>P . 2 .Z0
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
Structural Health Monitoring Using Large Sensor Arrays
21
+)63' 7LOHFKD MOFK@FMIB LC >K >@@BIBOLJBQBO
M
M
q
R Piezoelectric q
M
M
Piezoelectric shear
Piezoresistive
M Strain gauges
+)63' %FBOBKQ PBKPFKD MOFK@FMIBP CLO PQ>KA>OA >@@BIBOLJBQBOP
22
A. Deraemaeker
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
.. x0
M Double capacitor
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
Structural Health Monitoring Using Large Sensor Arrays
23
+)63' 7LOHFKD MOFK@FMIB LC > MFBWLOBPFPQFSB PQO>FK D>RDB
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
24
A. Deraemaeker Longitudinal d33 mode
Transverse d31 mode
q
q
Shear d15 mode q
Poling direction Deformation applied
+)63' 4EOBB JLABP LC ABCLOJ>QFLK DBKBO>QFKD > @E>ODB LK > MFBWLBIB@ QOF@ J>QBOF>I
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
Structural Health Monitoring Using Large Sensor Arrays
25
Broadband light source
Optical fiber Reflected light grating
Strain applied on the grating
+)63' 7LOHFKD MOFK@FMIB LC > ?OB #O>DD (O>QFKD 3BKPLO '#(3
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
26
A. Deraemaeker
>KA QEB >MMIFBA QBKPFLK ! TEBOB FP QEB IBKDQE >KA FP QEB J>PP MBO RKFQ IBKDQE LC QEB @>?IB 9R >KA (RMQ> 4EB PQOFKD FK QEFP @>PB FP CBOOLJ>DKBQF@ >KA ?LQE BKAP >OB UBA QL QEB PQOR@QROB
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
Output signal
Input pulse
Wire
L
+)63' 7LOHFKD MOFK@FMIB LC > SF?O>QFKD TFOB
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
Structural Health Monitoring Using Large Sensor Arrays
27
QEB @>?IB @E>KDBP TFQE QEB >MMIFBA PQOBPP 4TL TFKAFKDP >OB FKPQ>IIBA >OLRKA QEB @>?IB " MRIPB FKMRQ @ROOBKQ FP >MMIFBA QL QEB OPQ @LFI OBPRIQFKD FK > J>DKBQF@ BIA 4EB @E>KDB FK QEB J>DKBQF@ BIA @>RPBP > AFBOBK@B LC MLQBKQF>I FK QEB PB@LKA @LFI TEF@E FP MOLMLOQFLK>I QL 4EB MBOJB>?FIFQV FP JB>PROBA >KA FP MOLMLOQFLK>I QL QEB >MMIFBA PQOBPP
T
Sensor coil
Current pulse generator
T +)63' 7LOHFKD MOFK@FMIB LC >K BIB@QOLJ>DKBQF@ @>?IB CLO@B PBKPLO "KLQEBO MLPPF?FIFQV FP QL JB>PROB QEB SF?O>QFLKP LC QEB @>?IB FK LOABO QL ABQBOJFKB QEB QBKPFLK 4EB MOFK@FMIB FP PFJFI>O QL QE>Q LC QEB SF?O>QFKD TFOB 'LO > PQOFKD TFQELRQ P>D QEB BFDBK COBNRBK@FBP >OB DFSBK ?V $
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
28
A. Deraemaeker
+)63' .B>PROFKD QEB CLO@B FK > @>?IB SF> JB>PROBJBKQ LC QEB >@@BIBO >QFLK PMB@QORJ
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
Structural Health Monitoring Using Large Sensor Arrays
29
+)63' 1OFK@FMIB LC > AFBOBKQF>I (13 PVPQBJ CLO QEB JB>PROBJBKQ LC SF?O>QFLKP LK > ?OFADB
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
30
A. Deraemaeker @O>@H FK QEB O>KDB LC SFPFLK LC > @>JBO>
%26+4+5+0/
/+54
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Actuator
Ampl
Ampl
ADC
DAC
Analog
(Real-time) Storage OS Digital
Fast Link PC
Storage
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Structural Health Monitoring Using Large Sensor Arrays Sensor
Actuator
Ampl
Ampl
ADC
DAC
31
Analog
Fast Link (USB)
Digital PC
Storage
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Sensor
Actuator
Ampl
Ampl
ADC
DAC
PC
Storage
Analog
Digital
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32
A. Deraemaeker
