New global sensitivity measure based on fuzzy distance

In this paper, a new fuzzy distance index is proposed to measure the effect of the fuzzy distribution parameters of random model inputs on the statistical characteristics of model output. First, the definition of the distance of fuzzy numbers is introduced. The effect of fuzzy distribution parameters is measured by using the average distance between the unconditional membership function of the statistical characteristics of output and the conditional membership function with one fixed distribution parameter. Second, to reduce the computational cost of the proposed index, the extended Monte Carlo simulation (EMCS) and unscented transformation-based Kriging surrogate model method (UT-Kriging) are adopted. Finally, four examples are used to verify the accuracy and the efficiency of the proposed methods.