A mixture distribution with fractional moments for efficient seismic reliability analysis of nonlinear structures

In this paper, an efficient approach is proposed for seismic reliability analysis of nonlinear structures with random parameters subjected to non-stationary stochastic ground motions. First, the first-passage reliability problem is equivalently transformed to the evaluation of the extreme value distribution (EVD) of the response. A mixture of inverse Gaussian and Lognormal distributions (MIGLD) is then proposed to reconstruct the EVD in the entire distribution domain, where the fractional moments are suggested as constraints to specify the unknown parameters. Only five low-order fractional moments of the EVD are actually required in the proposed method due to the inherent advantages of fractional moments. Then, the recently developed Latinized partially stratified sampling (LPSS) approach, is introduced to evaluate the fractional moments of the EVD with a small sample size. In this regard, the EVD could be reconstructed accurately in the entire distribution domain with high efficiency, particularly in the distribution tail, and the corresponding failure probabilities can be obtained in a straightforward way. Two numerical examples involving both linear and nonlinear shear-frame structures under non-stationary stochastic seismic ground motions are investigated to verify the efficacy of the proposed approach. The results indicate that the proposed method can result in accurate seismic reliability of nonlinear structures with high efficiency.