## 4 Example Verification
### Feature Vector Selection  
This paper uses the monitoring data of no-fault records with a sampling interval of 10 min in the first fourth months of its operation to complete feature selection. The active power information of the hydropower units is used to evaluate the operation state of the hydropower units. Therefore, when selecting the monitoring parameters, the parameters closely related to the active power are mainly selected. According to the above correlation analysis methods, the correlation between all simulated monitoring parameters (107 in total) of the monitoring system and the output active power of the hydropower units are calculated. Some results are shown in Table 4, and the vibrations mentioned in this paper are measured vibration. \begin{table}
\begin{tabular}{c c c} \hline
**Model** & **Frequency Response Range** & **Collection Data Type** \\ \hline Dp-VH-06-0400 low frequency vibration sensors & 0.5 Hz-200 Hz & Vibration data \\
811100-50-09-01 key phasor sensors & 0–10 KHz & Key phase data \\ BENTLY3300 XL sensors & 0–100 kHz & Obtain the swing data \\ SZCB-01 magnetoelectric speed sensors & 50–5000 Hz & Get the spindle speed \\ PM388 piezoresistive pressure sensors & 07 Mpa & Draft tube outlet pressure \\ \hline \end{tabular}
\end{table} 
Table 2: The main sensors used in the monitoring system. \begin{table}
\begin{tabular}{c c c c c} \hline
**Parameters** & **Number of Guide Vanes** & **Number of Runner Blades** & **Turbine Diameter (mm)** & **Hub Ratio** \\ \hline
16 & 4 & 6700 & 0.38 \\ \hline \end{tabular}
\end{table} 
Table 3: Basic dimension parameters of turbine model. Figure 2: The structure of the bulb tubular hydropower units and the location of some sensors. From Table 4, the correlation between each monitoring parameter and the active power parameter is quite different. To reduce the influence of weakly correlated or unrelated state parameters on the next step of modeling, the following Equations (14) and (15) are used to select the monitoring parameters closely related to the operation state of the unit, and these monitoring parameters are taken as the input eigenvectors of the initial selection. \[f(i)=\frac{1}{3}[M(i)+p(i)+G(i)] \tag{14}\]  
\[g=\frac{1}{N}\sum_{i=1}^{N}f(i) \tag{15}\]  
In Equations (14) and (15). \(N\) is the monitoring parameters of 107 measuring points collected from the hydropower station monitoring system. \(M(i)\) is the MIC value of the \(i\)th monitoring parameter. \(P(i)\) is the PCC value of the \(i\)_th_ monitoring parameter. \(G(i)\) is the GCD value of the \(i\)th monitoring parameter. When \(f(i)>g\), it is considered that the \(i\)th parameter is closely related to the unit operation state specifying it as a preliminary input feature. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Condition Monitoring Parameters**} & \multicolumn{3}{c}{**The Correlation Analysis Methods**} \\ \cline{2-4}  & **MIC** & **PCC** & **GCD** \\ \hline Swing Y of the water guide bearing & 0.22 & \(-\)0.03 & 0.72 \\ Vibration of oil receiver in the X direction & 0.21 & 0.39 & 0.88 \\ Vibration of oil receiver in the Y direction & 0.21 & 0.43 & 0.92 \\ Vibration of stator frame in the X direction & 0.15 & 0.30 & 0.88 \\ Vibration of stator frame in the Y direction & 0.26 & 0.49 & 0.86 \\ Vibration of combined bearing in the X direction & 0.20 & 0.37 & 0.92 \\ Vibration of combined bearing in the Y direction & 0.36 & 0.57 & 0.93 \\ Vibration of water guide bearing in the X direction & 0.20 & 0.36 & 0.83 \\ Vibration of water guide bearing in the Y direction & 0.20 & 0.37 & 0.93 \\ Temperature of No.1 forward thrust bearing bush & 0.35 & 0.45 & 0.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Correlation analysis results of the partial condition monitoring parameters using maximum information coefficient (MIC), Pearson correlation (PCC), and grey correlation degree (GCD). Figure 3: The installation position of RTZ bearing bush temperature sensors for collecting the temperature of water guide bearing bushe.