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Bayesian system identification based on hierarchical sparse Bayesian learning and Gibbs sampling with application to structural damage assessment

Huang, Yong and Beck, James L. and Li, Hui (2017) Bayesian system identification based on hierarchical sparse Bayesian learning and Gibbs sampling with application to structural damage assessment. Computer Methods in Applied Mechanics and Engineering, 318 . pp. 382-411. ISSN 0045-7825. https://resolver.caltech.edu/CaltechAUTHORS:20170511-081310764

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Abstract

Bayesian system identification has attracted substantial interest in recent years for inferring structural models based on measured dynamic response from a structural dynamical system. The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse Bayesian learning model from our previous work, we propose two Gibbs sampling algorithms. The algorithms differ in their strategies to deal with the posterior uncertainty of the equation-error precision parameter, but both sample from the conditional posterior probability density functions (PDFs) for the structural stiffness parameters and system modal parameters. The effective dimension for the Gibbs sampling is low because iterative sampling is done from only three conditional posterior PDFs that correspond to three parameter groups, along with sampling of the equation-error precision parameter from another conditional posterior PDF in one of the algorithms where it is not integrated out as a “nuisance” parameter. A nice feature from a computational perspective is that it is not necessary to solve a nonlinear eigenvalue problem of a structural model. The effectiveness and robustness of the proposed algorithms are illustrated by applying them to the IASE-ASCE Phase II simulated and experimental benchmark studies. The goal is to use incomplete modal data identified before and after possible damage to detect and assess spatially-sparse stiffness reductions induced by any damage. Our past and current focus on meeting challenges arising from Bayesian inference of structural stiffness serves to strengthen the capability of vibration-based structural system identification but our methods also have much broader applicability for inverse problems in science and technology where system matrices are to be inferred from noisy partial information about their eigenquantities.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.cma.2017.01.030DOIArticle
http://www.sciencedirect.com/science/article/pii/S0045782516305060PublisherArticle
https://arxiv.org/abs/1701.03550arXivDiscussion Paper
Additional Information:© 2017 Elsevier B.V. Received 5 June 2016, Revised 14 January 2017, Accepted 26 January 2017, Available online 3 February 2017. The first author acknowledges the financial support from the National Natural Science Foundation of China (NSFC grant no. 51308161) and the George W. Housner Research Fund at the California Institute of Technology. This research is also supported by the International Postdoctoral Exchange Fellowship Program 2014 by the Office of China Postdoctoral Council (No. 20140018), which partially supported the first author and this support is also gratefully acknowledged.
Funders:
Funding AgencyGrant Number
National Natural Science Foundation of China51308161
Caltech George W. Housner Research FundUNSPECIFIED
Office of China Postdoctoral Council20140018
Subject Keywords:Bayesian system identification; Sparse Bayesian learning; Hierarchical model; Gibbs sampling; Damage assessment; IASE-ASCE Phase II benchmark
Record Number:CaltechAUTHORS:20170511-081310764
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170511-081310764
Official Citation:Yong Huang, James L. Beck, Hui Li, Bayesian system identification based on hierarchical sparse Bayesian learning and Gibbs sampling with application to structural damage assessment, Computer Methods in Applied Mechanics and Engineering, Volume 318, 1 May 2017, Pages 382-411, ISSN 0045-7825, https://doi.org/10.1016/j.cma.2017.01.030. (http://www.sciencedirect.com/science/article/pii/S0045782516305060)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77367
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:12 May 2017 22:54
Last Modified:03 Oct 2019 17:56

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