Intelligent Control and Automation: International Conference on Intelligent Computing, ICIC 2006, Kunming, China, August, 2006 (Lecture Notes in Control and Information Sciences)
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Library of Congress Control Number: 2006930913 ISSN print edition: 0170-8643 ISSN electronic edition: 1610-7411 ISBN-10 3-540-37255-5 Springer Berlin Heidelberg New York ISBN-13 978-3-540-37255-4 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2006 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Cover design: design & production GmbH, Heidelberg Printed on acid-free paper
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Preface
The International Conference on Intelligent Computing (ICIC) was formed to provide an annual forum dedicated to the emerging and challenging topics in artificial intelligence, machine learning, bioinformatics, and computational biology, etc. It aims to bring together researchers and practitioners from both academia and industry to share ideas, problems and solutions related to the multifaceted aspects of intelligent computing. ICIC 2006 held in Kunming, Yunnan, China, August 16-19, 2006, was the second International Conference on Intelligent Computing, built upon the success of ICIC 2005 held in Hefei, China, 2005. This year, the conference concentrated mainly on the theories and methodologies as well as the emerging applications of intelligent computing. It intended to unify the contemporary intelligent computing techniques within an integral framework that highlights the trends in advanced computational intelligence and bridges theoretical research with applications. In particular, bio-inspired computing emerged as having a key role in pursuing for novel technology in recent years. The resulting techniques vitalize life science engineering and daily life applications. In light of this trend, the theme for this conference was “Emerging Intelligent Computing Technology and Applications”. Papers related to this theme were especially solicited, including theories, methodologies, and applications in science and technology. ICIC 2006 received over 3000 submissions from 36 countries and regions. All papers went through a rigorous peer review procedure and each paper received at least three review reports. Based on the review reports, the Program Committee finally selected 703 high-quality papers for presentation at ICIC 2006. These papers cover 29 topics and 16 special sessions, and are included in five volumes of proceedings published by Springer, including one volume of Lecture Notes in Computer Science (LNCS), one volume of Lecture Notes in Artificial Intelligence (LNAI), one volume of Lecture Notes in Bioinformatics (LNBI), and two volumes of Lecture Notes in Control and Information Sciences (LNCIS). This volume of Lecture Notes in Control and Information Sciences (LNCIS) includes 142 papers covering 4 relevant topics and 1 special session topics. The organizers of ICIC 2006, including Yunan University, the Institute of Intelligent Machines of the Chinese Academy of Science, and Queen’s University Belfast, have made enormous effort to ensure the success of ICIC 2006. We hereby would like to thank the members of the ICIC 2006 Advisory Committee for their guidance and advice, the members of the Program Committee and the referees for their collective effort in reviewing and soliciting the papers, and the members of the Publication Committee for their significant editorial work. We would like to thank Alfred Hofmann, executive editor from Springer, for his frank and helpful advice and guidance throughout and for his support in publishing the proceedings in the Lecture Notes series. In particular, we would like to thank all the authors for contributing their
VI
Preface
papers. Without the high-quality submissions from the authors, the success of the conference would not have been possible. Finally, we are especially grateful to the IEEE Computational Intelligence Society, The International Neural Network Society and the National Science Foundation of China for the their sponsorship. June 2006
De-Shuang Huang Institute of Intelligent Machines Chinese Academy of Sciences, China Kang Li Queen’s University Belfast, UK George William Irwin Queen’s University Belfast, UK
ICIC 2006 Organization
General Chairs:
De-Shuang Huang, China Song Wu, China George W. Irwin, UK
International Advisory Committee Aike Guo, China Alfred Hofmann, Germany DeLiang Wang, USA Erke Mao, China Fuchu He, China George W. Irwin, UK Guangjun Yang, China Guanrong Chen, Hong Kong Guoliang Chen, China Harold Szu, USA John L. Casti, USA Marios M. Polycarpou, USA
Mengchu Zhou, USA Michael R. Lyu, Hong Kong MuDer Jeng, Taiwan Nanning Zheng, China Okyay Knynak, Turkey Paul Werbos, USA Qingshi Zhu, China Ruwei Dai, China Sam Shuzhi GE, Singapore Sheng Zhang, China Shoujue Wang, China Songde Ma, China
Stephen Thompson, UK Tom Heskes, Netherlands Xiangfan He, China Xingui He, China Xueren Wang, China Yanda Li, China Yixin Zhong, China Youshou Wu, China Yuanyan Tang, Hong Kong Yunyu Shi, China Zheng Bao, China
Program Committee Chairs:
Kang Li, UK Prashan Premaratne, Australia
Steering Committee Chairs:
Sheng Chen, UK Xiaoyi Jiang, Germany Xiao-Ping Zhang, Canada
Organizing Committee Chairs:
Yongkun Li, China Hanchun Yang, China Guanghua Hu, China
Special Session Chair:
Wen Yu, Mexico
Tutorial Chair:
Sudharman K. Jayaweera, USA
Publication Chair:
Xiaoou Li, Mexico
VIII
Organization
International Liasion Chair:
C. De Silva, Liyanage, New Zealand
Publicity Chairs:
Simon X.Yang, Canada Jun Zhang, China
Exhibition Chair:
Cheng Peng, China
Program Committee Aili Han, China Arit Thammano, Thailand Baogang Hu, China Bin Luo, China Bin Zhu, China Bing Wang, China Bo Yan, USA Byoung-Tak Zhang, Korea Caoan Wang, Canada Chao Hai Zhang, Japan Chao-Xue Wang, China Cheng-Xiang Wang, UK Cheol-Hong Moon, Korea Chi-Cheng Cheng, Taiwan Clement Leung, Australia Daniel Coca, UK Daqi Zhu, China David Stirling, Australia Dechang Chen, USA Derong Liu, USA Dewen Hu, China Dianhui Wang, Australia Dimitri Androutsos, Canada Donald C. Wunsch, USA Dong Chun Lee, Korea Du-Wu Cui, China Fengling Han, Australia Fuchun Sun, China Girijesh Prasad, UK Guang-Bin Huang, Singapore Guangrong Ji, China Hairong Qi, USA Hong Qiao, China
Hong Wang, China Hongtao Lu, China Hongyong Zhao, China Huaguang Zhang, China Hui Wang, China Vitoantonio Bevilacqua, Italy Jiangtao Xi, Australia Jianguo Zhu, Australia Jianhua Xu, China Jiankun Hu, Australia Jian-Xun Peng, UK Jiatao Song, China Jie Tian, China Jie Yang, China Jin Li, UK Jin Wu, UK Jinde Cao, China Jinwen Ma, China Jochen Till, Germany John Q. Gan, UK Ju Liu, China K. R. McMenemy, UK Key-Sun Choi, Korea Liangmin Li, UK Luigi Piroddi, Italy Maolin Tang, Australia Marko Hoþevar, Slovenia Mehdi Shafiei, Canada Mei-Ching Chen, Taiwan Mian Muhammad Awais, Pakistan Michael Granitzer, Austria Michael J.Watts, New Zealand
Michiharu Maeda, Japan Minrui Fei, China Muhammad Jamil Anwas, Pakistan Muhammad Khurram Khan, China Naiqin Feng, China Nuanwan Soonthornphisaj, Thailand Paolo Lino, Italy Peihua Li, China Ping Guo, China Qianchuan Zhao, China Qiangfu Zhao, Japan Qing Zhao, Canada Roberto Tagliaferri, Italy Rong-Chang Chen, Taiwan RuiXiang Sun, China Saeed Hashemi, Canada Sanjay Sharma, UK Seán McLoone, Ireland Seong G. Kong, USA Shaoning Pang, New Zealand Shaoyuan Li, China Shuang-Hua Yang, UK Shunren Xia, China Stefanie Lindstaedt, Austria Sylvia Encheva, Norway Tai-hoon Kim, Korea Tai-Wen Yue, Taiwan Takashi Kuremoto, Japan Tarık Veli Mumcu, Turkey
Organization
Tian Xiang Mei, UK Tim. B. Littler, UK Tommy W. S. Chow, Hong Kong Uwe Kruger, UK Wei Dong Chen, China Wenming Cao, China Wensheng Chen, China Willi Richert, Germany Worapoj Kreesuradej, Thailand
Xiao Zhi Gao, Finland Xiaoguang Zhao, China Xiaojun Wu, China Xiaolong Shi, China Xiaoou Li, Mexico Xinge You, Hong Kong Xiwen Zhang, China Xiyuan Chen, China Xun Wang, UK Yanhong Zhou, China Yi Shen, China
IX
Yong Dong Wu, Singapore Yuhua Peng, China Zengguang Hou, China Zhao-Hui Jiang, Japan Zhen Liu, Japan Zhi Wang, China Zhi-Cheng Chen, China Zhi-Cheng Ji, China Zhigang Zeng, China Ziping Chiang, Taiwa
Reviewers Xiaodan Wang, Lei Wang, Arjun Chandra, Angelo Ciaramella, Adam Kalam, Arun Sathish, Ali Gunes, Jin Tang, Aiguo He, Arpad Kelemen, Andreas Koschan, Anis Koubaa, Alan Gupta, Alice Wang, Ali Ozen, Hong Fang, Muhammad Amir Yousuf, An-Min Zou, Andre Döring, Andreas Juffinger, Angel Sappa, Angelica Li, Anhua Wan, Bing Wang, Rong Fei, Antonio Pedone, Zhengqiang Liang , Qiusheng An, Alon Shalev Housfater, Siu-Yeung Cho, Atif Gulzar, Armin Ulbrich, Awhan Patnaik, Muhammad Babar, Costin Badica, Peng Bai, Banu Diri, Bin Cao, Riccardo Attimonelli, Baohua Wang, Guangguo Bi, Bin Zhu, Brendon Woodford, Haoran Feng, Bo Ma, Bojian Liang, Boris Bacic, Brane Sirok, Binrong Jin, Bin Tian, Christian Sonntag, Galip Cansever, Chun-Chi Lo, ErKui Chen, Chengguo Lv, Changwon Kim, Chaojin Fu, Anping Chen, Chen Chun , C.C. Cheng, Qiming Cheng, Guobin Chen, Chengxiang Wang, Hao Chen, Qiushuang Chen, Tianding Chen, Tierui Chen, Ying Chen, Mo-Yuen Chow, Christian Ritz, Chunmei Liu, Zhongyi Chu, Feipeng Da, Cigdem Turhan, Cihan Karakuzu, Chandana Jayasooriya, Nini Rao, Chuan-Min Zhai, Ching-Nung Yang, Quang Anh Nguyen, Roberto Cordone, Changqing Xu, Christian Schindler, Qijun Zhao, Wei Lu, Zhihua Cui, Changwen Zheng, David Antory, Dirk Lieftucht, Dedy Loebis, Kouichi Sakamoto, Lu Chuanfeng, Jun-Heng Yeh, Dacheng Tao, Shiang-Chun Liou, Ju Dai , Dan Yu, Jianwu Dang, Dayeh Tan, Yang Xiao, Dondong Cao, Denis Stajnko, Liya De Silva, Damien Coyle, Dian-Hui Wang, Dahai Zhang, Di Huang, Dikai Liu, D. Kumar, Dipak Lal Shrestha, Dan Lin, DongMyung Shin, Ning Ding, DongFeng Wang, Li Dong, Dou Wanchun, Dongqing Feng, Dingsheng Wan, Yongwen Du, Weiwei Du, Wei Deng, Dun-wei Gong, DaYong Xu, Dar-Ying Jan, Zhen Duan, Daniela Zaharie, ZhongQiang Wu, Esther Koller-Meier, Anding Zhu, Feng Pan, Neil Eklund, Kezhi Mao, HaiYan Zhang, Sim-Heng Ong, Antonio Eleuteri, Bang Wang, Vincent Emanuele, Michael Emmerich, Hong Fu, Eduardo Hruschka, Erika Lino, Estevam Rafael Hruschka Jr, D.W. Cui, Fang Liu, Alessandro Farinelli, Fausto Acernese, Bin Fang, Chen Feng, Huimin Guo, Qing Hua, Fei Zhang, Fei Ge, Arnon Rungsawang, Feng Jing, Min Feng, Feiyi Wang, Fengfeng Zhou, Fuhai Li, Filippo Menolascina, Fengli Ren, Mei Guo, Andrés Ferreyra, Francesco Pappalardo, Chuleerat Charasskulchai, Siyao Fu, Wenpeng Ding, Fuzhen Huang, Amal Punchihewa,
X
Organization
Geoffrey Macintyre, Xue Feng He, Gang Leng, Lijuan Gao, Ray Gao, Andrey Gaynulin, Gabriella Dellino, D.W. Ggenetic, Geoffrey Wang, YuRong Ge, Guohui He, Gwang Hyun Kim, Gianluca Cena, Giancarlo Raiconi, Ashutosh Goyal, Guan Luo, Guido Maione, Guido Maione, Grigorios Dimitriadis, Haijing Wang, Kayhan Gulez, Tiantai Guo, Chun-Hung Hsieh, Xuan Guo, Yuantao Gu, Huanhuan Chen, Hongwei Zhang, Jurgen Hahn, Qing Han, Aili Han, Dianfei Han, Fei Hao, Qing-Hua Ling, Hang-kon Kim, Han-Lin He, Yunjun Han, Li Zhang, Hathai Tanta-ngai, HangBong Kang, Hsin-Chang Yang, Hongtao Du, Hazem Elbakry, Hao Mei, Zhao L, Yang Yun, Michael Hild, Heajo Kang, Hongjie Xing, Hailli Wang, Hoh In, Peng Bai, Hong-Ming Wang, Hongxing Bai, Hongyu Liu, Weiyan Hou, Huaping Liu, H.Q. Wang, Hyungsuck Cho, Hsun-Li Chang, Hua Zhang, Xia Huang, Hui Chen, Huiqing Liu, Heeun Park, Hong-Wei Ji, Haixian Wang, Hoyeal Kwon, H.Y. Shen, Jonghyuk Park, Turgay Ibrikci, Mary Martin, Pei-Chann Chang, Shouyi Yang, Xiaomin Mu, Melanie Ashley, Ismail Altas, Muhammad Usman Ilyas, Indrani Kar, Jinghui Zhong, Ian Mack, Il-Young Moon, J.X. Peng , Jochen Till, Jian Wang, Quan Xue, James Govindhasamy, José Andrés Moreno Pérez, Jorge Tavares, S. K. Jayaweera, Su Jay, Jeanne Chen, Jim Harkin, Yongji Jia, Li Jia, Zhao-Hui Jiang, Gangyi Jiang, Zhenran Jiang, Jianjun Ran, Jiankun Hu, Qing-Shan Jia, Hong Guo, Jin Liu, Jinling Liang, Jin Wu, Jing Jie, Jinkyung Ryeu, Jing Liu, Jiming Chen, Jiann-Ming Wu, James Niblock, Jianguo Zhu, Joel Pitt, Joe Zhu, John Thompson, Mingguang Shi, Joaquin Peralta, Si Bao Chen, Tinglong Pan, Juan Ramón González González, JingRu Zhang, Jianliang Tang, Joaquin Torres, Junaid Akhtar, Ratthachat Chatpatanasiri, Junpeng Yuan, Jun Zhang, Jianyong Sun, Junying Gan, Jyh-Tyng Yau, Junying Zhang, Jiayin Zhou, Karen Rosemary McMenemy, Kai Yu, Akimoto Kamiya, Xin Kang, Ya-Li Ji, GuoShiang Lin, Muhammad Khurram, Kevin Curran, Karl Neuhold, Kyongnam Jeon, Kunikazu Kobayashi, Nagahisa Kogawa, Fanwei Kong, Kyu-Sik Park, Lily D. Li, Lara Giordano, Laxmidhar Behera, Luca Cernuzzi, Luis Almeida, Agostino Lecci, Yan Zuo, Lei Li, Alberto Leva, Feng Liang, Bin Li, Jinmei Liao, Liang Tang, Bo Lee, Chuandong Li, Lidija Janezic, Jian Li, Jiang-Hai Li, Jianxun Li, Limei Song, Ping Li, Jie Liu, Fei Liu, Jianfeng Liu, Jianwei Liu, Jihong Liu, Lin Liu, Manxi Liu, Yi Liu, Xiaoou Li, Zhu Li, Kun-hong Liu, Li Min Cui, Lidan Miao, Long Cheng , Huaizhong Zhang, Marco Lovera, Liam Maguire, Liping Liu, Liping Zhang, Feng Lu, Luo Xiaobin, Xin-ping Xie, Wanlong Li, Liwei Yang, Xinrui Liu, Xiao Wei Li, Ying Li, Yongquan Liang, Yang Bai, Margherita Bresco, Mingxing Hu, Ming Li, Runnian Ma, Meta-Montero Manrique, Zheng Gao, Mingyi Mao, Mario Vigliar, Marios Savvides, Masahiro Takatsuka, Matevz Dular, Mathias Lux, Mutlu Avci, Zhifeng Hao, Zhifeng Hao, Ming-Bin Li, Tao Mei, Carlo Meloni, Gennaro Miele, Mike Watts, Ming Yang, Jia Ma, Myong K. Jeong, Michael Watts, Markus Koch, Markus Koch, Mario Koeppen, Mark Kröll, Hui Wang, Haigeng Luo, Malrey Lee, Tiedong Ma, Mingqiang Yang, Yang Ming, Rick Chang, Nihat Adar, Natalie Schellenberg, Naveed Iqbal, Nur Bekiroglu, Jinsong Hu, Nesan Aluha, Nesan K Aluha, Natascha Esau, Yanhong Luo, N.H. Siddique, Rui Nian, Kai Nickel, Nihat Adar, Ben Niu, Yifeng Niu, Nizar Tayem, Nanlin Jin, Hong-Wei Ji, Dongjun Yu, Norton Abrew, Ronghua Yao, Marco Moreno-Armendariz, Osman Kaan Erol, Oh Kyu Kwon, Ahmet Onat, Pawel Herman, Peter Hung, Ping Sun, Parag Kulkarni, Patrick Connally, Paul Gillard, Yehu Shen,
Organization
XI
Paul Conilione, Pi-Chung Wang, Panfeng Huang, Peter Hung, Massimo Pica Ciamarra, Ping Fang, Pingkang Li, Peiming Bao, Pedro Melo-Pinto, Maria Prandini, Serguei Primak, Peter Scheir, Shaoning Pang, Qian Chen, Qinghao Rong, QingXiang Wu, Quanbing Zhang, Qifu Fan, Qian Liu, Qinglai Wei, Shiqun Yin, Jianlong Qiu, Qingshan Liu, Quang Ha, SangWoon Lee , Huaijing Qu, Quanxiong Zhou , Qingxian Gong, Qingyuan He, M.K.M. Rahman, Fengyuan Ren, Guang Ren, Qingsheng Ren, Wei Zhang, Rasoul Milasi, Rasoul Milasi, Roberto Amato, Roberto Marmo, P. Chen, Roderick Bloem, Hai-Jun Rong, Ron Von Schyndel, Robin Ferguson, Runhe Huang, Rui Zhang, Robin Ferguson, Simon Johnston, Sina Rezvani, Siang Yew Chong, Cristiano Cucco, Dar-Ying Jan, Sonya Coleman, Samuel Rodman, Sancho SalcedoSanz, Sangyiel Baik, Sangmin Lee, Savitri Bevinakoppa, Chengyi Sun, Hua Li, Seamus McLoone, Sean McLoone, Shafayat Abrar, Aamir Shahzad, Shangmin Luan, Xiaowei Shao, Shen Yanxia, Zhen Shen, Seung Ho Hong, Hayaru Shouno, Shujuan Li, Si Eng Ling, Anonymous, Shiliang Guo, Guiyu Feng, Serafin Martinez Jaramillo, Sangwoo Moon, Xuefeng Liu, Yinglei Song, Songul Albayrak, Shwu-Ping Guo, Chunyan Zhang, Sheng Chen, Qiankun Song, Seok-soo Kim, Antonino Staiano, Steven Su, Sitao Wu, Lei Huang, Feng Su, Jie Su, Sukree Sinthupinyo, Sulan Zhai, Jin Sun, Limin Sun, Zengshun Zhao, Tao Sun, Wenhong Sun, Yonghui Sun, Supakpong Jinarat, Srinivas Rao Vadali, Sven Meyer zu Eissen, Xiaohong Su, Xinghua Sun, Zongying Shi, Tony Abou-Assaleh, Youngsu Park, Tai Yang, Yeongtak Jo, Chunming Tang, Jiufei Tang, Taizhe Tan, Tao Xu, Liang Tao, Xiaofeng Tao, Weidong Xu, Yueh-Tsun Chang, Fang Wang, Timo Lindemann, Tina Yu, Ting Hu, Tung-Kuan Liu, Tianming Liu, Tin Lay Nwe, Thomas Neidhart, Tony Chan, Toon Calders, Yi Wang, Thao Tran, Kyungjin Hong, Tariq Qureshi, Tung-Shou Chen, Tsz Kin Tsui, Tiantian Sun, Guoyu Tu, Tulay Yildirim, Dandan Zhang, Xuqing Tang, Yuangang Tang, Uday Chakraborty, Luciana Cariello, Vasily Aristarkhov, Jose-Luis Verdegay, Vijanth Sagayan Asirvadam, Vincent Lee, Markus Vincze, Duo Chen, Viktoria Pammer, Vedran Sabol, Wajeeha Akram, Cao Wang , Xutao Wang, Winlen Wang, Zhuang Znuang, Feng Wang, Haifeng Wang, Le Wang, Wang Linkun, Meng Wang, Rongbo Wang, Xin Wang, Xue Wang, Yan-Feng Wang, Yong Wang, Yongcai Wang, Yongquan Wang, Xu-Qin Li, Wenbin Liu, Wudai Liao, Weidong Zhou, Wei Li, Wei Zhang, Wei Liang, Weiwei Zhang, Wen Xu, Wenbing Yao, Xiaojun Ban, Fengge Wu, Weihua Mao, Shaoming Li, Qing Wu, Jie Wang, Wei Jiang, W Jiang, Wolfgang Kienreich, Linshan Wang, Wasif Naeem, Worasait Suwannik, Wolfgang Slany, Shijun Wang , Wooyoung Soh, Teng Wang, Takashi Kuremoto, Hanguang Wu, Licheng Wu, Xugang Wang, Xiaopei Wu, ZhengDao Zhang, Wei Yen, Yan-Guo Wang, Daoud Ait-Kadi, Xiaolin Hu, Xiaoli Li, Xun Wang, Xingqi Wang, Yong Feng, Xiucui Guan, Xiao-Dong Li, Xingfa Shen, Xuemin Hong, Xiaodi Huang, Xi Yang, Li Xia, Zhiyu Xiang, Xiaodong Li, Xiaoguang Zhao, Xiaoling Wang, Min Xiao, Xiaonan Wu, Xiaosi Zhan, Lei Xie, Guangming Xie, Xiuqing Wang, Xiwen Zhang, XueJun Li, Xiaojun Zong, Xie Linbo, Xiaolin Li, Xin Ma, Xiangqian Wu, Xiangrong Liu, Fei Xing, Xu Shuzheng, Xudong Xie, Bindang Xue, Xuelong Li, Zhanao Xue, Xun Kruger, Xunxian Wang, Xusheng Wei, Yi Xu, Xiaowei Yang, Xiaoying Wang, Xiaoyan Sun, YingLiang Ma, Yong Xu, Jongpil Yang, Lei Yang, Yang Tian, Zhi Yang, Yao Qian, Chao-bo Yan, Shiren Ye,
XII
Organization
Yong Fang, Yanfei Wang, Young-Gun Jang, Yuehui Chen, Yuh-Jyh Hu, Yingsong Hu, Zuoyou Yin, Yipan Deng, Yugang Jiang, Jianwei Yang, Yujie Zheng, Ykung Chen, Yan-Kwang Chen, Ye Mei, Yongki Min, Yongqing Yang, Yong Wu, Yongzheng Zhang, Yiping Cheng, Yongpan Liu, Yanqiu Bi, Shengbao Yao, Yongsheng Ding, Haodi Yuan, Liang Yuan, Qingyuan He, Mei Yu, Yunchu Zhang, Yu Shi, Wenwu Yu, Yu Wen, Younghwan Lee, Ming Kong, Yingyue Xu, Xin Yuan, Xing Yang, Yan Zhou, Yizhong Wang, Zanchao Zhang, Ji Zhicheng, Zheng Du, Hai Ying Zhang, An Zhang, Qiang Zhang, Shanwen Zhang, Shanwen Zhang, Zhang Tao, Yue Zhao, R.J. Zhao, Li Zhao, Ming Zhao, Yan Zhao, Bojin Zheng, Haiyong Zheng, Hong Zheng, Zhengyou Wang, Zhongjie Zhu, Shangping Zhong, Xiaobo Zhou, Lijian Zhou, Lei Zhu, Lin Zhu, Weihua Zhu, Wumei Zhu, Zhihong Yao, Yumin Zhang, Ziyuan Huang, Chengqing Li, Z. Liu, Zaiqing Nie, Jiebin Zong, Zunshui Cheng, Zhongsheng Wang, Yin Zhixiang, Zhenyu He, Yisheng Zhong, Tso-Chung Lee, Takashi Kuremoto Tao Jianhua, Liu Wenjue, Pan Cunhong, Li Shi, Xing Hongjie, Yang Shuanghong, Wang Yong, Zhang Hua, Ma Jianchun, Li Xiaocui, Peng Changping, Qi Rui, Guozheng Li, Hui Liu, Yongsheng Ding, Xiaojun Liu, Qinhua Huang
A Unified Framework of Morphological Associative Memories Naiqin Feng1,2, Yuhui Qiu2, Fang Wang2, and Yuqiang Sun1 1
College of Computer & Information Technology, Henan Normal University, Xinxiang 453007 2 Faculty of Computer & information Science, South West-China University, Chongqing 400715 [email protected]
Abstract. The morphological neural network models, including morphological associative memories (MAM), fuzzy morphological associative memories (FMAM), enhanced morphological associative memories (EFMAM), etc., are extremely new artificial neural networks. They have many attractive advantages such as unlimited storage capacity, one-short recall speed and good noisetolerance to erosive or dilative noise. Although MAM, FMAM and EFMAM are different and easily distinguishable from each other, they have the same morphological theory base. Therefore in this paper a unified theoretical framework of them is presented. The significance of the framework consists in: (1) It can help us find some new methods, definitions and theorems for morphological neural networks; (2) We have a deeper understanding of MAM, FMAM and EFMAM while having the unified theoretical framework.
proposed the concept of morphological associative memories (MAM) and the concept of morphological auto-associative memories (auto-MAM) [7], which constitute a class of networks not previously discussed in detail. MAM is based on the algebraic lattice structure ( R, ∧, ∨ , + ) or morphological operations. MAM behaves more like human associative memories than the traditional semilinear models such as the Hopfield net. Once a pattern has been memorized, recall is instantaneous when the MAM is presented with the pattern. In the absence of noise, an auto-MAM will always provide perfect recall for any number of patterns programmed into its memory. The auto-MAM MXX is extremely robust in recalling patterns that are distorted due to dilative changes, while auto-MAM WXX is extremely robust in recalling patterns that are distorted due to erosive changes. In 2003, Wang and Chen presented the model of fuzzy morphological associative memories (FMAM). Originated from the basic ideas of MAM, the FMAM uses two basic morphological operations (∧, ⋅) , (∨ , ⋅) instead of fuzzy operation (∧, ∨ ) in fuzzy associative memory [13]. FMAM solves fuzzy rules memory problem of the MAM. Under certain conditions, FMAM can be viewed as a new encoding way of fuzzy associative memory such that it can embody fuzzy operators and the concepts of fuzzy membership value and fuzzy rules. Both auto-FMAM and auto-MAM have the same attractive advantages, such as unlimited storage capacity, one-shot recall speed and good noise-tolerance to either erosive or dilative noise. However, they suffer from the extreme vulnerability to noise of mixing erosion and dilation, resulting in great degradation on recall performance. To overcome this shortcoming, in 2005, Wang and Chen further presented an enhanced FMAM (EFMAM) based on the empirical kernel map [14]. Although MAM, FMAM and EFMAM are different and easily distinguishable from each other, we think that they have the same theoretical base, i.e. the same morphological base, therefore they can be unified together. This paper tries to establish a unified theoretical framework of MAM, FMAM and EFMAM. The more the thing is abstracted, the deeper the thing is understood. Consequently it is possible that some new methods and theorems are obtained. This is the reason why we research and propose the unified theoretical framework of MAM, FMAM and EFMAM
2 Unified Computational Base of MAM, FMAM and EFMAM Traditional artificial neural network models are specified by the network topology, node characteristics, and training or learning rules. The underlying algebraic system used in these models is the set of real numbers R together with the operations of addition and multiplication and the laws governing these operations. This algebraic system, known as a ring, is commonly denoted by ( R, +, ×) . The basic computations occurring in the morphological network proposed by Ritter et al. are based on the algebraic lattice structure ( R, ∧, ∨ , + ) , where the symbols ∧ and ∨ denote the binary operations of minimum and maximum, respectively, while the basic computations used in FMAM and EFMAM are based on the algebraic lattice structure ( R + , ∧ , ∨ , ⋅) ( R + = (0, ∞ )) .
A Unified Framework of Morphological Associative Memories
3
In unified morphological associative memories (UMAM), the basic computations are based on the algebraic lattice structure (U , ∧ , ∨ , O ) , where U=R, or U = R+; O=
㧙
+, , ⋅ , or /. If U=R and O=+, then (U , ∧ , ∨ , O ) = ( R , ∧ , ∨ , + ) , which is the computational base of MAM; If U=R+ and O= ⋅ , then (U , ∧ , ∨ , O ) = ( R + , ∧ , ∨ , ⋅ ) , which is the computational base of FMAM and EFMAM. Of course, the symbol O or /. also can be other appreciated operators, for example,
㧙
3 Unified Morphological-Norm Operators 3.1 Operators in MAM, FMAM and EFMAM As that described in the preceding section, morphological associative memories are based on the lattice algebra structure ( R, ∧, ∨ , + ) . Suppose we are given a vector pair
Щ
Щ
x=(x1,…, xn)ƍ Rn, , and y=(y1,…,ym) Rm. An associative morphological memory that will recall the vector y when presented the vector x is given by
W is called the max product of y and x. We also can denote the min product of y and x using operator ш Ƒ like (1) and (2). Similarly, let (x1, y1),…,(xk, yk) be k vector pairs with ȟ ȟ ȟ ȟ xȟ=(x1 ,…, xn )ƍ Rn and yȟ=(y1 ,…, ym )ƍ Rm for ȟ=1,…, k. For a given set of pattern ȟ ȟ associations {(x , y ): ȟ=1,…, k} we define a pair of associated pattern matrices (X,Y), j where X = (x1,", x k ) , Y = (y1 , ", y k ) . Thus, X is of dimension n×k with i, jth entry xi
Щ
Щ
j
and Y is of dimension m×k with i, jth entry yi . With each pair of matrices (X,Y), two natural morphological m×n memories WXY and MXY are defined by k Ƒ ( −x ȟ ) '] and M XY = ∨ k [ y ȟ щ Ƒ ( −x ȟ ) '] . WXY = ∧ ξ =1[ y ȟ ш ξ =1
(3)
Ƒ (-xȟ)ƍ= yȟщ Ƒ (-xȟ)ƍ. It therefore follows from this definition that Obviously, yȟш
WXYyȟш Ƒ (-xȟ)ƍ=yȟщ Ƒ (-xȟ)ƍMXY, ∀ ȟ=1,…, k.
(4)
In view of equations (2) and (3), this last set of inequalities implies that WXYщ Ƒ xȟ[yȟш Ƒ (-xȟ)ƍ] щ Ƒ xȟ=yȟ= [yȟщ Ƒ (-xȟ)ƍ] ш Ƒ xȟMXYш Ƒ xȟ
(5)
∀ ȟ=1,…, k or, equivalently, that
WXY щ Ƒ X Y MXY ш Ƒ X.
(6)
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N. Feng et al.
Ƒ X =Y, then WXY is called a щ Ƒ -perfect memory for (X, Y); if MXYш Ƒ X= Y, If WXYщ then MXY is called a ш Ƒ -perfect memory for (X, Y). The basic computations used in FMAM and EFMAM are based on the algebraic l l l lattice structure ( R + , ∧, ∨ , ⋅) ( R + = (0, ∞ )) . If the input vector x = ( x1 , " , xn ) ' is
defined in R + , and the output vector y = ( y1 , " , ym ) ' is defined in R + , by using some transformation, for example, exp (x) and exp (y) (acting on each component of n m x, y), the input vectors and output vectors can be transformed into R + and R + , respectively. Set X = (x1,", x k ) , Y = (y1 ,", y k ) , with each pair of matrices (X, Y), two new morphological m × n memories AXY and BXY are as follows: l
where ш ż and щ ż denote fuzzy composite operation (∧, ⋅) and (∨ , ⋅) often used in fuzzy set theory, respectively. In FMAM and EFMAM, the recall is given by AXYщ ż xl=(
ш y шż(x ) )щżx and B k l=1
l
l -1
l
ш
l XY ż x =(
щ y щż(x ) )шżx k l=1
l
l -1
l
(10)
With analyzing for MAM, FMAM and EFMAM, we can easily see that there exist reversible operators in memory and recall. For MAM, the reversible operators in memory and recall are – and +, respectively; for FMAM and EFMAM, they are / and ×, respectively. We unify them with the following definitions.
3.2 Unified Morphological-Norm Operators Definition 1. For an m×p matrix A and a p×n matrix B with entries from U, the o matrix product C =A щ B, also called the morphological max product norm of A and B, is defined by
cij = ∨ k =1aik Ο bkj = (ai1Οb1 j ) ∨ (ai 2 Οb2 j ) ∨ " ∨ (aip Ο bpj ) . p
o
(11) +
-
Φ
Where, щ is a unified morphological operator, which represents one of the щ , щ , щ , /
and щ . The symbol Ɉ represents a reversible operation, such as +,
㧙, ×, or /.
Definition 2. For an m×p matrix A and a p×n matrix B with entries from U, the o matrix product C =A ш B, also called the morphological min product norm of A and B, is defined by
A Unified Framework of Morphological Associative Memories
5
cij = ∧ k =1aik Ο bkj = (ai1Οb1 j ) ∧ (ai 2 Οb2 j ) ∧ " ∧ (aip Ο bpj ) . p
(12)
o
+
Φ
-
Where, ш is a unified morphological operator, which represents one of the ш , ш , ш , /
and ш . The symbol Ɉ represents a reversible operation, such as +,
㧙, ×, or /.
Definition 3. For an m×p matrix A and a p×n matrix B with entries from U and the + + max product C =A щ B, the morphological operator щ is defined by:
Similarly, we can define the morphological operators
(14)
ш- , Φш , or ш/ .
ȟ
Щ
Definition 5. Let (x1, y1),…,(xk, yk) be k vector pairs with xȟ=(x1 ,…, xn )ƍ Rn and ȟ ȟ yȟ=(y1 ,…, ym )ƍ Rm for ȟ=1,…, k. For a given set of pattern associations {(xȟ, yȟ): ȟ=1,…, k} and a pair of associated pattern matrices (X,Y), where X = (x1,", x k ) , Y = (y1 , ", y k ) , the morphological min-product memory WXY is defined by ȟ
Since y ȟ ш ( x ȟ ) ' = y ȟ щ ( x ȟ ) ' , WXY and MXY follow from this definition that WXY y ȟ ш ( x ȟ ) ' = y ȟ щ ( x ȟ ) ' MXY ∀ξ = 1, " , k o
o
(17)
Let ш represents the reverse of ш , and щ represents the reverse of щ , that is, Ɉ and Ĭ are reversible each other. If Ɉ=+ or ×, then Ĭ= or ÷; on the contrary, if Ɉ= or ÷, then Ĭ=+ or ×. Then, WXY and MXY satisfy that Ĭ
o
Ĭ
㧙
o
㧙
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WXY щ x ξ ≤ [ y ξ ш Ĭ
Ɉ
щ
(18)
Ĭ
(19)
(xξ ) '] щĬ xξ = y ξ = [yξ o (xξ ) '] шĬ xξ ≤ MXYшĬ xξ
∀ξ = 1, " , k or equivalently, that Ĭ
WXY щ X ≤ Y ≤ MXY ш X o
Definition 6. A matrix A=(aij)m×n is said to be a щ -perfect memory for (X,Y) if and o o only if Aщ X =Y. The matrix A=(aij)m×n is said to be a ш -perfect memory for (X,Y) if o
and only if Aш X = Y. In fact, in the existing MAM there are only two memories WXY and MXY defined by using operators ш and щ , respectively. In the existing FMAM and EFMAM, it is also the same, i.e. there are only two memories WXY and MXY defined by using / / operators ш and щ , respectively. But according to the definitions 1 to 6, there will be four memories in MAM, FMAM or EFMAM, respectively. The two additional + + Φ Φ memories defined by using operators ш and ш (for MAM), and by using ш and щ (for FMAM or EFMAM), respectively. That is to say, there are more methods in the unified framework than there are in MAM, FMAM and EFMAM.
4 Unified Morphological Theorems Ritter gave 7 theorems with respect to MAM in [7]. Wang et al. also proved 6 theorems with respect to FMAM in [13] and 4 theorems with respect to EFMAM in [14]. Our research result shows that these theorems can be unified. We give two of them and their proofs as two examples. Theorem 1: If A is щ -perfect memory for (X, Y) and B is ш -perfect memory for (X, Y), then o
o
AWXYMXYB and WXY
щo X = Y =M шo X. XY
Proof of Theorem 1: If A is щ -perfect memory for (X, Y), then (A щ xȟ )i =y i for all ȟ = 1,…, k and all i=1,…, m. Equivalently o
∨
n j =1
( a ij Ο x ξj ) = y iξ
o
∀ ξ = 1, " , k
and
ȟ
∀ i = 1, " , m .
For MAM, U=R, Ɉ=±, Ĭ= B , it follows that for an arbitrary index j ∈ {1, " , n} we have
a ij Ο x ξj ≤ y iξ
∀ ξ = 1, " , k
⇔ a ij ≤ y iξ Θ x ξj ⇔ a ij ≤
For FMAM and EFMAM, U=R+, Ɉ=× or also can be derived.
∧ξ
k =1
∀ ξ = 1, " , k
( y iξ Θ x ξj ) = w ij
(20)
㧛, Ĭ=㧛 or ×, the set of inequalities (20)
A Unified Framework of Morphological Associative Memories
7
This shows that AWXY. In view of (19), we now have Y=A щ XWXY щ XY, o
o
and therefore, WXY щ X=Y. A similar argument shows that if B is ш -perfect memory o
o
for (X, Y), then MXYB and MXY ш X=Y. Consequently we have AWXYMXYB o
̱
and WXY щ X = Y =MXY ш X. o
o
o
Theorem 2: WXY is щ -perfect memory for (X, Y) if and only if for each ȟ = 1,…, k, o
Ĭ
each row of the matrix [yȟ щ (xȟ)ƍ]- WXY contains a zero entry. Similarly, MXY is ш perfect memory for (X, Y) if and only if for each ȟ = 1,…, k, each row of the matrix Ĭ MXY -[yȟ щ (xȟ)ƍ] contains a zero entry.
Proof of Theorem 2: We only prove the theorem in one domain for either the memory WXY or the memory MXY. The result of proof for the other memory can be derived in an analogous fashion. o WXY is щ -perfect memory for (X, Y) ⇔ ( WXY щ x ξ ) i = y iξ ∀ȟ =1,…,k and ∀i =1,…,m o
⇔ y iξ − ( WXY щ x ξ ) i = 0 ∀ȟ =1,…,k and ∀i =1,…,m o
∨
⇔ y iξ −
∧ ⇔ ∧ ⇔ ∧ ⇔
n j =1 n j =1 n
n j =1
( wij Ο x ξj ) = 0 ∀ȟ =1,…,k and ∀i =1,…,m
( y iξ − ( wij Ο x ξj )) = 0 ∀ȟ =1,…,k and ∀i =1,…,m ( y iξ Θ x ξj − wij ) = 0 ∀ȟ =1,…,k and ∀i =1,…,m Ĭ
([ y ξ щ ( x ξ ) '] − WXY ) ij = 0 ∀ȟ =1,…,k and ∀i =1,…,m
j =1
This last set of equations is true if and only if for each ȟ=1,…,k and each integer i Ĭ =1,…,m, each column entry of the ith row of [yȟ щ (xȟ)ƍ]- WXY contains at least one zero entry.
̱
We need to note that the conditions the equation set given above holds are different for MAM and for FMAM or EFMAM. For MAM, it holds in U=R; for FMAM or EFMAM, it holds in U=R+.
5 Discussions What are the advantages of the unified framework of morphological associative memories? We think that there are at least three benefits in it: Firstly, the unified theoretical framework is beneficial to understanding the MAM, FMAM and EFMAM. This paper analyzes the common properties of MAM, FMAM and EFMAM, and establishes the theoretical framework of unified morphological associative memory (UMAM) by extracting these common properties. The more the thing is abstracted, the deeper the thing is understood. Therefore the UMAM is of great benefit to us in research and applications with respect to MAM, FMAM and EFMAM. Secondly, the UMAM can help us find some new methods. In fact, the method of defining the morphological memory WXY or MXY in MAM, FMAM or EFMAM is
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not unique. For example, according to (15) and (16), the WXY and MXY also can be defined by: WXY= ∧ ξK=1 ( y ξ
1
And MXY= ∨ ξK=1 ( y ξ
1
+ ξ ξ 2 K ξ Φ ш ( x ) ') or WXY= ∧ ξ =1 ( y ш ( x ) ')
+ ξ ξ 2 K ξ Φ щ (x ) ') or MXY= ∨ ξ =1 ( y щ (x ) ')
(21)
(22)
Consequently, there are more methods defining the memories WXY and MXY in the UMAM. Finally, the methods in the UMAM are complementary rather than competitive. For this reason, it is frequently advantageous to use these methods in combination rather than exclusively.
The three experiments given above show that the methods in UMAM are complementary, and therefore the UMAM can solve more associative memory problems, especially to hetero-MAM, hetero-FMAM and hetero-EFMAM.
7 Conclusions This paper introduces a new unified theoretical framework of neural-network computing based on lattice algebra. The main emphasis of this paper was on the unification of morphological associative memories, fuzzy morphological associative memories, and enhanced fuzzy morphological associative memories. Our research and experiments showed that the MAM, FMAM and EFMAM could be unified in the same theoretical framework. The significance of the unified framework consisted in: on the one hand we got a better and deeper understanding of the MAM, FMAM and EFMAM from the unified framework UMAM; on the other hand we obtained some new methods from it. Therefore the UMAM can solve more problems of the associative memories than the MAM, FMAM, and EFMAM do. The lattice algebraic approach to neural-network theory is new and a multitude of open questions await exploration. For example, new methods of morphological associative memory need further investigation; the application base of the unified framework needs expanding, etc. It is our hope that these problems will be better solved in the future.
A Unified Framework of Morphological Associative Memories
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Acknowledgments This research is supported by the Science Fund of Henan Province, China (0511012300) and key project of Information and Industry Department of Chongqing City, China (200311014).
References 1. Raducanu,B., Grana, M., Albizuri, F. X.: Morphological Scale Spaces and Associative Memories: Results on Robustness and Practical Applications, J. Math. Image. Vis., vol. 19, no. 2 (2003), 113-131. 2. Suarez-Araujo, C. P.: Novel Neural Network Models for Computing Homothetic in Variances: An Image Algebra Notation,” J. Math. Imaging and Vision, vol. 7, no. 1 (1997), 69-83. 3. Huang, D.S., Systematic Theory of Neural Networks for Pattern Recognition (in Chinese), Publishing House of Electronic Industry of China, May (1996) 4. Huang, D.S.,“On the Modular Associative Neural Network Classifiers, The 5th National United conf on Computer and Application, Beijing, Vol.3 Dec. (1999).7.285-7.290. 5. Ritter, G. X., Urcid, G.: Lattice Algebra Approach to Single-neuron Computation, IEEE Transactions on Neural Networks, Vol. 14, No. 2, (2003), 282-295. 6. Ritter, G. X., Sussner, P.: An Introduction to Morphological Neural Networks, in Proc. 13th Int. Conf. Pattern Recognition, Vienna, Austria, (1996), 709-717. 7. Ritter, G. X., Sussner, P., Diaz-de-Leon, J. L.: Morphological Associative Memories. IEEE Transactions on Neural Networks, Vol. 9, No. 2, (1998) 281-293. 8. Ritter, G. X., Recent Developments in Image Algebra, in Advances in Electronics and Electron Physics, P. Hawkes, Ed. New York: Academic, vol. 80, (1991) 243-380. 9. Davidson, J. L., Hummer,F.: Morphology Neural Networks: An Introduction with Applications, IEEE System Signal Processing, vol. 12, no. 2, (1993) 177-210. 10. Davidson, J. L., Ritter, G. X., A Theory of Morphological Neural Networks, in Digital Optical Computing , vol. 1215 of Proc. SPIE, July (1990) 378-388. 11. Davidson, J. L., Strivastava, R.: Fuzzy Image Algebra Neural Network for Template Identification, in 2nd Annu. Midwest Electrotechnol. Conf., Ames, IA, Apr. (1993) 68-71. 12. Pessoa,L. F. C., Maragos, P.: Neural Networks with Hybrid Morphological/rank/linear nodes: A Unifying Framework with Applications to Handwritten Character Recognition, Pattern Recognition, vol. 33, Jun. (2000) pp. 945-960. 13. Wang, M., Wang, S. T., Wu, X. J., Initial Results on Fuzzy Morphological Associative Memories, ACTA ELECTRONICA SINICA (in Chinese), vol. 31, May (2003) 690-693. 14. Wang, M., Chen, S. C., Enhanced FMAM Based on Empirical Kernel Map, IEEE Transactions on Neural Networks, vol. 16, no. 3, (2005) pp. 557-564, 15. Gader, P. D., Khabou, M. A., Koldobsky, A.: Morphological Regularization Neural Network s, Pattern Recognition, vol. 33, Jun. (2000) 935-944. 16. Sussner, P.: Generalizing Operations of Binary Morphological Associative Memories Using Fuzzy Set Theory, J. Math. Image. Vis., vol. 19, no. 2, (2003) 81-93.
A New Speech Denoising Method Based on WPD-ICA Feature Extraction Qinghua Huang, Jie Yang, and Yue Zhou Institute of Image Processing & Pattern Recognition, Shanghai Jiaotong University, Shanghai, China, 200240 {qinghua, jieyang, zhouyue}@sjtu.edu.cn
Abstract. Independent Component Analysis (ICA) feature extraction is an efficient sparse coding method for noise suppression. However, single channel signal can not be directly applied in ICA feature extraction. In this paper, we propose a new method using wavelet packet decomposition (WPD) as preprocessing for single channel data. Wavelet packet coefficients (WPCs) provide multi-channel data as input data to learn ICA basis vectors. Furthermore we project input data onto the basis vectors to get sparser and independent coefficients. Appropriate nonlinear shrinkage function is used onto the components of sparse coefficients so as to reduce noise. The proposed approach is very efficient with respect to signal recovery from noisy data because not only the projection coefficients are sparser based on WPCs but both the features and the shrinkage function are directly estimated from the observed data. The experimental results have shown that it has excellent performance on signal to noise ratio (SNR) enhancement compared with other filtering methods.
1 Introduction Data decomposition and representation are widely used in signal processing. One of the simplest methods is to use linear transformation of the observed data. Given observation (often called sensor or data) matrix X ∈ * m× N , perform the linear transformation X = AS + η .
A New Speech Denoising Method Based on WPD-ICA Feature Extraction
13
independence and sparsity are consistent since sparsity is equivalent to supergaussian or leptokurtosis. The coefficients of ICA basis vectors usually have a sparse distribution then resulting in statistically efficient codes. Therefore ICA as a feature extraction method has been widely used in extracting efficient speech features and reducing noise[2,3]. However ICA requires signal from at least two separate sensors. For single channel data many ICA feature extraction methods directly segment the data into data matrix[4,5] and learn ICA feature basis using noise-free training signal as a prior knowledge[6]. Direct segmentation is based on the assumption that signal is stationary within a short time. But the assumption is approximate and not strict. Noise-free signal isn’t obtained in many practical applications. To overcome these limitations, we propose to use WPD to pre-process the observed data from a single sensor and then use the WPCs at different frequencies as input to learn ICA basis vectors. Furthermore we apply the sparsity of projection coefficients to reduce noise. Our method has advantages over other filtering methods in that both speech features and the nonlinear shrinkage function are estimated directly from the signals. Based on the sparsity of WPCs, the projection coefficients of ICA basis vectors are sparser. Experimental results have shown that the presented method is more efficient to reduce the additive Gaussian noise compared with other denoising methods. The paper is organized as follows. In section 2, the WPD as preprocessor and ICA feature extraction are described. In section 3 detailed speech denoising is introduced. Experiments and conclusions are presented in section 4 and section 5 respectively.
2 WPD-ICA Feature Extraction 2.1 Wavelet Packet Decomposition Standard ICA requires signal at least as many as sources. In many applications, single sensor signal is often obtained. We develop a new method to decompose the data
S(0,0)
A(1,0)
AA(2,0)
D(1,1)
AD(2,1)
DA(2,2)
Fig. 1. Wavelet Packet Decomposition
DD(2,3)
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Q. Huang, J. Yang, and Y. Zhou
from a single sensor and then use the coefficients at different frequencies as input matrix to ICA. Projection of signal onto wavelet packet basis function is called wavelet packet decomposition. WPD has strong frequency resolution power and high time resolution power. It is a full binary tree decomposition [7,8,9] (Fig.1). WPD is used as a preprocessor to decompose the signal into a set of narrow band signals at first. If signal X is analyzed by n level full binary tree decomposition, we can get wavelet packet coefficient matrix (WPCM) X p using the following transformation
X p = Wp ⋅ X .
(2)
" C (0, N1 ) º " C (1, N1 ) »» , C(i,j) is the jth WPC of the ith node " " » » " C (m, N1 ) ¼ in n level decomposition, m = 0,1" 2n − 1 is the node index of n level of decomposition and N1 = N n (N is the number of samples) is the length of each node ª C (0,1) C (0, 2) « C (1,1) C (1, 2) where X p = « « " " « ¬C (m,1) C (m, 2)
coefficients. We use matrix X p to extract ICA feature. WPD is applied to decompose signal with noise. One of the primary properties of WPD is sparsity. That is, small WPCs are dominated by noise, while coefficients with a large absolute value carry more signal information than noise. The ICA feature vectors are learned from the WPCs, so the projection coefficients with a large absolute value also have more signal information than noise. Therefore the choice of wavelet and the level of decomposition play a critical role in this section and the following analysis. Concrete choice depends on the problem at hand. 2.2 ICA Feature Extraction
ICA as a feature extraction method can be detailed in the following n
X = AS = ¦ ai si .
(3)
i =1
where ai (each column of A) is a basis vector, all columns of A span a feature space which ensures that all projection coefficients s1 , s2 , " , sn satisfy mutually independent property. The idea of WPD-ICA is based on the following proposition [2]. Proposition 1: A (component-wise) linear operator T leaves the property of linear independence unaffected. Therefore we can use the ICA algorithm on the wavelet packet coefficient space to extract feature.
A New Speech Denoising Method Based on WPD-ICA Feature Extraction
15
We apply WPD as defined in Eq. (2) onto the two sides of Eq. (1) to get X p = Wp ⋅ X ° °S p = Wp ⋅ S ® °η p = W p ⋅η ° X = AS + η = A( S + η ) = AS p p p p p ¯ p
(4)
where X p , S p , η p are WPCM of signal, projection coefficients and noise respectively and Sp = S p + ηp , ηp = A−1η p . The covariance matrix of the noise in the wavelet packet domain equals Cη p = E[η pη Tp ] = E[Wpηη T W pT ] = Wp E[ηη T ]W pT . If
Wp is orthogonal and Cη = σ 2 I , then we get that Cη p = σ 2 I . In the same way if A is orthogonal, Cηp = σ 2 I . This means that orthogonal transformations leave the Gaussian noise structure intact, which makes the problem more simply tractable. The sparsity of X p means that the distribution of X p is highly peaky and heavy-tail than the Gaussian distribution. The property gives us the advantage to use ICA feature extraction. It enforces super-Gaussian distributions on the coefficients of ICA basis Sp in terms of the central limit theorem. We can be sure that the basis coefficients will be described by even more highly peaked distributions since the inputs of ICA are described by highly peaked ones. So we can learn better basis representation for the signal. ICA feature extraction algorithm is performed to obtain the estimation of projection coefficient matrix Sp and the basis matrix A by unmixing matrix W in the following equation
Yp = WX p .
(5)
where Yp is the estimation of Sp . ICA basis matrix can be calculated by the relation A = W −1 . By maximizing the log likelihood of projection coefficients, both the independent coefficients and basis matrix can be inferred at the same time. The learning rule is represented as ∆W ∝
∂ log p ( Y p ) ∂W
T T W W = η [ I − ϕ (Y p ) Y p ]W
(6)
.
here the updating algorithm is natural gradient method which speeds the convergence considerably[2]. The ϕ ( y ) is score function which is defined as
ϕ ( y) = −
p′( y ) ∂ log p( y ) . In this paper, we use the generalized gaussian =− p( y ) ∂y q
distribution to estimate the p.d.f of y, that is p( y ) ∝ exp(− y ) where q can be
16
Q. Huang, J. Yang, and Y. Zhou
learned from the data[10]. Combing with the learning rule in Eq. (6), the unmixing matrix is iterated until convergence is achieved. The basis function matrix is then obtained.
3 Speech Denoising Speech feature basis and sparse projection coefficients onto these basis vectors are acquired in section 2.2. In the noisy environment, Yp denotes the noisy coefficients. S p is the original noise-free coefficients. ηp is the projection coefficients of Gaussian noise. The relation between them can be described as Yp = S p + ηp .
(7)
We want to estimate S p from the noisy coefficients Yp . We can use the Maximum Likelihood (ML) estimation method. The ML estimation gives the relation Sˆ p = h(Yp ) where the nonlinear function h(⋅) is called as shrinkage function and its inverse is given by h −1 ( S p ) = S p + σ 2ϕ ( S p ) ( σ is the standard derivation of Gaussian
noise)[6,11]. In general, a model for elimination of noise or other undesirable components for single sensor data is depicted in the following steps and Fig.2.
X
Xp WPD
ICA (W)
Yp
Sp
Denoising
IICA (A)
X
Xp
IWPD
Fig. 2. Basic model for removing noise from single-sensor data
㧔1㧕Choose appropriate wavelet function and the best level of WPD. Use the WPCM
of observed noisy signal to learn ICA basis vectors and sparse projection coefficients. Apply the nonlinear shrinkage function on noisy coefficients to get the estimated noise-free coefficients. Inverse the ICA and WPD to obtain the recovered signal from the noisy signal.
㧔2㧕 㧔3㧕
4 Experiments In our experiments, male and female speech signals with added Gaussian noise are used to test the performance of the proposed method. The sampling frequency is 8kHz and 40000 samples of each signal are used. Signal added with white Gaussian noise is represented as X = X s + nw
nw ~ Ν (0, σ 2 ) .
(8)
A New Speech Denoising Method Based on WPD-ICA Feature Extraction
17
Noisy signal with a colored Gaussian noise is described as
X = X s + nc .
(9)
where nc is colored Gaussian noise and is modeled by an autoregressive process AR(2):
Firstly the Daubechies function of order 8 has been chosen as the wavelet function and speech signal is analyzed by WPD through six level of decomposition. Wavelet packet coefficients are represented as " C (0, 625) º " C (1, 625) »» » " " » " C (m, 625) ¼
ª C (0,1) C (0, 2) « C (1,1) C (1, 2) Xp = « « " " « C C (63,1) (63, 2) ¬
The unmixing matrix W is initialized by 64×64 identity matrix and the learning rate is gradually decreased during iterations. W is learned by the algorithm in Eq. (6) and it is used as the filter to get sparse coefficients. Estimated noise-free coefficients are obtained by denoising the sparse coefficients. Enhanced signal is reconstructed from the estimated noise-free coefficients. To judge the performance of noise suppression, the signal to noise ratio is used
¦ signal (t ) SNR = 10 log ¦ noise (t ) 2
t
2
.
(11)
t
As a measure of the signal approximation the root mean squared error (RMSE) defined as RMSE =
N
¦ (S
ideal i
− Sireconstructed ) / N .
(12)
i =1
can be used. The RMSE is only an overall measure of the performance. In the first experiment of male speech signal, the noisy male speech signal corrupted by four different intensity of additive white Gaussian noise are used to test the method. The SNR of the input noisy signals are 0.1175, -6.2592, -9.1718 and 13.6174dB respectively. We can get high SNR and satisfied reconstructed signal. The output SNR results of the recovered male speech signal are 4.8094, 3.1309, 0.0918, 0.8782dB and RMSE results are 0.0398, 0.0433, 0.0504, 0.0529 respectively. It can be seen that the SNR have much improvement. Fig.3 shows the denoising results of the noisy male speech with the input SNR of -13.6174dB and it was compared to the filtering results from the median filter and the wavelet filter method. Table 1 denotes the SNR and RMSE of denoised signal under the condition of additive white Gaussian noise.
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Q. Huang, J. Yang, and Y. Zhou
Fig. 3. The denoising results of noisy male speech when the input SNR is -13.6174dB (a) denotes the clean male speech signal (b) denotes the noisy signal with additive white Gaussian noise (c) denotes the denoising result of our method (d) denotes the denoising result of wavelet filter (e) denotes the denoising result of median filter with n=5 Table 1. Denoising results of male speech with white Gaussian noise
Input signal SNR(dB)
WPD-ICA denoised signal SNR(dB) RMSE
Wavelet denoised signal SNR(dB) RMSE
Median value filtered signal SNR(dB) RMSE
-13.6174 -9.1718 -6.2592 0.1175
-0.8782 0.0918 3.1309 4.8094
-2.2804 -1.7821 1.2803 1.4406
-8.0949 -6.0853 -4.8516 -1.8285
0.0529 0.0504 0.0433 0.0398
0.0568 0.0554 0.0475 0.0471
0.0759 0.0687 0.0646 0.0555
Female speech signal with four different intensity of additive colored Gaussian noise are used in another experiment. The SNR of the input noisy signals are 4.8004, 0.4854, -5.0242 and -12.6541dB respectively. Fig.4 denotes the results of three methods which suppress the additive colored Gaussian noise. The SNR and RMSE of denoised female speech can be seen from Table 2.
A New Speech Denoising Method Based on WPD-ICA Feature Extraction
19
Fig. 4. the denoising results of noisy female speech when the input SNR is -3.2423 dB (a) denotes the clean female speech signal (b) denotes the noisy signal with additive colored Gaussian noise (c) denotes the denoising result of our method (d) denotes the denoising result of wavelet filter (e) denotes the denoising result of median filter with n=5 Table 2. Denoising results of female speech corrupted by colored Gaussian noise
Input signal SNR(dB)
WPD-ICA denoised signal SNR(dB) RMSE
Wavelet denoised signal SNR(dB) RMSE
Median value filtered signal SNR(dB) RMSE
-17.1052
-8.1328
0.0797
-12.9301
0.1013
-13.0024
0.1016
-11.3516 -3.2423
-1.3560 2.1785
0.0568 0.0476
-3.7092 1.3112
0.0639 0.0497
-9.3792 -5.8208
0.0848 0.0710
2.5113
6.4278
0.0347
2.7661
0.0486
-4.2815
0.0657
5 Conclusions How to extract basis vectors directly from the single channel speech signal is the key problem in noisy speech denoising. Therefore in this paper we present a new approach to combine ICA feature extraction with WPD so as to extract basis function
20
Q. Huang, J. Yang, and Y. Zhou
directly from single channel data. WPD-ICA learns basis vectors using the high order statistics of the data. Projection coefficients onto the learned basis vectors are sparser and more suitable for reducing noise. Shrinkage function can also be obtained from data. Experiments on real speech signal with added Gaussian noise have shown that the proposed method can efficiently suppress noise and enhance signals.
References 1. Commo, P.: Independent Component Analysis, A New Concept? Signal Processing, Vol.36 (1994) 287-314 2. Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. Wiley, New York (2001) 3. Roberts, S., Everson, R.: Independent Component Analysis: Principles and Practice. Cambridge University Press, Cambridge (2001) 4. Lee, T.-W., Jang, G.-J.: The Statistical Structures of Male and Female Speech Signals. Proc. ICASSP, Salt Lack City, Utah, May (2001) 105-108 5. Lee, J.-H., Jung H.-Y., Lee, T.-W., Lee, S.-Y.: Speech Feature Extraction Using Independent Component Analysis. Proc. ICASSP, Istanbul, Turkey, Vol. 3, June (2000) 1631-1634 6. Hyvärinen, A.: Sparse Code Shrinkage: Denoising of Nongaussian Data by Maximum Likelihood Estimation. Technical Report A51, Helsinki University of Technology, Laboratory of Computer and Information Science (1998) 7. Mallet, S.: A Wavelet Tour of Signal Processing. Academic Press, second edition (1999) 8. Ravier, P., Amblard, P.O.: Wavelet Packets and De-noising Based on Higher-orderStatistics for Transient Detection. Signal Processing, Vol.81 (2001) 1909-1926 9. Donoho, D.L., Johnstone, I.: Adapting to Known Smoothness Via Wavelet Shrinkage. J. Amer. Stat. Assoc. Vol.90, Dec (1995) 1200-1224 10. Lee, T.-W., Lewicki, M.-S.: The Generalized Gaussian Mixture Model Using ICA. International workshop on Independent Component Analysis (ICA’00), Helsinki, Finland, June (2000) 239-244 11. Donoho, D.L.: De-noising by Soft Thresholding. IEEE Trans. Inf. Theory, Vol.41, No.3 (1995) 613-627
An Efficient Algorithm for Blind Separation of Binary Symmetrical Signals* Wenbo Xia and Beihai Tan School of Electronic and Communication Engineering, South China University of Technology 510640, China {WBX, northsea80}@163.com
Abstract. An efficient algorithm for blind separation of binary symmetrical signals is proposed, which don’t depend on the statistical characteristics of source signals. The mixture matrix is estimated accurately by using the relations of sensor signals in case of no noise and it is also proved in this paper, and the estimated mixture matrix is a primary column transformation of the original mixture matrix by the algorithm, through which the source signals are recovered by permutations and sign changes of their rows. In practice, they can be corrected by introducing headers in the bit-streams and differently encoding them. The algorithm is shown simple and efficient in last simulations.
1 Introduction Blind separation problem has been one hot topic in the recent years, which has gained much attention, see, e.g., [1],[2],[3],[4],[5],[6],[13],[15] etc. Blind source separation (BSS) is to recover the source signals without any information of both the source signals and the channels. In many previous researches, because one recovering independent components of sources by the sensor signals, so this kind of BSS problem is also called independent component analysis (ICA). There have existed a lot of algorithms and applications of BSS up to now. Specially, in paper [10], Xie’s conjecture corrected the famous Stone’s conjecture. BSS algorithms based on Xie’s conjecture should be without suspicion in basic theory. From now on, researches have a reliable basis to study BSS both in theory and algorithm design. In the same time, the applications of BSS cover many areas, such as: array processing, multi-user communication and biomedicine etc. For digital signals blind separation, there also were many algorithms, such as: AlleJan’ analysis method [7], K.Anand’s two-step clustering method [8], Li Yuanqing’s underdetermined algorithm [9] and others [11],[12],[14],etc. But these algorithms are *
The work is supported by the National Natural Science Foundation of China for Excellent Youth (Grant 60325310), the Guangdong Province Science Foundation for Program of Research Team (grant 04205783), the National Natural Science Foundation of China (Grant 60505005), the Natural Science Fund of Guangdong Province, China (Grant 05103553) and (Grant 05006508), the Specialized Prophasic Basic Research Projects of Ministry of Science and Technology, China (Grant 2005CCA04100).
complicated in computations and impreciseness for restoration completely. This paper proposes a novelty blind separation algorithm of binary symmetrical signals, which only use the relations of sensor signals to estimate the mixture matrix and recover source signals, and its good performance is also testified by the last simulations. For the sake of simplicity, we suppose that the binary symmetrical signals are BPSK signals in this paper for discussion.
2 Model of Blind Separation of BPSK Signals In digital signals blind separation, Let m narrowband BPSK signals from m different users, arrive at an array of d antennas [8]. The measured baseband signal at the p th element is given by: ∞
m
x p (t ) =
¦
qi a pi
i =1
¦ b ( j )s(t − jT − τ ) + w i
i
p (t ) ,
(1)
j =1
where T is baud period, q i is the amplitude of the i th user’s signal, a pi is response of the p th sensor to the i th user signal, bi (∗) = ±1 bit-stream transmitted by the i th user, s (*) is signal waveform of unit energy, τ i is time delay of the i th signal to the array and w p (*) is additive white noise at the p th sensor. We assume that the time
taken for electromagnetic waves to traverse the array is small compared to τ i and that the maximum multi-path delay is small compared to T . Here, we absorb the multipath effect into the coefficients a pi , and hence, a pi are not explicitly parameterized in terms of the directions-of-arrival (DOA’s). The a pi are unknown coefficients to be estimated as we estimate the bit-streams of the users. If the τ i are all equal (which is a simplifying assumption that is not necessarily true in practice and deserves more study), one can perform matched filtering over a symbol period T to obtain [8] m
x p ( n) =
¦q a i
pi bi ( n) + w p ( n)
,
(2)
i =1
where w p (n) is a white noise with 0 mean and variance is σ 2 , and it can be denoted as vector: x(n) = As (n) + w(n) ,
(3)
where s (n) = [b1 (n) bm (n)]T , x(n) = [ x1 (n) xd (n)]T , w(n) = [ w1 (n) wd (n)]T , A = [q1a1 q2 a 2 qm am ] , a r = [a1r a 2 r a dr ]T . If we have N snapshots and (3) can be denote as matrix X ( N ) = AS ( N ) + W ( N ) ,
(4)
where X ( N ) = [ x(1) x( N )] , S ( N ) = [ s (1), s (2) s ( N )] , and W ( N ) = [ w(1) w( N )] .
An Efficient Algorithm for Blind Separation of Binary Symmetrical Signals
23
Next, we suppose that there exits no noise, mixture matrix A is nonsingular and d = m , that is to say the number of the sensor signals are equal to the number of source signals. To combine (3) and (4), we have x(n) = As (n) , (5) X ( N ) = AS ( N ) .
(6)
3 An Efficient Algorithm for BPSK Signals Blind Separation In this paper, in order to separate digital signals, we must estimate mixture matrix first. When N is enough great, column vector s (n) in (3) has 2 m distinct vectors denoted as V = {s1 , s 2 s 2m } , that is to say all column vectors of matrix S (N ) in (4) come from one of the set V . Similarly, we also get 2 m distinct vectors of sensor signals through (5) denoted as U = {x1, x2 x2 m } , and obviously all column vectors of matrix X (N ) come from one of the set U , namely xi = Asi
(i = 1,2, 2 m ) .
(7)
It is also denoted as x1i = a11 s1i + a1m s mi x 2i = a21 s1i + a 2 m s mi
(i = 1,2, 2 m ) ,
(8)
x mi = a m1 s1i + a mm s mi where x i = [ x1i x mi ]T , s i = [ s1i s mi ]T . Because s ij ∈ {+1,−1}, i = 1 m; j = 1 2 m , so x i + x j = A( s i + s j ) (i ≠ j , i = 1,2, 2m , j = 1,2, 2m ) .
(9)
It can be denoted like (8) as x1i + x1 j = a11 ( s1i + s1 j ) + a1m ( s mi + s mj )
x 2i + x 2 j = a 21 ( s1i + s1 j ) + a 2 m ( s mi + s mj ) x mi + x mj = a m1 ( s1i + s1 j ) + a mm ( s mi + s mj )
(10)
From (10), we can know if ( s1i + s1 j ) = +2 or ( s1i + s1 j ) = −2 , but ( s ki + s kj ) = 0, k ≠ 1, k ∈ {1,2, m} we can have xi + x j = (+2)a1 or xi + x j = (−2)a1 , that is to say the sum of the i th vector and the j th vector in the set U is (+2) times of the first column a1 of mixture matrix A or (−2) times of it. Similarly, when ( s qi + s qj ) = +2 or ( s qi + s qj ) = −2 , but ( s ki + s kj ) = 0, k ≠ q, k ∈ {1,2, m} , then xi + x j = (+2)aq or xi + x j = (−2)aq , that means the sum of the i th vector and the j th vector in the set U is (+2) times of the column a q of mixture matrix A or (−2) times of it. Next, in
24
W. Xia and B. Tan
order to look for all column vectors in mixture matrix A , we will take any two vectors of the set U to add up, y l = x i + x j , l = 1C22m (i ≠ j , i = 1,2, 2 m , j = 1,2, 2 m ) .
(11)
Finally, let set Y = { yl , l = 1C22m } . Definition 1: In the set Y = { yl , l = 1C22m } , if y a = y b or ya = (−1) yb , a ≠ b , we will look on them as same cluster Gr , and r is the footnote of the cluster. Again, we define a set S = {sl , l = 1C22m } , s l = s i + s j , l = 1C22m (i ≠ j , i = 1,2, 2m , j = 1,2, 2m ) ,
(12)
y l = As l , l = 1C22m .
so
(13)
At the same time, according to definition 1, we also can cluster in the set S . When y a = y b or y a = (−1) y b , a ≠ b , we let their corresponding s a and s b into the same cluster H r . From definition 1 and combining equations (10), we can know that all column vectors of A must come from m clusters of Gr , and they are only different from the corresponding column vectors of m clusters of Gr by (+2) or (−2) times. Theorem 1: According to definition 1, when we classify Y = { yl , l = 1C22m } into different clusters, among all the clusters the m clusters which contain the column vectors of the mixture matrix A or the cluster whose element is zero vector, then the number of elements of them is most, and they are 2 m−1 respectively, but the number of elements of the other clusters is less than 2 m−1 . Proof: Let s l = s i + s j
γ
㧧 l = 1C 㧘 (i ≠ j, i = 1,2, 2 2 2m
m
, j = 1,2, 2m ) ;
< >; When sl = 0 , si can be taken 2 m distinct vectors. For every si , there exists a vector s j to make s i + s j = 0 , but because of symmetry, the number of appearance
2m = 2 m −1 . 2 < >; When sl = e1r , where e1r denotes a m × 1 vector whose r th element is (+2)
of sl = 0 is
δ
or (−2) , the other elements are all 0, and r is arbitrary. when e1r denotes the vector whose r th element is (+2) , the other elements are all 0, according to < >, the numsl = e1r
m −2
γ
e1r
is 2 . Similarly, when denotes the vector whose ber of appearance of r th element is (−2) , the other elements are all 0, the number of appearance of sl = e1r is 2 m −2 . So we can arrive a conclusion that the number of appearance of sl = e1r is 2 m −2 + 2 m− 2 = 2 m −1 , where e1r denotes a m × 1 vector whose r th element is (+2) or (−2) , the other elements are all 0.
An Efficient Algorithm for Blind Separation of Binary Symmetrical Signals
25
ε
2 2 < >; When sl = erk , where erk denotes a m × 1 vector whose r th element is (+2) and k th element is (−2) , the other elements are all 0; or whose r th element is (−2) and k th element is (+2) , the other elements are all 0, and r, k are arbitrary. 2 denotes the vector whose r th element is (+2) and k th element is (−2) , When erk
according to <
γ>, the number of appearance of s = e l
2 rk
is 2 m−3 , Similarly, when
2 erk denotes the vector whose r th element is (−2) and k th element is (+2) , the num2 is 2 m−3 . So we can arrive a conclusion that the number ber of appearance of sl = erk 2 is 2 m −3 + 2 m −3 = 2 m−2 . of appearance of sl = erk 2 2 , where erk denotes a m × 1 vector whose r th element Similarly, if when sl = erk is (+2) and k th element is (+2) , the other elements are all 0; or whose r th element is (−2) and k th element is (−2) , the other elements are all 0, and r, k are arbitrary, 2 is also 2 m −3 + 2 m −3 = 2 m−2 . the number of appearance of sl = erk Obviously, we know when the nonzero elements of the vector sl increase, the number of appearance of s l will decrease. Because sl is corresponding to yl , so when sl is zero vector or it has only a nonzero element, then the number of appear-
ance of sl is most, 2 m−1 , and the number of appearance of yl which come from the
̱
same cluster is most, and is 2 m−1 .
