Rare Event Estimation Using Polynomial-Chaos Kriging

AbstractStructural reliability analysis aims at computing the probability of failure of systems whose performance may be assessed by using complex computational models (e.g., expensive-to-run finite-element models). A direct use of Monte Carlo simulation is not feasible in practice, unless a surrogate model (such as kriging, also known as Gaussian process modeling) is used. Such metamodels are often used in conjunction with adaptive experimental designs (i.e., design enrichment strategies), which allows one to iteratively increase the accuracy of the surrogate for the estimation of the failure probability while keeping low the overall number of runs of the costly original model. This paper develops a new structural reliability method based on the recently developed polynomial-chaos kriging (PC-kriging) approach coupled with an active learning algorithm known as adaptive kriging Monte Carlo simulation (AK-MCS). The problem is formulated in such a way that the computation of both small probabilities of fail...