Parametric Identification of Nondegrading Hysteresis in a Laterally and Torsionally Coupled Building Using an Unscented Kalman Filter
Publication: Journal of Engineering Mechanics
Volume 139, Issue 4
Abstract
A parametric approach is proposed for identifying the inelastic response of individual elements, which provide resistance against lateral loads in torsionally coupled buildings. Depending on the severity of the ground shaking in each lateral direction and the amount of eccentricity, different lateral load resisting elements (LLREs) will experience different levels of permanent deformation and energy dissipation based on their location and orientation. The proposed method utilizes the well-known Bouc-Wen model for representing the hysteretic response of each LLRE. An unscented Kalman filtering approach is implemented for identifying the Bouc-Wen model parameters, and for direct estimation of the force-displacement loops experienced by each LLRE during damaging seismic events. The simulated response of a single-story building to ground motion is used for demonstrating the utility of the proposed method, which may also be applied to multistory frames in a straightforward fashion, if certain instrumentation requirements are met.
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Acknowledgments
The work presented in this manuscript was funded, in part, by the National Science Foundation Grant No. CMMI-0755333. The authors thank Dr. Andrew W. Smyth of Columbia University for providing access to the source codes of the example demonstrated in Wu and Smyth (2007). Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the sponsoring agencies.
References
Akesson, B. M., Jorgensen, J. B., Poulsen, N. K., and Jorgensen, S. B. (2008). “A generalized autocovariance least-squares method for Kalman filter tuning.” J. Process Contr., 18(7–8), 769–779.
Applied Technology Council (ATC). (2009). “Effects of strength and stiffness degradation on seismic response.” Rep. No. P440A, Applied Technology Council, FEMA, Washington, DC.
Baber, T., and Noori, M. N. (1986). “Modeling general hysteresis behavior and random vibration application.” J. Vibrat. Acoust. Stress Reliab. Des., 108(4), 411–420.
Bouc, R. (1971). “Modele mathematique d’hysteresis.” Acustica, 24(3), 16–25 (in French).
Cao, Y. (2008). “Learning the unscented Kalman filter: An implementation of unscented Kalman filter for nonlinear state estimation.” MATLAB Central: An open exchange for the MATLAB and Simulink user community. 〈http://www.mathworks.com/matlabcentral〉 (Apr. 1, 2010).
Chatzi, E. N., and Smyth, A. W. (2009). “The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing.” Struct. Contr. Health Monit., 16(1), 99–123.
Chatzi, E. N., Smyth, A. W., and Masri, S. F. (2010). “Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty.” J. Struct. Safety, 32(5), 326–337.
Chopra, A. K. (2001). Dynamics of structures, 3rd Ed. Prentice Hall, Upper Saddle River, NJ.
Foliente, G. C. (1995). “Hysteresis modeling of wood joints and structural systems.” J. Struct. Eng., 121(6), 1013–1022.
Ghanem, R., and Ferro, G. (2006). “Health monitoring for strongly non-linear systems using the ensemble Kalman filter.” Struct. Contr. Health Monit., 13(1), 245–259.
Hoshiya, M., and Saito, E. (1984). “Structural identification by extended Kalman filter.” J. Eng. Mech., 110(12), 1757–1770.
Ikhouane, F., Hurtado, J. E., and Rodellar, J. (2007). “Variation of the hysteresis loop with the Bouc-Wen model parameters.” Nonlinear Dyn., 48(4), 361–380.
Ismail, M., Ikhouane, F., and Rodellar, J. (2009). “The hysteresis Bouc-Wen model, a survey.” Arch. Comput. Methods Eng., 16(2), 161–188.
Julier, S. J., and Uhlmann, J. K. (1997). “A new extension of the Kalman filter to nonlinear systems.” Proc., 11th Int. Symp. on Aerospace/Defense Sensing, Simulation and Controls, Society of Photo-optical Instrumentation Engineers, Orlando, FL, 182–193.
Kalman, R. E. (1960). “A new approach to linear filtering and prediction problems.” Trans. ASME J. Basic Eng., 82(Series D), 35–45.
