^{a}and Jian-Bing Chen

^{b}

^{a}lyumz@tongji.edu.cn

^{b}chenjb@tongji.edu.cn

First-passage reliability assessment of engineering structures under disastrous stochastic dynamic excitations is of paramount importance for the performance-based decision-making of structural design. However, it is still of great challenge due to the coupling of nonlinearity and randomness in the high-dimensional systems. In the present paper, a globally-evolving-based generalized density evolution equation (GE-GDEE) is derived in terms of only one or two response quantities of interest in a high-dimensional nonlinear system. The established GE-GDEE is just a one- or two-dimensional partial differential equation (PDE) with respect to the transient probability density function (PDF) of the quantities of interest. The effective drift coefficient(s) in the GE-GDEE represents the physically driving force for evolution of the PDF in the global sense, and can be identified mathematically as the conditional expectation of the original drift coefficient(s) in the high-dimensional equation of motion. For this purpose, the proposed approach can be called as the physically driven GE-GDEE. Some representative deterministic analyses of the underlying physical system can be performed to provide data for the identification of effective drift coefficient(s), and then the GE-GDEE can be solved numerically. For the purpose of first-passage reliability, the GE-GDEE with respect to the absorbing boundary processes (ABPs) can be established to obtain the remaining PDF in the safe domain and time-variant first-passage reliability further. A numerical example is illustrated to verify its efficiency and accuracy.