Importance analysis on failure credibility of the fuzzy structure

To measure the effects of the fuzzy inputs on structural safety degree, this paper establishes the failure credibility-based global sensitivity by the fuzzy expected value of the absolute difference between the unconditional failure credibility and conditional one. To establish the failure credibility-based global sensitivity, the conditional failure credibility is firstly defined according to the original definition of conditional event and the relationship among the possibility, necessity and credibility, in which no extra assumption is introduced. After that, the equivalent expression of the failure credibility is deduced, on which the Bayesian transformation of the conditional failure credibility is obtained in this paper. Then, a single-loop method based on the sequential quadratic programming is applied to efficiently estimate the defined failure credibility-based global sensitivity. According to the result of the constructed failure credibility-based global sensitivity, designers can pay more attentions to the more important fuzzy inputs to have a better control of the structural safety degree. The presented examples demonstrate the feasibility of the constructed failure credibility-based global sensitivity and the efficiency of the proposed solution.