Updating Structural Parameters with Spatially Incomplete Measurements Using Subspace System Identification
Publication: Journal of Engineering Mechanics
Volume 143, Issue 7
Abstract
Civil infrastructures are subjected to various loads over their lifetime, which leads to structural degradation. To understand and predict these dynamic behaviors of physical infrastructures, many mathematical structural models have been developed, such as subspace system identification. These models often require structural responses from all degrees of freedom (DOFs) to estimate structural parameters. However, in practice, it is often difficult, if not impossible, to make such measurements owing to sensing constraints, a lack of data, or an excessive number of DOFs as in large-scale civil structures. This lack of measurements in space results in ill-posed problems with nonunique solutions. To address this challenge, this paper presents a structural parameter estimation algorithm that incorporates spatially incomplete measurements and inaccurate prior information on structural parameters within a subspace system identification framework. Additional constraints are imposed using prior information, and the prior information is updated with a new estimation. To sequentially update the parameters, the process is repeated as more measurements are collected. The proposed method is evaluated using a numerical model of a 5-story shear building for two damage scenarios with measurement noise. The structural parameters are estimated with 85–99% accuracy with spatially incomplete measurements (40–80%), and the iterative updating further improves these accuracies.
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References
Alvin, K. F., and Park, K. C. (1994). “Second-order structural identification procedure via state-space based system identification.” AIAA J., 32(2), 397–406.
Banan, M. R., and Hjelmstad, K. D. (1993). “Identification of structural system from measured response.”, Univ. of Illinois, Urbana, IL.
Beck, J. L., and Katafygiotis, L. S. (1998). “Updating models and their uncertainties. I: Bayesian statistical framework.” J. Eng. Mech., 455–461.
Brewer, J. W. (1978). “Kronecker products and matrix calculus in system theory.” IEEE Trans. Circuits Syst., 25(9), 772–781.
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. Saf., 32(5), 326–337.
Chen, C. T. (1999). Linear system theory and design, 3rd Ed., Oxford University Press, Oxford, U.K.
Chopra, A. K. (2001). Dynamics of structures: Theory and applications to earthquake engineering, 2nd Ed., Prentice Hall, Upper Saddle River, NJ.
Golub, G. H., and Loan, C. F. (1996). Matrix computation, 3rd Ed., Johns Hopkins University Press, Baltimore.
Hjelmstad, K. D., Banan, M. R., and Banan, M. R. (1995). “Time-domain parameter estimation algorithm for structures. I: Computational aspects.” J. Eng. Mech., 424–434.
Hjelmstad, K. D., and Shin, S. (1996). “Crack identification in a cantilever beam from modal response.” J. Sound Vib., 198(5), 527–545.
Hoshiya, M., and Saito, E. (1984). “Structural identification by extended Kalman filter.” J. Eng. Mech., 1757–1770.
Juang, J. N., and Parra, R. S. (1985). “An eigensystem realization algorithm for modal parameter identification and model reduction.” J. Guidance Control Dyn., 8(5), 620–627.
Kang, J. S., Park, S.-K., Shin, S., and Lee, H. S. (2005). “Structural system identification in time domain using measured acceleration.” J. Sound Vib., 288(1–2), 215–234.
Katayama, T. (2005). Subspace methods for system identification, Springer, London.
Kim, J., Kim, K., and Sohn, H. (2013). “Data-driven physical parameter estimation for lumped mass structures from a single point actuation test.” J. Sound Vib., 332(18), 4390–4402.
Kim, J., Kim, K., and Sohn, H. (2014a). “In situ measurement of structural mass, stiffness, and damping using a reaction force actuator and a laser Doppler vibrometer.” Smart Mater. Struct., 22(8), 085004.
Kim, J., Kim, K., and Sohn, H. (2014b). “Subspace model identification of guided wave propagation in metallic plates.” Smart Mater. Struct., 23(3), 035006.
Kim, J., and Lynch, J. P. (2012a). “Autonomous decentralized system identification by Markov parameter estimation using distributed smart wireless sensor networks.” J. Eng. Mech., 478–490.
Kim, J., and Lynch, J. P. (2012c). “Subspace system identification of support excited structures—Part I: Theory and black-box system identification.” Earthquake Eng. Struct. Dyn., 41(15), 2235–2251.
Kim, J., and Lynch, J. P. (2012b). “Subspace system identification of support excited structures—Part II: Gray-box interpretations and damage detection.” Earthquake Eng. Struct. Dyn., 41(15), 2253–2271.
Koh, B. H., Nagarajaiah, S., and Phan, M. Q. (2008). “Reconstructing structural changes in a dynamic system from experimentally identified state-space models.” J. Mech. Sci. Technol., 22(1), 103–112.
Luenberger, D. G. (1989). Linear and nonlinear programming, 2nd Ed., Addison Wesley, Boston.
