Abstract
Engineering structures are often subjected to dynamic loads, such as earthquakes, winds or sea waves, which are most appropriately characterized as random processes. In the past much effort has been paid to evaluate the first excursion probability of randomly excited nonlinear dynamical systems. However, analytical solutions are available for a restricted class of systems only, whereas Monte Carlo simulation technique offers a feasible alternative for solution of first excursion probabilities except prohibitive computational costs. This paper investigates the variance reduction technique, which is the importance sampling technique utilizing the measure transformation method for the non-linear dynamic system. To attain the purpose, the importance sampling function is obtained by using the stochastic terminal state control theory. The efficiency of the proposed method is demonstrated by numerical examples of non-linear restoring force systems under the external white noise excitation.
