Bayesian model updating utilizing scaled likelihood ratio and BCT-PCA with frequency response function

Bayesian inference has now been widely practiced for model updating. In this study, the discussion is conducted about two issues facing the implementation of Bayesian model updating when the Gaussian distribution is assumed. To begin with, the problem of the normal likelihood function used in Markov chain Monte Carlo (MCMC) is demonstrated and presented with an alternative approach by defining the scaled likelihood ratio (SLR). Then, a data preprocessing technique is proposed by introducing the Box-Cox transformation and principal component analysis (BCT-PCA) to address the obstacles in the practice of frequency response function (FRF)based Bayesian model updating. The differential evolution adaptive metropolis (DREAM) is applied to explore the posterior distribution of the parameters. In addition, a novel procedure for FRF-based Bayesian model updating is presented. The effectiveness of the proposed methodology is verified in both numerical and experimental cases of dynamical model updating. In the numerical case, the results of eigenfrequency-based model updating show that the SLR is advantageous over the normal likelihood ratio (NLR) in estimating the posterior distribution of parameters. The results of FRF-based model updating show that the consistency and robustness of model updating performance as achieved through the BCT-PCA method are improved when different schemes of frequency selection are implemented. The results of the experimental case also show the superiority of the proposed method.

Automated summary

This study discusses two issues in implementing Bayesian model updating with the assumption of a Gaussian distribution. First, it presents an alternative approach to the problem of the normal likelihood function used in Markov chain Monte Carlo (MCMC) by defining the scaled likelihood ratio (SLR). Second, a data preprocessing technique is proposed to address obstacles in FRF-based Bayesian model updating using the Box-Cox transformation and principal component analysis (BCT-PCA). The effectiveness of the proposed methodology is verified in numerical and experimental cases.