System Identification via Unscented Kalman Filtering and Model Class Selection
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10, Issue 1
Abstract
Identifying the mechanical properties of civil structures is required for life-cycle assessment. Kalman filters are exploited for this goal, enabling the online update of a numerical model, acting as the digital twin of the structure, and quantifying the uncertainty of the estimated properties. As uncertainty about model formulation is usually disregarded in the identification, model class evidence has been recently formulated to compare different parametrizations of the properties of the monitored structure through a metric, allowing selection of the most plausible one. When dealing with parameter estimation, predominantly model evidence is deployed in batch Bayesian estimation. Here, the formulation of model class evidence is proposed for the unscented Kalman filter, which allows online calculation of model class evidence for a system without the need to compute the mapping gradient in time. This formulation was inspired by the model class evidence developed for the extended Kalman filter. Numerical results related to shear buildings are presented to validate the metric, showing the impact of under- and over-parametrizations on identification.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
The models and the code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The corresponding author acknowledges the economic support of the University of New Hampshire during his time there as visiting Ph.D. candidate. The authors are indebted to Rodrigo Astroza, Universidad de Los Andes (Chile) for the valuable discussions.
References
Adeagbo, M. O., H.-F. Lam, and Y.-J. Chu. 2022. “Bayesian system identification of rail-sleeper-ballast system in time and modal domains: Comparative study.” J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 8 (3): 04022020. https://doi.org/10.1061/AJRUA6.0001242.
Astroza, R., H. Ebrahimian, and J. P. Conte. 2015. “Material parameter identification in distributed plasticity FE models of frame-type structures using nonlinear stochastic filtering.” J. Eng. Mech. 141 (5): 04014149. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000851.
Bittanti, S., G. Maier, and A. Nappi. 1985. “Inverse problems in structural elastoplasticity: A Kalman filter approach.” In Proc., Current Trends and Results in Plasticity, Plasticity Today, Modelling, Methods and Applications, 311–329. Amsterdam: Elsevier.
Buckley, T., B. Ghosh, and V. Pakrashi. 2022. “A feature extraction & selection benchmark for structural health monitoring.” Struct. Health Monit. 22 (3): 2082–2127. https://doi.org/10.1177/14759217221111141.
Cabboi, A., C. Gentile, and A. Saisi. 2017. “From continuous vibration monitoring to FEM-based damage assessment: Application on a stone-masonry tower.” Constr. Build. Mater. 156 (Dec): 252–265. https://doi.org/10.1016/j.conbuildmat.2017.08.160.
Capacci, L., and F. Biondini. 2020. “Probabilistic life-cycle seismic resilience assessment of aging bridge networks considering infrastructure upgrading.” Struct. Infrastruct. Eng. 16 (4): 659–675. https://doi.org/10.1080/15732479.2020.1716258.
Castiglione, J., R. Astroza, S. Eftekhar Azam, and D. Linzell. 2020. “Auto-regressive model based input and parameter estimation for nonlinear finite element models.” Mech. Syst. Signal Process. 143 (Sep): 106779. https://doi.org/10.1016/j.ymssp.2020.106779.
Chatzi, E. N., and A. W. Smyth. 2009. “The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing.” Struct. Control Health Monit. 16 (1): 99–123. https://doi.org/10.1002/stc.290.
Corigliano, A., and S. Mariani. 2004. “Parameter identification in explicit structural dynamics: Performance of the extended Kalman filter.” Comput. Methods Appl. Mech. Eng. 193 (36–38): 3807–3835. https://doi.org/10.1016/j.cma.2004.02.003.
D’Alessandro, A., G. Vitale, S. Scudero, R. D’Anna, A. Costanza, A. Fagiolini, and L. Greco. 2017. “Characterization of MEMS accelerometer self-noise by means of PSD and Allan variance analysis.” In Proc., 7th IEEE Int. Workshop on Advances in Sensors and Interfaces IWASI, 159–164. New York: IEEE.
Eftekhar Azam, S., and S. Mariani. 2018. “Online damage detection in structural systems via dynamic inverse analysis: A recursive Bayesian approach.” Eng. Struct. 159 (Mar): 28–45. https://doi.org/10.1016/j.engstruct.2017.12.031.
Eftekhar Azam, S., S. Mariani, and N. K. A. Attari. 2017. “Online damage detection via a synergy of proper orthogonal decomposition and recursive Bayesian filters.” Nonlinear Dyn. 89 (Jul): 1489–1511. https://doi.org/10.1007/s11071-017-3530-1.
Evans, J. R., R. M. Allen, A. I. Chung, E. S. Cochran, R. Guy, M. Hellweg, and J. F. Lawrence. 2014. “Performance of several low-cost accelerometers.” Seismol. Res. Lett. 85 (1): 147–158. https://doi.org/10.1785/0220130091.
Fernández-Martínez, J. L., and Z. Fernández-Muñiz. 2020. “The curse of dimensionality in inverse problems.” J. Comput. Appl. Math. 369 (May): 112571. https://doi.org/10.1016/j.cam.2019.112571.