QEB PFDK>IQLKLFPB O>QFL IFKHBA QL QEB QVMB LC "%$%"$ QEB P>JMIFKD COBNRBK@V QEB QFJB ABI>VP QEB MOBPBK@B >KA QVMB LC >KQF>IF>PFKD IQBOP QEB QO>KPCBO O>QB QL QEB PQLO>DB E>OA AFPH QEB KRJ?BO LC @E>KKBIP LO MLPPF?FIFQV QL BUQBKA FQ QEB MLPPF?FIFQV QL RPB MOB>JMIFBA >@@BIBOLJBQBOP *&1& *KQBDO>I &IB@QOLKF@P 1FBWLBIB@QOF@ LO *$1 *KQBDO>QBA @FO@RFQ MFBWLBIB@QOF@
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Structural Health Monitoring Using Large Sensor Arrays
33
+)63' &U>JMIBP LC FKPQORJBKQBA ?OFADBP BSLIRQFLK LC QEB KRJ?BO LC PBKPLOP TFQE QFJB
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34
A. Deraemaeker
LK > @LK@OBQB ?IL@H 4TL TLLABK ?IL@HP >OB MI>@BA ?BQTBBK QEB @LK@OBQB ?>PB >KA QEB LLO QEFP FKQOLAR@BP BUF?FIFQV ?BQTBBK QEB @LK@OBQB >KA QEB LLO TEF@E FP KB@BPP>OV CLO QEB PBFPJF@ BU@FQ>QFLK ABP@OF?BA EBOB>CQBO
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Structural Health Monitoring Using Large Sensor Arrays
35
+)63' $>?IB QBKPFLK QRKFKD PVPQBJ FKPQ>IIBA >Q QEB QLM LC QEB MFII>O
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36
A. Deraemaeker
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Structural Health Monitoring Using Large Sensor Arrays
37
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38
A. Deraemaeker
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Structural Health Monitoring Using Large Sensor Arrays
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42
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
? Effect of a global change in stiffness
Effect of a local change in stiffness dB
dB
Undamaged
!a
!l
!
Undamaged
!a
!l
!b
!
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,)' .# )0 )( ( )( &/ .# . .# ** , ( )! ( 1 * %- $( .#
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Structural Health Monitoring Using Large Sensor Arrays
43
FAB> FP QL @LJMRQB QEB MLTBO PMB@QO>I ABKPFQV LC QEB QFJB ALJ>FK LRQMRQ LC QEB JLA>I IQBO ABKBA >P
TEBOB FP QEB >RQL@LOOBI>QFLK LC / + ABKBA ?V
;/ + / + <
; < FP QEB J>QEBJ>QF@>I BUMB@Q>QFLK *K >AAFQFLK CLO > IFKB>O PVPQBJ TFQE QO>KPCBO CRK@QFLK # QEB CLIILTFKD OBI>QFLKPEFM ELIAP 1OBRJLKQ
#2
FK TEF@E FP QEB MLTBO PMB@QO>I ABKPFQV LC QEB FKMRQ QL QEB PVPQBJ *C FP @LKPQ>KQ LKB B>PFIV PBBP QE>Q #
TEBOB FP > @LKPQ>KQ PL QE>Q FP MOLMLOQFLK>I QL QEB >JMIFQRAB LC QEB QO>KPCBO CRK@QFLK *C FP KLQ @LKPQ>KQ ?RQ PJLLQE KL PE>OM MB>HP QEB MB>HP FK TFII @LOOBPMLKA QL QEB BFDBKCOBNRBK@FBP LC QEB PVPQBJ &SBK FC PQOLKD @LJMLKBKQP BUFPQ >Q PMB@F@ COBNRBK@FBP FK QEB FKMRQ PMB@QORJ QEFP FP KLQ > MOL?IBJ >P ILKD >P QE>Q COBNRBK@V ALBP KLQ @LOOBPMLKA QL >K BFDBKCOBNRBK@V LC QEB PVPQBJ PFK@B QEB MB>H ABQB@QFLK TFII ?B MBOCLOJBA @ILPB QL QEB HKLTK BFDBKCOBNRBK@FBP LC QEB RKA>J>DBA PVPQBJ *K @LK@IRPFLK FK QEB DBKBO>I @>PB CLO > MBOCB@Q JLA>I IQBO LKIV LKB PE>OM MB>H TFII >MMB>O FK >KA QEB P>JB @LK@IRPFLKP TFQE OBPMB@Q QL QEB >MMB>O>K@B LC KBT MB>HP @>K ?B AO>TK 4EB KBUQ PQBM CLO >RQLKLJLRP A>J>DB ABQB@QFLK FP QL ABKB > MOL@BAROB QL ABQB@Q QEB >MMB>O>K@B LC QEB KBT MB>HP >RQLJ>QF@>IIV
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
44
A. Deraemaeker
JLA>I IQBOP QEB QLQ>I KRJ?BO LC MB>H FKAF@>QLOP BUQO>@QBA FP ' ' TEBOB ' FP QEB KRJ?BO LC BFDBKCOBNRBK@FBP FK QEB COBNRBK@V ?>KA CLO TEF@E QEB JLA>I IQBOP >OB @LJMRQBA
dB
Main peak of the modal filter
4 peak indicators
!
