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Structural Engineering and Mechanics Volume 81, Number 1, January10 2022 , pages 103-115 DOI: https://doi.org/10.12989/sem.2022.81.1.103 |
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Markov Chain Monte Carlo simulation based Bayesian updating of model parameters and their uncertainties |
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Partha Sengupta and Subrata Chakraborty
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| Abstract | ||
| The prediction error variances for frequencies are usually considered as unknown in the Bayesian system identification process. However, the error variances for mode shapes are taken as known to reduce the dimension of an identification problem. The present study attempts to explore the effectiveness of Bayesian approach of model parameters updating using Markov Chain Monte Carlo (MCMC) technique considering the prediction error variances for both the frequencies and mode shapes. To remove the ergodicity of Markov Chain, the posterior distribution is obtained by Gaussian Random walk over the proposal distribution. The prior distributions of prediction error variances of modal evidences are implemented through inverse gamma distribution to assess the effectiveness of estimation of posterior values of model parameters. The issue of incomplete data that makes the problem ill-conditioned and the associated singularity problem is prudently dealt in by adopting a regularization technique. The proposed approach is demonstrated numerically by considering an eight-storey frame model with both complete and incomplete modal data sets. Further, to study the effectiveness of the proposed approach, a comparative study with regard to accuracy and computational efficacy of the proposed approach is made with the Sequential Monte Carlo approach of model parameter updating. | ||
| Key Words | ||
| Bayesian updating; error variances; Markov Chain Monte Carlo; modal data; sequential Monte Carlo | ||
| Address | ||
| Partha Sengupta and Subrata Chakraborty: Department of Civil Engineering, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India | ||