So when yl is nonzero vector and its appearance number is 2 m−1 , it must be a column vector of mixture matrix A . From theorem 1, in order to restore A , we should find m clusters in which elements are nonzero and the number of elements are most. We denote the m clusters as a new set Gˆ = {Gˆ , Gˆ Gˆ } . We take a column vector from every Gˆ and make 1
2
m
i
them divided by 2 then denoted as aˆ , (i = 1,2 m) . A new matrix Aˆ is composed of aˆ , (i = 1,2 m) , and It is obvious that Aˆ is only a primary column transformation of i
mixture matrix A . So Aˆ = AP , where P is a primary matrix. Substituting (14) for (6) X ( N ) = Aˆ P −1 S ( N ) .
(14) (15)
Let Sˆ ( N ) = P −1 S ( N ) , we have X ( N ) = Aˆ Sˆ ( N ) .
(16)
−1
Because P is a primary matrix, so P is also a primary matrix and Sˆ ( N ) is only a primary row transformation of S ( N ) . From (16), Sˆ ( N ) = Aˆ −1 X ( N ) ,
(17)
so the source signals can be restored through Sˆ ( N ) by permutations or sign changes.
26
W. Xia and B. Tan
Algorithm summary, 1. Find 2 m distinct sensor signal vectors denoted as U = {x1 , x2 x2m } from N
sensor signals. Get the set Y = { yl , l = 1C22m } through equation (11) and cluster them by us-
Ձ
ing definition 1. Find m nonzero clusters whose elements’ number are all 2 m−1 in above clusters, and denoted as a set of them Gˆ = {Gˆ 1 , Gˆ 2 Gˆ m } . Take a column vector from every cluster Gˆ , (i = 1,2 m) and divide it by 2, then denoted as aˆ , (i = 1,2 m) .
Ղ
i
Form a new matrix Aˆ by aˆ , (i = 1,2 m) . 4. Restore source signals by (17).
4 Simulation Results In the experience, we suppose there are three BPSK source signals in the following fig.1, and take N = 1000 in case of no noise. Here, a 3 × 3 random mixture matrix ª 0.8304 0.0490 -1.8211º A = ««- 0.0938-1.3631 1.4675»» «¬- 0.4591- 0.2131 - 0.4641 »¼
is brought. The mixture signals are gotten by equation (6) and
the three mixtures are shown by the following fig.2. Then, a new mixture matrix ª- 0.0490-1.8211 0.8304º Aˆ = «« 1.3631 1.4675- 0.0938»» «¬ 0.2131- 0.4641- 0.4591»¼
is obtained by the above algorithm accurately and source sig-
nals are restored by equation (17) and shown by the fig.3.
Fig. 1. Three source signals
An Efficient Algorithm for Blind Separation of Binary Symmetrical Signals
27
Fig. 2. Three mixture signals
Fig. 3. Three restored source signals
We find that the estimated mixture matrix Aˆ is a primary column transformation of the original mixture matrix A through the algorithm, so the restored source signals are only different from the original source signals by permutations and signs, and source signals are restored successfully. Similarly, the algorithm can be applied to general binary symmetrical signals for blind separation through the example of BPSK signals.
28
W. Xia and B. Tan
5 Conclusions This paper gives a novel algorithm for blind separation of binary symmetrical signals and it doesn’t depend on the characteristics of statistical independence of source signals. According to the characteristics of binary symmetrical signals, we can estimate the nonsingular mixture matrix and proved in the paper. The simulations show the estimated matrix accurate and the algorithm simple with a little computation. Therefore, it has good performance and precision for blind separation of binary symmetrical signals.
References 1. Xie, S.L., Zhang, J.L.: Blind Separation of Minimal Information Based on Rotating Transform. Acta Electronica Sinica, v 30, n5, May(2002) 628-631 2. Li, Y., Wang, J., Zurada, J.M.: Blind Extraction of Singularly Mixed Source Signals. Neural Networks, IEEE Transactions on Volume 11,Issue 6, (2000) 1413 – 1422 3. Yang, H.H., Amari, S., Cichocki, A.: Information-theoretic Approach to Blind Separation of Sources in Nonlinear Mixture. Signal Processing, vol.64, (1998) 291-300 4. Zhang, J.L., Xie, S.L., He, Z.S.: Separability Theory for Blind Signal Separation. Zidonghua Xuebao/Acta Automatica Sinica, v30, n 3, May (2004) 337-344 5. Bofill, P., Zibulevsky, M.: Underdetermined Source Separation Using Sparse Representation.Signal processing, 81 (2001) 2353-2362 6. Xiao, M., Xie, S.L., Fu, Y.L.: A Novel Approach for Underdetermined Blind Sources Separation in Frequency Domain. Advances in Neural Networks-ISNN 2005, LNCS 3497 (2005) 484-489 7. Van der veen, A.J.: Analytical Method for Blind Binary Signal Separation, IEEE Trans. Signal Process, 45 (1997) 1078-1082 8. Anand, K., Mathew, G., Reddy, V.U.: Blind Separation of Multiple Co-channel BPSK Signals Arriving at an Antenna Array, IEEE Signal Process. Lett. 2 (1995) 176-178 9. Li, Y., Cichocki, A., Zhang, L.: Blind Separation and Extraction of Binary Sources. Communication and Computer Sciences, 86 (2003) 580-590 10. Xie, S.L., He, Z.S., Fu, Y.L.: A Note on Stone’s Conjecture of Blind Separation. Neural Computation, 16(2004) 245-319 11. Li, Y., Cichocki, A., Zhang, L.: Blind Deconvolution of FIR Channels with Binary Sources: A Grouping Decision Approach. Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03). 2003 IEEE International Conference on Volume 4 (2003) 289-292 12. Talwar, S., Viberg, M., Paulraj, A.: Blind Estimation of Synchronous Co-channel Digital Signals Using an Antenna Array. Part I: algorithms. IEEE Trans. Signal Process. 44 (1996) 1184-1197 13. Zhang, J.L., Xie, S.L.: Multi-input Signal-output Neural Network Blind Separation Algorithm Based on Penalty Function. Intelligent and Complex Systems, 2(2003) 353-362 14. Lee, C.C., Lee, J.H.: An effient method for blind digital signal separation of array data. Signal Processing 77 (1999) 229-234 15. Xie, S.L., He, Z.S., Gao, Y.: Adaptive Theory of Signal Processing. 1st ed. Chinese Science Press, Beijing (2006) 130-223
A New Blind Source Separation Algorithm Based on Second-Order Statistics for TITO ZhenLi Wang, XiongWei Zhang, and TieYong Cao Nanjing Institute of Communications Engineering P.O. Box 7, Nanjing, Jiangsu, 210007 China [email protected], [email protected]
Abstract. In this paper, we investigate a new blind source separation algorithm for TITO (two-input and two-output) channel system. Considering the case of the noisy instantaneous linear mixture of source signals, we form the matrix pair with the two 2×2 dimension symmetric, positive definite matrices via two covariance matrices. We apply a set of transforms such as the Cholesky factorization and SVD (singular value decomposition) to this formed matrix pair. And a unitary matrix is then obtained, which is an accurate diagonalizer of each matrix of this pair. Compared with the JADE algorithm and the SOBI algorithm, some numerical results show the better performance of the new algorithm.
1 Introduction Blind source separation (BSS), aiming at recovering unobserved signals or “sources” from observed mixtures, has recently received a lot of attention. This is due to the many potential application areas, such as communication [1], [2], biomedical measurements [3], [4], etc. It is often called “blind” because it exploits only on the assumption of mutual independence between the sources without relying on any α priori knowledge about mixing matrix. In our work, we concerned only with the separation of noisy linear combinations of the two source signals obtained from TITO channel system. In its form, one observes two sequences S1 (n) , S2 (n) recorded from two sensors, each observation X i ( n) being a noisy linear combination of two sources. Thus
propose a new blind source separation algorithm based on accurate diagonalization second-order statistics for TITO channel system. The remainder of this paper is organized as follows: Section 2 presents a new blind separation algorithm based on accurate diagonalization second-order statistics. Some numerical results are given in Section 3 to illustrate the validity of this algorithm. Finally, the conclusion is presented in Section 4.
2 The New Blind Source Separation Algorithm We consider exploiting second-order statistics information of the whitened observation signal X w (n) . For independent sources, the sample autocorrelation covariance matrices and its delayed counterpart are defined as the follows Rˆ (0) = X (n) X T (n) = ARˆ (0) AT + σ 2 I w
w
s
Rˆ ( k ) = X w ( n + k ) X wT ( n) , k ≥ 1 & k ∈ Z
(1) (2)
Where T denote the transpose of a vector or a matrix. Under the white noise assumption, the JADE algorithm and the SOBI algorithm both obtain an estimation σˆ 2 of the noise variance, which is the average of the m − n smallest eigenvalues of Rˆ (0) . Where m and n denote the numbers of the sample covariance matrices and the sources, respectively. For TITO channel system, this variance estimation can’t be performed since m = n . In this paper, the presented algorithm reduces the influence of disturbing noise via a series of transforms. It is introduced by the following steps: Step 1. Form the matrix pair ( P, Q ) with the two 2×2 dimension symmetric positive definite matrices as the follows
P = Rˆ (1) Rˆ T (1)
(3)
(4) Q = Rˆ (2) Rˆ T (2) Step 2. Compute the Cholesky factorization of matrix P and matrix Q , respectively.
P = RPT RP
(5)
Q = RQT RQ
(6)
By using upper-triangle matrices RP and RQ , a new matrix F is then defined as the following equation:
F = RP ⋅ RQ −1
(7)
Step 3. Compute SVD (singular value decomposition) of matrix F .
Σ = U F T FVF Where Σ = diag(σ 1 , σ 2 ) , σ 1 ≥ σ 2 > 0 .
(8)
A New BSS Algorithm Based on Second-Order Statistics for TITO
31
Step 4. Form a unitary matrix U according to equation (9), which is an accuracy diagonalizer of each matrix of the pair ( P, Q ) . Namely, matrix U satisfies with the form U T PU = D1 and U QU = D2 , where D1 and D2 are both diagonal matrices. T
U = RQ −1 ⋅ VF
(9)
Proof Applying (5) and (9) to the matrix product of PU , we shall get
PU = RPT RP ⋅ RQ −1VF = RPT ⋅ ( RP RQ −1 ) ⋅ VF
(10)
(7) and (8) are then applied to (10)
PU = RPT ⋅ F ⋅ VF = RPT ⋅ U F ΣVF T ⋅ VF = RPT ⋅ U F Σ VF TVF = I ,
= RQT ⋅ ( RP RQ −1 )T ⋅U F Σ = RQT ⋅ F T ⋅U F Σ = RQT ⋅ VF ΣTU F T ⋅ U F Σ , U F T U F = I = RQT ⋅VF ΣT Σ = RQT VF ⋅ Σ 2 = ( RQ −1VF ) −T Σ 2 = U −T Σ 2
(11)
We can find the expression U PU = Σ from (11). Similarly, (6) and (9) are applied to the matrix product of QU T
2
QU = RQT RQ ⋅ RQ −1VF = RQT ⋅ VF
= ( RQ −1VF ) −T = U −T
(12)
The other expression U T QU = I are got from (12). Now we can easily know that D1 = Σ 2 , D2 = I . Clearly, the global minimum of the nonnegative function
C (U ) = off(U T PU + U T QU )
(13)
is achieved when matrix U simultaneously and accurately diagonalize the pair ( P, Q) , And this minimum value equals to zero. In equation (13), the “off” is defined as off( H ) = ¦ | H ij |2 . The proof of the uniqueness of matrix U can be seen in i ≤i ≠ j ≤ n
appendix B of index [6]. Step 5. The source signals are estimated as Sˆ ( n) = U T X w (n) , and the demixing matrix is estimated as M = UTW , where W denotes the whitening matrix.
32
Z. Wang, X. Zhang, and T. Cao
3 Simulation Results The experiment in this Section is intended to illustrate the superiority of our algorithm compared to the JADE algorithm and the SOBI algorithm. In this test, the JADE algorithm and the SOBI algorithm use 3 fourth-order cumulant matrices and 150 covariance matrices for joint diagonalization, respectively. In order to evaluate the performance of three algorithms, we calculate the error measure proposed by Amari etc [9]. N
N
| gij |
i =1
j =1
max k | g ik |
E = ¦ (¦
N
N
| gij |
j =1
i =1
max k | g kj |
− 1) + ¦ (¦
− 1)
(14)
gij is the (i, j ) -element of the global system matrix G = MA and maxj gij represents the maximum value among the elements in the i th row vector of G , maxj g ji denotes the maximum value among the elements in the i th column vector of where
G . The data X (n) = [ x1 (n) x2 (n)]T are synthesized by mixing two independent sources s5, s6 [8] through the matrix A , which is randomly generated in the interval [0,1]. The synthesized X (n) is then corrupted with white noise. In the situation of noise level ranging from -50 dB to 0 dB, Fig.1 shows that three curves are obtained by averaging ten times runs, which correspond to the JADE algorithm, the SOBI algorithm and the proposed algorithm, respectively. The main conclusion can be drawn from this figure is that the new algorithm performs better than the other two algorithms when noise power is less than -20 dB. Again, the performance of the new algorithm is still superior to that of the JADE algorithm when noise power increases from -20 dB to 0 dB.
Fig. 1. Noise power versus error measure for three algorithms: the JADE algorithm (dashed line with diamond), the SOBI algorithm (the dotted line with triangle-right) and the proposed algorithm (the dash-dot line with circle)
A New BSS Algorithm Based on Second-Order Statistics for TITO
33
Fig.2 shows a set of speech spectrograms in the case of noise power equaling to -
ª0.8349 0.6305º » . From this picture we can know ¬0.2258 0.7041¼
25 dB and the mixing matrix A = «
that, compared to the previous algorithms, the proposed algorithm has comparative performance by only using little second-order statistics information, which reduces the computation amount of the new algorithm.
Fig. 2. Speech spectrograms . (a), (b): The two source signals. (c), (d): The two mixing signals corrupted with white noise. (e), (f): The two separated signals of the JADE algorithm. (g), (h): The two separated signals of the SOBI algorithm. (i), (j):The two separated signals of the proposed algorithm.
4 Conclusion A new algorithm, which is applicable to TITO channel system, has been introduced for blind sources separation. In the proposed algorithm, a series of transforms are used to the formed matrix pair exploiting second-order statistics information. And the proof of accurate diagonalization of this pair is also presented. The separation of the two noisy source signals is studied in simulation experiments. Results show that our algorithm performs better than the JADE algorithm and the SOBI algorithm at low noise power. Besides, our algorithm still keeps better performance compared with the JADE algorithm when disturbed noise power increases.
References 1. Anand, K., Mathew, G., Reddy, V.: Blind Separation of Multiple Co-channel BPSK Signals Arriving at an Antenna Array. IEEE Signal Processing Letters. 2 (1995) 176-178 2. Chaumette, E., Comon, P., Muller, D.: ICA-based Technique for Radiating Sources Estimation: Application to Airport Surveillance. IEE Proceedings-F. 140 (1993) 395-401 3. Karhunen, J., Hyvarinen, A., Vigario, R. (ed.): Applications of Neural Blind Separation to Signal and Image Processing. In Proc. ICASSP. 1 (1997) 131-134
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Z. Wang, X. Zhang, and T. Cao
4. Makeig, S., Bell, A., Jung, T.P, Sejnowski, T.J.: Independent Component Analysis of Electroencephalographic Data. In Advances in Neural Information Processing Systems. 8 MIT Press (1995) 5. Belouchrani, A., Cichocki, J.F.: Robust Whitening Procedure in Blind Source Separation Context. Electronics Letters. 36 (2000) 2050-2053 6. Belouchrani, A., Abed, M.K., Cardoso, J.F.(ed.): A Blind Source Separation Technique Using Second-order Statistics. IEEE Trans.Signal Processing. 45 (1997) 434-444 7. Cardoso, J.F., Souloumiac, A.: Blind Beamforming for Non-Gaussian Signals. IEE Proc. F (Rader and Signal Processing), 140 (1993) 362-370 8. http://www.kecl.ntt.co.jp/icl/signal/mukai/demo/hscma2005 9. Amari, S.I., Cichocki, A., Yang, H.H.: A New Learning Algorithm for Blind Signal Separation. In D.S Touretzky, M.C.Mozer & M.E. Hasselmo (Eds), Advance in Neural Information Processing Systems, Cambridge, MA: MIT Press (1996) 757-763
A New Step-Adaptive Natural Gradient Algorithm for Blind Source Separation Huan Tao, Jian-yun Zhang, and Lin Yu Information Engineering Dept., Electronic Engineering Institute, 230037 HeFei, China [email protected]
Abstract. The main differences between the mixed signals and origin signals: Gaussian probability density function, statistical independence and temporal predictability. The proposed BSS algorithms mainly derived from the Gaussian probability density function and statistical independence. A new adaptive method is proposed in the paper. The method uses the temporal predictability as cost function which is not studied as much as other generic differences between the properties of signals and their mixtures. Step-adaptive nature gradient algorithm is proposed to separate signals, which is more robust and effective. Compared to fixed step natural gradient algorithm, Simulations show a good performance of the algorithm.
In this paper, a new BSS method based on maximizing temporal predictability of signal mixtures has been introduced which has better separation performance.
2 Preliminaries 2.1 BSS Model As a general model for BSS let L observed signals be related to N independent source signals si (t )(t = 1,", N ) by L × N unknown channel matrix A:
x(t ) As (t ) n(t ) . Where
(1)
s (t ) = [ s1 (t ), s 2 (t ),", s N (t )]T and A is full-column rank matrix.
n(t ) (n1 (t ), n2 (t ), ", nm (t ))T is the vector of additive noise. Without loss of generality we assume in the derivation that signal are real-valued, L = N and no noise. The BSS can operate into two steps. The first step is to pre-whiten the observations according to a whitening matrix B which results in a set of uncorrelated and normalized signals. Pre-whitening can be carried out in any of known methods and it is not dealt with here. After pre-whitened, an appropriate cost function based on high-order statistics can separate the sources by forcing their independence. 2.2 Temporal Predictability In Reference [1], the definition of signal predictability F is: n
F (Wi, x) log
V (Wi , x) V log i log U (Wi , x) Ui
( y y ) i
i 1 n
~
( y y ) i
2
i
.
(2)
2
i
i 1
Where
yi Wi xi is the value of signal y at time i . The term U i reflects the extent ~
yi is predict by a short-term ‘moving average’ y i of values in y . In contrast, the term Vi is a measure of the overall variability of in y . As measured by
to which
the extend to which
yi is predicted by a long term ‘moving average’ y i of values in ~
y . The predicted value y i and y i of yi are both exponentially weighted sums of signal values measured up to time i 1 ,such that recent values have a larger weighting than those in the distant past:
A New Step-Adaptive Natural Gradient Algorithm for Blind Source Separation ~
~
y i MS y i1 (1 MS ) yi1 0 b MS b 1
37
.
(3)
y i ML y i1 (1 ML ) yi1 0 b ML b 1 The half-life
hL of ML is much longer than the corresponding half-life hS of MS .
The relation between a half-life
h and parameter M is defined as M 21/ h .
3 Step-Adaptive Nature Gradient Algorithm Equation (2) can be rewritten as:
F log
Wi C Wi t ~
.
(4)
Wi C Wi t
~
Where C is long-term covariance between signal mixtures, and C is short-term covariance, which can be expressed as: Reference [3] proved gradient ascent on F with respect to Wi could be used to maximize F .
∇F = Iteratively updating
2Wi − 2Wi ~ C− C. Vi Vi
(5)
Wi until a maximum of F is located: Wi +1 = Wi + µ∇F .
(6)
Commonly, the convergence time and stability is based upon the properly selection of step µ . Reference [4] has analyzed the stability conditions of nature gradient algorithm. A step-adaptive algorithm is desirable. Here we proposed a new step-adaptive algorithm. Intuitively, we can use the distance between the separation matrix and optimal separation matrix to adjust the step adaptively. But the optimal separation matrix is unknown before the signals separated. An alternation we use
∆W (k ) = Wi +1 − Wi
2 F
.
(7)
∆W (k ) , E (∆W (k )) is used to perform step-adaptive adjustment. In the process of adaptation, the increasing of E ( ∆W ( k )) means the To smooth the
fluctuation of algorithm, so a smaller step is desirable; on the contrary, the decreasing
38
H. Tao, J.-y. Zhang, and L. Yu
of E ( ∆W ( k )) means a larger step is wanted to accelerate the convergence of algorithm. The updating expression of step is:
µ (k + 1) = α (k ) µ (k ) .
α
(8)
can be expressed as follows:
1+ γE(∆W(k)),E(∆W(k)) < E(∆W(k −1)) 1 °° , E(∆W(k)) > E(∆W(k −1) α(k) = ® 1 + E ( ∆ W ( k )) β ° °¯ 1, else
(9)
Where 0 < β < 1,0 < γ < 1 γ is in charge of the convergence speed and controls the steady error when convergence. E (∆W (k )) can be get form:
E(∆W(k +1)) =
k 1 E(∆W(k)) + ∆W(k +1) . k +1 k +1
β
(10)
4 Simulation and Performance Compared to fixed step nature gradient algorithm, the performance of the stepadaptive nature gradient algorithm is evaluated through simulations. Here we use three source signals with the sample of 5000 points. The mixing matrix A is generated randomly. The simulation parameters are as follows: λ L = 0.9, λ S = 0.004, µ 0 = 0.001, β = 0.5, γ = 0.06 . After separation, the
1 º ª0.02 0.04 « 1 0.1 »» . separated result is: 0.06 « «¬ 1 0.008 0.003»¼ To evaluate the separation performance and the convergence speed of different algorithms, we use the correlation coefficiency between the original signals and recovered signals. The definition of correlation coefficiency is defined by (11).
ρ ij =
cov(s i , s j ) cov(s i , si ) cov(s j , s j )
.
(11)
A comparison between fixed step nature-gradient algorithm with different steps and step-adaptive nature-gradient algorithm is done based on correlation coefficiency. The result is depicted in Fig. 1.
A New Step-Adaptive Natural Gradient Algorithm for Blind Source Separation
39
0 step=0.0005 step=0.002 step=0.01 adaptive step
-10
ρ(k) [dB]
-20
-30
-40
-50
-60
-70
0
0.5
1
1.5 2 number of iterations k
2.5
3 4
x 10
Fig. 1. Comparison of step-adaptation with fixed steps of 0.0005,0.002 and 0.01
From Fig.1, we can clearly see the step-adaptive nature-gradient algorithm is superior to fixed step nature-gradient algorithm in convergence speed.
5 Conclusion A new adaptive separation algorithm is proposed based on maximizing temporal predictability of signal which is not studied as much as other generic differences between the properties of signals and their mixtures. The algorithm is stepadaptive. So it is more robust compare to fixed step natural gradient. Simulations show that it is effective and can get good separation precision. The step-adaptive nature gradient algorithm can also be used to other BSS method based on different cost function.
References 1. James, V. Stone.: Blind Source Separation Using Temporal Predictability, Neural computation(in press) (2001) 1196-1199 2. Belouchrani, A., Abed-Meraim, K., Cardoso, J.F.: A Blind Source Separation Using Second Order Statistics. IEEE Trans. On signal processing,Feb. Vol.45 (1997)434-444 3. Amari, S I.:Natural Gradient Works Efficiently in Learning. Neural Computation(1998) 251-276
40
H. Tao, J.-y. Zhang, and L. Yu
4. Amari, S. I., Chen, T. P.,Cichocki, A.: Stability Analysis of Adaptive Blind Source Separation, Neural Networks(1997) 1345-1351. 5. Sergio, A., Cruces-Alvarez, Andrzej Cichocki, Shun-Ichi Amari.: On A New Blind Signal Extraction Algorithm: Different Criteria and Stability Analysis.. IEEE SIGNAL PROCESSING LETTERS, VOL.9,NO.8,AUGUST (2002) 6. Yan, Li, Peng Wen, David Powers.: Methods for The Blind Signal Separation Problem. IEEE Int. Conf. Neural Networks&Signal Processing. December (2002)
An Efficient Blind SIMO Channel Identification Algorithm Via Eigenvalue Decomposition* Min Shi and Qingming Yi Department of Electronic Engineering, Jinan University, Guangzhou, 510632, PR China [email protected]
Abstract. An effective blind multichannel identification algorithm is proposed in this paper. Different from the Prediction Error Method, the new algorithm does not require the input signal to be independent and identical distribution, and even the input signal can be non-stationary. Compared with Least-Square Approach, the new algorithm is more robust to the overestimation of channel order. Finally, the experiments demonstrate the good performance of the proposed algorithm.
1 Introduction Blind identification of Single-Input Multiple-Output (SIMO) systems has many applications, or potential applications in wireless communications, equalization, seismic data deconvolution, speech coding, image deblurring, echo cancellation[1-8], etc. For the FIR SIMO system, as long as the FIR channels do not share the common zeros and all channels are fully activated, the SIMO system can be identified by just second-order statistics of the output [1], which further makes the blind identification of SIMO systems so important. So many researchers paid much attention on this problem. Because of the predominant advantage in computation cost and the weak requirement in data samples of the receiving signals, the second-order statistics (SOS)-based methods are very attractive and obtain much attention. Among them, the least-square approach (LSA) [1], the linear prediction methods (LP) [2] and the subspace methods (SS) [3]and are the three main classes. When the channel order is known, the channels can be very precisely estimated by SS-based approaches and LSA-methods, however, which are very sensitive to the estimation error of channel order. Contrastively, LP methods are not so accurate as the former two methods, but robust to the channel order overestimation. LP methods usually require the input signal is independent and identically distribution (i.i.d) while the other two methods is not limited by this requirement. Relatively, the LS approaches are a little simpler than SS ones. *
This work was supported by the National Natural Science Foundation of China(Grant 60505005), the Guangdong Provincial Natural Science Foundation(Grant 05103553), and Guangdong Province Science and Technology Project (Grant 2005B10101013).
In this paper, we present a new blind identification algorithm for SIMO FIR system by improving the LS approaches. The proposed algorithm is simply based on generalized eigenvalue decomposition. The new algorithm can be easy implemented and is robust to the channel order overestimation than SS and LS approaches.
2 Problem Statement The single-input m -output channel can be formulated as: L
x ( t ) = ¦ h (τ ) s ( t − τ ) + n ( t ) , t = 1, 2," , T
(1)
τ =0
where x ( t ) = ( x1 ( t ) ," , xm ( t ) ) ∈ R m×1 is the observed signa1 vector, s ( t ) is the input T
signal, h (τ ) = ( h1 (τ ) ," , hm (τ ) ) , (τ = 0," , L ) denotes the FIR channel impulse response. The order of the convolution is L . The additive noise is denoted as a vector T n ( t ) = ( n1 ( t ) ," , nm ( t ) ) ∈ R m×1 . The blind identification problem can be stated as T
follows: Given the receiving signals determine
{hˆ ( < )} i
m
i =1
the
channels
{h ( < )}
m
i
i =1
{ x ( t ) i = 1,", m; t = 1,", T }
up
i
to
a
nonzero
, we aim to
scaling
factor,
i.e.
= c {hi ( < )}i =1 , ( c ≠ 0 ) , then we can further recover the input signal s ( < ) . m
Xu, Tong, et al point out that if the channel order is known in advance, the necessary and sufficient identifiability condition of SIMO system (1) is that the FIR channels have no common zero [1]. So we assume that the FIR channels of system (1) do not share the common zeros.
3 Identification Equations According to reference [1], we have the following equations: xi ( t ) = hi ( t ) : s ( t ) ,
x j (t ) = h j (t ) : s (t ) ,
(2)
where : stands for convolution operation. Thus h j ( t ) : xi ( t ) = h j ( t ) : ¬ª hi ( t ) : s ( t ) ¼º = hi ( t ) : ª¬ h j ( t ) : s ( t ) º¼ = hi ( t ) : x j ( t ) , i.e., h j ( t ) : xi ( t ) = hi ( t ) : x j ( t ) , ( i ≠ j, i, j = 1," , m )
(3)
From equation (3), we have ªhj º ª¬ X i ( L ) : − X j ( L ) º¼ « » = 0 ¬ hi ¼
(4)
An Efficient Blind SIMO Channel Identification Algorithm
43
where hk = ( hk ( L ) ," , hk ( 0 ) ) and T
ª xk ( L ) « x ( L + 1) X k ( L) = « k «# « «¬ xk (T − L )
Denote h ª h1T ," , hmT º , and we construct the following matrices: ¬ ¼ ª º½ « 0 " 0 X i +1 ( L ) − X i ( L ) 0 0 »° « » °° X i ( L) = « # 0 0 » ¾ m − i blocks # % «0 " 0 X ( L) 0 " − X i ( L )» ° m « N
»° i −1 blocks m − i +1 blocks ¬ ¼ ¿°
(6)
where i = 1," , m .In equations (6), each block, e.g., 0 or { X k ( L ) , k = 1,", m} , has the size (T − L + 1) × ( L + 1) . In the noise free case, from SIMO system (1) we derive the following equations: X ( L) ⋅ h = 0
where matrix X ( L ) is
(7)
{(T − L + 1) ª¬m ( m − 1) 2º¼} × ª¬m ( L + 1)º¼ , and it is given by
ª º½ « X 1 ( L) »° « » °° m ( m + 1) X ( L) = « blocks # »¾ 2 « X m−1 ( L ) » ° «
»° ¬ m blocks ¼ °¿
(8)
Now the blind identification problem (1) boils down to solving equations (7).
4 Blind Identification Algorithm The solution of equation (7) is not unique. To find the practical solution, we usually add some appropriate constraints, e.g., h = 1 or c H h = 1 for a constant vector c . 2 The LS approaches identify the channels of system (1) by solving the following optimization problem with constraints: min J ( h ) = min X ( L ) ⋅ h 2 , 1 ° 2 h ® °¯ st : h 2 = 1.
(9)
44
M. Shi and Q. Yi
Xu, Tong et al [1] use the singular value decomposition (SVD) or fast subspace decomposition (FSD) to solve optimization problem (9). Of course, we can replace the constraint h = 1 by constraint c H h = 1 .Since the accurate channel order of 2
system (1) is unknown and estimating it is a challenging work in practice. Usually what we can do is overestimating the order. Without the loss of generality, we overestimate the channels order of system (1) as Lh ( Lh ≥ L ) . As mentioned in section 1, LSA algorithm is not robust to overestimation of channel order. To overcome this drawback, we attempt to improve the LSA algorithm, which intend to not only keep advantage of LSA algorithm, but also be robust to overestimation of channels order. Denote the ª¬ m ( Lh + 1) º¼ ×1 vector hˆ to be the estimation of h . Considering Lh ≥ L , if hˆ satisfies hk (τ ) = 0, (τ = L + 1,", Lh ; k = 1,"m ) , the overestimation of channel order will have not any influence on the channel identification of system (1). Hence the desirable estimation hˆ of h should be hˆ = ª hˆT ," , hˆT ºT , m¼ ¬ 1 ° ° T h −L § L · ® T °hˆk = c ¨ 0," , 0, hk ¸ = c ( 0," , 0, hk ( L ) ," , hk ( 0 ) ) , k = 1," , m,
To make hˆ be robust to overestimation of channel order and satisfy expression (10) as possible as it can, we solve the following optimization problem with constraints:
()
ª X ( L ) ⋅ hˆ 2 + hˆ T diag ( ȝ ) l hˆ º , ˆ ( ) »¼ h ° min J h = min 2 hˆ « ¬ ® ° st : hˆ = 1, ¯ 2
(12)
where l is a positive integer. Because 0 < µ < 1 , it is easy to know that 1 > µ > " > µ Lh and 1 > µ l > " > µ lLh . So under the constraints hˆ = 1 and 2
l X ( Lh ) hˆ = 0 , minimizing hˆT ª¬ diag ( ȝ ) º¼ hˆ will force hˆ to approximately satisfy expression (10) in some degree. The constraint hˆ = 1 means hˆT hˆ = 1 . Thus the optimization problem (12) can be 2
formulated into the following one without constraint:
An Efficient Blind SIMO Channel Identification Algorithm
45
ª X ( L ) ⋅ hˆ 2 + hˆ T diag ( ȝ ) l hˆ º ( ) ¼» h 2 ˆ = min ¬« h min e hˆ hˆ hˆ T hˆ
()
l hˆ T ª X T ( Lh ) X ( Lh ) + ( diag ( ȝ ) ) º hˆ ¬ ¼ = min hˆ hˆ T hˆ
(13)
From expression (13), we have
()
l e hˆ ⋅ hˆT hˆ = hˆT ª X T ( Lh ) X ( Lh ) + ( diag ( ȝ ) ) º hˆ ¬ ¼
(14)
For equation (14), calculating the derivative of the two sides with respect to hˆ , we get
( ) ⋅ hˆ hˆ + 2 e hˆ hˆ = 2 ª X () ¬
∂ e hˆ
T
∂hˆ
Let
T
( Lh ) X ( Lh ) + ( diag ( ȝ ) ) º¼ hˆ l
(15)
( ) = 0 , from equation (15), we have
∂ e hˆ ∂hˆ
( ) ⋅ hˆ hˆ = 2
∂ e hˆ ∂hˆ
T
{ª¬ X
T
( Lh ) X ( Lh ) + ( diag ( ȝ ) ) º¼ − e ( hˆ ) ⋅ I l
} hˆ = 0
(16)
Equation (16) means that one can estimate hˆ by doing the eigenvalue decomposition with respect to matrix ª X T ( Lh ) X ( Lh ) + ( diag ( ȝ ) )l º , and the ¬ ¼ eigenvector corresponding smallest value is just the estimation of hˆ . So we obtain the proposed algorithm as follows:
XP Input the received signalsG x ( t ) = ( x1 ( t ) ,", xm ( t ) )T , t = 1,", T UG Set µ SG integerG l Gand the channel orderG Lh UG YP Construct the matrix X ( Lh ) Gand ȝ UG ZP Compute the eigenvalues and corresponding eigenvectors of matrixUG 4) The eigenvector corresponding smallest value is just the estimationG hˆ ofG h U
5 Numerical Experiments and Result Analysis Root-mean-square-error (RMSE) is employed as a performance measure of channel estimation. Usually, when RMSE<0.8, the channels are well identified; when RMSE>1.0, the estimation of channels is not reliable. The input signal is supposed to be independent and identical distribution in the experiment. Computer simulations were conducted to evaluate the performance of the proposed algorithm in comparison with Least-Squares Approach (LSA) and Prediction Error Method (PEM). In the
46
M. Shi and Q. Yi
following two experiments, the related parameters of the proposed algorithm are set as: T = 1000 , µ = 0.99 and l = 2 experientially. All input signals are i.i.d Gaussian signals generated by Matlab command randn ( < ) . The channel coefficients are listed below.
h1 ( z ) = -0.4326+0.1253z −1 -1.1465z −2 , h2 ( z ) = -1.6656+0.2877z −1 +1.1909z −2 .
Table 1. The overestimation of channel order and corresponding RMSE for i.i.d input signal
Lh
2
3
4
5
6
7
8
9
LSA PEM Our
9.0984e-016 0.0424 9.3014e-006
0.99 0.08 0.03
0.97 0.26 0.14
1.04 0.27 0.14
0.10 0.31 0.14
1.03 0.31 0.14
1.08 0.32 0.14
1.10 0.32 0.14
(a) Noise free
(b) The received signals are added white Gaussian noise and the SNR is 40dB
Fig. 1. Performance comparison between LSA, PEM and the proposed algorithm
From Table 1 and Fig.1(a), when the order of channel is accurately given, LSA can obtain the precise estimation of channels. But for overestimation case without noise, we can see that both PEM algorithm and the proposed algorithm well identify the channels, but LSA does not do this. Additionally, Fig.1(b) shows the comparison result in the same simulation environment except adding white Gaussian noise to the receiving signals. All SNRs are 40dB. In this situation, we can see that only the proposed algorithm get the relatively satisfactory estimation (Fig.1(b)).
6 Conclusion Based on matrix eigenvalue decompostion, an effective blind multichannel identification algorithm is proposed in this paper. Different from the Prediction Error Method, the new algorithm does not require the input signal to be independent and
An Efficient Blind SIMO Channel Identification Algorithm
47
identical distribution, and even the input signal can be non-stationary. Compared with Least-Square Approach, the new algorithm is more robust to the overestimation of channel order and much faster.
References 1. Xu, G. H., Liu, H., Tong, L., Kailath T.: A Least-squares Approach to Blind Channel Identification. IEEE Trans on Signal processing, Vol.43 (1995) 2982-2993 2. Abed-Meraim K., Moulines E., Loubaton P.: Prediction Error Methods for Second-order Blind Identification. IEEE Trans on Signal processing, Vol. 45 (1997)694–705 3. Moulines E., Duhamel P., Cardoso J. F., Mayrargue S.: Subspace Methods for the Blind Identification of Multichannel FIR Filters. IEEE Trans on Signal Processing, Vol. 43 (1995) 516–525 4. Xie, S. L., He, Z. S., Fu, Y. L.: A Note on Stone's Conjecture of Blind Signal Separation. Neural Computation, vol. 17 (2005)321-330 5. He, Z. S., Xie, S. L., Fu, Y. L.: A Novel Framework of Multiphonic Acoustic Echo Cancellation. Progress in Natural Science (2005) 6. He, Z. S., Xie, S. L., Fu, Y. L.: A New Blind Deconvolution Algorithm for SIMO Channel Based on Neural Network. In: Machine Learning and Cybernetics, 2005. Proceedings of 2005 International Conference on, Vol. 6 (2005) 3602- 3616 7. Gazzah H. Regalia P. A., Delmas J. P., Abed-Meraim K.: A Blind Multichannel Identifaction Algorithm Robust to Order Overestimation. IEEE Transactions on Signal Processing, Vol. 50 (2002)1449-1458 8. Gazzah H. Regalia P. A., Delmas J. P.: Asymptotic Eigenvalue Distribution of Block Toeplitz Matrices Application to Blind SIMO Channel Identification. IEEE Transactions on Information Theory, Vol. 47 (2001) 1243 - 1251
An Improved Independent Component Analysis Algorithm and Its Application in Preprocessing of Bearing Sounds Guangrui Wen, Liangsheng Qu, and Xining Zhang College of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China {grwen, lsqu, zhangxining}@mail.xjtu.edu.cn
Abstract. Independent Component Analysis (ICA) is known as an efficient technique to separate individual signals from various sources without knowing their prior characteristics. Firstly, the basic principle of ICA is reviewed in Sec 2, and then an improved ICA algorithm based on coordinate rotation (CR-ICA) is proposed. Secondly, two advantages of the CR-ICA algorithm are discussed; the one is that the separation can be carried out without iteration, and the other is that less computation is needed to achieve the same effect. Finally, the experiment in recognition of mixed sound and practical application in preprocessing of bearing sounds proved that the CR-ICA algorithm is better than traditional ICA algorithm in separation precision and computation speed. Moreover, the advantages of the method and the potential for further applications are discussed in the conclusion.
An Improved ICA Algorithm and Its Application in Preprocessing of Bearing Sounds
49
gradient declined algorithm to complete maximum difference entropy simultaneously. Hereafter, many people including T.W.Lee etc. expanded the work of Bell and Sejnowski, and developed an improved expanding ICA algorithm.[3] The algorithm was useful for the signals displayed in super-gaussian and sub-gaussian condition. However, these ideas and algorithms were lack of computability or consistency essentially. I.e. the computation carried out with iteration and needed long computation time. In addition, the mixed signal seldom satisfied ideal symmetry distribution in practice, and they present skewness distribution generally [4]. This paper is a first attempt to apply the ICA in engineering diagnosis area. Case studies in this paper reveal its advantages. The potential application is also discussed.
2 Basic ICA Principle and Improved Algorithm 2.1 Basic ICA Principle ICA was originally developed to deal with the problems that are closely related to the cocktail-party problem [5,6]. Since the recent progress in ICA, it has become clear that this method will find widespread applications as well.
X = WS
(1)
where X is the observed vector, W is the mixed factor matrix, S is the source vector. Obviously, if we can get the inverse matrix of W , indicated by W T , we may easily obtain the source signal matrix S from the observed signal matrix X , the former S will be written as:
S =WT X
(2)
ICA can be used to estimate the source signals from the mixtures based on the information of their independence. As we know, independence of two random variables means that the joint probability distribution function (PDF) is equal to the product of individuals as Equation 4.
p(x1 , x 2 ) = p1 ( x1 ) p 2 (x 2 )
(3)
Basically speaking, ICA is an optimization problem; its objective is to optimize the coefficient matrix W so as to obtain the components S , the components of which are statistically as independent to each other as possible. Based on traditional ICA algorithms, this paper presents a new improved ICA algorithm, and applies it in engineering diagnostics area. 2.2 An Improved ICA Algorithm Based on Coordinate Rotation (CR-ICA) 2.2.1 Preprocessing for CR-ICA In the preceding section, we discussed the principle of the ICA algorithm. Practical detail algorithms based on these principles will be discussed in the next section. However, before applying an ICA algorithm on the data, it is usually very useful to do
50
G. Wen, L. Qu, and X. Zhang
some preprocessing. In this section, we discuss some preprocessing techniques that make the problem of ICA estimation simpler and better conditioned. a Centering The most basic and necessary preprocessing is to center X, i.e. subtract its mean vector M=E{X} so as to make X a zero-mean variable. This implies that S is zero-mean as well, as can be seen by taking expectations on both sides of Equation (1). This preprocessing is made solely to simplify the ICA algorithms. b Whitening Another useful preprocessing method is to whiten the observed variables. This means that before the application of the ICA algorithm (and after centering), we transform ~ the observed vector X linearly so that we obtain a new vector X which is white, i.e. its components are uncorrelated and their variances equal unity. With the original signal whitened, the correlation between the mix signals can be eliminated, and the independent component extraction algorithm can be simplified and its performance will be improved. Sometimes only whitening process may recover the waveform of source signals. In the rest of this paper, we assume that the data has been preprocessed by centering and whitening. 2.2.2 Algorithm Flow of CR-ICA ~ After mixed signals X are preprocessed, X becomes a unit covariance vector X , and ~ the components of X is perpendicular with each other. Then a new improved Inde~ pendent Component Analysis Algorithm is proposed to process this vector X . The algorithm is based on the coordinate rotation theory and can be used to search the optimum rotational angle with the help of the optimum algorithm. The detail steps of the algorithm are shown as follows: Step 1: Select rotation matrix R. By rotating transforms, matrix S will be obtained.
R =[
cos α sin α
~ − sin α ] S = R* X cos α
(4)
In order to obtain the optimum rotation angle, object function Q is built. Q = ¦ (cos α ⋅ xi − sin α ⋅ yi )3 i
(5)
~ ~ where xi , yi are two column elements of matrix X 2× n which is equal to X and n is ~ column number of matrix X . Step 2: Obtain object function Q’s derivative Q '
Q ' = 3* ¦ [(cos α ⋅ xi − sin α ⋅ yi )2 *(sin α ⋅ xi + cos α ⋅ yi )] i
(6)
Step 3: In order to obtain extremum of Q ' , Q ' is taken to zero. According to Equation (10)
An Improved ICA Algorithm and Its Application in Preprocessing of Bearing Sounds [sin α (cos α )2 ¦ xi3 − 2*cos α (sin α ) i
¦x y i
2 i
+ (cos α )
i
3
¦yx
2 i i
i
2
¦yx
2
i i
51
+ (sin α )3 ⋅
i
− 2sin α ⋅ (cos α ) 2 ¦ yi2 xi + cos α ⋅ (sin α )
2
i
¦y ]=0 3 i
(7)
i
Step 4: Suppose a = ¦ xi3 , b = ¦ yi xi2 , c = ¦ xi yi2 , d = ¦ yi3 , then formula (12) can i
i
i
i
be simplified as follow: c ⋅ tg 3α + (d − 2b)tg 2α + (a − 2c)tgα + b = 0
(8)
Step 5: Obtain the root value of Equation (12) using tgα as unknown. Step 6: Search an optimum angle from all angles obtained by step 5 to make object function obtain the minimum. Step 7: Use Equation (4) to do rotation transformation, then the independent component can be obtained.
3 Experiments In practical recongnition of signals, sound recongnition is one classical type [8]. Mixed sounds are made up of human voice and alarming whistel sound. The sounds are collected by two recorders and it is no doubtful that each sound collected by single sound recorder will receive another sound’s information. Fig.1(a) and (b).show the
(a)
(c)
(b)
(d)
Fig. 1. (a) (b) display the original mixed sound, and separated results are showed in Fig1.(c)(d)
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G. Wen, L. Qu, and X. Zhang Table 1. The performance of two algorithms in recognition of mixed sounds
SNR/dB
Algorithm CR-ICA FastICA
y1
y2
103.81 110.39
102.87 107.43
Computation Time/S 0.806 1.560
mixed sounds. By whitening the mixed sounds and then applying the improved ICA algorithm, the independent signals can be obtained and shown in Fig.1(c) and (d). Table 1 displays the SNR results by using two algorithms. It is obviously that the proposed CR-ICA algorithm is better than traditional FastICA algorithm in separation precision and computation speed under the same conditions.
4 Applications The condition monitoring and fault diagnosis of rolling bearing have been investigated for a long time. Many efficient methods have been proposed, such as resonance demodulation and ferrography. Herein, we recognize the bearing faults by sampling bearing sound. In experiment, two Sound level Meters were mounted to pick up the machine sound. One aimed at the motor sound, the other aimed at the bearing sound. It is sure that each collected sound contains other part sound information. We use the CR-ICA method to preprocess the mixed sound. The original signals collected are shown in Fig.2(a,b). The preprocessing results are shown in Fig.2(c,d).
(a)
(c)
(b)
(d)
Fig. 2. The observed signals are shown in Fig. (a,b) and the preprocessing results are shown in Fig. (c,d)
An Improved ICA Algorithm and Its Application in Preprocessing of Bearing Sounds
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As shown in Fig.2(c,d), the separated source like white noise is due to the motor, while the impulsive signal with periodic impacts was originated from the spall in the inner race of the tested bearing.
5 Conclusions This paper proposes an improved ICA algorithm (CR-ICA), and applies it to tackle the following problems in experiments and engineering diagnosis: recognition of mixed sound and preprocessing of bearing sound. The case studies show that the CRICA method performs better than the traditional ICA algorithms.
References 1. Comon P.: Independent component analysis, a new Concept, Signal Processing Vol.36 (1994) 287-314 2. Belland, A.J., Sejnowski, T.J.: An information-maximization approach to blind separation and blind separation and blind deconvolution, Neural Computation, Vol.7 (1995) 11291159 3. Lee, T.W., Girolami, M., Sejnowski, T.J.: Independent component analysis using an extended infmax algorithm for mixed sub-gaussian and super-gaussian sources, Neural Computation,11(2) (1999) 417-441 4. Li, X.F., Wen, G.R.: Analyzed method of skewness component in Blind Separation, Journal of Xi’an Jiaotong University, Vol.37 (2003) 703-707 5. Zhang, H., Qu, L.:Partially blind source separation of the diagnostic signals with prior knowledge. Proceedings of the 14th International Congress on Condition Monitoring and Diagnostic Engineering Management, Manchester, UK. Elsevier (2001) 177-184 6. Aapo Hyvarinen, Erkki Oja: Independent Component Analysis: Algorithms and Applications, Neural Networks, Vol 13 (2000) 411-430 7. Qu Liangsheng, He Zhengjia: Mechanical Fault Diagnostics, Shanghai Science & Technology press.(1986) 86-87 8. Aapo Hyvarinen, Erkki Oja: Independent Component Analysis by General Nonlinear Hebbian-Like Learning Rules, Signal Processing 64. (1998) 301-313 9. Xu Yonggang: Mechanical Dynamic Signal Processing, Doctor dissertation, Xi’an Jiaotong University (2003) 10. Liangsheng Qu, Guanghua Xu: The Fault Recognition Problem in Engineering Diagnostics, Insight, Vol 39, No 8 (1997) 569-574
Array Signal MP Decomposition and Its Preliminary Applications to DOA Estimation Jianying Wang, Lei Chen, and Zhongke Yin School of Information Sci. & Tech., Southwest Jiaotong University, Chengdu, 610031, China {jywang, chan, zkyin}@home.swjtu.edu.cn
Abstract. The idea of sparse decomposition is introduced into array signal processing, and a novel approach to DOA estimation is presented in this paper. The approach decomposes the array signal over an over-complete dictionary, the atoms of which are vectors established according to the array geometry. The sparse decomposition is implemented by matching pursuit (MP) in the proposed algorithm. High resolution of DOA estimation can be obtained according to the parameters of the atoms decomposed with MP. The DOA estimation resolution capabilities are shown to be much higher than MUSIC and ESPRIT, especially in the case of less array elements and lower SNR. Furthermore, the performance is not affected by the correlation of the signals to be resolved. Computer simulation confirms its validity.
Array Signal MP Decomposition and Its Preliminary Applications
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more and more research interests in recent years [8-10]. This paper introduced nonorthonormal decomposition into the array signal processing area. By establishing over-complete family of basis functions and adjusting atom vector density of overcomplete dictionaries, the received array signal can be projected onto one basis vector which approximates very close to the desired signal. Based on sparse representations of the array signal, high-resolution spatial estimation was implemented. In this paper, using the idea of sparse decomposition, based on matching pursuit (MP) decomposition [8], a new method of high-resolution DOA estimation is firstly proposed. Computer simulations show that the new algorithm obtains higher resolution than the conventional DOA estimation algorithm in the case of definite density of atom vectors, and the new method has better performance especially at low SNR.
2 Array Signal Model Consider D far-field narrow-band sources which have known center frequency ω 0 impinging on the array (as shown in Fig. 1). In such array, the distance d between two elements causes the propagation delays τ . Then the complex output of the lth element at time t can be written as: D
xl (t ) = ¦ ali si (t − τ li (θi )) + ni (t )
l = 1,2,, M
(1)
i =1
Where a li is the corresponding sensor element complex response at frequency ω 0 and τ li is the propagation delay between a reference point and the lth sensor element for the ith wavefront impinging on the array from direction θ i , ni (t ) is the additive noise that is assumed to be a stationary zero-mean random process.
θ
Fig. 1. Array geometry
The received data vectors of the array can be written as: X( t ) = AS( t ) + N( t )
(2)
Where X (t ) is the M × 1 snapshot data matrix, the vector S( t ) is the D × 1 data vector of impinging signals. N( t ) is the M ×1 data matrix of additive noise.
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A is the array steering vector A = [ a1 a2 aD ] , For the ith signal, the vector a i
in the matrix A is given by a i = [exp(− jω 0τ 1i ), exp(− jω 0τ 2i ),, exp(− jω 0τ Mi )]T
i = 1,2,, D
(3)
Where τ li is the propagation delay between the reference point and the lth sensor for the ith wavefront impinging on the array from direction θ i . τ li is given by
τ li (θ i ) =
(l − 1)d sin θ i c
(4)
According to the array signal model described above, DOA estimation can be calculated though (4), as long as τ li is estimated by some method.
3 The DOA Estimation Based on MP Decomposition The conventional methods of array signal processing are almost based on orthonormal decomposition of signals, so there are many limits as mentioned above. In this paper, we introduce a new method of array signal processing with matching pursuit. Matching pursuit is a greedy algorithm that chooses at each step of decomposition process a waveform that approximates best a part of the signal. By using MP, the array signal can be decomposed over a family of functions chosen flexibly according to the characteristic of the signal itself. The characteristic of expansion coefficient can be utilized to get the interested information. According to the array signal model, in order to obtain The DOA estimation with equation (4), the atom vectors can be written as: 1 º ª » « exp(− jω d sin θ c ) 0 m » Gθ m (ai , t ) = S (t ) « » « » « ¬exp(− jω0 ( M − 1)d sin θ m c )¼
m = 1,2, , M
(5)
Where θ m is the DOA parameter which can be set according to the required searching precision. M is the total number of atoms in the dictionary. The parameters of vector atoms determined only by θ m . We can decompose the array signal over the dictionaries described above. According to the equation (5), we can establish an overcomplete vector family, and decompose the array signal over the family. By using MP, the array signal x can be decomposed into x = PG x + Rx
(6)
Where x is the signal received by array sensors, PG x is the signal’s projection on the atom vector which best matches the source, namely PG ( x ) = sup PG ( x ) , and Rx is θ m
the residual vector after approximating x with G .
Array Signal MP Decomposition and Its Preliminary Applications
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In the MP decomposition, we must select a vector atom that matches x almost at best. This selection must follow a restriction which given by vector projection theorem as follow: x − Gθ i = inf x − Gθ y y∈ m
(7)
Obviously, the atom vector that best matches the original array signal can be obtained by searching the value of θi . Therefore the estimation of DOA can be obtained by the atom parameter θi . On the contrary, the noise does not have the same characteristic as the array signal, so the projection of noise on the atom vector is approaching zero. So this method can achieve the de-noised signal.
4 Simulation Results In this section, we present some simulation results to compare the performance of the new DOA estimation algorithm with the conventional algorithms (ESPRIT, MUSIC). We use a uniform linear array with pair spacing λ 2 . The signal is narrow band of 256 samples that is built by adding white Gaussian noise. The source is located at 60o. All the results are averaged over 128 simulations run at each point. Fig. 2 shows the DOA estimation result with a 3-element array. The simulation displays that the new DOA estimation method based on array signal MP decomposition has better performance than the conventional methods in the case of less array elements, so the new algorithm is an efficient method in reducing the hardware costs. In order to improve the algorithm’s performance at low SNR, an array of 10 elements is used in the next simulation. Fig. 3 shows the DOA estimation STD versus the signal-to-noise (SNR) for 256 snapshots. The simulation results indicate that the
Fig. 2. DOA Estimation STD versus SNR
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Fig. 3. DOA Estimation STD versus SNR
new DOA estimation method has obviously higher resolution than the conventional methods such as ESPRIT and MUSIC, especially at low SNR. Another main advantage of the algorithm proposed in this paper is that, in the DOA estimation based on MP, the powers of the received signals are used instead of the signal subspaces; hence the system performance is robust to correlation between the inputs from different angles.
5 Conclusion A central problem in the array signals’ DOA estimation is how to exactly estimate the time delay. By decomposing the array signals over one over-complete dictionary, the time delay estimation has been clearly improved compared with decomposing over an orthonormal basis. As a result, higher resolution has been achieved with MP decomposition of the array signals. The new algorithm works well in the case of less array elements; therefore it can reduce the hardware costs. It performs well too at very low SNR circumstance, and can also be used when the signals are correlated. The newly proposed method in this paper should be beneficial to radar and sonar systems. On the other hand, the new method is just a preliminary probe into array signal sparse decomposition; whereas it was shown that the technique can achieve higher resolution in parameter estimation. From the analysis above, the method is quite promising, thus further research is needed on the algorithms and its performance.
References 1. Capon, J.: High-resolution Frequency-wave Number Spectrum Analysis. Proc. Of IEEE, Vol. 57(8) (1969) 1408-1418 2. BURG, J.P.: Maximum Entropy Spectral Analysis. PhD Thesis, Stanford University, Stanford, USA (1975)
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3. Schmidt, R.O.: Multiple Emitter Location and Signal Parameter Estimation. IEEE Trans. Antennas and propagation, Vol. 34(3) (1986) 276-280 4. Roy, R., Kailath, T.: ESPRIT--Estimation of Signal Parameters via Rotational Invariance Techniques. IEEE Trans. Acoustics, Speech, and Signal processing, Vol. 37(7) (1989) 984-995 5. Mendel, J.M.: Tutorial on Higher-order Statistics (spectra) in Signal Processing and System Theory: Theoretical Results and Some Applications. Proc. of IEEE, Vol. 79(3) (1979) 278-305 6. Southall Hugh, L., Simmers Jeffrey, A., Donnell Teresa H.O.: Direction Finding in Phased Arrays with a Neural Network Beamformer. IEEE Transactions Antennas and Propagation, Vol. 43(12) (1995) 1369-1374 7. Xu, W., Liu, T., Schmidt, H.: Beamforming Based on Spatial-wavelet Decomposition. Sensor Array and Multichannel Signal Processing Workshop Proceedings, Vol. 4(6) (2002) 480-484 8. Mallat, S., Zhang, Z.: Matching Pursuits with Time-frequency Dictionaries. IEEE Trans. Signal Processing, Vol. 41(12) (1993) 3397-3415 9. Eldar, Y.C., Oppenheim, A.V.: MMSE Whitening and Subspace Whitening. IEEE Trans. Information Theory, Vol. 49(7) (2003) 1846-1851 10. Arthur, P.L., Philipos, C.L.: Voiced/unvoiced Speech Discrimination in Noise Using Gabor Atomic Decomposition. Proc. Of IEEE ICASSP[C], Hong Kong Vol. I (2003) 820-828
Mixture Matrix Identification of Underdetermined Blind Source Separation Based on Plane Clustering Algorithm* Beihai Tan and Yuli Fu College of Electronic and Communication Engineering, South China University of Technology 510640, China [email protected], [email protected]
Abstract. Underdetermined blind source separation and sparse component analysis aim at to recover the unknown source signals under the assumption that the observations are less than the source signals and the source signals can be sparse expressed. Many methods to deal with this problem related to clustering. For underdetermined blind source separation model, this paper gives a new plane clustering algorithm to estimate the mixture matrix based on sparse sources information. Good performance of our method is shown by simulations.
1 Introduction Blind source separation (BSS) has been applied to many fields, such as, digital communication, image processing, array processing and biomedicine, and so on. Also, it has a lot of potential applications. Therefor, it has been a hot topic in signal processing and neural networks field [1-6]. Blind separation comes from cocktail problem [7], just to say, we only can restore source signals by gotten sensor signals, what’s more, mixture channel and source signals’ distributions are unknown. So the mathematics model of BSS is X (t ) = AS (t ) + N (t ) , t = 1 T .
(1)
where X (t ) = [ x1 (t ), x 2 (t ) x m (t )]T is sensor signals, A ∈ R m×n is mixture matrix,
and S (t ) = [ s1 (t ), s2 (t ) sn (t )]T is source signals, and N (t ) = [n1 (t ), n2 (t )nm (t )]T is noise. BSS aims at restoring source signals only by known sensor signals, generally, we suppose noise doesn’t exist. In general, if m is more than n , that is, the number of sensor signals is more than that of source signals [8], it is overdetermined BSS. We consider the case that m is less than n in this paper, namely, underdetermined BSS. Although it is difficult to restore source signals, we can use some other information, such as, sparseness of *
The work is supported by the National Natural Science Foundation of China for Excellent Youth (Grant 60325310), the Guangdong Province Science Foundation for Program of Research Team (grant 04205783), the Natural Science Fund of Guangdong Province, China (Grant 05006508), the Specialized Prophasic Basic Research Projects of Ministry of Science and Technology, China (Grant 2005CCA04100).
Mixture Matrix Identification of Underdetermined Blind Source Separation
61
source signals, to restore source signals, and if some source signals aren’t sparse in time-domain, we can make them sparse through some transformation, such as, Fourier transformation or wavelet transformation, so BSS model is also written as x(t ) = a1 s1 (t ) + a 2 s 2 (t ) + a n s n (t ), t = 1 T .
(2)
Where x(t ) = [ x1 (t ), x m (t )]T , a i = [a1i , a mi ]T .
2 Sparse Representation of Underdetermined Blind Separation For underdetermined BSS, generally, some blind extraction algorithms [9], [10] are taken in past, but the algorithms can’t realize to restore all source signals. In order to restore all source signals in underdetermined BSS, researchers make use of some characteristics of signals, for example, sparse analysis is adopted to make signals sparse representation, so some underdetermined BSS algorithms are successfully. Among the good algorithms there are Belouchrani’s maximum likelihood algorithm [11] for discrete sources, Zibulevsky’s sparse decomposition algorithm [3], Lee [12] Lewicki [13] and Li’ overcomplete representation algorithms [5] and Bofill’ sparse representation in frequency domain [14]. Generally, sparse signal is that the one whose most sample points are zero or are near to zero, and a little sample points are far from zero. Here, we suppose that the source signal si (t ) is nonzero and the other source signals are zero or are near to zero at the time of t . So equation (2) can be written as (3) x(t ) = ai si (t ) . From above equation, we can known that ai and x(t ) are collinear so we can estimate mixture matrix A = [a1 , a2 , an ] by clustering x(t ) in all time. It is a very important algorithm for sparse component analysis solving underdetermined BSS, named by k-means clustering, and the algorithm includes two steps [5],[14], first, clustering centers are estimated by k-means clustering; second, source signals are estimated by known mixture matrix through linear programming. Because the above algorithms require that source signals are very sparse, so there is a lot of restriction for application. Recently, Pando Georgiev puts forward a new sparse component analysis method for underdetermined BSS based the next conditions [15]. A1) the mixture matrix A ∈ R m×n has the property that any square m × m submatrix of it is nonsingular. A2) each column of the source matrix S (t ) has at most m − 1 nonzero elements. A3) the sources are sufficiently rich represented in the following sense: for any index set of n − m + 1 elements I = {i1 , i2 in−m+1} ⊂ {1,2, n} there exist at least m column vectors of the matrix S such that each of them has zero elements in places with indexes in I and each m − 1 of them are linearly independent.
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B. Tan and Y. Fu
For simplicity, we suppose m = 3, n = 4 to explain the paper’s algorithm for the problem. If m = 3, n = 4 , the equation (2) can be written as: x(t ) = a1 s1 (t ) + a 2 s 2 (t ) + a 3 s 3 (t ) + a 4 s 4 (t ), t = 1 T .
(4)
where x(t ) = [ x1 (t ), x2 (t ), x3 (t )]T and ai = [a1i , a2i , a3i ]T , according to A2), if the i th source signal and the j th source signal are nonzero at the time of t , then x(t ) = a i s i (t ) + a j s j (t ), t = 1 T .
(5)
From equation (5), we can know the sensor signal vector is in the same plane with vector ai and vector a j . Again, according to A1, every two columns in mixture matrix are independent, there are defined C 42 different planes by every two columns in mixture matrix. From equation (5), the mixture matrix A = [a1 , a2 , a3 , a4 ] can be estimated through plane clustering of sensor signals in no noise or little noise. Next, the plane clustering algorithm is given in detail and source signals are restored by it.
3 Mixture Matrix Identification Based on Plane Clustering Pando Georgiev has proved that the mixture matrix is identifiable when the conditions A1 ,A2 ,A3 are met. Because the mixture matrix is very important, but Pando Georgiev doesn’t give substantial algorithm for it, so this paper gives the substantial novel algorithm for estimating mixture matrix. For simplicity, we still suppose m = 3, n = 4 to explain the algorithm. To identify C 42 = 6 planes, we turn to identify their six normal lines , and if their normal lines are identified, then we identify their planes. In order to begin plane clustering, we initialize the sensor signals x(t ), t = 1T , which are normalized. If m = 3 , a sensor signal correspond to one point in the spherical surface, and the points of the below half spherical surface need to turn them to above half spherical surface symmetrically. Then, the new sensor signals are
° ° ˆx(t ) = ® °− ° ¯
x(t ) x(t )
if x3 (t ) ≥ 0.
x (t ) x (t )
if x3 (t ) < 0.
, t = 1T .
(6)
Clustering xˆ (t ) is correspond to clustering x(t ) , and the points will locate in the above half spherical surface which are in the same planes with the planes by every two columns of the mixture matrix respectively. Similar to k-means cluster, normal lines clustering is to get their normal lines and modify them in clustering algorithm. For example, there are some initialized points y (t ) = [ y1 (t ), y 2 (t ), y3 (t )]T , t = 1,2, N 0 in a plane.To identify its plane, we suppose & its normal line is n 0 = [n 01 , n 02 , n 03 ]T , According to inner-product’ s definition, & & (7) (n0 , y (t )) = n01 ⋅ y1 (t ) + n02 ⋅ y2 (t ) + n03 ⋅ y3 (t ) = n0 ⋅ y (t ) × cos θ n&0 y (t ) ,
Mixture Matrix Identification of Underdetermined Blind Source Separation
63
& where θ n&0 y (t ) is the angle between the normal line n0 and the point y (t ) , so 0 ≤ θ n&0 y (t ) ≤ π , and −1 ≤ cos θ n&0 y (t ) ≤ 1 . From equation (7), if we need to identify the plane composed of the points y (t ) , & t = 1,2, N 0 , the normal line n0 = [n01 , n02 , n03 ]T must be found to let θ n&0 y (t ) tend to
π 2
& for any t ∈ {1,2, N 0 } , because n 0 = 1, y (t ) = 1 , so just to say
& n0 = arg min & n0
s.t.
N0
&
¦ (n , y(t )) 0
(8)
t =1
(n01 ) + (n02 ) + (n03 ) = 1. 2
2
2
Based on equation (8), the plane clustering algorithm is followed in detail. 1) 2) 3)
4)
Initialize the sensor signals x(t ), t = 1 T using equation (6) to get new sensor signals xˆ (t ), t = 1T . & & & & & & Bring six initialized normal lines randomly, n1 , n2 , n3 , n 4 , n5 , n6 . & Compute the inner-products of xˆ (t ), t = 1T and ni , i = 1 6 respectively, & & and take their absolute values, let X i = {xˆ (t ) | ( xˆ (t ), n i ) < ( xˆ (t ), n j ) , j ≠ i} . & Modify the initialized normal lines, let n = [sin θ cos ϕ , sin θ sin ϕ , cosθ ] , 0 ≤θ ≤
5)
π
㧘
0 ≤ ϕ ≤ π . For the sake of simplicity, the algorithm is shown by 2 the following Matlab programme. for i = 1 : 6 & & nˆ i = ni ; for θ = 0 : η1 : π / 2 for ϕ = 0 : η 2 : π & & if ( X i , n ) < ( X i , ni ) & & ni = n ; end end end end & & Where η1 ,η 2 denote step sizes respectively, ( X i , n ) , ( X i , ni ) respectively denote the sums of inner-product’s absolute value between all the elements of & & the set X i and normal lines n , and ni . & & If nˆi − ni < ε i i = 16 , the algorithm stops and ε i is a given little value,
㧘
otherwise, continue the step 3). Because each column vector ai in the mixture matrix compose a plane with other & & column a j ( j ≠ i ) , so ai must be orthogonal with three normal lines among n1 , n 2 , & & & & n3 , n 4 , n5 , n 6 and the three normal lines must be in the same plane. That is to say, if we find any three coplanar normal lines, the columns ai (i = 1, 4) will be estimated.
64
B. Tan and Y. Fu
4 Restoring Source Signals & Now, we suppose that the normal line is nk (k ∈ {1, 6}) of the plane composed of ai , a j (i ≠ j ) , and the set of the sensor signals is X l (l ∈ {1, 6}) which is coplanar with ai , a j (i ≠ j ) . For any x(t ) ∈ X l , so x(t ) = ai si (t ) + a j s j (t ) ,
(9)
x(t ) = Aij sij (t ) ,
(10)
or where Aij = [ai , a j ], sij (t ) = [ si (t ), s j (t )]T , so
sij (t ) = Aij # x(t ) .
(11)
Where Aij # denotes the generalized inverse matrix of Aij . So only the i th source signal and the j th source signal have nonzero values gotten by equation (11) at the time of t , but zero for the other source signals at the time of t .
5 Simulations Results In the experiment, a random 3 × 4 matrix brings for the simulation but meets the condition A1), and take N = 1000 , four source signals are denoted in fig 1, The iniª- 0.27574 0.18977- 0.67493 0.86583º « 0.59016 0.28866- 0.72862- 0.12535» , and the » « «¬ 0.75874- 0.93844 0.11652 0.48439»¼ ª 0.67479 0.86533- 0.27554- 0.19024º algorithm is « 0.7288 - 0.12444 0.59033- 0.28914» . » « «¬- 0.11622 0.48551 0.75867 0.93819»¼
tialized mixture matrix is
matrix by the above
Fig. 1. Four source signals
Fig. 2. Restored source signals
estimated mixture
Mixture Matrix Identification of Underdetermined Blind Source Separation
65
From the estimated mixture matrix and the above figures of restored source signals, the algorithm is successful except that the first and the fourth restored signals have sign difference from the third and the second source signals, which is allowed in BSS.
6 Conclusions This paper gives a novel and substantial algorithm for estimating the mixture matrix and restoring the sparse source signals in underdetermined BSS. The algorithm is feasible and its good performance is shown in the simulation results, and it also easy to expand the algorithm to high dimension underdetermined BSS by sparse component analysis.
References 1. Hyvarinen, A., Oja, E.: Independent Component Analysis: Algorithms and Applications. Neural Networks, 13 (2000) 411-430 2. Xie, S. L., Zhang, J. L.: Blind Separation Algorithm of Minimal Mutual Information Based on Rotating Transform. Acta Electronic Sinica, 30 (5) (2002) 628-631 3. Zibulevsky, M., Pearlmutter, B.A.: Blind Source Separation by Sparse Decomposition in a Signal Dictionary. Neural computation, 13 (4) (2001) 863-882 4. Xie, S. L., He, Z. S., Gao, Y.: Adaptive Theory of Signal Processing. 1st ed. Chinese Science Press, Beijing (2006) 130-223 5. Li, Y., Cichocki, A., Amari, S.: Analysis of Sparse Representation and Blind Source Separation. Neural Computation 16 (2004) 1193–1234 6. Zhang, J. L., Xie, S. L., He, Z.S.: Separability Theory for Blind Signal Separation. Zidonghua Xuebao/Acta Automatica Sinica, 30 (3) (2004) 337-344 7. Jutten, C., Herault, J.: Blind Separation of Sources, Part I: An Adaptive Algorithm Based on Neuromimetic. Signal Processing, 24 (1991) 1-10 8. Zhang, J. L., Xie, S. L.: Multi-input Signal-output Neural Network Blind Separation Algorithm Based on Penalty Function. Intelligent and Complex Systems, 2 (2003) 353-362 9. Li, Y., Wang, J., Zurada, J. M.: Blind Extraction of Singularly Mixed Source Signals. IEEE Trans on Neural Networks, 11 (2000) 1413-1422 10. Li, Y., Wang, J.:Sequential Blind Extraction of Instantaneously Mixed Sources. IEEE Trans. Signal Processing, 50 (5) (2002) 997-1006 11. Belouchrani, A., Cardoso, J. F.: Maximum Likelihood Source Separation for Discrete Sources. In Proc. EUSIPCO, Edinburgh, Scotland (1994) 768-771 12. Lee, T. W., Lewicki, M.S., Girolami, M., Sejnowski, T. J.: Blind Source Separation of More Sources Than Mixtures Using Overcomplete Representation. IEEE Signal Processing Letter, 6 (1999) 87-90 13. Lewicki, M. S., Sejnowski, T. J.: Learning Overcomplete Representations. Neural computation, 12 (2000) 337-365 14. Bofill, P., Zibulevsky, M.: Underdetermined Source Separation Using Sparse Representation. Signal processing, 81 (2001) 2353-2362 15. Georiev, P., Theis, F., Cichocki, A.: Sparse Component Analysis and Blind Separation of Underdetermined Mixtures. IEEE Transactions On Neural Networks, 16 (4) (2005) 992-996
Non-linear Blind Source Separation Using Constrained Genetic Algorithm Zuyuan Yang and Yongle Wan School of Electrics & Information Engineering, South China University of Technology, Guangzhou 510641, Guangdong, China [email protected], [email protected]
Abstract. In this paper, a novel adaptive algorithm based on constrained genetic algorithm (GA) is presented for solving non-linear blind source separation (BSS), which can both get out of the trap of local minima and restrict the stochastic decision of GA. The approach utilizes odd polynomials to approximate the inverse of non-linear mixing functions and encodes the separating matrix and the coefficients of the polynomials simultaneously. A novel objective function based on mutual information is used with the constraints to the separating matrix and the coefficients of the polynomials respectively. The experimental results demonstrate the feasibility, robustness and parallel superiority of the proposed method.
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in order. In [8], a constraint to the estimations was used, but this approach used a sigmoid function with only one parameter which may affect the approximation of the non-linear demixing functions. In [10], the assumptions to the coefficients of the polynomials simplified the contrast function. But the results violated the assumptions without the constraints corresponding to them in the algorithm. The post-nonlinear model is like following:
x(t ) = f ( A ⋅ s (t )) , y (t ) = W ⋅ g ( x(t )) .
(1)
Where x(t ) are mixtures of signals s (t ) , y (t ) are estimations of s (t ) . (see Fig. 1)
x1 s1
f1
sn
fn
g1
y1
gn
yn
xn
Fig. 1. Post-nonlinear mixing and demixing model
In this work, a novel objective function based on mutual information with the constraints to the separating matrix and the coefficients of the polynomials is used for post-nonlinear model. Instead of stochastic gradient descent method, GA is utilized to solve non-linear BSS. The parallel superiority of GA is used to get out of the trap of local minima for both separating matrix and coefficients of the polynomials, and the constraints are used to restrict the stochastic decision of GA. The paper is organized as follows: in Section 2, the algorithm to solve non-linear BSS is described in detail, including the construction of the fitness function. The experimental results are shown in Section 3. Finally, a conclusion is given in Section 4.
