First passage probabilities of structural dynamics system based on domain decomposition

The first passage problems of linear and nonlinear dynamical systems excited by Gauss white noise are considered. For linear dynamical system, the failure domain can be described as a union of mutually exclusive events, and every event is completely described by a local design point. The paper uses standard Gaussian distribution instead of chi-square distribution to estimate the parameter of first passage probability. For nonlinear dynamical system, the equivalent linear system is carried out based on the out-crossing theory. The linearization principle is that nonlinear and linear systems have the same up-crossing rate for a specified threshold. Finally the paper gives two examples. The results show that the method of the paper suggested is correct and effective by comparing with the Monte Carlo method.