A new efficient method for estimating failure probability function

Estimation of the failure probability function plays a crucial role in reliability-based optimization design. However, efficiently and accurately estimating the failure probability function remains a challenge. Compared to the traditional double-loop Monte Carlo simulation(DMCS) method, the single-loop probabilistic reanalysis (PRA) method can alleviate the computational dependence of the failure probability function on the distribution parameters of input variables. Nevertheless, for problems involving small failure probabilities, the computational cost of PRA is still impractical for engineering applications. Therefore, to further improve the computational efficiency of the failure probability function, this paper combines importance sampling-based subset simulation(SS-IS) with the PRA method, and proposes a novel SS-IS-based PRA(SS-IS-PRA) method. The proposed method transforms the final small failure probability function into a product of a series of larger conditional failure probability functions and then estimates all conditional failure probability functions simultaneously with a set of input-output samples by virtue of the advantages of the PAR method. Furthermore, considering that the design points under different distribution parameters are normally different, a new strategy for constructing the importance sampling density function in the SS-IS-PAR method is proposed based on the idea of mixed importance sampling. Finally, two examples verify the effectiveness and efficiency of the proposed SS-IS-PRA method.