2 Blind Separation Using GA 2.1 Fitness Function
The selection of fitness function is based on information theoretic criterion, the y ," yn mutual information between 1 is defined as follows [11]: n
I ( y1 ," yn ) = − H ( y1 ," yn ) + ¦ H ( yi ) .
(2)
i =1
The function g is approximated as follows by Weierstrass approximation theorem: P
g j ( x j ) = ¦ g jk x 2j k −1 , j = 1," , n . k =1
where g jk are adjustable parameters. Therefore, the fitness function is used [10]:
(3)
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Z. Yang and Y. Wan n n ° L (W , g ) = − ln det W − ¦ E[log g ′j ( x j ) ] − ¦ H ( yi ) . ® j =1 i =1 °¯ H ( yi ) ≈ C − (k3i ) 2 12 − (k4i ) 2 48 + 3(k3i ) 2 k4i 8 + (k4i )3 16
(4)
where h jk = g jk h j1 for k ≥ 2 , and E[ yi2 ] = 1, E[ yi ] = 0 so as to WW T = I , C is a constant, k3i = E[ yi3 ], k4i = E[ yi4 ] − 3 . Suppose that g j1 = 1 , h jk 1(k ≥ 2) , from (4),
we can obtain the following non-linear programming problem with constraints: n
P
n
Max: f = ln det W + ¦¦ g jk E[(2k − 1) x 2j k − 2 ] + ¦ H ( yi ) .
(5)
s.t. h(W ) = WW T − I = 0, h ( g ) = g jk − ε ≤ 0, k ≥ 2 .
(6)
j =1 k = 2
i =1
where ε < 0.1 is a positive constant , H ( yi ) is estimated from (4). And (6) is equal to h j ( w) = 0, hi ( g ) ≤ 0, j = 1," , m1 , i = 1," , m2 .
(7)
Where m1 , m2 is from (9). Under the constraints, the feasible domain Q can be defined as follows [9]: Q = {( w, g ) h j ( w) = 0, hi ( g ) ≤ 0, j = 1, 2," , m1 , i = 1, 2," , m2 } .
(8)
㧘 m = (n
(9)
Definitions: w = [W11 , W12 ,"Wnn ]T
1
2
+ n) 2 , m2 = n ⋅ p − n .
H j ( w) = h j ( w) ∇h j ( w) , H max ( w) = max{H j ( w)} ° °° H i ( g ) = hi ( g ) ∇h j ( g ) , H max ( g ) = max{0, H i ( g )} . ® ° k1 = arg{ j H j ( w) = H max ( w)}, j = 1, 2," , m1 ° °¯ k2 = arg{i H i ( g ) = H max ( g )}, i = 1, 2," , m2
Def.1
Def. 2
DSFD ( w, g ) = H max ( g )∇hk2 ( g ) + sgn(hk1 ( w)) H max ( w)∇hk1 ( w) .
(10)
(11)
m1
d ( w, g ) = v0 ∇ w f − ¦ v j ∇h j ( w) .
Def. 3
(12)
j =1
where v j is weight of the gradient direction. In general, v0 = 0.5 , and
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Def. 4
FD = d ( w, g )T ⋅ (− DSFD ( w, g )) .
(14)
Def. 5
p ° f ( w, g ) (1 + 1 FD ) , f ≥ 0 eval ( w, g ) = ® . p °¯ f ( w, g ) ∗ (1 + 1 FD) , f < 0
(15)
where p ≥ 1 , usually p = 2 . Then, the fitness function F ( w, g ) is given as e f ( w, g ) + e2 , ( w, g ) ∈ Q . F ( w, g ) = ® 1 ¯e1 ⋅ eval ( w, g ) + e2 , else
(16)
where e1 , e2 are positive real numbers such that F ( w, g ) ≥ 0 . 2.2 Operations Initial population: Select proper size N of the population, and encode the genes of the chromosome which corresponds to separating matrix W and coefficients of nonlinear function g with real number. Set proper parameters for the fitness function, crossover probability, mutation probability, maximum iteration number, and so on. Selection: Fitness-proportionate selection by roulette wheel is adopted, and the new generations come from combinational chromosomes with better fitness. Crossover: In the paper, the arithmetic combinatorial crossover operator is suggested:
° wi( k +1) = α ⋅ wi( k ) + (1 − α ) w(j k ) , ® ( k +1) = α ⋅ w(j k ) + (1 − α ) wi( k ) °¯ w j
° gi( k +1) = α ⋅ gi( k ) + (1 − α ) g (j k ) . ® ( k +1) = α ⋅ g (j k ) + (1 − α ) gi( k ) °¯ g j
(17)
Mutation: The weighted gradient direction from (12) is introduced for w :
w( k +1) = w( k ) + β ( k ) d ( w( k ) , g ( k ) ) and g ( k +1) = Mean( gi( k ) ), i = 1, 2," , m2 .
(18)
where β ( k ) is learning rate, and Mean( x) means the average of x . Stop rule: A maximum iteration number is determined to trigger the stop rule.
3 Experimental Results To provide an experimental demonstration of the validity of BSS with constrained GA, three sources will be used in post-nonlinear model. MSE and the residual crosstalk in decibels (Ct) [11] are used to evaluate accuracy of the algorithm. MSEi = E ( si (t ) − yi (t )) 2 , Cti = 10 log E[( yi − si ) 2 ] . where y, s are with unit variance.
(19)
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The linear mixing matrix and three nonlinear functions: ª 0.1870 A = «« 0.1624 ¬« 0.1286
f1 = tanh( x ) ° ® f 2 = tanh(0.8 x) . ° f = tanh(0.5 x) ¯ 3
(20)
Polynomials of fifth order were used as the approximations for g = f −1 , according to the algorithm, we have obtained the results as follows: g1 = x + 0.094569 x 3 + 0.039137 x5 ° 3 5 ® g 2 = x + 0.087650 x + 0.092012 x ° 3 5 ¯ g 3 = x + 0.098845 x + 0.045751x
Table 1. Crosstalk (Ct) and MSE corresponding to sources
Ct (dB) MSE
s1
s2
s3
-26.7264
-64.5408
-26.6678
0.0691
0.0016
0.0695
1 g1 h1
0 -1 -2
0
5
10
15
20
25
30
35
40
45
50
10
15
20
25
30
35
40
45
50
10
15
20
25
30
35
40
45
50
0 g2 h2
-0.5
-1
0
5
1 g3 h3
0
-1
0
5
Fig. 2. g i means the estimation of the non-linear demixing function according to the algorithm,
hi = f i −1 means the inverse of non-linear mixing function
Fig. 3. Original sources and the estimations
4 Conclusion In this paper, the post-nonlinear blind source separation model has been solved using constrained GA. The novelty of this approach is using reasonable constraints in the
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novel contrast function and a new fitness function is constructed. The experimental results show the validity of this method and the original sources are recovered acceptably up to scalings. It is proper to use constrained odd polynomials to approximate the inverse of non-linear distortion when it is under controlled. However, it may not work well under other conditions as it is a quite open question to estimate the inverse of a non-linear function, and there is still a long way for us to overcome it.
Acknowledgement This work is supported by the National Natural Science Foundation of China for Excellent Youth (60325310), the Guangdong Province Science Foundation for Program of Research Team (04205783), the Natural Science Fund of Guangdong Province, China (05103553), the Specialized Prophasic Basic Research Projects of Ministry of Science and Technology, China (2005CCA04100).
References 1. Li, Y., Andrzej, C., Amari, S.: Analysis of Sparse Representation and Blind Source Separation. Neural Computation, 16 (2004) 1193-1234 2. Gao, Y., Xie, S. L.: An Algorithm for Nonlinear Blind Source Separation Based on Signal Sparse Property and Kernel Function. Computer Engineering and Applications, 22 (2005) 33-35 3. Anthony, J. B., Terrence, J. S.: An Information-maximization Approach to Blind Separation and Blind Deconvolution. Neural Computation, 7(1995) 1129-1159 4. Tan Y., Wang, J.: Nonlinear Blind Source Separation Using Higher Order Statistics and A Genetic Algorithm. IEEE Trans on Evolutionary Computation, 5(2001) 600-612 5. Xie, S. L., He, Z. S., Gao, Y.: Adaptive Theory of Signal Processing. 1st ed. Chinese Science Press, Beijing (2006) 136-155 6. Gao, Y., Xie, S. L.: Two Algorithm of Blind Signal Separation Based on Nonlinear PCA Criterion. Computer Engineering and Applications, 22 (2005) 24-26 7. Zhang, J. L., He, Z. S., Xie, S. L.: Sequential Blind Signal Extraction in Order Based on Genetic Algorithm. Acta Electronica Sinica, 32 (2004) 616-619 8. Liu, H. L., Xie S. L.: Nonlinear Blind Separation Algorithm Based on Multiobjective Evolutionary Algorithm. Systems Engineering and Electronics, 27 (2005) 1576-1579 9. Richard, Y. K. F.,Tang, J. F., Wang, D.W.: Extension of A Hybrid Genetic Algorithm for Nonlinear Programming Problems with Equality and Inequality Constraints. Computers & Operations Research 29 (2002) 261-274 10. Martin-Clemente, R., Putonet, C. G., Rojas F.: Post-nonlinear Blind Source Separation Using Methaheuristics. Electronics Letters, 39 (2003) 1765-1766 11. Taleb, A., Jutten, C.: Source Separation in Post-nonlinear Mixtures. IEEE Trans on Signal Processing, 47 (1999) 2807-2820 12. Xie, S. L., He, Z. S., Fu, Y. L.: A Note on Stone's Conjecture of Blind Signal Separation. Neural Computation, 17 (2005) 321-330
A Distributed Wavelet-Based Image Coding for Wireless Sensor Networks Hui Dong, Jiangang Lu, and Youxian Sun National Laboratory of Industrial Control Technology Zhejiang University, Hangzhou 310027, China {dongh, jglu, yxsun}@iipc.zju.edu.cn
Abstract. The strict constrains of wireless sensor networks (WSN) on individual sensor node's resource brings great challenges to the information processing, especially in image capture sensor network. A Simple Wavelet Compression (SWC) processing of image coding is proposed to maximize compression and minimize energy cost in WSN. For low activity in WSN, we employ a Low-complexity Change Detection Algorithm (LCDA) to mark active blocks and we only encode these active regions to save energy. In particular, a position estimation and compensation method is presented to exploit the inherent correlations that exist between sensor readings based on distributed lifting scheme. The impact of this scheme on image signal quality is presented in the final. The simulation results showed that these approaches achieved significant energy savings without sacrificing the quality of the image reconstruction
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and Energy Efficient Wavelet Image Compression algorithm (EEWIC) for lossy compression of still image, which consists of two techniques attempting to conserve energy by avoiding the computation and communication of high-pass coefficients: “HH elimination” and “H* elimination” technique. Another energy efficient power aware image compression [5] noted that maximum compression before transmission dose not always provide minimal energy consumption, and present a heuristic algorithm for it. The heuristic algorithm algorithm tries to minimize total energy dissipation with selecting the optimal image compression parameters under given the network conditions and image quality constraints. However, their approaches mainly focus on power efficient techniques for individual components and can not provide a favorable energy performance trade-off in the case of WSN. Fundamentally different from conventional image sensor, image sequences in WSN for environmental monitor are often characterized by low activity and high spatial correlation. These differences are calling for novel approaches for WSN and in particular in network data processing for saving energy consumption in transmission and computation. Based on fast lifting scheme, we propose an energy efficient distributed spatial-frequency wavelet transform algorithm for image compression, enabling significant reductions in computation as well as communication energy needed, with minimal degradation in image quality. Finally, the superior performance of this algorithm is demonstrated by comparing it with several other popular image compression techniques. The paper is organized as follows. Section 2 introduces the background and proposed algorithm. The Comparison of the scheme is addressed in Section 3. Section 4 presents some preliminary results. In Section 5 we present our conclusion and discuss future works.
2 Background and Proposed Algorithm We consider a wireless networks composed of a set of stationary, battery-powered sensor nodes, which is developed as part of the low power wireless sensor project at MIT (AMPS) [6]. Each of sensors is equipped with CLOCK, SENSOR, ADC, LED, RADIO and APPLICATION. The system set-up is shown in Figure 1. Sensor 1 Sensor 2
...
A/D
N hops
A/D Cluster head SWC
Centre node
... ...
A/D Sensor n
Fig. 1. The architecture of wireless system
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In order to reduce the communications cost, WSNs can be organized according to a cluster architecture. For the sake of simplicity, we assume that the area under observation is an 2D model plane where sensors are located. Data sampling by the sensors are collected at a source sensor node, clustered by a head node, which is either a central controller or gateway to the fixed network. The sensors and the central node were assumed to be placed as in Fig 1, where the “N” is number of hops on the shortest path between the sources and the sink and “n” is the number of sources, which capture the image signal from the environment. Fig. 2 shows the block diagram of the image coding with the proposed position estimation and compensation in the wavelet domain. In the proposed coding scheme, an input image signal is decomposed by the integer wavelet transform and transmits to the cluster head node. The position estimation finds a similarity block in the neighborhood sensor, which is matched with the current block, and then gets the position vector. The wavelet block consists of the wavelet coefficients which are only related to a local region of the image. According to position vector, we can shift the wavelet coefficients buffer and make it has strong correlation between coefficients of different sensors. In the final, we encode the similar coefficients block with proposed simple wavelet compression. The residual signal can be quantized and encoded by embedded zerotree wavelet (EZW) coder [7] or by set partitioning in hierarchical trees (SPIHT) coder [8]. Position
Position vectors
estimation sensor
Wavelet DWC coefficient
Change detection
...
...
Input sensor
Marked block
Change detection
Cluster head
Position compensation
Centre node
DWC Bit stream
Reference frame
DWC
Entropy coder
Fig. 2. Block diagram of proposed image coding scheme
2.1 Change Detection Unlike typical multimedia video, image sequences in WSN for environmental monitor are often characterized by low motion, when no object is expected to move within the scene but in case of anomalies. In this section we present a low-complexity algorithm to scans the image and mark those active regions within one frame, and we only encode these active regions to save energy consumption. Each input image signal data is divided into 8x8 blocks. In order to decrease complexity, these pixels in each block are hierarchically subdivided into the subsets number 1. 2, and 3 in order of importance [2]. The algorithm scans the value in the block according to the order of importance, computing the difference between each value and the one in the same position in the reference frame; then, it attempts to classify the difference as noise, shadow or illumination change, or object motion. Accordingly, Di, R, U is defined as follow:
A Distributed Wavelet-Based Image Coding for Wireless Sensor Networks
Di = xori (i ) − xref (i ) n
R = ¦ Di i =1
75
(1)
n
¦x
ori
(i )
(2)
i =1
U = Max ª¬ xori (i ) − xref (i ) º¼ ( i = 1...n )
(3)
Moreover, two values N and M are defined and used as a threshold to classify the signal. A sensitivity parameter S is defined as the maximum allowed number of “active” bits in an inactive block and P is defined as the number of pixels for which Di exceeds M. The simple code is presented in Algorithm 1. The reference frame is updated by copying the marked blocks of the marked frame onto the current reference frame. The threshold are automatically computed and updated during the analysis and encoding process[2]. Algorithm 1 For i=0 to n scan each pixel according to the order of importance if P>S then mark the block as activity encode this block proceeding with next block endif End For calculate R if RN and U>M then mark the block as activity encode this block proceeding with next block end if if RM then classify the block content as shadow or illumination. proceeding with next block end if update the reference frame compute the threshold and update it 2.2 The Wavelet Transforms Based on Lifting Scheme
The lifting scheme is an alternative method to compute wavelet transforms. It allows a faster implementation, along with a full in-place calculation of the coefficients [10, 11]. Lifting scheme contains three stages: split, prediction and update. The data is
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split into two disjoint sets, followed by a series of prediction and update steps to transform the coefficient data (Fig.3), where sn denotes the high-pass data and d n denotes the low-pass data after the transform is computed.
d j+1 sj
split
predict
update
+
s j+1
Fig. 3. Block diagram of the lifting process
The 5/3 filter structure is an ideal choice in low energy systems, which greatly relaxes computational requirements. It is given by: ª s 0 (2 n ) + s 0 ( 2 n + 2) º ° d 1 ( n ) = s 0 ( 2 n + 1) − « » 2 ° ¬ ¼ ® ( d ( n − 1) + d ( n )) 1 ª º 1 1 ° s ( n ) = s (2 n ) + + » 0 « °¯ 1 4 2¼ ¬
(4)
The wavelet transforms based on lifting scheme has received widespread recognition in the field of image processing for its notable success in coding and obtained very good compression performance. The proposed wavelet transforms is just an extension of standard wavelet transforms. The entire process is carried out by executing standard wavelet transforms twice, one is executed inside sensor node (to reduce the temporal redundancy), and the other in cluster node (to reduce the spatial redundancy). 2.3 Position Estimation and Compensation
High spatial density of sensor networks induces a high level of network data redundancy, where spatially proximal sensor readings are highly correlated. The sensor nodes can compress their data based on the fact that there is another sensor measuring data that is correlated with it. In video coding, several types of interframe predictions have been used to reduce the interframe redundancy. Motion compensated prediction has been used as an efficient scheme for temporal prediction. Likely, a Position Estimation and Compensation method is proposed to fully exploit the spatial inherent correlations that exist between sensor readings. Different from the conventional motion estimation, the proposed position compensation is executed in wavelet domain, which can be overcome the shortcoming of shift-variant property [9]. In this section we present an algorithm on how to exploit the correlation between sensors using position estimation and compensation. The correlation degree between sensors is determined by the overlapping sensing area of correlated nodes. We consider a 2-D model for the sensing area of image sensors illustrated by Fig. 4a. Here S1, S2 is the location of the sensor node, R is the sensing, radius, V is the center line of sight of the camera's field of view which will be termed sensing direction, and Į is the offset angle of the field of view on both sides of V. Figure 4b is the experimental
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result of sensing, which illustrate the similarity of two sensor reading. We can examine every block therein and determine if it also falls in others’ sensing areas, and then use a block-matching algorithm (Position Estimation and Compensation) to reduce the spatial redundancy. Y
YĻ
object
V2
V1
bĻ
bĻ
b
b
b ß
a
ß
a
a
a
S1 S1
X'
S2
S2
X
b
a
Fig. 4. a. Sensing model of image sensors. b. Experimental image.
The image block matching schemes are based on mapping coordinate locations, in one image to corresponding locations in a second image. Assume that the distance between the location and the image plane for all sensors are the same and denoted by d, which can characterize the correlation between sensor readings. The (x1, y1), (x2, y2) is the location of the block b in S1, S2 respectively, and the b’ (x’,y’) is the virtual location of the block b(x2, y2) coordinate transformation. As 2-D model, coordinate transformation formula is: T
ª x2 º ªx 'º « y '» = « y » « 2» « » «¬1 »¼ ¬«1 »¼
Where the (a, b) is the location of node S2 in S1 coordinate. Given the b and b’ loca)))* tion, we can get the position estimation vector bb ' . Fig. 4b illustrates the mapping. Following the same approach we can also determine the mapping relation between S1 and Sn. It is worth to be emphasized that the position estimation algorithm can be executed offline, so it is not a energy burden for wireless sensor network. Different from the position estimation, the position compensation is executed wavelet domain, which can be overcome the shortcoming of shift-variant property. Like motion compensation introducing in the MPEG standards, the block-based position compensation often produces discontinuities between the blocks because the neighboring motion vector are not coherent. These discontinuities lead to highfrequency components in the residual signals and generate large signals of the wavelet coefficients in the high-bands, so the coding efficiency can be degraded. The wavelet transform decomposes an image into four bands of LL, HL, LH, and HH, which are the low–low, the high–low, the low–high, and the high–high bands along the horizontal and the vertical directions, respectively. The so-called wavelet coefficient block (WCB) consists of those wavelet coefficients of an image that are
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only related to a local region of the image (as shown in Fig. 5). We first makes posi)))* tion estimation in spatial domain and obtains position vectors ( bb ' ) for each prediction block. Then, with taking advantage of local spatial-frequency characteristic of )))* wavelet coefficients, we shift the WCB’s order in coefficients buffer according to bb ' to compensate the WCB of prediction block with that of reference block.
Fig. 5. a. Original image. b. Coefficient after the transform.
3 Comparison of the Scheme In order to fairly compare other distributed approach and the proposed algorithm, a cost function that takes into account both processing costs and transmission costs have to be defined. The total energy dissipated at each sensor will be split into three main components: E = E p + Et + Er
(6)
where E p is the energy consumption due to wavelet transform processing, Et , Er is energy dissipation for radio transmission and reception, which has also been developed to model by a sensor node when transmitting and receiving data [12]:
ET = Eelec k + ε amp kd 2
(7)
ER = Eelec k
(8)
Equation (7), (8) stand for the energy dissipated to transmit a k-bit packet over a distance d to receive the k-bit packet respectively, where Eelec is the energy dissipated to run transmit or receive electronics, and ε amp is the energy dissipated by the transmit power amplifier to achieve an acceptable E/N at the receiver. We assume that the energy used to transmit a bit is equivalent to the energy used to receive a bit over very short distances. For our radio, we use the parameters Eelec = 50nJ / b and ε amp = 100 pJ / b / m 2 . To determine the energy efficiency of each algorithm, we take a closer look at the computational complexity of the wavelet transform computed using lifting [10]. We analyze energy efficiency by determining the number of times certain basic operations are performed for a given input, which in turn determines the amount of switching activity, and hence the energy consumption. For standard wavelet algorithm, in the forward wavelet decomposition using the above filter (5/3 filter), 2 shift and 4 add
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operations are required to convert the sample image pixel into a low-pass coefficient. Similarly, high-pass decomposition requires 2 shift and 4 add. We model the energy consumption of the low/high-pass decomposition by counting the number of operations and denote this as the computational load. Thus, for a given input M x N bits image signal and wavelet decomposition applied through L transform levels, we can estimate the total computational load as follows: L
N DWC = MN (8 A + 4S )¦ l =1
1 4l −1
(9)
Besides various arithmetic operations, the transform step involves a large number of memory accesses. Since the energy consumed in external and internal data transfers can be significant, we estimate the data-access load by counting the total number of memory accesses during the wavelet transform. At a transform level, each pixel is read twice and written twice. Hence, with the same condition as the above estimation method, the total data-access load is given by the number of reads and writes operations: L
N R _ DWC = NW _ DWC = 2MN ¦ l =1
1 4l −1
(10)
The overall computation energy is computed as a weighted sum of the computational load and data-access load. A simple energy model can be used to model the active energy dissipation due to computation of the SA-1100 as a function of supply voltage [12]:
E p = NCVdd2
(11)
Where N is the number of clock cycles per task, which is determined by N SDWC , N R _ SDWC and NW _ SDWC . C is the average capacitance switched per cycle, and
Vdd is the supply voltage. For the StrongARM SA-1100, C is approximately 0.67 nF. Obviously, the cost of the proposed lifting algorithm for computing the wavelet transform is one half of the cost of standard algorithm asymptotically. For the HH elimination technique in EEWIC [3], the result is given as flow: CR _ HH = CW _ HH =
CHH =
E L 7 1 1 MN ¦ l −1 + 2 MM ¦ l −1 4 4 4 l =1 l = E +1
L MN (22 A + 19 S ) E 1 1 + MN (12 A + 10 S ) ¦ ¦ l −1 l −1 2 l =1 4 l = E +1 4
(12)
(13)
where E is applied to the first E transform levels out of the L total transform levels [3]. To get an idea of the impact on image data quality, we also measured the distortion that the wavelet algorithm brought. Reconstruction data quality is often measured
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using a metric know as Peak Signal to Noise Ratio (PSNR). This is defined as (in decibels):
PSNR = 20 log10
2b − 1 E x ( i, j ) − y ( i, j )
(14)
where x(i,j) is the pixel value of original image, y(i,j) is of the reconstructed image and b is the bit-depth (bpp) of the original image. We recognize the PSNR does not always accurately model perceptual image quality, but use it because it is a commonly used metric in the literature.
4 Simulation Results We performed a set of experiments in 2D model as proof of concept of our approach. In particular, the quality of image using the proposed method is studied. Peak Signal to Noise Ratio (PSNR) in dB between the original and reconstructed signal was calculated for objective quality assessment. In the experiments, all sensors have the same parameter setting. The size of image captured by a sensor is 176x 144 pixels. The sensing offset angle is π / 8 and the angle between sensing directions of the two sensors π / 4 . The Sampling frequency of image sensor is 1 frame/s .
Fig. 6. Different energy used between EEWIC and SWC without Change Detection Algorithm with respect to the number of sources (n) and the degree of correlation (d)
Fig.6 shows the different energy used in EEWIC and proposed SWC without Change Detection Algorithm, where nodes number N is 1000ҏ, sampling time T=4s and ҏwavelet decomposition layer k=3. The sources number (n) and the distance (d) is varied for 0 to 100 and 0 to 10 (m) respectively. Note that for the case of the number of sources n =10, energy expenditure of our algorithm is actually few change due to the propose algorithm concentrating on exploiting the correlation between sensors. On the other hand, we can find that the extent of correlation in the data from different sources can be expected to be a function of the distance (d) between them. The figure shows a steeply decreasing convex curve of energy difference that reaches saturation when the sensor distance (d) over 5m. Thus, under experimental condition, we
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defined the two sensors are so-called strongly correlated while the distance (d) between sensors is within [0m, 5m], otherwise they are weakly correlated. To get an idea of the impact on image quality, we present the comparisons of the proposed algorithm and EEWIC algorithm. Fig. 7 shows the PSNR value versus CR for case of specific data sensor reading while wavelet decomposition layer k=3. We can see in the figure, as the compression ratio increase, the quality of reconstruction data degrades. However, in doing so, by applying the SWC and WTIC techniques at same case, different result is obtained. For the compression ratio CR<10 case, There is no perceivable difference in the quality of the two approach. But as the value of CR increasing, the quality of reconstruction data of EEWIC algorithm suffer a sharply drop, and the SWC algorithm outperform.
Fig. 7. PRD of reconstruction data for AWIC and SWC with respect to CR
5 Conclusions We have proposed a method of reducing energy consumption by using simple wavelet distributed compression for WSN’s image capture in low motion scenario. This algorithm exploit the fact that the inherent correlations between sensor readings using Position Estimation and Compensation. We also proposed a change detection algorithm to reduce computation complexity without sacrificing the quality of the image reconstruction. Experimental results show that the proposed scheme has not only high energy efficiency in transmission but also graceful degradation in PSNR performance in terms of image reconstruction quality. Several extensions of the problem studied in this paper are worth further investigation. The above experimental is run without Low-complexity change detection algorithm (LCDA), since the other algorithm (such as MPEG, EEWIC) is not designed to work at very low bit-rates and low motion scenario (environment monitor), so the comparison is unfair. Additional, we have not considered the 3-D sensing model in this work, in which the location and sensing directions for two sensors may not be in the same plane; whether our conclusions hold up under these circumstances remains to be seen.
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H. Dong, J. Lu, and Y. Sun
Acknowledgment This work was supported by the National Natural Science Foundation of China (No. 20206027), the Key Technologies R&D Program in the 10th Five-year Plan of China (No. 2004BA210A01), the Key Technologies R&D Programs of Zhejiang Province (No. 2005C21087 and No. 2006C31051), and the Academician Foundation of Zhejiang Province (No. 2005A1001-13).
References 1. Akyildiz, F., Su, W., Sankarasubramaniam, Y., Cayirci, E.: Wireless Sensor Networks: a Survey, Computer Networks, 38 (2002) 393-422 2. Magli, E. Mancin, M., Merello, L.: Low-complexity Video Compression for Wireless Sensor Networks, Multimedia and Expo, 2003. ICME '03. Proceedings. 2003 International Conference on Volume 3, 6-9 July (2003) 585-588 3. Lee, D.G., Dey, S.: Adaptive and Energy Efficient Wavelet Image Compression for Mobile Multimedia Data Services. Communications 2002, ICC 2002, IEEE International Conference on Volume 4, 28 April-2 May (2002) 2484 – 2490 4. Martina, M., Masera, G., Piccinini, G.: Embedded IWT Evaluation in Reconfigurable Wireless Sensor Network. Electronics, Circuits and Systems 2002, 9th International Conference on Volume 3, 15-18 Sept. (2002) 855 – 858 5. Huaming W., Abouzeid, A.A.: Power Aware Image Transmission in Energy Constrained Wireless Networks. Computers and Communications, 2004. Proceedings. ISCC 2004. Ninth International Symposium on Volume 1, 28 June-1 July (2004) 202 – 207 6. Min, R., Bhardwaj, M., et al.: An Architecture for a Power-aware Distributed Microsensor Node, Proc. IEEE Workshop Signal Processing Systems (SiPS ’00), Oct. (2000) 581-590 7. Shapiro, J.M.: Embedded Image Coding using Zerotrees of Wavelet Coefficients, IEEE Trans on signal processing, 12 (1993) 3445-3462 8. Said, A., Pearlman, W.A.: A New, Fast and Efficient Image Codec based on Set Partitioning in Hierarchical Trees, IEEE Trans. Circuits Syst. II, 6 (1996) 243–250 9. Park, H.W., Kim, H.S.: Motion Estimation Using Low-band-shift Method for Waveletbased Moving-picture Coding, IEEE Transactions on Image Processing, Volume 9, Issue 4, April (2000) 577 – 587 10. Sweldens, W.: The lifting scheme: A Construction of Second Generation Wavelets, SIAM Journal of Mathematical Analysis, 29 (1998) 511-546 11. Daubechies, I., Sweldens, W.: Factoring Wavelet Transforms into Lifting Steps. J. Journal of Fourier Analysis and Application, 4(3), (1998) 245-267 12. Wang, A., Chandraksan, A.: Energy-efficient Dsps for Wireless Sensor Networks, IEEE Signal Processing Magazine, Volume 19, Issue 4, July (2002) 68 - 78
Development of Secure Event Service for Ubiquitous Computing* Younglok Lee1, Seungyong Lee1, and Hyunghyo Lee2,** 1
Dept. of Information Security, Chonnam National University, Gwangju, 500-757, Korea [email protected], [email protected] 2 Div. of Information and EC, Wonkwang University, Iksan, 570-749, Korea [email protected]
Abstract. In ubiquitous computing, application should adapt itself to the environment in accordance with context information. Context manager is able to transfer context information to application by using event service. Existing event services are mainly implemented by using RPC or CORBA. However, since conventional distributed systems concentrate on transparency hiding network intricacies from programmers - treating them as hidden implementation details that the programmer must implicitly be aware of and deal with, it is not easy to develop reliable distributed services. Jini provides some novel solutions to many of the problems that classical systems have focused on, and makes some of the problems that those systems have addressed simply vanish. But there is no event servicein Jini. In this paper, we design and implement a secure event service, SeJES, based on Jini in order to provide reliable ubiquitous environment. By using the proposed event service, event consumers are able to retrieve events based on the content. In addition, it enables only authorized suppliers and consumers to exchange event each other. We use SPKI/SDSI certificates in order to provide authentication and authorization and extend JavaSpaces package in order to provide a contentbased event retrieval service.
1 Introduction In ubiquitous computing environment, application should be able to properly adapt itself according to its own context information coming from ubiquitous sensors. Most of the existing communications are based on request-reply communication model. However, many ubiquitous computing applications require more flexible and indirect or asynchronous communication mechanism. Event Service[1] is the one which can be used for these asynchronous communications. By using CORBA Event Service, a number of event suppliers and consumers can asynchronously communicate even with no background knowledge with each other. Suppliers and consumers never directly connect to each other and communicate with each other through the event channel. *
Generally, the Event Service of CORBA (Common Object Request Broker Architecture) can be really applied to many applications. However, in the case of using the event service of CORBA, problems such as persistency and filtering should be solved. Also since the existing distributed system such as CORBA can not provide a reliable environment to develop distributed service, Jini was emerged to solve the problem. In addition, the several features and services of Jini support the characteristics of ubiquitous computing environment. Among those Jini’s services is JavaSpaces[2]. But there is no event service in Jini. JavaSpacesTM is a networked repository for java objects, which provides methods of sharing and transferring objects even if Jini applications do not have any knowledge with each other. Even though applications can utilize an object transferring functions provided by JavaSpaces in order to asynchronously communicate, there are still two problems in doing it. One is that the remote listener which receives the event from JavaSpaces has to call a read() method on the JavaSpaces proxy. The other is that the event acquired by that remote method read() is not guaranteed as the latest. By modifying and extending JavaSpaces, we implemented JES (JavaSpaces based Event Service)[3]. But there is no security service in JES In this paper, we implement SeJES (Secure JavaSpaces based Event Service) by extending JES to be more applicable to ubiquitous environment. No matter what degree of computing power event consumers have, the proposed SeJES provides secure communication and content based filtering services. Our SeJES performs basic but essential security services such as authentication and authorization using SPKI/SDSI certificates as well. Also, our SeJES provides an enhanced security by transmitting renewed secure session key to event service consumers and suppliers, and some functions of QoS. This paper consists of as follows: Section 2 briefly reviews related work, and section 3 explains a system model of the SeJES. Section 3 also briefly describes how each component consisting of the system model can be implemented. Section 4 describes how the SeJES be implemented. In this section, we define interfaces furnished to consumer and suppliers, which use Event service. We explain the implementation scenario applied on our system. Finally, conclusion and the further research work are shown in Section 5.
2 Related Work Many CORBA vendors have developed Event Services, compliant with the OMG specification. Some have even added their own functionality to overcome the drawbacks depending on the application domain in which the Event Service is to be used. This section describes some commercial and academic event models that are CORBA based, and looks at their advantages and drawbacks[4]. IONA Technologies provides two different types of message service products; OrbixEvents[5] and OrbixTalk[6]. OrbixEvents is a C++ implementation of the OMG CORBA Event Service and the only commercial available Event Service that supports
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both, untyped and typed events for the push and pull communication models. OrbixTalk is used for distributing IDL-based operations over UDP using either a simple or reliable multicasting, which is ideal in systems that have many consumers and suppliers, since with UDP there is no need to maintain the connection between each consumer and supplier. However, since it is based on UDP it cannot interoperate with any other ORB system. jEVENTS[7] is a Java implementation of CORBA Event Service for untyped messages, produced by a company called Outack Resource Group Inc. jEVENT supports both push and pull style communication between suppliers and consumers, is also IIOP compliant and may be used with any ORB that supports IIOP. The VisiBroker Event Service is available in both, C++ and Java versions from Inprise Corporation. Both versions are compliant with the OMG CORBA Event Service implementing untyped events for push and pull communication models. When used with VisiBroker ORB and its Smart Agent architecture that is vendor specific, it becomes a highly available self-recovering service. ICL have developed a multicast Event Service called DAIS[8]. A multicast service was developed due to the requirements from a customer that needed to communicate sixty messages per second, each being a few hundred bytes in size, to over eight hundred consumers. With these requirements, a standard CORBA Event Channel would have to produce nearly half a million individual messages per second, clearly unfeasible for a distributed system. To minimize the amount of network traffic between supplier and consumer applications, messages are collected into packets and sent in a single UDP packet. However, existing distributed systems such as CORBA do not consider transferring delay and system performance as a part of program models. They also treat problems concerning network programming as what a programmer should deal with by himself. Therefore, existing distributed systems have difficulty in providing reliable distributed service. But Jini[11], ubiquitous middleware, provides some novel solutions to many of the problems that classical systems have focused on, and makes some of the problems that those systems have addressed simply vanish. Jini supports serendipitous interactions among services and users of those services. Jini allows services to come and go without requiring any static configuration or administration. Also Communities of Jini services are largely self-healing[12]. But in Jini, there is no event service.
3 System Model The system model of the SeJES consisting of four components can be distributed among hosts across the network as shown in figure 3.1. The main function of the SeJES is that only the authorized event consumers and producers can exchange events by verifying their identities and capabilities. Event service registers itself with lookup service, which allows event producers and consumers to get the event service proxy. We implement each component of the model described above as follows:
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1. Event Service registration
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3. Applications communicate with events after checking securities
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Fig. 3.1. System Model of SeJES
• Discovery Service – Event producer and event supplier applications discover the ev ent service by using Lookup Service. We use reggie, developed by Sun, which com plies with discovery service specification of Jini. • Secure Event Service – Our SeJES(Secure JavaSpaces based event service) consists of four components(LRC, JES, SSCM, and ERC) as shown in figure 3.2. Major tasks of the LRC (Listener Registration Controller) are not only to retrieve events based on event types and contents, but also register consumers’ listener with the JES (JavaSpaces based Event Service) in order for the only authorized consumers to listen events. The JES plays a central role in notifying events provided by event suppliers to its registered consumers and storing the events for content based retrieval. The SSCM(SPKI/SDSI Certificate Manager) proves whether certificate list given from consumer is correct or not, and then returns ACLs (Access Control Lists), related to the events which consumers wish to get, to consumers. The ERC (Event Registration Controller) registers the type of event and ACL, sent by event suppliers, with the SSCM, and checks whether supplied events are authorized or not. SeJES retrieval( ) registerConsumer( ) registerListener( )
LRC
validate Cert( )
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Fig. 3.2. Functional Components of SeJES
registerProducer( ) publish()
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• Event consumer – Event consumer applications are classified as two types. One is run in machines with powerful computing power and the other does with low cost equipment. In the case of the former, event consumer owns certificate chain discovery algorithm and directly calculates certificate paths which prove that the consumer can get the event, and then delivers them to the SSCM. However, the latter sends all of its name certificates and authorization certificates to the SSCM in order to discover certificate chain lists, which authorize the consumers to get the event. Event consumer applications are able to retrieve with the events as content based after finding event service from discovery service. Furthermore, the consumer is able to get notified of what it wants, as registering remote listener with event service in real time. • Event supplier – Before sending event object instances to the SeJES, event supplier sends a event type and the ACL corresponded with the event type. After getting secure session ID from the SeJES, event supplier inquires SeJES if it is able to send event by using session ID, and then if permitted, it sends the event object instance.
4 The Design and Implementation of SeJES 4.1 Components of SeJES System This section describes the functions of each component of our SeJES and explains interfaces provided in each module. In addition, we define ACL which event suppliers will provide with and SPKI/SDSI certificates [9] which event consumer will use. Finally, we show the details of SeJES operation by providing the event service usage scenario. 4.1.1 ACL and SPKI/SDSI Certificate ACL(Access Control List) is a form of expressing security policy that defines which event supplier(issuer) delegates authorization to event consumers(subjects) who will get his events. < issuer, subject, delegation-bit, authorization tag, validity > Event consumer is granted the following SPKI/SDSI name and authorization certificates from event supplier. Name certificate - Authorization certificate - Figure 3.3 explains the S-expression of the authorization certificate that Bob grants its authority “get event 2” to subject called XMan in his local name space, from Nov., 20, 2005 to June, 18, 2006. Name and authorization certificates are sent to event service with their event types when event consumer registers its remote listener with the event service. That is, after finding ACL which fits a
Fig. 3.3. S-expression of authorization certificate
event type by calling SeJES.retrival() on the SeJES proxy, event consumer invoke SeJES.registerConsumer() with the first input “eType” and the second input “certificate-Path”. 4.1.2 LRC The LRC (Listener Registration Controller) is responsible for registering event listener which event consumer hopes to register with the JES. Using parameter information provided by event consumer, the LRC retrieves ACLs corresponded with the event type and provides methods which can retrieve event based on the event content. It requests authorization check by sending the event type and a bundle of certificates to the SSCM and decides whether it register the event listener or not depending on its returned value.
ListenerRegistrationController retrieval(eType) retrieval(eTemplate, principal, SessionID) registerConsumer(eType, certificate-Path) registerConsumer(eType, certificate-List) registerListener(eTemplate, Listener, principal, sessionID) Fig. 3.4. Interfaces of the LRC
• retrieval(eType), retrieval(eTemplate, principal, sessionID) An Event Consumer invokes the method retrieval(eType) in the LRC proxy so that it can realize if he or she has authorization concerned the event type “eType”. After
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finding ACL which represents appropriate authorization related to the event type as a result value, this method returns the ACL to the consumer. In addition, after checking authorization, consumer can invoke a method retrieval(eTemplate, principal, sessionID) of event service proxy in order to retrieve the event based on content. By using three parameters, this method proves if consumer is properly authorized and updates session key as a new value and returns the event which coincides with the eTemplate to the consumer. LRC.retrieval(nType) Output: eSessionKey lease-Time LRC.retrieval(nTemplate, principal, sessionID) Input:
Input:
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• registerConsumer(eType, cert-Path), registerconsumer(eType, cert-List) Event Consumer, running in the machine with computing power, calls a method registerConsumer(eType, certificate-Path) on the LRC proxy in order to send the first parameter “eType” and he second parameter “certificate-path” that event consumer can prove its authorization suitable for the event type “eType” to the LRC. After proving that the certificate-path is valid, the LRC creates a session key and encodes it. Then it stores the event type, the public key of event consumer, just created session key, nonce, and lease-time in order to check consumers’ authorization later on. As the values of results, this methods returns encoded session key and lease-time to consumer. LRC.registerConsumer(eType, certificate-Path ) Input:
eType certificate-Path
Output: eSessionKey lease-Time
However, event consumer, running low cost equipment, calls registerConsumer(eType, cert-List), to send all of the certificates which it owns. • registerListener(nTemplate, Listener, principal, sessionID) After checking consumer’s authorization and if the result is true, the LRC updates nonce and registers remote listener with the JES. LRC.registerListener(eTempl, Listener, principal, sessionID) Input:
eTempl Listener principal SessionID
Output: boolean
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4.1.3 SSCM By using certificate list sent by the event consumer of low cost equipment, the SSCM prove that the consumer can achieve the event instance of the event type. Also it checks the proof of certificate-Path directly sent by the event consumer in machines with powerful computing power. As a result, the SSCM includes the algorithm of “Certificate Chain Discovery”[10] and returns Boolean value of each case to the LRC(Listener Registration Controller). The SSCM interfaces are as Figure 3.5.
• storeACLs(eType, ACLs, leaseTime) The ERC calls this method of the SSCM module in order to store ACL which is a collection of authorizations for the consumer to achieve events provided by event supplier. • validateCert(eType, Certificate-Path), validateCert(eType, Certificate-List) These methods are invoked by the LRC in order to request authorization proof of event consumer. The first method owns Certificate-Path as parameter, a collection of certificates proven by consumers and the second one owns Certificate-List, a collection of all name and authorization certificates held by consumers. • getACLs(eType) This method finds and returns ACL which is necessary for consumers to achieve designated types of event 4.1.4 ERC The ERC (Event Registration Controller) is responsible for checking the proof of event types and ACL which are provided by event suppliers. It also checks the replication of events. Furthermore, the ERC has a responsibility of transferring events
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provided by event suppliers to the JES. Interfaces provided by the ERC are shown in Figure 3. 6. • registerProducer(eType, ACLs, certificate-Path) By sending an event type “eType”, ACLs and authorization proof information “certificate-Path” to the SSCM, this method let the SSCM store them in its cash. Furthermore, this method creates encoded session key by using two parameters of producer’s principal derived from certificate-Path and session key, a random nonce. This encoded session key is used to prove whether the event is authorized to provide itself to the JES or not. • publish(event, principal, sessionID) This is the method that publishes suppliers’ event. After checking if the event sent by suppliers is authorized and then if only if the return value is true, this method sends the event to the JES. 4.2 Testing of SeJES Service This section summarizes how a consumer and a supplier use our SeJES service, implemented in Jini environment. In addition, it shows GUI screen that shows, in order to get event which the consumer is interested in, whether listener’s registration in the SeJES is successfully committed or not. It also exhibits GUI screen including procedures and results necessary for suppliers to publish event. 4.2.1 Test Scenario A scenario to test SeJES services is as follows: Susan who possesses event supplier sensor1 sets ACL, <self, Bob, 1, “get event1”, (05-11-20, 06-03-29)> in sensor1 in advance. When Susan turns sensor1 on, event supplier application in sensor1 registers event type(event1) and its ACL set by Susan with SeJES. In the meantime, Bob hopes to get the event1 published by gadget1 of Susan. In order to get the event1 instance, Bob asks SeJES to send ACL corresponded with the event1. And then Bob calculates Certificate-Path establishing a chain from name and authorization certificates in its certificate cash to ACL of event1 which she wants to get. Now Bob registers his remote listener with SeJES and waits till the event arrives. In the meantime, unauthorized Charlie also tries to register his remote listener to get the event1 of sensor1. In this case, since he can’t prove his authorization, his request is rejected. Purchasing sensor2, Eve tries to use event service in order to publish event2, but it is rejected as well. Figure 4.1 shows the order of methods invoked in order for event consumer to be notified and for supplier to provide the event.
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SeJES
Gadget 1 Event Consumer SPKI/SDSI certificates Remote Event Listener web server
Figure 4.2 exhibits a screen dump showing that consumer Bob tried to register his listener with the SeJES in order to get an event “Alice location” and the SeJES notified those events to Bob.
Figure 4.3 shows that the SSCM proves whether the certificate-path provided by the event consumer “Bob” is correct or not.
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Fig. 4.3. Proving process of authorization certificate-path
Figure 4.4 shows the event producer of gadget1 Susan’s log of event publishing.
Fig. 4.4. Example the Screen of Event Publishing
5 Characteristics of Our SeJES System SeJES is distinguished with CORBA in three aspects. Firstly, event service based on CORBA uses event channel. Accordingly, it is not totally an isolated model because event consumers and event suppliers communicate each other through the channel. Secondly, event service based on CORBA transfers its filtering responsibility to consumer programmers. Therefore, any events written in the channel are to be transferred to every consumer listening to the channel, which is an inefficient process by increasing excessive expenses of communication. However, our system can deliver only necessary events to a particular consumer in need because content based filtering using JavaSpace is available in the SeJES system. Finally, no persistency is existed in CORBA based event service. If the channel is down, it loses all information concerning consumers and suppliers connected to the channel. For that reason, there is no
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way for consumers to take events provided while the channel is disconnected even after they are successfully connected again. However Our SeJES system is able to do that because of its lease () function.
6 Conclusions and Further Work In this paper, we design and implement a secure event service, SeJES. Event consumers are able to register their listeners with the SeJES and disconnect their listeners at any time. Furthermore, the SeJES enables only authorized consumer and supplier to securely exchange their events by using SPKI/SDSI certificate. In addition, our SeJES guarantees that event is transferred to only all of the authorized event consumers and enhances the security by delivering event consumer and suppliers secure session key. The proposed event service, SeJES, is able to store event for lease-time. While being leased, event consumer commits a filtering based on content during the lease-time. However, our SeJES is not able to federate event servers and does not provide the event service with priority. Also we want to implement our SeJES which has more QoS and more Filtering functions. Most of them are our future work.
References 1. Object Management Group: CORBAServices: Common Object Services Specification. Revised Edition. (1995) 2. Philip Bishop , Nigel Warren: JavaSpace IN PRACTICE. Addison-Wesley (2003) 3. Lee, Younglok., et al.: Development of Event Manager and its Application in Jini Environment. EUC Workshops 2005, LNCS 3823, Springer-Verlag, Nakasaki (2005) 704 – 713 4. Paul Stephens: Implementation of the CORBA Event Service in Java. A Thesis for the Degree of Masters of Computer Science, Trinity College, Dublin (1998) 5. IONA: OrbixEvents Programmer’s Guide. IONA Technologies PLC (December 1997) 6. 6. IONA: OrbixTalk-The White Paper. Technical Report, IONA Technologies PLC, April (1996) 7. OUTBACK: jEVENTS-Java-based Event Service User’s Guide. OutBack Resource Group Inc. (1997) 8. ICL Object Software Laboratories: DAIS Multicast Event Service. White Paper (1998) 9. Andrew J. Maywah: An Implementation of a Secure Web Client Using SPKI/SDSI Certificates. Master Thesis, M.I.T, EECS (2000) 10. Dwaine Clarke, Jean-Emile Elien, Carl Ellison, Matt Fredette, Alexander Morcos, Ronald L. Rivest: Certificate Chain Discovery in SPKI/SDSI. Journal of Computer Security, 9 (2000) 285-322 11. Sun Microsystems: .Jini™ Architecture Specification. Sun Microsystems (1997-2000) 12. Keith Edwards, W., Edwards, W.: Core Jini. Pearson Education, (2000)
Energy Efficient Connectivity Maintenance in Wireless Sensor Networks Yanxiang He and Yuanyuan Zeng School of Computer, Wuhan University, 430072, Hubei, P.R. China [email protected], [email protected]
Abstract. Connectivity maintenance in energy stringent wireless sensor networks is a very important problem. Constructing a connected dominating set (CDS) has been widely used as a connectivity topology strategy to reduce the network communication overhead. In the paper, a novel energy efficient distributed backbone construction algorithm based on connected dominating set is presented to make the network connected and further prolong the network lifetime, balance energy consumption. The algorithm is with O(n) time complexity and O(n) message complexity. The results show that our algorithm outperforms several existing algorithms in terms of network lifetime and backbone performance.
backbone. The length of time is dependent on the residual energy of the MCDS nodes. When this length of time expires, the sensor nodes coordinate with each other again and compute the next MCDS as the backbone for the next period of time. By doing so, the energy consumption of all nodes in the network is balanced and the lifetime of the network is extended. The remainder of this paper is organized as follows. Section 2 briefly introduces the related work in the literature. Section 3 discusses out distributed algorithm for constructing the CDS as backbone to make connectivity. Section 4 is the performance analysis and simulations. Section 5 is the conclusion and future work.
2 Related Work In the last few years, researchers actively explored advanced power conservation topology control approaches for wireless sensor networks. Extensive work has been done on the connectivity maintenance issue. Research in [4] focused on energy conservation by controlling sensor transmission power in order to maintain network connectivity. It demonstrated that the network connectivity can be maintained if each sensor has at least one neighbor in every cone of 2 /3. Xu et al. [5] proposed two algorithms that can conserve energy by identifying redundant nodes of connectivity. In GAF [6], nodes use geographic location information to divide the world into fixed square grids. Nodes within a grid switch between sleeping and listening, with the guarantee that one node in each grid stays up to route packets. SPAN [7] is another protocol that achieves energy efficiency for wireless sensor networks by introducing off-duty and on-duty cycles for sensor nodes. Dominating set based topology control leads to a virtual backbone for the deployed ad hoc and sensor networks. The virtual backbone is formed by representing the connected routing nodes as a connected dominating set (CDS). Since the minimal CDS problem is NP-hard, most previous work has focused on finding distributed heuristics for reducing the size of CDS. Current MCDS approximation algorithms include centralized and distributed algorithms. Following the increased interest in wireless ad hoc and sensor networks, many distributed approaches have been proposed because of no requirements for global network topology knowledge. These algorithms contain two types. One type is to find a CDS first, then prune some redundant nodes to attain MCDS. Wu and Li proposed in [11] a distributed algorithm with message complexity and O( 3) time complexity, the approximation factor at most n/2. Butenko et al [12] constructs a CDS starting with a feasible solution, and recursively removes nodes from the solution until a MCDS is found. The other type is to form a maximal independent set (MIS) at first, and then find some connectors to make the independent nodes connected together. P. J .Wan et. in [9] proposes a distributed algorithm with performance ratio of 8. Min et al in [11] propose an improved algorithm by employing a Steiner tree in the second step to connect the nodes in the MIS with performance ratio of 6.8.
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3 Distributed Algorithm for Energy Efficient MCDS When all sensor nodes have the same transmission range, the network topology is modeled as a UDG G= (V, E). An edge represents that nodes u and v are within each other’s transmission range. Each node u is associated with a unique ID, denoted by id(u) (this can be, for instance, IP or MAC address). The aim of our algorithm is to compute a sub-optimal MCDS as a backbone for wireless sensor networks. Our algorithm consists of two phases. In the first phase, we compute a maximal independent set (MIS) of the network graph. An independent set of a graph is a subset of V that no two nodes in the subset have an edge. An MIS of a graph is an independent set that cannot include any more node in V. An MIS is a DS of a graph. Note that this DS (obtained as the MIS) may not be connected. The second phase of the algorithm is to choose the minimal number of nodes (called connectors) to make the DS connected, i.e., a CDS. Each time when constructing a CDS, the length of operating time of this CDS is determined according to the residual energy of the CDS nodes. When this operating time expires, the next CDS is computed. To extend the lifetime of the network, we always give higher priority to the nodes with higher residual energy to be as backbone nodes. Thus, nodes will be usually acting as backbone nodes in turn and the energy consumption of nodes is well balanced. For each node u, we define weight as: w(u)={energy(u), degree(u)}. The higher significant part of w(u) is the residual energy of u. When two nodes have the same energy, the node with a higher degree has a higher priority. This policy would make the size of the CDS smaller (under the condition of energy balance). 3.1 MIS Construction Since any two nodes in MIS cannot have an edge, that is, when a node is in MIS, any other node that has an edge incident to this node cannot be included in the MIS. We use colors to indicate if a node is in MIS or not. The algorithm always starts from a node that initiates (invokes) the execution of the algorithm. We call this node initiator. We use black to indicate the nodes in MIS and grey to indicate non-MIS nodes. Each node is in one of the four states: white, black, grey and transition. Initially, all nodes are in white, and at the completion of the algorithm all nodes in the network must be either in black (MIS nodes) or in grey (non-MIS nodes). The state transition of a node is done in response to the message it receives. There are three types of messages: 1) BLACK message sent out when a node becomes a black node; 2) GREY message, sent out when a node becomes a grey node; 3) INQUIRY message, sent out when a node inquires the weights and states of its neighbors. Every message contains node state, id and weight in format. As the start of the algorithm, the initiator colors itself in black. A node that colors itself in black will broadcast a BLACK message to its neighbors (to indicate itself as an MIS node). A neighbor that receives a BLACK becomes a grey node (a non-MIS node), and it broadcasts a GREY message to its neighbors. A node that receives a GREY message needs to compete to become a black node. So it broadcasts an INQUIRY message to its neighbors to inquire their states and weights. It sets a timeout to wait for the replies of the INQUIRY message. The node is in the transition state during this timeout period, because it cannot determine whether it would become
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black or grey. If it finds it has the highest weight among all its transition state neighbors based on the replies from all its neighbors, its color is changed to black, and it does the same as the other black nodes do. If this node is still in the transition state when the timeout expires, its color changes to white. The algorithm is fully distributed and all nodes execute the same algorithm concurrently. Any node whose neighbors are all colored in black or grey terminates. The MIS construction procedure ends when every node terminates. MIS construction algorithm: initiator () { Color itself black; Broadcast a BLACK msg; } Each node i, responses to the msg it receives: MIS-algorithm { Receive a msg; If it is black/grey then Ignore the msg; If its neighbors have no white neighbors then Return; end if else Switch on message-type { Black: Color itself grey; Broadcast a GRAY msg; Grey: Broadcast an INQUIRY msg; Enter transition state; Set a timeout waiting for replies; If w(i) is the highest then Color itself black; Broadcast a BLACK msg; end if If in transition after timeout then Color itself white; end if Inquiry: Reply its own color and w(i); } end Switch end if } Theorem 1: The set of black nodes represented as B that computed by the first section algorithm is an MIS of the network graph. Proof: The algorithm colors the nodes of the graph layer by layer, and propagates out from the initiator to reach all nodes in the network, with one layer of black and the next layer as grey. At each layer, black nodes are selected by gray nodes of previous layer and are marked black. The construction incrementally enlarges the black node set by adding black nodes 2 hops away from the previous black nodes set. Also the
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newly colored black nodes could not be adjacent to each other, for the interleaving coloring layer of black and grey nodes. Hence every black node is disjoint from other black nodes. This implies that B forms an independent set. Further, the algorithm will end up with black or grey nodes only. Each grey node must have at least one black neighbor, so if coloring any grey node black, B will not be disjoint anymore. Hence B is a maximal independent set. Theorem 2: Considering the propagation layer of MIS, Let Bi and Gi be the set of nodes marked black and grey at ith layer. For a MIS node in Bi, there always exists that it has a neighbor in Gi connecting at least another MIS node in Bi+1 with it. Proof: For any node gę*L is a non-MIS node formed at the ith layer. In the construction algorithm, it must be selected to be marked grey from white state on receiving a Black message from its black neighbor in Bi. Next, after determining its state, the grey node g sends out a Grey message to all its neighbors in the i+1th layer. The neighbor finds itself with the highest weight among all its transition neighbors will become a black node in Bi+1. This implies that there always exists a non-MIS neighbor node gę*L has at least two MIS nodes in Bi and Bi+1 respectively. So for a MIS node in Bi, there always exists that it has a neighbor in Gi connecting at least another MIS node in Bi+1 with it. 3.2 Connected Dominating Set Construction In this section, we make interlacing selection of interconnecting nodes (called connectors) into the formation of connected DS based on previous MIS construction, i.e. connectors of black nodes are established in an interlaced fashion during the construction of MIS. When all grey neighbors of a black node terminate the MIS procedure, this implies the first section algorithm for this node and its grey neighbors terminates. Then the black node will enter the second CDS construction to find connectors. Apparently, the CDS section algorithm starts from MIS initiator too because of propagation order of the MIS procedure algorithm. Our main idea is to employ a Steiner tree in this subsection to connect nodes in MIS. In a graph, a Steiner tree for a given subset of nodes, called terminals. Every node other than the terminals in the Steiner tree is called a Steiner node. The constructed MIS nodes are terminals, and the selected connectors from non-MIS nodes are Steiner nodes. The internal nodes in the Steiner tree become a CDS. We expect to select a small number of Steiner nodes from non-MIS nodes with higher power in order to obtain good efficiency of CDS. We use a greedy approximation algorithm that every black node selects the grey node with maximal black neighbor number as a connector. If two grey nodes have the same black neighbor number, then the one with higher energy level has higher priority. Each MIS node is in one of the three states: black, transition and blue. Each nonMIS node is in one of the three states: grey, compete and blue. The black and grey are initial state of CDS procedure (after finishing the first MIS procedure), and blue state is final state to indicate the node is in CDS or not. The transition and compete state is the unsure state when a node can’t decide itself as a CDS node. There are three types of messages: 1) INQUIRY message, sent out when a black node inquires its grey neighbors about their state and number of black neighbors. 2) INVITE message, sent
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out to invite a grey neighbor to be a connector. 3) BLUE message, sent out when a node changes blue. At the start of the algorithm, the MIS initiator colors itself in blue. A node that colors itself in blue will broadcast a Blue message to its neighbors (to indicate itself as a CDS node). Next, the black and grey nodes (after finishing MIS procedure) will execute corresponding state transition mechanism. When a node is black initially, if the node and its grey neighbors have finished the MIS procedure, the black node will broadcast an INQUIRY message and enters transition state. It sets a timeout to wait for the replies of the INQUIRY message. The node is in the transition state during this timeout period, because it cannot determine which node should be selected to behave as a connector. If a node in transition state receives a BLUE message will enter blue state. This implies that it already has a grey neighbor as a connector. Otherwise, the node still has no neighbor as a connector will try to select one. The selection of connectors is based on replies of INQUIRY message, which include the information of black neighbor number and energy level of its grey neighbors. The connector selection rules are: 1) the selected neighbor should be adjacent to at least a blue node. 2) The selected grey node is with maximal black neighbor number. If multiple nodes are found, then we use node energy level as a tie breaking mechanism (higher energy node wins). The rule 1 protects the constructed CDS is a complete component of Steiner tree merged together. The rule 2 protects the CDS with smaller size and energy efficiency. The intuition of transition state is to wait for replies of INQUIRY from its neighbors, and make decision to select a neighbor as a connector. When the node selects a grey neighbor matching the above two condition, it sends out an INVITE message to neighbor, and changes itself to blue state. When enters in blue, the node broadcasts a BLUE message to indicate itself CDS node. When grey initially, a node response the received messages. A grey node that receives a BLUE message will update its information about number of black neighbors. A grey node that receives an INQUIRY message replies the sender with the number of black neighbors and its energy, and then enters compete state. The intuition behind compete state is to probe the network to see if itself suits as a connector. If a grey node in compete state receives an INVITE message, it is invited as a connector and colored in blue. When enters blue state, the node broadcasts a BLUE message to neighbors. The CDS construction algorithm continues until: 1) Any MIS node colored blue and no white neighbors terminates the procedure. 2) Any nonMIS node terminates the procedure when all its neighbors are colored blue or grey. The same operation continues until every node terminates. The CDS algorithm ends when every node terminates. CDS construction: Initiator() { Color itself in blue; Broadcast a BLUE msg;} Each node i, execute operation according to its state: CDS-algorithm{ Switch on state-type{ Black: If all neighbors terminate then Broadcast an INQUIRY msg; Enter the transition state;
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end if Grey: Receive a msg; If receive an INQUIRY msg then Reply its black neighbor number; Reply its energy(i); Enter the compete state; end if If receives a BLUE msg then Update its black neighbor number; Update its energy(i); If all neighbors color in blue or grey then Return; Transition: Set a timeout waiting for replies; Receive a msg; If receive a BLUE msg then Color itself in blue; else Find a neighbor as a connector; Send out an INVITE msg to the node; Color itself in blue; end if Compete: Receive a msg; If receive an INVITE msg then Color itself in blue; Blue: Broadcast a BLUE msg; If all neighbors color in blue or grey then Return ;} end Switch} Theorem 3: The set of blue nodes computed by the algorithm is a CDS of the network graph. Proof: The set of blue nodes are contained by MIS and connectors. MIS is a dominating set, so we only need to proof the connectivity. Let {b0,b1…bn} be the independent set, which elements are arranged one by one in the construction order. Hi be the graph over {b0,b1…bi}(İL˘n) in which pairs of nodes are interconnected by connectors. We prove connectivity by induction on j that Hj is connected. Since H1 consists of a single node, it is connected trivially. Assume that Hj-1 is connected for some Mı2 . Considering message propagation layer in our algorithm, let Bi-1 and Gi-1 be the set of nodes marked black and grey at the i-1th layer, respectively. The gray node in Gi-1 with maximal number of black neighbor and adjacent to a blue node is selected as connecters. According to theorem 2, it’s enough to find grey nodes which interconnect Bi-1 nodes at i-1th layer with Bi nodes in the ith layer. As Hj-1 is connected, so must be Hj. So the nodes in MIS and connectors set are connected together, and they also form a dominating set. Therefore the set of blue nodes computed by the algorithm is a CDS.
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4 Performance Evaluation and Simulations The message complexity and time complexity of our distributed algorithm are analyzed at first. Since each node sends out a constant number of messages, the total number of message is O(n). The use of linear message takes at most linear time. Theorem 4: Our distributed algorithm has O(n) time complexity, and O(n) message complexity. Next, we analyze the size of energy efficient CDS. The following important property of independent sets is that: Lemma 1: In a unit disk graph, every node is adjacent to most five independent nodes. Lemma 2: In any unit disk graph, the size of every maximal independent set is upperbounded by 3.8opt+1.2 where opt is the size of minimum connected dominating set in this unit disk graph. Theorem 5: In the CDS construction phase, the number of the connectors will not exceed 3.8opt, where opt is the size of MCDS. Proof: Let B be the independent set and S be the connectors set of a graph. From lemma2: |B_İRSW. From theorem2 and lemma1, it can be deduced that connectors has black neighbor number ranged from 2 to 5. The worst case occurs when all nodes are distributed in a line. By analyzing utmost situation, the number of gray connecting nodes must be less than the number of MIS nodes (details omitted). |S_İ_%_İRSW. The number of output connecting node will not exceed 3.8opt. Theorem 6: The approximation factor of our algorithm is not exceeding 7.6. Proof: Our distributed algorithm includes two phases. One is the MIS construction, and the other the forming of CDS by Steiner nodes. From Lemma2, the performance ratio in the first phase is 3.8. From Theorem 5, the performance ratio is 3.8 in the second phase, so the resulting CDS will have size bounded by 7.6. In our algorithm, the node with higher power will have bigger chance to become a CDS node. The reconstruction mechanism makes the balance of energy consumption in networks as energy level changes. Our algorithm guarantees that the CDS nodes have good energy efficiency and extend the network lifetime. The simulation network size is 100-300 numbers of nodes in increments of 50 nodes respectively, which are randomly placed in a 160X160 square area to generate connected graphs. Radio transmission range is 30 or 50m. Each node is assigned initial energy level 1 Joule (J). A simple radio model is used: Eelec is energy of actuation, sensing and signal emission/reception. Eamp is energy for communication, varies according to the distance d between a sender and a receiver. Eamp=¯fs, when d
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The data routing takes flooding protocol. We take parameter timeout in MIS construction algorithm as 0.5s. The simulation makes average solutions over 30 iterations of random generating scenes. Fig. 1, 2 shows the size of the dominating set with the increasing number of nodes in the network for a certain transmission radius. ECDS has a good performance with smaller CDS size when comparing with WAA and WLA as the network size increases. Fig. 3 shows the average CDS residual energy as the network size increases for working 150s (one event every 0.5s) with r=50m. ECDS achieves better energy efficiency with much higher residual energy comparing with WAA and WLA. And WLA has the worst energy efficiency for its big size of dominating set. Fig. 4 shows the network lifetime (length of working time until can’t construct a backbone for the network) as the network size increases from 100 to 300 nodes when r=50m. ECDS has much better energy performance comparing with WAA and WLA. It can work with longest time until can’t construct a backbone any more. Apparently, ECDS has better network lifetime when compared with the other two algorithms. 65
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Fig. 4. Network lifetime as the network size increases when r=50m
5 Conclusion and Future Work A distributed energy efficient backbone based on connected dominating set algorithm for connectivity maintenance of wireless sensor networks is presented. The nodes with higher weight have more chance to be selected as backbone nodes to efficiently manage the network. The algorithm makes energy consumption balanced by computing a new CDS when nods residual energy of network cut down to a certain level. The algorithm time complexity and message complexity of this algorithm are both O(n). The performance ratio is 7.6. Moreover, the algorithm is fully distributed, only uses simple local node behavior to achieve a desired global objective. The simulation results show that the algorithm can efficiently prolong network lifetime and balance node energy consumption with a smaller backbone size, comparing with existing classic algorithms. The future work will focus on simulations under various settings and MCDS improvement with QoS consideration.
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References 1. Pottie, G.J., Kaiser, W.J.: Wireless Integrated Network Sensors, Communications of ACM. 43 (2000) 51-58 2. Akyildiz, I.F, Su, W., Sankarasubramaniam, Y., Cayirci, E.: A Survey on Sensor Networks, IEEE Communications Magazine, 40 (2002) 102-114 3. Ephremides, A., Wiselthier, J., Baker, D.: A Design Concept for Reliable Mobile Radio Networks With Frequency Hoping Signaling, Proc. IEEE, 75 4. Wattenhofer, R., Li, L., Bahl, P., Wang, Y.: Distributed Topology Control for Power Efficient Operation in Multihop Wireless Ad Hoc Networks, Proc. of InforCom (2001) 5. Xu, Y., Bien, S., Mori, Y., Heidemann, J., Estrin, D.: Topology Control Protocols to Conserve Energy in Wireless Ad Hoc Networks, Technical Report 6, University of California, Los Angeles (2003) 6. Xu, Y., Heidemann, J., Estrin, D.: Geography-Informed Energy Conservation For Ad Hoc Routing, In: proc. of 7th Annual Int’l Conf on Mobile Computing and Networking (MobiCom), Rome, Italy. (2001) 70-84 7. Chen, B., Jamieson, K., Balakrishnan, H., Morris, R.: Span: An Energy-Efficient Coordination Algorithm for Topology Maintenance in Ad Hoc Wireless Networks, Proc. MobiCom. (2001) 85-96 8. Clark, B.N., Coloburn, C.J., Bhargavan V.: Unit Disk Graphs, Discrete Mathematic, 86 (1990) 165-177 9. Wan, P.J., Alzoubi, K., Frieder, O.: Distributed Well Connected Dominating Set in Wireless ad hoc networks, in proc. of INFOCOM (2002) 10. Alzoubi, K.M., Wan, P.J.: New Distributed Algorithm For Connected Dominating Set In Wireless Ad Hoc Networks. Proc. 35th Hawaii Int’1 Conf, System Sciences (2002) 3881-3887 11. Min, M., Huang, C.X., Huang, S.C.-H., Wu, W., Du, H., Jia, X.: Improving Construction for Connected Dominating Set with Steiner Tree in Wireless Sensor Networks, to appear in Journal of Global Optimization (2004) 12. Wu, W., Du, H., Jia, X., Li, Y., Huang, C.-H., Du D-Z.: Minimum Connected Dominating Sets And Maximal Independent Sets In Unit Disk Graphs, Technical Report 04-047, Department of Computer Science and Engineering, University of Minnesota (2004)
The Critical Speeds and Radii for Coverage in Sensor Networks* Chuanzhi Zang1,2, Wei Liang1, and Haibin Yu1 1
Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China 2 Graduate School of the Chinese Academy of Sciences, Beijing 100049, China {zangcz, weiliang, yhb}@sia.cn
Abstract. In sensor network the coverage problem is very important to topology control, energy saving, routing and et al. Compared to the well known sensor model and exposure model, a modified sensor model and a modified exposure model are used to analyze the critical parameters for coverage. The modified sensor model can deal with more general conditions, and the modified exposure model is more reasonable than the known ones. Based on these models, the sensor physical characteristics and the target properties, we analyze the coverage problem mathematically and identify two critical speeds and two critical radii of influence of the sensor node. Using these results, it is easy to estimate the critical sensor density or the critical number of sensor nodes required to cover a given area. Keywords: sensor network, coverage, exposure.
1 Introduction Recent technological advances in distributed embedded systems have prompted significant research efforts in both the industry and the academia. Among such systems, wireless ad-hoc sensor networks are particularly noteworthy due to their potentially numerous, economically attractive applications and their ability to bridge the interface between the user, and the physical world[1,2]. Unlike traditional embedded systems, the new wireless sensor network nodes have remarkable computational and storage capabilities. An important problem receiving increased consideration recently is the sensor coverage problem, centered on a fundamental question: How well do the sensors observe the physical space? In some ways, it’s one of the measurements of the quality of service (QoS) of sensor networks. The coverage concept is subject to a wide range of interpretations due to a variety of sensors and applications. Different coverage formulations have been proposed, based on the subject to be covered (area versus *
This paper is supported by Natural Science Foundation of China under contract 60434030 and 60374072.
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discrete points)[3,4], the sensor deployment mechanism (random versus deterministic), as well as other wireless sensor network properties (e.g. network connectivity and minimum energy consumption). For example, in the battlefield, the sensor nodes are randomly deployed to detect enemy movement. Upon detection, nodes transmit the information to the user via multi-hop communication. An important question in such scenarios is to determine the number of sensors to be deployed so that the entire area is covered and probability of detection is high. Deploying small number of nodes might leave blind spots or sensing holes, which can allow the enemy to pass through. Thus knowing the sensing capacity as a function of number of nodes to be deployed is crucial for design of sensor networks. Density of nodes is also a crucial parameter in scenarios where network is deployed to monitor environmental variables. Leaving blind spots in such cases can reduce the accuracy of the results obtained. In the example described above, typically the target is a signal source, and the nodes receive the signal via a channel. Depending upon the strength of the signal received, the node detects the target. Thus the sensing capacity of the sensor network would depend upon the target characteristics as well as sensor sensitivity and calibration. Thus the density evaluation must take into account the nature and characteristics of both the sensor as well as the target. In this paper we focus on the area coverage with random sensor deployment. All sensors have the same characteristics. Compared to the well known sensor model and exposure model in [3-7], a modified sensor model and a modified exposure model are used to analyze the critical parameters for coverage. The modified models can deal with more general conditions. Based on the sensor physical characteristics and the target properties, we analyze the coverage problem mathematically and identify two critical speeds: the undetectable speed and partial detectable speed. When the target speed is greater than undetectable speed it can’t be detected, and when the target originates from a sensor and its speed is greater than partial detectable speed, it can’t be detected. We also identify two critical radii: the radius of complete influence and radius of no influence. The target within the radius of complete influence can be detected and the target beyond the radius of no influence can escape from the detection. Using these results, it is easy to estimate the critical sensor density or the critical number of sensor nodes required to cover a given area. The remainder of the paper is organized as follows. In the next section we summarized the related work. Section 3 gives various models which are used to analyze the coverage problem. In section 4 we analytically evaluate the critical speeds and radii, and thus estimate the critical sensor density and number required to cover a given area. Section 5 gives the simulations which verify the theoretical result. The last section concludes the paper.
