A probabilistic procedure for quantifying the relative importance of model inputs characterized by second-order probability models

This paper develops a new global sensitivity analysis (GSA) framework for computational models with input variables being characterized by second-order probability models due to epistemic uncertainties. Firstly, two graphical tools, called individual effect (IE) function and total effect (TE) function, are defined for identifying the influential and non-influential input variables. Secondly, two probabilistic GSA indices, called T-indices, are introduced for comparing the relative importance of pairwise influential input variables. Thirdly, the expected Sobol' indices are introduced for ranking the importance of the input variables. For efficiently estimating the proposed GSA indices, the extended Monte Carlo simulation (EMCS), whose computational cost is the same as the Monte Carlo simulation for estimating the Sobol' indices, is firstly introduced, and then a procedure combining Kriging surrogate model and EMCS procedure is introduced for further reducing the computational cost. Three numerical examples and a ten-bar structure are introduced for illustrating the significance of the proposed GSA framework and demonstrating the effectiveness of the computational methods.