Regional and parametric sensitivity analysis of Sobol׳ indices

•The regional main and total effect functions are developed.•The parametric main and total effect functions are introduced.•The proposed sensitivity functions are all generalizations of Sobol׳ indices.•The Monte Carlo estimators are derived for the four sensitivity functions.•The computational cost of the estimators is the same as that of Sobol׳ indices.

Nowadays, utilizing the Monte Carlo estimators for variance-based sensitivity analysis has gained sufficient popularity in many research fields. These estimators are usually based on n+2 sample matrices well designed for computing both the main and total effect indices, where n is the input dimension. The aim of this paper is to use such n+2 sample matrices to investigate how the main and total effect indices change when the uncertainty of the model inputs are reduced. For this purpose, the regional main and total effect functions are defined for measuring the changes on the main and total effect indices when the distribution range of one input is reduced, and the parametric main and total effect functions are introduced to quantify the residual main and total effect indices due to the reduced variance of one input. Monte Carlo estimators are derived for all the developed sensitivity concepts based on the n+2 samples matrices originally used for computing the main and total effect indices, thus no extra computational cost is introduced. The Ishigami function, a nonlinear model and a planar ten-bar structure are utilized for illustrating the developed sensitivity concepts, and for demonstrating the efficiency and accuracy of the derived Monte Carlo estimators.