2 Related Work The computational geometry method is often used to solve the coverage problems. The Art Gallery Problem [8] deals with determining the number of observers necessary to cover an art gallery room such that every point is seen by at least one observer. It has found several applications in many domains such as the optimal antenna placement
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problems for wireless communication. The Art Gallery problem was solved optimally in 2D and was shown to be NP-hard in the 3D case. Reference [8] proposes heuristics for solving the 3D case using Delaunay triangulation. Sensor coverage for detecting global ocean color where sensors observe the distribution and abundance of oceanic phytoplankton [9] is approached by assembling and merging data from satellites at different orbits. It seems that Meguerdichian et al.[4] were among the first several researchers to identify the importance of using Delaunay triangulation and Voronoi diagram in sensor network coverage. Given a wireless sensor network, it is interesting in designing a localized algorithm that finds a path connecting a point s and a point t which maximizes the smallest observability of all points on the path. It is called the best coverage problem[4]. Meguerdichian et al presented a centralized method using the Delaunay triangulation to solve the best coverage problem. Their algorithm has the best possible time complexity among centralized algorithms. Compared to the best coverage problem, the worst coverage problem is to find the path that maximizes the distance of the path to all sensor nodes. Meguerdichian et al. presented a centralized method using the Voronoi diagram to solve the worst coverage problem. Several related problems were also studied recently. The minimum exposure problem[5,6] is to find a path connecting two points in the domain that minimizes the integral observability over the time traveled from the source point to the destination point. Using a multiresolution technique and Dijkstra and/or Floyd-Warshall shortest path algorithms, Meguerdichian et al.[5,6] presented an efficient and effective algorithm for minimal exposure paths for any given distribution and characteristics of sensor networks. The algorithm works for arbitrary sensing and intensity models and provides an unbounded level of accuracy as a function of run time. Adlakha et al[7] researched the critical density thresholds for coverage in wireless sensor networks. In [7], Adlakha et al evaluated the critical number of nodes required for target detection in a sensor network. They used physical characteristics of sensors and target to derive an equation for effective sensor radius. Using this effective radius they estimated the critical density for coverage in sensor network. They incorporated physical characteristics of sensor and target in evaluating the sensing capacity of sensor networks. Such modeling enables sensor network design, where the user can decide the density of nodes to be used depending upon the target characteristics it is trying to detect as well the nature of sensor deployed. The sensor models used in [4-7] has no definition when the sensor and the target at the same position, and when the target is very close to the sensor, the value received by sensor can be greater than any given positive real number which isn’t reasonable. Having these in mind, we can understand why the result in [7] is wrong when the sensor is very close to the target. Compared to the result in [7], ours is more general and understandable.
3 Sensor Network Models Before analyzing the critical speed and radii we will describe the sensor model, exposure model and target model.
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3.1 Sensor Model Sensing devices generally have widely different theoretical and physical characteristics. Thus, numerous models of varying complexity can be constructed based on application needs and device features. However, for most kinds of sensors, the sensing ability diminishes as distance increase. Given a sensor s and a target located at point p, Meguerdichian et al.[5,6] defined the sensor model as
S (s, p ) =
λ
(1)
[d (s, p )]
k
where d(s,p) is the Euclidean distance between the sensor s and the point p, the positive constants Ȝ is the signal amplitude and k is sensor technology-dependent parameter. From (1), one can easily find the shortages of the sensor model as following. lim S ( s, p) = ∞
(2)
d →0
So when the target and the sensor at the same position, model (1) has no definition. On the other hand, given a sensor, the value that the sensor can read has an upper bound, denoting which as Fmax. From (2), one can easily find that the value S has no upper bound. It is infeasible. In order to overcome those shortages we give a modified sensor model: S (s, p ) =
λ
(3)
[d (s, p ) + 1]
k
where Ȝ denotes the signal amplitude, and for simplicity, we only consider the signal which has a positive constant value. When the sensor and target at the same position, using (3), we can get S=Ȝ which is the signal original value. Since each sensor requires certain signal to noise ratio (SNR) to detect the signal, beyond a certain noise figure Fmin, the signal would not be detected. This is because the signal strength would fall below the noise floor. Thus if S(s, p) < Fmin, the sensor would not detect the signal. Thus the domain of S is Fmin <S(s, p) < Fmax, so we have: 0 ° ° ° S (s, p ) = ® Fmax ° λ ° ° [d (s, p ) + 1]k ¯
λ
[d (s, p ) + 1]
k
< Fmin
[d (s, p ) + 1]
k
> Fmax
λ
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otherwise
3.2 Exposure Model
Depending upon the type of detection and the application, Meguerdichian et al.[5,6] and Adlakha et al[7] identified two kinds of exposure model: integrator model and derivative model. Those models determine how the signal received from the target is processed to make a decision. For example, an acoustic sensor can sense the target for a fixed period of time, integrate the acoustic energy and if the energy exceeds the threshold, it
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declared that the target is detected. This was the integrator model and it was first introduced in [5,6]. Suppose an object O is moving in the field F from point p(t1) to point p(t2) along the curve (or path) p(t). Meguerdichian et al.[5,6] define the integrator model as t2
Exposure (5) depends on the arc length, which also means that the exposure depends on the target speed. In real world the exposure model sometimes has no relationship with the target speed. For example, for an acoustic sensor, when the target’s trace is a circle around the sensor, in spite of the target speed, the signal strength received by sensor is not changed (see figure 1).
target
sensor
Fig. 1. The target runs along a circle around the sensor
So in this paper we only consider the exposure model (see (7)) which doesn’t depend on the target speed. Note that the integrator model pertains to sensors that are energy detectors. Thus when the total signal energy or exposure (which is the total signal strength over the time) exceeds a threshold, the sensor declared the target as detected. t2
E = ³ S (s, p )dt
(7)
t1
In this paper, each sensor makes its own decision separately and detection occurs if E>Et (Ethreshold). 3.3 Target Model
The sensor networks have various applications and different applications has different target model. In this paper we only consider the cases in which the sensor network is used to detect the moving target. The target can be a person, a soldier, or a vehicle. We
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assume the target moves in a straight-line path with constant speed v for a time T. The time T also can be considered as the sensor detecting time.
4 Finding the Critical Parameters First, we give two critical speeds associated with a given sensor network. Definition 1: the undetectable speed vc1. When the target speed is greater than vc1, the sensor network can’t detect the target. Definition 2: the partial detectable speed vc2. When the target speed is greater than vc2, the target originating from a sensor can’t be detected by the sensor.
Second, we give two critical radii associated with a given sensor. Definition 3: the critical radius rc1. It is also named as Radius of complete influence by Adlakha et al[7]. The targets originating within this radius are surely detected. Definition 4: the critical radius rc2. It is also named as Radius of no Influence by Adlakha et al[7]. The targets originating beyond this radius can’t be detected.
In following subsections we will derive analytical result for the critical radii and speed. We use the senor model (4), the exposure mode (7) to analyze the relationship between a target and a sensor. The target moves in a straight-line path with speed v and travels distanceįduring time T. The signal amplitude Ȝ is a constant. The effective value of S(s,p) is between Fmin and Fmax. 4.1 The Biggest Exposure Direction (BED) and Least Exposure Direction (LED)
Let (xs,ys) denote the sensor position, (x,y) denote the target position, (xo,yo) denote the target original position, and (xe,ye) denote the target final position. From (3), we get 2
− 1· , i=1,…,m. Thus we can S ¸¹ get a set of contour lines which are circles centered on the sensor. It is well known that the gradient is perpendicular to those contour lines (see figure 2) and thus the line on which the gradient is passes the sensor. For function f, the gradient direction ∇f is its fastest increasing direction and −∇f is its fastest decreasing direction. So for function
the target. Let S(x,y)=Si, Si
i
k
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S, ∇f is its fastest decreasing direction and −∇f is its fastest increasing direction. Given the sensor position (xs,ys) and target original position (xo,yo), we define the least exposure direction (LED) as the direction from the sensor to the target or as the direction of vector (xo,yo)-(xs,ys) and we define the biggest exposure direction (BED) as the direction from the target to the sensor or as the direction of vector (xs,ys)- (xo,yo). Thus we can get the following theorem.
Fig. 2. The LED and BED
Theorem 1. Given the sensor position (xs,ys) and the target original position (xo,yo), we can calculate the LED and BED. When the target moves along the LED, the sensor can get the minimal exposure value, when the target moves along the BED, the sensor can get the maximal exposure value, and when the target moves along the other direction, the exposure value received by sensor is between the minimal and maximal exposure. The benefit of theorem 1 is that when we consider the coverage problem we only need to analyze the LED and BED cases. So for simplicity, in the remainder of this paper, we place the sensor at the origin position and limit the target original position (xo,yo) and its path to x axis. And we let k=2, so we get
We let Ȝ
The Critical Speeds and Radii for Coverage in Sensor Networks T
T
0
0
E = ³ S (s, p )dt = ³ λdt = λT
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(13)
When Et>ȜT, the sensor network can’t detect the target. To ensure the sensor can detect the target, we let E t ≤ λT
(14)
Lemma 1. Given the threshold Et, the amplitude Ȝ, the target speed v and the moving time T, when the target path passes the sensor and is symmetric to y axis (see figure 3), the sensor can get maximal exposure. Intuitively, the lemma is right, but the proof is very trivial. In this paper we don’t show the proof.
sensor
target (xo,yo)
(xe,ye)
Fig. 3. The maximal path
Given the threshold Et, the amplitude Ȝ, and the moving time T, using lemma 1, we get that the critical speed vc1 satisfies the following equations T
Et = 2
2
³
T
S (s, p )dt =
0
2
³ (v 0
λ
c1t + 1)
2
dt , v c1
T ≤ rmax 2
(15)
or T
Et = 2
rmax 2
³ S (s, p )dt = 0
vc1
³ (v 0
λ
c1t + 1)
2
dt , vc1
T > rmax 2
(16)
Using (15) and (16), we get (17) and (18) respectively 2λ 2 − Et T
(17)
2λ rmax E t 1 + rmax
(18)
v c1 = v c1 =
Note that when the target speed v>vc1, the sensor network can’t detect the target.
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Based on the definition of critical speed vc2, we get that the critical speed vc2 satisfies the following equations T
T
³
³ (v
E t = S (s, p )dt = 0
0
λ
c2
t + 1)
2
dt , v c 2T ≤ rmax
(19)
or rmax T
E t = S (s, p )dt =
³
vc 2
³ (v
0
0
λ
c2
t + 1)
dt v c 2T > rmax
2
(20)
Using (19) and (20), we get (21) and (22) respectively.
λ
vc2 = vc2 =
Et
−
1 T
(21)
λ rmax E t 1 + rmax
(22)
Note that when the target speed v>vc2, the target originating from origin can’t be detected by the sensor. 4.3 The Critical Radii
In this subsection we assume that the target speed v<=vc2. Given the threshold Et, the amplitude Ȝ, the target speed v and the moving time T, based on the definition of critical radius rc1, we get that the critical radius rc1 satisfies the following equations T
T
³
³ (r
Et = S (s, p )dt = 0
λ
dt , vT ≤ rmax
+ vt + 1)
2
c1
0
(23)
or T
rmax
E t = S (s, p )dt =
³ 0
v
³ (r 0
λ
c1 + vt + 1)
2
dt , vT > rmax
(24)
Using (23) and (24), we get (25) and (26) respectively.
The rc1 is the positive root of (25) or (26). Note that the targets originating within rc1 are surely detected.
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Given the threshold Et, the amplitude Ȝ, the target speed v and the moving time T, based on the definition of critical radius rc2, we get that the critical radius rc2 satisfies the following equations T
T
³
³ (r
Et = S (s, p )dt = 0
λ
− vt + 1)
2
c2
0
dt , vT ≤ rmax
(27)
or T
rmax
E t = S (s, p )dt =
³ 0
v
³ (r 0
c2
λ
− vt + 1)
2
dt , vT > rmax
(28)
Using (27) and (28), one can easily proof that rc 2 = rc1 + vT
(29)
Note that the targets originating beyond rc2 can’t be detected. Based on the critical radii, we define two critical densities as
ρ c1 =
1 1 , ρ c2 = 2 2 πrc1 πrc 2
(30)
Given a square area L*L, where L is the line length, we define two critical number as N c1 = L2 ρ c1 , N c 2 = L2 ρ c 2
(31)
5 Simulations In order to verify our result, we develop two simulations using MATLAB software. The first simulation is to verify the critical sensor numbers and it verifies the critical radii indirectly. The second is to verify the critical sensor speed. In the simulations, we consider random uniform deployment of sensors over a square area and the target moves in a straight-line path with constant speed v for a time T. In the first simulation, we let L=300, Ȝ=1, k=2, Fmin=0.001, Fmax=1, Et=0.01, T=2, v=5, so we can calculate vc1=193.6754, vc2=96.8377, rc1=9, rc2=19, Nc1=354, Nc2=79. The sensors are deployed on the 300*300 square randomly. The target original position and direction are randomly selected. We let the sensors number change from 1 to 2*Nc1. Under each given sensor number, we let the target present 100 times and the detection probability is the average detected times over the target presenting times. Figure 4 shows one of our simulations result. The simulations tell us when deploying Nc1 sensor nodes randomly the detection probability is about 90%, and when deploying Nc2 sensor nodes randomly the detection probability is about 40%. When deploying more sensors than Nc1 the probability converges at 1. In the second simulation, we let L=100, Ȝ=1, k=2, Fmin=0.001, Fmax=1, Et=0.01, T=2, n=39, so we can calculate vc1=193.6754, vc2=96.8377. The sensors are deployed on the 100*100 square randomly. The target original position and direction are randomly selected. We let the target speed change from 1 to [vc1]. Under each given
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C. Zang, W. Liang, and H. Yu Area=300*300 simulation=100 Probability
1
0.8
(354,0.92)
0.6 (79,0.51)
0.4
0.2 The Number of Sensors 0
0
100
200
300
400
500
600
700
800
Fig. 4. Probability of detection Vs. number of nodes
speed, we let the target present 100 times and the detection probability is the average detected times over the target presenting times. Figure 5 shows the simulations result. Figure 5 shows that when the speed turns greater the probability turns less. When the speed greater than the vc1, the sensor network can’t detect the target. However, we can’t explain why the probability increases when the speed increases before it reaches 20.
Fig. 5. Probability of detection Vs. speed of target
6 Conclusions In this paper we use modified sensor model and exposure model which are more reasonable than known models to analyze the coverage problem in the sensor network mathematically. We find the biggest exposure direction and least exposure direction which simplify the analytical process. We also identify several critical parameters, such as speed, radius, number and density. These parameters are very important when
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designing or analyzing a sensor network. The simulations verify our theoretical results. As part of our future work, we would analyze the critical parameters when the target speed vc2
References 1. Estrin, D., Govindan, R., Heidemann, J., Kumar, S.: Next Century Challenges: Scalable Coordination in Sensor Networks. In Proc. of MobiCOM, (1999)263–270. 2. Akyildiz, I F., Su, W., Sankarasubramaniam, Y., Cayirci, E.: Wireless Sensor Networks: a Survey. Computer Networks. VOL.38, NO.2, (2002)393-422. 3. Li, X., Wan, P., Wang, Y., Frieder, O.: Coverage in Wireless Ad-hoc Sensor Networks. IEEE Transactions on Computers, VOL.52, NO>6, (2003)753-763. 4. Meguerdichian, S., Koushanfar, F., Potkonjak, M., Srivastava, M B.: Coverage Problems in Wireless Ad-hoc Sensor Networks. In IEEE INFOCOM, (2001)1380–1387. 5. Meguerdichian, S., Koushanfar, F., Qu, G., Potkonjak, M.: Exposure in Wireless Ad-hoc Sensor Networks. In Proceedings of the 7th International Conference on Mobile Computing and Networking (MobiCom'01), Rome, Italy, (Best Student Paper Award), (2001)139-150. 6. Meguerdichian, S., Koushanfar, F., Qu, G., Veltri G., Potkonjak M.: Exposure in Wireless Ad-hoc Sensor Networks: Theory and practical solutions. Journal of Wireless Networks, VOL.8, NO.5, (2002)443-454. 7. Adlakha, S., Srivastava, M.: Critical Density Thresholds for Coverage in Wireless Sensor Networks. In IEEE Wireless Communications and Networking Conf. (WCNC), (2003)1615 –1620. 8. Marengoni, M., Draper, B A., Hanson, A., Sitaraman, R A.: System to Place Observers on a Polyhedral Terrain in Polynomial Time. Image and Vision Computing, VOL.18, (1996)773-780. 9. Gregg, W W., Esaias, W E., Feldman, G C. et al.: Coverage Opportunities for Global Ocean Color in a Multimission Era. IEEE Transactions on Geoscience and Remote Sensing, VOL.36, (1998)1620-1627. 10. Zhao, F., Guibas, L.: Wireless Sensor Networks: an Information Processing Approach. Elsevier, 2004.
A Distributed QoS Control Schema for Wireless Sensor Networks Jin Wu1,2 1
School of Computer Science and Engineering, Beihang University 100083 Beijing, China 2 Sino-German Joint Software Institute, Beihang University 100083, Beijing, China [email protected]
Abstract. Wireless ad-hoc sensor networks have recently emerged as a premier research topic. They have great long-term economic potential, ability to transform our lives, and pose many new system-building challenges. One major challenge for its real deployment is its QoS issue. This is a rich area because sensor deaths and sensor replenishments make it difficult to specify the optimum number of sensors (this being the service quality that we address in this paper) that should be sending information at any given time. Through literature survey, we discover that current solution towards this problem remains some unreasonable assumptions in practice. So we proposed a new control schema allowing the control method to be more feasible in real environment. A distributed control schema is introduced in this paper. Every sensor node runs a control algorithm in a distributed fashion. This distributed QoS control schema can handle limitations exist in current QoS control methods.
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researchers, a special QoS parameter to mean the resolution of sensor networks is a unique parameter typically measures the performance for Wireless Sensor Network in terms of the data gathering ability. Reference [1, 3] defines QoS to mean sensor network resolution. Specifically, depending on the different stimuli present in the sensor network, it is defined as the optimum number of sensors sending information toward information-collecting sinks. This is a very important issue, because in any sensor network we want to accomplish two things: 1) maximize the lifetime of the sensor network by having sensors periodically power-down to conserve their battery energy, and 2) have enough sensors powered-up and sending packets toward the information sinks so that enough data is being collected when stimuli presents. Note that the information sinks need a certain amount of information gathered from the different sensors, but sensors in close proximity to each other allow many of those sensors to be powered-down. This is the optimization problem we address, and it is a rich research area because sensors are always placed in the sensing field in random fashions with redundancy. Sensor deaths (e.g., as a result of damage or battery failure) and sensor replenishments make it difficult to control the optimum number of sensors that should be activated and sensing the field at any given time [2, 3]. This issue is firstly described in ref [3], and some improvements are given in ref [1, 4]. However, there is significant weak point for those solutions is that two assumptions are made where 1) broadcast channel exists for collection point to all nodes, and 2) sensor nodes are able to acknowledge the information for collection point even when it is powered off for energy saving. The above two assumptions are not supported by main-stream sensor node equipments. In this paper we present a distributed control algorithm for duty-cycle management to improve the QoS of Wireless Sensor Networks. We consider the sensor network can operate under the following model. Sensor nodes are distributed across the sensing field and simultaneously operating. Each sensor nodes swap in two states, active and sleep. Sensor node itself has to decide when in active (or sleep) state. A control algorithm runs on each sensor node to determine the operation state. We borrow the concept of control from a well-known Active Queue Management algorithm, Random Early Detection. The reminder of this paper is organised as follows. Section 2 gives the related works for this research. Definitions and models related to this paper are presented in Section 3. Section 4 gives a detailed description of the control algorithm for duty cycle. Finally, conclusions are given in Section 5.
2 Background The study of wireless sensor networks is still a burgeoning field, many aspects of sensor networks, such as routing, preservation of battery power, adaptive selfconfiguration, etc., have already been studied in previous papers. Ref. [6] might be the earliest work to the present study as it actively probes the question of QoS that the base stations are receiving from the sensors. However, it defines QoS as total coverage in a static fashion. That is, it does not allow a data sink to dynamically alter the QoS it is receiving from the sensors, depending on varying circumstances.
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Reference [3] proposed a solution that uses the idea of allowing the base station to communicate QoS information to each of the sensors using a broadcast channel and we use the mathematical paradigm of the Gur Game to dynamically adjust to the optimum number of sensors. The result is a robust sensor network that allows the base station to dynamically adjust the number of sensors being activated, thereby controlling the resolution of QoS it is receives from the sensors, depending on varying circumstances. This research attracts some research attentions and some new papers [1, 4] can be found in the literature to extend the idea.
3 Definitions and Models In this section, Placement Model, Sensing Model, and Converge Measures are defined, respectively. In the rest of this paper, these definitions and models will be used to study the decision fusion policy and its affect to overall performance. In this paper, a commonly used sensor placement model is applied. This model has been used by many researchers, e.g. in ref. [5]. Large number sensors are randomly placed over a two-dimensional geographical region. It is also assumed that the locations of sensors are uniformly and independently distributed in the region. Such a random initial deployment is desirable in scenarios where priori knowledge of the field is not available. Also, the random deployment can be the direct result of certain deployment strategies. Based on this assumption, the locations of sensors can be modelled by a stationary two-dimensional Poisson point process. Denote the density of the underlying Poisson point process as λ , which is measured by the number of sensors per unit area. The number of sensors located in a region A, N(A), follows a Poisson distribution of parameter λ A , where A represents the area of the region [5].
P( N ( A) = k ) =
e
−λ A
(λ A ) k
(1)
k!
In this paper, for the sake of simplicity, the Boolean sensing model is being used. The Boolean sensing model has been widely used in many researches. In the Boolean model, each sensor has a certain uniform sensing range, r. A sensor can only sense the environment and detect phenomenon within its sensing range. A location is said to be “covered” by a sensor if it lies within the sensor’s sensing range. The degree of coverage is defined by the coverage density. It is defined as, fc(p), the positive integer for sensors’ number by which a particular point p within the sensing field is covered with. The Coverage Density represents redundancy level of sensor deployment for a certain point in the detection area. Note that the definition of a location being covered depends on the specific sensing model under consideration. The Boolean sensing model is considered in this paper, where a location is covered if it is within the sensing area of a sensor. If there are n sensors got the ability to detect the event that takes place at the point p, then the value of fc(p), in terms of resolution, equals to n. Therefore, if there is an event takes place at the point p, basically, n sensors will be able to claim detection for this event. However, some sensors in the sensor network might face
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some problems in terms of miss detection and false detection, so the detection reported by sensors might not exactly equals to n. Detail performance of n will be discussed in Section 4.
4 Duty-Cycle Management Algorithm for QoS Control Suppose we have a collection of n sensor nodes, M1 through Mn, placed over a sensing field with area of S. Sensor nodes are placed and operating following the definition in Section 3. This section analyse the duty cycle management problem to support QoS of Wireless Sensor Network in terms of resolution. Also, a duty cycle management algorithm is given. For the sake of simplicity, it is assumed that all sensor nodes have similar hardware and software specifications and configurations, and they are placed over a flat screen in quite radio environment. As defined in Section 3, every node is running independently. In order to have every node periodically power-down to conserve its battery energy, sensor nodes need to compute what time to sleep and what time to wake up. For any node i, it is awake for the first time deployment, suppose the time for the hth sleep is tsleepi|h, and the time for the hth wake up is twakei|h. Then, the hth sleep interval can be represented as
∆titvl
i
= t wake
i
h
h
− t sleep
i h
When in active state, a sensor node will emit a beacon signal through the radio channel for every ∆t beacon . Without loss of generality, we can define
∆t beacon >> Z beacon / Rate where Zbeacon and Rate represent for the packet size of beacon and the transmission rate of radio channel. The beacon density, ni(t), measures the probability of receiving a beacon for node i at time t. Then, it can be easily discovered that the resolution of a event takes place at point x, x ⊂ S , is
R f c ( x, t ) = n x (t ) ⋅ ∆t beacon ⋅ ( ) 2 + 1 r
(2)
where R and r are the range for sensing and transmission respectively. Defined the minimum threshold of fc(x,t) as f’, then the minimum threshold of beacon density nx(t) can be represented as
f '−1 r n' ( x ) = ( ) 2 ⋅ c R ∆t beacon
(3)
Based on the above analysis, it can be considered as when the incoming beacon probability is lower than n’(x), it means that the number of nodes that cover the point x are too small to provide certain degree of resolution, or vice versa. Therefore, the algorithm that controls the sleep interval can be given as follows.
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Twakei|0=0; Tsleepi|0=0; n=1; if ((tnow-last_update)>update_itvl) { if (((tnow-twakei|n-1)/ tbeacon)*x)>Maxth {tsleepi|n=tnow; twakei|n=tnow+Max_sleep; }; if (((((tnow-twakei|n-1)/ tbeacon)*x)<Maxth)&((((tnow-twakei|n-1)/ tbeacon)*x)>Minth)) {tsleepi|n=tnow; twakei|n=tnow+ Max_sleep*((((tnow-twakei|n-1)/ tbeacon)*x-Minth)/(Maxth-Minth)); }; if ((((tnow-twakei|n-1)/ tbeacon)*x)<=Minth) {tsleepi|n=+ ; twakei|n=tnow; }; if tsleepi|n<=tnow Set_wake(twakei|n); x=0; n++; last_update tnow; Sleep; }; Minth=(r/R)2*(fc’-1); Maxth=Minth+a*(N-Minth);
Ğ
㧩
Fig. 1. Duty-cycle Control Algorithm for QoS Control
In the algorithm shown in Figure 1, tnow is current time, and the update_itvl is the time slot for update interval. α ⊂ (0,1) is a parameter related to the stability of system.
5 Conclusions and Future Work Sensor networks are an exciting area with very real applications in the near future. Although many aspects of sensor networks have been studied before, quality of service (QoS) for sensor networks remains largely open. In this paper, we present an idea of using the duty-cycle control algorithm running on each sensor node to balance the trade off between energy consumption and resolution. It is expected that even without using such critical assumptions as ref [3] did, we still can control the Wireless Sensor Networks will to achieve some sort of QoS. It is believed that our newly proposed control method is effective, and has significant advantage against the method in literature. In the future, simulation experiments will be done to numerate the significant
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improvement of the newly proposed algorithms. Also, the stability of the control system will be given and parameter configuration methods will be provided to better tune the duty-cycle management system.
Acknowledgement The author acknowledges the support from the National Natural Science Foundation of China (NSFC) under the grant numbers 90104022, 90412011, and 90612004.
References 1. Frolik, J.: QoS Control for Random Access Wireless Sensor Networks. In the Proceedings of the WCNC 2004, (2004)1522-1527 2. Heinzelman, W., Kulik, J., Balakrishnan, H.: Adaptive Protocols for Information Dissemination in Wireless Sensor Networks. In the Proceedings of the 5th ACM/IEEE Mobicom Conference, (1999) 174-185 3. Iyer, R., Kleinrock, L.: QoS Control for Sensor Networks. In the Proceedings of the 2003 IEEE International Conference on Communications, ICC'03. Vol.1. (2003) 517-521 4. Kay, J., Frolik, J.: Quality of Service Analysis and Control for Wireless Sensor Networks. In the Proceedings of the 2004 IEEE International Conference on Mobile Ad-hoc and Sensor Systems, (2004) 359-369 5. Liu, B., Towsley, D.: A Study of the Coverage of Large-scale Sensor Networks. In the Proceedings of the 2004 IEEE International Conference on Mobile Ad-hoc and Sensor Systems, (2004) 475-483 6. Meguerdichian, S., Farinaz, K., Miodrag, P., Srivstava, M.: Coverage Problems in Wireless Ad Hoc Sensor Networks. In the Proceedings of the 20th Annual Joint Conference of the IEEE Computer and Communications Societies, Vol. 3. (2001) 1380-1387 7. Shakkottai, S., et. al.: Unreliable Sensor Grids: Coverage, Connectivity, and Diameter, In the Proceedings of the 22th Annual Joint Conference of the IEEE Computer and Communications Societies, Vol. 2. (2003) 1073-1083 8. Tian, D., Georganas, N.: A Coverage-preserving Node Scheduling Scheme for Large Wireless Sensor Networks. In the Proceedings of the 1st ACM International Workshop on Wireless Sensor Networks and Applications, (2002) 32-41 9. Ye, F., et al.: Peas: A Robust Energy Conserving Protocol for Long-lived Sensor Networks. In the Proceedings of the 23rd International Conference on Distributed Computing Systems, (2003) 28-37
A Framework of In-Situ Sensor Data Processing System for Context Awareness Young Jin Jung1, Yang Koo Lee1, Dong Gyu Lee1, Mi Park, Keun Ho Ryu1,*, Hak Cheol Kim2, and Kyung Ok Kim2 1
Database/Bioinformatics Laboratory, Chungbuk National University, Korea {yjjeong, leeyangkoo, dglee, pmi386, khryu}@dblab.chungbuk.ac.kr 2 Electronics and Telecommunications Research Institute (ETRI), Korea {david90, kokim}@etri.re.kr
Abstract. We propose a framework of the context awareness system which processes a large amount of sensor data from the application areas. The proposed framework consists of a context acquisition, a knowledge base, a rule manager, and a context information manager, etc. we implement the proposed framework of in-situ sensor data processing system that manages the data transmitted from various sensors and notifies the manager of the alarm message for specific conditions. Our proposed framework is able to be applied to the prevention of a forest fire, the warning system for detecting environmental pollution, etc.
1 Introduction It is very necessary to detect the environmental conditions of remote places in real time in order to prevent natural disasters such as a flood, a typhoon, an earthquake, etc. according to the global environment deterioration at an alarming rate with the progress of civilization. The sensors included in a forest, a factory district, a river in ubiquitous sensor network environment transmit sensor data to a concentration node and a control center through routing among sensors. A ubiquitous sensor network environment can collect data through the communications among various sensors and provide an intelligent environment of physical space. In order to provide a suitable service in the situation of users with minimum intervention, the context aware techniques are the core of the service. Context aware service includes the ability of understanding, analyzing, and reasoning user situation. When a user wants to get some service, the service provider should be aware of the context and provide the most suitable service at the user-requested time. It is necessary to manage the sensor data and to abstract the context information depending on the requirements predicted in applications with the hiding of the complex situation of used sensors. Some techniques are required not only to manage the sensor data, but also to understand context for providing optimal service, as the *
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context information has some properties changed from the attributes of time and space. In this paper, in order to handle real time sensor data and understand a situation, we design and implement the prototype of the context awareness system for monitoring disaster or accident to deal with the plentiful sensor data in a vast area such as the prevention of a forest fire, the warning system for detecting environmental pollution, etc. The proposed system can manage the data transmitted from various sensors and notify the manager of the alarm message for specific conditions. The remainder of the paper is organized as follows. Section 2 briefly describes the existing sensor data processing and context aware system. Section 3 introduces the proposed system structure. Section 4 presents in-situ sensor data processing and the database schema for storing sensor and context information. Section 5 illustrates the implemented system. Section 6 concludes.
2 Related Work Sensor Web Enablement (SWE) of the Open Geospatial Consortium, Inc. (OGC) builds revolutionary framework of open standards for exploiting web-connected sensors and sensor systems [1]. In addition, SWE contains some research sensorML [2], Observations & Measurements [3], Sensor Observation Service, Sensor Planning Service, Web Notification Service. The sensorML is information model for discovering, querying and controlling web-resident sensors. The observations & measurements are the information model for observations and measurements. The sensor observation service is the service to fetch observations from a sensor or constellation of sensors. The sensor planning service assists in "collection feasibility plans" and to process collection requests for a sensor or sensor constellation. The web notification service executes and manages message dialogue between a client and web services for long duration asynchronous processes. The goal of the SWE activity is to allow all types of web and/or Internet-accessible sensors, instruments, and imaging devices to be accessible and, where applicable, controllable via the internet. A context-aware application is one which adapts its behavior to a changing environment [4]. Typically, a context-aware application needs to know the location of users and equipment, and the capabilities of the equipment and networking infrastructure [5]. There are many projects to understand context information and provide suitable services such as SOCAM(Service-oriented Context-Aware Middleware) [6], CASS (Context-awareness sub-structure) [7], CoBrA(Context Broker Architecture) [8], Context Toolkit [9], Gaia project [10], Hydrogen project [11], CORTEX [12], etc. The SOCAM has the architecture for the building and the rapid prototyping of context-aware mobile services. The CASS is centralized middleware approach designed for contextaware mobile applications. The CoBrA has an agent based architecture for supporting context-aware computing in so called intelligent spaces. Intelligent spaces are physical spaces such as living rooms, vehicles, corporate offices and meeting rooms. The Context Toolkit takes a step towards a peer-to-peer architecture but it still needs a centralized discoverer where distributed sensor units (called widgets), interpreters and aggregators are registered in order to be found by client applications. The Hydrogen project's context acquisition approach is specializing in mobile devices. The Gaia project extends typical operating system
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concepts to include context-awareness. It aims at supporting the development and execution of portable applications for active spaces. The CORTEX system is an example for a context-aware middleware approach based on the Sentient Object Model.
3 Proposed Framework In order to prevent disasters, provide intelligent public services and personalized services, the structure of context awareness system for modeling and processing large scale condition information from a variety of sensor data is shown in Fig. 1.
Fig. 1. The structure of context awareness system
In-situ and remote sensor data transmitted from sensor network middle interface are stored into a context information database in knowledge base through converting the data into knowledge with a sensor data collection, a sensor data abstraction, and a sensor data refiner. The context information manager module can understand the situation of the area using sensor in real world through analyzing and reasoning the situation through detecting rules defined in the rule manager. It can also provide the summarized context information to a service provider through utilizing a data provider and the knowledge base. In this paper, we focus on the sensor data processing in the context aware system with the sensor model language and rule management for a specific context.
4 In-Situ Sensor Data Processing in the Framework We briefly explain how in-situ sensor data is processed for prevent accidents in the framework such as the sensor data processing steps, database schema to store the rules to check the sensor data, and alarm messages to suggest a safety guideline.
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Fig. 2. In-situ sensor data processing for context awareness
Fig. 2 shows the sensor data processing to notify alarm messages through utilizing the rules to evaluate the conditions and knowledge base to support the additional messages. Detailed data processing is summarized as follows:
၃ Sensor data is transmitted into the system through a sensor network middleware interface with transduerML(Transducer Markup Language). ၄ In order to know sensor types and get the detected data from sensors after ၅ ၆ ၇
installing in-situ sensors, registration of sensor information is required in the system. Summarized sensor meta data is stored in the knowledge base. The abstracted sensor data will be processed with context analysis and rule processing after combining sensor meta data and observed data The rule processing module in the rule manager searches the rules to satisfy the abstracted sensor data in the rule information database of the knowledge base. The service information supply module finds the additional message to help the user understand the situation easily in the environment database. The additional message changed depending on the place is provided in the safety guidelines.
Sensor Model Language(SensorML) which is an XML schema for defining the geometric, dynamic, and observational characteristics of a sensor is designed to support a wide range of sensors including both dynamic and stationary platforms and including both in-situ and remote sensors. The sensor structure tables in the database store the properties of sensors extracted from the sensorML files. The tables include the elements of the sensorML such as an identifiedAs, a classifiedAs and, a measures, etc. The measures illustrates the characters of measurement such as sample period, relative accuracy, etc. others tables also store sensor metadata such as sensor locations, document events, the manager mail address, etc. The rule tables for context awareness provide context information, detail conditions such as time, node id, the measured values of sensors safety guidelines for users in the cases that the sensor values are satisfied with the rules for presenting a specific situation.
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5 Implementation and Running Examples In this section, in order to show the usage of the sensor data processing in context aware system, we describe a process for handling the sensorML, for managing the sensor data transmitted from sensor network.
Fig. 3. The provided alarm message and the focused on a sensor
Fig. 3 shows the served warning message and alarm of the sensor when the measured values of a specific sensor are satisfied with the detailed conditions that user defined. In the view, the specific sensor is focused on alarm and the summarized message is also served to notify users and managers. The context aware system includes three parts: a view, a sensor information bar, a navigation panel. The view displays and handles the geometry and sensor information through utilizing sensor information bar and navigation panel. The sensor information bar shows the list, the structure, the last values of sensors. The navigation panel provides the functions to move to the specific sensor, to rotate the view, and to handle the tilt of the view.
6 Conclusion Recently, the interest in sensor data processing and context aware system increases rapidly on a large scale. In this paper, we proposed the framework of the context aware system based on sensor network to provide the warning message and suitable safety guideline services depending on the transmitted values and the location of sensors in real-time. The implemented system would be useful to process various sensor data for understanding contexts user defined in a variety of applications [13] in sensor network such as an intelligent transportation management, an intelligent robot system, a disaster management system, etc. Currently we are focusing on extending the rules for capturing and reasoning situation under the ontology concepts [14] to satisfy users’ various requirements based on the sensor network.
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Acknowledgements This work was supported by RRC program of MOCIE and ITEP, by Electronics and Telecommunications Research Institute, and by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment).
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
11. 12.
13. 14.
Botts, M.,: Sensor Web Enablement. http://www.opengeospatial.org/press/ (2005) Botts, M.,: Sensor Model Language. http://vast.nsstc.uah.edu/SensorML/ (2004) Cox, S.,: Observations and Measurements. http://www.opengeospatial.org (2003) Seo, S.B., Kang, J.W., Ryu, K.H.: Multivariate Stream Data Reduction in Sensor Network Applications. EUC Workshops (2005) 198-207 Harter, A., Hopper, A., Steggles, P., Ward, A., Webster, P.: The Anatomy of a ContextAware Application. Mobile Computing and Networking (2002) Gu, T., Wang, X.H., Pung, H.K., Zhang, D.Q.: A Middleware for Context-Aware Mobile Services. IEEE Vehicular Technology Conference. Milan, Italy (2004) Fahy, P., Clarke, S.: CASS – Middleware for Mobile Context-Aware Applications. MobiSys (2004) Chen, H., Finin, T., Joshi, A.: Using OWL in a Pervasive Computing Broker. Workshop on Ontologies in Agent Systems, AAMAS (2003) Salber, D., Dey, A. K., Abowd, G. D.: The Context Toolkit: Aiding the Development of Context-Enabled Applications. In Proceedings of ACM CHI 99, Pittsburgh, PA. (1999) Román, M., Hess, C., Cerqueira, R., Ranganat,,A.: Campbell, R. H., Nahrstedt, K.: Gaia: A Middleware Infrastructure to Enable Active Spaces. In IEEE Pervasive Computing (2002) Hofer, T., Schwinger, W., Pichler, M., Leonhartsberger, G., Altmann, Jo.: ContextAwareness on Mobile Devices – the Hydrogen Approach. (2002) Biegel, G., Cahill,,V.: A Framework for Developing Mobile, Context-aware Applications. In Proceedings of 2nd IEEE conference on Pervasive computing and Communications, Percom (2004) Seo, S.B., Kang, J.W., Lee, D.W., Ryu, K.H.: Multivariate Stream Data Classification Using Standard Text Classifiers. Dexa (2006), to be accepted. Hwang, J.H., Gu, M.S., Ryu, K.H.: Context-Based Recommendation Service in Ubiquitous Commerce. ICCSA Vol. 2 (2005) 966-976
A Mathematical Model for Energy-Efficient Coverage and Detection in Wireless Sensor Networks Xiaodong Wang, Huaping Dai, Zhi Wang, and Youxian Sun National Laboratory of Industrial Control Technology, Institute of Industrial Process Control Zhejiang University, Hangzhou 310027, P.R. China {xdwang, hpdai, wangzhi, yxsun}@iipc.zju.edu.cn
Abstract. The tradeoff between system lifetime and system reliability is a paramount design consideration for wireless sensor networks. In order to prolong the system lifetime, random sleep scheme can be adopted without coordinating with its neighboring nodes. Based on the random sleep scheme, an accurate mathematical model for expected coverage ratio and point event detection quality is put forward in this paper. Furthermore, the model also takes the border effects into account and thus improves the accuracy of performance and quality analysis. Our model is flexible enough to capture the interaction among the essential system parameters. Therefore, this model could provide beneficial guidelines for optimal sensor network deployment satisfying both the lifetime and reliability requirements. Additional simulation results confirm the correctness and effectiveness of our analysis.
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hardware devices usually consume too much energy and the cost is too high for tiny sensors. Furthermore, coordination among nodes also takes additional energy. It is expected that scheduling algorithms could work without geography information. Moreover, none of the aforementioned literature considered the border effects, that is, the points near the border of deployment area generally have less chance to be covered than the points in central area. When the proportion of the node’s sensing range to the range of the deployment area is not small enough, the border effects should not be ignored ([6], [7]). In [6], a mathematical method was proposed to evaluate the number of nodes needed to reach the expected coverage ratio with the consideration of border effect. However, it can only apply to determine the number of active nodes, and when dynamic management of nodes duty cycle is adopted, the total number of nodes can not be derived from this model. In [7], a mathematical expression was formulated for expected k-coverage with the consideration of both the border effects and the uncoordinated node scheduling scheme. Though the border effects were considered in [6] and [7], the network performance of border area such as coverage and detection can not be predicted accurately from these models. In this paper, we present a mathematical model for energy-efficient coverage and detection quality with the consideration of border effects. We base our analysis on random deployment since this deployment strategy is easy and inexpensive for sensor networks [8]. And for individual nodes, we adopt the model of random sleep scheme. In this model, nodes sleep and wake up randomly and independently of each other. The obvious advantage of this scheme is its simplicity for implementation, without incurring control overhead. Since the deployment and the sleep scheme we choose are random, it is more reasonable to study this problem from a probabilistic perspective. The main contributions of this paper include:
㧔1㧕The model is flexible enough to capture the interaction among the system pa-
rameters such as sensor node numbers, random sleep ratio, etc. Hence, it can provide guidelines for optimal sensor network deployment. Our model can help to determine the sleep ratio for a desired coverage and acceptable detection quality. We pay more attention to the quality of service (QoS) that the sensor network provides for the border area. If the applications in border area demand high degree of accuracy, the QoS is desired to be upgraded to a higher level. In this case, how many nodes should we deploy? This problem is also answered analytically in our model.
㧔2㧕 㧔3㧕
The rest of the paper is organized as follows. In section 2 we present our network models and assumptions. Section 3 formulates the network coverage problem and section 4 considers point event detection. In section 5 we present the simulation results and section 6 concludes the paper.
2 Network Models and Assumptions In this section, we present the notations and assumptions for our derivations. First of all, we assume that n sensor nodes are uniformly and independently distributed in a two-dimensional circular area Z with radius of R . For simplicity, we use the Boolean
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sensing model and assume that sensor’s sensing range is a circular area centered at this sensor with a radius of S . In addition, all sensor nodes are supposed to have the same sensing radius and no two sensors are deployed exactly at the same location. A point event E that occurs within Z can be detected if it lies within at least one active sensor node’s sensing range. So we define a point’s neighboring area ` as a region that any sensor node, if it is located within the region, can cover this point. When border effects are not taken into account, for all points in Z , ` Z = π r 2 . If border effects are considered, we divide the area Z into two parts as shown in Figure 1 for the convenience of analyzing this problem.
l Z' Z = Z '+ Z "
Z"
Fig. 1. Illustration of central area, border area and neighboring area
The central area Z ' that is concentric with Z , has a radius of R − r . Obviously, for any point in Z ' , its neighboring area is ` Z ' = π r 2 . However, for an arbitrary point
d in border area Z " , only the shadowed part has the probability of being deployed
with sensor nodes. Hence, ` d < π r 2 . In our analysis, we assume that all sensors have the same sensing period T and the same sleep ratio α ( 0 ≤ α ≤ 1 ) that defines the percentage of time the sensor is in sleep state. Each sensor node determines independently for each common time unit called slot to be inactive with probability α .
3 Network Coverage Analysis First, according to our assumptions, since nodes are deployed with a uniform distribution, the probability that a sensor node falls on a point’s neighboring area is φ = ` π R 2 . Hence, it is well-known that the number of nodes within ` conforms to a binomial distribution B(n, ` π R 2 ) . Hence, the probability that an arbitrary point is covered by at least one node is Ρ = ¦ k =1 Cnk φ k (1 − φ )n − k = 1 − (1 − φ )n n
(1)
Considering the random sleep scheme, the probability of a point event E is covered by at least one active sensor is Ρ ' = 1 − ¦ k = 0 α k Cnk φ k (1 − φ )n − k = 1 − [1 − (1 − α )φ ] n
n
(2)
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For each point in Z ' , the probability that a sensor node falls on its neighboring area is the same: φZ ' = π r 2 π R 2 = r 2 R 2 . According to Formula 2, the probability of being n
covered is also same: 1 − ª¬1 − (1 − α )(r R )2 º¼ . Then the expected coverage ratio of area Z ' is Ρ 'Z ' = 1 − [1 − (1 − α )φ Z ' ] = 1 − ª¬1 − (1 − α )(r R) 2 º¼ n
n
(3)
In particular, the neighboring areas of points in Z " have various values, determined by the distance l between the point and the center of Z as shown in Figure 1. In order to evaluate the average coverage ratio of area Z " , we have to compute the average probability of being covered for all points in Z " . For any point d in Z " , its neighboring area ` d ∈Z " can be calculated using the formula proposed in [6]: ` d ∈Z "
1 R2 − r 2 − l 2 R2 − r 2 − l 2 = π ( R 2 + r 2 ) + r 2 arcsin + 2 2lr 2l R2 − r 2 + l 2 R2 − r 2 + l 2 − R 2 arcsin − 2lR 2l
Furthermore, we are also interested in the average coverage ratio of whole area Z when all the deployed sensors are active. Based on this value, we can explore how much the QoS will be disrupted under the random sleep scheme and the quantitative quality differences between the central area Z ' and border area Z " . The average neighboring area of all points in Z can be obtained by:
{ = {π r ( R − r )
}
` Z = π r 2 × π ( R − r ) 2 + ` Z " ª¬π R 2 − π ( R − r ) 2 º¼ π R 2 2
2
}
+ ` Z " ª¬ R − ( R − r ) º¼ 2
2
R
2
(7)
Hence, according to formula 1 and 7, the average coverage ratio of Z without adopting the sleep scheme is Ρ Z = 1 − (1 − φ )n = 1 − (1 − ` Z π R 2 )n
(8)
In this paper, we are only concerned with 1-coverage. Our model can be easily extended to k-coverage.
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4 Point Event Detection Analysis In this section, we propose a mathematical model to analyze the probability of detection delay for the point event. Even the points in area Z are all covered, it may not be guaranteed that all the point events are detected instantaneously when they occur due to the random sleep scheme we adopt. Now consider an arbitrary point covered by at least one node in Z . As Figure 2 illustrates, we call the period from time t1 to t3 the Worst Case Sleep Time (WCST), during which all nodes within this point’s neighboring area happen to be in sleep state, but unfortunately an event occurs during this time period (As shown in Figure 2, the event occurs at time t2 ). Hence, a detection delay td (td = t3 − t2 ) unavoidably occurs for the reason that the event can only be detected when at lest one node wakes up at time t3 . [9] also considered this scenario, but they only targeted large scale wireless sensor networks.
t1
t3
t2
Fig. 2. Illustration of point event detection delay
Intuitively, increasing the number of nodes deployed in the area, or decreasing the sleep ratio of each node can decrease delay time. But, how many nodes we should deploy? How to choose the sleep ratio? Due to the border effects, we need not only to guarantee the detection quality of point events in central area Z ' , but also to pay much attention to analyze the detection delay probability of the point events in area Z " , if the applications require a high degree of accuracy of detection in the whole region Z . Based on Figure 2 and above analysis, it is necessary to calculate the conditional probability (denoted by Ρ S C ) that a point is not covered by any active node even it could be covered ΡS C
n n α k Cnk φ k (1 − φ )n − k [1 − (1 − α )φ ] − (1 − φ ) n ¦ k =1 = =
1 − (1 − φ ) n
(9)
1 − (1 − φ )n
Then, the probability of a given point event is uncovered for at least τ slots is τ
{
Ρ td (td ≥ τ ) = Ρ S C − ¦ i =1 ª¬1 − (1 − φ ) n º¼ = Ρ S C − ¬ª1 − (1 − φ )n ¼º
−1
τ
−1
¦ i =1
¦ k =1α ik (1 − α k )Cnk φ k (1 − φ )n − k
{
n
n
}
i i +1 ¬ª1 − (1 − α )φ ¼º − ¬ª1 − (1 − α )φ ¼º
n
}
(10)
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From previous section we can calculate φZ ' and φZ " . Hence, if node number n and sleep ratio α are known in advance, the detection delay of point event can be evaluated analytically. Equivalently, given other parameters, the number of sensors to be deployed can also be estimated.
5 Simulation Results In this section, we demonstrate that the analytical results are consistent with simulation results. In our simulation, locations of nodes are generated conforming to uniform random distribution over a circular area Z with radius R . The area Z is divided into many small grids with size 0.1× 0.1 .The node’s sensing range r is set to 10. Then, R can be determined by the value of r R (1, 0.5, and 0.1 respectively). The period T is chosen to 10s , and let time slot be 1s . In the first set of experiments r R is set to 1, and the number of nodes n is varied from 1 to 10 with an increment of 1. We first obtain the simulation results of coverage ratio (denoted by SC − Z ) of whole area Z when deployed nodes are all active. Then, the random sleep scheme is adopted. We measure the coverage ratio of both central area Z ' and border area Z " under different combinations of n (1, 2,3!,10) and α (0.3, 0.6), denoted by SC − Z '− 0.3 , SC − Z '− 0.6 , SC − Z "− 0.3 , and SC − Z "− 0.6 respectively. The coverage ratio is obtained as follows. The simulation coverage ratio for a single time slot is obtained by calculating the proportion of the number of covered grids to the total number of grids in the area. For each deployment, 1000 time slots are examined. Besides, we generated 100 deployments for every combination of parameters, and get the average simulation results as shown in Figure 3(a). Comparing with the analytical results ( AC − Z , AC − Z '− 0.3 , AC − Z '− 0.6 , AC − Z "− 0.3 , AC − Z "− 0.6 ), we observe that the simulation results match the analytical curves well. In the second set of experiments, for a given node number, we study the detection delay probability of central area Z ' and border area Z " under different combination of sleep ratio α (0.3, 0.6) and time slots τ (1, 2, !, 20) , denoted by SD − Z '− 0.3 , SD − Z '− 0.6 , SD − Z "− 0.3 and SD − Z "− 0.6 respectively. The node number is selected intentionally. As Figure 3(a) shows, when 8 deployed sensor nodes are all waking up, the whole area Z is almost fully covered. Then we can explore how much the detection quality will be disrupted under the different α values, and the quantitative quality differences between the central area and border area. For each time slot τ , when random sleep scheme is applied, the area coverage ratio Ρτ' can be obtained by calculating the proportion of the number of the covered grids to the total number of grids in this area. Then, Ρ S C can be estimated by the long run average of 1 − Ρτ' . Every grid is assumed as a point event. For each grid, we record the number of experiments where the detection delay is larger than or equal to 1s, 2 s,3s, !, 20 s respectively. The simulation results shown in Figure 3(b) are averages over 100 runs.
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We also conducted additional experiments with r R = 0.5 and r R = 0.1 to examine the accuracy of our theoretical results, and the simulation results are showed in Figure 4 and Figure 5. Our observations from simulation are summarized as follows: 1) The simulation results are very close to the analytical results, which validates the correctness of our derivations. 2) The QoS of central area Z ' outperforms that of border area Z " on both coverage and detection quality. 3) The coverage ratio increases with the increasing number of deployed nodes. For a given nodes number, coverage ratio increases with the decrease of α . 4) For a given node number, the probability of detection delay increases with the increase of α . 1
Fig. 5. Comparing analytical results with simulation results (r/R=0.1)
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6 Conclusions In this paper, we presented an accurate mathematical model for energy-efficient coverage and detection with the consideration of border effects. The correctness and effectiveness of our analytical model are justified through extensive simulation experiments. This model enables us to analyze the tradeoff between network lifetime and system reliability of wireless sensor networks more effectively, and provides guides for optimal sensor network deployment.
Acknowledgment This research is supported by Chinese National Natural Science Foundation under the Grant 60304018, 60434030, Technology Fund of Ningbo City (No.2005C100067), the Key Technologies R&D Programs of Zhejiang Province (No.2005C21087), Academician Foundation of Zhejiang Province (No.2005A1001-13), and Specialized Research Fund for the Doctoral Program of Higher Education (No.20050335020).
References 1. Shih, E., Cho, S., Ickes, N., Min, R., Sinha, A., Wang, A., Chandrakasan, A.: Physical Layer Driven Protocol and Algorithm Design for Energy-efficient Wireless Sensor Networks. Proceedings of the seventh annual international conference on Mobile computing and networking (MobiCom 01), Rome, Italy, July (2001) 272-287 2. Tian, D., Georganas, N.D.: A Coverage-preserved Node Scheduling scheme for Large Wireless Sensor Networks. Proceedings of First International Workshop on Wireless Sensor Networks and Applications (WSNA’02), Atlanta, USA, September (2002) 32-41 3. Ye, F., Zhong, G., Lu, S., Zhang, L.: Energy Efficient Robust Sensing Coverage in Large Sensor Networks. UCLA Technical Report, (2002) 4. Xing, G., Wang, X., Zhang, Y, Lu, C., Pless, R., Gill, C.: Integrated Coverage and Connectivity Configuration for Energy Conservation in Sensor Networks. ACM Trans. Sensor Networks, in press 5. Lu, J., Suda, T.: Coverage-aware Self-scheduling in Sensor Networks. Proceedings IEEE 18th Annual Workshop on Computer Communications, (2003) 117–123 6. Liu, M., Cao, J.N., Li X., Lou, W.: Coverage Analysis for Wireless Sensor Networks. Proc. 1st International Conference on Mobile Ad-Hoc and Sensor Networks (MSN'05), (2005) 711-720 7. Yen, L.H., Yu, C. W, Cheng, Y.M.: Expected K-coverage in Wireless Sensor Networks. Ad Hoc Networks, in press 8. Tilak, S., Abu-Ghazaleh, N.B., Heinzelman, W.: Infrastructure Tradeoffs for Sensor Networks. Proceedings of First International Workshop on Wireless Sensor Networks and Applications (WSNA’02), Atlanta, USA, (2002) 49-57 9. Hsin, C.F., Liu, M.: Network Coverage using Low Duty Cycled Sensors: Random & Coordinated Sleep Algorithms. International Symposium on Information Processing in Sensor Networks, (2004) 433–442
A Method of Controlling Packet Transmission Rate with Fuzzy Logic for Ad Hoc Networks Kyung-Bae Chang, Tae-Hwan Son, and Gwi-Tae Park ISRL, College of Science, Korea University. Anam-dong 5-ga Seongbuk-gu, Seoul, Korea {lslove, chlilla, gtpark}@korea.ac.kr
Abstract. In this research, a packet transmission rate control scheme between nodes on a wireless Ad-hoc network is proposed considering the characteristics of Wireless LAN rent transmission efficiencies by different transmission distances. Many energy efficient routing algorithms researches have been conducted only on the assumption of ideal experimental cases. This paper considers the way of finding suitable transmission rate for the transmission distances between nodes on a mobile Ad-hoc networks so that a more realizable method is presented. In this research, a controlling algorithm for transmission data rates by the distances between mobile nodes is realized using Fuzzy logic, possibly available to be applied to Ad-hoc network routing, and simulations are conducted to verify the enhancements in throughput.
the maximum [5]. The maximum transmission rate is only realized under the condition of host nodes within the transmission range. For instance, the transmission rates of 1/2Mb/s, 5.5 Mb/s, 11 Mb/s are ideal at the distances of 100m, 60m, 30m, respectively [2]. Appropriate data transmission rates for transmission distances between mobile nodes should be considered for more realistic Ad Hoc network routing method as well as researches on developing various mobile routing methods. In this research, Fuzzy logic is suggested for the logical transmission rate selection as the method of controlling transmission rate between nodes in Ad Hoc network, considering the characteristics of IEEE 802.11 which possesses different transmission efficiency by transmission distances. A method of controlling packet transmission rate by distances is realized, which is possibly applied to a generic Ad Hoc network routing and the proposed method is verified its validity with a computer simulation.
2 Ad Hoc Routing Algorithm There are two mainstreams of researches in developing routing algorithms for Ad Hoc networks. First off, methods of routing for energy saving of mobile nodes are being researched [1]. Nodes in an Ad Hoc network critically depend on batteries since they are remotely operated using only batteries. Therefore, a network structuring optimization problem is very important for minimum power consumption with providing satisfactory communication. At present, researches on using a periodic sleeping and a clustering of nodes are lively being conducted to span the lifetime of batteries by distributing the energy consumption to the whole network. Secondly, there are a number of researches on realizing the shortest distance adapted to the dynamic node changes [3] [4]. In a mobile Ad Hoc network, the phase of the network continuously varies due to the mobility of nodes. The network phase is possible to be rapidly and arbitrarily changed since it is a multiple hops. At this point the existence of a multiple links might bring on a unpredicted bad influences to the protocol performance and the application on the upper layer. Therefore an enhanced routing method resolving this problem should be importantly considered. Fig. 1 depicts an example of arbitrary routing route decision about dynamic nodes. There are a couple of significant results of researches on DSR, AODV, SPAN and GPSR. However, those researches only use a fixed transmission rate not relevant to distances between nodes in the simulations. In a real system, the distance between
Fig. 1. An Example of Temporary Topology
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nodes certainly affects the network such as signal intensity, transmission delay and packet loss by distances. As seen in Fig. 1, even in an optimized network there might be 2 possible node distances having 2 times different ranges according to their node densities. Therefore, such distance different are considered in this research for the realization of better routing.
3 Transmission Characteristic of 802.11b IEEE 802.11b shows different transmission characteristics in accordance with distances of mobile nodes. The transmission rate is possible up to 11Mbps. However, it varies by transmission distances and performances of links. In general, receiving signal intensity is illustrated by RSSI (Received Signal Strength Indication) value. Transmission rate of 1 or 2 Mbps, 5.5Mbps and 11Mbps are ideal at distances of 100m, 60m and 30m, respectively [2]. The relation between distances and transmission rates in IEEE 802.11b is depicted in Fig. 2. Fig. 2 indicates the different error rates as the packet transmission rates at over a certain distance.
Fig. 2. Transmission Rate Evaluation at Different Distances
A high data transmission rate possesses a high throughput, and on the other hand a low data transmission rate enables a long distance data transmission. Hence, the most appropriate transmission rate should be selected at a certain mobile distance as shown in Fig. 3.
Fig. 3. Transmission Rate Changes According as Distances
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4 Fuzzy Logic Control and Max-Min Algorithm In Fuzzy logic theory, a value is represented as a degree of truth similar to be represented in probabilistic theory on the contrary to the conventional logic representing a value with binary logic (0 or 1, black or white, yes or no). Fuzzy logic enables a medium value between 0 and 1. In this paper, a Fuzzy logic controller for data transmission rate decision is constructed using 2 inputs, RSSI values and packet delays in Ad Hoc network. MAX-MIN composition is used as the method for combining input values. MAX-MIN method is shown in (1). R1 $ R 2 ( x , z ) = ∨ ( R1 ( x , y ) ∧ R2 ( y , z )) =
{
y ∈Y
ª ( x , z ), max{min{ µ ( x , y ) R1 «¬ y , µ R 2 ( y , z )}} x ∈ X , y ∈ Y ,∈ z
. (1)
}
5 Simulation A Fuzzy logic control proposed in the simplest method is simulated in this research. The amount of packet transmission with increasing the moving area of mobile nodes is measured between one host node and one other mobile node. The result is compared to the cases using fixed packet transmission rate (2Mbis, 5.5Mbps and 11Mbps). Simulation is conducted with membership functions representing RSSI values and packet delays under the assumption that every node has the same RSSI values. Fig. 4 (a) illustrates the membership function about RSSI value between mobile nodes. A RSSI value is a value derived from calculating internal electric signals of devices so that it is possible for membership functions representing a RSSI value to have different values by different calculating formulas and devices. The membership function for packet delay between mobile nodes is shown in Fig. 4 (b).
Fig. 4. Membership Function for RSSI Value (a) and Packet Delay (b)
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A Fuzzy control logic shown in Table 1 is constructed with those two membership functions. The constructed controller controls transmission rate in three ways of increasing, sustaining and decreasing. Table 1. Logic Table
R S S I
Strong
High Zero
Packet delay Normal Up
Low Up
Fair
Down
Zero
Up
Weak
Down
Down
Zero
Fig. 5. Comparison of Transmission Rate According as Node Distances
The Fig. 5 shows the comparison between the amount of packet transmissions in accordance with increasing moving area of mobile nodes. A transmission rate of 2Mbps is stable throughout the whole region but it shows a relatively insufficient transmission amount to other transmission modes. In the case of 5.5Mbps, the transmission rate decreases through the whole region but it doesn’t show a large difference. This mode can be concluded as stable and not worse in performance considering other modes. The transmission mode of 11Mbps shown an abrupt decrease in transmission rate as it approaches 30m of distance. So it is said to be sensitive to distances. The modes using Fuzzy logic control shows the highest transmission rate in all cases and it has similar decreasing transmission amount with other modes. This shows that the mode controlled by Fuzzy logic is the most efficient and stable mode in all cases.
6 Conclusion In this paper, Fuzzy logic algorithm is used as a dynamic control method for transmission rate according as varying distances between two mobile nodes. The simulation
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shows the proposed Fuzzy logic controller possesses better performances than networks using fixed transmission rates. Expanding the result of this research to apply to a multi hop routing algorithm might enable a more stable and faster network. The result shows only the cases of simple comparison in transmission rates. Considerations about transmission data loss and transmission delay are remained as the further research. In addition, a more specific realization is planned using the proposed method with currently researched multi hop routing algorithm.
References 1. Chen, B., Jamieson, K., Balakrishnan, H., Morris, R.: SPAN: An Energy-Efficient Coordination Algorithm for Topology Maintenance in Ad Hoc Wireless Networks. Wireless Networks 8 (2002) 481-494 2. Andren, C., Webster, M.: CCK Modulation Delivers 11 Mbps for High Rate 802.11 Extension. Proc. Wireless Symposium/Portable by Design Conference (1999) 3. Broch, J., Johnson, D., Maltz, D.: The Dynamic Source Routing Protocol for Mobile Ad Hoc Networks. Internet Draft, IETF Mobile Ad Hoc Networking Working Group (1998) 4. Perkins, C.E., Royer, E.M.: Ad Hoc On-Demand Distance Vector Routing. Proc. 2nd IEEE Workshop on Mobile Computer Systems and Applications (WMCSA’99). (1999) 90–100 5. Williams, J., Hanzo, L., Steele, R.: Channel-Adaptive Modulation. Proc. 6th Internet. Conference Radio Receivers and Associated Systems (1995) 344–147
A Novel Algorithm for Doppler Frequency Rate Estimation of Spaceborne Synthetic Aperture Radar Shiqi Huang, Daizhi Liu, Liang Chen, and Yunfeng Liu Xi’an Research Inst. of Hi-Tech, Hongqing Town, 710025 Xi’an, P.R. China [email protected]
Abstract. Synthetic Aperture Radar (SAR) can obtain high-resolution radar images under all weather, day and night and long distance conditions, and has been applied widely in military and civil fields. Range-Doppler (RD) algorithm is a simple and typical imaging algorithm. The key of it is Doppler parameters estimations, including Doppler centroid frequency and Doppler frequency rate. Doppler frequency rate is variational with range. If the estimation of it is inaccurate, it will bring severe defocusing effect and blurring in azimuth direction. The previous estimations of Doppler frequency rate usually use image field instead of data field, the calculated amount is very large and the imaging speed is slow. In order to improve them, this paper proposes a novel Doppler frequency rate estimation algorithm for spaceborne SAR imaging. The raw data of ERS are used to test effectiveness and feasibility of this method.
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calculation complex, calculated amount great and unusable to real-time imaging. Then others present some algorithms to estimate Doppler frequency rate from raw data, such as reflectivity displacement method [7] and Shift-and-Correlation (SAC) method [8]. However, the two methods are only fit for airborne SAR Doppler frequency rate estimation and can't be used on spaceborne SAR. In real-time imaging, it demands that the algorithm can satisfy some accuracy requirement and less calculated amount. So a novel Doppler frequency rate estimation algorithm, Mean Frequency Shift Correlation (MFSC) method, is presented in this paper. MFSC algorithm directly estimates Doppler frequency rate from echo data and does not image. Therefore, the computational efficiency of it improves, and it is fit for real-time processing. Obviously is it better than traditional MD algorithm. So it has some theory and practical value for studying spaceborne SAR imaging. The algorithm is validated to be feasibility and validity with ERS-2 raw data of ESA.
2 Doppler Frequency Rate The key technique of azimuth compression or azimuth focus is Doppler parameter estimation, namely, Doppler centroid frequency and Doppler frequency rate estimations. The equation of Doppler frequency rate is given by [9]
f DR = − 2V 2 λR0 .
(1)
Where V is the ground track velocity, Ȝ is wavelength, R0 is range from target to spacecraft track. And the R0 is given by
R0 = H 2 + Rg2 = Rnear + n × (c / Fs ) .
(2)
Where H is spacecraft height, Rg is ground range, Rnear is the distance to the first range bin, c is velocity of light, Fs is the sampling frequency of range direction, n is sampling point number, namely, the number of range gate. The changes of fDR are shown in Fig.1.
Fig. 1. The changes of Doppler frequency rate with range
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3 Mean Frequency Shift Correlation Algorithm Jorgen presented Shift and Correlation algorithm in 1991[8]. He uses the correlation characteristics of Doppler signal to estimates Doppler frequency rate f DR , obtaining very much high efficiency. An echo of a point target is
s (t ) = exp[iπf DR (t − t 0 ) 2 ] ; t 0 − T 2 ≤ t ≤ t 0 + T 2 .
(3)
Signal s(t) is divided into two parts which are SL(f) and SU(f) in frequency field and they are the lower half and the upper half of Doppler spectrum, respectively. SAC algorithm refers to relative frequency shift of SL and SU, and then makes correlation. The sketch diagram of principle of SAC algorithm is shown in Fig.2. s(t) has the characteristic of wide-time-bandwidth accumulation, and the corresponding time field signal of SL(f) and SU(f) is sl(t) and su(t), respectively.
°sl (t ) = exp[iπf DR (t − t 0 ) 2 ] t 0 − T / 2 ≤ t ≤ t ; . ® °¯su (t ) = exp[iπf DR (t − t 0 ) 2 ] t 0 ≤ t ≤ t 0 + T / 2
(4)
Then, sl(t) and su(t) make frequency shift processing, SL(f) shifts FRF/4 to upper half of spectrum and SU(f) shifts PRF/4 to lower half of spectrum. The results are
°SL+ ( f ) = SL( f + PRF / 4) . ® + °¯SU ( f ) = SU ( f − PRF / 4) The corresponding time field signal is
(5)
sl + (t ) and su + (t ) .
sl + (t ) = sl(t) exp(i2π ⋅ PRF 4 ⋅ t) = exp[−iπf DR (δ 2) 2 + iπf DRt 0δ ] exp[iπf DR (t − t 0 + δ 2) 2 ] su + (t ) = su(t ) exp(−i2π ⋅ PRF 4 ⋅ t ) = exp[−iπf DR (δ 2) 2 − iπf DRt 0δ ] exp[iπf DR (t − t 0 − δ 2) 2 ]
δ = PRF 2 ⋅ f DR
; t0 −T 2 ≤ t ≤ t0 .
(6)
t0 ≤t ≤t0 +T 2.
(7)
;
sl + (t ) and su + (t ) correlate each other, the correlation peak will appear in position δ , which Fig. 2(e) shows. Assume the position δ of correlation peak and pulse repeat frequency PRF is given, f DR may be gained, as is Where
. If
called shift and correlation method. It is a pity that SAC method is only adapt to airborne SAR and the high contrast grade terrain. If we directly utilize it to image for spaceborne SAR, the result is that none can be obtained, which is shows in Fig.4(a). This article proposes using the geometry of spaceborne SAR, which are V, λ and
R0 , to estimate Doppler frequency rate of every range gate cursorily, then compute is estimated with SAC acts as adjustable value of Doppler frequency rate estimation.
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The basic value plus adjustable value may gain accurate Doppler frequency rate. As is the Mean Frequency Shift Correlation algorithm. The flow chat is displayed in detail in Fig.3.
Fig. 2. Sketch diagrams of Shift and Correlation
MFSC method is an autofocus algorithm that has high computed efficiency and has some similar sections as MD algorithm. In order to obtain Doppler frequency rate errors, MD algorithm makes azimuth correlation with the corresponding images of lower half and upper half of azimuth spectrum. It is autofocus algorithm with image field. Its operation quantity is quite large and needs reiterative operation to form an image. Therefore, it is not fit for real-time imaging processing. However, MFSC doesn’t need reiterative operation, which may reduce operation quantity greatly. And it may reach good accuracy for Doppler frequency rate estimation and not only be fit for real-time imaging processing but also agrees with all kinds of terrain.
Fig. 3. Flow chart for MFSC algorithm
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4 Experimental Results and Performance Comparisons
㧘
In order to prove efficiency and correctness of MFSC algorithm we utilize real measured data to image with MFSC algorithm. The experimental results are shown in Fig.4(c)-4(f), note that these images are cut out. These data comes from ERS-2, and some parameters as follows: V is 7040 m/s, is 5.7cm, n is from 0 to 5615, c is 3E8m/s, Fs is 18.96MHz, and Rnear is 838000m. The Fig.4 (a) explains that SAC algorithm can’t image for spaceborne SAR. No focus processing also can’t obtain legible image that is shown in Fig.4 (b), in other words, the Doppler frequency rate is estimated with
¬
f DR = −
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Whereas, MFSC algorithm can image to all kinds of terrains for spaceborne SAR, which are shown in Fig.4(c)-(f). Table.1 is the performance compare of several algorithms including MFSC algorithm, MD algorithm, time-frequency analysis algorithm and image contrast algorithm.
(a) SAC algorithm image
(b) No focus image
(d) Mountain image
(e) Ocean image
(c) Countryside image
(f) Urban image
Fig. 4. Experiment results of real test data. (a) directly using SAC algorithm for spaceborne SAR imaging, (b) no focus, (c)-(f) the image of countryside area, mountain area, ocean area and urban area with MFSC algorithm, respectively.
We may know from it that MD algorithm, time-frequency algorithm and image contrast are all work in image field, so their real-time feature is bad and their account scalar is large. The terrain adaptability of MD algorithm and image contrast is bad and they demand strong contrast terrain. MFSC algorithm and rime-frequency algorithm have good terrain adaptability, but the work filed of MFSC algorithm is data filed, so it has good real-time feature and less account scalar.
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Table 1. Performance compare of several algorithms
MD MFSC Time frequency analysis Image contrast
Image or data field image field
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5 Conclusions The processed object of Doppler frequency rate estimation method was images instead of data ago. In general, they need repeating replace operation, so their account scalar is large, account course is complex and real-time is very bad. MFSC algorithm directly estimates Doppler frequency rate with echo data, without repeating replace operation, which reduces a lot of account scalar and imaging time, and its adaptability for terrain is wide. Experiment proves that it is right and effective. This has some theory and practice reference value for next studying the imaging and application of spaceborne SAR.
References 1. Li F. K., Held D. N., Curlander J., Wu C.: Doppler Parameter Estimation for Spaceborne Synthetic Aperture Radars. IEEE Transactions on Geosciences and Remote Sensing, 23(1) (1985) 47-56 2. Blacknell D., White R. G., Wood J. W.: The Prediction of Geometric Distortions in Airborne SAR Imagery from Autofocus Measurements. IEEE Transactions on Geosciences and Remote Sensing, 25(6) (1987) 775-781 3. Terry M.C.: Subaperture Autofocus for Synthetic Aperture Radar. IEEE Trans. AES, 30(2) (1994) 615-621 4. Liu Y.T., et al: Radar Imaging Technique. Ha’erbin Industry University publishing house, Ha’erbin, China (2001) 5. Curlander J. C., Wu C., Pang A.: Automatic preprocessing of spaceborne SAR data. ICASS'02, (1982) 31-36 6. Cheng Y. P.: Study of Several Problems in SAR Imaging, Xidian University Doctor Degree Paper, Xi’an, China (2000) 7. Moreira J.: A New Method of Aircraft Motion Error Extraction from Radar Raw Data for Real Time Motion Compensation. IEEE Trans. GRS, 28(7) (1990) 620-626 8. Dall J.: A New Frequency Domain Sutofocus Algorithm for SAR. Proceeding of IGARSS'91, Helsinki: June, (1991) 1069-1072 9. Curlander, McDonough: Synthetic Aperture Radar, Systems & Signal Processing, Chapter 4, John Wiley & Sons, New York (1991)
A Novel Genetic Algorithm to Optimize QoS Multicast Routing Guangbin Bao, Zhanting Yuan, Qiuyu Zhang, and Xuhui Chen College of Computer and Communication, Lanzhou University of Technology, 730050 Lanzhou, P.R. China {baogb, yuanzt, zhangqy, xhchen}@lut.cn
Abstract. Multicast routing service is becoming a key requirement of computer networks supporting multimedia applications. And multicast routing problem has been demonstrated technically as a NP-complete. This paper proposes a novel QoS-based multicast routing algorithm using the genetic algorithms (GA), which has the following characteristics: the preprocessing mechanism, the tree structure coding method, novel heuristic algorithms for creation of random individuals crossover, and the instructional mutation process. The result of simulation shows that the proposed GA-based algorithm has the advantage over the conventional algorithms in efficiency.
