## 2 Experimental Setup and Measurement  
While emerging short circuit turns within the stator windings will not affect the performance of the rotating machine significantly, it can progress rapidly, causing severe damages to the machine. Thus, detecting and correcting such flaws at an early stage is critical. Various short circuit faults can take place within the stator winding, including the turn-turn, coil-coil, phase-neutral, and phase-to-ground, as shown in Figure 2[40]. FRA measurements are conducted on two TPIMs of different ratings with normal and short-circuited stator windings, as shown in the experimental setup of Figure 3. The parameters of the investigated motors are listed 19 in Table 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Indicators** & **Mathematical Expression** & **Indicators Description** & **References** \\ \hline Correlation Coefficient (CC) & \(\text{CC}_{(X,Y)}=\frac{\sum_{i=1}^{N}X(i)\cdot Y(i)}{\sqrt{\sum_{i=1}^{N}|X(i )|^{2}\times\sum_{i=1}^{N}|Y(i)|^{2}}}\) & It only measures linear relationships between \(Xi\) and \(Yi\). & [34] \\ \hline Absolute Sum Logarithmic Error (ASLE) & \(\text{ASLE}_{(X,Y)}=\frac{\sum_{i=1}^{N}|20 log_{10}Y_{i}-20 log_{10}X_{i}|}{N}\) & The ASLE scales the data regardless of the data size from & [33; 34; 35] \\ \hline Standard Deviation (SD) & \(\text{SD}_{(X,Y)}=\sqrt{\frac{\sum_{i=1}^{N}|Y(i)-X(i)|^{2}}{N-1}}\) & Similar trend as ASLE & [31] \\ \hline Absolute Difference (DABS) & \(\text{DABS}=\frac{\sum_{i=1}^{N}|y(i)-x(i)|}{N}\) & & [36; 37] \\ \hline Mean Square Error (MSE) & \(\text{MSE}=\frac{\sum_{i=1}^{N}(i)-X(i))^{2}}{N}\) & MSE magnifies errors due to the squaring operation in the equation. & [33; 36] \\ \hline Root Mean Squared Error (RMSE) & \(\text{RMSE}=\sqrt{\frac{\sum_{i=1}^{N}(X(i)-Y(i))^{2}}{N}}\) & Only sensitive to outliers & [36; 37] \\ \hline Covariance (COVAR) & \(\text{COVAR}(x,y)=\frac{1}{N}\sum_{i=1}^{N}(x(i)-\overline{x}(i)(y(i)-\overline {y}(i))\) & This indicator is based on a Chinese standard. & [38; 39] \\ \hline Minimum-Maximum Ratio (MM) & \(\text{MM}=\frac{\sum_{i=1}^{N}\text{min}(X(i))}{\sum_{i=1}^{N}\text{max}(X(i))}\) & MM allows comparing the similarity of a data set. & [36; 37] \\ \hline \hline \end{tabular}
\end{table}
Table 2: Statistical indicators used in FRA.  
Figure 3: Laboratory setup, and FRA measurement, (**a**) short-circuit fault implementation, (**b**) experimental view on one of the tested motors.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Motor** & **1** & **2** \\ \hline RPM & 2840 rpm & 1500 rpm \\ Made & JILANG & JILANG \\ Model & Y90L-2 & 110 RK-3 DS \\ Power rating & 2.2 kW/3 HP & 0.75 kW/1 HP \\ Voltage rating & 415 V/50 Hz & 415 V/50 Hz \\ \hline \hline \end{tabular}
\end{table}
Table 3: Specifications of the investigated 3-phase induction motors.  
Figure 2: Schematic diagram of different stator winding SC faults.  
The FRA measurement of each phase of the stator windings is conducted as per the schematic of Figure 4. The FRA analyzer injects a low voltage (<20 V) AC input signal, V\({}_{\text{in}}\) of wide frequency range at one winding terminal of each phase. The output voltage, V\({}_{\text{out}}\) can be measured at the other winding terminal of the same phase or another phase terminal. The FRA signature is usually provided as the magnitude of the winding transfer function TF\({}_{\text{dB}}\) = 20 log10 \(\mid\)V\({}_{\text{out}}\)/V\({}_{\text{in}}\)\(\mid\) plotted against frequency.