An efficient method for solving the system failure possibility of multi-mode structure by combining hierarchical fuzzy simulation with Kriging model

The system failure possibility of multi-mode structural system (referred to as system) under fuzzy uncertainty is the joint membership function of input vector at the system fuzzy design point, and it can reasonably measure the safety degree of the system. The system fuzzy simulation (S-FS) can be combined with adaptive Kriging model (AK-S-FS) to solve the system failure possibility. In the current AK-S-FS method, the system fuzzy design point is searched in the maximum value region of the fuzzy input vector corresponding to the 0 membership level, and its computational efficiency still needs to be improved. Thus, a hierarchical system fuzzy simulation combined with adaptive Kriging model (AK-HS-FS) method is proposed to improve the efficiency of searching the system fuzzy design point in this paper. The efficiency of the proposed AK-HS-FS method comes from the innovative strategies of three aspects. The first is the strategy of the hierarchical system fuzzy simulation (HS-FS). Compared with the S-FS with the system fuzzy design point searched roughly in the maximum possible value region, the strategy of the HS-FS is to exploratively expand the search region by transferring from a larger membership level to a smaller one. The overall search region of the system fuzzy design point can be reduced without losing the search accuracy in the HS-FS. The second is the strategy of the hierarchical training. Compared with training the system Kriging model in the combined candidate sample pool (CSP) of all layers, it is more time-saving to train the system Kriging model layer by layer in the hierarchical CSP. The third is the strategy of iteratively reducing the CSP. According to the properties of the system fuzzy design point and the probability properties of the Kriging prediction, the required time of training the system Kriging model can be further reduced by iteratively reducing the CSP, and the reduction of the CSP can ensure the accuracy without introducing any computational cost and complexity. The results of case studies fully verify that the AK-HS-FS is much more efficient than the AK-S-FS under satisfying the computational accuracy.