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The paper is arranged as follows. Section 2 describes the network model and definition in QoS multicast routing problem formally. Section 3 presents a genetic algorithm for the QoS multicast routing problem. Section 4 evaluates the performance of the proposed algorithm. And section 5 is the conclusions of this paper.
2 Network Model and Problem Definition 2.1 Network Model The problem considered here is how communication paths are generated through a packet-switched network for multicast traffic. As far as multicast routing is concerned, a network [3] is usually represented as a directed graph G=(V, E), consisting of a set of switches, V, and a set of directed links, E. Let the link from node i to node j be denoted by e (i, j). Each link e ∈ E is associated with a cost C(e) and several QoS parameters, such as a delay, loss probability, and jitter. The cost function, C(e) is a positive real function, i.e., C:E → R+. The cost function reflects the amount of resources required to support the quality of service provided by the link [4]. The QoS supported on a link is described by QoS functions. Each QoS function, Qi(e), is a positive real function which gives the quality of the parameter that can be guaranteed on the link e. For a multicast connection, packets originating at the source node s ∈ V, have to be delivered to a set of destination nodes M ⊆ V - s. We refer to M as the destination group, and s M the multicast group. Multicast packets are routed from the source to the destinations via the links of a multicast tree T=(VT, ET). A multicast tree is a subgraph of G spanning S and the nodes in M. In addition, V may contain relay nodes, that is, nodes in the multicast tree but not members of the multicast group. 2.2 QoS Metrics The QoS guarantee for a multicast connection is defined as follows. Let q1, …, qn be the n QoS functions and Q1, …, Qn be the corresponding QoS constraints that need to be satisfied. A multicast tree is said to be able to provide the required QoS guarantee if the end-to-end QoS of each source-destination pair of the multicast connection is satisfied. In this thesis, we only consider QoS parameters that are additive, i.e., the end-to-end QoS of a path is the sum of individual QoS of each link on the path. QoS parameters such as a delay and jitter are additive in nature. The end-to-end loss probability of a path can be approximated by the sum of loss probabilities of all links of the path if the link loss probability is very small. Formally, for each v ∈ M, the end to end QoS is guaranteed by
¦
qi (e) ≤ Qi, ∀v ∈ M , i = 1, 2,..., n
e∈P ( s ,v )
Where P(s, v) is the path in T from s to v.
(1)
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The multiple-constraint multicast routing problem is defined as follows
min ¦ C (e) S .t e∈T
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e∈P ( s , v )
(2)
Two important QoS metrics are considered in this dissertation [5]: 1. Source-destination delay ( ∆ ): The parameter ∆ represents an upper bound on the acceptable end-to-end delay along any path from the source to the destination nodes. This parameter reflects the fact that the packet delivered ∆ time units after its transmission at the source is of no value to the receivers. 2. Inter destination delay variation ( δ ): is the parameter that represents the maximum difference between end-to-end delays along the paths from source to any two destination nodes that can be tolerated by the application. In essence, this parameter defines a synchronization window for the various receivers. By supplying values for parameters ∆ , δ , the application in effect imposes a set of constraints on the paths of the multicast tree. Given the delay ∆ and delay variation δ tolerances, our objective then is to determine a multicast tree such that the delays along all source-destination paths are within the two tolerances. Or mathematically can be stated as: Given a network G=(v, A), a source node s ∈ V, a multicast group M ⊆ V - s, a link-delay function D:A → R+, a delay ∆ and delay variations δ , is there a tree T=(vt, AT) spanning s nodes in M, such that
¦
D(l ) ≤ ∆, ∀v ∈ M
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l∈PT ( s , v )
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Where Eq. 3 is the source-destination constraint, and Eq. 4 is the inter-destination delay constraint. A tree T is feasible if and only if T satisfies both Eq. 3 and Eq. 4.
3 Algorithm Description 3.1 Construction of Routing Table In the network graph, G=(V, E), there are |V|(|V|-1) possible source-destination pairs. There are usually many possible routes between any source-destination pair. Our algorithm assumes that a routing table, consisting of R possible routes, has been constructed for each source-destination pair using the k-shortest path algorithm [6]. The size of the routing table, R, is the parameter of our algorithm. 3.2 Generating the Initial Population For a given source node s and a destination set M={m1, m2, …, mk}, a chromosome can be represented by a string of integers with length k. A gene, gi , 1 ≤ I, … ≤ k, of the
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chromosome is a integer in {1,2, ,r} which represents a possible route between s and mi, where mi ∈ M [7]. Obviously, a chromosome represents a candidate solution for the multicast routing problem since it guarantees a path between the source node to any of the destination nodes. However a chromosome does not necessarily represent a tree. Therefore, we trim the extra edges using a minimum directed spanning tree algorithm, modified form the optimum branching algorithm proposed in [7]. 3.3 Generating the New Population Select two chromosomes from the population of the current generation of which is the best chromosomes (parent 1) and the other a randomly selected chromosomes (parent 2). Make a crossover operation between the two chromosomes producing two new genomes (child 1 and child 2). Make a mutation operation to both of the children Perform a selection to obtain the new generation. 3.4 Crossover Operation Crossover operation generates two children from parents. The children inherit genes randomly from the parents. Whether the crossover is made at all is determined [8] by the parameter pc(usually in the interval [0.5,1.0] ). If pc=1.0, crossover is always made. If pc ≤ 1.0, crossover is made with probability pc. If the crossover operation is not made to the parents, the genes are copied to the children unchanged. If crossover is made to the parents, then in this algorithm the (method of two points) is used in which two randomly selected genes the starting point and the ending point are determined for parent 2. Then, the genes between these points are exchanged between the parents. 3.5 Mutation Operation When the children chromosomes have been created both of them undergo mutation operations. The number of the operations nop is determined by the parameter pm (usually in the interval [0.01,0.2]) and is calculated as follows
nop = ( p )( pm)
(5)
Where nop is the number of mutations, p is the length of chromosome, and pm is a user-defined parameter, in the interval [0.01,0.2]. The mutation operations are performed by selecting nop random genes of the chromosome and replacing the value of the selected gene by a random i integer from the feasible interval of the corresponding integer variable. 3.6 Steps of the Algorithm The algorithm is outlined in the following steps: Step 1: Initialize a population of chromosomes. The algorithm first generates P different chromosomes at random, which form the first generation. The set of chromosomes is called the chromosomes pool (or population), and P is the size of the gene pool.
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Step 2: evaluate each chromosome in the chromosome pool [9-10]. The fitness value of a chromosome is the value of the fitness function for the solution (e.g., a multicast tree) represented by the chromosome. Given a chromosome pool H={h1, h2, …, hp}, the fitness value of each chromosome is computed as follows. Let C(hi) be the overall line the costs of all links of the network, and Qi be QoS constraints( ∆ , δ ). The fitness value of the chromosome hi, F (hi), is given by
C (hi ) , if ¦ qi (e) ≤ Qi∀v ∈ M , i = 1, 2,..., n °1 − fhi = ® C ( E ) e∈P ( s ,v ) ° 0, Otherwise ¯
(6)
Where P(s, v) is the path from source s to destination v, derived from chromosome hi. After evaluating the fitness values of all chromosomes, chromosomes are then sorted according to their fitness values such that F(h1) ≥ F(h2) ≥ … ≥ F(hp). That is the first chromosome in the pool and is the best solution found so far. Step 3: If the number of generations is larger than the pre-defined maximum number of attritions, MaxGen(Maximum number of generations), then stop and output the best chromosome (solution), otherwise, go to step 4. Step 4: Discard duplicated chromosomes. There might be duplicated chromosomes in the pool. Apply some of the genetic operations [11], e.g. crossover, on two duplicate chromosomes will yield the same offspring. Therefore, too many redundant chromosomes will reduce the ability of searching. Once this situation occurs, the redundant chromosomes must be discarded. New randomly generated chromosomes replace them. Step 5: Generate next generation of chromosomes by applying generic operations: reproduction, crossover, and mutation. Step 6: Stop when the number of generations reaches the maximum of generation, MaxGen, or when no further improvement is observed on the fitness function.
4 Performance Evaluation To evaluate the proposed algorithm, we compared its performance with conventional algorithm using computer simulations. 4.1 Simulation Conditions For the simulations, we make the following assumptions: • • • •
The number of nodes is 60. The delay of each link varies from 0 to 50 ms. The cost of each link varies from 0 to 200. When the number of nodes is 60, the number of destination nodes is 20. The Destination Cost Constraint Function is considered 3000 and the Destination Delay Constraint Function varies from 90 to 240 [12]. • The number of generations is limited to 30. • Test the computation time and success ratio.
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4.2 Simulation Results and Considerations The characteristic of search success ratio versus delay constraint for 60 nodes is shown in Fig. 1.
Fig. 1. Success ratio of algorithm
The proposed algorithm has the higher search success ratios than the conventional algorithm. In this figure, when the delay constraint is small, the search success ratio of both algorithms is almost 0. This is because the route that satisfies the required delay does not exist. While, when the delay constraint is large, the search success ratio of both algorithms increases [13]. This is because many routes that satisfy the required delay exist. However, the proposed algorithm has higher search ratio compared with conventional algorithm.
Fig. 2. Computation time of algorithm
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The characteristic of computation time versus delay constraint for 60 nodes is shown in Fig. 2. From the figure, it is clearly that the computation time of proposed algorithm is lower than computation time of the conventional algorithm [14]. The computation time for the minimum path is decreased. This is why the computation time of proposed algorithm is smaller than the conventional algorithm.
5 Conclusions In this paper, we study the QoS multicast routing problem which is known to be NP-complete, and proposed a genetic algorithm for the problem. From the simulation results, we conclude that our proposed algorithm has better search success ratio and computation time compared with the conventional algorithm. By modifying the fitness function, the proposed genetic algorithm can also be applied to other multicast problems. In the future, we plan to apply the proposed genetic algorithm to the multilevel hierarchical routing, and study the ways of implementing such genetic algorithm efficiently for various network conditions.
Acknowledgments This research is supported by Natural Science foundation of GANSU province (grant NO. ZS022-A25-027 and 3ZS042-B25-002).
References 1. Wang, Z., Crowcroft, J.: Quality of Service for Supporting Multimedia Applications, in IEEE Journal on Selected Areas in Communications 14 (7) (1996) 1228-1234 2. Zhengying, S. Bingxin, Z. Erdun: Bandwidth-delay-constrained Least-cost Multicast Routing Based on Heuristic Genetic Algorithm, in Computer Communications, 2001(Vol.24) 685-692 3. Kawano, K., Masuda, T., Kinoshita, K., Murakami, K.: An Efficient Method to Search for the Location of Network Services with Multiple QoS Guarantee, in Transaction of IEICE, Vol.J84-B, 2001(No.3) 443-451 4. Rouskas, G.N., Baldine, I.: Multicast Routing with End-to-end Delay and Delay Variation Constraints, in IEEE Journal on Selected Areas in Communications 15 (3) (1997) 346-356 5. Sriram, R., Manimaran,G., Murthy, S.R.: Algorithms for Delay Constrained Low-cost Multicast Tree Construction, in Computer Communications 21 (18) (1998) 1693-1706 6. Koyama, A., Barolli, L., Matsumoto, K., Apduhan, B. O.: GA-based Multi-purpose Optimization Algorithm for QoS Routing, in Proc. of AINA, Vol.1, (2004) 23-28 7. Palmer, C. C., Kershenbaum, A.: Two Algorithms for Finding Optimal Communication Spanning Trees, in Technical Report, IBM T. J. Watson Research Center, Yorktown Height, NY, (1993) 8. Handan, M., El-Hawary, M.: Genetic Algorithm for Multicast Routing with Delay and Delay Variation Constraints, in Accepted for Publication, CCECE, May (2004) 9. Barolli, L., Koyama, A., Motegi, S., Yokoyama, S.: Performance Evaluation of a Genetic Algorithm based on Routing Method for High-speed Networks, in Transaction IEE, Vol.119-C, No.5, (1999) 624-631
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10. Roch A. Guerin, Ariel Orda: QoS Routing in Networks with Inaccurate Information: Theory and Algorithms, in IEEWACM Trunsuctions, vol. 7, no. 3, (1999) 350-364 11. Sherif, M. R., Habib, I. W., Nagshineh, M., Kermani, P.: A Generic Bandwidth Allocation Scheme for Multimedia Substreams, in Adaptive Networks Using Genetic Algorithms, IEEE ( 1999) 1243-1247 12. Gelenbe, E. et al., Cognitive Packet Networks: QoS and performance, Keynote Paper, in IEEE MASCOTS Conference, San Antonio, TX, October, (2002) 14-16 13. Gelenbe, E., Liu, P., Lain, J._e.: Genetic Algorithms for Route Discovery, in SPECTS’03, Summer Simulation Multiconference, Society for Computer Simulation, Montreal, July, (2003) 20-24 14. Goto, T. Hasegawa, H. Takagi, Y. Takahashi (Eds.): Performance and QoS of Next Generation Networking, Springer, London, (2001) 3-17
A Probe for the Performance of Low-Rate Wireless Personal Area Networks Shuqin Ren, Khin Mi Mi Aung, and Jong Sou Park Computer Engineering Dept., Hankuk Aviation University, Koyang City, South Korea {sqren, maung, jspark}@hau.ac.kr
Abstract. Low-rate wireless personal area networks (LR-WPANs) are characterized by low power consumption, low cost, low computation and low rate, which are based on IEEE 802.15.4 and ZigBee standards. In this article, we first give an overview of the network structure, including its architecture, feasibility and functions. We also analyze several application scenarios with NS-2 simulator, and get some experiment results. For a better view of this kind of network, a preliminary performance evaluation is given according to the results, focusing on the beacon-enabled mode for star-topology and treetopology networks. Our performance evaluation study is to reveals the factors which affect network performance such as association, collision, packet delivery ratio and throughput under different superframe structures and traffic types.
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The paper is organized as following. The architecture of LR-WPANs is discussed in section 2; in section 3, the performance evaluation process is proposed and the experiment results about the performance are given; and section 4 gives a conclusion.
2 Architecture of LR-WPANs 2.1 Structure of LR-WPANs The LR-WPAN architecture is built as the following model: physical layer (PHY), medium access control (MAC) sublayer, service specific convergence sublayer (SSCS), IEEE802.2 Logical Link control (LLC), routing and upper layer. A LRWPAN has such features as: 1)27 channels with three data rates: 1 channel with the rate of 20kb/s in 868MHz band, 10 channels with the rate of 40kb/s in 915MHz band, 11 channels with the rate of 250kb/s in 2.4GHz band; 2) Supporting both star and peer-to-peer connections; 3) Three data transmission types (direct, indirect and guaranteed time slot (GTS)); 4) 16 bit short or 64 bit extended addresses; 5) Carrier sense multiple access with collision avoidance (CSMA-CA) channel access. 2.2 Topologies of LR-WPANs There are two types of components in a LR-WPAN: a full-function device (FFD) and a reduced-function device (RFD). A FFD can communicate with RFDs or other FFDs, while an RFD can only talk to an FFD. A FFD can operate in three modes serving as a network coordinator (PAN Coor), a coordinator, or a device. An RFD just can serve as a device. There are two types of topologies in LR-WPANs: star and peer-to-peer connections. In the former type, there is only one central controller called the PAN Coor that is in charge of the routing communication around the networks, and other devices need establish connections with this PAN Coor; in the latter, any two FFD devices in the transmission range can communicate each other, but the RFD may only communicate with one FFD device at a time. There is also a PAN Coor not only for routing but for managing network. Combining these two topologies, there is also another topology called as cluster tree, in which the PAN Coor is also the first cluster head (CH0), and some FFD devices serve as other cluster head to extend the scale of the network. 2.3 Data Transfer Models in LR-WPANs There are two kinds of communication models in LR-WPANs: beacon-enabled mode and non beacon enabled mode. We can optionally use the superframe for beaconenabled mode. And in the non beacon-enabled mode, we just use CSMA/CA for accessing channel and then send data; and polling mechanism is used by device to check whether there is data from coordinator. The superframe format (Fig.1) is defined by coordinator and it comprises an active part and an optional inactive part, and is bounded by beacons. The active part is
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consisted of beacon, Contention Access Period (CAP) and Contention Free Period (CFP). The CAP is used by devices for accessing channel, applying for GTS, and sending/receiving data through CSMA/CA backoff algorithm. The CFP is optional and may accommodate up to seven guaranteed time slots (GTS). And the CFP is used for transferring data by using GTS.
Fig. 1. Examples of the superframe structure
3 Performance Evaluation About LR-WPANs 3.1 Experiment Environment There are four frame types: beacon, command, acknowledgment, and data frames in LR-WPANs. In this section we will analyze the performance of the LR_WPAN under different traffic and different superframes. We evaluated the LR-WPANs’ performance by running some simulation experiments using NS2. In this simulator, there are 14 PHY primitives for 802.15.4 PHY; 35 MAC primitives for 802.15.4 MAC; Service Specific Convergence Sublayer (SSCS) is an interface to access MAC primitives. We used some functions provided by SSCS to do some experiments. The process to build a sensor network in NS-2 is: setting some network parameters as traffic type, the maximum distance to send and receive in a single hop; setting the topography and channel; configuring the nodes in the network by assigning the Link Layer, MAC protocol, antenna, radio propagation and so on; setting up the traffic between nodes; and starting the simulation and stopping it after some time. 3.2 Performance Metrics A LR-WPAN can work in beacon-enabled mode or non-beacon enabled mode. The beacon-enabled mode in the IEEE 802.15.4 makes applications to save more power, and to extend the life of the network. And the performance of the beacon-enabled mode is affected by beacon order (BO) and superframe order (SO). Here we will discuss the network performance as following measurements. 1) Association efficiency: The average number of attempts per successful association. Successful association rate: The ratio of devices successfully associated with a coordinator to the total number of association request.
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2) Packet delivery ratio: The ratio of packet received to packets sent in MAC sublayer. 3) Throughput: the ratio of the packets received to the time receiving these packets. 3.3 Experiment Results We did 2 experiments to evaluate the star and tree topography network performance respectively. Fig. 2 gives the scenario of the tree example. The performance is evaluated based on the trace file. In our experiments, we set the same value for BO and SO from 0 to 7. This scenario consists of 13 nodes, with 1 PAN Coor, 7 FFD, and 5 RFD. The number above every node is the parent node id. And we compared the performance using FTP, CBR or Poisson traffic, which are the normal data packet types. In our future studying, we will discuss the traffic with attacking data packets.
Fig. 2. Experiment scenarios
Successful Association Rate and Collision Rate To associate with coordinator, the device can scan channel executing actively or passively. Here we just used the active channel scan in which a beacon request is sent to locate a coordinator. If there has been a coordinator, the device will send association request; after receiving the ACK, the device will send a data request; if the ACK and the association response from coordinator are received respectively, the association is built successfully. We tested the association efficiency under different BO (0~7) with the same value as SO given different traffic (Fig.3a). For the BO with more than2, no failure for building association. Yet only the association efficiency is not enough to represent the network performance. We also examined the relationship of collision rate and the BO (Fig. 3b). For the smaller BO, more collisions happened, about 75% of collision happened for BO=0. The collision of BO with 2 is also higher, from BO with 3, the collision began decreases.
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From the definitions of BI and SD(BI= 2 B O × α B aseS up erfram eD uration , SD= 2 SO × α BaseSuperframeDuration ), larger BO means larger beacon interval, so the coordinator reacts slowly; and the lower BO means higher collision probability because of the higher frequency of beacons, and these collision may bring down the association ratio. Also the CSMA-CA algorithm requires a transaction which should be finished before the end of CAP, or else the transaction should be delayed until the beginning of next frame. So at the beginning of a superframe, more collisions will happen for smaller beacon order because of short time for CAP. 80
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Fig. 3. (a) Successful association efficiency with different beacon order and different traffic; (b) Collision Ratio under different beacon order for the ftp traffic; (c) Packet delivery ratio under different beacon order for the ftp and cbr traffic; (d) Throughput under different beacon order for the ftp m
R p acketR to S =
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Packet Delivery Ratio and Throughput We used packet delivery ratio and throughout to measure the data transmission performance. In our experiments, we measured the effective packet delivery ratio as the number of data packets receiving at the device divided by the number of data packets originally sent as Equation 1, where m is the number of devices that received data packets whose destination address is the node address, and n is the number of devices that sent data packets originally. The throughout is the bit size of the data packets in unit time (Equation 2).These performances are also affected by the BO and SO for beacon-enabled mode (Fig. 3c and Fig. 3d). The packet delivery ratio is higher in BO with 2, 3, and 4 with 100%, 90% and 100% respectively. And the highest throughput is at the BO with 2, then 4 and 3. So selecting the suitable BO that should be neither too small nor too large is very important for the trade-off between these performance metrics. And also different traffic leads to different packet delivery ratio. The experiment results showed us that packet delivery ratio is higher for ftp traffic by BO with 0 and 2, cbr traffic has higher packet delivery ratio with other BO value.
4
Conclusion
Based on the description of the IEEE 802.15.4 standard and the relevant performance evaluation experiments, we find that for a better performance, the suitable combination of SO and BO is necessary given specific traffic. And selecting an optimized solution based on simulation is economic and useful for designing a sensor network application. Our ongoing works are implementing and analyzing the orphaning recovery performance of LR-WPANs with a simple and feasible recovery algorithm. We will analyze the work patterns of the LR-WPAN under attacks with real test bed.
Acknowledgements This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment).
References 1. Callaway, E., et Al.: Home Networking with IEEE 802.15.4: A Developing Standard for Low-Rate Wireless Personal Area Networks”, IEEE Communications Magazine, (2002) 69-77 2. Howitt, D., Gutierrez,J.A.: IEEE 802.15.4 Low Rate - Wireless Personal Area Network Coexistence Issues, Wireless Communications and Networking, (2003) 1481-1486 3. Lu, G. et al..: Performance Evaluation of the IEEE 802.15.4 MAC for Low-rate Low-power Wireless Networks, IEEE International Conference on Performance, Computing, and Communications (IPCCC), (2004)701-706
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4. Institute of Electrical and Electronics Engineers, Inc., IEEE Std. 802.15.4-2003, IEEE standard for information technology - telecommunications and information exchange between systems - local and metropolitan area networks specific requirements part 15.4: wireless medium access control (MAC) and physical layer (PHY) specifications for low-rate wireless personal area networks (LR-WPANs). IEEE Press, New York, (2003) 5. Jianliang, Zheng., Myung J. Lee.: A Comprehensive Performance Study of IEEE 802.15.4, IEEE Press Book, http://ees2cy.engr.ccny.cuny.edu/zheng/pub/.(2004) 6. Kinney, P., ZigBee.: Technology: Wireless Control that Simply Works, White Paper dated 2 October (2003) 7. William, M. Bulkeley.: Wireless’s New Hookup, The Wall Street Journal, Feb.,B1(2005)
AG-NC: An Automatic Generation Technique of Network Components for Dynamic Network Management* Eun Hee Kim1, Myung Jin Lee2, and Keun Ho Ryu1,** 1
Database and Bioinformatics Laboratory, Chungbuk National University, Korea {ehkim, khryu}@dblab.chungbuk.ac.kr 2 Research and Development Center, GALIM Information Technology, Korea [email protected]
Abstract. In this paper, we propose an automatic generation method of network components for active network management based on SNMP. At most the components in the network have been managed manually. It wastes time and cost for network management program development. Thus, we propose an active program generator, which is called AG-NC, in order to solve these disadvantages. AG-NC consists of NE Basic Info Handler, MIB Handler, Template Handler, and Operation Handler. This can generate a network management program automatically using information that was provided along with SNMP library. Therefore, we can make the network structure expansion because the development time and cost of the network management program can be reduced dramatically through AG-NC.
1 Introduction Due to internet development with spread of the Web, most information systems are constructed based on the network environment connected with various network devices. The Network management has become important because the network structure is complex and growing fast. However, it requires the information of network components such as node, interface, and service rather than the simple status of the network. In addition, we need a standard network management scheme to manage network in a common way for the different network devices. IETF (Internet Engineering Task Force) made SNMP (Simple Network Management Protocol) [1] as standardization for easy internet management. It has been broadly used for most internet managements until now. Its advantages were easiness of implementation and interoperability. Therefore, it exposed many limitations in network management and operation in the SNMP-based network management as high-speed telecommunication network appeared. *
In this paper, we propose an active program generator, which is called the AG-NC (Automatic Generation of Network Component) in order to automate the generation of information for network management. The proposed AG-NC can generate a network management program automatically using information that has been provided along with the network equipments and SNMP library. Thus, we will make the network structure expansion by reducing the development time and cost of the network management program dramatically through AG-NC. This paper is organized as the following. In Section 2, we briefly review related works and describe their weaknesses. We introduce a framework of AG-NC in Section 3. We describe the result of analysis of experiment through AG-NC in Section 4, followed by the conclusion which summarizes our contributions and discusses future work in Section 5.
2 Related Work SNMP has many advantages like easy implementation and a simple structure. However, the high-speed telecommunication network enlarges volume of network and makes structure of network complex. Especially, network management application development is more difficult. The network management application should orchestrate network components automatically. In order to complement, the disadvantages of the SNMP-based network management system many researchers have applied XML as a scheme to transfer and process large amount of data generated from a broad network [2], [3] effectively. These researches are to express managed information using XML and transfer these XML documents by HTTP [3], [4]. Moreover, when data is stored in database or processed by user application, it uses XML standardization [5]. Web based structure accelerated lots of new application program by providing various kinds of data which was distributed in the internet and platform-independent easily. Therefore, there is a number of research integrating existing different managed protocols and tools by applying web techniques into the network management or system management [6], [7], [8], [9]. However, the researches do not concentrate on management as they are SNMP agent, and depend on manual work in order to develop a network management program. Therefore, it requires expensive cost and time for developing a network management program. Also, a network manager spends a lot of time on modifying errors. Moreover, commercial network management systems such as What'sUPGold [10] and VisualRoute[11] generates network management program manually. This paper focuses on how to solve the problems that increase the cost and time in development of network management applications. Whenever changes happen in the network the network manager must modify or create a new management application to manage network components. We need a tool to generate management program automatically for the newly added network components [12].
3 AG-NC Framework AG-NC framework is used as a supporting tool for network management system. Network management program generated from the framework is used to operate and
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manage network by integrating with SNMP manager. Network managers and network program developers input managed object which will be newly added to the network using user interface. AG-NC framework generates network management program and sends it to network management system. The network management system can monitor the network elements which are newly added or changed.
Fig. 1. AG-NC framework
Fig. 1 shows proposed AG-NC framework. In order to generate network management program automatically, AG-NC consists of NE Basic Info Handler, MIB Handler, Template Handler, and Operation Handler. The functions of these components in AG-NC are described in detail in the next section. 3.1 The Function of These Components A. NE Basic Info Handler This component takes charge of storing and creating basic information of network management objects that will manage as network application. In order to create basic information, we need some information. First, a class name of new network management program and program name of network management objects. Second, a file name of MIB that network manager uses to specify network management objects. Third, object name for the specific network management object. Fourth, acceptance or rejection of method for set operation of SNMP. Finally, acceptance or rejection of method switching over from a specific numeric data contained in MIB to character data. We will generate a network management program based on this information. B. Operation Handler Operation handler manages operations for SNMP execution. SNMP protocol has four kinds of operation such as Get, Get Next, Set, and Trap. Get operation reads management information such as status and run-time of network management object. Get Next operation takes lower layer information from the hierarchical tree structure. Set operation has the control of handling MIB of the network management object. Trap operation is threshold or event which is reported to the manager.
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C. MIB Handler MIB handler takes charge of building MIB information tree to generate network management application. MIB information tree makes a hierarchy of MIB objects. MIB handler extracts identification values of MIB objects which is a target for the network management application from MIB information tree, and builds a tree after parsing the content of MIB file. The MIB objects are managed and classified by single and entry objects single object means that MIB object attribute corresponds to one attribute value in MIB information tree. The MIB information tree creates a process of two steps. The first step is MIB file reading process. In this step, MIB handler reads MIB files corresponding to more than one MIB file names selected in the basic data selection step (NE Basic Handler). After reading MIB file, we generate MIB file information tree from the read MIB file (MIB file information tree is generated from the read MIB file). In order to generate MIB information tree, we use default MIB file and user-added MIB file. D. Template Handler Template Handler supports formal information such as template header and template tail, which are commonly used in generated network management application. In the template header, name of network management application and necessary application variables are defined. In the template tail, source code that configures method for debugging is defined. In the next section, we will analyze the performance of the framework by applying the generated network management application to an actual network management system.
4 Experiments and Analysis In this section, we evaluate the efficiency of the generated application through our framework. Efficiency of application is how exactly the information is obtained from various kinds of network components. Table 1. Example of Network components Node type
Node IP
Node Name
Router
211.196.xxx.127
ROUTER
Windows Server
211.196.xxx.133
KT-9Z25FJCHPIZ8
Therefore we would compare the network management program which is created manually with which is generated automatically in the same network environment and for the same network managing component. We would analyze the reliability of proposed AG-NC through the test about how exactly to manage network status of network management components. In order to verify the generated network management program through our framework, we get information from two kinds of network components as shown in Table 1.
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4.1 Analysis Result We obtain the result that the collected information from Router and Windows Server components using the generated network management program through AG-NC has no errors. Also, we can reduce consuming cost for maintenance and management of network management system. Fig. 2 shows the monitoring results of input/output traffics of Router connecting to the network using generated network program through AG-NC.
Fig. 2. Result of Router using generated network program through AG-NC
Fig. 3 shows the monitoring results of input/output traffics of Windows server connecting to the network using generated network program through AG-NC.
Fig. 3. Result of Windows Server using generated network program through AG-NC
We observe that regular operations don’t have errors in the execution of generated network management program through AG-NC when applied in the real world application (i.e. another kinds of network components such as Linux server, switch and so on). We can ensure how our application causes no errors and has high efficiency.
5 Conclusion The existing SNMP based network management system created the network management program manually for managed objects, when adding new network
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device or network components to the network. Generating network management program manually depreciates maintainability and efficiency of a network management system when network volume is enlarged or organization gets diverse. Therefore, in this paper we proposed a framework for automatic generation of network management program. We called it as AG-NC (Automatic Generation of Network Components). The proposed AG-NC consists of NE Basic Info Handler, MIB Handler, Template Handler, and Operation Handler. It can create an automatic network management program that accomplishes network management with SNMP manager using information of network components. Generated results via our framework can be easily extensible and available for network management. It can develop and maintain the network management program. Moreover, we show capability to reduce time and cost for maintaining network with evaluation of time consumed and error rate in the generation of network management program by applying in an actual network management system. The network management system generates network management program through our framework in this experiment.
References 1. Stallings, W.: SNMP, SNMPv2, SNMPv3, and RMON 1 and 2. 3rd edn, Addison-Wesley, Reading, MA, USA (1999) 2. Ju, H.T., Han, S.H., Oh, Y.J., Yoon, J.H., Lee, H.J., Hong, J.W.: An Embedded Web Server Architecture for XML-Based Network Management. the IEEE/IFIP Network Operations and Management Symposium, Florence, Italy (2002) 5-18 3. Kim, Y.D., Cho, K.Y., Heo, J.H., Cheon, J.K., Cho, S.H.: Network 0anagement System by Using Transfer SNMP. Proc. of KNOM Conference, Taejeonn, May (2001) 102-106 4. Barillaud, F., Deri, L., Fedirum, M.: Network Management Using Internet Technologies. Proc. IEEE/IFIP International Symp. On Integrated Network Management, San Diego CA (1997) 5. Deri, L.: HTTP-Based SNMP and CMIP Network Management. Internet Draft, IBM Zurich Research Laboratory (1996) 6. Pell, H.A., Mellquist, P. E.: Web-Based System and Network Management. Internet Draft, Hewlett-Packard (1996) 7. WBEM : http://wbem.freerange.com 8. Perkins, D., McGinnis, E.: Understanding SNMP MIBs, Prentice-Hall (1997) 9. Case,J.(et al): Management Information Base for Version 2 of the Simple Network Management Protocol (SNMPv2). IETF, RFC1907 (1996) 10. WhatsUp Gold: http://www.ipswitch.com 11. VisualRoute: http://www.visualroute.com 12. Lee. M. J.: A Network Management System Based on Active Program Generation. Ph.D. Thesis, Chungbuk National University, Korea (2005)
Clustering Algorithm in Wireless Sensor Networks Using Transmit Power Control and Soft Computing Kyung-Bae Chang, Young-Bae Kong, and Gwi-Tae Park ISRL, College of Science, Korea University. Anam-dong 5-ga Seongbuk-gu, Seoul, Korea {lslove, ybkong, gtpark}@korea.ac.kr
Abstract. Minimizing power consumption of node is important in wireless sensor networks. Transmit power control and clustering can reduce the energy consumption efficiently when nodes are non-homogeneously dispersed in space. This paper presents the clustering algorithm in wireless sensor networks. The clustering algorithm is based on the optimization of transmit power level by using the soft computing approaches. This solution determines the node transmit power level statistically and achieves energy savings efficiently.
Moreover, nodes in a wireless sensor network have mobility so that the density of the nodes also varies as time. Hence, the clustering method should dynamically vary in accordance as the movement of nodes considering the node density due to the mobility of nodes. In order for this, a method determining the transmission power level of each node with minimum computation and shortest time is in need. In this paper, a method of clustering by determining optimized power level using soft-computing in a non-homogeneously distributed network is proposed. With the aid of the proposed method, communications in a cluster can be carried out with optimized transmission power, and higher level of transmission powers are used for the communications to nodes in other clusters. In this way, the proposed method possibly resolves problems occurred in case of non-homogeneously distributed nodes. This paper is organized as follows: Section 2 describes clustering algorithm in more detail. Section 3 describes the clustering characteristics for transmit power control. Finally, Section 5 concludes this paper and discusses future work.
2 Clustering Algorithm The method proposed in this paper is a clustering method which generates clusters with determining transmission power level by using soft-computing technique in nonhomogeneously distributed network. 2.1 Clustering Algorithm The transmission power for clustering is determined by Bayesian classification based on Priority probability. This method is applied in the way to calculate the probability for an arbitrary node to belong to a specific transmission power level, and to select the class having the highest probability. By assuming xi as an arbitrary node in a network and
ci as a transmission power level, the optimized transmission power C best is cal-
culated by (1).
C best = ArgMax [
p ( x i | c j ) p (c j ) P ( xi )
] .
(1)
P( xi ) is the probability that an arbitrarily extracted node from the node set is xi and P (c j ) implies the probability for an arbitrarily extracted node from the node set to belong to transmission power set,
c j . P ( xi | c j ) is the probability that an arbitrarily
extracted node from a node set belonging to a transmission power set, c j is xi . (1) Determines the transmission power set having the highest possibility to the power level by calculating P ( xi | c1 ), P ( xi | c2 ), P ( xi | c3 ), and P ( xi | ck ) for a given node x j . By using (1), internal nodes in a network attain transmission power level based on Bayesian Classification. Through this procedure, an arbitrarily extracted node, x i clusters with the optimized transmission power C best . This procedure is repeated until all nodes in the network are finished to be clustered. 2.2 Cluster-Based Routing In general, cluster based routing uses the modified routing table. The routing table has cluster id and transmit power level. If source node and destination node are in the same cluster, routing can discover the path only uses with the decided the transmit power level of the cluster. The transmit power level can be realized by using the optimized power level, Cbest which is simply enough to connect nodes. But source node and destination node are in the different cluster, routing must use the more high transmit power level for route discovery. Fig.3. presents the example of the routing algorithm in a clustered network. First, transmit power level of 1mW is firstly used to transmit a packet from the source node
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Fig. 3. Cluster-Based routing example
S to the destination node D1 because S and D1 are in the same cluster1. In second case, source node S is in the cluster1 and destination node D2 is in the clutser2. So the node S must use the more high transmit power level to forward packet into the 10mW cluster where the destination node belongs to.
3 Simulation and Clustering Characteristics We simulated the clustering using MATLAB. Our simulation is involving 100 node placed non-uniformly on a 100m x 100m area and. And we assume that the node can control the transmit power level and there are only a few discrete power levels available. Simulations show that the clustering for transmission power control can perform the well-structured clustering for wireless sensor network.
Fig. 4. (a) fixed transmit power (b) transmit power control using bayes’ rule
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Our proposed methods have the following characteristics. • Since the proposed clustering algorithm is based on the transmit power level, it is not fixed and provides a distributed clustering. Thus it has simple structure and can do the clustering efficiently in wireless sensor networks. • It is possibly applied to all kinds of proactive and reactive routing protocols. In case of proactive routing protocols such as DSDV [3], routing tables holding different power levels are maintained by HELLO packets to construct the clustering. On the other hand, reactive routing protocols like AODV [4], can be transmitted to every power level applicable to be used by Discovery Request. • Transmit power level might be dynamically changed by node mobility and we adapt Bayesian classification based on Priority probability. The proposed clustering algorithm is possible to predict the node transmit power without any network resources and excessive computing time. Therefore. The clustering algorithm is an efficient for wireless sensor network varying in density between many nodes.
4 Conclusion We discuss the clustering algorithm using the bay Bayesian classification based on Priority probability and the cluster-based routing. Minimizing power consumption is indeed important in the field of researching sensor networks. This paper proposes a solution for transmission power and clustering in non-homogeneously distributed network. The proposed method indicates an efficient way of clustering by using transmission power. Moreover, efficient traffic transmission can be realized, transmission routes considering transmission power are possible provided and the method is able to minimize collisions occurring in MAC by using the proposed method. Based on MATLAB simulation, our algorithms will give efficient clustering mechanism for wireless sensor network. In order to verify our methods, we should extend the network simulator ns [6] to simulate our algorithms.
References 1. Narayaswamy, S., Kawada, V., Sreenivas, R.S., Kumar, P.R.: Power Control in Ad-Hoc Networks: Theory, Architecture, Algorithm, and Implementation of the COMPOW Protocol. European Wireless Conference, (2002) 2. Kawadia, V., Kumar, P.R.: Power Control and Clustering Ad Hoc Networks. IEEE INFOCOM , (2003) 3. Kecman, V.: Learning and Soft Computing. 61-103 4. Perkins, C.E., Elizabeth M.R.: Highly Dynamic Destination-Sequenced Distance-Vector Routing (DSDV) for Mobile Computers. SIG-COMM `94: Computer Communication Review. (1994) 234-244 5. Perkins, C.E., Elizabeth M.R.: Ad Hoc On-Demand Distance Vector Routing. Proceedings of the 2nd IEEE Workshop on Mobile Computing Systems and Applications. (1999) 90–100 6. UCB/LBNL/VINT Network Simulator – ns2. http://www-mash.cs.berkeley.edu/ns/, (1998)
Discriminating Fire Detection Via Support Vector Machines Heshou Wang1,2, Shuibo Zheng2, Chi Chen2, Wenbin Yang2, Lei Wu2, Xin Cheng2, Minrui Fei1, and Chuanping Hu2 1
School of Mechatronical Engineering and Automation, Shanghai University, Shanghai 200072, China 2 Shanghai Fire Research Institute of Ministry of Public Security, Shanghai 200032, China [email protected]
Abstract. Many researchers are exploiting multi-sensor detection to discriminating between fire and nuisance sources. Multi-sensor detectors can monitor multiple aspects of a wide variety of signatures produced by flaming fires, smoldering fires and nuisance source. A new method based on support vector machines (SVMs) is proposed to identify flaming fires, smoldering fires and nuisance sources incorporating smoke, temperature and carbon monoxide (CO) sensors. The usefulness and acceptability of the fire discriminating method has been demonstrated.
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optimal and unique solution, and sparse representation of solution. a particular advantage of SVMs over other learning algorithms is that it can be analyzed theoretically using concepts from computational learning theory, and at the same time can achieve good performance when applied to real problems. SVMs learning are based on some beautifully simple ideas and provides a clear intuition of what learning from examples is about. Second, it can lead to high performances in practical applications. In this paper, an early fire detection method consisting of an array of smoke, temperature and carbon monoxide sensors is presented, with discrimination provided by SVMs analysis of the sensor responses.
2 Support Vector Regression Algorithm Considered two set xi ∈ X ⊆ R n , yi ∈ Y ⊆ R . A primal space is transformed into a
high-dimensional feature space by a nonlinear map ĭ ( x ) = (φ1 ( x ), φ2 ( x ), , φn ( x ) ) .
Approximating the data set with a nonlinear function f ( x ) = ȦT ĭ ( x ) + b.
(1)
The coefficients Ȧ and b can be obtained by solving the primal objective function: 1 2
min
l
2
Ȧ + C ¦ (ξi + ξi* ) i =1
yi − Ȧ ĭ ( xi ) − b ≤ ε + ξi ° T * ® Ȧ ĭ ( xi ) + b − yi ≤ ε + ξi ° * ≥ 0, ¯ ξi , ξi T
s.t.
(2)
where C is the regularization constant which determines the trade-off between the flatness of f and the amount up to which deviations larger than ε are tolerated. ξ i , ξ i* are positive slack variables. A Lagrange function from the primal objective function was constructed as follows:
L=
1 2
l
l
i =1
i =1
Ȧ + C ¦ (ξ i + ξi* ) − ¦ α i (ε + ξi − yi + ȦT ĭ ( xi ) + b) 2
l
(3)
l
− ¦ α (ε + ξ + yi − Ȧ ĭ ( xi ) − b) − ¦ (ηi ξi + η ξ ). * i
i =1
* i
* * i i
T
i =1
This Lagrange function has a saddle point with respect to the primal and the dual variables at the optimal solution. The dual variables in Eq.(3) satisfy positive constraints, i.e. α i , α i* ,ηi ,ηi* ≥ 0 .
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By means of Karush-Kuhn-Tucker (KKT) conditions, we obtain l ∂L = Ȧ − ¦ (α i − α i* )ĭ ( xi ) = 0 ∂Ȧ i =1 l ∂L = ¦ (α i − α i* ) =0 ∂b i =1 ∂L = C − α i − ηi =0 ∂ξi
° ° ° ° ° ® ° ° ° ° °¯
∂L = C − α i* − ηi* * ∂ξ i
(4)
= 0.
SVMs avoid computing explicitly the map ĭ ( x ) and exploit kernel function
K ( xi , x j ) = ĭ ( xi )T ĭ ( x j ) instead. Any function which satisfiers Mercer condition can be used as kernel function. Utilizing Eq.(4) to eliminate the primal variables (Ȧ, b, ξi , ξi* ) in (3), the Wolfe dual optimization problem is as follows: 1 l * * ° - 2 ¦ (α i − α i )(α j − α j ) K ( xi , x j ) − ° i , j =1 max ® l l ° ε (α + α * ) + y (α − α * ) ¦ i i i i i °¯ ¦ i =1 i =1 s.t.
° ® ° ¯
l
¦ (α
i
(5)
− α i* ) = 0
i =1
0 ≤ α i , α i* ≤ C.
By solving quadratic program, regression function is rewritten as: l
f ( x ) = ¦ (α i − α i* ) K ( xi , x ) + b,
(6)
i =1
where α i , α i * satisfy α i × α i * = 0, α i ≥ 0, α i * ≥ 0 . Only a few coefficients (α i − α i * ) are nonzero values, and the corresponding training data points have approximation errors equal to or larger than ε . These data points are called support vectors. Different kernels can be used as follows: (1) Linear Kernel: K ( x , xi ) = x T xi (2) RBF Kernel: K ( x, xi ) = exp(−
|| x − xi ||2 ) 2σ 2
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(3) Polynomial Kernel: K ( x , xi ) = ((γ xT xi ) + r )d , d = 1, 2, , N . where σ , γ , r and d are kernel parameters.
3 SVMs Model Selection When applying the SVMs to modelling, the first thing is what kernel is to be used. RBF kernel is used as kernel function because it has less hyperparameters that influence the complexity of model selection than the polynomial kernel. Our goal is to find SVMs regression model have the best generalization performance. To achieve this goal, the best set of hyperparameters such as C and σ (RBF kernel parameter) has to be selected. As the size of data is severely limited, the cross-validation [11] procedure via parallel grid-search is employed to prevent the overfitting problem. Basic pairs of ( C and σ ) are tried and the one with the best crossvalidation performance is picked. Exponentially growing sequences of C and σ is a practical method to identify good parameters (for example C = e −4 , e −2 , e10 , σ = e −10 , e −8 , , e −2 ). The procedure of S -fold cross-validation divides given data D at random into S subsets {G1 , G2 , , GS } , and uses S − 1 subsets for training, and uses the remaining one for the validation. This process is repeated S times by changing the remaining subset, and the generation performance is evaluated by using the following MSE (mean squared error) over all validation results. MSECV =
1 N
S
¦ ¦ (y
v
− y ( x v θˆi )) 2
(7)
i =1 v∈Gi
Here Gi denotes the i − th subset for the validation. And θˆi denotes the optimal parameter vector obtained by using D − Gi for training. By using S -fold cross-validation with grid-search, the hyperparameters are optimized so that the cross-validation error MSECV is minimized.
4 Discriminating Fire with SVMs Support vector machines were applied to signal processing from smoke, temperature and CO sensors. The system input signals are smoke, temperature rising trend and CO. The output quantity is the probability of fire and nonfire. We used the data collected in a standard laboratory to simulate flaming fire, smoldering fire and nuisance source. Scaling training data is very important. The signals are likely to be measured in different physical units. These attributes in greater numeric ranges dominate those in smaller numeric ranges. Each attribute is recommended to linearly scale to the range [-1, 1] or [0, 1].
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The training set is 80 samples and 50 samples are used as the test set. RBF kernel is chosed with width σ =9, the loss function with ε =0.001 and regularization constant C =110 in SVMs. Some training samples and training results are given in Table 1. Table 1. Training samples from sensors and training probability results
S∆ - Amplitude of smoke M ∆ - Amplitude of CO PF - Probability of flame fire
Tτ - Trend of temperature
PS - Probability of smoldering fire
PN - Probability of nuisance source PˆF - Estimated probability of flame fire PˆS - Estimated probability of smoldering fire Pˆ - Estimated probability of nuisance source N
Some test samples and test results are shown in Table 2. The results indicate SVMs are capable of discriminating fire by means of multi-sensor signals. SVMs have strong ability to learn a small number of samples. It can be seen good generalization performance can be achieved to prevent the overfitting problem. Table 2. Test samples from sensors and test probability results
S∆ (V) 0.051 0.048 0.053 0.055 0.058 0.058
M∆ (V) 2.7 2.5 2.9 2.83 2.92 2.65
Tτ 2.0 3.5 3.5 1.0 0.5 0.5
PF
PS
PN
0.15 0.10 0.20 0.23 0.10 0.90
0.25 0.3 0.30 0.68 0.70 0.10
0.75 0.70 0.80 0.3 0.35 0.05
PˆF
PˆS
PˆN
0.134 0.108 0.225 0.225 0.108 0.882
0.258 0.315 0.284 0.671 0.726 0.078
0.742 0.734 0.788 0.318 0.365 0.043
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5 Conclusions This paper presented a new method based on support vector machines to identify flaming fires, smoldering fires and nuisance source incorporating multi-sensors. The research result indicates the application of SVMs to discrimination fire detection is effective and feasible.
Acknowledgement This work was supported by Doctoral Program Foundation of Science & Technology Special Project in University (20040280017), Key Project of Science & Technology Commission of Shanghai Municipality under grant 04JC14038, and Shanghai Leading Academic Disciplines (T0103).
References 1. Grosshandler, W.L.: A Review of Measurements and Candidate Signatures for Early Fire Detection, NISTIR 5555, Gaithersburg, MD, National Institute of Standards and Technology, (1995) 2. Thuillard, M.: New Methods for Reducing the Number of False Alarms in Fire Detection Systems, Fire Technology, 30(2) (1994) 250-268 3. Luck, H.: Remarks on the State of the Art in Automatic Fire Detection, Proceeding of the 10th International Conference on Fire Detection-AUBE’95, Duisberg Germany, April 4, (1995) 4. Pfister, G.: Multisensor/Multicritera Fire Detection: A New Trend Rapidly Becomes State of the Art, Fire Technology, 33(2) (1997) 99-114 5. Okayama, Y.: A Primitive Study of a Fire Detection Medthod Controlled by Artificial Neural Net. Fire Safety Journal, 17(6) (1991) 535 - 553 6. Hall, J.R.: The Latest Statistics on U.S. Home Smoke Detectors, Fire Journal, 83(1) (1989) 39-41 7. Vapnik, V.N.: Statistical Learning Theory. New York: Wiley, (1998) 8. Van, G.T.: Financial Time Series Prediction Using Least Squares Support Vector Machines within the Evidence Framework, IEEE Transactions on Neural Networks, July, v12(4) (2001) 809-821 9. Vapnik, V.N.: An Overview of Statistical Learning Theory, IEEE Trans. Neural Network , 10(5) (1999) 988 - 999 10. Smola, J., Schölkopf, B.: A Tutorial on Support Vector Regression. NeuroCOLT2 Technical Report Series, Royal Holloway College, University of London, UK, (1998) 11. Duric, Petar M.: Model Selection by Cross-Validation. IEEE International Symposium on Circuits and Systems. (1990) 2760-2763
Dynamic Deployment Optimization in Wireless Sensor Networks Xue Wang, Sheng Wang, and Junjie Ma State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, P.R. China [email protected][email protected][email protected]
Abstract. Sensor deployment is one of the key topics addressed in wireless sensor networks (WSNs) study. This paper proposes a self-organizing technique for enhancing the coverage of WSNs which consists of mobile and stationary nodes. The mobile nodes will relocate themselves to find the best deployment under various kinds of situations for covering largest area. The new locations of mobile nodes are determined by parallel particle swarm optimization (PPSO) which is suitable for solving multi-dimension function optimization in continuous space. Especially, the mobile nodes deployment with PPSO is useful in situations while some area need cooperative measuring with multiple nodes, and can be adjusted dynamically according to the requirement of environment. The experimental results verify that mobile nodes deployment with PPSO has good performance in quickness, coverage and connectivity.
1 Introduction In WSNs, dynamic deployment optimization has become one of the key topics addressed. T. Wong et al. [1] and S. Zhou et al. [2] proposed the “Virtual Forces” algorithm which can effectively enhance the coverage and connectivity of WSNs in single measurement, but little attention has been focused on the dependability and precision of sensor nodes. Actually, because of the high robust and precision requirement, cooperative measurement is required in most applications. The proposed PPSO based dynamic deployment optimization algorithm is useful in deployment of cooperative measurement with the effective coverage performance taken as criterion while precision and speed of optimization is satisfied.
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Fig. 1. (a) Random deployment. (b) Effective coverage performance evaluation.
2.2 Performance Evaluation for WSNs
If an area is in detection range of n nodes at time t, the area’s synthesis detection dependability can be calculated directly as: n
R ( t ) = 1 − ∏ (1 − ri ( t ) )
(1)
i =1
where ri ( t ) is the detection dependability of ith sensor nodes. Effective coverage performance can be represented by the proportion of effective area where synthesis detection dependability can satisfy the detection acquirement. As shown in Fig. 1(b), gridding algorithm divides the area into grids and calculates the proportion of effective detected grids. The simulation results verify that the error is between 0.5% and 0.1% while granularity is between 4% and 0.25%. Unfortunately, the execution time increases fast when granularity decreases. For reducing the execution time, we can analyze the effective detection area formed by stationary nodes at first, and then solve the remaining area during dynamic adjustment. As illustrated in Fig.1, sensors are divided into two connected groups. In WSNs, if a node can not be connected to the sink node, its information will not be received. For grouping, each node detects its neighbors and all connected nodes label them in same group. We define the group connected with sink node as activated group. The number of connected nodes and coverage are focused. The coverage ratio is as follows:
Cm =
ci ,i ∈ S A
(2)
where ci is the coverage of a sensor i, S is the set of nodes, and A is the total size of the area to be monitored. Let N m denotes the number of sink-connected nodes after placing mobile nodes. To represent the improvement, we define:
N im =
N m − N0 × 100% N0
(3)
where N 0 is the number of connected nodes before placing any mobile nodes. We also define cim as the improvement of coverage with m mobile nodes, as:
Cim =
Cm − C0 ×100% C0
(4)
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3 PPSO Based Dynamic Deployment Optimization 3.1 Principle of Particle Swarm Optimization
PSO is a swarm-intelligence-based evolutionary algorithm [3]. In PSO, the potential solutions, called particles, “fly” through the search space to find optimal solution [4]. Each particle keeps the best location pbest and the global optimal solution gbest. The current location is called pnow. During optimization, each particle changes its velocity toward pbest and gbest position with the bounded random acceleration. pbest and gbest are updated according to (5) and (6) respectively: ° pbest if f ( pnow ) ≥ f ( pbest ) pbest = ® °¯ pnow if f ( pnow ) < f ( pbest )
(5)
gbest = min { pbest1 , pbest2 , , pbestn }
(6)
Velocity and position of particle are updated according to equations (7) and (8): vij ( t + 1) = ω ( t ) × vij ( t ) + c1 r1 j ( t ) ( pij ( t ) − xij ( t ) ) + c2 r2 j ( t ) ( pgj ( t ) − xij ( t ) )
(7)
xij ( t + 1) = xij ( t ) + vij ( t + 1)
(8)
where c1 and c2 are acceleration constants, r1 j ( t ) and r2 j ( t ) are two separate random functions in the range [0,1] for ith particle in jth dimension, xij ( t ) and vij ( t ) represent position and velocity at time t separately, pij ( t ) is the pbest, and pgj ( t ) is the gbest. Variable ω ( t ) is the inertia weight used to balance the global and local search. The simulation results illustrate that an inertia weight starting with a value 0.9 and linearly decreasing to 0.4 greatly improve the performance of PSO [5]:
ω ( t ) = 0.9 −
t × 0.5 MaxNumber
(9)
where MaxNumber is the number of maximum iterations. 3.2 PSO Based Dynamic Deployment Optimization
The elements in position vector X i = ( xi1 , xi 2 , xin ) present coordinates of all mobile nodes, and the correlative fitness is presented by the proportion of effective detected area. Granularity should decreases gradually for the tradeoff between speed and precision. After adjusting granularity, we should renew the velocities of particles randomly and re-analyze the gbest’s and pbest’s fitness associated with new granularity for keeping the validity. The process of optimization is as follows: 1. Initialize a population of particles with random positions and velocities and granularity. Analyze the effective detection area formed by stationary nodes. 2. Evaluate the effective coverage performance. Compare and update optimal pbest value of each particle and global optimal gbest of whole population. 3. Change velocity and position of particle according to (7) and (8) respectively.
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4. Halve the granularity when gbest is not evolved in recent 10 iterations, renew the velocities randomly, and re-analyze the fitness. 5. Loop to step 1 until a criterion is met, usually a sufficiently small granularity, a sufficiently good fitness or a maximum number of iterations. 3.3 PPSO Based Dynamic Deployment Optimization
Large amount of computation and limited computing ability of each node constrain the utility of PSO based dynamic deployment optimization. So we use PPSO algorithm which divides the whole detecting area into n groups which contain same number of nodes, where n equals to the number of intelligent nodes, as illustrated in Fig. 2. Because of random deployment, the uncovered area in each part is not equal. Then, the mobile nodes are divided into n parts:
ni =
si ¦s
×N
(10)
where si is the uncovered area of ith part, N is the total number of mobile nodes.
Fig. 2. Sensor node division map, each group contains same number of nodes
Significantly, the nodes in the edge will affect the nearby area which must be considered during optimization. Because the furthest area that nodes can affect is determined by the detection radius rd , the region should be enlarged by rd . As illustrated in Fig. 2, the dash dot lines form the boundary of actual optimized area. Furthermore, because each intelligent node performs optimization independently, some mobile nodes may overlap with others. So, if the distance between two mobile nodes is less than the detection radius rd , their positions should be re-optimized in whole area with other optimized mobile nodes considered as stationary ones.
4 Simulation Results We simulate a WSN including n = 80 stationary nodes and n = 20 mobile nodes, with detection radius r = 7m and communication radius r = 2r = 14m . The mobile nodes are randomly deployed in a square region with area A = 100 × 100 = 10000m . As illustrated in Fig. 3(b), with only 20 mobile nodes, connectivity and coverage are greatly improved. But two mobile nodes at about x = 550m, y = 700m overlap. Fig. 3(c) shows the adjusted result. s
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Fig. 3. Demonstration of optimization. (a) No mobile nodes. (b) 20 mobile nodes before adjustment. (c) 20 mobile nodes after adjustment.
(a)
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Fig. 4. (a) Coverage improvement with different iterations in one node. (b) Coverage and (c) Connectivity improvement with different number of mobile nodes.
Fig. 4(a) represents the coverage improvement in one intelligent node during the execution of PPSO. Fig. 4(b) and (c) represent how the coverage and connectivity increase with mobile nodes. As illustrated, the coverage and connectivity are doubled when there are 2 mobile nodes. It can be verified that our algorithm can greatly improve the connectivity and coverage of WSNs. Experiment results shows that the time descends significantly when the number of intelligent nodes increases, and the PPSO algorithm has great performance at speedup and efficiency. Furthermore, execution time of optimization will increases with the number of sensor nodes, but the increase is almost linear. Moreover, we assumed that target should be tracked by at least 4 nodes for detection dependability. As illustrated
(a)
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Fig. 5. Dynamic position change of mobile nodes, (a) before adjustment; (b) after adjustment; (c) another adjustment; where circles denote the available range for nodes to track the target
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in Fig.5, the proposed algorithm can dynamically change the positions of nearest and fewest mobile nodes according to current situation. After the target moving away, the nodes will go back to its former position for enlarge the coverage.
5 Conclusions PPSO based dynamic deployment optimization, which takes gridding effective coverage and connection performance evaluation as criterion, can optimize the deployment dynamically according to the detection demand and states of nodes. The simulation results verify that the proposed algorithm is useful for both cooperative and single measurement. Furthermore, the parallel mechanism reduces the execution time and the time increases slowly with the number of nodes. We can make a conclusion that PPSO is suitable for the dynamic deployment optimization of WSNs. Acknowledgement. This paper is sponsored by National Natural Science Foundation of China (No. 60373014; No. 50175056).
References 1. Wong, T., Tsuchiya, T., Kikuno T.: A Self-organizing Technique for Sensor Placement in Wireless Micro-Sensor Networks. Proc. of the 18th Int. Conf. on Adv. Info. Networking and Application, IEEE, Piscataway, NJ (2004) 78-83 2. Zhou, S., Wu, M. Y., Shu, W.: Finding Optimal Placements for Mobile Sensors: Wireless Sensor Network Topology Adjustment. In Proc. of the IEEE 6th Circuits and Systems Symposium on Emerging Technologies, IEEE, Piscataway, NJ (2004) 529-532 3. Ciuprina, G., Ioan, D., Munteanu, I.: Use of Intelligent-Particle Swarm Optimization in Electromagnetics. IEEE Trans. on Magnetics, (38) 2 (2002) 1037-1040 4. Eberhart, R. C., Shi, Y.: Particle Swarm Optimization: Developments, Applications and Resources. Proc. Congress on Evolutionary Computation, IEEE, Piscataway, NJ (2001) 81-86 5. Shi, Y., Eberhart, R. C.: Fuzzy Adaptive Particle Swarm Optimization. Proc. Congress on Evolutionary Computation, IEEE, Piscataway, NJ (2001) 101-106
Energy-Efficient Aggregation Control for Mobile Sensor Networks Liang Yuan, Weidong Chen, and Yugeng Xi Department of Automation, Shanghai Jiao Tong University, Shanghai, China [email protected]
Abstract. A primary purpose of sensing in a sensor network is to collect and aggregate information about a phenomenon of interest. The interesting phenomenon is often an event. In this paper, we develop control algorithms aggregate the interesting event based on energy-efficient communication topology. The communication topology is that each node keeps the k closest neighbors by adjusting the transmit power in the aggregating process. And it can not only remain communication connection but also decreases the energy consumption. Moreover we design local feedback controller for completing the g1obal target. We simulate the aggregation motion. As the results, the sensor nodes converge to different formation and the utility of our proposed method is validated.
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a mobility models integrated in simulator. The mobility models for simulation include random waypoint model, random direction model and Brownian-like motion etc [5, 6]. These models can’t stand for the real-life movements of the sensor nodes. Our aim focuses on completing the energy-efficient aggregation motion in an interest area. We present the k-closest neighbors method that decrease energy consumption through adjusting the radio power for each node, while ensure that the communication topology remains connection. Moreover, each node can depend on the local sensing information to converge to different stable formation. The outline of this paper is as follows. In Section 2, we model the sensor network. In Section 3, we propose energy-efficient aggregation control algorithms to acquire different formation. In Section 4, we simulate the aggregation motion and validate the utility of our proposed method. Next, in Section 5, we summarize the paper.
2 Sensor Networks Modeling Consider a sensor network consisting of N identical coupled linear oscillators (nodes) as follows. The state equations of the sensor network can be written as [7]: .
N
.
x i = f (xi ) + c
¦
a ij Γ x j ,
i = 1 , 2 ... , N
(1)
j =1
Щ
where xi= (xi1, xi2, … , xin) RN are the state variables of node i and the constant c>0 represents the coupling strength of the network. f(xi) is a random motion equation of the sensor nodes initially. For simplicity, we take ī=diag(r1, r2, …, rn) RN×N with ri=1 for a particular i and rj=0 for j i [7]. If there is a connection between node i and node j (i j), then aij=aji=1; otherwise, aij=aji=0(i j). We take
Щ
ҁ
ҁ
ҁ
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a ii = −
¦a
ij
= −ki ,
i = 1, 2 , ..., N
.
(2)
j = 1, j ≠ i
where the degree ki of node i is defined to be the number of connection incidents on node i. Defined that the sensor network (1) is (asymptotically) stable if x 1 ( t ) = x 2 ( t ) = ... = x N ( t ) = s ( t )
as
t → ∞
.
(3)
3 Control Algorithms 3.1 Aggregation Control We assume that each node knows the exact position of the target point P and the other nodes and move simultaneously to cover the point P. s(t) can be an equilibrium point, a stable formation. To achieve such the goal (3), we apply artificial potential field method on the nodes of the sensor networks. We assume that the dangerous radius of the target point is Rd. SR is the dangerous area. AR is the attractive potential field of the target point P.
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Definition: we suppose that all sensor nodes can find the target point initially. Due to the attractive potential field of the target point P, each node can move toward P. Thus, the attractive potential field force of node i is defined:
ˈ
Щ
° d ( x p − x i ) f a ( xi ) = ® 0 , °¯
x p − xi ≥ Rd
.
(4)
x p − xi < Rd
where xi N is the position of node i. xp represents the target position. d (d>0) is a coefficient that show the degree of the attractive potential field force. So, the controlled network can be described: ° x i = f ( x i ) + c ® ° u = f (x ) a i ¯ i
N
¦
a ij Γ x
j
+ ui,
i = 1 , 2 ..., N
j =1
.
(5)
Actually, the equation (5) is a local feedback controller. d is a feedback control gain. The constant c and d influence the convergence speed of the whole sensor networks. In equation (4), we only assume that the interest event area is a circle. Actually, we can also define different the attractive potential field of the target point P according to different formation of the interest event area, for example, ellipse, line or column. 3.2 Energy-Efficient Topology For mobile sensor networks, how to decrease the communication energy consumption is very important. It involves with network topology control. Topology control is how to set the radio range for each node so as to ensure the communication connected, while still minimizing energy usage [8]. For the purpose of keeping the connection of communication and decreasing the energy consumption of communication, we adopt the k-neighbors method to realize the topology control of MSN [9, 10]. The algorithm based on k-neighbors uses the idea of changing radio power depending on the number of neighbors. Initially, a node finds all neighboring nodes using an initial power Po. If the number of neighbors is less than the required number of neighboring nodes k, then the transmission power is increased (see Fig. 1). If the number of neighbors is greater than the required number of neighboring nodes k, the closest k neighbors are reserved as the neighbor nodes and the rest nodes are deleted from the neighbors of node i (see Fig. 1). Hence each node is forced to maintain k
(a)
(b)
Fig. 1. Adjusting radio power of node i (a) increasing radio power of node i. (b) decreasing radio power of node i.
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neighbors. Thus, it helps maintaining high connectivity even when the distribution of the sensor nodes is sparse. Especially, in the process of aggregation, the distance between the sensor nodes is gradually decreasing. The topology control method is actually effective. So, we can benefit from adjusting nodes different transmission ranges in decreasing energy usage. According to the sensor networks communication model [4], the communication energy cost is totally determined by the value of transmission ranges of each node. Thus the goal of the energy efficient topology becomes to minimize transmission ranges of each node in the process of the aggregation motion: T
min
n
¦ ¦ rα i
.
(6)
t = 0 i =1
where ri denotes the range assigned to node i and Į is the coefficient that depends on the environmental conditions. T is the time to complete the aggregation motion. Meanwhile, the value of the k closest neighbors number must be considered for keeping the network connection. In [10], Xue and Kumar present the number of neighbors needed connectivity of wireless networks. If each node is connected to less than 0.074logn nearest neighbors then the network is asymptotically disconnected with probability one as n increases, while if each node is connected to more than 5.1774logn nearest neighbors then the network is asymptotically connected with probability approaching one as n increasing. Thus, the number of neighbors always keeps as k. From equation (2), we know that the coupling matrix A is a symmetric matrix and the diagonal elements are:
aii = −k ,
i = 1,2,..., n .
(7)
where k satisfies [5.1774logn ]+1kn-1. [5.1774logn] stands for the smaller but nearest integer to the real number 5.1774logn. In the process of aggregation, the distance between the nodes can gradually be reduced. If we specify the k value, the transmit radius ri of each node on the basis of remaining the k closest neighbors is diminished. Thus, communication energy consumption is greatly decreased. But, if the transmit radius ri of each node keep the constant, communication energy will be more wasted in the process of aggregation.
4 Experiments and Results Considered that a mobile senor networks. Initially, the sensor nodes are randomly moving. Assumed that the number of the sensor nodes is 10 and the system has an unstable equilibrium point: xp=25. We can stabilize the sensor networks onto the originally unstable equilibrium point xp by applying the local linear feedback control equation (5). Fig. 2 shows the processof controlling a 10-nodes network by a completed coupled networks, that k=7.
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Based on equation (6), the distance between the nodes can constantly be reduced in the process of aggregation. Simultaneously, we can diminish the transmit radius of each node. Thus, communication energy usage is greatly decreased trough topology control. But, if we don’t use topology control, the transmit radius of each node keep the same value, communication energy is more wasted. Fig. 3 shows average energy consumption for 10 nodes in the process of aggregation motion with topology control and without topology control, that k=7, c=10, d=30, Į=3. 800
the transmit power of each node
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Fig. 3. Average energy consumption for 10 nodes in the process of aggregation motion
A common character in the simulation study is that the sensor nodes can converge to the stable state by the local feedback controller. Fig. 4 shows different stable formation by changing xp in c=10, d=30. 5
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5 Summary In this paper, we develop a control algorithm to aggregate the interesting event based on synchronous theory of complex dynamical networks. And assumed that the event point has a strong attractive potential field, all nodes can move to the event point in the field force. Each node keeps k closest neighbors by adjusting the radio power in the aggregating process. It can decrease the communication energy consumption and guarantee that the sensor network keeps the connection of communication. We present the g1obal target by local feedback controller. As the results, the sensor nodes can converge to circle, ellipse and line formation only through local sensing information.
Acknowledgements This work is partly supported by the National Hi-Tech Research and Development Program under grant 2005AA420010, the Natural Science Foundation of China under grant 60475032 and the “Shu Guang” Project of Shanghai.
References 1. Howard, A., Mataric, M. J., Sukhatme, G. S.: Mobile Sensor Network Deployment Using Potential Fields: A Distributed, Scalable Solution to The Area Coverage Problem. The 6th International. Symposium on Distributed Autonomous Robotic Systems (2002) 299–308 2. Poduri, S., Sukhatme, G. S.: Constrained Coverage for Mobile Sensor Networks. IEEE International Conference on Robotsics and Automation (2004) 165-171 3. Cortes, J., Martinez, S., Karatas, T. , Bullo, F.: Coverage Control for Mobile Sensing Networks. IEEE Transactions on Robotics and Automation. 20 (2004) 243-255 4. Santi, P.: Topology Control in Wireless Ad Hoc and Sensor Networks. John Wiley & Sons, Ltd (2005) 5. Heo, N., Varshney, P. K.: Energy-Efficient Deployment of Intelligent Mobile Sensor Networks. IEEE Transactions on Systems, Man, and Cybernetics-part A: Systems and Humans. 35(2005) 78-92 6. Bettstetter, C., Resta, G., Santi, P.: The Node Distribution of The Random Waypoint Mobility Model for Wireless Ad Hoc Networks. IEEE Transactions on Mobile Computing. 2 (2003) 257-269 7. Wang, X. F., Chen, G.: Pinning Control of Scale-Free Dynamical Networks. Physica A. 310 (2002) 521-531 8. Yuan, L., Chen, W. D., Xi, Y. G.: A Review of Control and Localization for Mobile Sensor Networks. The 6th World Congress on Intelligent Control Automation (2006). In Appear 9. Gurumohan, P. C., Taylor, T. J., Syrotiuk, V. R.: Topology Control for MANETs. WCNC (2004) 599-603 10. Xue, F., Kumar, P. R.: The Number of Neighbors Needed for Connectivity of Wireless Networks. Wireless Networks. 10 (2004) 169-181
Intelligent MAC Protocol for Efficient Support of Multiple SOPs in UWB-Based Sensor Networks Peng Gong, Peng Xue, and Duk Kyung Kim Dept. of Information and Communication Engineering, INHA University, Incheon, 402-751, South Korea [email protected], [email protected]
Abstract. Ultra-wideband (UWB) technique has been considered as a possible candidate for high rate Wireless Sensor Network (WSN) because of its higher capacity with low power operation. The IEEE 802.15.3 Medium Access Control (MAC) protocol works on a Time Division Multiple Access (TDMA) basis within a piconet. With multiple overlapped piconets, the current protocol uses Parent/ Child (P/C) or Parent /Neighbor (P/N) configuration to avoid interpiconet interference, but the throughput of P/N or P/C cannot exceed that of single piconet. In this paper we propose an intelligent MAC protocol to cooperate with the UWB system based on Multi-Carrier Code Division Multiple Access (MC-CDMA). The proposed protocol uses Intermediate Sensor Device (ISDEV) to connect Piconet Coordinators and adaptively arrange 2 simultaneous data transmission links during each Channel Time Allocation (CTA). Our simulation results demonstrate the proposed scheme can achieve a higher throughput with an acceptable compromise at link success probability in multiple overlapped sensor networks.
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computer. Due to the movement of objects in sensor networks, the multiple piconets may be geographically overlapped. Then, Co-Channel Interference (CCI) is generated between the piconets. Dynamic channel selection and parent/child (P/C) or parent/neighbor (P/N) piconet are used to avoid the CCI in the IEEE 802.15.3 MAC [3]. In fact the channels defined for MB-OFDM system are not orthogonal, so there is serious CCI even using dynamic channel selection [4]. On the other hand, the child piconet or neighbor piconet works in a private CTA within the parent superframe. This provides the interference mitigation but limits the throughput. The MC-CDMA system uses spreading matrix to provide additional degree of diversity to improve the performance of MB-OFDM system [5], but it did not take the CCI into account. There is still serious CCI within Simultaneously Operating Piconets (SOPs), so the problem of overlapped SOPs is still not solved. Although the MCCDMA is not a perfect solution for the overlapped SOPs, it has the potential to be used in UWB sensor network owing to its additional diversity and flexible data rate by means of frequency domain spreading. A combined MC-CDMA and MAC approach [6] motivates us to propose an intelligent MAC to cooperate with modified MC-CDMA system for SOPs in UWB-based sensor networks. The intelligent MAC protocol uses senior PNC to allocate the CTAs to all of the SDEV in overlapped SOPs through ISDEV. It limits the simultaneous pairs of communicating SDEVs to 2 during each CTA. The spreading code matrixes are used to provide the additional degree of diversity to the system. Additionally, based on twice transmissions of the same OFDM symbol, a joint Minimum Mean Square Error (MMSE) estimator [7] has been adopted in the receiver. We evaluate the system performance in terms of throughput and link success probability as measures of quality and quantity of the modified MC-CDMA system with intelligent MAC protocol in overlapped sensor networks. The paper is organized as follows. Section 2 gives the overview about IEEE 802.15.3 MAC and the problem in SOPs. Section 3 describes the proposed MCCDMA system. Section 4 introduces the intelligent MAC protocol for overlapped SOPs. In the section 5, the proposed scheme is valuated by intensive link and system level simulations. Finally, section 6 draws the benefits and conclusions.
