基于传统幂律与机器学习模型的风速垂直外推性能对比

Comparison of Vertical Wind Speed Extrapolation Performance Based on Power-Law and Machine Learning Models

摘要: 准确获取风机轮毂高度风速对风功率预测具有重要意义。针对直接观测成本高的问题，本文系统评估了多种风速垂直外推方法的性能差异。基于天津02001测风塔风速资料，利用幂律、机器学习和深度学习模型，将10 m高度的不同分辨率风速序列外推至70 m和100 m。同时引入去趋势波动分析(Detrended Fluctuation Analysis, DFA)标度指数作为附加特征，探究其对机器学习外推效果的影响。结果表明：① 相比幂律模型，机器学习可大幅度降低外推误差，其中RMSE降低了12.0%~27.5%；② 不同模型对数据分辨率的适应性存在差异，对6 h低频数据，K近邻 + DFA外推精度高且训练时间短。对于10 min高频数据，深度学习表现最佳但对计算资源要求高；③ DFA标度指数对模型外推能力的提升取决于数据特性与外推高度，高频数据外推至更高高度时提升效果好，而在低频数据下对深度学习模型无效。本研究揭示了不同风速外推方法的适用性与局限性，为不同场景下的轮毂高度风速估算提供了参考依据。

Abstract: Accurate estimation of wind speed at hub height plays a critical role in power forecasting. Due to the high cost of direct measurements, this study evaluated the performance of several vertical wind speed extrapolation methods. Observations from the Tianjin 02001 wind measurement tower were used to extrapolate wind speed time series at 10 m to 70 m and 100 m using power-law, machine learning, and deep learning models applied to data with different temporal resolutions. The detrended fluctuation analysis (DFA) scaling exponent was introduced as an additional feature to assess its influence on machine learning extrapolation. The results show that: (1) compared with the power-law model, machine learning methods significantly reduce extrapolation errors, with the root mean square error (RMSE) reduced by 12.0%~27.5%; (2) model performance depends on data resolution. For low-resolution data, the k-nearest neighbors (KNN) model with DFA achieves high accuracy and low computational cost. For high-resolution data, deep learning provides the best performance but requires more computational resources; (3) the effect of the DFA scaling exponent depends on both data resolution and extrapolation height. It improves model performance for high-frequency data, especially at higher extrapolation heights, but shows limited benefit for deep learning under low-frequency conditions. These results reveal the applicability and limitations of different extrapolation methods and provide guidance for hub-height wind speed estimation under various scenarios.