A novel learning function of adaptively updating Kriging model for reliability analysis under fuzzy uncertainty

In the existing method combining adaptive Kriging and fuzzy simulation (AK-FS) for estimating the failure possibility, the AK is required to correctly identify the state of each sample point in the candidate sample pool of FS. However, the states of some sample points have no contributions to the accuracy of estimating the failure possibility, and identifying their states by the existing AK-FS only results in a loss of efficiency. Therefore, this paper proposes a new probability learning strategy to improve the efficiency of the existing AK-FS. According to the theory of failure possibility, when taking the product of the failure domain indicator function and the joint membership function as the failure pointer of the point, failure possibility is the maximum, and the corresponding point is called fuzzy design point. Based on the probabilistic prediction property of Kriging, the proposed strategy establishes a global strategy. The probability of the failure indicator at arbitrary candidate point greater than the predicted maximum failure pointer is analytically derived for the single and multiple failure modes, respectively, and this probability represents the degree of the point to be fuzzy design point, thus it can be used to measure the contribution of the point to improve the accuracy. By adaptively adding the points with the largest contribution to the training sample set, the real failure possibility can be approximated gradually. The efficiency and accuracy of the proposed strategy are verified by several examples.