Extraction of Bridge Frequencies from a Moving Test Vehicle by Stochastic Subspace Identification
Publication: Journal of Bridge Engineering
Volume 21, Issue 3
Abstract
The technique for extracting bridge frequencies from a moving vehicle was proposed only recently. However, its efficacy may be reduced by road-surface roughness. To this end, the stochastic subspace identification (SSI) is modified to deal with the present time-variant coupled noisy vehicle–bridge interaction system. First, the governing equations for the vehicle and bridge are expressed in state space, including the effects of road roughness and multiple vehicles. Then, they are discretized and transformed to a form suitable for SSI by separating the known from the unknown parameters. Using the Hankel matrix along with the orthogonal projection theorem and singular value decomposition, the observability matrix derived with the vehicle effect suppressed can be used to identify the bridge dynamic properties. It is demonstrated that (1) the proposed SSI approach is more effective for identifying bridge frequencies below 20 Hz for the cases studied, compared with conventional approaches; (2) adding a little damping to the test vehicle can help suppress the vehicle frequency using the proposed approach; and (3) the ongoing traffic is beneficial for amplifying the frequencies of bridges with rough surface.
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Acknowledgments
The research reported herein is sponsored in part by the National Science Council (ROC) through grant number NSC 102-2221-E-002-132-MY2. Also, the senior author acknowledges the sponsorship from the Chongqing Science & Technology Commission via the contract number CSTC 2015 JCY JYS 30003 and the Tongji University 973 project with grant number 2011CB013800.
References
Åström, K. J., and Bohlin, T. (1965). “Numerical identification of linear dynamic systems for normal operating records.” Proc. 2nd IFAC Symp. Theory of Self-Adaptive Systems, Teddington, U.K., 96–111.
Bu, J. Q., Law, S. S., and Zhu, X. Q. (2006). “Innovative bridge condition assessment from dynamic response of a passing vehicle.” J. Eng. Mech., 1372–1379.
Cerda, F., Chen, S., Bielak, J., Garrett, J. H., Rizzo, P., and Kovačević, J. (2014). “Indirect structural health monitoring of a simplified laboratory-scale bridge model.” J. Smart Struct. Syst., 13(5), 849–868.
Chang, K. C., Wu, F. B., and Yang, Y. B. (2011). “Disk model for wheels moving over highway bridges with rough surfaces.” J. Sound Vib., 330(20), 4930–4944.
Gomeza, H. C., Fanning, P. J., Feng, M. Q., and Lee, S. (2011). “Testing and long-term monitoring of a curved concrete box girder bridge.” Eng. Struct., 33(10), 2861–2869.
Ho, B. L., and Kalman, R. E. (1966). “Effective construction of linear state-variable models from input/output functions.” Regelungstechnik, 14(12), 545–548.
ISO. (1995). “Mechanical vibration-road surface profiles-reporting of measured data.” ISO 8608, International Organization for Standardization, Geneva .
Katayama, T. (2005). Subspace methods for system identification, Springer-Verlag, London.
Kim, C. W., and Kawatani, M. (2008). “Pseudo-static approach for damage identification of bridges based on coupling vibration with a moving vehicle.” J. Struct. Infrastruct. Eng., 4(5), 371–379.
Kim, J., and Lynch, J. P. (2012). “Experimental analysis of vehicle–bridge interaction using a wireless monitoring system and a two-stage system identification technique.” J. Mech. Syst. Signal Process., 28, 3–19.
Li, W. M., Jiang, Z. H., Wang, T. L., and Zhu, H. P. (2014). “Optimization method based on generalized pattern search algorithm to identify bridge parameters indirectly by a passing vehicle.” J. Sound Vib., 333(2), 364–380.
Lin, C. W., and Yang, Y. B. (2005). “Use of a passing vehicle to scan the bridge frequencies - An experimental verification.” Eng. Struct., 27(13), 1865–1878.
Oshima, Y., Yamamoto, K., and Sugiura, K. (2014). “Damage assessment of a bridge based on mode shapes estimated by responses of passing vehicles.” J. Smart Struct. Syst., 13(5), 731–753.
Siringoringo, D. M., and Fujino, Y. (2012). “Estimating bridge fundamental frequency from vibration response of instrumented passing vehicle: Analytical and experimental study.” Adv. Struct. Eng., 15(3), 417–433.
Verhaegen, M., and Dewilde, P. (1992a). “Subspace model identification, Part 1: The output-error state-space model identification class of algorithms.” Int. J. Control, 56(5), 1187–1210.
Verhaegen, M., and Dewilde, P. (1992b). “Subspace model identification, Part 2: Analysis of the elementary output-error state space model identification algorithm.” Int. J. Control, 56(5), 1211–1241.
Yang, Y. B., and Chang, K. C. (2009a). “Extraction of bridge frequencies from the dynamic response of a passing vehicle enhanced by the EMD technique.” J. Sound Vib., 322(4–5), 718–739.
Yang, Y. B., and Chang, K. C. (2009b). “Extracting the bridge frequencies indirectly from a passing vehicle: Parametric study.” Eng. Struct., 31(10), 2448–2459.
Yang, Y. B., Chang, K. C., and Li, Y. C. (2013a). “Filtering techniques for extracting bridge frequencies from a test vehicle moving over the bridge.” Eng. Struct., 48, 353–362.
Yang, Y. B., Chen, W. F., Yu, H. W., and Chan, C. S. (2013b). “Experimental study of a hand-drawn cart for measuring the bridge frequencies.” Eng. Struct., 57, 222–231.
Yang, Y. B., Li, Y. C., and Chang, K. C. (2012). “Using two connected vehicles to measure the frequencies of bridges with rough surface - A theoretical study.” Acta Mech., 223(8), 1851–1861.
Yang, Y. B., Li, Y. C., and Chang, K. C. (2014). “Constructing the mode shapes of a bridge from a passing vehicles: A theoretical study.” Int. J. Smart Struct. Syst., 13(5), 797–819.
Yang, Y. B., Liao, S. S., and Lin, B. H. (1995). “Impact formulas for vehicles moving over simple and continuous beams.” J. Struct. Eng., 1644–1650.
Yang, Y. B., and Lin, B. H. (1995). “Vehicle-bridge interaction analysis by dynamic condensation method.” J. Struct. Eng., 1636–1643.
Yang, Y. B., and Lin, C. W. (2005). “Vehicle-bridge interaction dynamics and potential applications.” J. Sound Vib., 284(1–2), 205–226.
Yang, Y. B., Lin, C. W., and Yau, J. D. (2004). “Extracting bridge frequencies from the dynamic response of a passing vehicle.” J. Sound Vib., 272(3–5), 471–493.
Yang, Y. B., and Yau, J. D. (1997). “Vehicle-bridge interaction element for dynamic analysis.” J. Struct. Eng., ASCE, 123(11), 1512–1518. (Errata: 124(4), p. 479).
Yin, S. S., and Tang, C. Y. (2011). “Identifying cable tension loss and deck damage in a cable-stayed bridge using a moving vehicle.” J. Vib. Acoust., 133(2), 021007.
Zhang, Y., Wang, L., and Xiang, Z. H. (2012). “Damage detection by mode shape squares extracted from a passing vehicle.” J. Sound Vib., 331(2), 291–307.
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© 2015 American Society of Civil Engineers.
History
Received: Oct 4, 2014
Accepted: Mar 13, 2015
Published online: Sep 24, 2015
Discussion open until: Feb 24, 2016
Published in print: Mar 1, 2016
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