Tracking Dynamic Characteristics of Structures Using Output-Only Recursive Combined Subspace Identification Technique
Publication: Journal of Engineering Mechanics
Volume 146, Issue 5
Abstract
Identifying the dynamic characteristics of structures under ambient conditions is very important for heath monitoring and damage assessment. In this study, an output-only recursive combined subspace identification technique is proposed for tracking the modal parameters of a time-varying structure under unknown and unmeasured nonstationary input. The technique consists of two parts: initial input estimation and online tracking. For initial input estimation, a short-duration input is first reconstructed through an iterative oblique projection and an orthogonal projection. The reconstructed input and the measured output are then used to form a cross-correlation matrix for initial estimation of modal parameters. An orthogonal projection and an instrumental variable approach are then incorporated in order to eliminate the effects of nonstationary input and measurement noise, respectively. A bi-iteration subspace tracker is applied to extract the unknown input and the structural modal parameters. The proposed technique was validated numerically on a four-degree-of-freedom structure and experimentally on a three-degree-of-freedom building model. Both results showed that the proposed technique can simultaneously reconstruct the unknown input and track the time-varying structural modal parameters using only output measurements.
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Data Availability Statement
All data, models, and code generated during the study are proprietary in nature and may only be provided with restrictions.
Acknowledgments
This study was supported by the Hong Kong Research Grants Council Competitive Earmarked Research Grant No. 611112.
References
Akaike, H. 1975. “Markovian representation of stochastic processes by canonical variables.” SIAM J. Control 13 (1): 162–173. https://doi.org/10.1137/0313010.
Alicioğlu, B., and H. Luş. 2008. “Ambient vibration analysis with subspace methods and automated model selection: Case studies.” J. Struct. Eng. 134 (6): 1016–1029. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:6(1016).
Bapat, R. B., S. J. Kirkland, K. M. Prasad, and S. Puntanen. 2013. Combinatorial matrix theory and generalized inverses of matrices. New York: Springer Science and Business Media.
Chen, J., and J. Li. 2004. “Simultaneous identification of structural parameters and input time history from output-only measurements.” Comput. Mech. 33 (5): 365–374. https://doi.org/10.1007/s00466-003-0538-9.
Fassois, S. D. 2001. “MIMO LMS-ARMAX identification of vibrating structures—Part I: The method.” Mech. Syst. Signal Process. 15 (4): 723–735. https://doi.org/10.1006/mssp.2000.1382.
Hong, A. L., B. Raimondo, and C. Lin. 2009. “Identification of dynamic models of a building structure using multiple earthquake records.” Struct. Control Health Monit. 16 (2): 178–199. https://doi.org/10.1002/stc.289.
Huang, C. S., S. L. Hung, W. C. Su, and C. L. Wu. 2009. “Identification of time-variant modal parameters using time-varying autoregressive with exogenous input and low-order polynomial function.” Comput.-Aided Civ. Infrastruct. Eng. 24 (7): 470–491. https://doi.org/10.1111/j.1467-8667.2009.00605.x.
Juang, J. N., J. E. Cooper, and J. R. Wright. 1988. “An eigensystem realization algorithm using data correlations (ERA/DC) for modal parameter identification.” Control Theory Adv. Technol. 4 (1): 5–14.
Juang, J. N., and R. S. Pappa. 1985. “An eigensystem realization algorithm for modal parameter identification and model reduction.” J. Guidance Control Dyn. 8 (5): 620–627. https://doi.org/10.2514/3.20031.
Juang, J. N., M. Phan, L. G. Horta, and R. W. Longman. 1993. “Identification of observer Kalman/filter Markov parameters-theory and experiments.” J. Guidance Control Dyn. 16 (2): 320–329. https://doi.org/10.2514/3.21006.
Li, Z., and C. C. Chang. 2012. “Tracking of structural dynamic characteristics using recursive stochastic subspace identification and instrumental variable technique.” J. Eng. Mech. 138 (6): 591–600. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000370.
