Global sensitivity analysis method for multivariate output based on fuzzy Hausdorff distance

To measure the effects of the model fuzzy inputs on the performance of the model outputs, the global sensitivity index (GSI) based on fuzzy vector Hausdorff distance is proposed. In the proposed GSI, the Hausdorff distance is used to measure the difference between the conditional model outputs and the unconditional model outputs while the fuzzy input is fixed. Based on the weighted average of the difference, the global sensitivity index evaluating the effects of the fuzzy input on the model outputs is established. The proposed GSI is also extended to the condition that the distribution parameters of the random inputs have fuzzy uncertainty, and is used to measure the effects of fuzzy distribution parameters on the statistical characteristics of the random model output. An efficient solution to evaluation of the effects of the fuzzy distribution parameters on the mean of the model outputs is established by combining the unscented transformation with the Kriging meta-model. The accuracy and efficiency of the proposed method is demonstrated by some examples after the procedure of the solution for the proposed GSI is presented in detail.