Estimate of Small First Passage Probabilities of Nonlinear Random Vibration Systems

Abstract

Estimates of the small probabilities of failure, i.e., small first passage probabilities, of nonlinear random vibration systems is of great importance in the structural reliability analysis and reliability-based design. Some methods have been developed for estimating the small probabilities, but their computational efficiency is not high enough for analyzing the large-scale systems. In order to overcome the challenge of the computational efficiency of the estimate of the small probabilities, a new method is developed. The method mainly consists of two uncoupled procedures, i.e., modeling the distribution tails of the extreme values of the responses of nonlinear random vibration systems and constructing the Copula of the extreme values of the nonlinear responses. The former is used to estimate the small first passage probabilities of the scalar response processes, while the latter is used to estimate the small first passage probabilities of the vector response processes. Some numerical examples are presented to demonstrate the accuracy and efficiency of the developed method.