!a
+)63' 'B>QROB BUQO>@QFLK COLJ QEB LRQMRQ LC QEB JLA>I IQBO FK QEB COB NRBK@V ALJ>FK @LJMRQ>QFLK LC MB>H FKAF@>QLOP FK COBNRBK@V ?>KAP >OLRKA QEB K>QRO>I COBNRBK@FBP LC QEB RKA>J>DBA PVPQBJ
-BQ RP >PPRJB QE>Q QEB BKQFOB COBNRBK@V ?>KATFAQE FP AFSFABA FKQL COB NRBK@V ?>KAP ;1 2 < >OLRKA B>@E K>QRO>I COBNRBK@V LC QEB PQOR@QROB QEB ?>KATFAQE FP DFSBK FK LC QEB K>QRO>I COBNRBK@V QVMF@>I S>IRBP >OB LO 0KB KLQBP * >KA @LJMRQBP QEB CLIILTFKD NR>KQFQFBP
'FDROB +>OJ>K BQ >I
4EB COBNRBK@V @BKQBO '$
*
*
4EB OLLQ S>OF>K@B COBNRBK@V 26'
2 *
*
Structural Health Monitoring Using Large Sensor Arrays
45
s()
2 +)63' 2BPQOF@QFLK LC * QL QEB COBNRBK@V ?>KA ;1 2 < CLO QEB @LJMRQ>QFLK LC QEB MB>H FKAF@>QLO 1
4EB MB>H FKAF@>QLO FP DFSBK ?V
2 1
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
46
A. Deraemaeker
>
s()
?
1
2 3 4 5 67 8
s()
Intervals for the computation of the peak indicators
+)63' * @LJMRQBA COLJ QEB LRQMRQ LC > JLA>I IQBO QRKBA QL JLAB > RKA>J>DBA PQOR@QROB ? A>J>DBA PQOR@QROB >KA ABKFQFLK LC QEB FKQBOS>IP CLO QEB @LJMRQ>QFLK LC QEB MB>H FKAF@>QLOP
Structural Health Monitoring Using Large Sensor Arrays
47
+)63' 6>IRB LC QEB MB>H FKAF@>QLO FK B>@E FKQBOS>I CLO > QEB RKA>J >DBA PQOR@QROB ? QEB A>J>DBA PQOR@QROB
.1307'& '#, /&+%#503 4+/) +)/#- 30%'44+/) '%*/+26'4 *K LOABO CLO QEB MB>H FKAF@>QLO QL ?B JLOB PBKPFQFSB FK@OB>PB LC PFDK>IQLKLFPB O>QFL > QB@EKFNRB @>IIBA PB@LKAABOFS>QFSB J>Q@EBA IQBOFKD %>KFBIPPLK BQ >I FP MOLMLPBA -BQ * ?B QEB PFDK>I QL ?B IQBOBA >KA ! ?B QEB IQBOFKD CRK@QFLK 3FJMIB IQBOFKD @LKPFPQP LC @LJMRQFKD QEB CLIILTFKD @LKSLIRQFLK FKQBDO>I *
! *
*K LOABO QL OBJLSB ?>@HDOLRKA KLFPB QEB PB@LKA ABOFS>QFSB FP @LJMRQBA *
! *
! *
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
48
A. Deraemaeker
AFPQOF?RQFLK >KA FQP PB@LKA ABOFS>QFSB >OB OBMOBPBKQBA FK 'FDROB 4EBFO >K>IVQF@>I BUMOBPPFLKP >OB DFSBK ?V
! .
