## 4 Verification of Results  
### MWPTR Results  
The SCADA data used in this study are obtained from a mountain wind farm which has 24 sets of 2 WM wind turbines. The cut-in wind speed \(v_{\text{in}}\) is 3 m/s, the cut-out wind speed \(v_{\text{out}}\) is 25 m/s, and the rated wind speed \(v_{\text{rated}}\) is 11 m/s. In this study, 10 min of SCADA data are used, and the wind speed data are collected from the nacelle sensor. In addition, the SCADA data pertains to the period from 1 January 2013 and 31 December 2017. The analysis of the operation conditions of all the wind turbines in the wind farm indicated that the T01 wind turbine demonstrates relatively stable performance with fewer maintenance activities during its service. Through a comparative analysis with other wind turbines, with reference to the wind resource and maintenance records, data of the T01 wind turbine from June to July 2015 are selected as the baseline data. The length of the time window \(T\) is 4320 (30 days), and the slide step size \(\Delta T\) is 432(3 days). HV curve of the T01 wind turbine is calculated and given in Figure 6, it can be seen that a larger HV corresponds to poorer power performance. In addition, if two health values are farther from each other along the horizontal axis, there may be downtime. From Figure 6, it can be noted that HV is between 0.4 and 0.5 before Date A. During the time interval between Dates A and C, HV changes violently. During Dates C and D, the wind turbine operates in a stable manner, fluctuating only in a remarkably short interval with little downtime, which is consistent with the actual maintenance record. To clarify whether the HV can actually reflect the variations between the reference data and the actual data, the wind speed and power data of Dates A, B and C are plotted, as shown in Figure 7. From Figure 7a, it can be found that the deviation between Date A and Date C is extremely pronounced, and Point B indicates a transition from Date A to Date C. Therefore, the HV with the presented method accurately quantifies the power performance changes. More importantly, the gradual change of the HV is objectively presented. Further trend analysis will be meaningful for the turbine operation and maintenance activities. To further prove the validity of the presented method, a comparative study is performed using the PC2-Dev method [27]. T01 and T07 are both selected as research objects and analyzed using two different methods. The respective results are shown in Figures 8 and 9, in which the blue and red lines respectively represent the results obtained using the PC2-Dev method and the PAM method. From Figure 8, two HV curves reflect the change trend of the actual power curve well; meanwhile, the inflection points in the two curves occur nearly simultaneously. In addition, in Figure 9, from March 2014 to January 2017, the two health value curves also demonstrate a similar trend. However, it must be noted that from January 2017 to September 2017, the HV curves obtained using the PAM method change slightly with the date while the HV curves obtained using the PC2-Dev method exhibit large fluctuations, demonstrating distinct differences. For analyzing the reason, two points with the largest changes in the PC2-Dev method are selected and named Date A and Date B; next, their data together with the baseline data are plotted, as shown in Figure 10. Figure 10a shows data of Dates A and B; the overlapped part is marked in blue, as shown in Figure 10c, while others are marked in different color, as shown in Figure 10d. Based on the observation from Figure 10, Dates A and B data are remarkably similar to the baseline data, both containing a large amount of overlapped information. Therefore, it can be implied that the resultant large fluctuation of curves comes from the small number of non-overlapped data. By analyzing the non-overlapped data in Figure 10d, it can be noted that the data of Date A are mainly locate in the wind speed interval [3.0, 7.0], and the data of Date B are located in the speed interval [7.0, 11.0].