Uncertainty importance analysis using parametric moment ratio functions

This article presents a new importance analysis framework, called parametric moment ratio function, for measuring the reduction of model output uncertainty when the distribution parameters of inputs are changed, and the emphasis is put on the mean and variance ratio functions with respect to the variances of model inputs. The proposed concepts efficiently guide the analyst to achieve a targeted reduction on the model output mean and variance by operating on the variances of model inputs. The unbiased and progressive unbiased Monte Carlo estimators are also derived for the parametric mean and variance ratio functions, respectively. Only a set of samples is needed for implementing the proposed importance analysis by the proposed estimators, thus the computational cost is free of input dimensionality. An analytical test example with highly nonlinear behavior is introduced for illustrating the engineering significance of the proposed importance analysis technique and verifying the efficiency and convergence of the derived Monte Carlo estimators. Finally, the moment ratio function is applied to a planar 10-bar structure for achieving a targeted 50% reduction of the model output variance.