Two-stage failure probability function estimation method based on improved cross-entropy importance sampling and adaptive Kriging

In structural reliability design, determining distribution parameters of uncertainty variables is essential for minimizing failure probability, expressed as the failure probability function (FPF). Existing FPF estimation methods face challenges in computational accuracy and efficiency. This paper enhances the improved crossentropy importance sampling (ICE-IS) method and proposes AICE-IS for FPF estimation in the augmented space and OICE-IS for FPF estimation in the original space. To enhance the efficiency of active learning, this paper proposes the global entropy reduction (GER) learning function. Subsequently, the GER learning function and Kriging were integrated with AICE-IS and OICE-IS, respectively, leading to the development of the two-stage FPF estimation methods ALK-AICE and ALK-OICE, which are suitable for expensive finite element problems. The performance of the GER learning function was validated across three benchmark examples, while ALK-AICE and ALK-OICE demonstrated efficiency and accuracy in four numerical examples. These methods were further applied to resonance reliability design of axially functionally graded material (FGM) pipes and aircraft landing gear impact reliability analysis.