Bayesian Finite Element Model Updating Using an Improved Evolution Markov Chain Algorithm

Model updating algorithms are used to minimise the differences between the experimental results of a structure and the analytical solutions of its finite element model (FEM). In simple model updating procedures, iterative optimisation techniques can be easily used to update models and reduce the errors between experimental and analytical results. Unfortunately, experimental results as well as analytical models may have some degree of uncertainty that comes from different sources. As a result, iterative optimisation techniques may not be enough to quantify the uncertainty associated with structures. Uncertainty quantification approaches, such as the Bayesian approach, have the ability to incorporate the uncertainties associated with experiments as well as the modelling process into the updating procedure. In Bayesian finite element model updating, the uncertainty associated with the structural system is described by a posterior distribution function, while numerical tools are essential to approximate the solution of the complex posterior distribution function. In this paper, an improved evolution Markov chains Monte Carlo algorithm is used to solve the Bayesian model updating problem. In the proposed approach, the Markov chain Monte Carlo (MCMC) method is combined with the differential evolution optimising algorithm, while the final updating procedure is modified and extended with a snooker updater. The proposed approach is tested by updating a structural example, and the results are compared with the results obtained by the Metropolis-Hastings and the standard Differential Evolution Markov Chain (DE-MC) methods.