Simultaneous Input and Parameter Estimation of Hysteretic Structural Systems Using Quasi-Monte Carlo-Simulation-Based Minimum Variance Unbiased Estimator
Publication: Journal of Bridge Engineering
Volume 26, Issue 11
Abstract
This work proposes an efficient identification scheme for simultaneous input and parameter estimation of the hysteretic systems. For this purpose, a quasi-Monte Carlo (QMC)-simulation-based approach is adopted, where the sigma point generation scheme is coupled with a minimum variance unbiased estimator. In this process, additional bounds and constraints on the parameters are introduced to control the stability and convergence. The accuracy of the proposed algorithm is validated using a synthetic experiment on a frame whose nonlinear behavior is characterized by the Bouc–Wen–Baber–Noori model, that is, with degradation and pinching. Once the proposed algorithm is validated, its performance is further demonstrated using the shake table test of a full-scale bridge pier. The identified parameters in this case are utilized for damage quantification using a modified Park and Ang damage index. Overall, this study shows the robustness of the proposed algorithm for combined input estimation and condition assessment of inelastic reinforced concrete structures with a significant level of accuracy.
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Acknowledgments
Authors wish to acknowledge Dr. Matthew Schoettler and Professor Jose Restrepo for sharing the full-scale bridge pier test data in the public domain (i.e., DESIGNSAFE-CI platform).
References
Azam, S. E., E. Chatzi, and C. Papadimitriou. 2015. “A dual Kalman filter approach for state estimation via output-only acceleration measurements.” Mech. Syst. Sig. Process. 60: 866–886. https://doi.org/10.1016/j.ymssp.2015.02.001.
Baber, T. T., and M. N. Noori. 1985. “Random vibration of degrading, pinching systems.” J. Eng. Mech. 111 (8): 1010–1026. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:8(1010).
Bouc, R. 1967. “Forced vibrations of mechanical systems with hysteresis.” In Proc., 4th Conf. on Nonlinear Oscillations, 315. Prague, Czechia: Prague, Academia.
Calabrese, A., S. Strano, and M. Terzo. 2018. “Adaptive constrained unscented Kalman filtering for real-time nonlinear structural system identification.” Struct. Control Health Monit. 25 (2): e2084. https://doi.org/10.1002/stc.v25.2.
Chang, C.-M., S. Strano, and M. Terzo. 2016. “Modelling of hysteresis in vibration control systems by means of the Bouc–Wen model.” Shock Vib. 2016 (2): 1–14.
Chang, G., and J. B. Mander. 1994. Seismic energy based fatigue damage analysis of bridge columns: Part I-Evaluation of seismic capacity. Technical Rep. NCEER-94-0006. Buffalo, NY: National Center for Earthquake Engineering Research.
Chatzi, E. N., and A. W. Smyth. 2013. “Particle filter scheme with mutation for the estimation of time-invariant parameters in structural health monitoring applications.” Struct. Control Health Monit. 20 (7): 1081–1095. https://doi.org/10.1002/stc.1520.
Chatzi, E. N., A. W. Smyth, and S. F. Masri. 2010. “Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty.” Struct. Saf. 32 (5): 326–337. https://doi.org/10.1016/j.strusafe.2010.03.008.
Chen, Z., R. Zhang, J. Zheng, and H. Sun. 2020. “Sparse Bayesian learning for structural damage identification.” Mech. Syst. Sig. Process. 140: 106689. https://doi.org/10.1016/j.ymssp.2020.106689.
Dertimanis, V. K., E. Chatzi, S. E. Azam, and C. Papadimitriou. 2019. “Input-state-parameter estimation of structural systems from limited output information.” Mech. Syst. Sig. Process. 126: 711–746. https://doi.org/10.1016/j.ymssp.2019.02.040.
Duník, J., O. Straka, and M. Šimandl. 2011. “The development of a randomised unscented Kalman filter.” IFAC Proc. Volumes 44 (1): 8–13. https://doi.org/10.3182/20110828-6-IT-1002.01828.
Ebrahimian, H., R. Astroza, J. P. Conte, and C. Papadimitriou. 2018. “Bayesian optimal estimation for output-only nonlinear system and damage identification of civil structures.” Struct. Control Health Monit. 25 (4): e2128. https://doi.org/10.1002/stc.v25.4.
Friedland, B. 1969. “Treatment of bias in recursive filtering.” IEEE Trans. Autom. Control 14 (4): 359–367. https://doi.org/10.1109/TAC.1969.1099223.
Genz, A., and J. Monahan. 1998. “Stochastic integration rules for infinite regions.” SIAM J. Sci. Comput. 19 (2): 426–439. https://doi.org/10.1137/S1064827595286803.
