Asymptotic sampling for high-dimensional reliability analysis

Computational procedures for reliability analysis in many cases suffer from substantially increased effort with increasing dimensionality. This means that methods which are well-suited for cases with a small or moderately large number of random variables may not be tractable for situations involving a large number of random variables. Such situations typically occur when random processes or random fields are discretized in terms of spectral representations. The present paper introduces a novel asymptotic sampling strategy which allows a reasonably accurate estimation of the generalized reliability index using a small number of random or quasi-random samples. This strategy utilizes well-established asymptotic results from reliability theory together with a simple regression technique. Several numerical examples demonstrate the applicability, versatility, and accuracy of the approach.