Abstract: To explore the origin of the variance of the output response in cases where the correlated input variables are involved, it is necessary to divide the variance based importance measure (VBIM) into correlated and uncorrelated contributions. For this purpose, a novel method adaptable for the nonlinear output responses is proposed based on second order nonlinear regression. The correlated contribution is composed of the components of the individual input variable correlated with each of the other input variables. An effective method simple in concept is further proposed to decompose the correlated contribution into its components, based on which an importance matrix is defined for explicitly exposing the contribution components of the correlated input variable to the variance of the output response. The VBIMs of the numerical and engineering examples show that the proposed novel method can accurately decompose the contribution of the correlated input variables to the variance of the second order nonlinear output response. For output models more complicated than the second order nonlinear output response, the VBIM decomposition with high precision can be obtained by extending the second order nonlinear regression to a more reasonable approximation of the response.

Key words: sensitivity analysis, importance measure, correlated variable, variance decomposition, regression analysis, importance matrix