2 Backgrounds In this section, we explain the IEEE 802.15.3 MAC protocol and its problem in overlapped SOPs based on the MB-OFDM technique. The IEEE 802.15.3 MAC timing within a piconet is based on the superframe. The superframe consists of three parts: beacon, Contentions Access Period (CAP) and Channel Time Allocation Period (CTAP). During CAPs, the SDEVs access the channel with CSMA/CA. Channel access in the CTAP is based on TDMA. The CTAP is divided into CTAs, which are used for PNC-SDEV and SDEV-SDEV communications. The child or neighbor piconet works within the parent superframe. The PNC of the parent piconet allocates private CTA for child or neighbor piconet(s). The PNC of the child or neighbor piconet broadcasts its beacon and allocates CTAs inside private CTA. Because every link has the guaranteed time slots, there is no inter-piconet interference in P/C or P/N configuration.
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The support of data rates 55, 110, 200Mb/s is mandatory for MB-OFDM UWB system [4]. Time-Frequency Code (TFC) has been used to interleave coded data over 3 frequency bands and define separate logical channels or independent piconets. It shall be mandatory for all devices to support Mode 1 operation (operating in 3 lowest bands). In order to mitigate the symbol collision probability, the repeater had been adopted for the 3 mandatory data rates. Four TFC channel patterns for model 1 devices are listed in [4]. According to the IEEE 802.15.3 MAC, when the PNC detects some overlapped SOPs the PNC can use dynamic channel selection to change the channel. In fact, the 4 logical channels for model 1 device in [4] are not orthogonal. Any two piconets experience collisions in the transmitted symbols even when the PNC changes the channel. When the number of SOPs increases, the collision would be more serious.
㧘
3 The Modified MC-CDMA System Fig. 1 (a) shows the structure of the proposed transmitter of the MC-CDMA system, where tone interleaving, pilot tones, guard tones, and cyclic prefix are omitted for simplicity. After mapping the coded-bits onto one of QPSK constellation points, the signal is spread in frequency domain. The chip duration is equal to the QPSK symbol duration. Wash-Hadamard code with a length of 8 has been chosen herein as an example. Among 8 possible code sequences, the proposed transmitter utilizes n code sequences to enable n simultaneous transmissions (n=1, .., 4). Then the signals are sent into the IFFT (Inverse Fast Fourier Transform). The OFDM symbol is transmitted twice according to the TFC pattern as in [4].
Fig. 1. Proposed MC-CDMA structure
The transmitted signal experiences fading channel [8] and AWGN (Additive White Gaussian Noise). Fig. 1 (b) describes the structure of the proposed receiver of the MC-CDMA system. After FFT processing, the receiver combines the received OFDM symbols with joint MMSE [7], which minimizes the effect of noise. The reference signals are detected by dispreading with the same spreading matrixes used in the
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transmitter. Eight symbols are grouped and sent into despreader. Finally, the despreader can recover n symbols which are simultaneously transmitted over each group.
4 Intelligent MAC Protocol for Overlapped SOPs The average collision probability reaches 38%, 55.7% and 70.7% for 2, 3 and 4 SOPs, respectively with the TFC pattern in [4]. Especially, it is difficult to mitigate the CCI in case of 3 and 4 SOPs without coordination. So we propose to limit the number of interference-source to one. That means no matter how many piconet are overlapped, there are only 2 simultaneous data transmission links during each CTA. In order to separate the 2 links, we assign two different spreading matrixes to them. Each spreading matrix has a size of 4 and the spreading codes belonging to different spreading matrix are designed to have a good cross-correlation property as in Table 1. Each link can adjust n code sequences (n=1,..,4) flexibly based on the link quality. Table 1. Spreading matrix
Now we give an example of 2 overlapped SOPs working based on the proposed MAC protocol. Two piconets may approach and their coverage areas are partially overlapped as in Fig. 2. When the intelligent MAC protocol is applied, DEV-A belonging to P-1 (piconet -1) first hears the beacon from PNC-2 (the PNC of P-2). Secondly, SDEV-A can act as an ISDEV and send out a heartbeat signal, which has copied the beacon signal of P-2, to PNC-1. We consider PNC-1 as senior PNC. Then PNC-1 adjusts the superframe duration, performs beacon alignment, and assigns the spreading matrixes. When the senior PNC finishes the coordination, it broadcasts the beacon with the information of the coordinated superframe. After receiving beacon from PNC-1, the ISDEV-A sends the beacon of PNC-1 to PNC-2 by heartbeat signal. Then the beacon signal will be broadcasted in the piconets. Each SDEV listens to the beacon from its PNC and keeps synchronization with the coordinated superframe. Fig. 3 (a) shows the coordinated superframe for 2 overlapped SOPs, where the beacon-1 and beacon-2 are assigned in different time slots [9]. During CTA-1, there are 2 simultaneous data transmission links (link-1 in P-1 and link-1 in P-2) with different spreading matrixes. Fig. 3 (b) illustrates the coordinated superframe for 3
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overlapped SOPs. The senior PNC adaptively chooses 2 links for each CTA in coordinated superframe and those 2 links should belong to different piconets; in the CTA-1 L-1 in P-1 works with L-1 in P-2, and in the CTA-2 L-2 in P-1 works with L-1 in P-3. When SOPs move far from each other, each piconet can work based on its original superframe and no coordination is needed. SDEV-2 PNC-2
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(a) Coordinated Superframe for 2 SOPs
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Fig. 3. Coordinated superframes
5 Simulation Results 5.1 Link Level Simulations In the link level simulation, a Packet Error Ratio (PER) of less than 8% is required with a frame body length of 1024 octets of pseudo-random data [4]. All of the simulation assumptions are the same as in [10]. Owing to additional diversity by means of frequency domain spreading, lower code rates are adopted such as 1/2 instead of 11/32 for 55 and 100 Mb/s, and 3/4 instead of 5/8 for 200Mb/s. With the 4 simultaneous transmissions with spreading factor of 8 and reduced coding rate, we can achieve three corresponding data rates 40, 80, and 120Mb/s for the MC-CDMA system. With a smaller number of codes, the data rate can be scalable down to 10 Mbps. Formally, the SINR is defined as the desired received power divided by the total interference plus noise power. Since the CCI is created by frequency-hopped collision, Guassian approximation is no longer suitable for the interference power. The interference power is just effective on the collided symbols and the collision probability is dependent on the number of overlapped SOPs. Tables 2 and 3 give the required SINR (SNR) to achieve 8 % PER from our intensive link level simulations of MB-OFDM and MC-CDMA systems with different number of SOPs.
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Table 2. Link level simulation results for MB-OFDM system
Data Rate (Mbps) Coding rate SNR for 8% PER (1 SOP) SINR for 8% PER (2 SOPs) SINR for 8% PER (3 SOPs)
55 11/32 6.6dB 5.5dB 6.1dB
110 11/32 7.4dB 6.3dB 6.9dB
200 5/8 9.8dB 8.5dB 9.1dB
Table 3. Link level simulation results for MC-CDMA system
Data Rate (Mbps) Coding rate Spreading matrix size SINR for 8% PER (2&3 SOPs)
10 1/2 1x8 3.4dB
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120 3/4 7.2dB
5.2 System Level Simulations There are 3 SOPs with an equal separation distance between the PNCs as configured in Fig. 4. The separation between PNCs is defined as PNC distance (D). The piconet range is set to be 10m. Each piconet has 20 homogeneous SDEVs. Links among the SDEVs in each piconet are randomly created. The system chooses the highest data rate, which satisfying 8% PER requirement based on the required SINR (SNR) in Tables 2 and 3. If all of the data rates cannot satisfy the required error rate criterion, the link is considered as unsuccessful link. Reference and interference signals are not time aligned due to different propagation delay. We consider three different scenarios in the simulation. The SOPs with P/C or P/N configuration are considered in the scenario 1. The SOPs without coordination exist in the scenario 2. Finally, the SOPs with the proposed scheme are considered for scenario 3.
Fig. 4. Configuration of three overlapped SOPs
Table 4 summarizes the parameters used in the system level simulations. The throughput is defined as the total number of the information bits in the packets that are correctly received in a given time duration. The link success probability is the percentage of the successful links among the total links, which has been allocated CTAs in the superframe.
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Channel model Modulation Spreading matrix Packets size Transmit power Pass loss model Noise power per bit
Channel model 1 in [8] QPSK Table 1 1024bytes -10.3dBm 44 . 2 + 20 log 10 ( d ) dB − 174 + 10 * log 10 ( data rate ) dBm
FFT size Superframe
Beacon time CAP time CTAP time CTA size Piconet No.
128 65 ms 0.5 ms 4.5ms 60 ms 1 ms 2,3
Fig. 5 compares the throughput and link success probability (LSP) in three scenarios. Scenario 1 has a constant average throughput because of the TDMA structure within a superframe. Due to the overhead of beacons and CAP durations, the case of 3 SOPs has a lower throughput compared with the case of 2 SOPs. Without coordination, the throughput increases as the distance between PNCs increases, and it is higher than the P/C configuration when two PNCs are farther than 12 meters (so called partial overlap). However, from Fig. 5 (b) the LSP is too low even with a slight overlap, e.g., the PNC distance is longer than 18 meters. The proposed MAC protocol combined with the MC-CDMA technique is a compromise between the throughput and the LSP. When each link is assigned only 4 codes for transmission, the throughput can increase 150 % approximately while maintaining the LSP higher than 77 %. When a single code is allowed flexibly based on the link quality, the LSP can be increased up to 93 % even with a perfect overlap (D = 0). When two PNCs are within the piconet range of 10 meters, it is easy to have a direct communication between them and form a P/C configuration. However, when they are apart each other farther than 10 meters, their coverage are partially overlapped and the IDEV is required to achieve coordination. It is shown that the P/C configuration is inefficient in terms of throughput with partial overlap as shown in Fig. 5 (a). The proposed scheme mitigates this problem and is beneficial in terms of throughput at a cost of slight degradation in LSP.
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Fig. 5. Comparisons of throughputs and link success probabilities in three scenarios
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6 Conclusions In this paper we proposed an intelligent MAC protocol to cooperate with the modified MC-CDMA technique in UWB-based sensor networks. Using MC-CDMA technique, the data rate can be flexibly changed by varying the number of simultaneous code transmissions, depending on the link quality. And the simultaneous links within a CTA is controlled to be two at most, which greatly reduce the collision probability. Additionally, the proposed MC-CDMA improves the SINR requirements owing to the frequency domain diversity and joint MMSE. This proposed scheme was found efficient in the multiple overlapped sensor networks, which achieves an increase in throughput by 50 % approximately with an acceptable compromise in LSP. Acknowledgments. This research was supported by University IT Research Center (INHA UWB-ITRC), Korea.
References 1. Giuliano, R., Mazzenga, F.: Performance Evaluation of UWB Sensor Network with Aloha Multiple Access scheme. IWWAN (2005) 2. Oppermann, I.: UWB Wireless Sensor Networks: UWEN - A Practical Example. IEEE Communications Magazine, vol. 38 (2004) 393–422 3. Wireless Medium Access Control (MAC) and Physical Layer (PHY) Specifications for High Rate Wireless Personal Area Networks (WPANs). IEEE Standard 802.15.3. Institute of Electrical and Electronics Engineers (2003) 4. Batra, A.: Multi-band OFDM Physical Layer Proposal for IEEE 802.15 TG3a. IEEE P802.15-03/268r3 (2003) 5. Ramachandran, I.: Symbol Spreading for Ultrawideband System Based on Multiband OFDM. Proc. PIMRC, vol. 2 (2004) 1204-1209 6. Schoo, K., Choi, H.: MC-CDMA In personal area networks - A Combined PHY and MAC Approach. ITS- Project (2005) 7. Taketa, K., Adachi, F.: Inter-chip Interference Cancellation for DS-CDMA with Frequency-domain Equalization. VTC2004, vol. 4 (2004) 2316 - 2320 8. Foerster, J.: Channel Modeling Sub-committee Report Final. IEEE P802.15-02/368r5 (2002) 9. Mesh Dynamics and Advanced Cybernetics Group-Dynamic Beacon Alignment: http:// www.meshdynamics.com/Publications/ MDPBEACONALIGNMENT. Pdf 10. Ghassemzadeh, S.S.: Parameter assumptions for the simulation of the proposed 802.15.3a PHYs. DCN# 15-04-0488-00-003a (2004)
Topology Control in Wireless Sensor Networks with Interference Consideration Yanxiang He and Yuanyuan Zeng School of Computer, Wuhan University, 430072, Hubei, P.R. China [email protected], [email protected]
Abstract. Topology control incurs large interference will increase communication sign collision, induce great delay in data delivering and consumes more energy. In the paper, we design a distributed algorithm considering interference based on existing connected dominating set backbone. The simulation shows that our algorithms considering interference have good performance and are more suitable for realistic application environments.
1 Introduction In the last few years, researchers actively explored topology control approaches for wireless sensor networks. Interference plays a very important role in many applications of wireless sensor networks. Some literatures have pointed out that a node can interference with another node even if it is beyond its communication range. If a topology has a large interference, either many signals sent by nodes will collide, or the network may experience a serious delay at delivering the data for some nodes, and even consumes more energy. To improve the network performance, designing topology control algorithms with consideration of interference are imminent and necessary. In this paper, we’ll design a distributed interference-aware connected dominating set based backbone algorithm suitable for application environment.
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3 Model and Assumptions We use G = (V, E) to represent such networks. We assume that all nodes have an equal transmission range r and are stationary. All nodes in the network use the same maximal interference range R. Simultaneous transmissions on proximate edges may interfere with each other resulting in collisions. Many interference models have been put forward by literature [5]. Here we present a static interference model based on existing models. I(e1) denote the set of edges which interfere with edge e1. The interference model defines the set I(e1) for each edge e1 in the networks. Let the two nodes incident to e1 be u and v, and the nodes incident to e2 be x and y. We define interference disk of a node u as the disk centered at u with radius of R. If node u or node v are covered by one of the interference disks of node x and y, then we say the edge e1 interference with edge e2. A hierarchical clustering constructed in network graph G is network topology G’. Let e be any link in G’. The link interference number of edge e denoted as |I(e)|. The node interference number is defined as the maximum interference of all links incident on a node, denoted as |I(u)|. The topology interference of sub graph G’, donated by |I(G’)| is max |I(e)|. The interference-aware topology control problem tries to construct a sub graph G’, which is connected and can cut down topology interference effectively.
4 Distributed Interference-Aware Topology Control Algorithm Our method is based on local minimum connected dominating set (MCDS). We present a distributed interference-aware MCDS backbone construction algorithm. We call our method as I-CDS. I-CDS algorithm is based on [4]. Firstly constructs a maximal independent set (i.e., an MIS, which is a subset of V that no two nodes in the subset have an edge. It’s also a dominating set of a graph), and the nodes in the MIS are dominators, nodes not in MIS are dominatees. In the second phase, each dominatee identifies the dominators that are at most two-hop away from it, and then connect the dominators together by choosing some connectors. We consider interference into node ranking as a function: rank(u)={ |I(u)|, id(u)}. Each node is in one of the four states: candidate, dominatee, dominator and connector. After finishes the algorithm, nodes in dominator and connector state will become a cluster-head. Other nodes are as cluster-member, belonging to local clusters. Interference-aware minimal CDS backbone (I-CDS) Algorithm
Step 1: Every node u sends out a TEST message with higher power reaching R to collect local interference information and compute the node interference number, and broadcasts its |I(u)| to its one-hop neighbors. Step 2: Node u with the minimal |I(u)| among all its neighbors with candidate state become a dominator. If the node interference number is the same, the node with lower ID wins. The node declares itself as a dominator will broadcast a DOMINATOR message. Step 3: Whenever a neighboring node receives the DOMINATOR message, it declares itself as a dominatee and broadcasts a DOMINATEE message.
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Step 4: Upon receiving DOMINATOR and DOMINATEE messages from all its neighbors, node maintains a list1 with the IDs of the neighboring dominator. When a node finishes the list, it broadcast corresponding LIST1 messages. Step 5: Upon receiving the LIST1 message from its neighbor, a dominatee maintain a list2 (the IDs of the neighbors two hops away), and broadcast a LIST2 messages. Step 6: Upon receiving both LIST1 and LIST2 messages from a neighbor, a dominator adds the neighbor into a maintained list3 (the IDs of the neighbors which connecting a two-hop away dominator) according to the increasing order of node interference number. And then select the dominatee neighbor in list3 with minimal node interference number (if the interference number is the same, the lower ID node wins) as a connector by sending a LIST3 message. Step 7: Upon receiving a LIST3 from its neighbors, a dominatee declares itself as a connector and sends out CONNECTOR1 message. Upon receiving the CONNECTOR1, a dominatee is selected as a connector if it could reach node’s two hops away dominators, and sends out CONNECTOR2 message. Theorem 1: I-CDS contains a CDS and thus is interference-aware. Proof: As we can see, the step_1 to setp_3 determine the state of nodes (dominator and dominatee) in the network graph in a non-overlapping way. The dominator nodes and the dominatee nodes are interleaving with each other. There are no two dominator nodes that have an edge. It is not difficult to see the nodes sends out DOMINATOR forms a maximal independent set. And the nodes in the MIS are nodes with minimal interference number among its neighbors. So the constructed set is with less interference comparing with many existing algorithms. The step_4 to setp_8 collects one-hop and two-hop dominators and dominatees information. And the senders of CONNETOR1 message connect dominators one-hop away, and senders of CONNECTOR2 message connect dominators two-hop away. All dominators will be connected together by those dominatees, which are invited as connectors. In the connectors selections, we consider the interference by always selecting nodes with minimal interference number as a connector. So our constructed optimum minimal CDS backbone will efficiently cut down link interference in realistic communication. Theorem 2: Algorithm 2 is with O(n) message complexity and O(m+n) time complexity. Proof: Each node in algorithm 2 sends out a constant number of messages, the total number of messages is O(n). Our algorithm is based on [14] with time complexity O(n). Step_2 to setp_8 has the same time complexity with [14]. Step_1 in algorithm2, which makes a computation of local interference number with time complexity O(m).
5 Simulations The simulation network size is 100 to 300 numbers of nodes in increments of 25 nodes respectively, which are randomly placed in a 160X160 square area to generate connected graphs. The radio transmission range is 30m, and the interference range is
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twice the transmission range: 60m. Each node is assigned initial energy level 1 Joule (J). The transceiver energy model: mimics a “sensor radio” with Eelec50nJ/bit, fs 4 10pJ/bit/m2, mp 0.0013pJ/bit/m . We study the performance of constructing topology in terms of link interference, when comparing CDS construction algorithm (CDS) [4] with our I-CDS algorithm. Fig. 1 shows that interference of I-CDS will be less than original CDS algorithm version. Less interference in the network will cut
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down the signal collision and save energy. Also less interference will reduce network delay at delivering data. Fig.2 shows that our I-CDS will both improve the network energy performance. Fig. 3 shows the comparison of average network delay. Our topology with interference consideration effectively reduces signal collision and less delay.
6 Conclusion In the paper, we study on topology control problems in wireless sensor networks with interference consideration. We propose a distributed interference-aware CDS based backbone construction algorithm to make hierarchical network construction. Simulation shows that our algorithm substantially outperforms the existing CDS backbone algorithm without interference consideration.
References 1. Xu, Y., Heidemann, J.,.Estrin, D.: Geography-Informed Energy Conservation for Ad Hoc Routing. In Proceedings of the ACM/IEEE International Conference on Mobile Computing and Networking (MOBICOM), Rome, Italy. (2000) 70-84 2. Wu, J., Li, H.: On Calculating Connected Dominating Set for Efficient Routing in Ad Hoc Wireless Networks. In Proc. the 3rd ACM Int’l workshop Disc. Algor. and Methods for Mobile Computing and Commun. (1999) 7-14 3. Wan, P. J., Alzoubi, K., Frieder, O.: Distributed Well Connected Dominating Set in Wireless Ad Hoc Networks. In Proc. IEEE INFOCOM (2002) 4. Alzoubi, K., Wan, P. J.. Frieder, O.: New Distributed Algorithm for Connected Dominating Set in Wireless Ad Hoc Networks. In Proc. 35th Hawaii Int’1 Conf(HICSS'02) (2002) 3881-3887 5. Gupta, P., Kumar, P.: The Capacity of Wireless Networks. IEEE Transactions on Information Theory, vol. 46, no.2. (2000) 388-404 6. Burkhart, M., Rickenbach, P. V., Wattenhofer, R.,Zollinger, A.: Does topology control reduce interference. In Proc. ACM MOBIHOC. (2004)42004 7. Li, X.-Y., Neijad, K. M., Song, W.-Z., Wang, W.-Z.: Interference-aware topology control for wireless sensor networks. In Proc. IEEE SECON (2005)
Adaptive Depth Control for Autonomous Underwater Vehicles Based on Feedforward Neural Networks Yang Shi1 , Weiqi Qian2 , Weisheng Yan3 , and Jun Li3 1
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Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, Saskatchewan, S7N 5A9, Canada 2 Institute of Computational Aerodynamics, China Aerodynamics Research and Development Center, Mianyang, Sichuan, 621000, P.R. China Institute of Underwater Robotics, Northwestern Polytechnical University, Xi’an 710072, P.R. China
Abstract. This paper studies the design and application of the neural network based adaptive control scheme for autonomous underwater vehicle’s (AUV’s) depth control system that is an uncertain nonlinear dynamical one with unknown nonlinearities. The unknown nonlinearity is approximated by a feedforward neural network whose parameters are adaptively adjusted on-line according to a set of parameter estimation laws for the purpose of driving the AUV to cruise at the preset depth. The Lyapunov synthesis approach is used to develop the adaptive control scheme. The overall control system can guarantee that the tracking error converges in the small neighborhood of zero and all adjustable parameters involved are uniformly bounded. Simulation examples are given to illustrate the design procedure and the applicability of the proposed method. The results indicate that the proposed method is suitable for practical applications.
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Introduction
Autonomous underwater vehicles (AUVs) have various potential applications and great advantages in terms of operational cost and safety: When performing manipulations or inspection tasks, AUVs can help us better understand marine and other environmental issues, protect the ocean resources, and efficiently utilize them for further development. So far, there are more than 46 AUV models worldwide, and numerous worldwide research and development activities have occurred in the area of AUVs [19]. However, a number of complex issues due to the unstructured, hazardous underwater (or undersea) environment make it difficult to travel in the ocean even though todays technologies have allowed humans to land on the moon and robots to travel to Mars. Major facts that make it difficult to control AUVs include: (1) the highly nonlinear, time-varying dynamic behavior of the AUVs; (2) uncertainties in D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 207–218, 2006. c Springer-Verlag Berlin Heidelberg 2006
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hydrodynamic coefficients; (3) disturbances by ocean currents. It is difficult to fine-tune the control gains during cruise underwater. Therefore, it is highly desirable to have an AUV control system that has a self-adaptive ability when the control performance degrades during operation due to changes in the dynamics of the AUV and its environment. In recent years, several advanced control techniques have been developed for autonomous underwater vehicles (AUVs), aimed at improving the capability of tracking given reference position and attitude trajectories [3]. AUVs performing manipulations or inspection tasks need to be controlled in six degrees of freedom. Even though the control problem is kinematically similar to the control of a rigid body in a six-dimensional space, which has been largely studied in the literature, the presence of hydrodynamic effects makes the problem of controlling an AUV much more challenging. Reference [13] presents the state of the art of several existing AUVs and their control architecture. Typical results include sliding control [6,15], nonlinear control [10], adaptive control [11], neural network based control [16,17,18,8], and fuzzy control [2,9]. Since neural networks (NNs) have an inherent capability of approximating nonlinear functions, it is attractive to apply them in motion control systems, e.g., AUVs. In [16,17], a neural network control system has been proposed using a recursive adaptation algorithm with a critic function (reinforced learning approach), and thus the system adjusts itself directly and on-line without an explicit model of vehicle dynamics. In [8], a self-organizing neural-net-controller system (SONCS) was developed for the heading keeping control of AUVs, which features with the fast adaptation method. In this paper, inspired by the successful application of feedforward neural networks in missile control systems in [4], the development of a feedforward neural network based adaptive control for AUV’s depth control system is proposed. By employing a feedforward NN to on-line approximate the uncertain nonlinear dynamics of the AUV without explicit knowledge of its dynamic structure, the depth tracking performance is further investigated. The on-line parameter estimation laws of the NN is developed in the context of the Lyapunov stability concept. Boundedness of all parameters involved as well as the convergence of the tracking errors to zero is guaranteed. The rest of the paper is organized as follows. In Section 2 we discuss the uncertain nonlinear model of the AUV’s depth control system. In Section 3 the feedforward NN is then briefly introduced and its universal approximation property is reviewed. In Section 4, by using the feedforward NN as an on-line approximator, we propose the adaptive control law and associated parameter estimation laws, and analyze the tracking performance and the stability of the whole AUV depth control system. In Section 5 we present an illustrative example to demonstrate the effectiveness of the proposed method. Finally, we offer some concluding remarks in Section 6.
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Dynamics of AUVs, including hydrodynamic parameter uncertainties, are highly nonlinear, coupled, and time varying. Several modeling and system identification
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techniques for underwater robotic vehicles have been proposed by researchers [14,3]. The motion of an AUV is discussed in 6 degrees of freedom (DOF) since 6 independent coordinates are necessary to determine the position and orientation of a rigid body AUV, and 6 different motion components are conveniently defined as: surge, sway, heave, roll, pitch, and yaw. When analyzing the motion of AUVs in 6 DOF it is convenient to define two coordinate frames as illustrated in Figure 1.
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$89IL[HG FRRUGLQDWHV Y1
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Fig. 1. AUV
In this work, we focus on the depth control system of the AUV. Suppose the AUV has a rigid body, and assume that the forward speed v is constant and that the sway and yaw modes can be neglected, then the following equations of motion of the AUV’s depth system include the angular velocity in pitch ωz1 , the pitch angle θ, the attack angle α, the depth ye , and the stern plane deflection δe . ⎧ v˙ ⎪ ⎪ ⎪ ⎪ α ˙ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ω˙z1 ⎪ ⎪ ⎪ ⎪ ⎪ θ˙ ⎪ ⎪ ⎪ ⎪ y˙ e ⎪ ⎩ x˙ e
where Θ = θ − α, xe is the moving distance on the Xe direction, δe is the controller to be designed, and ki (is are subscripts appearing in the above equations) are coefficients appropriately defined in [14].
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From (1), we have y¨e = v(θ − α) cos(θ − α) = v cos(θ − α)(ωz1 −˙α) = v cos(θ − α)ωz1 − cos(θ − α)[k21 v 2 α + k22 vωz1 + k231 α cos(α) +k232 sin α + k24 α sin(θ − α) + k25 cos(θ − α) + k25 cos(θ − α) +k26 cos θ + k27 sin θ + k28 + k29 v 2 δe ] := f (x) + g(x)δe , where x = [ye θ α wz1 ]T , and f (x) := v cos(θ − α)ωz1 − cos(θ − α)[k21 v 2 α + k22 vωz1 + k231 α cos(α) +k232 sin α + k24 α sin(θ − α) + k25 cos(θ − α) + k25 cos(θ − α) +k26 cos θ + k27 sin θ + k28 ], g(x) := k29 [−v 2 cos(θ − α)]. Therefore, the model of the AUV can be represented in the following compact form (2) y¨e = f (x) + g(x)δe .
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NNs are promising tools for identification and control applications because of the universal approximation property [7,5]. A three-layer feedforward NN (shown in Figure 2) can perform as an online approximator [4]. The NN’s vector output can be represented in matrix form ˆ n (xa , W ˆ ih , W ˆ ho ) = W ˆ ho σ(W ˆ ih xa ), Y
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ˆ ih ∈ IRp×(n+1) and W ˆ ho ∈ IRm×p are the input-hidden weight matrix where W and hidden-output weight matrix, respectively; x ∈ IRn×1 is the input vector; xa = (xT , −1)T ∈ IR(n+1)×1 is the augmented neural input vector (the −1 term denotes the input bias), ˆ ih (i)xa ) := σi (W
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⎤ ˆ ih (1) W ⎥ ⎢ .. := ⎣ ⎦, . ˆ Wih (p) ⎡
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ˆ ih includes the threshold. where W NN’s universal approximation property is stated formally in the following theorem [7,5]. ¯ ∈ D (a compact subset of IRn ), Y(x) : D → IRm Theorem 1. [7,5] Let x be a continuous function vector. For an arbitrary constant > 0, there exists an integer p (the number of hidden neurons) and real constant optimal weight ∗ ∗ ∈ IRp×(n+1) and Who ∈ IRm×p such that matrices Wih ∗ ∗ Y(x) = Yn∗ (xa , Wih , Who ) + n (x),
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Adaptive Control Design for AUV Depth System
For the AUV’s depth control system modeled in (2), the control objective is to drive the AUV to track an expected depth trajectory yem . The tracking performance can always be characterized by the tracking error e := yem − ye . In order to increase the robustness of the controller to be designed, a sliding surface is introduced as: S = e˙ + λe, where λ is a small positive constant. Define S η if |η| ≤ 1, S∆ = S − ε · sat , sat(η) = sgn(η) otherwise. ε If S ≤ ε, S∆ = S˙ ∆ = 0; and if S > ε, S∆ = S − ε and S˙ = S˙ ∆ . Then the derivative of S is
which is uncertain, and can be on-line approximated by a feedforward NN described in Section 3. 4.1
Using NN as an Online Approximator
When the AUV cruises underwater, additional force and moment coefficients are added to account for the effective mass of the fluid that surrounds the vehicle and must be accelerated with the AUV. These coefficients are referred to as added (virtual) mass and include added moments of inertia and cross coupling terms such as force coefficients due to linear and angular accelerations. It would be difficult task to obtain the exact values of hydrodynamic coefficients, let alone those disturbances from currents and waves. The main idea of NN based control schemes is to apply NNs to online approximate the unknown nonlinear functions involved in the nonlinear systems to be controlled. On the basis of Theorem 1, we can see that there exists an op∗ ∗ , Who ) over a properly defined timal neural network approximator Yn∗ (xa , Wih ˆ ih , W ˆ ho ) to model the ˆ compact set, and we design a NN approximator Yn (xa , W ˆ ˆ unknown function Y (x), given the estimates Wih and Who . The NN approximation error Y˜n and the wight matrix estimation error are defined as follows, respectively ˆ ih , W ˆ ho ), Y˜n := Y (x) − Yˆn (¯ xa , W ∗ ˆ ih , ˜ ih := W − W W ih
˜ ho := W∗ − W ˆ ho . W ho According to Theorem 1, we can re-write the NN approximation error as ˆ ho σ(W ˆ ih xa ) Y˜n = W∗ σ(W∗ xa ) + n (x) − W ho
ih
˜ ho σ(W∗ xa ) + W ˆ ho σ(W∗ xa ) + n (x) − W ˆ ho σ(W ˆ ih xa ). =W ih ih Taking the Talor-series expansion on
(8)
∗ σ(Wih xa ),
we have ∗ ˜ ih xa ), (9) ˆ ih xa ) + σ (W ˆ ih xa ) W∗ xa − W ˆ ih xa + (W σ(Wih xa ) = σ(W ih dσ1 (z) dσ1 (z) ˆ ih xa ) = diag dσ1 (z) | ˆ where σ (W , | , · · · , | ˆ ˆ z=Wih1 xa z=Wih2 xa z=Wihp xa dz dz dz
∈ IRp×p , and (·) is the sum of the high-order terms of the argument in the Taylor-series expansion. Substituting (9) into (8), we can get ˆ ih xa ) − σ (W ˆ ho σ (W ˜ ho σ(W ˆ ih xa )W ˆ ih xa +W ˆ ih xa )W ˜ ih xa +Ψ, (10) Y˜n = W ˜ ho σ (W ˆ ih xa )W∗ xa + W ˜ ho (W ˜ ih xa ) + n (x). where Ψ = W ih
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Adaptive control and estimation laws to be designed will suppress the NN approximation error, and thus achieve satisfactory tracking performance. In order to facilitate the following design, we analyze the lumped term Ψ in the NN approximation error and explore its upper bound, following the approach used in [4]. Sigmoid function and its derivative are always bounded by certain constants, hence we assume c1 and c2 are some constants, and ∗ ˆ ih xa ) − σ(Wih ˆ ih xa ) ≤ c2 . σ(W xa ) ≤ c1 , σ (W
Therefore, ∗ ˜ rmih xa ) = σ(W ˆ ih xa ) − σ(Wih ˆ ih xa )W ˜ ih xa ˆ (W (W xa ) − σ ˜ ih xa . ≤ c1 + c 2 W
(11)
According to Theorem 1, the norm of the optimal weight matrices of the trained ¯ ih NNs should be bounded by certain constants that are assumed to be W ¯ and Who , ∗ ∗ ¯ ih , Who ¯ ho , Wih F ≤ W F ≤ W T where · F := tr (·) (·) with tr indicating the trace of a matrix, representing the Frobenius norm of a matrix. It is noted that the Frobenius norm of a vector is equivalent to the 2-norm of a vector. Then the norm on the residual term Ψ of the NN approximation error is ˆ ih xa )W∗ xa + W ˜ ho (W ˜ ih xa ) + n (x) ˜ ho σ (W Ψ = W ih ˜ ih F · xa + ˜ ho F · c2 · W ¯ ih · xa + W ¯ ho c1 + c2 W ≤ W ˆ ho F xa ¯ ho + + 2c2 W ¯ ih W ¯ ho xa + c2 W ¯ ih W ≤ c1 W ¯ ho W ˆ ih F xa , +c2 W := bT w where
¯ ho + 2c2 W ¯ ih W ¯ ho c2 W ¯ ih c2 W ¯ ho T ∈ IR1×4 , b = c1 W ˆ ho F xa W ˆ ih F xa ∈ IR4×1 . w = 1 xa W
Then we have Ψ ≤ bT w.
(12)
It is also noticed that g(x) is uncertain in that the involved coefficient k29 is unknown. Therefore, we need to adaptively estimate k29 . For the convenience of expression, define k := k29 , and the parameter estimation error k˜ =then the estimated g(x) can be expressed as: gˆ(x) = kˆ −v 2 cos(θ − α) .
(13)
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Control and Parameter Estimation Laws
Once Yˆn and gˆ are employed as on-line approximators, we can design an adaptive AUV depth control system based on NNs: δe = gˆ−1 (−Yˆn + uc ),
(14)
where uc is the compensation control term and has the following form S ˆT uc = −sat b w, ε
(15)
ˆ ∈ IR4×1 is an unknown vector to be estimated. where b The parameter estimation laws for the NN and associated unknown coefficients are designed as follows T ˆ ih xa ) − σ (W ˆ˙ ho = Γho σ(W ˆ ih xa )W ˆ ih xa S∆ , (16) W T ˆ˙ = Γih xa S∆ W ˆ ih xa ) , ˆ ho σ (W W ih
(17)
˙ kˆ = Γk S∆ −v 2 cos(θ − α) ,
(18)
ˆ˙ = Γw |S∆ |w. b
(19)
Figure 3 depicts the structure of the depth control system developed herein. In the implementation of the controller, the depth ye can be measured by a pressure meter, the pitch angle θ can be measured by an inclinometer while the pitch rate ωz1 requires a rate gyro or rate sensor. Parameter Estimation Laws
Expected Depth
+
+
•
-
•
NN Approximation
Yˆn
-
+ +
X
AUV System
AUV System Output
•
AUV System States
Compensation Control
Approximation
uc
gˆ −1
•
Adaptive NN Control
Fig. 3. Block diagram for the control scheme
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Stability Analysis
Theorem 2. (Stability) Consider the AUV depth control system described by (1) or (2) with the control given by (14) and parameter estimation laws provided by (16), (17), (18), and (19). Then the AUV depth tracking error will asymptotically converge to a neighborhood of zero, and all adjustable parameters will remain bounded. Proof. Choose a Lyapunov function V = V1 + V2 , where V1 =
1 2 S , 2 ∆
(20)
and V2 =
1 ˜ b ˜T. ˜ T ) + 1 tr(W ˜ T ) + 1 Γk k˜2 + 1 bw ˜ ho Γ −1 W ˜ ih Γ −1 W tr(W ho ih ho ih 2 2 2 2
(21)
In the following, the time derivative V˙ is to be evaluated for two cases: (1) |S| > ε, and (2) |S| ≤ ε. (1) Case 1: If |S| > ε, then S∆ = S − ε. Hence, the time derivative of V1 can be derived as follows: V˙1 = S∆ S˙ ∆ . Substituting (6), (14), and (15) into the above equation yields V˙ 1 = S∆ [−ΛS + Y (x) + g(x)δe ] = S∆ −ΛS + Y˜n (x)+ Yˆn (x) +[˜ g (x) + gˆ(x)] gˆ−1 (x) −Yˆn (x) + uc (22) = S∆ −ΛS + Y˜n (x) + g˜(x)δe + uc . Taking the NN approximation error Y˜n (x) (10) and the control law δe (14) into (22), we have V˙ 1 = −S∆ ΛS∆ − S∆ ε + S∆ uc + S∆ k˜ −v 2 cos(θ − α) δe ˆ ih xa )W ˆ ih xa ˜ ho σ(W ˆ ih xa ) − σ (W +S∆ W ˆ ih xa )W ˜ ih xa + Ψ ˆ ho σ (W +W According to (12), we can further obtain 2 ˆ ih xa )W ˆ ih xa ˆ ih xa ) − σ (W ˜ ho σ(W V˙ 1 ≤ −ΛS∆ + tr S∆ W ˜ T w. ˆ ho σ (W ˆ ih xa )W ˜ ih xa + k˜ −v 2 cos(θ−α) δe S∆ +|S∆ |b +tr S∆ W (23) On the other hand, the time derivative of V2 is T T ˜ ho Γ −1 W ˜ ih Γ −1 W ˆ˙ ) − tr(W ˆ˙ ) − Γ −1 k˜ kˆ˙ − b ˆ˙ ˜ T w−1 b. V˙ 2 = −tr(W ho ih ho ih k
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Substituing the parameter estimation laws (16), (17), (18), and (19), and the control law (14) into the above equation yields T T ˜ T w−1 b ˆ˙ ˆ˙ ) − tr(W ˆ˙ ) − Γ −1 k˜ kˆ˙ − b ˜ ho Γ −1 W ˜ ih Γ −1 W V˙ 2 = −tr(W ho ih ho ih k ˆ ih xa ) − σ (W ˜ ho σ(W ˆ ih xa )W ˆ ih xa = −tr S∆ W ˆ ih xa )W ˜ ih xa − k˜ −v 2 cos(θ − α) δe S∆ −|S∆ |b ˜ T w. ˆ ho σ (W −tr S∆ W
(24) Combining (23) and (24) leads to 2 V˙ ≤ −ΛS∆ .
(25)
(2) Case 2: If |S| ≤ ε, then S∆ = 0. Hence, V˙ = 0.
(26)
Considering the above two cases, (25) and (26) obviously imply that : (1) S∆ , ˜ ho , W ˜ ih , and w are all bounded; (2) S∆ ∈ L2 . According to the boundedness W of all the adjustable parameters, we can straightforwardly see that δe , uc , and ∞ S˙ ∆ are also bounded. Furthermore, limt→∞ 0 S∆ dt is bounded, and S∆ is uniformly continuous. Applying the Barbalat Lemma [12] yields lim S∆ = 0,
t→∞
(27)
which implies that the depth tracking error will asymptotically converge to a neighborhood of zero.
5
AUV Case Study
The simulation study is based on the model structure of certain AUV developed in [14]. Preset the expected cruising depth yem = 50m. Assume the following initial conditions: v = 30m/s, ye = 0; ωz1 (0) = 0. Then we employ a feedforward NN with the structure - 8 inputs, 10hidden neurons, and 1 output - to approximate the uncertain nonlinearity. The adaptive update gain matrices are set to be Γho = diag(5, · · · , 5) ∈ IR10×10 , Γih = diag(0.2, · · · , 0.2) ∈ IR8×8 , and Γk = 0.05, and all the initial weights are set to 0. For the sliding surface, we choose S = e˙ + 4e, and ε = 0.3. Figure 4 illustrates the depth response of the AUV (ye ), and Figure 5 shows the control input (δe ) - the stern plane deflection. A better performance may be obtained by further tuning the update gain and increasing the number of neurons in the hidden layer. A higher update gain gave a better tracking performance but, when the gain was too high, oscillatory behavior may happen.
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Fig. 4. Depth response of the AUV (ye )
Fig. 5. Control input - the stern plane deflection of the AUV (δe )
6
Conclusion
An adaptive NN controller for an AUV’s depth control system has been developed. The NN controller offers guaranteed tracking performance. Feedforward NN has been used to on-line approximate the uncertain nonlinear dynamics of the AUV. Without explicit prior knowledge of the vehicle dynamics, the proposed control technique could achieve satisfied tracking performance, and all the adjustable parameters involved are bounded during the course. Case studies show the effectiveness of the proposed method for AUV system. Whereas this work is only for the AUV’s depth channel, the next stage of the study is to apply the proposed NN based adaptive control scheme for AUV’s three-channel control system design.
References 1. Curtin, T. B., Bellingham, J. G., Catipovic, J., Webb, D. Autonomous Oceanographic Sampling Networks. Oceanography. 6 (1989) 86–94 2. DeBitetto, P. A.: Fuzzy Logic for Depth Control of Unmanned Undersea Vehicles. Proc. Symposium of Autonomous Underwater Vehicle Technology. (1994) 233–241
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3. Fossen, T.: Guidance and Control of Ocean Vehicles. Chichester: Wiley. (1994) 4. Fu, L.C., Chang, W.D., Yang, J.H., Kuo, T.S.: Adaptive Robust Bank-to-turn Missile Autopilot Design using Neural Networks. Journal of Guidance, Control, and Dynamics. 20 (1997) 346–354 5. Funahashi, K.I.: On the Approximate Realization of Continuous Mappings by Neural Networks. Neural Networks. 2. (1989) 183–192 6. Healey, A. J., Lienard, D.: Multivariable Sliding Mode Control for Autonomous Diving and Steering of Unmanned Underwater Vehicles. IEEE Journal of Oceanic Engineering. 18 (1993) 327–339 7. Hornik, K., Stinchcombe, M., White, H.: Multilayer Feedfroward Networks are Universal Approximators. Neural Networks. 2 (1989) 359–366 8. Ishii, K., Fujii, T., Ura, T.: Neural Network System for Online Controller Adaptation and its Application to Underwater Robot. Proc. IEEE International Conference on Robotics & Automation. (1998) 756–761 9. Kato, N.: Applications of Fuzzy Algorithm to Guidance and Control of Underwater Vehicles. Underwater Robotic Vehicles: Design and Control. J. Yuh (Ed.), TSI: Albuquerque. (1995) 10. Nakamura, Y.,Savant, S.: Nonlinear Tracking Control of Autonomous Underwater Vehicles. Proc. IEEE Int. Conf. on Robotics and Automation. 3. (1992) A4–A9 11. Nie, J., Yuh, J., Kardash, E., Fossen, T. I.: Onboard Sensor-based Adaptive Control of Small UUVs in the Very Shallow Water. Proc. IFAC-Control Applications in Marine Systems. Fukuoka, Japan. (1998) 201–206 12. Slotine, J.J. E., Li, W.: Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs. (1991) 13. Valavanis, K. P., Gracanin, D., Matijasevic, M., Kolluru, R.,: Demetriou, Control Architecture for Autonomous Underwater Vehicles. IEEE Contr. Syst.. (1997) 48– 64 14. Xu, D., Ren,., Yan, W.: Control Systems for Autonomous Underwater Vehicle. Xi’an: NPUP. (1990) 15. Xu, D., Yan, W., Shi, Y.: Nonlinear Variable Structure Double Mode Control of Autonomous Underwater Vehicles. Proc. IEEE International Symposium on Underwater Technology. Tokyo. (1990) 425–430 16. Yuh, J.: A Neural Net Controller for Underwater Robotic Vehicles. IEEE Journal Oceanic Engineering. 15 (1990) 161–166 17. Yuh, J.: Learning Control for Underwater Robotic Vehicles. IEEE Control System Magazine. 14 (1994) 39–46 18. Yuh, J.: An Adaptive and Learning Control System for Underwater Robots. Proc. 13th World Congress International Federation of Automatic Control. San Francisco, CA. A (1996) 145–150 19. Yuh, J.: Design and Control of Autonomous Underwater Robots: a Survey. Autonomous Robots. (2000) 7–24
Adaptive Fuzzy Sliding-Mode Control for Non-minimum Phase Overload System of Missile Yongping Bao1, Wenchao Du2,3, Daquan Tang4, Xiuzhen Yang5, and Jinyong Yu5 1
School of Mathematics and Information, Lu Dong University,Yantai,264001, P.R. China [email protected] 2 Graduate Students’ Brigade, Naval Aeronautical Engineering Institute, Yantai 264001, P.R. China 3 Special Missiles Representatives Office in Beijing of Military Representatives Bureau of NED in Tianjin, Beijing, 100076, P.R. China 4 School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics,Beijing 100083, P.R. China 5 Department of Automatic Control Engineering, Naval Aeronautical Engineering Institute, Yantai 264001, P.R. China
Abstract. An adaptive fuzzy logic system is incorporated with the Varibale Structure Control (VSC) system for the purpose of improving the performance of the control system. A sliding surface with an additional tunable parameter is defined as a new output based on the idea of output redefinition, as a result the overload system of missile with the characteristic of non-minimum phase can be transformed into minimum-phase system by tuning the parameters of the sliding surface, and a sliding-mode controller can be designed. For the existence of uncertainty of the parameters, a fuzzy logic system is used to approximate it, thus the chattering effects can be alleviated. Finally, the simulation results have been given to show the effectiveness of the proposed control scheme.
phase system is not stable, the feedforward controller can not be used unless the desired input or the upper bound of the input is known. Conventional sliding-mode control can not be applied to the system with non-minimum phase, because its equivalent control term tends to infinity, such that Shkolnikov and Yuri B.Shtessel[4] designed dynamic sliding mode control for non-minimum phase systems. The acceleration system of tail-controlled missiles is a non-minimum phase system, namely the tail fins deflection first generates a small force on the fin opposed to the desired acceleration. In [5], the approximating lineariztion and feedback linearization is adopted, the dynamic model of missile is transformed into minimum phase parametric affine model. In [6] the model of missile with the acceleration as the output is simplified as a minimum phase system via partly linearization and singular perturbation-like technique, and I/O is exactly linearized. In [7], output redefinition and inversion is used to deal with the non-minimum phase characteristic of missile. In this paper, a new sliding surface with an additional tunable parameter is defined as a new output, thus output redefinition can be combined with Sliding-Mode Control(SMC) perfectly, and the non-minimum phase system of the missile overload can be controlled. Besides, fuzzy logic system is used to approximate the uncertain part of system, so that the control gain of SMC can be more fitting, and the chattering effect can be alleviated. This paper is organized as follows. In Section II, the original overload system of missile is transformed into a new one by refining a sliding surface as a new output. In Section III, a fuzzy sliding mode controller is designed and the stability is proved via Lyapunov stability theorem. In Section IV, a simulation example is provided to illustrate the performance of the proposed control scheme. Conclusion remarks are finally made in Section V.
2 Description of Missile Overload System Conventional acceleration model of the pitch channel of missiles [7] concludes three equations, but some researchers often treat the motor as a one order system, thus the control to design is not fin deflection but the control voltage, and the total equations are as follows
ω z = a24α + a22ω z + a25δ z
(1a)
α = ω z − a34α − a35δ z
(1b)
δz = − wδ z + wuδ
(1c)
ny = Where
ω z in(1a)
v v a34α + a35δ z g g
is angular acceleration ,
α
in (1b) is attack angle,
(1d)
n y in (1d) is
overload. (1a), (1b) and (1d) formulate the acceleration model of the pitch channel of missiles. (1d) is the mode of the motor. In Appendix a conclusion is given that the derivation of the overload is approximately proportional to the angular acceleration,
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which can be expressed as
221
V n yb ≈ ω z . In the control scheme proposed in this paper, g
the derivation of the overload is only play the role of damping, so that the value of it precise or not is not a matter of cardinal significance. When the angular acceleration is used to replace the derivation of the overload, the sliding surface chosen as (2) becomes meaningful.
S = k1 (n y − n yd ) + k 2 (ω z − ω zd )
(2)
Where k1 is an additional tunable parameter which can not be seen in the traditional from of sliding surface. Take the sliding surface as new output , after some mathematical manipulations, it can obtain that
= −A1S 2 − A2 S ≤0 thus the asymptotical stability of the system can be guaranteed. When there exists uncertainty, (3) can be changed into the following form
f = ( m 31 + ∆ m 31 )α + ( m 32 + ∆ m 32 )ω z + ( m 33 + ∆ m 33 ) S + D 3 + ∆ D 3
(17)
g = b + ∆b
(18)
S = f + gu δ
(19)
then (16) can be rewritten as
For the existence of uncertainty, fuzzy logic system is introduced to approximate it, which is not to tune the weights but the centers of the member function of the output. And the bell member functions are expressed in the form of (20)
µ ij (u j ) = 1 /(1 + where
u j − cij
2 bij
aij
)
(20)
cij presents the center of the member function, a ij determine the width of the
bell function and
bij characterize the slope. And the following rule sets are adoped
IF u1 is U1 AND um is Um THENF =ξi Rulei
i = 1,2,...R ,
(21)
Where u and F are input and output of the FLC , U i and ξ i are input and output linguistic variables. For FLS we chose product-operation rule of fuzzy implication and center of average deffuzifier as (22)
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m
i =1
j =1
R
m
FTOTAL = ¦ ξ i ∏ µ ij (u j ) / ¦∏ µ ij (u j ) i =1 j =1
R
(22)
= ¦ ξ iω ni = ξ T ω n i =1
where m
R
m
ω ni = ∏ µ ij (u j ) / ¦∏ µ ij (u j )
(23)
i =1 j =1
j =1
R, m are numbers of rules and inputs, ω ni is the ith element of the vector
ω n = (ω n1 , ω n 2 ,..., ω nR ) T ,for SISO FLC , m = 1 . Let
f = f + ∆f
(24)
g = g + ∆g
(25)
where f = m 31α + m 32 ω z + m 33 S + D 3 , ∆ f = ∆ m 31α + ∆ m 32ω z + ∆ m 33 S + ∆ D3 ,
g =b
㧘 ∆ g = ∆ b , then (16) can be rewritten as
S = f + ∆ f + ( g + ∆ g ) u δ
(26)
Fuzzy logic system is adopted to approximate ∆f , ∆g , that is T ∆fˆ = ξˆ f ω nf
(27)
T ∆gˆ = ξˆg ω ng
(28)
Firstly, define optimal parameters ξ f , *
ξ g * and minimal approximating error
me = (∆f − ∆f * ) − ~
Let ξ f
* = ξ f − ξˆ f
㧘 ξ~
(∆g − ∆g * ) uδ g + ∆gˆ
(29)
* = ξ g − ξˆg
g
And the following theorem can be got. Theorem 1: If control laws and adaptive laws are adopted as shown in(30)-(33)
ξˆ f = l1ω nf S
ξˆg = −
1 l 2ω ng uδ S g + ∆gˆ
(30) (31)
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uc = − ua =
Where
1 ( f + ∆ fˆ + A1 S ) g + ∆ gˆ 1 ( − A 2 sign ( S )) g + ∆ gˆ
225
(32)
(33)
l1 ,l 2 and A1 , A2 are positive real numbers, and A2 > me , then the system
(16) stable asymptotically. Proof Choose the candidate Lyapunov function as
V1 =
1 2 1 ~T~ 1 ~T~ ξg ξg S + ξf ξf + 2 2l1 2l2
(34)
derivate it, we will have
1 ~ T ~ 1 ~ T ~ V1 = SS + ξ f ξ f + ξ g ξ g l1 l2 = S{ f + ∆f + ( g + ∆g)[− −
1 ( f + ∆fˆ + A1S ) g + ∆gˆ
1 T~ T~ A2 sign(S )]} − Sωnf ξ f − Sωng ξ g uδ ˆ g + ∆g g + ∆g )uc − A1S − A2 sign(S ) = S{ f + ∆f − f − ∆fˆ + (1 − g + ∆gˆ
g + ∆g T~ T~ ) A2 sign(S )]} − Sωnf ξ f + Sωng ξ g uδ g + ∆gˆ ∆g~ + (∆g − ∆g * ) ~ uδ − A1S = S (∆f + (∆f − ∆f * ) − g + ∆gˆ T~ T~ − A2 sign(S )) − Sωnf ξ f + Sωng ξ g uδ
+ (1 −
~T = S (ξ f ωnf −
1 ~T 1 ~ ~ ξ g ωnguδ − ωnf Tξ f + ωngTξ g uδ g + ∆gˆ g + ∆gˆ
− A1S − A2 sign(S ) + (∆f − ∆f * ) −
(∆g − ∆g * ) uδ ) g + ∆gˆ
= S (− A1S − A2 sign(S ) + me ) ≤ − A1S 2 − ( A2 − me ) S ≤0 thus the asymptotical stability of the system can be guaranteed.
(35)
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4 Simulation
n
y
Į̬e
/g
Take the pitch channel overload model of some missile as an example, suppose the model of the motor is a one order system as − 17 (s + 17) , to verify the correctness and
t(s)
t(s) Fig. 1. Response curve of overload
α
Ȧ
z
u̬ V
(DŽ
Fig. 2. Response curve of
t(s) t(s)
ωz
Fig. 4. Curve of control voltage
n
y
S
/g
Fig. 3. Response curve of
t(s)
t(s) Fig. 5. Response curve of
S
Fig. 6. Response curves of verloadwith ± 20% parameter perturbation
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effectiveness of the proposed control scheme, simulations are made for the nominal system and the system with parameter perturbation respectively when the reference input is square wave signal. The simulation results are shown as Figure1-6, where Figure1-5 are for the nominal system, the curve of overload is given in Figure 1,the curve of α is given in Figure 2, the curve of ω z is given in Figure 3, and the curve of control voltage is given in Figure 4, the curve of sliding surface is given in Figure 5. Curves of the overload with ± 20% parameter perturbation are shown in Figure 6(solid line for + 20% ,dashed line for − 20% ).
5 Conclusion In this paper, an adaptive fuzzy logic system is incorporated with the VSC system for the purpose of improving the performance of the control system. A sliding surface with an additional tunable parameter is defined as a new output based on the idea of output redefinition, as a result the overload system of missile with the characteristic of non-minimum phase can be transformed into minimum-phase system by tuning the parameters of the sliding surface, and a sliding-mode controller can be designed. For the existence of uncertainty of the parameters, a fuzzy logic system is used to approximate it, thus the chattering effects can be alleviated. Finally, the simulation results have been given to show the effectiveness of the proposed control scheme.
References 1. Kravaris, C., Wright, R.A.: Nonminimum-phase Compensation for Nonlinear Processes. AIChE. J. 38 (1992) 26-40 2. Yang, H., Hariharn, K., Marcelo, H.: Tip-trajectory Tracking Control of Single-link Flexible Robots via Output Redefinition. Proceedings of International Conference on Robotics and Automation Detroit, Michigan. (1999) 1102-1107 3. Zinober, A., Owens, D. (Eds.): Nonlinear and Adaptive Control. LNCIS 281, Springer-Verlag Berlin Heidelberg (2003) 239-248 4. Iiya, A.S., Yuri, B.S.: Aircraft Nonminimum Phase Control in Dynamic Sliding Manifolds. Journal of guidance ,control and dynamics, 24(3) (2001) 566-572 5. Chwa, D.K., Choi, J.Y.: New Parametric Affine Modeling and Control for Skid-toTurn Missiles. IEEE Transactions on Control Systems Technology, 9(2) (2001) 335-347 6. Lee, J.I., Ha, I.J.: Autopilot Design for Highly Maneuvering STT Missiles via Singular Perturbation-Like Technique. IEEE Transactions on Control System Technology, 7(5) (1999) 527-541 7. Ryu, J.H., Park, C.S., Tank, M.J.: Plant Inversion Control of Tail-Controlled Missiles. AIAA-97. 3766 (1997) 1691-1696
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Appendix To make the sliding surface S = k1 ( n y − n yd ) + k 2 (ω z − ω zd ) converge,
ω z
should be proportional to n y , which will be proved in the following conclusion. Conclusion 1: The acceleration of angular is approximately proportional to the derivation of overload of missile Proof Take the pitch channel model as an example, there exists the following relation
α = ω z − a34α − a35δ z
(A1)
V (a34α + a35δ z ) g
(A2)
n y =
substitute (A1) into (A2), it can obtain that
n y =
V (ω z − α ) g
(A3)
V (ω z − α) g
(A4)
derivate (A3) and we will have
n y =
Because α is not easy to obtain and the value of which in small compared with the relation of (A5) can be got.
n y ≈
V ω z g
ω z , so (A5)
An Improved Genetic & Ant Colony Optimization Algorithm and Its Applications Tiaoping Fu1,2, Yushu Liu1, Jiguo Zeng1, and Jianhua Chen2 1
School of Computer Science and Technology, Beijing Institute of Technology, Beijing 100081, China [email protected] 2 Naval Arms Command Academy, Guangzhou 510430, China
Abstract. It is a crucial research to improve the efficiency of weapon-target assignment (WTA) of warship formation. However, the WTA problem is NP hard. Some heuristic intelligent algorithms usually result in local optimal. A novel genetic & ant colony optimization (GACO) algorithm is proposed which is based on the combination of genetic algorithm and ant colony algorithm. Genetic algorithm phase adopts crowding replacement and changeable mutation operator to create multiple populations. Due to the good initial pheromone distribution, ant colony optimization phase can avoid getting into local optimal. Then, a further study of how to use the algorithm on WTA is made. Some experiments are made. The results demonstrate that GACO has better efficiency than other classical algorithms. The bigger the WTA problem is concerned, the more advantage the algorithm makes. The proposed algorithm is viable for other NP-hard problems.
At the aspect of WTA problem, people bring forward many methods such as neural networks, genetic algorithms with greedy eugenics, expert system. However, these algorithm all have their advantage and shortage, cannot give attention to both speed and quality performances, so is hard to fit the real-time and precise firepower distribution demand of warship formation anti-air missiles attacking numerous targets. Facing for the urgent requirement, avoiding the shortage of present algorithm, an improved genetic & ant colony optimization (GACO) algorithm based on the combination of genetic algorithm and ant colony algorithm is proposed.
2 Air Defense WTA Problem for Warship Formation 2.1 Analyzation of WTA Problem Weapon-target assignment problem is an important research which make all weapons in a region cooperate action for protecting the own-force assets. Its mission is exerting multiple weapons colligating advantage as a whole, finding an optimal assignment of weapons to targets for a scenario with the objective of minimizing the expected threat of own warship formation. We have know the characters of assaulting target and anti-air missiles units and n ≥ m (when assaulting targets is more than anti-air missiles units or m > n , we can choose the n most dangerous assaulting targets based on the threat parameters and deal with other target in other groups). Aerial threat toward warship formation is very fearful. In the actual operation, the survival of formation is much more important than the cost of operation. In other words, we will not think over using the cheaper weapon resource but the safety of the warship formation can be confirmed. So, we proposed: we should stress on the protection of warship formation operation capability when assigning weapons to targets. Then, the considered WTA problems are to minimize the following colligation threat parameters function: m ª n x º min C = ¦ v j «∏ (1 − kij ) ij » j =1 ¬ i =1 ¼
(1)
Paying attention less to the cost of operation, but we take the threat parameter of every target into count during the WTA course. Thus, the direct results are reducing the dashing probability of the most dangerous targets and getting the basic intention of anti-air operation. On the other hand, the design will improve the algorithm efficiency greatly and meet the real-time requirement of decision-making. xij is decision variable. When weapon i attacks target j , xij = 1 , otherwise,
xij = 0 . v j is the threat parameter of target j . Threat parameter has relation with distance, bearing, speed of coming target and moving speed, direction of warship formation etc. kij is the damage probability of weapon i to target j . Also, we can get
kij by distance, bearing, speed of coming target and weapons capability of warship formation.
kij can be provided by C3I system of warship formation platform.
An Improved GACO Algorithm and Its Applications n
st.
¦x
ij
≤ g i , ( j = 1, 2, , m)
(2)
i =1
m
¦x
ij
≤ 1,
231
( i = 1,2,, n)
(3)
( i = 1,2,,n ; j = 1,2,,m)
(4)
j =1
xij ∈{0,1}
Formulation (2) replaces that the weapons assigned to target j can not exceed at some time. Formulation (3) represents that weapon some time.
i
gi
can only attack one target at
2.2 Computation of Target Threat Parameter The problem of threat judgment has relation with many factors, but these factors themselves are uncertain. However, fuzzy theory is a good tool to solve this kind of uncertain problem. Threat parameter has relation with distance, bearing, speed of coming target and moving speed, direction of warship formation etc which expressed by variable γ . Shown in Fig.1, we suppose warship formation lies on point W, target lies on point T. VT V ș VW
T
d
W Fig. 1. Sketch of the situation between the target and ship formation
We
suppose
there
are
target
Ti , their attribution parameters are
di , θ i , VRi (i=1,2,3…..n). When have n target, their attribution parameters are di ' , θ i ' , Vi ' after dealt without dimension. Thus, we can get the threat variable of each parameter γid , γiθ , γiV [2] , then, we can get the colligation threat value of target i toward warship formation. Then, we can put the threat value
vi got by ( F * γ ) 1/ 2
into the goal function of warship formation anti-air WTA optimization.
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3 The Improved Genetic & Ant Colony Optimization Algorithm for WTA Problem 3.1 Design of Improved Genetic Algorithm in GACO Algorithm Some researches have been done on the combination of genetic algorithm and ant colony optimization algorithm. But they mainly focus on the combination of simple genetic and ant colony optimization algorithm. However, they have some shortages. For example, the population variety of simple genetic algorithm is poor. It is easy to get into local optimal when the evolution generations are still very few. When ant colony optimization algorithm continues anaphase search based on the local Pareto optimum solutions, the entirely astringency of ant colony optimization is hard to ensure. If we increase the evolution generations of anaphase algorithm simply, the runtime of algorithm will increase greatly, the advantage of combination algorithm will disappear. It is a good way to maintain the variety of population by using crowding replacement. Crowding replacement can prevent the individual of high fitness from overpopulated by restricting that filial generation can only replace nearest parental generation. On the other hand, the property of individual that distance is farther has much more difference. Thus, the algorithm can get individuals that distance is farther and property has more difference when adopting crowding replacement. The implementation flow of genetic algorithm using crowding replacement in GACO is shown as: Step 1: Initialization Firstly, initial population and adaptive function is set in reason based on the character of the WTA problem. Real-number encoding can be closer to the problem, has strongpoint thereinafter: ameliorating the computing complexity and improving the computing efficiency of genetic algorithm; convenient for the hybrid with other classical optimization algorithm; good for designing genetic operator contraposing the problem; convenient for dealing with the complex constraint conditions. So, we adopted the real-number encoding in chromosome.
Ԙ
ԙ
Ԛ
ԛ
The chromosome string of the ith individual
xti of the tth generation is
aik11 aik22 ainkn . Thereinto n is the length of chromosome string, corresponding to the target number; gene bit
k
aij j replaces the serial number of weapon allocating to the
assaulting target in weapon units set:
k
a ij j
0 ° ° =® °k j °¯
no target unit allocates to the i th w eapon the k j target unit allocates to the i th w eapon, k j ∈ {0,1, 2, , m }
(5)
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Choose s individuals in the feasible region of solution space(s is the scale of colony, representing the s allocation plan), build up the initial colony X t {xti | i 12"V}. Step 2: Tournament option operators During the anaphase of genetic algorithm, the adaptability values of individuals in colony are equal approximately. Thus, if we choosing operators according to the adaptability values proportion simply, the choosing strength is poor. Tournament option operators has the function of automatically adjusting adaptability values proportion, choosing strength having nothing to do with the relative adaptability values among individuals, fitting for joining with crowding replacement especially. So, we adopt tournament option operators [3] choosing individuals to multiply. The tournament scale of tournament option is Size , the numeric area is [2, N]. The tournament scale has the relation formula with choosing strength and multiformity loss as SelIntTour (Size) = 2(log(Size) − log 4.14 log(Size) ) LossDivSize ( Size ) = Tour
1 − Size −1
− Tour
(6)
Size − Size −1
(7) ~
xts based on their fitness δ ( X ) and Size individuals are chosen from xt1᧨xt2᧨ the individuals of highest fitness to multiply set are saved to form the multiply
xt . set xt ᧨xt ᧨ Step 3: Crossover operators '1
'2
's
Choose two individuals
xt'i᧨xt'j ∈ xt'1᧨xt'2᧨ xt' s , deletes xt'i᧨xt'j from
xt'1 , xt'2 , xt's . Take
xt'i᧨xt'j as parents to disperse recombined, their offspring are xt'' k , xt''l . '' k
''l
'i
'j
''1
''2
'' s
Choose xt , xt or xt , xt to add into xt , xt ,, xt . Repeat the process s/2 times. Step 4: Time varying mutation operators If n bits of all chromosomes in whole colony get the same value, the searching space is only (1/ 2) n of the whole space when purely through crossover computing. This will decrease searching space greatly. Thus, we must adopt mutation operators to change the premature phenomena. Already having many experimental compare researches, the judgment of mutation is more important than crossover sometimes has been affirmed. Essentially, GA is a process of dynamic and adaptability. It will departure from the evolution spirit if adopting the way of fixing parameters. So, we hope modifying the value of strategy parameters during the GA computing course [4]. In our paper, we modify strategy parameters obeying the certain rule, changing the parameters based on genetic generations. Initial stages of algorithm, adopt larger mutation value, avoiding prematurity and maintaining the colony multiformity. Following the increasing of the genetic generations, mutation value drops continuously, making the computing converge to global optimization. The way is given by
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pm = 0.3 − 0.2×t / G
(8)
t is genetic generations, G is the total generations. ''1 ''2 xt''s to form next Based on mutation probability, mutation disturbs for xt ᧨xt ᧨ i "V}. generation colony Xt 1 {xt 1 | i 12
where
Step 5: Individual crowding replacement As for xti+1 , 1 ≤ i ≤ S , suppose xt j , 1 ≤ j ≤ S is the nearest parent individual, also mean Euclid distance d ( xti+1 , xti ) is shortest. The d ( xti+1 , xti ) is given by d ( xti+1 , xti ) = (aik11 − a kj11 ) 2 + ( aik22 − a kj 22 ) 2 + (ainkn − a kjnn )
(9)
If δ ( xti+1 ) > δ ( xti ) , replacing xt by xt +1 , otherwise, reserving xt . Step 6: If currently generation t reaches the total iteration times tmax , then break and save the computing result. Otherwise, t++, turn to Step2. Step 7: Put finally colony into objective function, get the r Pareto optimum solutions, code these chromosomes of r Pareto optimum solutions, get r optimal assignments of weapon units to targets, keep the r assignments as the inputting of anaphase algorithm. i
i
i
3.2 Design and Link of Ant Colony Optimization Algorithm in GACO Algorithm Ant colony optimization was used to solve TSP problem [5] originally, searching the shortest route among all cities through ant colony randomly searching under the inspire of pheromone. In order that ACO can be used to WTA problem, in this paper, we express WTA problem into bipartite graph G=(V U E). V is the set of n points, representing n weapon units separately, corresponding n nodes of one side of bipartite graph. U is the set of m points, representing m targets separately, corresponding m nodes of the other side of bipartite graph. E is the border joining targets nodes with weapon units nodes E = {eij | i = 1,2,n; j = 1,2,m} . If some weapon unit i is
㧘㧘
assigned to target j, there is a border Otherwise, there isn’t border.
τ ij
between weapon unit i and target j,
eij linking weapon unit i with target j.
is the trace of border
eij . If there isn’t border
τ ij = 0 . The feasible route composed with many
borders in bipartite graph, is correspond with an assignment project between targets set and weapon units set. So, seeking the optimal solution on WTA problem is searching the optimal route in bipartite graph. The ant colony optimization in GACO is described as: Step 1: Initialization (1) encode r optimal assignments of former phase(GA), form the initial r routes of ant colony optimization. (2) the initial pheromone distribution between target set and weapon unit set is given by
An Improved GACO Algorithm and Its Applications
τ ij (t0 ) = τ 0 + ∆τ ij ; i = 1, 2, , n; j = 1, 2, , m. where τ ij (t0 ) represents the trace of border
235
(10)
eij at initial time( t0 = 0), τ 0 is
pheromone constant, being a small positive real number.
∆τ ij is given by
r
∆τ ij = ¦ ∆τ ijk
(11)
k =1
where ∆τ ij represents the trace of border k
eij of route k, r is the optimal assignments
of GA, corresponding the initial r routes. QSk ° ° ∆τijk = ® ° 0 °¯
has border between target j and weapon i in kth assignment project hasn't border between target j and
(12)
weapon i in kth assignment project
where Q is adjustment parameter, S k is the objective function value of the kth assignment project. (3) make every ant correspond with only one weapon node or target node and put the node into weapon Tabu Table or target Tabu Table. Step 2: Node choosing Any ant i (corresponding with weapon node i) chooses target node j basing on β °arg max j∈allowi [τ ij (t )(ηij ) ] j=® J °¯
when q ≤ q0 otherwise
where q0 is the threshold value enacted in advance,
(13)
q0 =0.9, q is a random number
uniformly distributing in (0, 1), allowi is the set of all the targets which still now is not assigned to ant i, τ ij (t ) is the trace between weapon i and target j at time t. On WTA problem, the mathematical models of ηij are given based on different optimal rule. For example, we need decrease the threat value toward warship formation to maximum extent. The mathematical model should be the arithmetic product of damage probability kij and the threat value v j of target j.
ηij = kij × v j
(14)
J is the serial number of some weapon in allowi set, the value of J is decided by the way of roulette based on probability
Pis (t )
τ ij ( t )(η ij ) β °° β Pij ( t ) = ® ¦ τ ij ( t )(η ij ) j∈allowi ° 0 °¯
j ∈ allowi other
(15)
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Step 3: Local pheromone updating After every ant chooses its target node, use “local pheromone update” to update the trace of border eij .
τ ij (t + 1) = (1 −ψ )τ ij (t ) + ψ∆τ
(16)
where 0 < ψ ≤ 1 is a constant, representing the volatilization probability.
∆τ ij =
Q cbjk
(17)
k
where cbj is the total benefit of the current ant k from first node to now. One result of “local pheromone update” is that ants will not converge to a single route. Approved by experiment, the way is good for finding more latency optimal solutions and improves the quality of searching. Otherwise, all ants probably trap in an extraordinary small searching interspace. Step 4: Check of finishing node assignment (1) after all ants choose their target nodes and local update pheromone, set the Recorder Stack of ants. If the assigned weapons to the targets nodes have reached the maximum limitation, the target node will be set in the Recorder Stack of ant. Then ant moves to the next null weapon node which has not been assigned any target. Turn to Step 2. (2) if all weapon nodes have been traversed, then turn to Step 5. Step 5: Whole pheromone update After all ants having traversed all targets nodes, m solutions have been built up. These m solutions were taken into objective function and get the local optimal solutions. The best solution is preserved, using “whole pheromone update” to update the trace of borders of the best solution. The update rule of the “whole pheromone update” is given by
τ ij (t + 1) = (1 − ρ )τ ij (t ) + ρ∆τ ij (t )
(18)
where 0 < ρ ≤ 1 is the parameter which controls the attenuation process of pheromone. 1 ° ∆τ ij (t ) = ® C elitist °¯ 0
if ij is one border of the best assignment otherwise
(19)
Step 6: Check of finishing evolution If currently generation t reaches the total iteration times Tmax, loop is terminated and the optimization resolution is got. Otherwise, turn to Step 2. 3.3 Flow of Warship Formation WTA Problem Based on GACO Algorithm In the first phase of computing, adopts genetic algorithm, making full use of the GA’s characters of rapidity, randomicity and global astringency. Its function is producing initial pheromone distribution of certain problem for next phase. In the second phase
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of algorithm, adopts ant colony optimization. Under the circumstances of having initial pheromone distribution, ant colony optimization converges on the optimal path through pheromone accumulation, renewal and the parallel processing, global searching ability of ACO. Its overall frame is given in the Fig.2. Warship formation air defense WTA Define object function based on decreasing threat to maximum extent Create a set of real-number encoding randomly
Calculate the probability; ant moves to next node based on the probability
Choose multiply set through tournament option operators
After ant chooses the target node, use “local update” to update border eij trace
Disperse recombine on crossover probability
After n ants traversed m target nodes, use “whole update” to update all borders trace
Mutate disturbance based on time varying operators
Reach genetic generations?
