Global sensitivity analysis for model with random inputs characterized by probability-box

Global sensitivity analysis techniques for computational models with precise random inputs have been studied widely in the past few decades. However, in real engineering application, due to the lack of information, the distributions of input variables cannot be specified uniquely, and other models such as probability-box (p-box) need to be introduced to characterize the uncertainty of model inputs. Based on the classical variance-based indices and global reliability sensitivity analysis indices, we develop the corresponding sensitivity indices for the p-box type of uncertainty so as to measure the relative importance of each input and propose an efficient computational procedure called extended Monte Carlo simulation, to compute the developed sensitivity indices. The developed sensitivity indices are well interpreted, and the extended Monte Carlo simulation procedure is efficient as the computational cost is the same with the classical Monte Carlo estimators for Sobol's indices. Two numerical test examples and two engineering applications are introduced for illustrating the developed sensitivity indices and demonstrating the efficiency and effectiveness of the extended Monte Carlo simulation procedure.