Sampling methods for solving Bayesian model updating problems: A tutorial

Adolphus Lye

doi:10.1016/j.ymssp.2021.107760

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Sampling methods for solving Bayesian model updating problems: A tutorial

2021-10-01

Adolphus Lye

Alice Cicirello

Edoardo Patelli *

DOI：10.1016/j.ymssp.2021.107760

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Abstract

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This tutorial paper reviews the use of advanced Monte Carlo sampling methods in the context of Bayesian model updating for engineering applications. Markov Chain Monte Carlo, Transitional Markov Chain Monte Carlo, and Sequential Monte Carlo methods are introduced, applied to different case studies and finally their performance is compared. For each of these methods, numerical implementations and their settings are provided. Three case studies with increased complexity and challenges are presented showing the advantages and limitations of each of the sampling techniques under review. The first case study presents the parameter identification for a spring-mass system under a static load. The second case study presents a 2-dimensional bi-modal posterior distribution and the aim is to observe the performance of each of these sampling techniques in sampling from such distribution. Finally, the last case study presents the stochastic identification of the model parameters of a complex and non-linear numerical model based on experimental data. The case studies presented in this paper consider the recorded data set as a single piece of information which is used to make inferences and estimations on time-invariant model parameters. (C) 2021 Elsevier Ltd. All rights reserved.

Keywords:

Bayesian inference

Model updating

Markov Chain Monte Carlo

Transitional Markov Chain Monte Carlo

Sequential Monte Carlo

DLR-AIRMOD

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