State dependent parameter method for importance analysis in the presence of epistemic and aleatory uncertainties

For the structure system with epistemic and aleatory uncertainties, a new state dependent parameter (SDP) based method is presented for obtaining the importance measures of the epistemic uncertainties. By use of the marginal probability density function (PDF) of the epistemic variable and the conditional PDF of the aleatory one at the fixed epistemic variable, the epistemic and aleatory uncertainties are propagated to the response of the structure firstly in the presented method. And the computational model for calculating the importance measures of the epistemic variables is established. For solving the computational model, the high efficient SDP method is applied to estimating the first order high dimensional model representation (HDMR) to obtain the importance measures. Compared with the direct Monte Carlo method, the presented method can considerably improve computational efficiency with acceptable precision. The presented method has wider applicability compared with the existing approximation method, because it is suitable not only for the linear response functions, but also for nonlinear response functions. Several examples are used to demonstrate the advantages of the presented method.