A novel hypercube-based fuzzy simulation and its combination with adaptive Kriging for estimating failure credibility

How to accurately and efficiently estimate the failure credibility is widely concerned in safety analysis under fuzzy uncertainty. To solve this issue, an iterative method combining the adaptive Kriging with fuzzy simulation (AK-FS) was put forward by Ling et al. But for the problem with multidimensional fuzzy inputs and/or high safety degree, AK-FS is inefficient. In order to improve the computational efficiency of AK-FS, a novel hypercube-based fuzzy simulation (HBFS) combined with adaptive Kriging (shorten as AK-HBFS) is proposed in this paper. The first key technique of the proposed method is to develop the HBFS for constructing the candidate sampling pool. In the HBFS, the active point is defined at first. Then, the estimation of the failure credibility is transformed into seeking for the active point. By using an adaptive hypercube shrinkage strategy, the active point can be quickly searched from the samples whose joint membership functions (JMFs) are smaller than the JMF of the active point. Thus, the size of the candidate sampling pool in the AK-HBFS is smaller than that of the original AK-FS, and it helps save the training time of the Kriging model in the AK-HBFS compared to the AK-FS. The second key technique of the proposed method is that the process for finding the active point is efficiently realized by the U-learning function based AK model, rather than calling the true performance function directly. The merits of the proposed AK-HBFS are demonstrated by four test cases.