A progressive stratified importance sampling method for estimating generalized failure probability function in high-dimensional and high-reliability scenarios

Analyzing generalized failure probability function considering probabilistic inputs and fuzzy state is crucial for capturing how variations in distribution parameters within their design regions affect structural safety levels. The existing single-loop importance sampling method can avoid the highly time-consuming problem resulting from redundant reliability analysis and the large sample pool in high reliability requirements for direct double-loop Monte Carlo method. However, this method still cannot handle the time-consuming issues of constructing unified importance sampling density and low sampling efficiency. To address this, this paper constructs an explicit and easy to sample expression of the unified importance sampling density and proposes its progressive stratification strategy, which render the importance samples of constructing unified importance sampling density cover the regions with higher contribution to generalized failure probability, and enhance the computational efficiency by reducing the estimate variance. Compared to the existing single-loop importance sampling density method, the main innovation of the proposed method is the pro-gressive stratification strategy adopted when constructing unified importance sampling density, which alleviates the optimization requirement with high additional computational cost, thus enhancing the efficiency of exploring target fuzzy failure domain to construct unified importance sampling density and estimate the generalized failure probability function in high-dimensional and high-reliability scenarios. This superiority is fully validated by the examples presented in this paper.