An improved sequential importance sampling method for structural reliability analysis of high dimensional problems

Reliability analysis for rare events has proven to be a significant challenge, particularly in non-linear and complex scenarios. Despite the effectiveness of Sequential Importance Sampling (SIS) and Subset Simulation (SUS) in addressing high-dimensional small failure probability problems, the computational burden associated with mechanical simulations for complex structures remains substantial. To address this issue, this paper introduces a novel approach referred to as SIS and Kriging Metamodel Integration (SISAK), designed for computing small failure probabilities in high dimensions. This method involves generating a small number of samples from the original distribution to construct an adaptive metamodel, which is then iteratively optimized using a series of intermediate distributions introduced by SIS. By substituting the function for intermediate distributions with a continuously optimized metamodel, the enhanced approach significantly reduces the computational load associated with mechanical model evaluations compared to the direct use of SIS. This approach does not depend on determining the most probable failure point and does not require consideration of the failure domain shape. Additionally, it inherits the advantages of SIS in addressing high-dimensional small failure probabilities, making it well-suited for structural reliability analysis of nonlinear systems, discontinuous failure domains, cascading functions, and high-dimensional problems.