Least-Squares Estimation with Unknown Excitations for Damage Identification of Structures
Publication: Journal of Engineering Mechanics
Volume 133, Issue 1
Abstract
System identification and damage detection for structural health monitoring of civil infrastructures have received considerable attention recently. Time domain analysis methodologies based on measured vibration data, such as the least-squares estimation and the extended Kalman filter, have been studied and shown to be useful. The traditional least-squares estimation method requires that all the external excitation data (input data) be available, which may not be the case for many structures. In this paper, a recursive least-squares estimation with unknown inputs (RLSE-UI) approach is proposed to identify the structural parameters, such as the stiffness, damping, and other nonlinear parameters, as well as the unmeasured excitations. Analytical recursive solutions for the proposed RLSE-UI are derived and presented. This analytical recursive solution for RLSE-UI is not available in the previous literature. An adaptive tracking technique recently developed is also implemented in the proposed approach to track the variations of structural parameters due to damages. Simulation results demonstrate that the proposed approach is capable of identifying the structural parameters, their variations due to damages, and unknown excitations.
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Acknowledgments
This research is supported by the National Science Foundation Grant Nos. NSFNSF-CMS- 0140710 and NSF0554814.
References
Chang, F.-K. (2003), ed., “Structural health monitoring,” Proc., 4th International Workshop on Structural Health Monitoring, Stanford Univ., Stanford, Calif., DEStech, Lancaster, Pa.
Doebling, S. W., Farrar, C. R., and Prime, M. B. (1998). “A summary review of vibration-based damage identification methods.” Shock Vib., 30(2), 91–105.
Goodwin, G. C., and Sin, K. S. (1984). Adaptive filtering, prediction and control, Prentice-Hall, Englewood Cliffs, N.J.
Johnson, E. A., Lam, H. F., Katafygiotis, L. S., and Beck, J. L. (2004). “Phase I IASC-ASCE structural health monitoring benchmark problem using simulated data.” J. Eng. Mech., 130(1), 3–15.
Lin, J. W., Betti, R., Smyth, A. W., and Longman, R. W. (2001). “On-line identification of nonlinear hysteretic structural systems using a variable trace approach.” Earthquake Eng. Struct. Dyn., 30, 1279–1303.
Ling, X., and Haldar, A. (2004). “Element level system identification with unknown input with Rayleigh damping.” J. Eng. Mech., 130(8), 877–885.
Maruyama, O., and Hoshiya, M. (2001). “System identification of an experimental model by extended Kalman filter.” Proc., Structural Safety and Reliability (CD-ROM), ICOSSA 2001, Swet & Zeitinger, Lisse.
Shinozuka, M., and Ghanem, R. (1995). “Structural system identification. II: Experimental verification.” J. Eng. Mech., 121(2), 265–273.
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.
Wang, D., and Haldar, A. (1994). “Element-level system identification with unknown input.” J. Eng. Mech., 120(1), 159–176.
Wang, D., and Haldar, A. (1997). “System identification with limited observations and without input.” J. Eng. Mech., 123(5), 504–511.
Wen, Y. K. (1989). “Methods of random vibration for inelastic structures.” Appl. Mech. Rev., 42(2), 39–52.
Xia, Q., Rao, M. Y., and Shen, X. (1994). “Adaptive fading Kalman filter with an application.” Automatica, 30, 1333–1338.
Yang, J. N., Huang, H., and Lin, S. (2006a). “Sequential non-linear least-square estimation for damage identification of structures.” Int. J. Non-Linear Mech., 41, 124–140.
Yang, J. N., Lei, Y., Pan, S., and Huang, N. (2003a). “Identification of linear structures based on Hilbert-Huang transform. Part I: Normal modes.” Earthquake Eng. Struct. Dyn., 32, 1443–1467.
Yang, J. N., Lei, Y., Pan, S., and Huang, N. (2003b). “Identification of linear structures based on Hilbert-Huang transform. Part II: Complex modes.” Earthquake Eng. Struct. Dyn., 32, 1533–1554.
Yang, J. N., and Lin, S. (2004). “On-line identification of nonlinear hysteretic structures using an adaptive tracking technique.” Int. J. Non-Linear Mech., 39, 1481–1491.
Yang, J. N., and Lin, S. (2005). “Identification of parametric variations of structures based on least squares estimation and adaptive tracking technique.” J. Eng. Mech., 131(3), 290–298.
Yang, J. N., Lin, S., Huang, H., and Zhou, L. (2006b). “An adaptive extended Kalman filter for structural damage identification.” J. Struct. Control Health Monitoring, 13, 849–867, ⟨www.interscience.wiley.com⟩ (Apr. 4, 2005).
Zhou, D. H., and Frank, P. M. (1996). “Strong tracking filtering of nonlinear time-varying stochastic systems with coloured noise: Application to parameter estimation and empirical robustness analysis.” Int. J. Control, 65(2), 295–307.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 133 • Issue 1 • January 2007
Pages: 12 - 21
Copyright
© 2007 ASCE.
History
Received: Mar 25, 2005
Accepted: Feb 24, 2006
Published online: Jan 1, 2007
Published in print: Jan 2007
Notes
Note. Associate Editor: Raimondo Betti
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