A single-loop Kriging coupled with subset simulation for time-dependent reliability analysis

Time-dependent reliability analysis (TRA) plays an important role in improving the validity and practicability of product reliability evaluation over an interested life interval. Conventional TRA for high-reliability product, however, requires tackling two main challenges: (1) the inaccurate analysis of small failure probability problem and (2) the computationally expensive time-variant performance function. In this paper, a single-loop Kriging coupled with subset simulation (SLK-co-SS) method is proposed to address these challenges. By introducing time-dependent intermediate failure events, the estimation of small failure probability is first converted into a product of larger condition probabilities, which can be estimated by a proposed most probable extreme value method based on the trained Kriging model. We then develop an improved maximum error-guided adaptive sampling strategy to sequentially train and update the Kriging model in every intermediate failure event. To make more training samples located at the high potential region of time-dependent limit state surface, the error-tolerance threshold of updating stopping criterion varies with the intermediate failure events. The comparison results on four examples demonstrate the good capability and applicability of proposed SLK-co-SS method.