Identification of Hysteretic Dynamic Systems by Using Hybrid Extended Kalman Filter and Wavelet Multiresolution Analysis with Limited Observation
Publication: Journal of Engineering Mechanics
Volume 139, Issue 5
Abstract
The availability of methods for the identification of nonlinear hysteretic systems is crucial for the assessment of the health and the repair of civil infrastructures during and after severe earthquakes. However, most methods used to identify hysteretic systems suffer from two problems: (1) the structural responses at all dynamic degrees of freedom (DOFs) must be measured, which is obviously impractical for real applications; and (2) the nonlinear model of a system is assumed to be known, and only the model parameters are to be identified, meaning that the nonlinear characteristics of the underlying structures may not be captured accurately. To overcome these two problems, this paper proposes a novel method that does not assume a nonlinear model and that does not require measurements at all DOFs. The new approach alternately uses the extended Kalman filter (EKF) and wavelet (W) multiresolution analysis. Within each time step, the identification can then be divided into two stages. In stage one, based on limited-state observations and the structural model at previous step, the structural responses at all DOFs are estimated using the EKF method. In stage two, based on the estimated full states, wavelet multiresolution analysis is used to identify the tangent stiffness matrix and the hysteresis-restoring force curves of the structure (i.e., the structural model is updated using the estimated full states). Two model structures with various nonlinearities at different locations, and with various state-observation schemes, are employed to conduct the numerical study. The numerical results verify the efficiency and accuracy of the proposed method. The best location for state observation is also discussed in the numerical study.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study was financially supported by the National Nature Science Foundation of China (China-US collaborative project with grant No. 51161120359); the Ministry of Science and Technology of China (grant No. 2011BAK02B02); and the Institute of Engineering Mechanics, China Earthquake Administration (grant No. 2007B15).
References
Billings, S. A., Chen, S., and Backhouse, R. J. (1989). “The identification of linear and non-linear models of a turbocharged automotive diesel engine.” Mech. Syst. Signal Process., 3(2), 123–142.
Dolce, M., and Cardone, D. (2001). “Mechanical behavior of shape memory alloys for seismic applications 2: Austenitic NiTi wires subjected to tension.” Int. J. Mech. Sci., 43(11), 2657–2677.
Ghosh, S. J., Roy, D., and Manohar, C. S. (2007). “New forms of extended Kalman filter via transversal linearization and application to structural system identification.” Comput. Methods Appl. Mech. Eng., 196(49–52), 5063–5083.
Haase, M., and Widjajakusuma, J. (2003). “Damage identification based on ridge and maxima lines of the wavelet transform.” Int. J. Eng. Sci., 41(13–14), 1423–1443.
Kerschen, G., Worden, K., Vakakis, A. F., and Golinval, J. C. (2006). “Past, present and future of nonlinear system identification in structural dynamics.” Mech. Syst. Signal Process., 20(3), 505–592.
Kitada, Y. (1998). “Identification of nonlinear structural dynamic systems using wavelets.” J. Eng. Mech., 124(10), 1059–1066.
Korenberg, M., Billings, S. A., Liu, Y. P., and McIlroy, P. J. (1988). “Orthogonal parameter estimation algorithm for non-linear stochastic systems.” Int. J. Control, 48(1), 193–210.
Kosmatopoulos, E. B., Smyth, A. W., Masri, S. F., and Chassiakos, A. G. (2001). “Robust adaptive neural estimation of restoring forces in nonlinear structures.” J. Appl. Mech., 68(6), 880–893.
Leontaritis, I. J., and Billings, S. A. (1985a). “Input-output parametric models for non-linear systems, part I: Deterministic non-linear systems.” Int. J. Control, 41(2), 303–328.
Leontaritis, I. J., and Billings, S. A. (1985b). “Input-output parametric models for non-linear systems, part II: Stochastic non-linear systems.” Int. J. Control, 41(2), 329–344.
Masri, S. F., Chassiakos, A. G., and Caughey, T. K. (1992). “Structure-unknown non-linear dynamic systems: Identification through neural networks.” Smart Mater. Struct., 1(1), 45–56.
Masri, S. F., Chassiakos, A. G., and Caughey, T. K. (1993). “Identification of nonlinear dynamic systems using neural networks.” J. Appl. Mech., 60(1), 123–133.
