An efficient method for solving system failure probability functions based on subset simulation and probability reanalysis techniques

Estimating the system failure probability function (FPF) is critical in reliability-based system design and optimization. However, multiple failure modes in a system challenge the estimation process. The probability reanalysis (PRA) method can estimate failure probabilities under various distribution parameters using only a single set of input-output samples. However, combining it with efficient numerical simulation methods can improve its computational efficiency. This paper combines the importance sampling subset simulation (SS-IS) method with the PRA method to propose the SS-IS-PRA method for estimating the system FPF. The proposed method transforms the system FPF into a product of a series of conditional FPFs. Then, a single set of input-output samples is used to solve conditional FPFs layer by layer based on the PRA approach. Furthermore, this paper introduces an IS center selection strategy based on mixed sampling and K-means clustering to enhance the applicability of the SS-IS-PRA method in multi-failure mode problems without additional computational cost. Finally, an adaptive Kriging surrogate model is embedded within the SS-IS-PRA method to enhance the computational efficiency of SS-IS-PRA and better suit real engineering structure analysis. Hence, the SS-IS-PRA-AK method is obtained. The effectiveness and efficiency of the proposed method are validated through four examples.