Estimation of the Generalized Sobol's Sensitivity Index for Multivariate Output Model Using Unscented Transformation

Global sensitivity analysis is frequently applied to models with multivariate output. The generalized Sobol's sensitivity index has been defined to evaluate the importance of input variables on the multivariate output, and the corresponding Monte Carlo simulation (MCS) has been proposed to estimate this index. However, MCS needs a large number of samples for the estimation of the index, which is time-consuming for practical engineering application. The unscented transformation (UT) is a sampling method for estimating the mean and covariance of model output with known mean and covariance of input variables, and it needs much fewer samples than MCS. Thus the estimation of the generalized Sobol's index for multivariate output by use of UT is proposed in this paper to decrease the computational cost. The proposed estimation by use of UT includes double-loop sampling and single-loop sampling, and the efficiency of the latter is higher than the former. Numerical and engineering examples demonstrate the accuracy and high efficiency of UT.