Bayesian Updating of Structural Model with a Conditionally Heteroscedastic Error Distribution

AbstractThe existing literature on Bayesian updating of structural models has assigned equal variances (homoscedasticity) in the measured observables across all modes by assuming a Gaussian error distribution. This paper relaxes the assumption by allowing the error distribution to be conditionally h...

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Bibliographic Details
Published in:Journal of engineering mechanics 2019-12, Vol.145 (12)
Main Authors: Lyngdoh, Gideon Arthur, Rahman, Mohammad Arshad, Mishra, Sudib Kumar
Format: Article
Language:English
Subjects:
Algorithms
Bayesian analysis
Computer simulation
Gaussian distribution
Immunity
Markov chains
Mathematical models
Model testing
Modelling
Parameter estimation
Parameter uncertainty
Stiffness
Technical Papers
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Summary:AbstractThe existing literature on Bayesian updating of structural models has assigned equal variances (homoscedasticity) in the measured observables across all modes by assuming a Gaussian error distribution. This paper relaxes the assumption by allowing the error distribution to be conditionally heteroscedastic but marginally follow the Student’s t-distribution. Modeling heteroscedasticity in structures is necessary because higher modal parameters are prone to higher uncertainty—an idea that is supported by experimental data obtained from a scaled building model. We adopted a hierarchical modeling framework for system equations and employed Bayesian techniques to update the parameters. Estimation used Gibbs sampling, a well-known Markov chain Monte Carlo (MCMC) algorithm. The proposed framework is illustrated in various simulated data obtained from a 10-story shear building for varying levels of noise contamination. The model was also implemented for experimental data from an eight-degrees-of-freedom spring-mass model tested at the Los Alamos National Laboratory. We show that our framework provides several advantages over the homoscedastic model, including a more stable and accurate inference about the stiffness and modal parameters and a noticeable improvement in noise immunity compared to those reported in the literature. The importance of the heteroscedasticity is also highlighted because it leads to a better exploration of the associated uncertainty in the observables, not captured by its homoscedastic counterpart. The paper also discusses some limitations and provides possible extensions for future research.
ISSN:0733-9399
1943-7889
DOI:10.1061/(ASCE)EM.1943-7889.0001668