Lin, C. S., and D. Y. Chiang. 2013. “Modal identification from nonstationary ambient response data using extended random decrement algorithm.” Comput. Struct. 119 (Apr): 104–114. https://doi.org/10.1016/j.compstruc.2013.01.010.
Ljung, L. 1999. System identification: Theory for the user. 2nd ed. Upper Saddle River, NJ: Prentice Hall.
Ljung, L., and S. Gunnarsson. 1990. “Adaptation and tracking in system identification—A survey.” Automatica 26 (1): 7–21. https://doi.org/10.1016/0005-1098(90)90154-A.
Loh, C. H., C. Y. Lin, and C. C. Huang. 2000. “Time domain identification of frames under earthquake loadings.” J. Eng. Mech. 126 (7): 693–703. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:7(693).
Lus, H., R. Betti, and R. W. Longman. 1999. “Identification of linear structural systems using earthquake-induced vibration data.” Earthquake Eng. Struct. Dyn. 28 (11): 1449–1467. https://doi.org/10.1002/(SICI)1096-9845(199911)28:11%3C1449::AID-EQE881%3E3.0.CO;2-5.
Manolakis, D. G., V. K. Ingle, and S. M. Kogon. 2000. Statistical and adaptive signal processing: Spectral estimation, signal modeling, adaptive filtering and array processing. New York: McGraw-Hill.
Peeters, B., and G. De Roeck. 2001. “Stochastic system identification for operational modal analysis: A review.” J. Dyn. Syst. Meas. Contr. 123 (4): 659–667. https://doi.org/10.1115/1.1410370.
Rabiul, S. M. R., X. Huang, and D. Sharma. 2012. “Wavelet based denoising algorithm of the ECG signal corrupted by WGN and Poisson noise.” In Proc., Int. Symp. on Communications and Information Technologies, 165–168. New York: IEEE.
Shi, T., N. P. Jones, and J. H. Ellis. 2000. “Simultaneous estimation of system and input parameters from output measurements.” J. Eng. Mech. 126 (7): 746–753. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:7(746).
Strobach, P. 2008. “The fast householder Bi-SVD subspace tracking algorithm.” Signal Process. 88 (11): 2651–2661. https://doi.org/10.1016/j.sigpro.2008.05.004.
Su, W. C., C. Y. Liu, and C. S. Huang. 2014. “Identification of instantaneous modal parameter of time-varying systems via a wavelet-based approach and its application.” Comput.-Aided Civ. Infrastruct. Eng. 29 (4): 279–298. https://doi.org/10.1111/mice.12037.
Tangirala, A. K. 2014. Principle of system identification: Theory and practice. Boca Raton, FL: CRC Press.
Van Overschee, P., and B. De Moor. 1994. “N4SID-Subspace algorithms for the identification of combined deterministic-stochastic systems.” Automatica 30 (1): 75–93. https://doi.org/10.1016/0005-1098(94)90230-5.
Van Overschee, P., and B. De Moor. 1996. Subspace identification for linear systems: Theory–implementation–applications, 57–93. Boston: Kluwer Academic Publishers.
Wang, D., and A. Haldar. 1994. “Element-level system identification with unknown input.” J. Eng. Mech. 120 (1): 159–176. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:1(159).
Yu, D. J., and W. X. Ren. 2005. “EMD-based stochastic subspace identification of structures from operational vibration measurement.” Eng. Struct. 27 (12): 1741–1751. https://doi.org/10.1016/j.engstruct.2005.04.016.
Zhang, K., H. Li, Z. Duan, and S. S. Law. 2011. “A probabilistic damage identification approach for structures with uncertainties under unknown input.” Mech. Syst. Sig. Process. 25 (4): 1126–1145. https://doi.org/10.1016/j.ymssp.2010.10.017.
Zhong, K., and C. C. Chang. 2016. “Recursive combined subspace identification technique for tracking dynamic characteristics of structures under earthquake excitation.” J. Eng. Mech. 142 (12): 04016092. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001156.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 5 • May 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Jun 5, 2017
Accepted: Sep 24, 2019
Published online: Mar 13, 2020
Published in print: May 1, 2020
Discussion open until: Aug 13, 2020
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