Importance analysis for models with correlated input variables using state dependent parameters approach

For clearly exploring the origin of the variance of the output response in case the correlated input variables involved and establishing efficient method to calculate the importance measures of correlated input variables, a novel method on the state dependent parameters (SDPs) approach is proposed to decompose the contribution by correlated input variables to the output variance into two parts: the uncorrelated contribution due to the unique variations of a variable and the correlated one due to the variations of a variable correlated with other variables. In the proposed method, the transformation of the correlated inputs into independent and orthogonal ones and the calculation of the importance measures of the transformed independent ones are obtained by the SDP method simultaneously, thus it can improve the computational efficiency considerably in case of acceptable accuracy. In addition, the relationship between the existing independent orthogonalisation-based and the regression-based importance measures of the correlated input variables is revealed in the paper, which is then demonstrated by the numerical examples. The proposed method not only possesses higher computational efficiency in case of acceptable precision, but also has wider applicability compared with the polynomial chaos expansion (PCE) based method. Several numerical and engineering examples are used to demonstrate the advantages of the proposed method.