Ghahari, S. F., F. Abazarsa, H. Ebrahimian, and E. Taciroglu. 2020. “Output-only model updating of adjacent buildings from sparse seismic response records and identification of their common excitation.” Struct. Control Health Monit. 27 (9): e2597. https://doi.org/10.1002/stc.v27.9.
Ghosh, S., D. Datta, and A. A. Katakdhond. 2011. “Estimation of the Park–Ang damage index for planar multi-storey frames using equivalent single-degree systems.” Eng. Struct. 33 (9): 2509–2524. https://doi.org/10.1016/j.engstruct.2011.04.023.
Gillijns, S., and B. De Moor. 2007a. “Unbiased minimum-variance input and state estimation for linear discrete-time systems.” Automatica 43 (1): 111–116. https://doi.org/10.1016/j.automatica.2006.08.002.
Gillijns, S., and B. De Moor. 2007b. “Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough.” Automatica 43 (5): 934–937. https://doi.org/10.1016/j.automatica.2006.11.016.
Ibarra, L. F., R. A. Medina, and H. Krawinkler. 2005. “Hysteretic models that incorporate strength and stiffness deterioration.” Earthquake Eng. Struct. Dyn. 34 (12): 1489–1511. https://doi.org/10.1002/(ISSN)1096-9845.
Ikhouane, F., V. Mañosa, and J. Rodellar. 2007. “Dynamic properties of the hysteretic Bouc–Wen model.” Syst. Control Lett. 56 (3): 197–205. https://doi.org/10.1016/j.sysconle.2006.09.001.
Ikhouane, F., and J. Rodellar. 2005. “On the hysteretic Bouc–Wen model.” Nonlinear Dyn. 42 (1): 63–78. https://doi.org/10.1007/s11071-005-0069-3.
Ishihara, S., and M. Yamakita. 2009. “Efficient unscented filtering for nonlinear systems with state constraints.” In Proc., 2009 European Control Conf., 5045–5050. New York: IEEE.
Julier, S. J., and J. K. Uhlmann. 1997. “New extension of the Kalman filter to nonlinear systems.” In Vol. 3068 of Signal processing, sensor fusion, and target recognition VI, 182–193. Bellingham, WA: International Society for Optics and Photonics.
Kandepu, R., L. Imsland, and B. A. Foss. 2008. “Constrained state estimation using the unscented Kalman filter.” In Proc., 2008 16th Mediterranean Conf. on Control and Automation, 1453–1458. New York: IEEE.
Kitanidis, P. K. 1987. “Unbiased minimum-variance linear state estimation.” Automatica 23 (6): 775–778. https://doi.org/10.1016/0005-1098(87)90037-9.
Lei, Y., D. Xia, K. Erazo, and S. Nagarajaiah. 2019. “A novel unscented Kalman filter for recursive state-input-system identification of nonlinear systems.” Mech. Syst. Sig. Process. 127: 120–135. https://doi.org/10.1016/j.ymssp.2019.03.013.
Liu, X., Y. Wang, and E. I. Verriest. 2021. “Simultaneous input-state estimation with direct feedthrough based on a unifying mmse framework with experimental validation.” Mech. Syst. Sig. Process. 147: 107083. https://doi.org/10.1016/j.ymssp.2020.107083.
Lourens, E., C. Papadimitriou, S. Gillijns, E. Reynders, G. De Roeck, and G. Lombaert. 2012. “Joint input-response estimation for structural systems based on reduced-order models and vibration data from a limited number of sensors.” Mech. Syst. Sig. Process. 29: 310–327. https://doi.org/10.1016/j.ymssp.2012.01.011.
Mandela, R., V. Kuppuraj, R. Rengaswamy, and S. Narasimhan. 2012. “Constrained unscented recursive estimator for nonlinear dynamic systems.” J. Process Control 22 (4): 718–728. https://doi.org/10.1016/j.jprocont.2012.02.001.
Naets, F., J. Croes, and W. Desmet. 2015. “An online coupled state/input/parameter estimation approach for structural dynamics.” Comput. Methods Appl. Mech. Eng. 283: 1167–1188. https://doi.org/10.1016/j.cma.2014.08.010.
Nayek, R., S. Chakraborty, and S. Narasimhan. 2019. “A Gaussian process latent force model for joint input-state estimation in linear structural systems.” Mech. Syst. Sig. Process. 128: 497–530. https://doi.org/10.1016/j.ymssp.2019.03.048.
Nithin, V. L. 2021. “Stochastic simulation of main shock-aftershock sequences and their use in damage-based seismic design of reinforced concrete structures.” Ph.D. thesis, Dept. of Civil Engineering, Indian Institute of Technology Guwahati.
