Moment-independent importance measure of dynamic reliability for double random vibration systems and its state dependent parameter solution

A moment-independent importance measure index of dynamic reliability for double random vibration systems,in which the randomness of structural parameters and excitation was taken into account,was introduced to analyze the effect of input variables on dynamic reliability. Based on the expressions of unconditional dynamic reliability and conditional probability density function( PDF),the importance measure index was numerically obtained. The index can effectively describe the mean effect of the PDF on dynamic reliability from the distribution density of the basic variable. Then,on the basis of the state dependent parameter( SDP) model,the SDP method was established to estimate the defined moment-independent importance measure index. Additionally,two examples were given to illustrate the advantages of the presented method. Comparing with the direct Monte Carlo method,the results show that the established solution can considerably improve computational efficiency with acceptable precision and be suitable for analyzing nonlinear dynamic reliability responses of double random vibration systems.