## 4 Status Monitoring of Propeller Motor
### Status Monitoring and Early Warning Results  
In order to test the early warning performance of the model, we selected both normal data and the data with pitch fault to establish the model for status monitoring. The experiment was based on the data of the No. 1 turbine. For the detection of the normal state, 8000 records from 10 March 2012 to 5 May 2012 were randomly chosen as training samples, and 400 records from 6 May 2012 to 9 May 2012 were used as the test data. Figure 2 shows the true and predicted values by the ESN model on the training data set and the prediction errors, respectively. In these two subplots, the x-axis indicates the time indices, and the y-axis represents the temperature and the prediction error, respectively. It can be seen that the prediction error of ESN is between \(-10\)\({}^{\circ}\)C and \(10\)\({}^{\circ}\)C. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multicolumn{2}{c}{**No. 1 Fan**} & \multicolumn{2}{c}{**NO. 12 FAN**} \\ \cline{2-5}  & **RMSE** & **MAPE** & **RMSE** & **MAPE** \\ \hline ANFIS & 6.1784 & 11.3118 & 8.4236 & 18.7611 \\ NN & 5.6404 & 16.0484 & 5.5059 & 12.8966 \\ NN + Dropout & 5.5189 & 15.3089 & 6.5862 & 21.7037 \\ ESN & 3.0569 & 9.4110 & 3.2302 & 11.9049 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental results of pitch motor temperature prediction. Figure 2: Prediction of pitch motor temperature by ESN model on training data set. Furthermore, Figure 3 shows the performance of the model on the test set. The upper subplot illustrates the prediction error, and the lower subplot depicts the error frequency. It can be seen from Figure 3 that the prediction error of the model is concentrated between \(-6\)\({}^{\circ}\)C and \(6\)\({}^{\circ}\)C, with an RMSE of 3.0186 and the corresponding MAPE of 5.5088. Overall, the ESN model performs well on the test data. In order to achieve status monitoring, the EWMA method was adopted to calculate the upper and lower bounds of pitch motor temperature. Figure 4 shows the experimental results of the test set. In addition, the corresponding EWMA warning lines were also plotted, in which the red and green curves represent the upper and lower warning bounds, respectively. Notice that the wind turbine is in a normal state on the test data set, hence there is no alarm, and the experimental results are consistent with the expectation. In order to test how well the ESN model works for the early warning of pitch motor faults, some data of the No. 1 wind turbine containing pitch motor faults were utilized. In the recorded data, a pitch motor fault occurred at 3:50 a.m. on 5 August 2013. In this specific experiment, we selected 8000 records before the fault, that is, the data from 7 June 2013 to 3 August 2013, as the training data, and tested whether the fault can be predicted. Figure 5 shows the true and predicted values on the training set as well as the prediction error. Similarly, the \(x\)-axis represents the time index and the \(y\)-axis denotes the pitch motor temperature. The training data are all generated during the normal operation of the turbine. It can be seen from Figure 5 that the prediction error is basically between \(-10\)\({}^{\circ}\)C and \(10\)\({}^{\circ}\)C.  
Figure 4: Early warning of models on test set. Figure 3: Temperature prediction error of pitch motor on test set. Figure 6 shows the predicted results of the trained ESN model on the test set. Here, the prediction error and error frequency histograms are shown. It can be observed that the prediction error range of the model is similar to that of the training set, and most of the errors lie between \(-5\)\({}^{\circ}\)C and \(5\)\({}^{\circ}\)C.  
Since there is a fault record in the test set at this time, the purpose of ESN is to detect the occurrence of the fault point in advance. Figure 7 displays the true and predicted values on the test set as well as the EWMA fault warning diagram corresponding to the ESN model.