A method of combined metamodel and subset simulation for reliability analysis of rare events

Reliability analysis of large, complex structures with high reliability has always been a challenging task. The Subset Simulation (SUS) has proven highly effective for high-dimensional and small failure probability problems. However, the computational demands of time-consuming numerical simulations in the field of mechanical engineering remain substantial. Metamodeling techniques provide an effective means to reduce simulation computational costs. This paper introduces a novel approach, termed SUSAK, which combines the Subset Simulation with Kriging metamodels to address the challenge of small failure probability calculations. By using the original distribution of input variables representing the structural system, the SUSAK method establishes an adaptive metamodel and iteratively optimizes it with intermediate failure domain samples corresponding to the intermediate events. By replacing the performance function in subsequent calculations of the probability associated with intermediate events with metamodels, the enhanced method significantly reduces the computational burden compared to using the SUS method. This approach does not rely on solving for the design point, is not constrained by the shape of the failure domain, and retains the advantages of the SUS method in high-dimensional small failure probability calculations. As a result, it is well-suited for calculating small failure probabilities in nonlinear, discontinuous failure domains, multiple failure domains, and high-dimensional problems.