Importance measure analysis in the presence of epistemic and aleatory uncertainties

In the presence of both epistemic and aleatory uncertainties, two importance measures are developed to quantify the effect of input variable on output response. One importance measure is defined as the effect of input variable on the membership function of structural failure probability, and the other is defined as the effect of the input variable on the membership function of the variance of structural performance function. Monte Carlo method and a novel point estimation method are investigated, to evaluate the two importance measures. A numerical example and an engineering example of wing model structure illustrate the directive significance of the two proposed importance measures in structure design, and the examples also demonstrate that the proposed point estimation is more efficient than the Monte Carlo simulation with acceptable precision.