Importance analysis in the presence of epistemic and aleatory uncertainties under fuzzy state

To analyze the effect of epistemic uncertainty on failure probability under the condition of fuzzy state, two importance measures: Correlation Coefficient and Correlation Ration are defined. For the problem of large computational cost of Monte Carlo method, an approximate method is utilized by introducing a proportional coefficient to decrease a "three-loop" procedure to a "double-loop" procedure. In order to decrease the computational cost further, a novel Moving Least Square (MLS) method is constructed in the presence of epistemic and aleatory uncertainties. This method fits the approximate mapping relationship between epistemic parameters and output by moving least square strategy, which can be used to compute the conditional expectation of output conveniently, and then the proposed importance measure can be obtained. Some examples are employed to validate the reasonability and efficiency of the proposed method.