Assessing small failure probability by importance splitting method and its application to wind turbine extreme response prediction

This study presents an effective simulation framework with importance splitting (ISp) method for estimating small failure probabilities of dynamic structures with multi-correlated stochastic excitations, and addresses its application to predictions of large wind turbine extreme responses. The ISp method, also referred to as subset simulation with splitting, splits important sample paths into multiple branches at various stages in the simulation. It permits the estimation of a small failure probability of a rare event through estimations of conditional probabilities of intermediate subset events. The framework presented in this study combines the ISp method with multivariate autoregressive (MAR) modeling of stochastic excitations. The MAR model of excitations is established based on their cross power spectral density matrix, which transfers the stochastic excitations as the output of a loading system with a vector-valued uncorrelated white noise process as input. This scheme is very efficient in generating offsprings of loading and response time histories conditional on the intermediate events with very low rejection rate, which facilities the application of ISp method to different kinds of stochastic single and multiple excitations. The effectiveness and accuracy of the proposed new scheme are verified by a reliability problem of earthquake-excited 5-story building, and by the estimation of extreme responses of a 5 MW onshore wind turbine with very small exceeding probabilities. Finally, this framework is applied to validate the extrapolation procedure of estimating wind turbine long-term extreme responses with various mean recurrence intervals from short-term simulations of turbine response histories, which is mandated by current wind turbine design standards.