Efficient reliability analysis combining kriging and subset simulation with two-stage convergence criterion

Reliability assessment of real-world structures is a significant challenge owing to its complex input variables, extremely low failure probability, and significant computational costs. In recent times, a series of surrogate models with variance reduction techniques have been proposed to address these limitations. However, achieving a balance between estimation accuracy and computational cost still remains challenging. To this end, this study proposes a novel two-stage convergence criterion that merges into the exterior subset simulation (SS) framework and the interior Kriging model to improve the efficiency of the active learning process. Based on the error analysis of the Kriging model, two groups of parameters are established to describe the estimation accuracy, eventually forming a two-stage convergence criterion. The first stage aims to control the hierarchical modeling error for each intermediate conditional failure event, and the second stage is devoted to ensuring the global accuracy of estimation of the final failure probability. To validate the proposed method, four case studies were performed, including three numerical examples with explicit limit state functions and a real-world model of a cracked steel deck with finite element analysis. The results indicate that the proposed method can both ensure accuracy and improve the efficiency of the reliability analysis.