First-passage reliability of high-dimensional nonlinear systems under additive excitation by the ensemble-evolving-based generalized density evolution equation

Abstract

The reliability analysis of high-dimensional stochastic dynamical systems subjected to random excitations has long been one of the major challenges in civil and various engineering fields. Despite great efforts, no satisfactory method with high efficiency and accuracy has been available as yet for high-dimensional systems even when they are linear systems, not to mention generic nonlinear systems. In the present paper, a novel method by imposing appropriate absorbing boundary condition on the newly developed ensemble-evolving-based generalized density evolution equation (EV-GDEE) combined with a feasible numerical method is proposed to capture the time-variant first-passage reliability of high-dimensional systems enforced by additive white noise excitation. In the proposed method, the equivalent drift coefficients in EV-GDEE can be estimated by analytical expression or captured by some representative deterministic dynamic analyses. Further, imposing the absorbing boundary condition and then solving the EV-GDEE, a one-or two-dimensional partial differential equation (PDE), yield the remaining probability density of the response of interest. Consequently, by integrating the remaining probability density, the numerical solution of time-variant first-passage reliability can be obtained. Several numerical examples are illustrated to verify the efficiency and accuracy of the proposed method. Compared to the Monte Carlo simulation, the proposed method is of much higher efficiency. Problems to be further studied are finally discussed.