Using Metropolis – Hasting algorithm of Markov Chain Monte Carlo method in reliability analysis

Abstract

In reliability analysis literature, Monte Carlo simulation method offers a simple and robust means for estimating the failure probability for a specified structure and loading conditions regardless of the complexity of the performance functions. However it is not suitable for finding small probabilities because of the number of samples, and hence the number of structure analyses required to achieve a given accuracy is proportional to 1/Pf. A more advanced method is Markov Chain Monte Carlo (MCMC) which compensates for this drawback. This article presents the application of the Markov Chain Monte Carlo method (MCMC) based on Metropolis–Hastings algorithm, which is developed by Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller (1953) and generalized by Hastings (1970), to analyse the reliability of structures with uncertainty parameters. The document illustrates the principles of the methodology on two simple examples. Finally, a comparison of two simulation methods (MCS and MCMC) is done, which is employed for the estimation of failure probabilities for a nonlinear (Bouc-Wen type) single degree of freedom system subjected to seismic excitation generated by Boore\'s model.