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

Abstract

Time-dependent system reliability analysis still faces severe challenges including the simultaneous consideration of time-dependent uncertainties under multiple failure modes and the accurate estimation of small failure probability. Therefore, this paper proposes a nested single-loop Kriging (NSLK) model coupled with subset simulation (SS) method, named NSLK-co-SS, for time-dependent system reliability assessment. Firstly, based on the rationale of SS method, the small time-dependent system failure probability is converted into the product of a series of large intermediate failure probabilities by introducing a series of intermediate failure events. Then, by reformulating the time-dependent system reliability problem as a nested system reliability one, the NSLK method is developed to estimate each intermediate failure probability. Meanwhile, a system reliability theory-based U (SYSU) learning function is proposed to identify both the best training sample and mode and sequentially update the Kriging models of multiple modes in a series of small intermediate sample pools. Two numerical examples and an engineering example were investigated to demonstrate the efficiency and accuracy of the proposed method.