# Anomaly Detection of Wind Turbines Based on Deep Small-World Neural Network
## 4 Case Studies
### Prediction Analysis for the Pitch Abnormalities (Case A)  
The three blades of the wind turbine have three groups of pitch driving devices, which are independent and synchronous. When the wind speed changes suddenly and the blades need to change the pitch angles frequently, the failure of synchronous action of the three pitch drives often leads to multiple failures occurring at the same time. Table 2 shows a record of multiple alarms that occurred on 1 January 2017. It is confirmed that the main reason was that the pitch action of the three blades was out of sync after the last maintenance. This kind of failure is caused by typical mechanical wear, and its fault characteristics will be hidden in SCADA data. Therefore, the relevant signals monitored can be expressed as Equation (22). We applied the dataset \(X_{A}\) to train the DSWNN, DBN and DNN models, then calculated the prediction errors by using the recorded failure SCADA data, as shown in Figure 7.  
\[X_{A}=[v_{0},\theta_{1},\theta_{2},\theta_{3},T_{1},T_{2},T_{3},\Omega,P]. \tag{22}\]  
It can be seen from Figure 7 that the prediction error obtained by DSWNN fluctuated within the adaptive threshold range before time T3. But after T3, the error approached its upper limit and then gradually exceeded its upper limit. According to the alarm record, the first fault named \"Pitch angle 1 out of sync\" occurred at 07:58:12. This means that the DSWNN can detect an abnormality approximately 3 h ahead of actual downtime, which can provide sufficient time to take some actions for pitch system maintenance. In addition, from Figure 7a,b, the DNN and DBN models can also predict failures 1.1 h and 2.3 h in advance, respectively. The proposed DSWNN can detect incipient faults earlier than that of the DBN and DNN. Moreover, the error calculated by the DSWNN was the smallest in the three models, which shows that the DSWNN model can extract more sufficient dynamic features from normal SCADA data. Hence, on the one hand, the DSWNN model in terms of describing the dynamic behavior of the pitch system is more accurate. On the other hand, the adaptive threshold can effectively track the prediction error, which can increase the adaptability of the prediction models and provide a more accurate judgment basis for the system to reduce false alarms and omissions.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No.** & **Signals** & **Notation** & **No.** & **Signals** & **Notation** \\ \hline
1 & Wind speed & \(v_{0}\) & 7 & Pitch moment 3 & \(M_{3}\) \\
2 & Pitch angle 1 & \(\theta_{1}\) & 8 & Pitch motor temperature 1 & \(T_{1}\) \\
3 & Pitch angle 2 & \(\theta_{2}\) & 9 & Pitch motor temperature 2 & \(T_{2}\) \\
4 & Pitch angle 3 & \(\theta_{3}\) & 10 & Pitch motor temperature 3 & \(T_{3}\) \\
5 & Pitch moment 1 & \(M_{1}\) & 11 & Generator speed & \(\Omega\) \\
6 & Pitch moment 2 & \(M_{2}\) & 12 & Power & \(P\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Description of wind turbine pitch system signals.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Device Name** & **Wind Speed (m/s)** & **Abnormal Message** & **Set Time** & **Reset Time** \\ \hline FKD\_F088 & 8.42 & Pitch angle 1 out of sync & 1 January 2017 07:58:12 & 1 January 2017 08:37:04 \\ FKD\_F088 & 5.05 & Pitch 1 drive error & 1 January 2017 07:58:35 & 1 January 2017 08:37:04 \\ FKD\_F088 & 5.04 & Pitch 2 drive error & 1 January 2017 07:58:35 & 1 January 2017 08:37:04 \\ FKD\_F088 & 6.76 & Storage relay not reset & 1 January 2017 08:00:04 & 1 January 2017 08:37:04 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Fault alarm records for the pitch system of the wind turbine.