First passage failure probabilities of dynamical systems subjected to non-stationary earthquake

In the reliability analysis of dynamical systems subjected to uncertain excitations, the first passage failure is the most important issue. This paper suggests a procedure for estimating failure probabilities of linear systems subjected to a non-stationary earthquake based on importance sampling technique. By using of Gisranov Theorem, the probability measure of Wiener processes is transformed and a control function is constructed. The simulation results show that the method is correct and effective. The number of samples and the computational time are reduced significantly, compared with direct Monte Carlo simulations.