Targeted random sampling: a new approach for efficient reliability estimation for complex systems

Abstract

A novel approach, targeted random sampling, is presented for estimating failure probabilities for systems with complex limit states. The method, underpinned by the refined stratified sampling concept by Shields et al., refines the sampling strata in the vicinity of the limit state to concentrate samples near the limit state and accurately resolve the failure domain in a very small number of samples - even for problems with strongly non-linear limit states. The method is compared with importance sampling and subset simulation. It produces very accurate estimates for complex problems where the importance sampling density is difficult, or impossible, to identify and is shown to converge much more rapidly than subset simulation for problems with moderate dimension, producing very accurate estimates with greatly reduced coefficient of variation in a fraction of the number of samples. Some challenges in the method are discussed including the extension to high dimensional reliability assessment.