Masri, S. F., Caffrey, J. P., Caughey, T. K., Smyth, A. W., and Chassiakos, A. G. (2004). “Identification of the state equation in complex non-linear systems.” Int. J. Non-Linear Mech., 39(7), 1111–1127.
Moustafa, A. (2011). “Damage-based design earthquake loads for single-degree-of-freedom inelastic structures.” J. Struct. Eng., 137(3), 456–467.
Nasrellah, H. A., and Manohar, C. S. (2011). “Finite element method based Monte Carlo filers for structural system identification.” Probab. Eng. Mech., 26(2), 294–307.
Pei, J. S., and Smyth, A. W. (2003). “More transparent neural network approach for modeling nonlinear hysteretic systems.” Proc. SPIE, Vol. 5057, Society of Photo-optical Instrumentation Engineers, Bellingham, WA, 516–523.
Pei, J. S., and Smyth, A. W. (2005). “A new approach to designing multilayer feedforward neural networks for modeling nonlinear restoring forces.” Proc., SPIE, Vol. 5765, Society of Photo-optical Instrumentation Engineers, Bellingham, WA, 345–353.
Pei, J. S., Smyth, A. W., and Kosmatopoulos, E. B. (2004). “Analysis and modification of Volterra/Wiener neural networks for the adaptive identification of non-linear hysteretic dynamic systems.” J. Sound Vibrat., 275(3–5), 693–718.
Pei, J. S., Smyth, A. W., and Wright, J. P. (2005). “A constructive neural network approach for simulation and identification of nonlinear dynamic systems.” Proc., 2005 Structures Congress and the 2005 Forensic Engineering Symp., ASCE, Reston, VA, 85, 171.
Saadat, S., Buckner, G. D., Furukawa, T., and Noori, M. N. (2004a). “An intelligent parameter varying (IPV) approach for non-linear system identification of base excited structures.” Int. J. Non-linear Mech., 39(6), 993–1004.
Saadat, S., Noori, M. N., Buckner, G. D., Furukawa, T., and Suzuki, Y. (2004b). “Structural health monitoring and damage detection using an intelligent parameter varying (IPV) technique.” Int. J. Non-linear Mech., 39(10), 1687–1697.
Sajeeb, R., Manohar, C. S., and Roy, D. (2009). “A conditionally linearized Monte Carlo filter in non-linear structural dynamics.” Int. J. Non-linear Mech., 44(7), 776–790.
Smyth, A. W., Masri, S. F., Kosmatopoulos, E. B., Chassiakos, A. G., and Caughey, T. K. (2002). “Development of adaptive modeling techniques for non-linear hysteretic systems.” Int. J. Non-linear Mech., 37(8), 1435–1451.
Spanos, P. D., Giaralis, A., Politis, N. P., and Roesset, J. M. (2007). “Numerical treatment for seismic accelerograms and of inelastic seismic structural responses using harmonic wavelets.” Comput. Aided Civ. Infrastruct. Eng., 22(4), 254–264.
Takewaki, I., and Nakamura, M. (2000). “Stiffness-damping simultaneous identification using limited earthquake records.” Earthqu. Eng. Struct. Dynam., 29(8), 1219–1238.
Thouverez, F., and Jezequel, L. (1996). “Identification of NARMAX models on a modal base.” J. Sound Vibrat., 189(2), 193–213.
Wang, D., and Haldar, A. (1997). “System identification with limited observations and without input.” J. Eng. Mech., 123(5), 504–511.
Wu, M., and Smyth, A. W. (2007). “Application of the unscented Kalman filter for real-time nonlinear structural system identification.” Struct. Contr. Health Monit., 14(7), 971–990.
Xie, Z., and Feng, J. (2012). “Real-time nonlinear structural system identification via iterated unscented Kalman filter.” Mech. Syst. Signal Process., 28(14), 309–322.
Yang, J. N., Pan, S., and Huang, H. (2007). “An adaptive extended Kalman filter for structural damage identifications II: Unknown inputs.” Struct. Contr. Health Monit., 14(3), 497–521.
Information & Authors
Information
Published In
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Oct 24, 2008
Accepted: Jul 27, 2012
Published online: Aug 2, 2012
Published in print: May 1, 2013
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.