Abstract
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.
Highlights
In engineering design problems, mathematical models are used to investigate the virtual behaviour of structures under operational and extreme conditions
The last case study presents the stochastic identification of the model parameters of a complex and non-linear numerical model based on experimental data
Bayesian inference is a popular approach for model updating in Engineering Applications
Summary
Mathematical models are used to investigate the virtual behaviour of structures under operational and extreme conditions. The conventional model updating technique is the Finite Element model updating [2,3] This approach is employed to perform point-estimates of physical parameters. The parameter(s) of a mathematical model describing the material properties of a plate can be updated in order to minimise the difference between the theoretical and experimental natural frequencies of the plate. This type of approach faces three main problems: (i) it assumes that the mathematical model employed is able to capture the physics of the problem in full
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