Computing upper probabilities of failure using optimization algorithms together with importance sampling

Abstract This paper addresses efficient computation of the upper probability of failure of an engineering structure, when the uncertainty is modeled by a family of probability densities. We develop an algorithm significantly reducing the sample sizes required in the optimization algorithm by adopting a recursive approach. The algorithm is based on importance sampling, reweighting, comparing sample ratios and setting up an iterative scheme that allows one to re‐use previously computed sample points in the optimization. The efficiency of the method is analyzed by means of a moderate scale engineering structure.