Gobat, G., S. E. Azam, and S. Mariani. 2020. “SHM and efficient strategies for reduced-order modeling.” Eng. Proc. 2 (1): 98. https://doi.org/10.3390/engproc2020002098.
Han, X., and D. M. Frangopol. 2022. “Risk-informed bridge optimal maintenance strategy considering target service life and user cost at project and network levels.” J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 8 (4): 04022050. https://doi.org/10.1061/AJRUA6.0001263.
Hilber, H. M., T. J. R. Hughes, and R. L. Taylor. 1977. “Improved numerical dissipation for time integration algorithms in structural dynamics.” Earthquake Eng. Struct. Dyn. 5 (3): 283–292. https://doi.org/10.1002/eqe.4290050306.
Hoshiya, M., and E. Saito. 1984. “Structural identification by extended Kalman filter.” J. Eng. Mech. 110 (12): 1757–1770. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:12(1757).
Ito, K., and K. Xiong. 2000. “Gaussian filters for nonlinear filtering problems.” IEEE Trans. Autom. Control 45 (5): 910–927. https://doi.org/10.1109/9.855552.
Julier, S. 2002. “The scaled unscented transformation.” In Vol. 6 of Proc., 2002 American Control Conf. (IEEE Cat. No.CH37301), 4555–4559. New York: IEEE.
Kalman, R. 1960. “On the general theory of control systems.” In Proc., 1st Int. IFAC Congress on Automatic and Remote Control, 491–502. Laxenburg, Austria: International Federation of Automatic Control https://doi.org/10.1016/S1474-6670(17)70094-8.
Lesieutre, G. 2001. “Damping in FE models.” In Encyclopedia of vibration, edited by S. Braun, 321–327. Amsterdam: Elsevier.
Mariani, S., and A. Corigliano. 2005. “Impact induced composite delamination: State and parameter identification via joint and dual extended Kalman filters.” Comput. Methods Appl. Mech. Eng. 194 (50): 5242–5272. https://doi.org/10.1016/j.cma.2005.01.007.
Mariani, S., and A. Ghisi. 2007. “Unscented Kalman filtering for nonlinear structural dynamics.” Nonlinear Dyn. 49 (Jul): 131–150. https://doi.org/10.1007/s11071-006-9118-9.
Messore, M. M., L. Capacci, and F. Biondini. 2021. “Life-cycle cost–based risk assessment of aging bridge networks.” Struct. Infrastruct. Eng. 17 (4): 515–533. https://doi.org/10.1080/15732479.2020.1845752.
Niederer, S. A., M. S. Sacks, M. Girolami, and K. Willcox. 2021. “Scaling digital twins from the artisanal to the industrial.” Nat. Comput. Sci. 1 (5): 313–320. https://doi.org/10.1038/s43588-021-00072-5.
Pandey, A., and M. Biswas. 1994. “Damage detection in structures using changes in flexibility.” J. Sound Vib. 169 (1): 3–17. https://doi.org/10.1006/jsvi.1994.1002.
Papadimitriou, C., J. L. Beck, and L. S. Katafygiotis. 1997. “Asymptotic expansions for reliability and moments of uncertain systems.” J. Eng. Mech. 123 (12): 1219–1229. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:12(1219).
Ramancha, M., R. Astroza, J. Conte, J. Restrepo, and M. Todd. 2020. Bayesian nonlinear finite element model updating of a full-scale bridge-column using sequential Monte Carlo. Berlin: Springer.
Rosafalco, L., S. Eftekhar Azam, A. Manzoni, A. Corigliano, and S. Mariani. 2022. “Unscented Kalman filter empowered by Bayesian model evidence for system identification in structural dynamics.” In Proc., Computer Sciences & Mathematics Forum, 3. Basel, Switzerland: Multidisciplinary Digital Publishing Institute.
Simon, D. 2006. Optimal state estimation: Kalman, H infinity, and nonlinear approaches. New York: Wiley.
Wan, E., and R. Van Der Merwe. 2000. “The unscented Kalman filter for nonlinear estimation.” In Proc., IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symp. (Cat. No.00EX373), 153–158. New York: IEEE.
Wan, E. A., and A. T. Nelson. 2001. Dual extended Kalman filter methods, 123–173. New York: Wiley.
Yuen, K.-V. 2010. Bayesian model class selection, 213–256. New York: Wiley.
Yuen, K.-V., and L. Dong. 2020. “Real-time system identification using hierarchical interhealing model classes.” Struct. Control Health Monit. 27 (12): e2628. https://doi.org/10.1002/stc.2628.
Yuen, K.-V., and H.-Q. Mu. 2015. “Real-time system identification: An algorithm for simultaneous model class selection and parametric identification.” Comput. -Aided Civ. Infrastruct. Eng. 30 (10): 785–801. https://doi.org/10.1111/mice.12146.
Information & Authors
Information
Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10 • Issue 1 • March 2024
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Mar 8, 2023
Accepted: Jul 27, 2023
Published online: Dec 22, 2023
Published in print: Mar 1, 2024
Discussion open until: May 22, 2024
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.