Stochastic dynamic response analysis and reliability assessment of non-linear structures under fully non-stationary ground motions

In this paper, stochastic dynamic response analysis and reliability assessment of nonlinear structures under fully non-stationary ground motions is investigated based on the probability density evolution method (PDEM). To handle this problem, a new method is proposed for points selection in high-dimensional random-variate space for PDEM, which is of paramount importance to the tradeoff of accuracy and efficiency. First, the original high-dimensional space is decomposed into several two-dimensional orthogonal subspaces. Then, each subspace is partitioned via the Voronoi cells and the representative points and assigned probabilities in each subspace are specified accordingly. Finally, the representative points and assigned probabilities in each subspace are randomly paired to formulate the representative points and assigned probabilities in high-dimension. A numerical example is studied to validate the proposed method, which indicates that the proposed method is of efficiency and accuracy for high-dimensional stochastic dynamic problem of structures. The problem, which needs to be further investigated, is also pointed out.