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Keywords: system identification in structures, state space models, Kalman filter, stochastic subspace methods, modal analysis, benchmark problems.

Summary

This paper presents a time-domain stochastic system identification method based on maximum likelihood estimation (MLE) with the expectation maximization (EM) algorithm [1]. The effectiveness of this structural identification method is evaluated through numerical simulation in the context of the ASCE benchmark problem on structural health monitoring [2].

The benchmark structure is a four-story, two-bay by two-bay steel-frame scale model structure built in the Earthquake Engineering Research Laboratory at the University of British Columbia, Canada. This paper focuses on Phase I of the analytical benchmark studies. A MATLAB-based finite element analysis code obtained from the IASC-ASCE SHM Task Group web site [3] is used to calculate the dynamic response of the prototype structure. A number of 100 simulations have been made using this MATLAB-based finite element analysis code in order to evaluate the proposed identification method.

There are several techniques to realize system identification. In this work, stochastic subspace identification (SSI) [4] method has been used for comparison. SSI identification method is a well known method and computes accurate estimates of the modal parameters. The principles of the SSI identification method has been introduced in the paper and next the proposed MLE with EM algorithm has been explained in detail.

The advantages of the proposed structural identification method can be summarized as follows: (i) the method is based on maximum likelihood, that implies minimum variance estimates; (ii) EM is a computational simpler estimation procedure than other optimization algorithms; (iii) estimate more parameters than SSI, and these estimates are accurate. On the contrary, the main disadvantages of the method are: (i) EM algorithm is an iterative procedure and it consumes time until convergence is reached; and (ii) this method needs starting values for the parameters.

Modal parameters (eigenfrequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using both the SSI method and the proposed MLE + EM method. The numerical results show that the proposed method identifies eigenfrequencies, damping ratios and mode shapes reasonably well even in the presence of 10% measurement noises. These modal parameters are more accurate than the SSI estimated modal parameters.

References

1: R.H. Shumway, D.S. Stoffer, "Time series analysis and its applications", Springer. 2006.
2: E.A. Johnson, H.F. Lam, L.S. Katafygiotis, J.L. Beck, "Phase I IASC - ASCE structural health monitoring benchmark problem using simulated data", J. Eng. Mech., 130(1), 315, 2004. doi:10.1061/(ASCE)0733-9399(2004)130:1(3)
3: IASC-ASCE SHM Task Group, Task group website, URL
4: P. Van Overschee, B. De Moor, "Subspace Identification for Linear Systems. Theory - Implementation - Applications", Kluwer Academic Publishers, 1996.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 93 PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: Paper 66 Maximum Likelihood Estimation of Modal Parameters in Structures Using the Expectation Maximization Algorithm F.J. Cara¹, J. Carpio¹, J. Juan¹ and E. Alarcon² ¹Department of Organization Engineering, Business Administration and Statistics, ²Department of Structural Mechanics and Industrial Constructions, Polytechnical University of Madrid, Spain doi:10.4203/ccp.93.66 purchase the full-text of this paper Full Bibliographic Reference for this paper F.J. Cara, J. Carpio, J. Juan, E. Alarcon, "Maximum Likelihood Estimation of Modal Parameters in Structures Using the Expectation Maximization Algorithm", in , (Editors), "Proceedings of the Tenth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 66, 2010. doi:10.4203/ccp.93.66 Keywords: system identification in structures, state space models, Kalman filter, stochastic subspace methods, modal analysis, benchmark problems. Summary This paper presents a time-domain stochastic system identification method based on maximum likelihood estimation (MLE) with the expectation maximization (EM) algorithm [1]. The effectiveness of this structural identification method is evaluated through numerical simulation in the context of the ASCE benchmark problem on structural health monitoring [2]. The benchmark structure is a four-story, two-bay by two-bay steel-frame scale model structure built in the Earthquake Engineering Research Laboratory at the University of British Columbia, Canada. This paper focuses on Phase I of the analytical benchmark studies. A MATLAB-based finite element analysis code obtained from the IASC-ASCE SHM Task Group web site [3] is used to calculate the dynamic response of the prototype structure. A number of 100 simulations have been made using this MATLAB-based finite element analysis code in order to evaluate the proposed identification method. There are several techniques to realize system identification. In this work, stochastic subspace identification (SSI) [4] method has been used for comparison. SSI identification method is a well known method and computes accurate estimates of the modal parameters. The principles of the SSI identification method has been introduced in the paper and next the proposed MLE with EM algorithm has been explained in detail. The advantages of the proposed structural identification method can be summarized as follows: (i) the method is based on maximum likelihood, that implies minimum variance estimates; (ii) EM is a computational simpler estimation procedure than other optimization algorithms; (iii) estimate more parameters than SSI, and these estimates are accurate. On the contrary, the main disadvantages of the method are: (i) EM algorithm is an iterative procedure and it consumes time until convergence is reached; and (ii) this method needs starting values for the parameters. Modal parameters (eigenfrequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using both the SSI method and the proposed MLE + EM method. The numerical results show that the proposed method identifies eigenfrequencies, damping ratios and mode shapes reasonably well even in the presence of 10% measurement noises. These modal parameters are more accurate than the SSI estimated modal parameters. References 1 R.H. Shumway, D.S. Stoffer, "Time series analysis and its applications", Springer. 2006. 2 E.A. Johnson, H.F. Lam, L.S. Katafygiotis, J.L. Beck, "Phase I IASC - ASCE structural health monitoring benchmark problem using simulated data", J. Eng. Mech., 130(1), 315, 2004. doi:10.1061/(ASCE)0733-9399(2004)130:1(3) 3 IASC-ASCE SHM Task Group, Task group website, URL 4 P. Van Overschee, B. De Moor, "Subspace Identification for Linear Systems. Theory - Implementation - Applications", Kluwer Academic Publishers, 1996. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £145 +P&P)
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