Global sensitivity analysis under mixed uncertainty based on possibilistic moments

For the structures with fuzzy uncertainty and random uncertainty simultaneously, to measure the influence of fuzzy and random input variables on the statistical characteristic of output response, a new global sensitivity index is proposed. Based on the definition of possibilistic moments of the fuzzy variable, the characteristic of the output response under mixed uncertainty is analyzed. With respect to the possibilistic moments of the output response, the possibilistic expectation of output response is taken as an example, and the average difference between the unconditional probability density function (PDF) and the conditional PDF of the model output possibilistic expectation is used to establish the global sensitivity indices for both the fuzzy input and the random input. The properties of the proposed global sensitivity indices are discussed, and the Kriging surrogate model is applied to solving the proposed index efficiently. Finally, some examples are used to verify the rationality and effectiveness of the proposed method.