An enhanced subset simulation algorithm integrating importance sampling for structural reliability analysis

Introduction Conducting reliability analyses for engineering problems with small failure probabilities and expensive computational models is challenging. Subset simulation (SS) is an excellent method that has been applied in many fields. However, SS still has several limitations that need to be addressed, such as correlated samples, a large coefficient of variation (COV), the risk of deviating from dominant failure regions, and inaccuracies in problems with multiple failure regions. Methods In this paper, a subset simulation algorithm integrating importance sampling is developed to address the aforementioned limitations, focusing on complex reliability problems characterized by low-to-moderate dimensionality and small failure probabilities. First, a seed placement strategy on intermediate limit-state curves is developed to reduce the COV and generate independent samples within each subset. Second, interval estimation combined with clustering algorithms is applied to precisely identify seeds. This strategy is designed to handle problems featuring multiple failure regions while mitigating the risk of divergence from dominant failure regions. Results The performance of the proposed algorithm is demonstrated through seven case studies from the literature, including problems with multiple failure regions, nonlinear problems, system reliability problems, SS counterexamples, and structural reliability problems. Discussion The results show that the proposed method provides more accurate and robust failure probability estimates than the other tested methods.