An Adaptive Two-Stage Framework for AK-MCS in Reliability Analysis

Using reliability assessment methods to calculate failure probability for a product is of vital importance in the design process of the product. The active learning reliability method combining Kriging and Monte Carlo simulation (AK-MCS) is a famous reliability analysis approach for evaluating engineering problems. However, the efficiency of establishing high-precision Kriging models has also been a major obstacle hindering the further employment of the AK-MCS method. This paper proposes an adaptive two-stage framework for AK-MCS to enhance computational efficiency in structural reliability analysis. The core innovation lies in the task decomposition strategy: Stage 1 employs a global exploration criterion to rapidly identify the region containing the true limit-state surface, while Stage 2 switches to a local refinement criterion for precise failure-probability estimation. Comparative studies across six benchmark cases demonstrate that the Two-Stage AK-MCS method reduces the average number of function evaluations by 2.0% to 10.0% compared to the standard AK-MCS method. These results confirm that the proposed two-stage strategy effectively enhances fitting efficiency without compromising accuracy.