Initialize parameters; create initial pheromone distribution; put n ants on n weapon nodes
No
Yes Create some sets of optimal solution
Stop criterion satisfied?
No
Yes Optimal solutions output
Fig. 2. Flow of warship formation WTA based on GACO
4 Experimental Results and Analysis We make experiments aiming at air defense missile-target assignment problem of warship formation to test the performance of GACO. We suppose that the formation has eight missile weapon units, facing for eight targets at the same time. The threat values of these targets to formation and the damage probability of every missile to these targets are different. The damage probability kij can be calculated based on distance, bearing, speed of coming target and the missiles performance of warship formation.
kij is provided by
C 3 I system of warship formation. The genetic generations of GA in GACO are 20; crossover probability initial mutation probability
pcross =0.6;
pmutation =0.3. Initial pheromone of every routs of ACO is
60; trace update parameter ρ =0.2, ψ =0.2, iteration times are 30. As for 8 missiles assign to 8 targets problem, we adopt GACO and GAGE [1] algorithms which can meet the real-time demand in air defense missile-target assignment problem of warship
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fitness value
Fig. 3. The fitness curves of GACO and GAGE
formation. All experiments are performed on a 2.8GHz machine with 512 megabytes main memory. Programs are written in Windows/Visual C++ 6.0. The comparing results of the two algorithms are shown in the Fig.3. As a whole, the fitness value of GACO and GAGE drops following the generations continuously. The fitness curve descending extent of GA in GACO prophase is less than GAGE. The cause may lie in GAGE has been imported with Greedy Eugenics. The fitness value descending extent of GA anaphase in GACO becomes slow continuously. The cause may lie in GA is helpless for the using of feedback information in system. When computing to more generations, usually makes redundancy iteration and has low efficiency when searching precision solution. However, because GACO adopts the design of crowding replacement , time varying mutation operators and makes full use of the GA’s characters of randomicity and global astringency, it can maintain the variety of population well and produce good initial pheromone distribution for ACO. During ACO phase in GACO, the fitness value drop greatly, finally, the optimization value stabilizes at a number lower than GAGE’s. The cause lies that ACO has good initial pheromone distribution and makes use of the characters of parallel processing and positive feedback, realizing to find further precision solutions and avoid getting into local optimal. So, GACO has better optimization performance and speed performance than GAGE when solving the problem of air defense missile-target assignment. For testing the performance of GACO on cosmically assignment problem, we compare GACO with other intelligent optimization algorithms, for example: GA, GAGE, Simple Genetic & Ant Algorithm [6](GAAA), Niching Genetic and Ant Algorithm[7](NGAA). The results are shown in the Table.1. The strategy parameters of GA and ant colony algorithm are same as GACO for confirming the fairness. The number out of bracket is optimization value of objective function; the number in bracket is operation time of every algorithm. We can see from the Table.1, GACO has better effective and efficient performance than the other four algorithms obviously. The bigger the assignment problem is concerned, the more advantage the algorithm makes.
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Table 1. Comparison of optimization performance and speed performance among algorithms Algorithms GA GAGE GAAA
5 Conclusions The improved genetic & ant colony optimization adopts the advantages of genetic and ant colony optimization, overcoming their shortage and achieving a good result when using on WTA problem of warship formation. We make experiments on the algorithm and compare the experimental results with other algorithms. The results demonstrate: GACO has good searching efficiency and speed performance; GACO is a preferable optimization algorithm and can meet the real-time and precision demand in WTA problem. GACO is also viable for other NP-hard problems. Following the increasing of problem scale, the improvement is more greatly. Acknowledgments. This work was partially supported by the National Defense Science Foundation of China (Grant No. 10504033). We would like to thank Doctor. Yunfei Chen for his helpful and constructive comments.
References 1. Lee, Z. J.: Efficiently Solving General Weapon-Target Assignment Problem by Genetic Algorithms with Greedy Eugenics. IEEE Transactions on Systems, 33 (1) (2003) 113-121 2. Hu, S., Z, Y.: Determining the Threatening Degrees of Objects Using Fuzzy Operations. Acta Armarmentarii, 20 (1) (1999) 43-46 (in Chinese) 3. Georges, R. Harik.: Finding Multimodal Solutions Using Restricted Tournament Selection. In Larry. J. Eshelman, editor, Proceedings of the Sixth International Conference on Genetic Algorithms, Morgan Kaufmann, (1995) 24-31 4. Holland, J.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, MI, MIT Press, Cambridge, MA (1992) 5. Dorigo, M.: Bonabeau E, Theraulaz G. Ant Algorithm and Stigmery. Future Generation Computer Systems, 16 (8) (2000) 851-871 6. Kumar, G. M, Haq, A. N.: Hybrid Genetic and Ant Colony Algorithms for Solving Aggregate Production Plan. Journal of Advanced Manufacturing Systems, 4 (1) (2005) 103-111 7. Chen, Y., Liu, Y, Fan, J., Zhao, J.: A Niching Genetic and Ant Algorithm for Generalized Assignment Problem. Transactions of Beijing Institute of Technology, 25 (6) (2005) 490494 (in Chinese)
Application of Adaptive Disturbance Canceling to Attitude Control of Flexible Satellite Ya-qiu Liu, Jun Cao, and Wen-long Song Northeast Forestry University, Harbin 150040, China [email protected], [email protected], [email protected]
Abstract. An adaptive inverse disturbance canceling method of an orbiting flexible satellite during normal pointing for “modal vibration disturbance”, which is difficult to cancel by the PID method since it’s modal frequency low and dense, and damping small, is proposed. Here, the adaptive inverse disturbance canceling, compared with the conventional feedback disturbance rejection method, performs in inner loop and is independent of dynamic response control loop. Since the adaptive inverse disturbance canceling performed is based on the PID control of dynamics response in this paper, the control structure is designed as following. Fist, the conventional PID method is designed for the dynamical control system of rigid satellite. Second, the modal vibration disturbance control is performed by adaptive inverse disturbance canceling method. The key of this approach is estimation of modal vibration disturbance, the difference is between disturbed output of the plant and disturbance-free output of the copy model, which is then input to the disturbance canceling filter which is a least squares inverse of rigid satellite model. Simulation results demonstrate the effectiveness of the controller design strategy for attitude control and modal vibration disturbance suppression.
extending the disturbance canceling method used for linear plants to encompass nonlinear plants as well. The adaptive inverse control has advantages in disturbance canceling [4]. Based on inverse thought the adaptive inverse disturbance canceling has performed in inner loop through a separate adaptive inverse filter, and it is independent of dynamics response control. By handing the problem in this way, we can improve as much as possible performance, a compromise is not required in the design process to obtain good dynamic response and good disturbance control [1,5]. Thus the adaptive inverse canceling method for normal pointing attitude control and vibration suppression of an orbiting spacecraft with flexible appendage is proposed by defining the correlative vibration as “modal vibration disturbance”. The key to this method is regard effect produced in modal vibration as a kind of correlated disturbance on the base of rigid controlling, and disturbance canceling has performed in inner loop separately. In this paper, the rigid spacecraft model and adaptive inverse disturbance canceller is modeled using NARX (Nonlinear AutoRegressive with eXogenous inputs model)[5,6,7], and improved RTRL-LMBP algorithm is designed for improve convergence speed and obtain better effect of disturbance canceling control.
2 Dynamics Description The slewing motion of a rigid hub with flexible appendage attached to the hub is graphically presented in Fig.1. The rotational motion only without any translation of the center of mass of the whole structure is considered in this paper. Define the OXY and oxy as the inertial frame and the frame fixed on the hub, respectively. The attitude angle denotes the relative motion between these two frames. Denote as the flexible deformation at point with respect to the oxy frame. It is assumed that the control torque is applied to the rigid hub only. Using Lagrangian method, the governing equations of motion for the spacecraft model are given by [8].
where Ih is the moment of inertia of the center body; T is the control torque; Fn is coupling coefficients; qn, ςn and pn is modal variable, damping ratio, constrained Modal frequency of the nth modal of flexible appendages respectively.
m
Y
x w(x,t)
¦Ñ, E y R
T
o
θ
O b
Ih
l X
Fig. 1. Spacecraft model with single-axis rotation
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For the latter analysis, the model (1) can be transformed as the following form Is θ ( s ) − 2
¦
Fn s qn ( s ) = T ( s ), qn ( s ) =
− Fn s
2
n
2
s + 2ς pn s + pn 2
2
θ (s)
(2)
where s is the Laplace variable. The transfer function from control torque T to attitude angle ș can be written as: θ ( s) =
1 Is
2
⋅ (1 +
¦s n
Kn ⋅ s 2
2
+ 2ρn Λ n s + Λ n 2
)T ( s ) 1
(3)
where k n = Fn I , K n = k n (1 − k n ) , ρ n = ς (1 − k n ) 2 , Λ n = pn (1 − k n ) . The 2
2
2
block diagram of transfer function is then shown in Fig.2.
T ( s)
1 Is 2
+
¦s n
Kn ⋅ s 2 2 + 2ρn Λn s + Λ2n
θ ( s)
+
Fig. 2. Block diagram for flexible spacecraft with single-axis rotation
3 Dynamic Neural Networks A layered network is a feedforward structure that computes a static nonlinear function. Dynamics is introduced via the taped delay lines at the input to the network, resulting in a dynamic neural network, which is called NARX filter. It is general enough to approximate any nonlinear dynamical system, and either its structure or adaptive algorithm is more complicated than static network, but the ability to describe nonlinear dynamic system is strengthened greatly. 3.1 Adaptive Dynamic System Identification
NARX models have implicit feedback of delayed versions of their output to the input of the model. This feedback is assumed in all block diagrams in Fig. 3. The purpose of Fig. 3 is to show that this feedback, when training an adaptive plant model, may be connected to either the model output or the plant output. The first method is called a parallel connection for system identification, and the second method is called a seriesparallel connection for system identification. Networks configured in series-parallel may be trained using the standard backpropagation algorithm. Networks configured in parallel must be trained with either real-time recurrent learning (RTRL) or backpropagation through time (BPTT). The series-parallel configuration is simple, but is biased by disturbance. The parallel configuration is more complex to train, but is unbiased by disturbance. Therefore, in this work, nonlinear system identification is
Application of Adaptive Disturbance Canceling
243
first performed using the series-parallel configuration to initialize weight values of the plant model. When the weight values converge, the plant model is reconfigured in the parallel configuration and training is allowed to continue. This procedure allows speedy training of the network, but is not compromised by disturbance. Zk
XN 3ODQW
P
yk
yk
6HULHV3DUDOOHO
B
3DUDOOHO 0RGHO
ek
yˆ k
Pˆ
Fig. 3. Adaptive plant modeling
3.2 Adapting Dynamic Neural Networks
LM (Levenberg-Marquardt backpropagation) algorithm is the combination of the steepest decent algorithm with the Gauss-Newton algorithm. Compared with a conjugate gradient algorithm and a variable learning rate algorithm, the LevenbergMarquardt algorithm is much more efficient than either of them on the training steps and accuracy. With the aid of the approximate second derivative, the LM algorithm is more efficient than the gradient method. Therefore, it can be applied to online control. As the matrix is positive definite, the solution always exists, such that LM method is preferable to Gauss-Newton method. To improve training speed, the improved LMBP-RTRL algorithm based on the LM method is proposed. An NARX filter computes a function of the following form yk = f ( xk , xk −1 , , xk − n , yk −1 , yk − 2 , , yk −m , W ).
(4)
The familiar “sum of squared error” cost function is Vk = 1/ 2E (ek ek ). T
(5)
To Stochastic approximate Vk, we need to construct Vk ≈ (1/ 2)ek ek . T
(6)
For adapting NARX filters, it was fist done by RTRL algorithm, defining the Stochastic approximate function (6), where, ek=dk-yk. Then the Jacobians presentation is as follows. J (W )
dy k dW
=
∂y k ∂W
=
dek dW
n
+
¦ i =0
= −
∂y k dxk − i ∂xk − i dW
(7)
dy k dW m
+
¦ i =1
∂y k dy k − i ∂y k − i dW
(8) .
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Y.-q. Liu, J. Cao, and W.-l. Song
The first term ∂yk/∂W in (8) is the direct effect of a change in the weights on yk, which is denoted a Jacobians J0(W); The second term is zero; The final term can be broken up into two parts. The first, ∂yk/∂yk-i, can by obtained by BP algorithm. The second part, dyk-i/dW, is simply a previously calculated and stored value of dk/dW. When the system is “turn on,” dyi/dW are set zero for i=0,-1,-2,…, and the rest of the terms are calculated recursively from that point on. In the case of hiding time, a similar presentation follows,
where, N = S M , n = S1 (R + 1) + S 2 (S1 + 1) + + S M (S M −1 +1) . The elements of J0(W) can be computed by improving algorithm of backpropagation. By defining new sensitivity m m si , h = ∂y h ∂ni , then
[ J 0 ]h , l =
∂yh
=
∂wl
[ J 0 ]h , l =
∂yh ∂wl
∂yh ∂wij
m
∂yh
=
∂yh ∂ni
m
=
∂bi
m
m m −1 = si , h a j .
∂ni ∂wij m
m
∂yh ∂ni
(12)
m
=
∂ni ∂bi m
m
m = si , h
(13)
And it is initialized at the final layer
siM, h =
∂yh ∂n
M i
f M ( niM )
i=h
¯0
i≠h
=®
(14)
It can also be shown that the sensitivities satisfy the following recurrence relation m m m m +1 T m +1 S = F (n )( W ) S
(15)
.
Continue, J0(W) may be calculated via (12) and (13). Let (d w y ) k
ª¬( dyk −1 dW )
T
( d x y ) k [( ∂yk ∂y k −1 )
( dy
k −2
( ∂y
k
dW )
T
∂yk − 2 )
J (W ) = − [ J 0 (W ) + ( d x y ) k ( d w
( dy
k −m
( ∂y y) ] k
.
k
dW )
T
º¼
T
∂yk − m )].
(16)
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245
Obtained the Jacobian matrix, the weights and offsets may be adjusted by LM method. The update becomes −1
∆W = − ª¬ J (W ) J (W ) + µ I º¼ J (W )e(W ). T
T
(17)
Where the parameter ȝ is multiplied by some factor ȕ whenever a step would result in an increased V(W). When a step reduces V(W), ȝ is divided by ȕ. Notice that when ȝ is large the algorithm becomes steepest descent, while for small ȝ the algorithm becomes Gauss-Newton. The LM algorithm can be considered a trust-region modification to Gauss-Newton. The algorithm is summarized as follow: 1) Let all inputs to the network and compute the corresponding network outputs and errors, and then compute value of the cost function. 2) Compute the Jacobian matrix. Networks configured in series-parallel may be trained using the standard backpropagation algorithm. A Networks configured in parallel must be trained with RTRL based on LMBP algorithm as (16). 3) Solve (17) to obtain ∆Wk; 4) Re-compute the cost function using Wk+∆Wk. If this new value is smaller than that computed in step 1, then reduce ȝ by ȕ, Let Wk+1=Wk+∆Wk, and go back to step 1. If the value is not reduced, then increase ȝ by ȕ and go back to step 3. 5) The algorithm is assumed to have converged when the norm of the gradient is less than predetermined value, or when value of the cost function has been reduced to some error goal.
4 Control Strategy During normal pointing attitude control of an orbiting flexible spacecraft, the modal vibration of flexible appendages is regarded as a kind of correlated disturbance defined as “modal vibration disturbance”, which is difficult canceling by the PID method since it’s modal frequency low and dense, damping small. An adaptive inverse control has advantage in disturbance canceling, which implemented only in the inner loop. Since the adaptive inverse disturbance canceling performed is based on the PID control of dynamics response in this paper, the control structure is designed as following. Fist, the conventional PID method is designed for the dynamical control system of rigid spacecraft. Second, the modal vibration disturbance control is performed by adaptive inverse disturbance canceling method. The PID controller design is not provided here, and in the following part only the disturbance canceller design is described. According disturbance canceling technology of adaptive inverse control [1,5], structure diagram illustrating the adaptive inverse “modal vibration disturbance” canceling for flexible satellite during normal pointing control mode as Fig.4. First, the dynamical system of the rigid spacecraft we wish to control is modeled using NARX neural network Pˆ . Second, a very close copy Pˆ of Pˆ , disturbance-free match to plant, is fed the same input as the plant NP, which is dynamics module based on reaction wheels of constrained mode of flexible spacecraft with single-axis rotation as Fig.2. The difference between the disturbed output of the plant and the disturbance-free output of the copy model is estimation of modal COPY
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Y.-q. Liu, J. Cao, and W.-l. Song
vibration disturbance ηˆ , which is then input to a copy of disturbance canceller k
COPY −1 z Qˆ k ( z ) , and z Qˆ k ( z ) is a best least squares inverse of rigid spacecraft model PˆCOPY . −1
At the same time, the output of z Qˆ ( z ) is subtracted from the plant input to effect cancellation of the plant disturbance, such that the incentive element of modal vibration is cancelled in principle and the vibration can be effective reduced. The unit −1
COPY
k
delay z-1 of Qˆ ( z ) in recognition of the face that digital feedback links must have at least one unit of delay around each loop [1]. Thus, the current value of the plant disturbance ηˆ can be used only for the cancellation of future values of plant disturbance and cannot be used for instantaneous self-cancelation. The effects of these unit delays are small when the system is operated with a high sampling rate, however. COPY
k
k
z −1
Qˆ kCOPY ( z )
B
PˆCOPY _
0 _
Km Tm s + 1
PID
s
ηˆ k
θ
Flexible Satellite Model
NP +
1 Tf s +1 The saved attitude angle information
Modeling input Offline identification
Desired response Low-pass filter process
Pˆ
Synthetic noise source
PˆCOPY
=
Qˆ k ( z ) error
n
Offline process for generating Qˆ k ( z )
Fig. 4. Adaptive inverse disturbance canceling for flexible satellite during normal pointing control mode
However, considering uncertainty of parameter of spacecraft in modeling or orbiting, the model Pˆ is required adaptively. At the same time, considering convergence speed, the model Pˆ is adapted using offline method, which performed as following: Fist, the modeling input is obtained by low-pass filtering saved signal of controller output and desired response is attitude angle of “quasi-rigid”, which obtains by filter “modal vibration disturbance” from attitude angle signal of flexible spacecraft, where the filter process based on 1-D DWT (Discrete Wavelet Transform). Second, real-time is to adjust the weight of Pˆ according to adaptive reference signal, which is the difference between the saved and filtered attitude angle signal of orbiting spacecraft and the output of model Pˆ . Finally, in order to improve convergence speed, the adaptive disturbance canceller ˆ Q ( z ) is generated by offline process, in which requires a synthetic noise source that has the same statistic characteristic with plant disturbance. In this application, the synthetic noise is superposed using sine signal, which should has any order modal k
Application of Adaptive Disturbance Canceling
247
vibration frequency (here considering only the first 5 order modal). Since the offline compute speed is much faster than real-time, to a specific Pˆ ( z ) , the optimal Qˆ ( z ) can be generated by offline process. In practice, in a sampling cycle of real system, offline compute the Qˆ ( z ) can be iterated hundreds or thousands times. In addition, considering dynamic describe performance of canceller Qˆ ( z ) , it is performed using NARX neural network. The whole process of scheme as shown in Fig.4 is performed as following: k
k
k
k
1) Data storage: The adaptive modeling signals of current Pˆ are provided by sample saved queue in the certain time, which has two components: the modeling input (output of controller) and attitude angle signal of flexible spacecraft. The queue is updated per certain time (for example 10 second), at the same time we have adapting once the Pˆ and updating the Pˆ , continue training Qˆ ( z ) and updating z Qˆ ( z ) . 2) Adaptation of model: Using the pairs of input-output, Pˆ is adapted, which are composed of both components of the queue processed through low-pass filter. Here the low-pass filter process is based on 1-D DWT, for example to obtain quasi-rigid attitude angle desired response a5, and we decompose disturbed output signal of the plant using the db10 wavelet into 5 levels. 3) Training of canceller: The Qˆ ( z ) is trained as soon as Pˆ was updated. Since the scheme in Fig.5 aim at rejection of “modal vibration disturbance”, so the synthetic noise is composed of superposed signal using sin waves with first 5 order modal frequency. Once z Qˆ ( z ) is updated, the disturbance canceling loop works on the new parameters, such the adaptive process is performed “real-time”. The above three processes go on continually, such can be performed well disturbance canceling control since Pˆ and z Qˆ ( z ) are adaptive. COPY
−1
k
COPY
k
k
−1
COPY
COPY
k
−1
COPY
COPY
k
5 Simulation Results In order to test the proposed control schemes, numerical simulations have been performed. The numerical model of the spacecraft is from the [9]. The low-frequency modes are generally dominant in a flexible system, in this paper, and the first five modes frequency and coupling coefficient are shown in table 1, a concerning modal truncation we can consult [10]. Fist, according to conventional method design the PID controller of rigid spacecraft with single-axis rotation as Fig.1. The parameter of PID is selected by Matlab toolbox rltool as KP=6, KI=0.05, and so the phase and amplitude margins of close loop system is 80°and 18dB respectively. In this simulation, the adaptive modeling signals of Pˆ ( z ) are provided by sample saved queue in 500s, the modeling input-output data is obtained through low-pass k
248
Y.-q. Liu, J. Cao, and W.-l. Song Table 1. Some Coefficients in Simulation Model Solved By Constrained Modes Order 1 2 3 4 5
Coupling coefficients Fn (kg1/2 m) 2.6917 0.4301 0.1537 0.0785 0.0475
filter, which processes the queue by 1-D wavelet decompose using db10 into 5 levels, and an input of training Qˆ ( z ) is synthetic noise of 10000 samples. Both plant model [4,5] and N . and canceller are structured using NARX neural network N The parameter of training neural network is no longer provided. For comparative purposes, seven different cases of disturbance canceling control for normal pointing control are conducted: 1) only using the PI control, as showed in Fig.5; 2) applying the PI control with adaptive inverse disturbance canceller, as showed in Fig.6; 3) and 4) cases are the case of 2) with ±20% variance for modal k
( 2 , 2 ),10 ,1
(a) curve of attitude angle
(b) curve of attitude rate
Fig. 5. Response to PI case
(a) curve of attitude angle
(b) curve of attitude rate
Fig. 6. Response to PI with adaptive inverse disturbance canceller
( 5 ,5 ), 30 ,1
Application of Adaptive Disturbance Canceling
249
frequency, Pˆ and z Qˆ ( z ) without adaptively updated, plotted in Fig.7 and Fig.8; 5) and 6) cases are the case of 2) considering -20% variance for inertia, Pˆ and z Qˆ ( z ) without adaptively updated, which is showed in Fig.9 and Fig.10; 7) case 2) considering –50% variance for inertia, Pˆ and z Qˆ ( z ) (a) without and (b) with adaptively updated, which result showed in Fig.11. −1
COPY
k
COPY
COPY
−1
COPY
k
−1
COPY
(a) curve of attitude angle
COPY
k
(b) curve of attitude rate
Fig. 7. Response to PI with adaptive inverse disturbance canceller considering -20% variance −1 COPY and z Qˆ ( z ) without adaptively updated for modal frequency, Pˆ COPY
k
(a) curve of attitude angle
(b) curve of attitude rate
Fig. 8. Response to PI with adaptive inverse disturbance canceller considering +20% variance −1 COPY and z Qˆ ( z ) without adaptively updated for modal frequency, Pˆ COPY
k
The simulation results of PI control with disturbance canceller, considering ±20% and z Qˆ ( z ) without adaptively updated are shown in variance for inertia, Pˆ Fig.9 and Fig.10. Analysis of Fig.5~Fig.10 is shown that: (1) both effective rejection attitude dither (modal vibration) and great advance steady precision are performed using adaptive inverse disturbance canceling (Fig.5~Fig.6); (2) the adaptive inverse disturbance canceller has finite stability of scheme for uncertainty and variance of parameter (Fig.7~Fig.8). −1
COPY
COPY
k
250
Y.-q. Liu, J. Cao, and W.-l. Song
(a) curve of attitude angle
(b) curve of attitude rate
Fig. 9. Response to PI with adaptive inverse disturbance canceller considering -20% variance −1 COPY and z Qˆ ( z ) without adaptively updated for inertia, Pˆ COPY
k
(a) curve of attitude angle
(b) curve of attitude rate
Fig. 10. Response to PI with adaptive inverse disturbance canceller considering +20% variance −1 COPY and z Qˆ ( z ) without adaptively updated for inertia, Pˆ COPY
k
(a)
(b)
Fig. 11. The curve of attitude angle considering –50% variance for inertia (a) PˆCOPY and −1 COPY −1 COPY z Qˆ k ( z ) without adaptively updated (b) PˆCOPY and z Qˆ k ( z ) with adaptively updated
Application of Adaptive Disturbance Canceling
251
The above simulation results only demonstrate the action effect and stability of adaptive inverse disturbance canceller, and does not reflect that disturbance canceller requires disturbance control loop to adapt necessarily for work well. Therefore, to demonstrate adaptivity of Pˆ
COPY
and z Qˆ −1
COPY
k
( z ) is necessary.
and z Qˆ −1
Considering case (2) with –50% variance for inertia, (a) Pˆ
COPY
adaptively updated, as showed in Fig.11(a), and (b) Pˆ adaptively updated, which is showed in Fig.11(b).
COPY
COPY
k
and z Qˆ −1
( z ) without
COPY
k
( z ) with
6 Conclusions An adaptive inverse disturbance canceling method for “modal vibration disturbance”, which is difficult canceling by the PID method since it’s modal frequency low and dense, and damping small, is proposed. From the controlling effect, we can draw the conclusion that the modal vibration disturbance is rejected effectively and the precision of normal pointing attitude control is improved greatly; at the same time, the design of adaptive inverse disturbance canceller can ensure the parameter robustness. On the other hand, from design scheme, we can obtain that the control performance of disturbance rejection is improved, which does not affect system dynamic response since adaptive inverse disturbance canceling, compared with the conventional feedback disturbance rejection method, performs in inner loop and is independent of dynamic response control loop. Simulation results demonstrate that all above problems are solved by the research productions in this paper. The further work is to apply this method to the experimental study.
References 1. Widrow, B., Walach, E.: Adaptive Inverse Control, Prentice Hall P T R, Upper Saddle River, NJ (1996) 2. Carbonell Oliver, D.: Neural Networks Based Nonlinear Adaptive Inverse Control Algorithms. Thesis for the Engineer degree, Stanford University, Stanford, CA. (1996) 3. Bilello, M.: Nonlinear Adaptive Inverse Control. Ph.D. thesis, Stanford University, Stanford, CA. (1996) 4. Plett, G. L.: Adaptive Inverse Control of Plants with Disturbances. Ph.D. dissertation, Stanford Univ., Stanford, CA. (1998) 87-91 5. Plett, G. L.: Adaptive Inverse Control of Linear and Nonlinear Systems Using Dynamic Neural Networks. IEEE transactions on neural networks. 14 (2003) 360-376 6. Siegelmann, H.T., Horne, B.G.: Computational Capabilities of Recurrent NARX Neural Networks. IEEE Trans. on Systems, Man and Cybernetics - Part B: Cybernetic. 27 (1997) 208-215 7. Haykin, S.: Neural networks: A Comprehensive Foundation. Second Edition. Prentice Hall International (1999) 8. Junkins, J. L., Youdan K.: Introduction to Dynamics and Control of Flexible Structures. AIAA, (1993) 82-100 9. Jin Jun, S.: Study on CSVS Method for the Flexible Spacecraft, PhD thesis, Harbin Institute of Technology (2002) 10. Liu, D., Yang, D.M.: Modeling and Truncation of Satellite with Flexible Appendages. Journal of Astronautics. 4 (1989) 87-95
Application of Resource Allocating Network and Particle Swarm Optimization to ALS Jih-Gau Juang, Bo-Shian Lin, and Feng-Chu Lin Department of Communications and Guidance Engineering National Taiwan Ocean University, Keelung 20224, Taiwan, ROC [email protected] Abstract. This paper presents two intelligent aircraft automatic landing control schemes that use neural network controller and neural controller with particle swarm optimization to improve the performance of conventional automatic landing systems. Control signals of the aircraft are obtained by resource allocating neural networks. Control gains are selected by particle swarm optimization. Simulation results show that the proposed automatic landing controllers can successfully expand the safety envelope of an aircraft to include severe wind disturbance environments without using the conventional gain scheduling technique.
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population-based optimization methods which dose not use filtering operation (such as crossover and mutation). Members of the entire population are maintained through the search procedure. This method was developed through the simulation of a social system, and it has been found to be robust in solving continuous nonlinear optimization problems [5]-[7]. The method is also suitable for determination of the control parameters which give aircraft better adaptive capability in severe environments. PSOs are best-suited for function optimization tasks. Their structure gives them some sort of a real time solution, while tuning some parameters, such as initial area, swarm size, and neighborhoods. There has also been proof of PSO being able to solve the Traveling Salesman Problem and doing multi-objective optimization tasks [8]. On the other hand, the ability to optimize functions makes PSO effective for adjusting neural network weights or some parameters to other evolutionary algorithms and techniques. Therefore, PSO is suitable for determining control parameters, which give aircraft better adaptive capability in severe environments. Recently, some researchers have applied intelligent concepts such as neural networks and fuzzy systems to intelligent landing control to increase the flight controller's adaptively to different environments [9]-[14]. Most of them do not consider the robustness of controller due to wind disturbances [9]-[12]. In [13], a PD-type fuzzy control system is developed for automatic landing control of both a linear and a nonlinear aircraft model. Adaptive control for a wide range of initial conditions has been demonstrated successfully. The drawback is that the authors only set up the wind disturbance at the initial condition. Persistent wind disturbance is not considered. In [14], wind disturbances are included but the neural controller is trained for a specific wind speed. Robustness for a wide range of wind speeds has not been considered. Juang [15]-[16] had presented a sequential learning technique that uses a conventional neural network with back-propagation through time algorithm in successful landing control. But the number of hidden units was determined by trial and error and the speed of convergence was slow. For sequential learning of Radial Basis Network, Platt [17] had developed an algorithm known as Resource Allocation Network (RAN). It starts with no hidden units and grows by allocating new hidden units based on the novelty in the observations that arrive sequentially. If an observation has no novelty, then the existing parameters of the network are adjusted by an LMS algorithm to fit that observation. RAN had been used for several applications varying from function approximation to nonlinear system identification. Its powerful approximation ability and fast convergence characteristic has been demonstrated. Here, we present two control schemes, RAN controller and RAN controller with PSO algorithm, to guide the aircraft to a safe landing and make the controller more robust and adaptive to the ever-changing environment.
2 System Description The pilot descends from cruising altitude to an altitude of approximately 1200ft above the ground. The pilot then positions the airplane so that the airplane is on a heading towards the runway centerline. When the aircraft approaches the outer airport marker, which is about 4 nautical miles from the runway, the glide path signal is intercepted (as shown in Fig. 1). As the airplane descends along the glide path, its pitch, attitude and speed must be controlled. The aircraft maintains a constant speed along the flight path. The descent rate is about 10ft/sec and the pitch angle is between -5 to +5 degrees.
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J.-G. Juang, B.-S. Lin, and F.-C. Lin
Finally, as the airplane descends 20 to 70 feet above the ground, the glide path control system is disengaged and a flare maneuver is executed. The vertical descent rate is decreased to 2ft/sec so that the landing gear may be able to dissipate the energy of the impact at landing. The pitch angle of the airplane is then adjusted, between 0 to 5 degrees for most aircraft, which allows a soft touchdown on the runway surface. Altitude 1200 ft Glide Path
| 50 ft
Flare Path
Runway Position
0 ft Touchdown
Fig. 1. Glide path and flare path
A simplified model of a commercial aircraft that moves only in a longitudinal and vertical plane is used in the simulations for implementation ease [14]. To make the ALS more intelligent, reliable wind profiles are necessary. Two spectral turbulence forms modeled by von Karman and Dryden are mostly used for aircraft response studies. In this study the Dryden form [14] was used for its demonstration ease. Fig. 2 shows a turbulence profile with a wind speed of 30 ft/sec at 510 ft altitude. Wind Gust velocity components: Longitudinal (Solid) & Vertical (Dashed) 20
10
ft/sec
0 -10 -20 -30
-40 0
5
10
15
20 25 30 Time (sec.)
35
40
45
50
Fig. 2. Turbulence profile
3 Landing Control In this study, the aircraft maintains a constant speed along the flight path. We assumed that the change in throttle command is zero. The aircraft is thus controlled solely by the
Application of Resource Allocating Network and PSO to ALS
255
pitch command. In this section, we present an intelligent neural network controller that uses the Resource Allocation Network to guide the aircraft to a safe landing in a wind disturbance environment. And then, Particle Swarm Optimization is used in the automatic landing system to improve the performance of the previous intelligent landing controller and make the controller more robust and adaptive to the ever-changing environment. 3.1 Resource Allocating Network Controller RAN is a modified neural network from Radial Basis Network. The output of the RAN algorithm has the following form: J
J
j =1
j =0
F (x ) = ¦ w j ϕ j (x ) + θ = ¦ w j ϕ j (x )
(1)
where ϕ j (x ) is the response of the jth hidden neuron to the input x and w j is the weight connecting the jth hidden unit to the output unit. θ = w0ϕ 0 is the bias term.
Here, J represents the number of hidden neurons in the network. ϕ j (x ) is a Gaussian function given by
where m j = m j1 ,, m jp is the center, and σ j is the width of the Gaussian function.
The learning process of RAN involves allocation of new hidden units as well as adjusting network parameters. The network begins with no hidden units. As observations are received, the network grows by using some of them as new hidden units. The following two criteria must be met for an observation (x0 , y 0 ) to be used to add a new hidden unit to the network: xn − m j > εn
(3)
en = y n − F (x n ) > emin
(4)
where m j is the center (of the hidden unit) closest to x n . ε n and emin are thresholds to be selected appropriately. When a new hidden unit is added to the network, the parameters associated with the unit are w j +1 = e n m j +1 = x n
(5)
σ j +1 = κ x n − m j
κ is an overlap factor, which determines the overlap of the responses of the hidden units in the input space.
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J.-G. Juang, B.-S. Lin, and F.-C. Lin
When the observation (x0 , y 0 ) does not meet the criteria for adding a new hidden
[
T
]
T T
unit, the network parameters W = w0 , w1 , , w j , m1 , , m j
are updated using the
LMS as follows: W (n ) = W (n − 1) + ηe n a n
(6)
where Ș is the learning rate. a n is the gradient vector and has the following form:
[
T
]
T T
a n = 1, w1 , , w j , m1 , , m j
ª 2w j 2w T = «1, ϕ1 (x n ), , ϕ j (x n ), ϕ1 (x n ) 21 (x n − m1 ) , , ϕ j (x n ) 2 x n − m j σ1 σj «¬
(
º
)» T
T
(7)
»¼
Therefore, the learning process is defined as: If x n − m j > ε n And en = y n − F (x n ) > emin
᧶
adding a new hidden unit, and parameters are chosen as w j +1 = e n m j +1 = x n
σ j +1 = κ x n − m j Else
W (n ) = W (n − 1) + ηe n a n
End In the scheme, the RAN algorithm is used to tune the neural controller and guide the aircraft to a safe landing in a wind disturbance environment. The RAN structure is shown in Fig. 3. Fig. 4 describes the control scheme in an intelligent automatic landing system, which consists of a PI controller, RAN controller, aircraft model, command, and a wind model. 3.2 Resource Allocating Network Controller with Particle Swarm Optimization
In the PSO algorithm, each member is called “particle,” and each particle flies around in the multi-dimensional search space with a velocity, which is constantly updated by the particle’s own experience - the experience of the particle’s neighbors or the experience of the whole swarm. PSO can be used to solve many of the same kinds of problems as the genetic algorithm (GA). This optimization technique does not suffer, however, from some of GA’s difficulties. Interaction in the group enhances, rather than detracts from, progress toward the solution. Further, a particle swarm system has memory, which the genetic algorithm does not have. Each particle keeps track of its coordinates in the problem space, which are associated with the best solution (fitness) it has achieved so far. This value is called pbest. Another value that is tracked by the global version of the particle swarm optimizer is the overall best value, and its location, obtained so far by any particle in the population. This location is called gbest. At each
Application of Resource Allocating Network and PSO to ALS
257
time step, the particle swarm optimization concept consists of velocity changes of each particle toward its pbest and gbest locations. Acceleration is weighted by a random term, with separate random numbers being generated for acceleration toward pbest and gbest locations. This is illustrated in Fig. 5, where
x k is the current position of a
x k +1 is its modified position, v k is its initial velocity, v k +1 is its modified velocity, v pbest is the velocity considering its pbest location, and v gbest is the velocity
particle,
considering its gbest location.
Fig. 3. Structure of RAN
Fig. 4. Aircraft automatic landing system with RAN controller
The operation of particle swarm optimization is shown in Fig. 6. The definition of the parameters is
vid(k ) : velocity of individual i at iteration k, Vdmin w : inertia weight factor,
≤ vid( k ) ≤ Vdmax
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J.-G. Juang, B.-S. Lin, and F.-C. Lin
c1 , c2 : acceleration constant, rand1, rand2 : uniform random number between 0 and 1,
xid(k ) : current position of individual i at iteration k , pbesti : pbest of individual i, gbest : gbest of the group.
k (v )
(v
k +1
x k +1 ) ( v gbest )
xk
( v pbest )
x k −1 Fig. 5. Movement of a PSO particle
In here, Initial conditions are: number of particles is 20, V min = −0.5 , V max = 0.5 , c1 = c 2 = 1.5 . The fitness function is defined as: For Turbulence strength=min : Į : max Do{ The Process of Landing } -3 ≤ h(T ) ft/sec ≤ 0, 200 ≤ x (T ) ft/sec ≤ 270, If -300 ≤ x(T ) ft ≤ 1000, -1 ≤ θ (T ) degree ≤ 5 Fitness =Turbulence strength Else Fitness = Turbulence strength - Į End End
® ¯
4 Simulation Results In the simulations, successful touchdown landing conditions are defined as follows: -3 ≤ h(T ) ft/sec ≤ 0, 200 ≤ x (T ) ft/sec ≤ 270, -300 ≤ x(T ) ft ≤ 1000, -1 ≤ θ (T ) degree ≤ 5,
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where T is the time at touchdown. Initial flight conditions are: h(0)=500 ft, x (0) =235 ft/sec, x(0) =9240 ft, and γ o =-3 degrees. After using RAN, the controller can successfully guide the aircraft flying through wind speeds of 0 ft/sec to 70ft/sec. Table 1 shows the results from using different wind turbulence speeds with the original control gains that were used in [14] as shown in Fig. 7. Fig. 8 to Fig. 11 show the results of using RAN. The results indicate that the RAN controller can result in fast online adjusting, and it can implement a more robust network structure than [14]-[16] which can only overcome turbulence to 30 ft/sec, 50 ft/sec, and 65 ft/sec, respectively.
Initialize a population of particles with random positions and velocity
Calculate fitness function f(x)
Compare each particle’s fitness Generate initial pbest and gbest K=1
Vidnew
w u Vid C1*rand()*(Pbest Xid) C 2 * rand () * (Gbest Xid ) X idnew
X idold Vidnew
Calculate fitness function F(new)
Yes
K+1
F(new)>Fp(old)
Pbest(n)=Xnew(n)
No Fp(new)>Fg(old)
No
Xold=Xnew Vold=Vnew
No Terminate condition
Yes Yes
Gbest=Pbest(n)
Optimal solution
Fig. 6. Operation of PSO
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J.-G. Juang, B.-S. Lin, and F.-C. Lin Table 1. The Results From Using RAN Controller (k1=2.8; k2=2.8; k3=11.5; k4=6.0;)
Application of Resource Allocating Network and PSO to ALS
Fig. 10. Aircraft altitude and command
261
Fig. 11. Growth number of RAN hidden unit
Fig. 12. Aircraft pitch and pitch command Fig. 13. Vertical velocity and velocity command
Fig. 14. Aircraft altitude and command
Fig. 15. Growth number of RAN hidden units
In previous section, the control gains of the pitch autopilot in glide-slope phase and flare phase are fixed (as shown in Fig. 7). After using PSO, optimal control gains can be obtained. The controller can successfully overcome turbulence to 95 ft/sec. Table 2 shows the results from using different wind turbulence speeds. Fig. 12 to Fig. 15 show
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J.-G. Juang, B.-S. Lin, and F.-C. Lin
Table 2. The Results From Using RAN Controller with PSO (K1=2.3003; K2=2.3003; K3=11.6411; K4=20.913;)
the results from using RAN with PSO. In comparison, while using RAN with the PSO algorithm, the controller is more adaptive to ever-changing environments.
5 Conclusion The purpose of this paper is to investigate the use of hybrid neural networks and evolutionary computation to aircraft automatic landing control and to make the automatic landing system more intelligent. Current flight control law is adopted in the intelligent controller design. Tracking performance and adaptive capability are demonstrated through software simulations. For the safe landing of an aircraft with a conventional controller, the wind speed limit of turbulence is 30 ft/sec. In this study, the RAN controller with original control gains can overcome turbulence to 70 ft/sec. The RAN controller with PSO algorithm can reach 95 ft/sec. These results are better than those without using the PSO algorithm. Especially, the PSO algorithm adopted in RAN has the advantage of using fewer hidden neurons. This is because the PSO method can be used to generate high quality solutions on complex parameter searches. From these simulations, the proposed intelligent controllers can successfully expand the controllable environment in severe wind disturbances. Acknowledgement. This work was supported by the National Science Council, Taiwan, ROC, under Grant NSC 92-2213-E-019 -005.
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References 1. Buschek, H., Calise, A.J.: “Uncertainty Modeling and Fixed-Order Controller Design for a Hypersonic Vehicle Model,” Journal of Guidance, Control, and Dynamics, vol. 20, no. 1, 42-48, (1997) 2. Federal Aviation Administration, “Automatic Landing Systems,” AC 20-57A, Jan. (1971) 3. Boeing Publication.: “Statistical Summary of commercial Jet Airplane Accidents”, Worldwide Operations (1959-1999) 4. Kennedy, J., Eberhart, R. C.: “ Particle Swarm Optimization,” Proceedings of IEEE International Conference on Neural Networks, Vol. IV, pp. 1942-1948, Perth, Australia, (1995) 5. Shi, Y., Eberhart, R. C.: “Empirical Study of Particle Swarm Optimization,” Proceedings of the 1999 Congress on Evolutionary Computation, 1945-1950, Piscataway, (1999) 6. Peter, J. A.: “Using Selection to Improve Particle Swarm Optimization,” Proceedings of IEEE International Conference on Evolutionary Computation, pp. 84-89, Anchorage, May (1998) 7. Zheng, Y. L., Ma, L., Zhang, L., Qian, J.: “On the Convergence Analysis and Parameter Selection in Particle Swarm Optimization,” Proceedings of the Second IEEE International Conference on Machine Learning and Cybernetics, November 2-5, (2003)1802-1807 8. Kennedy, J., Eberhart, R. C.: Swarm Intelligence, Morgan Kauffman publishers, San Francisco, CA, (2001) 9. Izadi, H., Pakmehr, M., Sadati, N.: “Optimal Neuro-Controller in Longitudinal Autolanding of a Commercial Jet Transport,” Proc. IEEE International Conference on Control Applications, CD-000202, 1-6, Istanbul, Turkey, June (2003) 10. Chaturvedi, D.K., Chauhan, R., Kalra, P.K.: “Application of generalized neural network for aircraft landing control system,” Soft Computing, vol. 6, 441-118, (2002) 11. Iiguni, Y., Akiyoshi, H., Adachi, N.: “An Intelligent Landing System Based on Human Skill Model,” IEEE Transactions on Aerospace and Electronic Systems, vol. 34, no. 3, 877-882, (1998) 12. S. Ionita and E. Sofron, “The Fuzzy Model for Aircraft Landing Control,” Proc. AFSS International Conference on Fuzzy Systems, pp. 47-54, Calcutta, India, February 2002. 13. Nho, K., Agarwal, R.K.: “Automatic Landing System Design Using Fuzzy Logic,” Journal of Guidance, Control, and Dynamics, vol. 23, no. 2, 298-304, (2000) 14. Jorgensen, C.C., Schley, C.: “A Neural Network Baseline Problem for Control of Aircraft Flare and Touchdown,” Neural Networks for Control, 403-425, (1991) 15. Juang, J.G., Chang, H.H., Cheng, K.C.: “Intelligent Landing Control Using Linearized Inverse Aircraft Model,” Proceedings of American Control Conference, vol. 4, 3269-3274, (2002) 16. Juang, J.G., Chang, H.H., Chang, W.B.: “Intelligent Automatic Landing System Using Time Delay Neural Network Controller,” Applied Artificial Intelligence, vol. 17, no. 7, 563-581, (2003) 17. Platt, J.: “A Resource Allocating Network for Function Interpolation,” Neural Computation, vol. 3, 213~225, (1991)
Case-Based Modeling of the Laminar Cooling Process in a Hot Rolling Mill Minghao Tan1, Shujiang Li1, Jinxiang Pian2, and Tianyou Chai2 1
School of Information Science and Engineering, Shenyang University of Technology, 110023 Shenyang, China [email protected] 2 Research Center of Automation, Northeastern University, 110004 Shenyang, China [email protected]
Abstract. Accurate mathematical modeling of the laminar cooling process is difficult due to its complex nature (e.g., highly nonlinear, time varying, and spatially varying). A case-based temperature prediction model is developed for the laminar cooling process using case-based reasoning (CBR) and the dynamical process model. The model parameters for the current operating condition are found by retrieving the most similar cases from the case base according to the current operating condition and reusing the solutions of the retrieved cases. The resulting model can predict the through-thickness temperature evolutions of the moving strip during the cooling process. Experimental studies based on industrial data from a steel company show the effectiveness of the proposed modeling approach.
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laminar cooling process was developed in [8] which calculates the through-thickness temperatures at the strip center line during the cooling process. The heat transfer coefficients were determined by specific onsite experiments on the runout table cooling hardware. However, the heat transfer coefficients determined in this way can not reflect the changes in operating conditions and the model can only be used for offline development purposes. Accurate description of key process parameters during laminar cooling is essential to modeling the laminar cooling process. This paper takes a knowledge-based approach to modeling the laminar cooling process in which case-based reasoning (CBR) [9], [10] is integrated with the first principles dynamical model. The key process parameters are obtained using case-based reasoning [11] and physical analysis according to the operating conditions of the cooling process. Experimental studies with industrial data show superior accuracy of the proposed modeling approach.
2 Typical Laminar Cooling Process The schematic of a typical laminar cooling process is shown in Fig.1. After leaving the last finishing stand F7 the strip is cooled on the runout table by top and bottom water headers. At the entry to the cooling area the temperature and thickness of the strip is measured by the infrared pyrometer P1 and the X-ray gauge D1. At the end of the runout table the final cooling temperature of the strip is measured by P2 before it is wound at the downcoiler. The strip speed during the cooling process is tracked by speed tachometers. Nineteen banks of four headers are installed on the runout table, with each header having a constant flow rate. There are four spray patterns for the four headers in each water bank [2]. Speed
Top headers
F7 Bank 1
Bank 2
Bank 15
Bank 16
D1 P 1
Runout table 7.68 m 4.62m
Bank 19
Strip
Bottom headers
P2
Coilers 10.10 m
27.95 m
Water cooling area 100.8m
Fig. 1. Schematic of the laminar cooling process
The strip temperature is related to the operating conditions of the moving strip, such as the strip material, strip gauge, entry temperature, and the control signals such as the activated headers and the flow rate of cooling headers. The output of the laminar cooling process is the strip temperature. If the strip is divided into M through-thickness layers, the inputs of the laminar cooling process include the strip gauge d, the strip length L, the steel grade Gr,
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the entry temperature Te, the water temperature Tw, the environment temperature Ten, the strip speed v, the strip acceleration ac, the first activated top header Ht, the first activated bottom header Hb, the number of activated headers H, the header flow rate q, and the spray pattern π. The process outputs include the strip temperature on the top surface T0, the strip temperature on the bottom surface TM, and the temperatures of the through-thickness layers inside the strip T1…TM-1.
3 Physical Model of the Laminar Cooling Process [2] The temperature of the ith lengthwise strip segment is described by the following equation [2]
∂Ti ( y , t (i )) ∂ 2Ti ( y , t (i )) =a ∂t ( i ) ∂y 2
(1)
with the initial condition
Ti ( y , t (i )) = Ti 0 ( y )
(2)
and the boundary conditions
λ
t (i ) ∂Ti ( y, t (i )) d = α 0 [Tw 0 ( xk 0 + ³t v(t )dt, t ) − T ( i , t (i ))] d ∂y 2 y=
(3)
t (i ) ∂Ti ( y, t (i)) d = α M [TwM ( xi 0 + ³ v(t )dt, t ) − T (− i , t (i))] t d ∂y 2 y=−
(4)
i0
i
2
λ
i0
i
2
∂Ti ( y,t (i )) ∂y
=0
(5)
y =0
where a is the thermal diffusivity of the strip, Ti(y,t(i)) is the temperature of the ith strip segment at location y and instant t(i), λ is thermal conductivity of the strip, Tw0, TwM are the temperature of cooling water on the top and bottom surface of the strip, α0, αM are heat transfer coefficients on the top and bottom surface of the strip, di is the thickness of the ith strip segment, xi0 is the position of the ith strip segment at the initial time instant ti0.
4 Case Based Modeling Strategy of the Laminar Cooling Process The proposed case-based modeling strategy for the laminar cooling process is shown in Fig. 2. The dynamical model is established from physical analysis of the heat transfer process. The features of the current operating condition are extracted from the operating data and used to retrieve matching cases in the case base. The solution parameters of the current operating condition are determined by reusing the solutions
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π Ht Hb H
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ac w L Tw T en
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M odels of heat transfer coefficients and thermal conductivities
T0 T1 ,…TM
Fig. 2. Case-based modeling strategy for the laminar cooling process
of the retrieved cases. The obtained solutions are then tested by calculating the heat transfer coefficients, thermal conductivities, and thermal diffusivities and performing statistical analysis of the temperature predictions. 4.1 Dynamical Model of the Laminar Cooling Process
We can discretize (1)-(5) using finite difference as
a ∆Γα 0 a ∆Γα 0 ∆Γ ∆Γ − 0 )T0 ( n ) + a0 T1 ( n ) + 2 0 TW ∆ yλ 0 ( ∆y ) 2 ∆yλ0 ( ∆y ) 2 a j ∆Γ
a j ∆Γ
T j +1 ( n + 1) ( ∆y ) ( ∆y ) ( ∆y ) 2 (j=1,2, …, M-1) a j ∆Γ a j ∆Γ a j ∆Γ = T n + − T n + ( ) ( 2 2 ) ( ) ) T ( n ) j −1 j j +1 ( ∆y ) 2 ( ∆y ) 2 ( ∆y ) 2
(2 + 2
2
)T j ( n + 1) −
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T j −1 ( n + 1) −
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(7)
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(1 + aM aM
∆Γ α ∆Γ ∆Γ + aM M )TM (n + 1) − aM TM −1(n + 1) = 2 (∆y) (∆y)2 ∆yλM
∆ΓαM ∆ΓαM ∆Γ ∆Γ T (n) + (1 − aM )TM (n) + 2aM TW − aM 2 M −1 2 (∆y) (∆y) ∆yλM ∆yλM
(8)
where j is the jth through-thickness layer (j=0, 1, … M), T is the strip temperature, n is the nth time step, ∆Γ is time step size, aj is thermal diffusivity at layer j; λ0, λM is thermal conductivities at top and bottom surface; α0, αM is heat transfer coefficients at the top and bottom surface. Equations (6) and (8) describe the heat transfer on the surface of the moving strip and (7) describes the heat conduction between various layers within the strip. The determination of the heat transfer coefficients α0, αM, thermal conductivities λ0, λM and thermal diffusivities aj (j=0, M) is key to improving the model accuracy. When the header is activated, the heat transfer coefficients during water cooling are related to the spray intensity, the strip surface temperature and the strip speed, etc. Because the header flow rate is constant the heat transfer coefficients at the top and bottom surface are modeled as follows [2]
α0 = (2 − ((Hc − Ht ) /10.0+ 1)0.12)β1 (
v β2 d β3 T0 β4 ) ( ) ( ) 1.1vh dh Th
(9)
αM = (2 − ((Hc − Hb ) /10.0+1)0.12)β1 (
v β2 d β3 TΜ β4 ) ( ) ( ) Th 1.1vh dh
(10)
where Hc is the specified header, v is the strip speed at the specified header, d is the strip gauge at the specified header, Tj (j=0, M) is the strip temperature at the specified header, q is the cooling water flow rate at the specified header; vh is the speed of the strip head at the entry to the cooling section, dh is the thickness of the strip head measured at D1, Th is the temperature of the strip head measured at P1. β1 ,β2 ,β3 ,β4 are parameters to be determined. When the header is deactivated the heat transfer coefficients at the top and bottom surface are calculated by [2]
α0 = σ × ε ×
(T04 − Ten4 ) + 6.5 + 5.5 × v 0.8 T0 − Ten
α M = 0.8 × σ × ε ×
(T04 − Ten4 ) T0 − Ten
(11)
(12)
where σ is the Stefan-Boltzmann constant, ε= 0.82 is the emissivity. The thermal conductivities at the top and bottom surface λj (j=0, M) are found by [2]
λj = 56.43-(0.0363-c (v – 1.1⋅vh) )×Tj (j= 0, M)
(13)
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The thermal diffusivity at layer j is calculated by [2] 8.65 − 0.0146 (T j − 400) °5.0 − 0.045 (T − 650) ° j aj =f(Tj)= ® T + 2 . 75 0 . 025 ( j − 700) ° °¯5.25 + 0.00225(T j − 800)
T j ∈ [400, 650) T j ∈ [650, 700) (j=0,…, M) T j ∈ [700, 800) T j ∈ [800, 1000]
(14)
Because the parameters β1 ,β2 ,β3 ,β4 and c vary with operating conditions, casebased reasoning is used to determine these parameters according to the changing operating conditions. 4.2 Case Representation and Retrieval
The case base stores knowledge of the laminar cooling process in the form of organized cases. Each case, consisting of two parts, case descriptors and case solutions, is a specific experience in modeling the laminar cooling process for a given operating condition. The case solutions include the parameters β1, β2, β3, β4 and c in (10), (11), and (14). They are mainly related to the key features of the process operating conditions, namely the steel grade, the strip gage, the strip speed, and the strip temperature, which are chosen as the case descriptors. The case structure is shown in Table 1. Table 1. Case Structure Case descriptors F f1 f2 f3 f4 Gr vh dh Th
Case solutions S s2 S3 s4
s1
β1
β2
β3
β4
s5 c
The current operating condition of the strip is defined as Cin, and the descriptors of Cin are F =(f1, f2, f3, f4). The solutions of Cin are defined as S=(s1, s2, s3, s4, s5). Assume there are m cases in the case base, C1, C2,…Cm. The descriptor vector of P P P P P Ck (k=1,…m) is defined as Fk = ( f k ,1 , f k , 2 , f k ,3 , f k , 4 ) , the solution vector of Ck is defined as
S kP = ( sk,P1 , sk,P2 , sk,P3 , sk,P4 , sk,P5 )
(15)
Due to the limited space the similarity functions between various descriptors are omitted in this paper. The reader is referred to chapter 2 of [2] for details. The similarity between the current operating condition Cin and the stored case Ck (k=1,…m) is 4
SIM ( C in , C k ) =
¦ω
l
× sim ( f l , f kP,l )
l =1
(16)
4
¦ω l =1
l
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SIM max = Max ( SIM (Cin , Ck )) k∈{1,m}
(17)
All cases with similarities greater than the threshold SIMth are retrieved from the case base. 4.3 Case Reuse
If no exact match for the current operating condition is found in the case base the solutions of the retrieved cases have to be adapted before they can be reused for the current operating condition. Suppose r cases have been retrieved from the case base {C1R , ..., C rR } , where the similarity between C kR (k=1,…r) and the current operating condition is SIMk. Assume SIM1 ≤ SIM2 ≤ ··· ≤ SIMr ≤ 1, then the solutions of the retrieved cases are
The solution of the current operating condition is S=(s1, s2, s3, s4, s5), where r
¦w
k
sl =
× s k,Rl
k =1
(19)
r
¦w
k
k =1
(l=1,…5)
and wk (k=1,…r) is found as follows If Then
SIMr =1
1 k = r ½ ¾ ¯0 k ≠ r ¿
wk= ®
Else wk =SIMk End If
(20)
(k=1,…r)
4.4 Case Revision and Case Retention
Case revision performs the evaluation test on the validity of the reused solutions that results from case reuse. The flowchart of case revision is shown in Fig. 3. The heat transfer coefficients, the thermal conductivities, and thermal diffusivities are calculated from the solutions of case reuse. Then the final cooling temperatures of the strip segments are calculated according to (6)-(8). The statistical evaluation signal ∆T is calculated by N
∆T = ¦ | T0 (i ) − Tcm (i ) | / N i =1
(21)
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where Tcm(i) is the final cooling temperature measurement (i=1,…N), N is the number of cooling temperature measurements, T0(i) is the final cooling temperature prediction by this model. In case ∆T < 10 , the case is retained into the case base. In case ∆T > 10 , case revision is performed to improve the accuracy of the solution from reuse. The revised case is tested of its redundancy before it is retained in the case base.
͠
͠
Given s1 ... s5 from case reuse
Calculate ∆T
∆ T > 10 ° C?
N
Y
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β 1 = median ( β1,1, β1,2, ..., β 1,N )
Adjust ci in the same way as β 1 (i=1,...N)
c = median ( c1, c2,..., cN)
Adjust β 1, β 2, β 3, β 4, c
Calculate ∆T
N
∆ T ≤ 10 ° C?
Y
Case retention
Fig. 3. Flow chart of case revision
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5 Experimental Study In this experiment we use 61 data samples collected from a rolling mill and compare the model predictions with the results of [12]. The case descriptors for the experiment are shown in Table 2. Table 2. Case Descriptors Gr 316
dh 12
vh 2.9
Th 835
According to the descriptors in Table 2 one case was retrieved from the case base with SIMmax =0.62. Table 3 lists the case solutions calculated by the case-based reasoner for the specified operating condition. The model predictions of the proposed modeling method and ref [12] are plotted against the real cooling temperature measurements in Fig. 4. Table 3. Reasoning Results
β1
β2
β3
β4
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Table 4. Model Accuracy Comparison SIM N 0.62 61
͠
Measurements ±10 This paper Ref [12] 61 39
Real measurements
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Coiling temperature
Seg. No.
Fig. 4. Comparison of final cooling temperature predictions
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Thirty-nine temperature predictions of the model in [12] are within 10°C of the temperature measurements, as can be seen from Table 4. Fig. 4 shows the model in [12] lost track of many of the cooling temperature measurements, esp. towards the final period. In sharp contrast, 100% (61/61) of the predictions of this paper are within 10°C of the measurements. It is evident that the proposed approach is very good at tracking the evolution of the strip temperature and capable of much better accuracy than the model in [12].
6 Conclusions The development of an accurate model is essential to better understanding and successful control of the laminar cooling process. This paper has introduced a novel hybrid approach to modeling the laminar cooling process that combines first principles modeling and case-based reasoning. Experiments based on data collected from the laminar cooling process of a hot mill have demonstrated the superior model accuracy of the hybrid modeling approach. The results in this paper can be generalized to a wide range of similar processes.
Acknowledgements This work was partly supported by the Ph.D. Funding Program of Shenyang University of Technology, the Program of Liaoning Department of Education under Grant No.2004D309, Shenyang Science and Technology Program under Grant No.10530842-05, the China National Key Basic Research and Development Program under Grant No.2002CB312201, and the Funds for Creative Research Groups of China under Grant No.60521003.
References 1. Chai, T.Y., Tan, M.H., et al Intelligent Optimization Control for Laminar Cooling. In: Camacho, B., Puente, D. (eds.): Proc. of the 15th IFAC World Congress. Elsevier, Amsterdam (2003) 691-696 2. Tan, M.H.: Intelligent Modeling of the Laminar Cooling Process. Tech. Rep. 18. Research Center of Automation, Northeastern University, Shenyang (2004) 3. Groch, A.G., Gubemat, R., Birstein, E.R.: Automatic Control of Laminar Flow Cooling in Continuous and Reversing Hot Strip Mills. Iron and Steel Engineer. 67(9) (1990) 16-20 4. Ditzhuijzen, V.G.: The Controlled Cooling of Hot Rolled Strip: A Combination of Physical Modeling, Control Problems and Practical Adaptation, IEEE Trans. Aut. Cont. 38(7) (1993) 1060-1065 5. Moffat, R.W.: Computer Control of Hot Strip Coiling Temperature with Variable Flow Laminar Spray. Iron and Steel Engineer. 62(11) (1985) 21-28 6. Leitholf, M.D., Dahm, J.R.: Model Reference Control of Runout Table Cooling at LTV. Iron and Steel Engineer. 66(8) (1989) 31-35
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7. Yahiro, K. J.: Development of coiling temperature control system on hot strip mill. Kawasaki Steel Mizushima Works Tech. Rep. 24. (1991) 8. Evans, J.F., Roebuck, I.D., Howard, R.W.: Numerical Modeling of Hot Strip Mill Runout Table Cooling. Iron and Steel Engineer. 70(1) (1993) 50-55 9. Kolodner, J.L.: Case-Based Reasoning. 1st edn. Morgan Kaufmann, New York (1993) 10. Watson, I., Marir, F.: Case-based reasoning: A review. Knowledge Engineering Review. 9(2) (1994) 355-381 11. A. Aamodt, and E. Plaza, "Case-based reasoning: Foundational issues, methodological variations, and system approaches," AI Communications, Vol. 7, pp. 39–59, 1994. 12. Shan, X.Y.: Transformation and Development of the Cooling Control System of the 2050mm Baosteel Hot Strip Mill. In: Ren, D. (eds.): Development of Science and Technology in Metallurgy. Metallurgical Industry Press, Hangzhou China (1999) 19-22
Fast Mesh Simplification Algorithm Based on Edge Collapse Shixiang Jia1, Xinting Tang2, and Hui Pan3 1
Department of Computer Science and Technology, Ludong University, 264025 Yantai, P.R. China [email protected] 2 Department of Computer Science and Technology, Ludong University, 264025 Yantai, P.R. China [email protected] 3 Department of Computer Science and Technology, Ludong University, 264025 Yantai, P.R. China [email protected]
Abstract. Firstly, we present a new mesh simplification algorithm. The algorithm is based on iterative half-edge contracting, and exploits a new method to measure the cost of collapse which takes the length of contracting edge and the dihedral angles between related triangles into account. The simplification does not introduce new vertex in original mesh, and enables the construction of nested hierarchies on unstructured mesh. In addition, the proposed algorithm adopts the Multiple-Choice approach to find the simplification sequence, which leads to a significant speedup with reduced memory overhead. Then we implement a mesh simplification system based on this algorithm, and demonstrate the effectiveness of our algorithm on various models.
system based on the proposed algorithm, and applied our algorithm on many models with various size. The rest of the paper is organized as follows. We first review the related work in Section2. Section 3 describes our algorithm in detail. The implementation is discussed in Section 4. Section 5 presents a discussion of results and performance analysis. Section 6 concludes the paper.
2 Related Work The problem of surface simplification has been studied in both the computational geometry and computer graphics literature for several years. Some of the earlier work by Turk [4] and Schroeder [5] employed heuristics based on curvature to determine which parts of the surface to simplify to achieve a model with the desired polygon count. Vertex clustering algorithm described by Rossignac and Borrel [6] is capable of processing arbitrary polygonal input. A bounding box is placed around the original model and divided into a grid. Within each cell, the cell’s vertices are clustered together into a single new representative vertex. The method is very fast and effective, however, the quality of the approximation is not often satisfactory. This approach usually leads to a vertex distribution which does not adapt to the local curvature of the surface, and can not guarantee a proper manifold topology of the resulting approximation. Hoppe [7,8] posed the model simplification problem into a global optimization framework, minimizing the least squares error from a set of point-samples on the original surface. Later Hoppe extended this framework to handle other scalar attributes, explicitly recognizing the distinction between smooth gradients and sharp discontinuities. He also introduced the progressive mesh [8], which is essentially a stored sequence of simplification operation, allowing quick construction of any desired level of detail along the continuum of simplifications. However, the algorithm provides no guaranteed error bounds. There is considerable literature on surface simplification using error bounds. Cohen and Varsheny [9] have used envelopes to preserve the model topology and obtain tight error bounds for a simple simplification. An elegant solution to the polygon simplification problem has been presented in [10,11] where arbitrary polygonal meshed are first subdivided into patches with subdivision connectivity and then multiresolution wavelet analysis is used over each patch. These methods preserve global topology, give error bounds on the simplified object and provide a mapping between levels of detail. Garland [12] used iterative contractions of vertex pairs to simplify models and maintains surface error approximation of polygonal modes. This algorithm is efficient and can rapidly produce high quality approximation. Incremental decimation algorithms typically lead to superior model quality. These algorithms simply models by iteratively executing atomic decimation step such as edge collapse (see Fig. 1). An edge collapse takes the two endpoints of the target edge, moves them to the same position, links all the incident edges to one of the vertices, deletes the other vertex, and removes the faces that have degenerated into lines or points. Typically, this removes two triangular faces per edge contraction. To minimize the approximation error, a cost function measuring the quality of the approximation is proposed to guide the process of simplification [7,12].
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t2 t3 8
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t5
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Fig. 1. Half-edge collapse. The (u, v) edge is contracted into point v. The t1 and t5 triangles become degenerate and are removed.
The particular sequence of edge collapse transformations must be chosen carefully, since it determines the quality of the approximating models. For those algorithms [7], the priority queue is a natural data structure to store the order of the edges to be simplified, which allows a variety of operations (inclusion, access and removal of the largest, etc.) to be efficiently performed. But it takes a long time to build the queue before starting the simplification process. Furthermore, each step of the decimation also consumes a significant amount of time to recompute the collapse cost of changed edges and to update their position in the priority queue. In order to accelerate this process, Wu and Kobbelt [3] have presented a technique called Multiple-Choice based on probabilistic optimization. It makes no use of a priority queue, but chooses the edge to be contracted from a small number of randomly selected edges. We provide a new algorithm which can preserve the visually important parts of the model by using a new cost function to measure the approximation error. In order to speed up the algorithm, we also use a probabilistic optimization strategy based on the Multiple-Choice Algorithm to find the optimal decimation sequence. Our system allows faster simplification than some quality method.
3 Simplification Algorithm 3.1 Atomic Decimation Operator Our algorithm is based on the half-edge collapse operation. Half-edge collapse is to choose an edge (u,v) and contract it to one of its endpoint v. After collapsing, all triangles adjacent to either u or v are connected to v, and triangles adjacent to both u and v are removed (see Fig. 1). We prefer half-edge collapse because of its simplicity. The methodology of halfedge collapse is in fact closely related to the vertex decimation approach. In each step of vertex decimation approach, a vertex is selected for removal. All the facets adjacent to that vertex are removed from the model and the resulting hole is triangulated. Instead of the vertex elimination and arising hole triangulation, half-edge contracting just merge one endpoint of the selected edge into the other endpoint. Half-edge contracting avoids the action of hole triangulation, and is generally more robust than vertex decimation. In this case, we do not need to worry about finding a plane onto which the neighborhood can be projected without overlap. In addition, half-edge contracting makes progressive transmission more efficient (no intermediate vertex coordinates) and enables the construction of nested hierarchies that can facilitate further applications.
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The change caused by edge collapse is quantified by collapse cost. The algorithm based on edge collapse has to solve two problems: one is how to calculate the collapse cost for every candidate; the other is how to find the simplification sequence. Then the algorithm can collapse the edge iteratively until the given criterion is satisfied. 3.2 Collapse Cost According to the characteristics of human vision system, observers are mainly sensitive with three attributes of the model: size, orientation and contrast [1,2]. According to the first attribute, the length of the edge should be considered when calculating its collapse cost. With the last two attributes, the dihedral angles between the related triangles are also important guidance. Our cost function will focus on the edge length and the sum of the dihedral angles.
t4 t5
D
t3 G t6 t7 t2 t1 t8
E
F
Fig. 2. The candidate for contracting
The principle of our algorithm is that the contracting edge should be at smooth areas (such as edge(a,b) in Fig. 2), so the dihedral angle between any two related triangles should be small. To calculate the collapse cost for edge(u,v) in Fig. 1, we need to do some work as follows: 1) Find out all the triangles adjacent to vertex u: t1, t2, t3, t4, and t5, and those adjacent to both vertex u and v: t1 and t5 2) Calculate the dihedral angle between t1 and t2, t3, t4, t5, and then those between t5 and t1, t2, t3, t4 3) Set the largest dihedral angle in step 2 as the final angle between the related triangles adjacent to edge(u,v). The final angle of edge(a,b) in Fig. 2 is very small(zero), so we can contract it. As a matter of fact, we can relax this condition to that when the edge is an exclusive edge we can also collapse it, such as edge(c,d) in Fig. 2. The collapse of edge(c,d) will have little influence to the appearance of the model. We can observe that the dihedral
t1
t2 t3
8
t4
t5
9
Fig. 3. The calculation of the triangles’ weight
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angle between t1 and t8 is very large while the one between t1 and t2 is very small. If we use the above algorithm for calculation, the collapse cost of edge(c,d) will be large, which is contrary to the fact, so we need to improve it. We give every triangle a weight when calculating the dihedral angle. For edge(u,v) in Fig. 3, when calculating the dihedral angle between t1 and the other triangles, we think the one between t1 and t2 is most important , so the weight of t2 to t1 should be largest, and the weights of t2, t3, t4 and t5 should decrease counterclockwise. While, when we calculate the dihedral angle between t5 and the other triangles, the weights of t4, t3,, t2 and t1 should decrease clockwise. We define that S is the set of triangles that are adjacent to vertex u, the number of the triangles in it is n and si (i=1, 2 , , ,n) indicates the ith triangle. B is the set of triangles that are adjacent to both u and v, the number of the triangles in it is m. We define the weight of si to bj as follows: W ( s i , b j ) = n /( n + D ( s i , b j )
(1)
where D(si, bj) in (1) denotes the number of triangles between si and bj. In Fig. 3, if bj is t1, D(si., t1) denotes the number of triangles which will be visited when traversing counterclockwise from t1 to si. For example, D(t2, t1)=1, D(t4, t1)=3. If bj is t5, D(si, t5) denotes the number of triangles which will be visited when traversing clockwise from t5 to si. Define fi (i=1, 2, , , n) indicates the unit normal vector of the ith triangle of S, and ej (j=1, 2, , , m) indicates the unit normal vector of the jth triangle of B. We define the collapse cost of edge (u, v) is: m
n
Cost (u , v ) =|| u − v || ×(¦¦ [(1 − (e j • f i )) × W ( si , b j )]) j =1 i =1
(2)
where ||u-v|| in (2) indicates the length of edge(u,v).
e j • f i =| e j | × | f i | × cosθ = cosθ
(3)
We use ej ⋅ fi to compare the value of the dihedral angleș, so we can avoid the calculation of arccosine. 3.3 Multiple-Choice Algorithm
Since the cost function has been defined, each possible atomic decimation operation (candidate) can be rated according to the function. So the remaining issue is to choose a candidate for each decimation step. In other words, we should find the optimal decimation sequence. Finding the optimal decimation sequence is a very complex problem [13] and consequently one has to find solutions with approximate optimality. Most of the algorithms adopt a greedy strategy to find a decimation sequence that is close to the optimal. For every decimation step, the algorithm will go through all possible candidates to find one with the lowest cost. An implementation of the greedy strategy usually requires a priority queue data structure for the candidates that has to be initialized and updated during the decimation. Our algorithm uses a different probabilistic optimization strategy based on Multiple-Choice algorithm to find the decimation sequence. The fundamental idea behind
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MCA is quite simple and intuitive and can be explained best by means of the wellestablished bins-and balls model [14,15]. In order to apply MCA to the model simplification problem we have to map balls, bins, and maximum load to the corresponding mesh entities [3]. Since the balls are enumerated in the outer loop (for each ball make a MC decision) they correspond to the decimation steps. The bins represent the possible choices in each step, hence they correspond to the possible candidates. The maximum load finally is the value that is to be optimized and consequently we associate it with the quality criterion that is used to rate the candidates. In this setup, the MCA approach to model simplification consists of testing a small set of d randomly selected candidates (edge collapses) in each step and performing that decimation operation among this small set that has the best quality value. Experiments show that using MCA approach our algorithm can produce approximations in almost the same quality as other algorithms based on greedy strategy when d = 6. Compared to the greedy optimization, the major benefit of the Multiple-Choice optimization is that the algorithmic structure is much simpler. For the Multiple-Choice optimization we do not need a priority queue and consequently we reduce the memory consumption and make the algorithm much easier to implement. 3.3 Algorithm Summary
Firstly, the importance of each vertex in a mesh should be evaluated. The most suitable edge for the contraction is searched in its neighborhood, and the one with the lowest cost is marked as the vertex’s importance. As for the most suitable edge for contraction we take the one that does not cause the mesh to fold over itself and preserves the original surface according to the criterion. Then we can decimate vertices one by one according their importance. Using the above idea of Multi-Choice techniques, the overall framework of our algorithm can be summarized as follows: 1. Determine the topology structure of the original mesh and calculate the unit normal of every triangle in the mesh. 2. For every vertex of the original model, calculate the cost of contracting the vertex to its neighborhood, which means to calculate the cost of all the edge adjacent to the vertex, picking the edge with the lowest cost as the vertex’s collapse edge. 3. Randomly choose d vertices from all candidates, and update the vertices needed to be recomputed among the d vertices. 4. Select the vertex with candidature edge of lowest cost from the d vertices, and contract its edge. After contracting, mark the related vertices needed to be updated. 5. Repeat step 3 and 4 until the given criterion is satisfied. Our algorithm does not need a global priority queue, so it is much easier to be implemented. In Table 1, we compare our algorithm with others.
