Regional importance effect analysis of the input variables on failure probability and its state dependent parameter estimation

To measure the effect of the different regions of the range of input variables on structural failure, two regional importance measures (RIMs) of the input variables are proposed in this paper, which are the "Contribution to Failure Probability-based Main Effect (CFPME)" and the "Contribution to the Total Failure Probability (CTFP)". The properties of the two proposed RIMs are analyzed and verified. Based on their characteristics, the highly efficient state dependent parameter (SDP) method is used to estimate them. By virtue of the advantages of the SDP method, a single set of input-output sample points is enough for CFPME and CTFP. Several numerical and engineering examples are used to demonstrate the effectiveness of the two proposed RIMs. The results show that CTFP can not only detect the important variables for the total failure probability as effectively as the existing failure probability-based importance measure but also identify regions of the input space that contribute substantially to the total failure probability. The results also show that CFPME can effectively instruct the engineer on how to achieve a targeted reduction of the failure probability-based main effect of each input variable. Besides, the efficiency and accuracy of the SDP-based method for estimating CFPME and CTFP are also demonstrated by the examples.