A new method on ANN for variance based importance measure analysis of correlated input variables

Due to the strong flexibility of artificial neural networks (ANNs), a new method on ANN is presented to analyze the variance based importance measure (VBIM) of correlated input variables. An individual input variable's global variance contribution to the output response can be evaluated and decomposed into the contributions uncorrelated and correlated with other input variables by use of the ANN model. Furthermore, the ANN model is used to decompose the correlated contribution into components, which reflect the contributions of the individual input variable correlated with each of other input variables. Combining the uncorrelated contributions and the correlated contribution components of all input variables, an importance matrix can be obtained to explicitly expose the contribution components of the correlated input variables to the variance of the output response. Several properties of the importance matrix are discussed. One numerical example and three engineering examples are used to verify the presented new method, the results show that the new ANN-based method can evaluate the VBIM with acceptable precision, and it is suitable for the linear and nonlinear output responses.