Kandepu, R., Imsland, L., and Foss, B. (2008). “Constrained state estimation using the unscented Kalman filter.” Proc., 16th Mediterranean Conf. on Control and Automation, Institute of Electrical and Electronics Engineers, New York, 1453–1458.
Koh, C. G., and See, L. M. (1994). “Identification and uncertainty estimation of structural parameters.” J. Eng. Mech., 120(6), 1219–1236.
Koh, C. G., See, L. M., and Balendra, T. (1991). “Estimation of structural parameters in time domain: A substructure approach.” Earthq. Eng. Struct. Dynam., 20(8), 787–801.
Lin, J. S., and Zhang, Y. (1994). “Nonlinear structural identification using extended Kalman filter.” Comput. Struct., 52(4), 757–764.
Lin, J. W., Betti, R., Smyth, A. W., and Longman, R. W. (2001). “On-line identification of non-linear hysteretic structural systems using a variable trace approach.” Earthq. Eng. Struct. Dynam., 30(9), 1279–1303.
Masri, S. F., Bekey, G. A., Sassi, H., and Caughey, T. K. (1982a). “Non-parametric identification of a class of nonlinear multi-degree dynamic systems.” Earthq. Eng. Struct. Dynam., 10(1), 1–30.
Masri, S. F., Sassi, H., and Caughey, T. K. (1982b). “Nonparametric identification of nearly arbitrary nonlinear systems.” J. Appl. Mech., 49(3), 619–628.
MATLAB 7.9 [Computer software]. Natick, MA, MathWorks.
Nayyerloo, M., Chase, J. G., Chen, X. Q., MacRae, G. A., and Moghaddasi, M. (2009). “Permanent deflection identification of non-linear structures under seismic excitation using adaptive LMS filters.” Proc., 2009 NZSEE Conf., Univ.of Canterbury, Christchurch, NZ.
Omrani, R., Hudson, R. E., and Taciroglu, E. (2012a). “Story-by-story estimation of the stiffness parameters of laterally-torsionally coupled buildings using forced or ambient vibration data: I. Formulation and verification.” Earthq. Eng. Struct. Dynam., 41(12), 1609–1634.
Omrani, R., Hudson, R. E., and Taciroglu, E. (2012b). “Story-by-story estimation of the stiffness parameters of laterally-torsionally coupled buildings using forced or ambient vibration data: II. Application to experimental data.” Earthq. Eng. Struct. Dynam., 41(12), 1635–1649.
PEER. (2000). PEER Strong Motion Database. Pacific Earthquake Engineering Research Center, Regents of the Univ.of California, Berkeley, CA. 〈http://peer.berkeley.edu/smcat〉 (Apr. 1, 2010).
Speyer, J. L., and Chung, W. H. (2008). Stochastic processes, estimation, and control. Society for Industrial and Applied Mathematics, Philadelphia.
Sues, R. H., Mau, S. T., and Wen, Y. K. (1988). “Systems identification of degrading hysteretic restoring forces.” J. Eng. Mech., 114(5), 833–846.
Wen, Y. K. (1976). “Method for random vibration of hysteretic systems.” J. Eng. Mech., 102(2), 246–263.
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.
Yang, J. N., Lin, S., Huang, H., and Zhou, L. (2006). “An adaptive extended Kalman filter for structural damage identification.” Struct. Contr. Health Monit., 13(4), 849–867.
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.
Yang, J. N., and Silian, L. (2004). “On-line identification of non-linear hysteretic structures using an adaptive tracking technique.” Int. J. Non-linear Mech., 39(9), 1481–1491.
Yang, Y., and Ma, F. (2003). “Constrained Kalman filter for nonlinear structural identification.” J.Vibrat. Contr. 9(12), 1343–1357.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 139 • Issue 4 • April 2013
Pages: 452 - 468
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Apr 26, 2011
Accepted: Jun 13, 2012
Published online: Jul 31, 2012
Published in print: Apr 1, 2013
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