Enhanced Adaptive Kriging Method for Estimating Fuzzy Failure Probability with Profust Model

Aiming at analyzing the structural fuzzy failure probability with probability inputs and fuzzy-state assumption (profust model), an adaptive kriging model-based sequentially truncated Monte Carlo simulation (MCS) method is investigated, where estimating the fuzzy failure probability can be transformed into identifying the absolute safety domain, the absolute failure domain, and the exact performance function values of the fuzzy safety–failure transition domain. To this end, in this study, three kriging models are sequentially constructed to realize the three aims, respectively. To further improve the efficiency of adaptively updating kriging model, adaptive radial-based importance sampling technique is embedded to divide the whole MCS candidate sampling pool (CSP) into several sub-CSPs. Then, the kriging model is updated sequentially in each sub-CSP instead of the whole CSP, and the samples dropped into the optimal hypersphere of the absolute safety domain can be truncated and do not participate in the CSP of updating the kriging model so that the size of whole MCS CSP and the size of CSP in each learning process of updating kriging are reduced simultaneously. As a result, the efficiency of estimating the fuzzy failure probability is enhanced. The results of two examples verify the effectiveness of the proposed method.