Modified replica exchange-based MCMC algorithm for estimation of structural reliability based on particle splitting method

Abstract

We consider the problem of evaluation of the reliability integral when the limit state functions could have complicating features such as (a) discontinuity/rapid changes in values of GU in the space spanned by U, (b) existence of multiple, possibly unimportant, regions of failure with rapid changes in performance function near one or more of the important regions, and (c) multiple regions of failure with substantial contributions to failure probability. We tackle this problem by using the particle splitting framework and introduce an improved Markov chain Monte Carlo sampler based on replica exchange strategy. This is shown to enhance the capacity of samples to detect and explore important regions of failure. The application of the bootstrap technique to deduce the sampling variance of the estimator of the probability of failure is developed. Also given are a few examples of problems in structural mechanics where limit state functions with the aforementioned difficulties arise. The performance of the proposed method in dealing with these difficulties is compared with those of existing methods.