An important sampling procedure for estimating failure probabilities of non-linear dynamic systems

The failure probability is one of the most important reliability measures in structural reliability assessment of dynamical systems. Here, a procedure for estimating failure probabilities of non-linear systems based on the important sampling technique was presented. Firstly, by using Rice formula, the equivalent linear version of the non-linear systems was derived. Using the equivalent linear equation, the design point of the equivalent linear systems was used to construct control function. Secondly, an important sampling technique was used to estimate the first excursion probabilities for the non-linear system. Finally, a Duffing oscillator was taken for example. The simulation results showed that the proposed method is correct and effective; the number of samples and the computational time are reduced significantly compared with those of direct Monte Carlo simulations.