Global sensitivity analysis for multiple outputs and their solutions

Aiming at solving the existing drawbacks of indices of the Mahalanobis distance, an importance measure based on the Moore-Penrose Mahalanobis distance weighted by spectral decomposition was proposed. Through building the generalized matrix inversion of covariance matrix of multi-output and the spectral decomposition, the problems that the covariance matrix was be inversed and misidentification for lacking the adequate consideration about the relation among the multiple outputs were solved. Thus, the limitations of indices of Mahalanobis distance were overcome. The results of numerical examples and engineer instance show that the proposed importance measurement can accurately get the effects of input variables on the integrated performance of multi-output structure system, thus providing effective information for reliability design.