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Novel sparseness-inducing dual Kalman filter and its application to tracking time-varying spatially-sparse structural stiffness changes and inputs

Huang, Yong and Yu, Jianqi and Beck, James L. and Zhu, Huiping and Li, Hui (2020) Novel sparseness-inducing dual Kalman filter and its application to tracking time-varying spatially-sparse structural stiffness changes and inputs. Computer Methods in Applied Mechanics and Engineering, 372 . Art. No. 113411. ISSN 0045-7825. https://resolver.caltech.edu/CaltechAUTHORS:20200929-104859401

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Abstract

While the theory of Bayesian system identification provides a probabilistic means for reliably and robustly inferring models of a dynamic system and their parameters based on measured dynamic response, exploiting sparseness during online tracking of changing model parameters is not well understood. The focus in this study is to implement the dual Kalman filter for real-time Bayesian sequential state and parameter identification based on noisy sensor signals while incorporating sparse Bayesian learning to impose sparse model parameter changes from their initial reference values. We also want out model to be able to capture the evolution of sparse model parameter changes between two successive time instants. To this end, we present a hierarchical Bayesian model for tracking the joint posterior distribution of the state and model parameter vectors for a monitored dynamical system, where the two afore-mentioned sparseness constraints (sparse changes from reference values and with time) are also effectively incorporated for each time. We show our stochastic model of the structural dynamical system can be represented as a coupled conditionally-linear Gaussian state space model for the state and model parameter vectors, leading to some interesting analytical properties of the method that allow quantities of interest to be calculated in real time by using Kalman filtering equations. The parameters for the measurement and state prediction errors are learned solely from the available data up to the current time and so our method resolves the well-known instability problem in Kalman filtering due to arbitrary assignment of the error-distribution parameters. Finally, two illustrative applications are presented, one for identification of stiffness degradation and the other for input time–history identification where both are based on noisy dynamic response measurements from a structure.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.cma.2020.113411DOIArticle
ORCID:
AuthorORCID
Huang, Yong0000-0002-7963-0720
Additional Information:© 2020 Elsevier B.V. Received 18 March 2020, Revised 25 July 2020, Accepted 31 August 2020, Available online 28 September 2020. This research was supported by grants from the National Natural Science Foundation of China (NSFC Grant Nos. 51778192 and 51638007). The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Funders:
Funding AgencyGrant Number
National Natural Science Foundation of China51778192
National Natural Science Foundation of China51638007
Subject Keywords:Bayesian system identification; Sparse Bayesian learning; Kalman filter; Online model error and noise identification; Dual sequential state and parameter estimation; Input time–history identification
Record Number:CaltechAUTHORS:20200929-104859401
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200929-104859401
Official Citation:Yong Huang, Jianqi Yu, James L. Beck, Huiping Zhu, Hui Li, Novel sparseness-inducing dual Kalman filter and its application to tracking time-varying spatially-sparse structural stiffness changes and inputs, Computer Methods in Applied Mechanics and Engineering, Volume 372, 2020, 113411, ISSN 0045-7825, https://doi.org/10.1016/j.cma.2020.113411. (http://www.sciencedirect.com/science/article/pii/S004578252030596X)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105633
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:29 Sep 2020 17:55
Last Modified:29 Sep 2020 17:55

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