Calculation of First Excursion Probabilities by Subset Simulation

A new simulation approach, called 'subset simulation', is applied to computing small first excursion probabilities for dynamical systems with stochastic excitations. The basic idea is to express the first excursion probability as a product of larger conditional failure probabilities by introducing intermediate failure boundaries. With a proper choice of the intermediate boundaries, the original problem of calculating a small failure probability, which is computationally demanding, is reduced to calculating a sequence of conditional probabilities, which are efficiently estimated by simulation using a special Markov chain. The proposed method is robust to the type of structural model (e.g., linear or nonlinear) and stochastic excitation model (e.g., stationary or nonstationary). Numerical studies are presented to demonstrate the efficiency of the method.