Local sensitivity analysis of failure possibility and its universal solution by fuzzy simulation

Failure possibility (FP) is widely used to measure safety degree of structure in the presence of fuzzy uncertainty, but how to quantify the effect of fuzzy distribution parameter on FP is seldom investigated. For searching the important parameter to FP and guiding the FP-based design optimization, the local sensitivity of FP (LS-FP) is firstly defined by the partial derivative of FP with respect to the fuzzy distribution parameter in this paper. Then, the analytical solution is derived for the LS-FP in special cases; a universal algorithm is proposed to solve LS-FP by use of the fuzzy simulation. The proposed universal algorithm includes three creative steps. The first is explicitly expressing FP as the joint membership function of the fuzzy inputs at the fuzzy most possible failure point (F-MPP) by use of the fuzzy simulation, on which LS-FP can be equivalently transformed as the partial derivative of F-MPP with respect to the fuzzy distribution parameter. The second is using the characteristic of F-MPP to derive the analytical solution of the partial derivative of F-MPP. The third is establishing an efficient method to estimate F-MPP for completing LS-FP, where new learning function and stopping criterion are proposed to improve the computational efficiency. The proposed algorithm has no limitation on the nonlinearity of performance function and can be applied in any fuzzy membership distribution form of the fuzzy input. Several examples are used to validate the wide applicability, the accuracy, and the efficiency of the proposed algorithm to solve LS-FP.