Hybrid Framework for the Estimation of Rare Failure Event Probability

Abstract

This paper presents a novel approach for computing the rare failure event probability. Within the framework of the proposed approach, adaptive hybrid polynomial correlated function expansion (H-PCFE) is first formulated by coupling sequential experimental design (SED) with H-PCFE. Next, a novel algorithm for reducing the surrogate error near the failure surface is presented. The proposed algorithms (i.e., adaptive H-PCFE and the algorithm for reducing prediction error near the failure surface) are coupled into the framework of subset simulation. Application of the proposed approach in estimating rare failure event probability is illustrated with five examples. The study illustrates that the proposed hybrid framework is more efficient than the subset simulation and is more accurate and robust than the conventional surrogate modeling approach. It is further demonstrated that the proposed approach is capable of accurately predicting rare failure probability, in the order of 10−5−10−12, from significantly fewer sample points.