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Abstract Quantile is an important quantity in reliability analysis, as it is related to the resistance level for defining failure events. This study develops a computationally efficient sampling method for estimating extreme quantiles using stochastic black box computer models. Importance sampling has been widely employed as a powerful variance reduction technique to reduce estimation uncertainty and improve computational efficiency in many reliability studies. However, when applied to quantile estimation, importance sampling faces challenges, because a good choice of the importance sampling density relies on information about the unknown quantile. We propose an adaptive method that refines the importance sampling density parameter toward the unknown target quantile value along the iterations. The proposed adaptive scheme allows us to use the simulation outcomes obtained in previous iterations for steering the simulation process to focus on important input areas. We prove some convergence properties of the proposed method and show that our approach can achieve variance reduction over crude Monte Carlo sampling. We demonstrate its estimation efficiency through numerical examples and wind turbine case study. 

The calibration of the wake effect in wind turbines is computationally expensive and with high risk due to noise in the data. Wake represents the energy loss in downstream turbines, and characterizing it is essential to design wind farm layout and control turbines for maximum power generation. With big data, calibrating the wake parameters is a derivative-free optimization that can be computationally expensive. But with stochastic optimization combined with variance reduction, we can reach robust solutions by harnessing the uncertainty through two sampling mechanisms: the sample size and the sample choices. We do the former by generating a varying number of samples and the latter using the variance-reduced sampling methods. 

Physical interactions among wind turbines, called wake effects, are known to be one of the significant factors that affect power generation performance in wind power systems. Among several wake modeling approaches, physics-based engineering models, such as Jensen's model, have been widely used due to their computational tractability. Although substantial efforts have been made to improve the accuracy of engineering wake models, few studies suggest calibrating the model parameters in the literature. We propose a new data-driven calibration approach for adjusting the model parameters using real operational data.