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Sequential sparse Bayesian learning with applications to system identification for damage assessment and recursive reconstruction of image sequences

Huang, Yong and Beck, James L. and Li, Hui and Ren, Yulong (2021) Sequential sparse Bayesian learning with applications to system identification for damage assessment and recursive reconstruction of image sequences. Computer Methods in Applied Mechanics and Engineering, 373 . Art. No. 113545. ISSN 0045-7825. https://resolver.caltech.edu/CaltechAUTHORS:20201117-111302958

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Abstract

Sparse Bayesian learning (SBL) has attracted substantial interest in recent years for reliable estimation of sparse parameter vectors of dimension much larger than the number of measurements. However, the theory of online sequential estimation of sparsely changing parameter vectors is much less studied. We present a sequential SBL framework for recursive learning of sparse vectors that also change sparsely between successive sampling time periods. Our method uses a hierarchical Bayesian model to recursively estimate the marginal posterior distribution of the parameter vector for each time period, incorporating the sparseness of both this vector and its temporal changes. Our Bayesian model is built around a linear Gaussian state space model and so many quantities of interest can be calculated by using the recursive Bayesian equations. The fast evidence maximization procedure for SBL is developed for recursive Bayesian analysis and the “noise” parameters are efficiently learned solely from the available data in an efficient manner. Numerical experiments verify that exploiting the sparseness of temporal changes of sparse vectors leads to better performance of sparse Bayesian learning. We also examine two applications of sequential SBL: structural system identification for estimating stiffness losses of sequential damage states and recursive reconstruction of image sequences. These illustrative applications validate the effectiveness and robustness of our method.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.cma.2020.113545DOIArticle
ORCID:
AuthorORCID
Huang, Yong0000-0002-7963-0720
Additional Information:© 2020 Elsevier B.V. Received 30 May 2020, Revised 23 October 2020, Accepted 26 October 2020, Available online 16 November 2020. This research was supported by grants from the National Natural Science Foundation of China (NSFC Grant Nos. 51778192 and 52078174). 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 China52078174
Subject Keywords:Sequential sparse Bayesian learning; Hierarchical Bayesian model; Recursive Bayesian estimation; Uncertainty quantification; Bayesian system identification; Bayesian compressive sensing
Record Number:CaltechAUTHORS:20201117-111302958
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20201117-111302958
Official Citation:Yong Huang, James L. Beck, Hui Li, Yulong Ren, Sequential sparse Bayesian learning with applications to system identification for damage assessment and recursive reconstruction of image sequences, Computer Methods in Applied Mechanics and Engineering, Volume 373, 2021, 113545, ISSN 0045-7825, https://doi.org/10.1016/j.cma.2020.113545. (http://www.sciencedirect.com/science/article/pii/S0045782520307301)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106702
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:17 Nov 2020 19:18
Last Modified:17 Nov 2020 19:18

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