To harvest more energy from wind, wind turbine size has rapidly increased, entailing the serious concern on the reliability of the wind turbine. Accordingly, the international standard requires turbine designers to estimate the extreme load that could be imposed on a turbine during normal operations. At the design stage, physics-based load simulations can be used for this purpose. However, simulating the extreme load associated with a small load exceedance probability is computationally prohibitive. In this study, we propose using importance sampling combined with order statistics to reduce the computational burden significantly while achieving much better estimation accuracy than existing methods.
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.
Climate studies based on global climate models (GCMs) project a steady increase in annual average temperature and severe heat extremes in central North America during the mid-century and beyond. However, the agreement of observed trends with climate model trends varies substantially across the region. The present study focuses on two different locations: Des Moines, IA and Austin, TX. In Des Moines, annual extreme temperatures have not increased over the past three decades unlike the trend of regionally-downscaled GCM data for the Midwest, likely due to a “warming hole” over the area linked to agricultural factors. This warming hole effect is not evident for Austin over the same time period, where extreme temperatures have been higher than projected by regionally-downscaled climate (RDC) forecasts. In consideration of the deviation of such RDC extreme temperature forecasts from observations, this study statistically analyzes RDC data in conjunction with observational data to define for these two cities a 95% prediction interval of heat extreme values by 2040. The statistical model is constructed using a linear combination of RDC ensemble-member annual extreme temperature forecasts with regression coefficients for individual forecasts estimated by optimizing model results against observations over a 52-year training period.
To help wind turbine reliability analysis in a design stage, aeroelastic simulators have been developed to generate stochastic load responses imposed on a wind turbine structure, given pre-specified turbulent wind conditions. In particular, system designers can use the simulators to estimate the extreme load responses during a turbine's design life. However, it has been shown that using the crude Monte Carlo sampling methods to simulate the extreme load associated with a small load exceeding probability is computationally prohibitive, and the estimation results are highly uncertain. Importance sampling methods can overcome the limitations of the crude Monte Carlo sampling methods. We develop adaptive algorithms to iteratively refine the importance sampling density to efficiently estimate the extreme load. Nomenclature P T Target probability of load exceedance l T Extreme load X Input vector Y Output variable p X Original input density of X q X Importance sampling density θ Parameter in the importance sampling density
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