! . .2 2 2
TEBOB FP QEB PQ>KA>OA ABSF>QFLK LC QEB (>RPPF>K AFPQOF?RQFLK QEB JB>K FP *Q FP >K >K>ILD LC QEB P@>IFKD C>@QLO FK T>SBIBQ >K>IVPFP 'LO >K LMQFJ>I IQBOFKD LC * LKB KBBAP QL ABKB > TEF@E FP KLQ @LKPQ>KQ TFQE COBNRBK@V FQ PELRIA FK C>@Q ?B > O>QFL LC QEB COBNRBK@V 4EFP FP ?B@>RPB QEB TFAQE LC > MB>H FK * FP MOLMLOQFLK>I QL QEB @BKQO>I COBNRBK@V LC QE>Q MB>H "P PELTK FK 'FDROB QEB TFAQE LC QEB IQBOFKD CRK@QFLK FP @ILPB QL >KA FC LKB >PPRJBP QE>Q QEB TFAQE LC > MB>H FK * FP >MMOLUFJ>QBIV LC QEB @BKQO>I COBNRBK@V LKB E>P f(x)
f’’(x)
x
x Gaussian distribution
second derivative of a Gaussian distribution
+)63' (>RPPF>K AFPQOF?RQFLK >KA FQP PB@LKA ABOFS>QFSB 4EB >MMOL>@E >ALMQBA QL IQBO QEB PFDK>I * FP >P CLIILTP @LJMRQB * %(" * "MMIV > PB@LKAABOFS>QFSB D>RPPF>K J>Q@EBA IQBO QL * *
2 2
TFQE
*
Structural Health Monitoring Using Large Sensor Arrays
49
OB@LSBO QEB IQBOBA PFDK>I *
4EB OBPRIQP LC QEB IQBOFKD CLO ?LQE QEB RKA>J>DBA >KA QEB A>J>DBA PQOR@QROB >OB PELTK FK 'FDROB 4EB MB>H FKAF@>QLOP >OB @LJMRQBA ?>PBA LK QEB IQBOBA PFDK>IP >KA PELTK FK 'FDROB 4EB OBPRIQP PELT QE>Q MB>HP >KA >OB KLT TBII ABQB@QBA >
sf()
?
sf()
+)63' 'FIQBOBA PFDK>I * @LJMRQBA COLJ * > RKA>J>DBA PQOR@ QROB ? A>J>DBA PQOR@QROB
50
A. Deraemaeker
+)63' 6>IRB LC QEB MB>H FKAF@>QLO FK B>@E FKQBOS>I CLO > QEB RKA>J >DBA PQOR@QROB ? QEB A>J>DBA PQOR@QROB @LJMRQBA LK QEB IQBOBA PFDK>I *
6.'3+%#- 9#.1-'
4EB PQOR@QROB @LKPFABOBA FP > QEOBBPM>K ?OFADB PFJFI>O QL QEB LKB MOB PBKQBA FK 9>K BQ >I >KA %BO>BJ>BHBO BQ >I 'FDROB 4EB JLQFLK FP OBPQOF@QBA QL FKMI>KB SF?O>QFLKP 4EB PQOR@QROB FP J>AB LC QTL J>QBOF>IP PQBBI >KA @LK@OBQB FQ FP BU@FQBA ?V > RKFCLOJ MOBPPROB >@QFKD LK QEB OPQ PM>K LC QEB ?OFADB 4EB BU@FQ>QFLK FP > ?>KAIFJFQBA TEFQB KLFPB FK QEB COBNRBK@V ?>KA )W @LKQ>FKFKD QEB OPQ BFDBKCOBNRBK@FBP LC QEB PQOR@QROB Steel Excitation
Concrete
Concrete
Damage
+)63' 4EOBBPM>K ?OFADB PR?GB@Q QL AFBOBKQ QBJMBO>QROB DO>AFBKQP >KA A>J>DB
'/'3#5+0/ 0( 4'6&0.'#463'.'/54 4EB ?OFADB FP AFP@OBQFPBA TFQE &RIBO#BOKLRIIF KFQB BIBJBKQP RPFKD QEB 3QOR@QRO>I %VK>JF@P 4LLI?LU
3%4LLIP RKABO .>QI>? 4EB OBPMLKPB FP @LJMRQBA FK QEB QFJB ALJ>FK RPFKD >K FKELRPB QFJB FKQBDO>QFLK P@EBJB ?>PBA LK %RE>JBI P CLOJRI>
1OBRJLKQ " QLQ>I LC >@@BIBOLJBQBOP >OB MI>@BA LKB >Q B>@E KLAB LC QEB KFQB BIBJBKQ JLABI BU@BMQ ?LRKA>OV @LKAFQFLKP 4EB QFJB
