Abstract

This work proposes a nonparametric method to compare the underlying mean functions given two noisy datasets. The motivation for the work stems from an application of comparing wind turbine power curves. Comparing wind turbine data presents new problems, namely the need to identify the regions of difference in the input space and to quantify the extent of difference that is statistically significant. Our proposed method, referred to as funGP, estimates the underlying functions for different data samples using Gaussian process models. We build a confidence band using the probability law of the estimated function differences under the null hypothesis. Then, the confidence band is used for the hypothesis test as well as for identifying the regions of difference. This identification of difference regions is a distinct feature, as existing methods tend to conduct an overall hypothesis test stating whether two functions are different. Understanding the difference regions can lead to further practical insights and help devise better control and maintenance strategies for wind turbines. The merit of funGP is demonstrated by using three simulation studies and four real wind turbine datasets.

摘要

这项工作提出了一种非参数方法来比较给定两个噪声数据集的基础均值函数。这项工作的动机源于比较风力涡轮机功率曲线的应用。比较风力涡轮机数据提出了新问题，即需要识别输入空间中的差异区域并量化具有统计意义的差异程度。我们提出的方法称为 funGP，使用高斯过程模型估计不同数据样本的基础函数。我们使用原假设下估计的函数差异的概率定律建立了一个置信带。然后，置信带用于假设检验以及识别差异区域。这种不同区域的识别是一个明显的特征，因为现有方法倾向于进行整体假设检验，说明两个函数是否不同。了解不同区域可以带来进一步的实际见解，并有助于为风力涡轮机设计更好的控制和维护策略。funGP 的优点通过使用三个模拟研究和四个真实的风力涡轮机数据集来证明。