A Comparison of Multiple Markov Chains Algorithms for Bayesian Updating

In this paper, three advanced multiple Markov chains algorithms are compared for Bayesian model updating problems. The algorithms, namely, the Differential Evolution Markov Chain (DE-MC), the Differential Evolution Markov Chain with snooker update (DE-MCS), and the Population Markov Chain Monte Carlo (Pop-MCMC), are advanced versions of evolutionary techniques that utilize the multi-chain mechanism to approximate the posterior Probability Density Function (PDF). This paper examines these algorithms to solve the Finite Element Model Updating (FEMU) problem based on the Bayesian approach. FEMU is an optimization problem that can be applied in structural dynamics to increase the correlations between the modelled structure using the Finite Element Method (FEM) and the experiment data. Furthermore, the associated uncertainties of the modelled structure are can also be obtained using Bayesian inference where the posterior PDF is used to describe the uncertain parameters of the FE model. This paper addresses the efficiency and the performance of the algorithms to solve the same Bayesian updating problem. The algorithms are detailed and introduced for the FEMU problem. Then, the three procedures are employed to update the same structural example with real data. The advantages and the limitations of each method are discussed. The obtained results are analysed and compared, while the performance of each algorithm is explained in detail and the optimum updating model will be highlighted.