A novel Kriging model-based stratified importance sampling method for estimating augmented failure probability

Due to the absence of sufficient or reliable data, the random input distribution parameters are often treated as random variables. Augmented failure probability (AFP) serves as an effective quantifier of safety levels in such cases. However, the efficient and accurate estimation of small AFP values remains a considerable challenge. To confront this challenge, this study proposes a novel Kriging model-based stratified importance sampling method. As per the proposed approach, a regular mixed importance sampling density function (MIS-DF) is formulated for the estimation of small AFP values. To enhance sampling efficiency and maintain algorithm robustness, a stratified strategy is introduced for the progressive construction of the MIS-DF. Furthermore, to reduce the computational consumption of this progressive construction and the extraction of samples, an economical Kriging model is integrated with a newly designed learning function, which accounts for not only the Euclidean distance from candidate sample points to limit state surface, but also the dissimilarity between these candidate points and the existing training points. Two numerical examples validate the method’s superior performance in estimating AFP.