Asymptotic subset simulation: An efficient extrapolation tool for small probabilities approximation

This study bridges the concepts of subset simulation with asymptotic approximation theory in multinormal integrals for the estimation of small probabilities. To meet this aim, for a sequence of scaled limit state functions (LSFs) with failure probabilities higher than the original LSF, it is found that the proposed asymptotic approximation and subset simulation can be applied within the same framework, and only a few steps of subset simulation could be sufficient to approximate small failure probabilities using extrapolation. The analogy of the formulation of the second-order reliability method (SORM) with the proposed concept is studied and, considering sequential sampling as a search algorithm, shown that the information obtained from a few steps of the design point search process could be enough to approximate the total failure probability of a problem. Solving intricate nonlinear and high-dimensional problems confirms the efficiency and robustness of the proposed framework for reliability analysis of real-world engineering problems with small probabilities.