Extreme wind turbine response extrapolation with the Gaussian mixture model

IF 3.6 Q3 GREEN & SUSTAINABLE SCIENCE & TECHNOLOGY Wind Energy Science Pub Date : 2023-10-27 DOI:10.5194/wes-8-1613-2023
Xiaodong Zhang, Nikolay Dimitrov
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Abstract

Abstract. The wind turbine extreme response estimation based on statistical extrapolation necessitates using a minimal number of simulations to calculate a low exceedance probability. The target exceedance probability associated with a 50-year return period is 3.8×10-7, which is challenging to evaluate with a small prediction error. The situation is further complicated by the fact that the distribution of the wind turbine response might be multimodal, and the extremes belong to a different statistical population than the main body of the distribution. Traditional theoretical probability distributions, mostly unimodal, may not be suitable for this task. The problem could be alleviated by applying a fit specifically on the tail of the distribution. Yet, a single unimodal distribution may not be sufficient for modeling diverse wind turbine responses, and an inappropriate distribution model could lead to significant prediction errors, including bias and variance errors. The Gaussian mixture model, a probabilistic and flexible mixture distribution model used extensively for clustering and density estimation tasks, is infrequently applied in the wind energy sector. This paper proposes using the Gaussian mixture model to extrapolate extreme wind turbine responses. The performance of two approaches is evaluated: (1) parametric fitting first and aggregation afterward and (2) data aggregation first followed by fitting. Different distribution models are benchmarked against the Gaussian mixture model. The results show that the Gaussian mixture model is capable of estimating a low exceedance probability with minor bias error, even with limited simulation data, and demonstrates flexibility in modeling the distributions of varying response variables.
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基于高斯混合模型的极端风力机响应外推
摘要基于统计外推的风力发电机极端响应估计需要使用最少的模拟次数来计算低超越概率。与50年回报期相关的目标超额概率为3.8×10-7,在预测误差较小的情况下对其进行评估具有挑战性。由于风力发电机响应的分布可能是多模态的,并且极端情况属于与分布主体不同的统计总体,因此情况进一步复杂化。传统的理论概率分布,大多是单峰的,可能不适合这个任务。这个问题可以通过专门对分布的尾部应用拟合来缓解。然而,单一的单峰分布可能不足以模拟不同的风力发电机响应,不适当的分布模型可能导致显著的预测误差,包括偏差和方差误差。高斯混合模型是一种广泛用于聚类和密度估计任务的概率和灵活的混合分布模型,在风能领域的应用很少。本文提出利用高斯混合模型外推风力机的极端响应。对两种方法的性能进行了评价:(1)先进行参数拟合,然后进行聚集;(2)先进行数据聚集,然后进行拟合。根据高斯混合模型对不同的分布模型进行基准测试。结果表明,即使在有限的模拟数据下,高斯混合模型也能以较小的偏差估计出较低的超越概率,并且在模拟不同响应变量的分布方面表现出灵活性。
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来源期刊
Wind Energy Science
Wind Energy Science GREEN & SUSTAINABLE SCIENCE & TECHNOLOGY-
CiteScore
6.90
自引率
27.50%
发文量
115
审稿时长
28 weeks
期刊最新文献
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