A novel safety measure with random and fuzzy variables and its solution by combining Kriging with truncated candidate region

For the safety assessment of models with random and fuzzy variables, this work proposes a novel measure of substandard credibility of reliability (SCR), which is defined by the credibility of reliability less than the minimum allowed reliability. In order to improve the computational efficiency of SCR, the truncated candidate region (TCR) based adaptive Kriging model (AK) combined with secant method (SM) is developed. In the proposed method, the solution of SCR is first divided into a double-loop process. In the inner loop, the fuzzy variables are converted into interval variables under a specific membership degree, and then the Kriging model is built and updated with TCR to search the adding points, which can accurately predict the reliability bounds. While in the outer loop, a numerical iterative method of SM is used to solve a one-dimensional root-finding problem to estimate SCR. Compared with traditional method, the proposed method of AK-TCR-SM introduces TCR into the Kriging model to reduce the size of the candidate sample pool, and in the iterative process, only a few new samples are added to sample pool, which significantly improves the computational efficiency. The advantages of the proposed AK-TCR-SM method are demonstrated by several examples.