Park, Y.-J., and A. H.-S. Ang. 1985. “Mechanistic seismic damage model for reinforced concrete.” J. Struct. Eng. 111 (4): 722–739. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:4(722).
Rathje, E. M., et al.2017. “Designsafe: new cyberinfrastructure for natural hazards engineering.” Nat. Hazard. Rev. 18 (3): 06017001. https://doi.org/10.1061/(ASCE)NH.1527-6996.0000246.
Schoettler, M. J., J. I. Restrepo, G. Guerrini, D. Duck, and F. Carrea. 2010. Large-scale validation of seismic performance of bridge columns [Data set]. NEES-2010-0987. San Diego, CA: University of California. Accessed May 22, 2020. https://doi.org/10.17603/DS2-D232.
Schoettler, M. J., J. Restrepo, G. Guerrini, D. E. Duck, and F. Carrea. 2012. A full-scale, single-column bridge bent tested by shake-table excitation. Center for Civil Engineering Earthquake Research, Dept. of Civil Engineering, Univ. of Nevada.
Sedehi, O., C. Papadimitriou, D. Teymouri, and L. S. Katafygiotis. 2019. “Sequential Bayesian estimation of state and input in dynamical systems using output-only measurements.” Mech. Syst. Sig. Process. 131: 659–688. https://doi.org/10.1016/j.ymssp.2019.06.007.
Sengupta, P., and B. Li. 2013. “Modified Bouc–Wen model for hysteresis behavior of RC beam–column joints with limited transverse reinforcement.” Eng. Struct. 46: 392–406. https://doi.org/10.1016/j.engstruct.2012.08.003.
Sengupta, P., and B. Li. 2017. “Hysteresis modeling of reinforced concrete structures: state of the art.” ACI Struct. J. 114 (1). https://doi.org/10.14359/51689422.
Shan, J., Y. Ouyang, H. Zhang, and W. Shi. 2019. “Model-reference damage tracking and evaluation of hysteretic structures with test validation.” Mech. Syst. Sig. Process. 118: 443–460. https://doi.org/10.1016/j.ymssp.2018.08.016.
Simon, D. 2006. Optimal state estimation: Kalman, H infinity, and nonlinear approaches. Hoboken, NJ: John Wiley & Sons.
Song, W. 2018. “Generalized minimum variance unbiased joint input-state estimation and its unscented scheme for dynamic systems with direct feedthrough.” Mech. Syst. Sig. Process. 99: 886–920. https://doi.org/10.1016/j.ymssp.2017.06.032.
Song, W., and S. Dyke. 2013a. “Development of a cyber-physical experimental platform for real-time dynamic model updating.” Mech. Syst. Sig. Process. 37 (1–2): 388–402. https://doi.org/10.1016/j.ymssp.2012.12.007.
Song, W., and S. Dyke. 2013b. “Real-time dynamic model updating of a hysteretic structural system.” J. Struct. Eng. 140 (3): 04013082. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000857.
Song, W., S. Hayati, and S. Zhou. 2017. “Real-time model updating for magnetorheological damper identification: An experimental study.” Smart Struct. Syst. 20 (5): 619–636.
Tamuly, P., A. Chakraborty, and S. Das. 2021. “Experimental verification of constrained minimum variance unbiased estimator for simultaneous input and state estimation of bounded input and bounded output (bibo) type Bouc–Wen hysteretic structural system.” Struct. Control Health Monit. 28 (1): e2648. https://doi.org/10.1002/stc.v28.1.
Wen, Y.-K. 1976. “Method for random vibration of hysteretic systems.” J. Eng. Mech. Div. 102 (2): 249–263. https://doi.org/10.1061/JMCEA3.0002106.
Williams, M. S., and R. G. Sexsmith. 1995. “Seismic damage indices for concrete structures: A state-of-the-art review.” Earthquake Spectra 11 (2): 319–349. https://doi.org/10.1193/1.1585817.
Wu, M., and A. Smyth. 2008. “Real-time parameter estimation for degrading and pinching hysteretic models.” Int. J. Non Linear Mech. 43 (9): 822–833. https://doi.org/10.1016/j.ijnonlinmec.2008.05.010.
Wu, M., and A. W. Smyth. 2007. “Application of the unscented Kalman filter for real-time nonlinear structural system identification.” Struct. Control Health Monit. 14 (7): 971–990. https://doi.org/10.1002/(ISSN)1545-2263.
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Journal of Bridge Engineering
Volume 26 • Issue 11 • November 2021
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© 2021 American Society of Civil Engineers.
History
Received: Jul 7, 2020
Accepted: May 26, 2021
Published online: Aug 31, 2021
Published in print: Nov 1, 2021
Discussion open until: Jan 31, 2022
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