## 2 Materials and Methods
### Optimization Method for Wind Turbine Health Region Based on Data Increment Inflection Points  
Defining the evaluation region is a crucial step in wind turbine performance assessment. However, the original wind power data in this study do not follow a normal distribution, making the use of confidence intervals for region delineation inaccurate and potentially impacting the subsequent wind turbine performance evaluation process. To enhance the reliability of the wind turbine performance evaluation region, this paper considers the concept of moving the wind turbine power curve (hereafter referred to as the \"moving power curve\") and delineates the performance evaluation region for the turbine by analyzing changes in the quantity of wind speed-power data after movement. To facilitate this discussion, the term \"data increment inflection point\" is introduced, referring to the \"wind speed-power\" coordinate point where a sudden change in the data increment between the static optimal power curve and the moving power curve reaches a certain threshold. In practical engineering applications, this threshold can be set to 1.16. The following approach is employed to delineate the health region of the wind turbine: using the absolute value of the slope of the data increment curve to represent the degree of change in data quantity. When a sudden change in data quantity occurs for the first time between the moving power curve and the static optimal power curve, the \"data increment inflection point\" as defined above appears. At this point, it can be considered that the moving power curve has reached the boundary of the wind turbine performance evaluation region, thereby delineating the performance evaluation region for the wind turbine. Delineation of Wind Turbine Performance Evaluation Region  
To define the health performance region of the wind turbine and accurately assess its health performance, an optimization method based on data increment inflection points is proposed for the wind turbine health region. The process is as follows. * After cleaning the original wind speed-power data using interpolation and clustering algorithms, the data are grouped into wind speed intervals of 0.5 m/s using the binning method, after sorting the wind speed-power data in ascending order. The average wind speed and power values within each interval, \(\mathrm{v_{imean}}\) and \(\mathrm{P_{imean}}\), are calculated, resulting in M data pairs \((\mathrm{v_{imean}},\mathrm{P_{imean}})\). * Power correction is applied to these M data pairs \((\mathrm{v_{imean}},\mathrm{P_{imean}})\). * The improved PCF algorithm is used to fit these corrected M data pairs \((\mathrm{v_{imean}},\mathrm{P_{imean}})\) into a static optimal power curve \(\mathrm{Tc}\). * The power curve \(\mathrm{Tc}\) obtained in the previous step is then moved horizontally (step size \(\Delta\mathrm{s}=0.25\) m/s) until the data volume percentage \(\mathrm{N_{d}}\) between the n-times horizontally moved power curve and the static optimal wind speed-power curve shows its first inflection point on the slope curve. At this point, the movement stops, and the horizontal optimal upper (or lower) limit power curve is determined. \[N_{d}=\frac{Lc_{n}-Lc_{\mathrm{Tc}}}{D}\times 100\% \tag{19}\]  
In Equation (19), D represents the total data volume of wind power after data cleaning, while \(\mathrm{Lc_{n}}-\mathrm{Lc_{Tc}}\) denotes the data volume between the n-th horizontally moved wind power curve and the static optimal wind power curve. Through multiple experimental validations, the best data effect is achieved when \(\mathrm{N_{d}}^{{}^{\prime}}\approx 34.21\%\) is at a specific value. * The obtained horizontal optimal power curve is then moved vertically (step size \(\Delta\mathrm{p}=5\) KW) until the data volume percentage \(\mathrm{N_{d}}^{{}^{\prime}}\) between the n-th vertically moved power curve and the static optimal power curve reflects the effect demonstrated in the slope curve mentioned in step (4).