A novel and rational method based on decomposition of correlated variables for analyzing importance measure

Sections 1 and 2 of the full paper explain the method mentioned in the title, which we believe is novel and rational. Their core consists of. "For exploring the origin of the variance of the output response in the case that correlated input variables are involved, it is necessary to divide the variance based importance measure (VBIM) into the correlated part and the uncorrelated one. Correlated variables are constructed by the linear combination of independent factors to divide the contributions by correlated input variables into correlated ones and uncorrelated ones, by which the novel method based on the decomposition of correlated variables for analyzing importance measure is proposed. The novel method not only can divide the contribution by an individual input variable into uncorrelated one and correlated one, but also can separate the latter into components of the individual input variable correlated with each of other input variables. For nonlinear responses, an iterative first-order Taylor expansion based method is established, which aims at analyzing the importance measure of correlated variables when the variance of response is consistent with its first-order Taylor expansion. " The proposed novel method is employed to obtain respectively the VBIMs of two examples. The calculated results, presented in Tables 1 and 3, and their analysis demonstrate preliminarily that the novel method based on the decomposition of correlated variables for analyzing importance measure is indeed rational.