An Adaptive Importance Sampling Method Based on Improved MCMC Simulation for Structural Reliability Analysis

Constructing an effective importance sampling density is crucial for structural reliability analysis via importance sampling (IS), particularly when dealing with performance functions that have multiple design points or disjoint failure domains. This study introduces an adaptive importance sampling technique leveraging an improved Markov chain Monte Carlo (IMCMC) approach. The method begins by efficiently gathering distributed samples across all failure regions using IMCMC. Subsequently, based on the obtained samples, it constructs the importance sampling density adaptively through a kernel density estimation (KDE) technique that integrates local bandwidth factors. Case studies confirm that the proposed approach successfully constructs an importance sampling density that closely mirrors the theoretical optimum, thereby boosting both the accuracy and efficiency of failure probability estimations.