Lus, H. (2012). “Physical parameter estimation from state-space models for systems with missing input information.” J. Eng. Mech., 1402–1410.
Mariani, S., and Corigliano, A. (2005). “Impact induced composite delamination: State and parameter identification via joint and dual extended Kalman filters.” Comput. Method Appl. Mech., 194(50–52), 5242–5272.
Nagarajaiah, S., and Basu, B. (2009). “Output only modal identification and structural damage detection using time frequency and wavelet techniques.” Earthquake Eng. Eng. Vib., 8(4), 583–605.
Nair, K. K., and Kiremidjian, A. S. (2007). “Time series based structural damage detection algorithm using Gaussian mixtures modeling.” J. Dyn. Syst., Meas. Control, 129(3), 285–293.
Nair, K. K., Kiremidjian, A. S., and Law, K. H. (2006). “Time series-based damage detection and localization algorithm with application to the ASCE benchmark structure.” J. Sound Vib., 291(1–2), 349–368.
Noh, H., Lignos, D. G., Nair, K. K., and Kiremidjian, A. S. (2012). “Development of fragility functions as a damage classification/prediction method for steel moment-resisting frames using a wavelet-based damage sensitive feature.” Earthquake Eng. Struct. Dyn., 41(4), 681–696.
Noh, H., Nair, K. K., Kiremidjian, A. S., and Loh, C. H. (2009). “Application of a time series-based detection algorithm to the benchmark experiment at the national center for research on earthquake engineering in Taipei, Taiwan.” J. Smart Struct. Syst., 5(1), 95–117.
Noh, H., Nair, K. K., Lignos, D. G., and Kiremidjian, A. S. (2011). “Use of wavelet-based damage-sensitive features for structural damage diagnosis using strong motion data.” J. Struct. Eng., 1215–1228.
Noh, H., Rajagopal, R., and Kiremidjian, A. S. (2013). “Sequential structural damage diagnosis algorithm using a change point detection method.” J. Sound Vib., 332(24), 6419–6433.
Park, S.-K., and Noh, H. (2014). “Structural parameter estimation using partial measurements in subspace system identification.” Proc., 6th World Conf. on Structural Control and Monitoring, CIMNE, Barcelona, Spain.
Park, S.-K., and Park, H. W. (2014). “Determination of optimal sampling rate and Hankel matrix size for subspace SI in shear building under earthquake.” Proc., SPIE: Health Monitoring of Structural and Biological Systems, SPIE, Bellingham, WA.
Park, S.-K., Park, H. W., Shin, S., and Lee, H. S. (2008). “Detection of abrupt structural damage induced by an earthquake using a moving time-window technique.” Comput. Struct., 86(11–12), 1253–1265.
Pawar, P. M., Reddy, K. V., and Ganguli, R. (2007). “Damage detection in beams using spatial Fourier analysis and neural networks.” J. Intell. Mater. Syst. Struct., 18(4), 347–359.
Phan, M. Q., and Longman, R. W. (2004). “Extracting mass, stiffness, and damping matrices from identified state-space models.” Proc., AIAA Conf. on Guidance, Navigation, and Control, American Institute of Aeronautics and Astronautics, Reston, VA.
Raghavendrachar, M., and Aktan, A. E. (1992). “Flexibility by multireference impact testing for bridge diagnostics.” J. Struct. Eng., 2186–2203.
Sim, S. H., Spencer, B. F., Park, J., and Jung, H. (2012). “Decentralized system identification using stochastic subspace identification on wireless smart sensor networks.” Proc., SPIE: Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems, SPIE, Bellingham, WA.
Sohn, H., Farrar, C. R., Hunter, N. F., and Worden, K. S. (2001). “Structural health monitoring using statistical pattern recognition techniques.” J. Dyn. Syst., Meas., Control, 123(4), 706–711.
van Overschee, P., and de Moor, B. (1996). Subspace identification for linear systems, theory—Implementation—Applications, Kluwer, Norwell, MA.
Verhaegen, M., and Dewilde, P. (1992). “Subspace model identification. Part 2: Analysis of the elementary output-error state-space model identification algorithm.” Int. J. Control, 56(5), 1211–1241.
Viberg, M. (1995). “Subspace-based methods for the identification of linear time-invariant systems.” Automatica, 31(12), 1835–1851.
Wu, M., and Smyth, A. W. (2007). “Application of the unscented Kalman filter for real-time nonlinear structural system identification.” J. Struct. Control Monit., 14(7), 971–990.
Zhu, D., Dong, X., and Wang, Y. (2014). “Substructure finite element model updating of a space frame structure by minimization of modal dynamic residual.” Proc., VI World Conf. on Structural Control and Monitoring, CIMNE, Barcelona, Spain, 2575–2582.
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 7 • July 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jul 26, 2015
Accepted: Nov 4, 2016
Published online: Feb 28, 2017
Published in print: Jul 1, 2017
Discussion open until: Jul 28, 2017
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