An Investigation into an Alternative Transition Criterion of the Transitional Markov Chain Monte Carlo Method for Bayesian Model Updating

One of the advanced Monte Carlo techniques employed to perform Bayesian model updating on the epistemic model parameter(s) is the Transitional Markov Chain Monte Carlo sampler. A key characteristic in its sampling approach involves the use of "transitional" distributions to allow samples to converge iteratively from the prior to the final posterior. Hence, the selection of the transition step size becomes of critical importance. Currently, the selection criterion is such that the optimal transition step size is one that realizes a 100% Coefficient of Variation in the statistical weights of the samples in a given iteration. The work presented here considers an alternative selection criterion on the transition step size involving the use of the Effective Sample Size as a metric. The optimal step size considered in this work is one which achieves an effective sample size equal to half the total sample size. To provide a comparative study, the standard Transitional Markov Chain Monte Carlo sampler, along with the modified Transitional Markov Chain Monte Carlo sampler imbued with the alternative selection criterion, are implemented to infer the friction force and the natural frequency of a single-storey frame structure with a metal-to-metal contact, whose dynamics is described by a non-linear differential equation. From there, the sampling performance is compared on the basis of the evolution of the tempering parameter, and the standard error of the estimates.

Keywords: Bayesian model updating, Transitional Markov Chain Monte Carlo, Parameter identification, Area metric, Non-linear dynamics, Coulomb friction.

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