Adaptive sequential sampling for reliability estimation of binary functions

Abstract

A novel method for estimation of rare event probability is proposed, which works also for computational models returning categorical information only: success or failure. It combines the robustness of simulation methods (counting failure events) with the strength of approximation methods which refine the boundary between the failure and safe sets. Two basic tasks are identified: (i) extension of the experimental design (ED) and (ii) estimation of probabilities. The new extension algorithm adds points for limit state evaluation to the ED by balancing the global exploration and local exploitation, and the estimation uses the pointwise information to build a simple surrogate and perform a novel optimized importance sampling. No connection is presumed between the limit function value at point and its proximity to the failure surface. A new global sensitivity measure of the failure probability to individual variables is proposed and obtained as a by-product of the proposed methods.