Structural Health Monitoring Using Large Sensor Arrays
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ALJ>FK OBPMLKPB PB@LKAP LC JB>PROBJBKQ >Q > P>JMIFKD O>QB LC )W FP @LJMRQBA CLO B>@E >@@BIBOLJBQBO *K LOABO QL PQRAV QEB FJM>@Q LC A>J>DB LK QEB MB>H FKAF@>QLOP MOLMLPBA >P KBT CB>QROBP CLO A>J>DB ABQB@QFLK QEB OBPMLKPB LC QEB ?OFADB FP DBKBO>QBA CLO F QEB RKA>J>DBA PQOR@QROB FF QEB A>J>DBA PQOR@QROB FK TEF@E QEB A>J>DB FP DO>AR>IIV FKQOLAR@BA FK QEB @BKQO>I PM>K LC QEB ?OFADB
'FDROB 4EB A>J>DB FP JLABIIBA ?V > PQFKBPP OBAR@QFLK DLFKD COLJ
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
IFKB>O @LJ?FK>QFLK LC QEB PBKPLO LRQMRQP / + @LJMRQB * *
/ +
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
52
A. Deraemaeker
+)63' &SLIRQFLK LC CLO FKQBOS>IP >KA >P > CRK@QFLK LC QEB P>JMIB KRJ?BO P>JMIBP RKA>J>DBA PQOR@QROB P>JMIBP DO>A R>IIV FK@OB>PFKD A>J>DB FP BUQO>@QBA ?LQE COLJ QEB RKIQBOBA PFDK>I * >KA QEB IQBOBA PFDK>I *
Structural Health Monitoring Using Large Sensor Arrays
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CRIIV >RQLJ>QBA MOL@BAROB CLO CB>QROB BUQO>@QFLK ?>PBA LK LRQMRQLKIV JB> PROBJBKQP LK PQOR@QROBP BU@FQBA ?V >J?FBKQ SF?O>QFLKP 4EB CB>QROBP BU QO>@QBA COLJ JLA>I IQBOP RPFKD QEB QB@EKFNRB ABP@OF?BA EBOB >?LSB @>K QEBK ?B RPBA CLO A>J>DB ABQB@QFLK >P FIIRPQO>QBA CLO BU>JMIB FK %BO>BJ>BHBO BQ >I TEBOB > @LJM>OFPLK TFQE QO>AFQFLK>I CB>QROBP JLABPE>MBP >KA BFDBKCOBNRBK@FBP FP J>AB 4EB J>FK >AS>KQ>DBP LC QEFP QB@EKFNRB >OB QEB SBOV ILT @LJMRQ>QFLK>I @LPQ >KA QEB >RQLJ>QFLK LC QEB MOL@BAROB
Bibliography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
54
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Subspace identification for operational modal analysis ">QCH /?SH>?LM ;H> $OC>I !? /I?=E Katholieke Universiteit Leuven, Structural Mechanics Division Kasteelpark Arenberg 40, B-3001 Leuven Abstract This chapter deals with the estimation of modal parameters from measured vibration data using subspace techniques. An in-depth review of subspace identification for operational modal analysis is provided. In addition, two recent developments are emphasised: the estimation of the probability density function of the modal parameters, and the use of an exogenous force in addition to the unmeasured operational excitation.
