A novel dual-stage adaptive Kriging method for profust reliability analysis

Profust reliability analysis (RA) is established on probability assumption for the model inputs and fuzzy state assumption, and it is a useful tool to measure the safety degree of the structure with fuzzy failure state. In order to overcome the inefficiency of the existing AK-MCS method in profust RA for the structure with small profust failure probability, a novel dual-stage adaptive Kriging (DS-AK) method is proposed. Firstly, to improve the sampling efficiency, the importance sampling (IS) is used to estimate the profust failure probability where the optimal importance sampling density (OISD) is derived in this paper. As the analytical expression of the OISD cannot be acquired, the Kriging model for the true performance function is employed to build an approximate OISD. Then, the profust failure probability can be expressed as the product of the augmented profust failure probability and the correction factor, which are estimated in two different stages of the proposed DS-AK method. In the first stage of the DS-AK method, a Kriging model is constructed and updated to obtain the approximate OISD and generate the IS samples, and the augmented profust failure probability can be estimated as a byproduct. In the second stage of the DS-AK method, the current Kriging model is continuously updated to accurately predict the membership functions of the fuzzy failure domain at the IS samples generated in the first stage, from which the correction factor can be calculated efficiently. Finally, the fuzzy failure probability can be estimated as the product of augmented failure probability estimate obtained in the first stage and the correction factor estimate acquired in the second stage. Results of the validation cases demonstrate the accuracy, efficiency and robustness of the proposed method in estimating profust failure probability.