## 4 Results and Discussion
### Performance Evaluation  
Three indicators are defined to evaluate the performance of the proposed method.  
* True detections (TD): the labeled root fault of an alarm list is the same as the actual fault;
* False detections (FD): the labeled root fault of an alarm list is different from the actual fault;
* Misdetection (MD): an alarm list is not assigned with a fault.  
The performance-evaluation results are shown in Table 5. The similarity between an alarm list and a feature vector is measured by the weighted Euclidean distance and the weighted Hamming distance, respectively. Test set one consists of 44 alarm lists. The root faults of these lists are among the selected six faults. Test set two consists of 150 alarm lists. The root faults of these lists are not among the selected six faults. Thus, the indicator TD for test set two does not exist. The overall performance of the weighted Hamming distance is better than that of weighted Euclidean distance. For test set one, the percentage of TD of weighted Hamming distance is higher, and the percentage of FD and MD is lower. For test set two, the percentage of FD and MD of weighted Hamming distance is lower.  
A multidimensional information processing method proposed in reference [25] is also applied in this paper. The Dempster-Shafer evidence theory is applied to the selected six faults. Each alarm list is labeled with the most possible fault. True detection and false detection can be used to evaluate the performance. The results are shown in Table 6. The percentage of TD is 81.8%. The percentage of FD is 18.2%. The number of the data set has a great influence on the method, which is based on probability analysis. The percentage of TD is a little lower than that of the proposed method.  
The more detailed analysis of test cases set one, with the weighted Hamming distance applied, is given as follows: Two alarm lists are labeled with a wrong fault. One alarm list, the actual root fault of which is pitch-motor driver fault, is wrongly labeled with pitch-system communication fault. The pitch-motor driver fault and pitch-system communication fault both belong to the faults of the pitch system. They are sensitive to the same alarms. Another alarm list, the actual root fault of which is hub speed encoder fault, is wrongly labeled with wind vane fault. This is because wind speed has a great influence on the hub speed. The coupling of alarms is responsible for both cases. Five root faults are not detected. All of them are wind vane faults. This is because the description of the wind vane fault in maintenance records is not detailed and accurate. The alarm lists generated when the fault occurs are more dispersive. The extracted feature vector cannot represent the occurrence of the fault well.  
The value of _fr_ is crucial for extracting the feature vector of faults; _fr_ is set to 0.5 in this paper. It is determined according to the percentage of TD. Figure 3 describes the percentage of TD for \(D_{WH}\) and \(D_{WE}\) with different _fr_. When _fr_ is 0.5, the percentage of TD is the greatest.  
\begin{table}
\begin{tabular}{c c} \hline \hline  & **Test Set One** \\ \hline The percentage of TD & 81.8\% \\ The percentage of FD & 18.2\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: The performance of multidimensional information processing method.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Test Set One**} & \multicolumn{2}{c}{**Test Set Two**} \\ \cline{2-5}  & \(D_{WE}\) & \(D_{WH}\) & \(D_{WE}\) & \(D_{WH}\) \\ \hline The percentage of TD & 77.3\% & 84.1\% & - & - \\ The percentage of FD & 6.8\% & 4.5\% & 12.0\% & 9.3\% \\ The percentage of MD & 15.9\% & 11.4\% & 88.0\% & 90.7\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: The performance of the proposed method.