As a clean and renewable energy source, wind energy has achieved remarkable growth around the world. Wind power/speed interval prediction has become an indispensable area of focus regarding the efficient dispatch of wind energy. As an important interval prediction method, the traditional lower and upper bound estimation (LUBE) has been a prevalent approach and a fundamental branch of energy prediction. However, the traditional LUBE model suffers from a low training efficiency owing to a lack of the gradient descent (GD) training mechanism. In this study, an improved LUBE model was designed using a novel training scheme based on the GD method for better efficiency and greater prediction performance. Initially, the new objective functions, which are continuous and differential, meeting the requirements of the GD method, were designed to obtain the best prediction interval (PI) quality with a narrower PI width and greater coverage probability. Then, different loss function forms have been proposed and compared, with the new Huber loss function having been confirmed to be more effective than other traditional loss functions. Finally, the new LUBE model with an objective part and adapting to the GD training method was constructed. Both traditional and improved LUBE models with different loss functions were compared experimentally, and the results indicate that the improved LUBE model with a Huber loss function significantly reduces the training time and improves the quality of the PI.

中文翻译：

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基于梯度下降训练法的风速区间上下界估计模型

作为清洁和可再生能源，风能在世界范围内取得了显着增长。关于有效分配风能，风力/速度间隔预测已成为不可或缺的重点领域。作为重要的区间预测方法，传统的上下限估计（LUBE）已成为一种普遍的方法，也是能量预测的基本分支。然而，由于缺乏梯度下降（GD）训练机制，传统的LUBE模型训练效率低下。在这项研究中，使用基于GD方法的新型训练方案设计了改进的LUBE模型，以实现更高的效率和更好的预测性能。最初，新的目标函数是连续的和微分的，可以满足GD方法的要求，旨在获得最佳的预测间隔（PI）质量，且PI宽度更窄，覆盖概率更大。然后，提出了不同的损失函数形式并进行了比较，新的Huber损失函数已被证实比其他传统损失函数更有效。最后，构建了具有目标部分并适应GD训练方法的新LUBE模型。实验比较了具有不同损失函数的传统和改进的LUBE模型，结果表明，具有Huber损失函数的改进的LUBE模型显着减少了训练时间并提高了PI的质量。新的Huber损失函数已被证实比其他传统损失函数更有效。最后，构建了具有目标部分并适应GD训练方法的新LUBE模型。实验比较了具有不同损失函数的传统模型和改进的LUBE模型，结果表明，具有Huber损失函数的改进的LUBE模型显着减少了训练时间并提高了PI的质量。新的Huber损失函数已被证实比其他传统损失函数更有效。最后，构建了具有目标部分并适应GD训练方法的新LUBE模型。实验比较了具有不同损失函数的传统模型和改进的LUBE模型，结果表明，具有Huber损失函数的改进的LUBE模型显着减少了训练时间并提高了PI的质量。