Long-term extreme response evaluation of stochastic models using adaptive stochastic importance sampling

The long-term extreme response, such as those observed over 20- or 50-year return periods, is critically important for extreme and reliability analysis as well as design optimization. However, it is often challenging to accurately evaluate this response due to the lack of extreme data in the tail of the response distribution. Monte-Carlo simulation, widely used for this purpose, typically involves complicated simulation models that cause substantial computational costs. In addition, most existing research treats these simulation models as deterministic, neglecting their intrinsic uncertainty. To address these challenges, this paper proposes a new method for evaluating long-term extreme response, which considers stochastic models and utilizes an adaptive weighted kernel density. This approach proposes the adaptive weighted kernel density for obtaining the optimal stochastic importance sampling function, which significantly reduces the required number of simulation samples while maintaining the accuracy of the extreme response evaluation. The bandwidth parameter in the kernel density estimation is optimized through a modification of the integrated square error. The proposed method is validated and compared with some state-of-the-art methods using two numerical examples and an engineering case that evaluates the extreme responses of a 5 mega-watt wind turbine.