Moment-independent importance measure of correlated input variable and its state dependent parameter solution

For clearly exploring the origin of the uncertainty of structure failure probability in case the correlated input variables are involved, a new moment-independent importance measure of the input variable is firstly proposed on the failure probability. The intrinsic relationship between the proposed moment-independent importance measure and the corresponding variance-based importance measure is exposed. Then, based on the existing independent orthogonalization-based importance measures of the correlated input variables, the proposed moment-independent importance measure is further decomposed 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. Finally, combining the highly efficient state dependent parameter (SDP) method for the variance-based importance analysis of independent variables, a SDP solution is established for the moment-independent importance measure of correlated variables. Several examples are used to demonstrate that the proposed importance measures can effectively describe the effects of the input variables on the reliability of the structure, and the established solution can obtain the moment-independent importance measures efficiently for both the independent input variables and the correlated ones.