A Differential Evaluation Markov Chain Monte Carlo algorithm for Bayesian Model Updating

TL;DR

This paper introduces a Differential Evaluation Markov Chain Monte Carlo (DE-MC) algorithm that combines differential evolution with MCMC to improve Bayesian finite element model updating, especially for complex systems.

Contribution

The paper presents a novel DE-MC algorithm that enhances Bayesian model updating by integrating differential evolution with MCMC techniques for better sampling.

Findings

DE-MC effectively approximates posterior distributions in FEM updating.

The method shows improved accuracy over traditional MCMC in structural examples.

DE-MC demonstrates robustness in complex system identification.

Abstract

The use of the Bayesian tools in system identification and model updating paradigms has been increased in the last ten years. Usually, the Bayesian techniques can be implemented to incorporate the uncertainties associated with measurements as well as the prediction made by the finite element model (FEM) into the FEM updating procedure. In this case, the posterior distribution function describes the uncertainty in the FE model prediction and the experimental data. Due to the complexity of the modeled systems, the analytical solution for the posterior distribution function may not exist. This leads to the use of numerical methods, such as Markov Chain Monte Carlo techniques, to obtain approximate solutions for the posterior distribution function. In this paper, a Differential Evaluation Markov Chain Monte Carlo (DE-MC) method is used to approximate the posterior function and update FEMs. The main idea of the DE-MC approach is to combine the Differential Evolution, which is an effective global optimization algorithm over real parameter space, with Markov Chain Monte Carlo (MCMC) techniques to generate samples from the posterior distribution function. In this paper, the DE-MC method is discussed in detail while the performance and the accuracy of this algorithm are investigated by updating two structural examples.