1
Introduction
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A. Deraemaeker et al.(eds.), New Trends in Vibration Based Structural Health Monitoring © CISM, Udine 2010
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76
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92 No.
E. Reynders and G. De Roeck Scenario
1 2 3 4 5 6 7 8
Date (1998) 04.08 09.08 10.08 12.08 17.08 18.08 19.08 20.08
9 10 11 12 13 14 15 16 17
25.08 26.08 27.08 31.08 02.09 03.09 07.09 08.09 09.09
Spalling of concrete, 12 2 Spalling of concrete, 24 2 Landslide at abutment Failure of concrete hinge Failure of anchor heads I Failure of anchor heads II Rupture of tendons I Rupture of tendons II Rupture of tendons III
1 reference measurement 2 reference measurement Lowering of pier, 20 Lowering of pier, 40 Lowering of pier, 80 Lowering of pier, 95 Tilt of foundation 3 reference measurement
Description / Simulation of real damage cause Healthy structure After installation of lowering system Settlement of subsoil, erosion
Settlement of subsoil, erosion After lifting of bridge to initial position Vehicle impact, carbonisation and subsequent corrosion of reinforcement Heavy rainfall, erosion Chloride attack, corrosion Corrosion, overstress Erroneous or forgotten injection of tendon tubes, chloride influence
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Subspace Identification for Operational Modal Analysis mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14
(Hz) 3.871 4.823 6.697 8.355 9.769 10.51 12.42 13.21 17.45 19.27 19.68 26.64 / 37.25
CSI-data (Hz) (%) 0.001 0.89 0.008 1.63 0.127 4.23 0.059 8.91 0.005 1.54 0.011 1.45 0.020 3.11 0.033 4.76 0.212 4.34 0.019 2.43 0.080 5.58 0.054 3.20 / / 0.198 3.69
(%) 0.05 0.06 1.45 1.77 0.03 0.06 0.03 0.29 0.38 0.10 0.31 0.11 / 0.48
(Hz) 3.871 4.818 6.722 8.346 9.772 10.50 12.42 13.21 17.52 19.28 19.65 26.62 33.18 37.20
CSI-data/ref (Hz) (%) 0.002 0.88 0.011 1.66 0.028 3.82 0.104 9.37 0.005 1.57 0.007 1.43 0.025 3.15 0.018 4.72 0.169 3.64 0.022 2.46 0.113 5.51 0.055 3.12 0.202 4.33 0.106 3.94
95 MAC (%) 0.04 0.04 0.62 1.33 0.02 0.04 0.12 0.17 1.39 0.06 0.29 0.11 1.78 0.61
1.00 1.00 0.98 0.96 1.00 1.00 1.00 1.00 0.92 1.00 0.98 0.95 / 0.95
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Subspace Identification for Operational Modal Analysis GI>?
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98
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Subspace Identification for Operational Modal Analysis GI>?
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7
Conclusions
1BCM =B;JN?L ;>>L?MM?> NB? ?RNL;=NCIH I@ ?CA?H@L?KO?H=C?M >;GJCHA L;NCIM GI>? MB;J?M ;H> QB?H?P?L JIMMC;F M=;FCHA @;=NILM @LIG G?;MOL?> IJ?L;NCIH;F >;N; =IHP?LMCIH ?FM NB;N ;L? @L?KO?HNFS OM?> CH @ILQ;L> GI>?FCHA I@ PC >CM=L?N?NCG? MN;N?MJ;=? GI>?FM NB;N ;L? C>?HNC?> @LIG G?;MOL?> >;N; Q;M >?LCP?> 1BCM =IH LGM NB;N NB? F;NN?L GI>?FM ;L? P;FC> ;FMI @LIG ; @ILQ;L> JICHN I@ PC?Q #OLNB?LGIL? CN Q;M MBIQH NB;N GI>?FCHA NB? IJ?L;NCIH;F ?R=CN;NCIH >O? NI NOL JL?MMOL? GC=LINL?GILM IL LI;>Q;S IL @IIN@;FF ?R=CN;NCIH
Subspace Identification for Operational Modal Analysis
103
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