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Table 1. Compared with others, our algorithm based on greedy strategy does not need a global priority queue
Algorithm step Initialize
Select candidate
Decimate
Our algorithm Others Initialize, Initialize, compute collapse cost for all compute collapse cost for all candidate, candidate perform global queue sorting Select d vertices randomly, update the vertex’s cost if Top of the queue necessary, pick the best out of d Perform operator Perform operator, locally recomputed cost, update global queue
4 Implementation Based on the above algorithm, we have developed a framework providing efficient simplification on models of various size. 9LHZ PRGHO
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Fig. 4. The structure of our simplification system. The system can read model file into internal data structure, simplify it interactively, and save the internal data back to model file.
The processing stage of the framework consists of the following steps (see Fig. 4): 1. 2. 3. 4. 5.
Read the input model file, and create internal data structure. Render the current model. Simplify the model according to the user’s aim. Render the simplified model. Repeat step 2-4 until the user is satisfied with the resulting model, then save it back to model file.
Step1 consists of reading the model file, triangulating the model, and storing all the points and triangles into the internal data structures. As our simplification algorithm can only deal with triangles as input, the models consisting of n-sided polygons need to be triangulated in the preprocessing phase.
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Class Vertex{ Vec3 location; // Vec3 is a vector class int index; set vertNeighbors; //vertices connected to this vertex set triNeighbors; //triangles of which this vertex is a part bool bActive; //false if vertex has been removed double cost; //cost of contracting the min cost edge int minCostNeighbor; // index of vertex at other end of the min cost edge } Class Face{ float weight; Vec3 direct; Vec3 normal;//normal of this triangle Vec3 point;// vertices of this triangle bool bActive; // active flag void getVerts(int& v1,int& v2,int& v3) } Class CShape { vector vertices; vector < Face > faces; Vertex& getvertex (int i); { return vertices( i ) }; Face& getface (int i ) { return faces( i );}; unsigned int vert_count( ) const; unsigned int face_count( ) const; unsigned int active_vert_count( ); unsigned int active_face_count( ); bool initialize( ); //find min cost edge for every vertex } Class CModel { vector shapes; void getshape (CShape& shape); bool initialize( ); //initialize every shape bool decimate(int percent); //control the process of simplification bool EdgeCollapse( int vertid )//contracting one edge }
As shown above, we define the basic internal data structure for model and simplification with the aid of Visual C++.
5 Results and Discussion In this section the efficiency of our algorithm is demonstrated. We have tried our implementation on various models of different sizes and varying shapes, and have
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achieved encouraging results. Table 2 summarizes the running time of our current implementation and compares it with Garland’s QEM algorithm [12] and Melax’s algorithm which is simple and fast [16]. All experiments are done on a commodity PC with Intel 2.4GMHz CPU and 1024M RAM. Table 2. Running time of different algorithms. All data reflects the time needed to simplify the model to 0 triangles
We also depict the absolute maximum geometric errors for the bunny and lamp model when decimating them to various levels of details (see Fig. 5 and Fig. 6). The approximation error is measured by the Hausdorff distance between the original model and the simplified result. The Hausdorff distance (sometimes called the L∞ norm difference) between two input meshes M1 and M2 is [17]:
K haus ( M 1 , M 2 ) = max(dev( M 1 , M 2 ), dev(( M 2 , M 1 )) 1
2
1
(4) 2
where dev(M , M ) in (4) measures the deviation of mesh M from mesh M . The Hausdorff distance provides a maximal geometric deviation between two meshes.
Fig. 5. Absolute maximum geometric error for bunny model. The size of bounding box is 15.6*15.4*12.1.
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Fig.7 demonstrates the visual quality of the approximations generated using our algorithm. In Fig.7 (i), the bunny model is drastically simplified (99%), but the major details of the original still remain.
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Fig. 6. Absolute maximum geometric error for lamp model. The size of bounding box is 15.6*15.6*22.6.
(a) telephone, 68575triangles
(d) lamp, 11672triangles
(b) 34287 triangles
(c) 1370 triangles
(e) 5836 triangles
(f) 232 triangles
Fig. 7. The visual quality of the approximations generated using our algorithm. The bunny model (i) is drastically simplified (99%), but the major details still remain.
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(g) bunny, 69451triangles
(h) 6945 triangles
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(i) 694 triangles
Fig. 7. (continued)
6 Conclusion We have presented a surface simplification algorithm which is capable of rapidly producing high fidelity approximations of 3d meshes. Our algorithm can preserve the visually important features of the model. We also applied generic probabilistic optimization principle of Multiple-Choice algorithm to the problem of finding a simplification sequence. Experiments show that the MCA approach can reduce the memory overhead and lead to a simpler algorithmic structure. Based on the proposed algorithm, we have implemented a simplification system. We have processed many 3D meshes of different sizes on this system, and achieved encouraging results. This demonstrates the effectiveness of our algorithm.
References 1. Campbell, F. W., Robson, J. G.: Application of Fourier Analysis to the Visibility of Gratings. Journal of Physiology 197 (1968) 551-566 2. Blakemore, C., Campbell, F. W.: On the Existence of Neurons in the Human Visual System Selectively Sensitive to the Orientation and Size of Retinal Images. Journal of Physiology, 203 (1969) 237-260 3. Wu, J., Kobbelt, L.: Fast Mesh Decimation by Multiple–choice Techniques. In Vision, Modeling and Visualization. IOS Press (2002) 241–248 4. Turk, G.: Re-tilling Polygonal Surfaces. In Proceeding of ACM SIGGRAPH (1992) 55-64 5. Schoroeder, W.J., Zarge, J.A., Lorensen, W. E.: Decimation of Triangle Meshes. In Proc. Of ACM SIGGRAPH (1992) 65-70 6. Rossignac, J., Borrel, P.: Multi-resolution 3D Approximation for Rendering Complex Scenes. In Geometric Modeling in Computer Graphics Springer Verlag (1993) 455-465 7. Hoppe, H., DeRose, T., Duchamp, T., McDonald, J. A., Stuetzle, W.: Mesh optimization. Computer Graphics (SIG-GRAPH ’93 Proceedings) (1993) 19–26 8. Hoppe, H.: Progressive Meshes. In SIG-GRAPH 96 Conference Proceeding. ACM SIGGRAPH Addison Wesley August (1996) 99-108 9. Cohen, J., Varshney, A., Manocha, D., Turk, G.: Simplification Envelopes. In Proc. Of ACM SIGGRAPH ’96 (1996) 119-128
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10. Derose, T., Lounsbery, M., Warren, J.: Multiresolution Analysis for Surfaces of Arbitrary Topology Type. Technical Report TR 93-10-05 Department of Computer Science University of Washington (1993) 11. Eck, M., Derose, T., Duchamp, T., Hoppe, H., Lousbery, M., Stuetzle, W.: Multiresolution Analysis of Arbitrary Meshes. In Proceeding of ACM SIGGRAPH (1995) 173-182 12. Garland, M., Heckbert, P. S.: Surface Simplification Using Quadric Error Metric. In Proc. SIGGRAPH'97 (1997) 209-216 13. Agarwal, P., Suri, S.: Surface Approximation and Geometric Partitions. In Proceedings of 5th ACM-SIAM Symposium on Discrete Algorithms (1994) 24-33 14. Azar, Y., Broder, A., Karlin, A., Upfal, E.: Balanced Allocations. SIAM Journal on Computing, 29(1) (1999) 180-200 15. Kolchin, V., Sevastyanov, B., Chist-yakov, V.: Random Allocations. John Willey & Sons (1978) 16. Melax, S.: A Simple, Fast, and Effective Polygon Reduction Algorithm. Game Developer November (1998) 44-49 17. Southern, R., Blake, E., Marais, P.: Evaluation of Memoryless Simplification. Technical Report CS01-18-00, University of Cape Town (2001)
Hierarchical Multiple Models Adaptive Feedforward Decoupling Controller Applied to Wind Tunnel System∗ Xin Wang1,2 and Hui Yang2 1
Center of Electrical & Electronic Technology, Shanghai Jiao Tong University, Shanghai, P.R. China, 200240, 2 School of Electrical & Electronic Engineering, East China Jiaotong University, Jiangxi, P.R. China, 330013 [email protected]
Abstract. For the biggest wind tunnel in Asia, during the aerodynamic research on the scale models, it is difficult to keep the Mach number in the test section and the stagnation pressure constant strictly because the interaction is strong, the operation conditions change abruptly and the transient response’s requirements are high. To cope with these problems, a Hierarchical Multiple Models Adaptive Feedforward Decoupling Controller (HMMAFDC) is presented in this paper. The controller is composed of multiple fixed controller models and two adaptive controller models. Multiple models are used to improve the transient response of the wind tunnel. Hierarchical structure is presented to reduce the number of the fixed models greatly. To the optimal model selected by the switching index, the interactions of the system are viewed as measurable disturbance and eliminated using the feedforward strategy. It not only decouples the system dynamically but also places the poles of the closed loop system arbitrarily. The significance of the proposed method is that it is applicable to a MIMO system with a much small number of models. The global convergence is obtained. Finally, several simulation examples in a wind tunnel experiment are given to show both effectiveness and practicality.
1 Introduction A 2.4m x 2.4m injector driven transonic wind tunnel in China Aerodynamics Research and Development Center (CARDC) is the biggest wind tunnel in Asia [1]. It is used for aerodynamic research on scale models, which is very important for national defense and civil aviation. Aerodynamic research data of scale models are measured at a given Mach number with a constant stagnation pressure. It is required that in the initial stage, the response time should be no longer than 7.0 seconds; in the experiment stage, the steady state tracking errors are within 0.2% in 0.8 second and the overshoot should be avoided [2]. Recently several controllers are designed to satisfy the transient response’s requirement above. According to a 1.5m wind tunnel (FFA- T1500) in Sweden, several separate SISO models are used to control it [3]. For a 1.6m x 2m wind tunnel in ∗
This work is supported by National Natural Science Foundation (No. 60504010, 50474020) and Shanghai Jiao Tong University Research Foundation.
Netherlands, it is regarded as a second-order system and a PID controller is given [4]. Later a predictive controller is designed to control the Mach number in this wind tunnel with the angle of attack changing [5]. In USA, a system of self-organization neural networks are developed and tested to cluster, predict and control the Mach number of a 16-foot wind tunnel in NASA [6]. However, if the descriptions for the aerodynamics of a wind tunnel are different with the size of a wind tunnel, the controller should be also different. For the 2.4m x 2.4m transonic wind tunnel in CARDC, two SISO stable linear reduced order models are established and two PID controllers are designed to control the Mach number and the stagnation total pressure respectively [2]. But when the Mach number in the test section varies from 0.3 to 1.2, the interaction becomes stronger and a multivariable decoupling controller is needed [7]. In [1], two feedforward static decouplers with four fixed PI controllers are designed to solve this problem. But when the Mach number steps from 0.3 to 0.4, 0.5,…,1.2, the parameters of the wind tunnel will jump accordingly. The poor transient response cannot satisfy the high requirements of the wind tunnel above. So some special controller structure and algorithms are needed. To solve this problem, some multiple models adaptive controllers (MMAC) are designed to improve the transient response [8, 9]. One adaptive model, one reinitialized adaptive model and lots of fixed models are used to cover the region where the parameters change. For example, about 300 models are needed to cover the region where only one parameter changes [10]. The number of the models is so large that it increases the calculation time, which affects the selection of the sampling period. To reduce the huge number of models needed in MMAC, Localization, Moving Bank and other methods are presented [11, 12]. However, these methods can only reduce a small number of the models, which can’t solve this problem essentially. In our former work, a Hierarchical Multiple Models Adaptive Controller (HMMAC) was proposed to reduce the number of the fixed models [13, 14]. In [13], a decoupling controller using pole-zero cansellation method is proposed to deal with minimum phase system, while non-minimum pahse system is solved in [14]. Unfortunately, their structures are not suitable for the distributed control system (DCS) In this paper, a novel Hierarchical Multiple Models Adaptive Feedforward Decoupling Controller (HMMAFDC) is presented. Multiple models are used to improve the transient response of the wind tunnel. Hierarchical structure is presented to reduce the number of the fixed models greatly. To the optimal model selected by the switching index, the interactions of the system are viewed as measurable disturbance and eliminated using the feedforward strategy. It not only decouples the system dynamically but also places the poles of the closed loop system arbitrarily. Several simulation examples in the wind tunnel experiment illustrate the HMMADC.
2 Description of the System The 2.4m x 2.4m wind tunnel is an intermittent wind tunnel constructed for the aerodynamic research aim by CARDC. It is a closed-circuit interjector driven transonic tunnel and used for testing scale models, mostly of airplanes, in the speed region of 0.3 to 1.2 (see fig.1). The interjector is used to realize high Mach numbers with the limited amount of air storage while the Reynolds number can be increased in order to decrease
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the influence of model factors on the measurements. At the initial stage of the aerodynamic experiment, the main control hydraulic servo valve is opened and air is allowed to flow from storage bottle into the tunnel. Part of the air is let out through the main exhaust hydraulic servo valve; the other is injected into the tunnel by the injector. After the stable flowing field is established, the experiment proceeds. It has more than 40 operation cases. One of these cases is as follows [1]. At the initial stage of the experiment, the main control hydraulic servo valve is tuned to give the initial value of the Mach number in the test section with the main exhaust hydraulic servo valve and the choke finger at the preset position. After the stable flowing field is established, the exhaust hydraulic servo valve is tuned to keep the stagnation total pressure to be 1.5, and the choke finger makes the Mach number in the test section vary with ∆ M = 0.1 from 0.3 to 1.2, while the main control hydraulic servo valve is controlled to ensure the injector total pressure constant and compensates for the loss of the air storage pressure. When the Mach number in the test section is larger than 0.8, the choke finger is opened at its maximal position and the plenum exhaust valve is used to tune the Mach number in the test section correspondingly.
flow Main control hydraulic servo valve
Injector
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Stagnation pressure control flow flow Test section
Choke finger
Stagnation
Main exhaust hydraulic servo valve
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Fig. 1. The structure of the transonic wind tunnel
From these two particular models[7], the linear reduced-order model of the wind tunnel can be established according to each Mach number as follows
β1 −0.4 s ª e − « α y s ( ) ª 1 º 1s + 1 « = « y ( s)» ¬ 2 ¼ « − β 3 s + 1 e −0.4 s « (α s + 1) 2 3 ¬
−
β2
º e −0.4 s » ªu ( s) º »⋅« 1 » , β4 » u (s) e −0.4 s » ¬ 2 ¼ α4 s + 1 ¼
(α 2 s + 1)2
(1)
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where y1 ( s ) , y2 ( s ) , u1 ( s ) , u2 ( s ) are the Mach number in the test section, the stagnation total pressure, the choke finger opening and the main exhaust hydraulic servo valve respectively. αi , β i are parameters. and satisfy αi ∈ [αi min , αi max ] , βi ∈ [ βi min , β i max ] .
Select the sampling period as 0.1 second. Then the linear discrete time multivariable minimum phase system is described as
(I + A z 1
−1
+ A2 z −2 ) y(t ) = ( B0 + B1 z −1 ) u(t − 4) + d .
(2)
When the Mach number varies, the parameters of the system change accordingly. So the system can be viewed as a linear MIMO discrete-time system, which admits DARMA representation of the form A(t , z −1 ) y(t ) = B(t , z −1 )u(t − k ) + d (t ) ,
(3)
where u(t ) , y(t ) are the n × 1 input, output vectors respectively and d (t ) is a n × 1 vector denoting the steady state disturbance. A(t , z −1 ), B(t , z −1 ) are polynomial matrixes in the unit delay operator z −1 and B0 (t ) is nonsingular, for any t . Here
A(t , z −1 ) is assumed to be a diagonal polynomial matrix. The system satisfies the assumptions as follows: (1) The system parameters are time variant with infrequent large jumps. The period between two adjacent jumps is large enough to keep the jumping parameters constant. (2) Φ (t ) = [ − A1 (t ),; B0 (t ),; d (t )] is the system model, which changes, in a
compact set Σ . (3) The upper bounds of the orders of A(t , z −1 ) , B(t , z −1 ) and the time delay k are known a prior; (4) The system is minimum-phase. To decouple the system, the interaction caused by the input u j ( t ) to the output yi (t ) , ( j ≠ i ) is viewed as measurable disturbance. So the system (3) can rewritten
A(t , z −1 ) y(t ) = B(t , z −1 ) u(t − k ) + B(t , z −1 )u(t ) + d (t ) ,
(4)
where B(t , z −1 ) = B(t , z −1 ) + B(t , z −1 ) . B(t , z −1 ) = diag ª¬ Bii (t , z −1 ) º¼ is a diagonal polynomial matrix and B0 (t ) is nonsingular, ∀t . B(t , z −1 ) = ª¬ Bij (t , z −1 ) º¼ and
Bii (t , z −1 ) = 0 . From assumption (1), Ai ( t ) , B j (t ) , B j (t ) , d (t ) are piecewise constant (time variant system with infrequent large jumping parameters). During the period when no jumps happen, (4) can be rewritten as A( z −1 ) y(t ) = B( z −1 )u(t − k ) + B( z −1 ) u(t − k ) + d .
(5)
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3 HMMAFDC To reduce the number of fixed models, a hierarchical structure with l levels is adopted. Iupu t an d O utput D ata
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Level 2
1
ಹ
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Fig. 2. Hierarchical principle of the HMMAFDC
(1) Utilizing the prior information, the set Σ , where the parameters of the system vary, is partitioned into m1 subsets Σ , ( s = 1, , m1 ) . In each subset, the center Φ and 1, s
1,s
its radius r are designed to satisfy that For any Φ ∈ Σ , Φ − Φ ≤ r . So the centers 1,s
1,s
1, s
1, s
Φ , s = 1, , m1 compose the level 1 fixed model set which covers the system 1,s
parameter set with their neighbors entirely. (2) According to the switching index, the best model in level 1 is selected as j1 . (3) Based on the best model j1 in level 1 and use the partition method presented above similarly, m2 centers are set up to compose the level 2 fixed model set on line dynamically, which covers the model j1 with their neighbors entirely. (4) According to the switching index, the best model in level 2 is selected as j2 . (5) Similarly, the best model in the last level i.e. level l is selected as jl , which is also the best model among all the fixed models. (6) At last, in level l + 1 , a free running adaptive model and a reinitialized adaptive model are added in. According to the switching index, the best model is selected among
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these three models above. The free running adaptive model is used to guarantee the stability of the wind tunnel while the reinitialized adaptive model’s initial value can be set to be that of the best model selected to improve the transient response of the wind tunnel. For the system (5), the cost function to be considered is of the form [15] 2
J c = P ( z −1 ) y(t + k ) − R( z −1 ) w(t ) +Q ( z −1 )u(t ) + S ( z −1 ) u(t ) + r ,
(6)
where w(t ) is the known reference signal. P ( z −1 ), Q ( z −1 ), R( z −1 ) are diagonal weighting polynomial matrices, S ( z −1 ) is a weighting polynomial matrix and r is the weighting vector respectively. Q ( z −1 ) is used to weight the control u(t ) and S ( z −1 ) is used to weight the interaction u(t ) , which is viewed as the measurable disturbance. Introduce the identity P ( z −1 ) = F ( z −1 ) A( z −1 ) + z − k G ( z −1 ) .
(7)
In order to get unique polynomial matrixes F ( z −1 ) , G ( z −1 ) , the orders of F ( z −1 ), G ( z −1 ) are chosen as n f = k − 1, ng = na − 1 .
(8)
Multiplying (5) by F ( z −1 ) and using (7), the optimal control law is as G ( z −1 ) y(t ) + H1 ( z −1 ) u(t ) + H 2 ( z −1 ) u(t ) + r = R( z −1 ) w(t ) ,
(9)
where H1 ( z −1 ) = F ( z −1 ) B( z −1 ) + Q ( z −1 ), H 2 ( z −1 ) = F ( z −1 ) B( z −1 ) + S ( z −1 ), r = Fd + r . From (9) and (5), the system equation can be derived as follows ª¬ P ( z −1 ) B( z −1 ) + Q ( z −1 ) A( z −1 ) º¼ y(t + k ) = B( z −1 ) R( z −1 ) w(t ) + ª¬Q ( z −1 )d − B( z −1 )r º¼ + ªQ ( z −1 ) B( z −1 ) − B( z −1 ) S ( z −1 ) º u(t ) . ¬ ¼
(10)
Note that (10) is not the closed loop system equation because there exists the input u(t ) , although it is viewed as the measurable disturbance. Equation (9) and (10) are just used to choose the polynomial matrixes to decouple the system. For the system, let Q ( z −1 ) = R1 B( z −1 ) S ( z −1 ) = R1 B( z −1 ) where R1 is a diagonal matrix. The system equation (10) can be rewritten as ª¬ P ( z −1 ) + R1 A( z −1 ) º¼ y(t + k ) = R( z −1 ) w(t ) + R1d − r .
(11)
From (11), considering P ( z −1 ), R( z −1 ), A( z −1 ) are diagonal matrices, it is concluded that by the choice of the weighting polynomial matrixes, the closed loop system can be decoupled dynamically. To eliminate the steady state error, the polynomial matrixes can be chosen as P ( z −1 ) + R1 A( z −1 ) = T ( z −1 ) , r = R1d .
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In the level l + 1 , the HMMADC is composed of three models. One is the fixed controller model Θ , i.e. the best model jl in level l , the others are a free-running l +1,1
adaptive controller model Θ and a re-initialized adaptive controller model Θ . l +1,2
l +1,3
To the adaptive controller models Θ , Θ , Multiplying (5) by F ( z −1 ) from the left l +1,2
l +1,3
and using (7), it follows that P ( z −1 ) y(t + k ) = G ( z −1 ) y(t ) + F ( z −1 ) B( z −1 )u(t ) + F (1)d .
(12)
Multiplying (5) by R1 from the left and using the chosen polynomial matrixes above, it follows that T ( z −1 ) y(t + k ) = P ( z −1 ) y(t + k ) + R1 A( z −1 ) y(t + k ) = G ( z −1 ) y(t ) + F ( z −1 ) B( z −1 )u(t ) + R1 B( z −1 ) u(t ) + F (1)d + R1d .
(13)
Using (7), (9) and the definitions of H ( z −1 ) , r , the recursive estimation algorithm of Θ and Θ is described as follows m +1
m+2
Ty(t + k ) = Gy(t ) + H1u(t ) + H 2 u(t ) + r ,
θˆi (t ) = θˆi (t − 1) + a (t )
X (t − k ) ⋅ ª y fi (t )T − X (t − k )T θˆi (t − 1) º¼ , 1 + X ( t − k )T X ( t − k ) ¬
θi = ª¬ g , , g ; g ,, g ,; h ,, h ;º¼ , i = 1, 2, , n . The scalar a (t ) is set to 0 i1
0 in
1 i1
1 in
0 i1
0 in
avoid the singularity problem of the estimation Hˆ (0) [16]. To a HMMAFDC, the switching index is as follows 2
2
y f (t ) − y f ( t )
e f (t ) J=
i ,s
i,s
1 + X (t − k ) X (t − k ) T
=
(16)
i,s
1 + X (t − k ) X (t − k ) T
where y f (t ) = T ( z −1 ) y(t ) is the auxiliary output of system, e f (t ) is the auxiliary i ,s
output error between the real system and the model s in level i . For level 1 to l , let ji = arg min( J ) s = 1, , mi , i = 1, 2, , l correspond to the model whose auxiliary i,s
output error is minimum , then Θ is chosen to be the best controller in level i . But for j
the level l + 1 , there are only three models left. So let jl +1 = arg min( J ) s = 1, 2, 3 , l +1, s
then Θ is chosen to be the HMMADC and used to control the system. j +1
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(1) If jl +1 ≠ 3 , which means Θˆ (t ) is not the minimum output error controller, then l +1,3
re-initialize Θˆ (t ) as the optimal controller parameter to improve the transient l +1,3
response, i.e. Θˆ (t ) = Θ . Θˆ (t ) , Θˆ (t ) are estimated using (15) respectively and l +1,3
l +1, jl +1
l +1,2
l +1,3
the controller is set as Θ (t ) = Θ . l +1, jl +1
(2) If jl +1
= 3 , Θˆ (t ) , Θˆ (t ) are estimated using (15) respectively and the controller l +1,2
l +1,3
is set as Θˆ (t ) = Θˆ (t ) . l +1,3
The optimal control law can be obtained from
Gˆ ( z −1 ) y(t ) + ª¬ Hˆ 1 ( z −1 ) + Hˆ 2 ( z −1 ) º¼ u(t ) + rˆ = R( z −1 ) w(t ) .
(17)
4 Applications to the Wind Tunnel System The wind tunnel system (2) is of second order and the time delay equals to 4. Every 60 steps, the Mach number in the test section varies from 0.3 to 1.2 with ∆ M = 0.1 , which causes the parameters of the system jump simultaneously. Because the sampling period is selected as 0.1 second, 1 second in experiment means 10 steps in the simulation. The stagnation total pressure is required to be 1.5 all the time. Case 1: A conventional adaptive decoupling controller is designed to control the wind tunnel. Its initial value is chosen close to the real controller parameter model. The responses of the system are shown in Fig. 3 and 4. In the initial stage, after 7 seconds’ operation, the overshoots of the system are all less than 0.2%, which satisfies the requirement. But in the experiment stage, after 0.8 second’s operation, the overshoots of the system are much larger than 0.2%. The largest overshoot is 68.74%, which 340 times the requirement. In fact, during all experiment period, i.e. after the initial stage, the overshoots of the system are all much larger than 0.2%. So the adaptive controller cannot satisfy the requirement and be used to control the wind tunnel. Case 2: A multiple models adaptive decoupling controller is designed to control the wind tunnel. In this case, 30 fixed models are used to cover the region where jumping parameters vary. Note that the real system model is not among these fixed system models. Then 30 corresponding fixed controller models are set up using the transformation proposed above and two adaptive controller models are added to compose the multiple controller models. These two adaptive controller models’ initial values are same as those of the adaptive model in case 1. The responses of the system are shown in Fig. 5 and 6. Compared with that in case 1, the transient response of the wind tunnel is improved greatly when only 30 fixed models are added. In the initial stage, the overshoots of the system are all less than 0.2%, which satisfies the requirement. However, in the experiment stage, the overshoots of the system are all larger than 0.2%, especially the stagnation total pressure (see Fig.6).
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Case 3: A multiple models adaptive decoupling controller with 1000 fixed models is designed to control the wind tunnel. It is designed using the same algorithm as in case 2 but the number of the fixed models. As the number of the fixed models increases, the transient response becomes better. Both in the initial stage and in the experiment stage, the overshoots of the system are all less than 0.2%, which satisfies the requirement (see Fig.7 and 8). Case 4: A HMMADC is designed to control the wind tunnel. In this case, the same algorithm is used as in case 2 and 3 except a hierarchical structure with 3 levels and 10 models at each level adopted. Totally there are 30 fixed models added, the same number as in case 2, but the overshoots of the system are much better than those in case 2. They are similar to those in case 3, all less than 0.2%, which satisfies the requirement both in the initial stage and in the experiment stage. But the number is 33 times less than that in case 3 (see Fig.9 and 10). The results show that although the same algorithm is adopted in case 2, 3 and 4, the HMMADC can get better transient response with fewer models. 1.4
1.2
1
y1
0.8
0.6
0.4
0.2
0 0
50
100
150
200 t/step
250
300
350
400
Fig. 3. The Test-section-Mach-number using ADC 1.8 1.6 1.4 1.2
y2
1 0.8 0.6 0.4 0.2 0 0
50
100
150
200 t/step
250
300
350
Fig. 4. The Stagnation-total-pressure using ADC
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1.2
1
y1
0.8
0.6
0.4
0.2
0 0
50
100
150
200 t/step
250
300
350
400
Fig. 5. The Test-section-Mach-number of MMADC using 30 models 1.8 1.6 1.4 1.2
y2
1 0.8 0.6 0.4 0.2 0 0
50
100
150
200 t/step
250
300
350
400
Fig. 6. The Stagnation-total-pressure of MMADC using 30 models 1.4
1.2
1
0.8 y1
296
0.6
0.4
0.2
0 0
50
100
150
200 t/step
250
300
350
400
Fig. 7. The Test-section-Mach-number of MMADC using 1000 models
HMMAFDC Applied to Wind Tunnel System 1.8 1.6 1.4 1.2
y2
1 0.8 0.6 0.4 0.2 0 0
50
100
150
200 t/step
250
300
350
400
Fig. 8. The Stagnation-total-pressure of MMADC using 1000 models 1.4
1.2
1
y1
0.8
0.6
0.4
0.2
0 0
50
100
150
200 t/step
250
300
350
400
Fig. 9. The Test-section-Mach-number of HMMADC using 10,10,10 models 1.8 1.6 1.4 1.2
y2
1 0.8 0.6 0.4 0.2 0 0
50
100
150
200 t/step
250
300
350
400
Fig. 10. The Stagnation-total-pressure of HMMADC using 10,10,10 models
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5 Conclusions This paper presents a Hierarchical multiple models adaptive decoupling controller. Compared with the MMADC, the better transient response can be got with much fewer models, which reduce the number of the fixed models greatly.
References 1. Zhang, G.J., Chai T.Y., Shao C.: A Synthetic Approach for Control of Intermittent Wind Tunnel, Proceedings of the American Control Conference, (1997) 203–207 2. Yu W., Zhang G.J.: Modelling and Controller Design for 2.4 M Injector Powered Transonic Wind Tunnel, Proceedings of the American Control Conference, (1997) 1544–1545 3. Nelson D.M.: Wind Tunnel Computer Control System and Instrumentation, Instrument Society of America, (1989) 87–101 4. Pels A.F.: Closed-Loop Mach Number Control in A Transonic Wind Tunnel, Journal A, 30 (1989) 25–32 5. Soeterboek R.A.M., Pels A.F., et al.: A Predictive Controller for the Mach Number in A Transonic Wind Tunnel, IEEE Control Systems Magazine, 11 (1991) 63–72 6. Motter M.A., Principe J.C.: Neural Control of the NASA Langley 16-Foot Transonic Tunnel, Proceedings of the American Control Conference, (1997) 662–663 7. CARDC.: Measurement and Control System Design in High and Low Speed Wind Tunnel, National Defence Industry Press, Beijing (2002) (in Chinese) 8. Narendra K.S., Xiang C.: Adaptive Control of Discrete-Time Systems Using Multiple Models, IEEE Trans. on Automatic Control, 45 (2000) 1669–1686 9. Wang X., Li S.Y., et al.: Multiple Models Adaptive Decoupling Controller for A Nonminimum Phase System, 5th Asian Control Conference, (2002) 166–171 10. Narendra K.S., Balakrishnan J., Ciliz M.K.: Adaptation and Learning Using Multiple Models, Switching, and Tuning, IEEE Control Systems Magazine, 15 (1995) 37–51 11. Zhivoglyadov P.V., Middleton R.H., Fu M.Y.: Localization Based Switching Adaptive Control for Time-Varying Discrete-Time Systems, IEEE Trans. on Automatic Control, 45 (2000) 752–755 12. Maybeck P.S., Hentz K.P.: Inverstigation of Moving Bank Multiple Model Adaptive Algorithms, Journal of Guidance Control Dynamics, 10 (1987) 90–96 13. Wang X., Li S.Y., Yue H.: Multivariable Adaptive Decoupling Controller Using Hierarchical Multiple Models, ACTA Automatica Sinica, 31 (2005) 223–230 14. Wang X., Li S.Y., Yue H.: Hierarchical Multiple Models Decoupling Controller for Nonminimum Phase Systems, Control Theory and Application, 22 (2005) 201–206 15. Wang X., Li S.Y., et al: Multiple Models Direct Adaptive Controller Applied to the Wind Tunnel System, ISA Transactions, 44 (2005) 131–143 16. Goodwin G.C., Ramadge P.J., Caines P.E.: Discrete Time Multivariable Adaptive Control, IEEE Trans. on Automatic Control, 25 (1980) 449–456 17. Landau I.D., Lozano R.: Unification of Discrete Time Explicit Model Reference Adaptive Control Designs, Automatica, 17 (1981) 593–611
Intelligent Backstepping Control for Chaotic Systems Using Self-Growing Fuzzy Neural Network Chih-Min Lin1, Chun-Fei Hsu2, and I-Fang Chung3 1
Department of Electrical Engineering, Yuan-Ze University, Chung-Li, Tao-Yuan, 320, Taiwan, Republic of China [email protected] 2 Department of Electrical and Control Engineering, National Chiao-Tung University, Hsinchu, 300, Taiwan, Republic of China [email protected] 3 Institute of Bioinformatics, National Yang-Ming University, Taipei, 115, Taiwan, Republic of China [email protected]
Abstract. This paper proposes an intelligent backstepping control (IBC) for the chaotic systems. The IBC system is comprised of a neural backstepping controller and a robust compensation controller. The neural backstepping controller containing a self-growing fuzzy neural network (SGFNN) identifier is the principal controller, and the robust compensation controller is designed to dispel the effect of minimum approximation error introduced by the SGFNN identifier. Finally, simulation results verify that the IBC system can achieve favorable tracking performance.
2 Description of Chaotic Systems Chaotic systems have been known to exhibit complex dynamical behavior. The interest in chaotic systems lies mostly upon their complex, unpredictable behavior, and extreme sensitivity to initial conditions as well as parameter variations. Consider a second-order chaotic system such as well known Duffing’s equation describing a special nonlinear circuit or a pendulum moving in a viscous medium under control [5-8].
x = − px − p1 x − p 2 x 3 + q cos( wt ) + u = f + u
(1)
where p , p1 , p2 and q are real constants; t is the time variable; w is the fre-
x
x
quency; f = − px − p1 x − p 2 x 3 + q cos( wt ) is the chaotic dynamic function; and u is the control effort. Depending on the choice of these constants, it is known that the solutions of system (1) may exhibit periodic, almost periodic and chaotic behavior. For observing the chaotic unpredictable behavior, the open-loop system behavior with u = 0 was simulated with p = 0.4 , p1 = −1.1 , p 2 = 1.0 and w = 1.8 . The phase plane plots from an initial condition point (1,1) are shown in Figs. 1(a) and 1(b) for q = 1.8 and q = 7.0 , respectively. It is shown that the uncontrolled chaotic system has different trajectories for different q values.
q=1.8
q=7.0
x
x
(a)
(b)
Fig. 1. Phase plane of uncontrolled chaotic system
3 Design of Ideal Backstepping Controller The control objective is to find a control law so that the state trajectory x can track a reference xc closely. Assume that the parameters of the system (1) are well known, the design of ideal backstepping controller is described step-by-step as follows: Step 1. Define the tracking error e1 = x − xc
(2)
and the derivative of tracking error is defined as e1 = x − x c .
(3)
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The x can be viewed as a virtual control in the equation. Define the following stabilizing function α = x c − c1e1 (4) where c1 is a positive constant. Step 2. Define e2 = x − α
(5)
then the derivative of e2 is expressed as e2 = x − α = x − xc + c1e1 .
(6)
Step 3. The ideal backstepping controller can be designed as [9] u * = xc − f − c1e1 − c2 e2 − e1
(7)
where c2 is a positive constant. Substituting (7) into (6), it is obtained that e2 = −c2 e2 − e1 .
(8)
Step 4. Define a Lyapunov function as e12 e22 (9) + . 2 2 Differentiating (9) with respect to time and using (3)-(5) and (8), it is obtained that V = e e + e e V1 =
(10) Therefore, the ideal backstepping controller in (7) will asymptotically stabilize the system.
4 Design of Intelligent Backstepping Controller Since the chaotic dynamic function f may be unknown in practical application, the ideal backstepping controller (7) can not be precisely obtained. To solve this problem, the descriptions of the SGFNN identifier and the design steps of the IBC system are described as follows: 4.1 SGFNN Identifier
A four-layer fuzzy neural network, which comprises the input (the i layer), membership (the j layer), rule (the k layer), and output (the o layer) layers, is adopted to implement the proposed SGFNN. The signal propagation and the basic function in each layer are as follows: Layer 1 - Input layer: For every node i in this layer, the net input and the net output are represented as
neti1 = xi1
(11)
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y i1 = f i1 (net i1 ) = neti1 , i = 1,2 where
(12)
1 i
x represents the i-th input to the node of layer 1.
Layer 2 - Membership layer: In this layer, each node performs a membership function and acts as an element for membership degree calculation, where the Gaussian function is adopted as the membership function. For the j-th node, the reception and activation functions are written as
net y 2j = f j2 (net 2j
2 j
(x =−
2 i
− mij )
2
(σ ) ) = exp(net ) ,
(13)
2
ij 2 j
j = 1,2,..., m
(14)
where mij and σ ij are the mean and standard deviation of the Gaussian function in the j-th term of the i-th input linguistic variable xi2 , respectively; and m is the total number of the linguistic variables with respect to the input nodes. Layer 3 - Rule layer: Each node k in this layer is denoted by ∏ , which multiplies the incoming signals and outputs the result of the product. For the k-th rule node net k3 = ∏ x 3j
(15)
y k3 = f k3 (net k3 ) = net k3 , k = 1,2,..., n
(16)
j
where x 3j represents the j-th input to the node of layer 3. Layer 4 - Output layer: The single node o in this layer is labeled as Σ , which computes the overall output as the summation of all incoming signals net o4 = ¦ wk4 xk4
(17)
y o4 = f o4 (neto4 ) = neto4 , o = 1
(18)
k
where the link weight wk4 is the output action strength associated with the k-th rule; xk4 represents the k-th input to the node of layer 4; and y o4 is the output of the SGFNN. For ease of notation, define the vectors m and ı collecting all parameters of SGFNN as m = [m11 m21 m12 m2 m ]T
(19)
ı = [σ 11 σ 21 σ 12 σ 2 m ]
(20)
T
Then, the output of the SGFNN can be represented in a vector form fˆ = w T ĭ(m, ı )
(21)
where w = [w14 w24 ...wn4 ] and ĭ = [x14 x24 ...xn4 ] = [Φ 1 Φ 2 ... Φ n ]T . According to the T
T
universal approximation theorem, an optimal SGFNN approximator can be designed to approximate the chaotic system dynamics, such that [10] f = f * + ∆ = w *T ĭ * (m * , ı * ) + ∆
(22)
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where ∆ is the approximation error, w * and ĭ * are the optimal parameter vectors of w and ĭ , respectively, and m * and ı * are the optimal parameters of m and ı , respectively. Let the number of fuzzy rules be n * and the fuzzy rules be divided into two parts. The first part contains n neurons which are the activated part and the secondary part contains n * − n neurons which do not exist yet. Thus, the optimal weights w * , ĭ * , m * and ı * are classified in two parts such as ªw *a º ªĭ *a º ªm *a º ªı *a º w * = « * » , ĭ * = « * » , m * = « * » and ı * = « * » ¬w i ¼ ¬ĭ i ¼ ¬m i ¼ ¬ı i ¼
(23)
where w *a , ĭ *a , m *a and ı *a are activated parts, and w *i , ĭ *i , m *i and ı *i are inactivated parts, respectively. Since these optimal parameters are unobtainable, a SGFNN identifier is defined as ˆ (m ˆ a , ıˆ a ) ˆ Ta ĭ fˆ = w a
(24)
ˆ , m ˆ a and ıˆ a are the estimated values of w *a , ĭ *a , m *a and ı *a , reˆa, ĭ where w a
~
spectively. Define the estimated error f as ~ ˆ +∆ ˆ Ta ĭ f = f − fˆ = w *aT ĭ *a + w *i T ĭ *i − w a ~ ~ T ˆ T T ~ ~ ˆ ĭ +w ĭ +∆ =w ĭ +w a
a
a
a
a
(25)
a
~ ~ = w* − w ˆ . In the following, some adaptive laws will ˆ a and ĭ a = ĭ *a − ĭ where w a a a be proposed to on-line tune the mean and standard deviation of the Gaussian function of the SGFNN approximator to achieve favorable estimation of the dynamic function. To achieve this goal, the Taylor expansion linearization technique is employed to transform the nonlinear radial basis function into a partially linear form, i.e.
~ ~ + BT ı ~ +h ĭa = AT m a a
(26)
ª ∂Φ ª ∂Φ 1 ∂Φ n º ∂Φ n º where A = « 1 » |m =mˆ a , B = « » |ı =ıˆ a , h is a vector of higher∂m a ¼ ∂ı a ¼ ¬ ∂m a ¬ ∂ı a ~ = m* − m ~ = ı * − ıˆ , and ∂Φ k and ∂Φ k are defined as ˆa, ı order terms, m a a a a a ∂m ∂ı a a
a
T
ª º ª ∂Φ k º ∂Φ k ∂Φ k 0 0 0» « » = «0( k −1)×2 ( m − k )×2 m m m ∂ ∂ ∂ 1k 2k ¬ ¼ ¬ a¼
(27)
T
ª º ª ∂Φ k º ∂Φ k ∂Φ k 0 0 0» « » = «0( k −1)× 2 ( m − k )× 2 ∂ı 1k ∂ı lk ¬ ¼ ¬ ∂ı a ¼ Substituting (26) into (25), it is obtained that ~ ~T ˆ ~ T Aw ~ T Bw ˆa +ı ˆ a +ε f = w a ĭa + m a a
(28)
(29)
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~ =m ~ T Aw ~ =ı ~ T Bw ˆ Ta A T m ˆ a and w ˆ Ta B T ı ˆ a are used since they are scalars; and where w a a a a ~ T T *T * ~ ˆ h + w ĭ + w ĭ + ∆ and assume it is bounded by the uncertain term ε ≡ w a
a
a
i
i
0 ≤ ε ≤ E , where E is a positive constant representing the approximation error bound. However, it is difficult to measure this bound in practical applications. Thus, a bound estimation mechanism is developed to observe the bound of the approximation error. Define the estimation error of the bound ~ (30) E = E − Eˆ where Eˆ is the estimated error bound. 4.2 Fuzzy Rule Generation In general, the selection of the number of fuzzy rules is a trade-off between desired performance and computation loading. If the number of fuzzy rules is chosen too large, the computation loading is heavy so that they are not suitable for practical applications. If the number of fuzzy rules is chosen too small, the learning performance may be not good enough to achieve desired performance. To tackle this problem, the proposed SGFNN identifier consists of structure and parameter learning phases. The first step of the structure learning phase is to determine whether or not to add a new node (membership function) in layer 2 and the associated fuzzy rule in layer 3, respectively. In the rule generating process, the mathematical description of the existing rules can be represented as the membership degree of the incoming data to the cluster. Since one cluster formed in the input space corresponds to one potential fuzzy logic rule, the firing strength of a rule for each incoming data xi1 can be represented as the degree that the incoming data belong to the cluster. The firing strength obtained from (16) is used as the degree measure
β k = y k3 , k = 1, 2, ..., n( N )
(31)
where n(N ) is the number of the existing rules at the time N. According to the degree measure, the criterion of generating a new fuzzy rule for new incoming data is described as follows. Find the maximum degree β max defined as
β max = 1≤max βk k ≤n ( N )
(32)
It can be observed that if the maximum degree β max is smaller as the incoming data is far away the existing fuzzy rules. If β max ≤ β th is satisfied, where β th ∈ (0,1) a pregiven threshold, then a new membership function is generated. The mean and the standard deviation of the new membership function and the output action strength are selected as follows:
minew = xi1 , σ inew = σ i , wnew = 0
(33)
where xi is the new incoming data and σ i is a pre-specified constant. The number
n( N ) is incremented n( N + 1) = n( N ) + 1 .
(34)
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4.3 IBC Design The proposed intelligent backstepping control (IBC) system is shown in Fig. 2, which encompasses a neural backstepping controller unb and an robust compensation controller u rc . The design of IBC for the chaotic dynamic system is described step-bystep as follows: Step 1. Define the tracking error e1 as (2), a stabilizing function α as (4) and e2 as (5). Step 2. The control law of the IBC is developed in the following equation uic = u nb + u rc
(35)
where
u nb = xc − fˆ − c1e1 − c2 e2 − e1
(36)
u rc = − Eˆ sgn(e2 )
(37)
and sgn(.) is a sign function and fˆ is the output of SGFNN. Substituting (35) into (6), it can be obtained that
e2 = f − fˆ − c2 e2 − e1 + u rc . By substituting (29) into (38), equation (38) becomes ~ T Aw ~ Tĭ ~ T Bw ˆ +m ˆa +ı ˆ a + ε − c2 e2 − e1 + u rc e2 = w a a a a
(38)
(39)
Step 3. Define the Lyapunov function as ~ ~ Tm ~ ~Tw ~ ~T ı ~ m ı e2 e2 w E2 V2 = 1 + 2 + a a + a a + a a + (40) 2 2 2η1 2η 2 2η 3 2η 4 ~ where E = E − Eˆ ; and η1 , η 2 , η 3 and η 4 are positive constants. Differentiating (40) with respect to time and using (39), it is obtained that
~ ~ ~ Tm ~ ~Tw ~ ~T ı ~ w m ı EE V2 = e1e1 + e2 e2 + a a + a a + a a +
η1
η2
η3
η4
~ T Aw ~ Tĭ ~ T Bw ˆ +m ˆa +ı ˆ a + ε − c2 e2 − e1 + u rc ) + = e1 (e2 − c1e1 ) + e2 (w a a a a ~ ~ ~ Tm ~ ~Tw ~ ~T ı ~ w m ı EE a a + a a+ a a +
η1
η2
η3
~ T (e ĭ ˆ + = −c1e12 − c2 e12 + w a a 2 ~ T ( e Bw ˆa+ ı 2 a
~ ı
a
η3
η4
~ w a
η1
~ m ~ T (e Aw ˆ a + a )+ )+m a 2
) + e2 (ε + u rc ) +
η2
~ ~ EE
η4
(41)
If the adaptive laws of the SGFNN identifier and the approximation error bound are chosen as
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~ = η e ĭ ˆ = −w ˆ w a a 1 2 a
(42)
~ = η e Aw ˆ a = −m ˆa m a 2 2
(43)
~ = η e Bw ˆa ıˆ a = −ı a 3 2
(44)
~ Eˆ = − Ǽ = η 4 e 2
(45)
then (41) can be rewritten as ~ ~ EE 2 2 ˆ V2 = −c1e1 − c2 e1 + ε e2 − E e2 +
(46) ~ ~ ~ ~ Similar to the discussion of (10), it can be concluded that w a , m a , ı a and E are bounded and e1 and e2 converge to zero as t → ∞ .
adaptive laws (42), (43), (44)
β th
ˆ , ıˆ ˆ , m w a a a
SGFNN identifier (24)
xc
neural backstepping u nb + controller (36)
+ c1
d/dt
α − + d/dt
uic +
robust compensation u rc controller (37)
−
+
rule generation (31), (32), (33)
fˆ
e1
−
n(N )
Eˆ
e2
bound estimation algorithm (45)
intelligent backstepping control
Fig. 2. IBC for chaotic system
Chaotic system (1)
x
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5 Simulation Results The IBC system has been tested on the abovementioned chaotic system to track a desired periodic orbit. The control parameters are selected as c1 = c2 = 1 ,
η1 = η 2 = η 3 = 20 , η 4 = 0.1 , σ i = 1.0 , and β th = 0.5 . These parameters are chosen to achieve favorable transient control performance considering the requirement of asymptotic stability and the possible operating conditions. The simulation results of the IBC for q = 1.8 and q = 7.0 are shown in Figs. 3 and 4, respectively. These results show that the proposed IBC design method can achieve favorable tracking performance. The simulation results not only the perfect tracking responses can be achieved but also the concise fuzzy rule’s size can be obtained since the proposed selforganizing mechanism and the online learning algorithms are applied. The simulation results show that by using the self organizing mechanism and the online learning algorithm, a perfect tracking response can be achieved as well as reduced fuzzy rule base size can be obtained.
control effort, u
state, x
xc
x
time (sec) (c)
time (sec) (a) control effort, u
state, x
x
xc
time (sec) (c)
time (sec) (a)
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state, x
x
xc
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time (sec) (b)
rule number
state, x
xc
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Fig. 3. Simulation results of IBC for q=1.8
time (sec) (d)
Fig. 4. Simulation results of IBC for q=7.0
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6 Conclusions In this paper, an intelligent backstepping control (IBC) system has been proposed for the chaotic system. The developed IBC system utilized a self-growing fuzzy neural network identifier to online estimate the chaotic dynamic function. The control law of the IBC system is synthesized using the Lyapunov function, so that the asymptotic stability of the control system can be guaranteed. Finally, simulation results verified that the proposed IBC system can achieve favorable tracking performance of the nonlinear chaotic systems.
Acknowledgment The authors appreciate the partial financial support from the National Science Council of Republic of China under grant NSC-90-2213-E-155-016.
References 1. Lin, C.T., Lee, C.S.G.: Neural Fuzzy Systems: A Neuro-Fuzzy Synergism to Intelligent Systems, Englewood Cliffs, NJ: Pretice-Hall (1996) 2. Juang, C.F., Lin, C.T.: An On-line Self-constructing Neural Fuzzy Inference Network and its Applications. IEEE Trans. Fuzzy Syst., (1998) 12-32 3. Li, C., Lee, C.Y., Cheng, K.H.: Pseudo-error-based Self-organizing Neuro-fuzzy System. IEEE. Trans. Fuzzy Syst., (2004) 812-819 4. Lin, C.T., Cheng, W.C., Liang, S.F.: An on-line ICA-mixture-model-based Selfconstructing Fuzzy Neural Network. IEEE Trans. Circuits Syst., (2005) 207-221 5. Jiang, Z.P.: Advanced Feedback Control of the Chaotic Duffing Equation. IEEE Trans. Circuits Syst., (2002) 244-249 6. Yassen, M.T.: Chaos Control of Chen Chaotic Dynamical System. Chaos, Solitons & Fractals, (2003) 271-283 7. Wang, J., Qiao, G.D., Deng, B.: H ∞ Variable Universe Adaptive Fuzzy Control for Chaotic System. Chaos, Solitons & Fractals, (2005) 1075-1086 8. Ji, J.C., Hansen, C.H.: Stability and Dynamics of a Controlled Van Der Pol-Duffing Oscillator. Chaos, Solitons & Fractals, (2006) 555-570 9. Slotine, J.E., Li, W.: Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, New Jersey (1991) 10. Wang. L.X.: Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Englewood Cliffs, NJ: Prentice-Hall (1994)
Modeling of Rainfall-Runoff Relationship at the Semi-arid Small Catchments Using Artificial Neural Networks Mustafa Tombul1 and Ersin O÷ul2 1
Anadolu University Engineering Faculty of Civil Engineering Department, Eskiúehir/Turkey 2 III.Regional Directorate of State Hydraulic Work, Eskiúehir /Turkey [email protected], [email protected]
Abstract. The artificial neural networks (ANNs) have been applied to various hydrologic problems in recently. In this paper, the artificial neural network (ANN) model is employed in the application of rainfall-runoff process on a semi-arid catchment, namely the Kurukavak catchment. The Kurukavak catchment, a sub-basin of the Sakarya basin in NW Turkey, has a drainage area of 4.25 km2. The performance of the developed neural network based model was compared with multiple linear regression based model using the same observed data. It was found that the neural network model consistently gives good predictions. The conclusion is drawn that the ANN model can be used for prediction of flow for small semi-arid catchments.
alternative for rainfall–runoff modeling [5, 2, 15, 16, 17, 18, 19, 20, 21, 10, 22, 23, 24, 25, 26]. The ANN models are powerful prediction tools for the relation between rainfall and runoff parameters. The results will support decision making in the area of water resources planning and management. In these hydrological applications, a feedforward back propagation algorithm is used [27]. The aim of this paper is to model the rainfall-runoff relationship in the semiarid small catchment (Kurukavak) located in Turkey using a black box type model based on ANN methodology.
2 The Study Catchment The Kurukavak catchment, a sub-basin of the Sakarya basin in north-west Turkey, has a drainage area of 4.25 km2 and ranges in altitude from 830 m to1070 m. The basin is equipped with three rain gauges (R1, R2 and R3) and one runoff recording station (H1) (Fig. 1). The Rainfall and Runoff daily data at the average of (R1, R2 and R3) stations were used for model investigation. The data contains information for a period of four years (1988 to 1991). The entire database is represented by 1460 daily values of rainfall and runoff pairs. The ANN model was trained using the resulting runoff and rainfall daily data. The database was collected by the Services of Rural Investigation Instute.
Fig. 1. Location of Kurukavak catchment in Turkey
3 The Structure of the ANN Artificial neural networks employ mathematical simulation of biological nervous systems in order to process acquired information and derive predictive outputs after the network has been properly trained for pattern recognition. The main theme of ANN research focuses on modeling of the brain as a parallel computational device for various computational tasks that were performed poorly by traditional serial computers.
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The neural network structure in this study possessed a three-layer learning network consisting of an input layer, a hidden layer and an output layer consisting of output variable(s) (Fig. 2). The input nodes pass on the input signal values to the nodes in the hidden layer unprocessed. The values are distributed to all the nodes in the hidden layer depending on the connection weights Wij and Wjk [28-29] between the input node and the hidden nodes. Connection weights are the interconnecting links between the neurons in successive layers. Each neuron in a certain layer is connected to every single neuron in the next layer by links having an appropriate and an adjustable connection weight.
Fig. 2. Architecture of the neural network model used in this study
In this study, the FFBP were trained using Levenberg–Marquardt optimization technique. This optimization technique is more powerful than the conventional gradient descent techniques [30]. The study [31] showed that the Marquardt algorithm is very efficient when training networks which have up to a few hundred weights. Although the computational requirements are much higher each iteration of the Marquardt algorithm, this is more than made up for by the increased efficiency. This is especially true when high precision is required. The Feed Forward Back Propagation (FFBP) distinguishes itself by the presence of one or more hidden layers, whose computation nodes are correspondingly called hidden neurons of hidden units. The function of hidden neurons is to intervene between the external input and the network output in some useful manner.
4 Method Application of ANN in Rainfall-Runoff Modeling The runoff at watershed outlet is related not only to the current rainfall rate, but also to the past rainfall and runoff situations because of its certain storage capacity. For a discrete lumped hydrological system, the rainfall-runoff relationship can be generally expressed as [32, 5]
[
Q(t ) = F R(t ), R(t − ∆t ),..., R(t − n x ∆t ), Q(t − ∆t ),...Q(t − n y ∆t )
]
(1)
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where R represents rainfall, Q represents runoff at the outlet of the watershed, F is any kind of model structure (linear or nonlinear), ∆t is the data sampling interval, and nx and ny are positive integers numbers reflecting the memory length of the watershed. In this study the Simplex search method is used to find a set of optimum values for those weights used in the ANN, which are denoted by w
by w
opt jk
opt ij
, 0 ≤ i ≤ n , 1 ≤ j ≤ l and
, 0 ≤ j ≤ l , 1 ≤ k ≤ l , 0 ≤ j ≤ l , 1 ≤ k ≤ m . The estimated runoffs, denoted by
Qˆ (t ) , are determined as a function of those optimum weights of the ANN, which is expressed as
[
Q(t ) = F R(t), R(t − ∆t),...,R(t − n x ∆t), Q(t − ∆t ),...Q(t − n y ∆t) woptij ,wopt kj
]
(2)
When the ANN is implemented to approximate the above relationship between the watershed average rainfall and runoff, there will be a number of n =n x +n y +1
nodes in the input layer, n =n x +n y +1 , while there is only one node in the output, i.e. m=1. The database collected represents four years daily sets of rainfall-runoff values for the Kurukavak basin. In this paper, we used the data for the last year (1991) for model testing, while the other remaining data (1988 to 1990) was used for model training/calibration. The training phase of ANN model was terminated when the mean squared error (RMSE) on the testing databases was minimal. The flow estimation simulations were carried out in two steps. First, only rainfall data was employed for the input layer. Then previous daily flow value was also incorporated into the input data group. They [17], indicated that a noticeable improvement in estimation performance was obtained with the incorporation of flow value into the input layer. In this present, then the flow at the precedent day (Q ) was also added to t-1 the input layer in order to increase the estimation performance.
5 Evaluation Measures the Model Performance The results of the network model (FFBP) applied in the study were evaluated for their performance by estimating the following standard global statistical measures. The statistical criteria consist of root mean squared of error (RMSE), coefficient of determination (R2) and the index of volumetric fit (IVF). They RMSE and (R2) is knowledge very well everybody. Also the index of volumetric fit (IVF)are defined as N ¦ Q sim,i i IVF = =1 N ¦ Qobs,i i =1
(3)
Modeling of Rainfall-Runoff Relationship at the Semi-arid Small Catchments
where
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Q obs ,i and Q sim,i are respectively, the actual and predicted value of flow
(normalized between 0 and 1). The coefficient of determination (R2) statistic measures the linear correlation between the actual and predicted flows values. The coefficient of determination is often used to measure the performance of a hydrological model. The value is in the range of [-∞, 1]. The zero value means the model performs equal to a naive prediction, that is, a prediction using an average observed value. The value less than zero means the model performs worse than the average observed value. A value between 0.6-0.8 is moderate to good. A value more than 0.8 is a good fit. A value of one is a perfect fit. The RMSE was used to measure the agreement between the observed and simulated water balance. The closer the RMSE value is to zero, the better the performance of the model. The another index emplyoed to assess the model performance is the simple index of volumetrik fit (IVF), which is expressed as the ratio of simulated run off volume to the correspondind observed one. A value of for IVF one is a perfect fit.
6 Results and Discussions The goal of the training process is to reach an optimal solution based on some performance measurements such as RMSE, coefficient of determination known as Rsquare value (R2), and the IVF. Therefore, required ANN model was developed in two phases: training (calibration) phase, and testing (generalization or validation) phase. In the training phase, a larger part for database (three years) was used to train the network and the remaining part of the database (one year) is used in the testing phase. Testing sets are usually used to select the best performing network model. In this research, the ANN was optimal at 50 iterations with 4 hidden nodes. The corresponding accuracy measures of this network model on testing and training data are given in the following table (Table 1). Generally, accuracy measures on training data are better than those on testing data. Table 1. Statistical parameter and accuracy measures of this network model at training and testing phases
Training Phases Testing Phases
RMSE 0.021 0.072
R2 0.75 0.726
IVF 1.02 1.03
The comparison between the predicted and actual flow values at training and testing phases show good agreement with the R2 are respectively 0,75 and 0,726 (Figure 3a, 4a). As regards to the volumetric fit, the value of the IVF is 1.02 in the calibration period and 1.03 in the verification period. From these results, there is no
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doubt the ANN model is very successful in simulating the non-linear rainfall-runoff relationship on the Kurukavak catchment. Root mean square error (RMSE) value for the training and testing period was considered for performance evaluation and all testing stage estimates were plotted in the form of hydrograph (Figure 3b, 4b).
Training phase
3
Actual flow (m /s)
0.4 0.3 0.2 0.1
R2 = 0.75
0.0 0.0 0.1 0.1 0.2 0.2 0.3 0.3 0.4 0.4 0.5 3
Predicted flow (m /s)
Fig. 3a. Comparision between the actual and ANN predicted flow values for traning phase
Flow (m3/s)
Training Phase
FFBP observed
0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0
100
200
300
400
500
600
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900 1000 1100 1200
Time (day)
Fig. 3b. Comparision between the actual and ANN Predicted flow values for traning phase
Also the statistical parameters of the predicted and actual values of flow for the entire database are practically identical (Table 2). In order to evaluate the performance of the ANN, the multiple linear regression (MLR) technique was applied with the same data sets used in the ANN model. Figure 5 shows the comparative results obtained by MLR technique. The R2 values for MLR and ANN models are presented in Table 3. Apparently, the ANN approach gives much better prediction than the traditional method (MLR).
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Actual flow (m3/s)
Testing phase 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
R2 = 0.7263 0
0.2
0.4
0.6
0.8
1
1.2
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Fig. 4a. Comparision between the actual and ANN predicted flow values for testing phase
Testing phase Observed
Daily mean flow (m3 /s)
1.6
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1.4 1.2 1 0.8 0.6 0.4 0.2 0 0
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200
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Fig. 4b. Comparision between the actual and ANN predicted flow values for testing phase Table 2. Statistical parameter of the predictetd and actual flow at training and testing phases Training phases
Testing phases
Minimum
Actual Flow(m3/s) 0
Predicted Flow(m3/s) 0
Actual Flow(m3/s) 1E-5
Predicted Flow(m3/s) 0
Maximum
0.42157
0.4099
1.4817
1.3880
Mean Standart of Deviation Coefficient of Variation
0.0152 0.0419 2.75
0.0157 0.0371 2.36
0.0267 0.1379 5.07
0.0273 0.1200 4.44
Statistical parameter
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FFBP(ANN)
MLR R2
Training phase Testing phase
0.75 0.72
0.66 0.60
Testing Phase
1,6
1,6
1,4
1,4
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Actual flow (m3/s)
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1,2 1 0,8 0,6 0,4
1,2 1 0,8 0,6 0,4 0,2
0,2
2
R = 0.6598 0 0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6
Predicted flow (m3/s) (a)
R2 = 0,6028
0 0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6
Predicted flow (m3/s) (b)
Fig. 5. Comparisionof correlation coefficients between actual and predicted flow ANN and MLR models.(a) Training phase (b) Testing phase
7 Conclusion In this study, the results obtained show clearly that the artificial neural networks are capable of model rainfall-runoff relationship in the small semi-arid catchments in which the rainfall and runoff are very irregular, thus, confirming the general enhancement achieved by using neural networks in many other hydrological fields. The results and comparative study indicate that the artificial neural network method is more suitable to prediction of for runoff flow small semi-arid catchments than classical regression model. The ANN approach could provide a very useful and accurate tool to solve problems in water resources studies and management.
References 1. Bertoni, J. C., Tucci, C. E., Clarke, R. T.: Rainfall-based Real-time Flood Forecasting. J. Hydrol., 131 (1992) 313–339 2. Shamseldin, A. Y.: Application of Neural Network Technique to Rainfall-runoff Modeling. J. Hydrol. 199 (1997) 272-294
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3. Rajurkar, M. P., Chaube, U. C.: 2002: Artificial Neural Networks for Daily Rainfall-runoff 4. Modeling. Hydrol. Sci. J., 478 (6)(2002) 865–877 5. Riad, S. J., Mania, L., Bouchaou, Y. Najjar.: Predicting Catchment Flow in Semi Arid Region via Artificial Neural Network Technique. Hydrological Process, 18 (2004) 2387-2393 6. Hsu, K. L., Gupta, H. V., Sorooshian, S.: Artificial Neural Network Modeling of the Rainfallrain of Process. Water Resour. Res, 31 (10) (1995)2517–2530 7. Chang, F. J., Suen, J. P.: A Study of the Artificial Neural Network for Rainfall-runoff process. Journal of Chinese Agricultural Engineering (In Chinese), 43 (1) (1997) 9-25 8. Smith, J., Eli, R. N.: Neural-network Models of Rainfallrunoff Process. J. Water Resour. Plan. Manage, 121 (6)(1995) 499–508 9. Thirumalaiah, K., Deo, M. C.: River Stage Forecasting Using Artificial Neural Networks. J. Hydrologic Eng, 3 (1) (1998) 26-31 10. Thirumalaiah, K., Deo, M. C.: Hydrological Forecasting Using Artificial Neural Networks. Hydrologic Eng, 5 (2) (2000) 180-189 11. Campolo, M., Andreussi, P., Soldati, A.: A River Flood Forecasting with a Neural Network Model. Water Resour. Res, 35 (4) (1999) 1191–1197 12. Imrie, C. E., Durucan, S., Korre, A.: River Flow Prediction Using Artificial Neural Networks: Generalization Beyond the Calibration Range. J. Hydrol, 233 (2000) 138-153 13. Liong, S. Y., Lim, W., Paudyal, G. N.: River Stage Forecasting in Bangladesh: Neural Network Approach. J. Comput. Civ. Eng, 14 (1) (2000) 1-18 14. 13.Tokar, A. S., Markus, M.: Precipitation-runoff Modeling Using Artificial Neuralnetworks and Conceptual Models. J. Hydrologic Eng, 5 (2) (2000) 156–161 15. Kim, G. S., Borros, A. P.: Quantitative Flood Forecasting Using Multisensor Data and Neural Networks. J. Hydrol., 246 (2001) 45–62 16. Sajikumar, N., Thandaveswara, B. S.: ANon-linear Rainfall–runoff Model Using an Artificial Neural Network. J. Hydrol., 216 (1999)32–55 17. Tokar, A. S., Johnson, P. A.: Rainfall–runoff Modeling Using Artificial Neural Networks. J.Hydrol. Eng., ASCE, 4(3)(1999)232–239 18. Cigizoglu, H. K, Alp, M.: Rainfall-Runoff Modeling Using Three Neural Network Methods. Artificial Intelligence and Soft Computing- ICAISC 2004, Lecture Notes in Artificial Intelligence, 3070 (2004) 166-171 19. Anctil, F., Perrin, C., Andreassian, V.: Impact of the Length of Observed Records on the Performance of ANN and of Conceptual Parsimonious Rainfall-runoff Forecasting Models. Environ.Modell.Software, 19 (2004) 357-368 20. Freiwan, M., Cigizoglu, H. K.: Prediction of Total Monthly Rainfall in Jordan using Feed Forward Backpropagation Method. Fresenius Environmental Bulletin, 14 (2) (2005) 142-151 21. Thirumalaiah, K., D., M. C.: Real-time Flood Forecasting Using Neural Networks. Computer-Aided Civil Infrastruct. Engng, 13 (2) (1998)101–111 22. Zealand, C. M., Burn, D. H., Simonovic, S. P.: Short term Streamflow Forecasting Using Artificial Neural Networks. J. Hydrol., 214 (1999) 32–48 23. Salas, J. D., Markus, M., Tokar, A. S.: Streamflow Forecasting Based on Artificial Neural Networks. In: Artificial Neural Networks in Hydrology, Govindaraju, R. S. and Rao, A. R. (eds.), Kluwer Academic Publishers, (2000) 24. Sivakumar, B., Jayawardena, A. W., Fernando, T. M. K. G.: River Flow Forecasting: use of Phase Space Recostruction and Artificial Neural Networks Approaches. J.of Hydrology, 265 (2002) 225-245
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25. Cigizoglu, H. K.: Estimation, Forecasting and Extrapolation of Flow Data by Artificial Neural Networks. Hydrological Sciences Journal, 48 (3) (2003) 349-361 26. Cigizoglu, H. K.: Corporation of ARMA Models into Flow Forecasting by Artificial Neural Networks. Environmetrics, 14 (4) (2003) 417-427 27. Kisi, O.: River Flow Modeling Using Artificial Neural Networks. ASCE J. of Hydrologic Engineering, 9 (1) (2004) 60-63 28. Lippmann, R. P.: An Introduction to Computing With Neural Nets. IEEE ASSP Magazine, (1987)4-22 29. Najjar, Y., Ali, H.: On the Use of BPNN in Liquefaction Potential Assessment Tasks. In Artificial Intelligence and Mathematical Methods in Pavement and Geomechanical Systems, (Edited by Attoh-Okine), (1998) 55-63 30. Najjar, Y., Zhang, X.: Characterizing the 3D Stress-strain Behavior of Sandy Soils: A Neuro-mechanistic Approach. In ASCE Geotechnical Special Publication Number 96, (Edited by G. Filz and D. Griffiths), (2000) 43-57 31. Cigizoglu, H. K., Kiúi, O.: Flow Prediction by Two Back Propagation Techniques Using k-fold Partitioning of Neural Network Training Data, Nordic Hydrology, (in press), (2005) 32. Hagan, M. T., Menhaj, M. B.: Training feedforward techniques with the Marquardt algorithm. IEEE Transactions on Neural Networks, 5 (6)(1994) 989-993 33. Chow, V. T., Maidment, D. R., Mays, L. W.: Applied Hydrology. McGraw-Hill, Inc., NY, (19
A Novel Multi-agent Based Complex Process Control System and Its Application Yi-Nan Guo, Jian Cheng, Dun-wei Gong, and Jian-hua Zhang College of Information and Electronic Engineering, China University of Mining and Technology, Xuzhou, 221008 Jiangsu,China [email protected]
Abstract. ComplH[ process control systems need a hybrid control mode, which combines hierarchical structure with decentralized control units. Autonomy of agents and cooperation capability between agents in multi-agent system provide basis for realization of the hybrid control mode. A novel multi-agent based complex process control system is proposed. Semantic representation of a control-agent is presented utilizing agent-oriented programming. A novel temporal logic analysis of a control-agent is proposed using Petri nets. Collaboration relationships among control-agents are analyzed based on extended contract net protocol aiming at the lack of reference[1].Taken pressure control of recycled gas with complicated disturbances as an application, five kinds of control-agents are derived from control-agent. Reachable marking tree and different transition of each derived control-agent are analyzed in detail. Actual running effect indicates multi-agent based hybrid control mode is rationality and flexible. Temporal logic analysis based on Petri nets ensures the reachability of the systems. Extended contract net protocol provides a reasonable realization for collaboration relationships.
analyze complex processes widely. But horizontal division of bottom control functions was not included. Although decentralized control is horizontally distributed, it lacks cooperation between control units which always leads to sub-optimum [4]. It is obvious that the architecture, which combines hierarchical structure with decentralized control units, is reasonable. But there is a lake of appropriate control theories for analysis of above control mode. Multi-agent system consists of multiple autonomous agents by some cooperation mechanism. Each agent can implement tasks independently. Through cooperation and interaction among agents, MAS can accomplish complex tasks and their optimization. It is obvious that MAS provides the foundation for realizing above control mode. Up to now, MAS have been adopted to analysis of complex process control systems by many researchers. Hybrid control systems based on multiple agents were proposed [5]-[6]. Breemen utilized decompose-conquer strategy of MAS to decompose a complex problem to many sub-problems. Each sub-problem was solved by an agent. And the whole task was accomplished by cooperation among agents [7]-[10]. It provides design foundation and common framework for complex process control systems. But there is lake of semantic representation of agents and temporal logic analysis and implementation of their collaboration relationships based on agentoriented programming. Thereby a novel multi-agent based complex process control system is put forward in the paper. It makes the best of autonomy of agent and cooperation capability among agents to realize complex processes control which makes systems flexible and opening. In the rest of the paper, the kernel of control-agents and the collaboration strategies between them are proposed in Section2.To validate rationality of the systems, they are applied to pressure control system of recycled gas in Section3.At last, future work planned to extend the cooperation strategies is included.
2 Multi-agent Based Complex Process Control Systems Multi-agent based complex process control systems adopt a hybrid control mode, which combines hierarchical structure with decentralized control units. How to decompose control functions, realize each control unit and cooperate among control units are key problems. Aiming at above problems, decompose-conquer strategy, agent-oriented programming, Petri Nets (PNs) and contract net protocol are introduced. Decompose-conquer strategy is adopted to simplify the design of complex process control systems. In the strategy, division and integration are two key problems. Division is how to separate a complex process control problem into a group of control sub-problems according to the requirement of control. Each control sub-problem is solved by an agent, called control-agent. Integration is how to synthesize the solutions of sub-problems effectively. A division method has presented by Breemen[1]. In this paper, we emphasize particularly on semantic representation of control-agents adopting agent-oriented programming and temporal logic analysis of their cooperation relationships utilizing contract net protocol.
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2.1 Structure of Control-Agent All of control-agents have same structure and basic functions. So the normal kernel of control-agents, which is called base class of control-agents, is abstracted and described using agent-oriented programming as follows [11]. ::=< function FD> ::=<structure description SD> <environment description ED> ::=<symbol >::=<waiting> <ED>::=
