A new learning function for estimating time-dependent failure possibility under fuzzy uncertainty

The method of combining adaptive Kriging surrogate model with fuzzy simulation can efficiently estimate time-dependent failure possibility (TDFP) under fuzzy uncertainty. However, there still exists potential to improve computational efficiency due to the possible conservative issue in current time-dependent U learning function. Thus, based on the stochastic property of Kriging model, a new learning function is proposed by considering the probability of Kriging model misclassifying the time-dependent state of structure. Comparing with the existing time-dependent U learning function, the proposed learning function cannot only select the fuzzy input point whose time-dependent failure state has been correctly recognized by current Kriging model, but also accurately quantify the time-dependent state misclassification probability of the fuzzy input point with unrecognizable time-dependent state. Using the proposed new learning function, the fuzzy input candidate sample, which contributes most to decrease the probability of the Kriging model misjudging the time-dependent state of structure, and the time candidate sample, which possesses most impact to the time-dependent state of the selected fuzzy input sample, can be selected to efficiently guide updating the Kriging model. Then, the efficiency of estimating TDFP is improved. Several case studies are introduced to verify the superiority of the proposed learning function to existing time-dependent U one in view of efficiency.