Investigation of the relation of importance analysis indices for model with correlated inputs

Nowadays, several importance analysis methods have been developed for model with correlated inputs. For choosing the most appropriate analysis methods to meet different requirements, it is necessary to make differences among these existing methods. In this paper, the importance indices, including the total, the structural and the correlative contributions, derived from the covariance decomposition, are firstly derived for the quadratic polynomial without interaction terms and the one with interaction terms. Then, based on these derived analytical solutions, the relation between the traditional variance based method and the newly covariance based method is explored. The results derived from the quadratic polynomials are then extended to general cases, and validated from the point of high dimensional model representation. Three examples are introduced for investigating the relation between the two groups of importance indices, and relative merits of each. The conclusions are instructive and meaningful to importance analysis and engineering design when the model inputs are correlated.