The moment-independence importance measure for fuzzy failure criterion and its Kriging solution

For analyzing the effects of the uncertainties of the fuzzy failure criterion and the input variables on fuzzy failure probability, the moment-independence importance measure (MIIM) model on the fuzzy failure probability for the fuzzy state structural system is proposed. Firstly, according to the fuzzy random theory, the fuzzy failure criterion is transformed into the equivalent additional random variable of the structural system, whose the probability density function (PDF) and cumulative distribution function (CDF) are obtained by analyzing the membership of the fuzzy failure criterion. Secondly, the equivalent performance function after introducing additional random variable is established. The difference between the conditional fuzzy failure probability and unconditional one is employed to define a moment-independent measure index in this paper. Through establishing surrogate model of equivalent performance function using kriging method, the kriging-based method is established to estimate the define MIIM index, which can reduce the computational cost effectively. An engineering example is used to demonstrate the feasibility and rationality of the proposed importance measure model and the efficient and precision of the kriging solution.