###### Abstract
The FRA method is recognized to identify the mechanical deformations within power transformers [13; 14]. The test is conducted offline by injecting a low amplitude of AC voltage with a variable frequency in the range 20 Hz-2 MHz to scan each phase and detect any variations from the healthy FRA signature of this phase. While the measurement method for power transformers is well documented in several standards such as the Cigre Working Group A2.26 [16], IEC 60076-18 [17] and IEEE-Std-C57 [18], not much attention was given to extend the technique to detect faults within rotating machines. Due to the reported high sensitivity of the FRA method, it can detect changes occurring within the machine at early stages [19; 20; 21]. For power transformers, interpretation of the obtained FRA results can be conducted using: (1) time-based comparison, where the obtained FRA data are compared with previously saved reference data for the same unit; (2) type-based comparison in which the measured FRA data are compared with another unit of the same design; (3) phase-based comparison in which measured FRA signatures of the three phases of the same unit are compared. There are few published studies in the literature that investigate the application of the FRA method for TPIMs. In [22], the FRA method is employed to detect broken bars with a squirrel cage induction motor. It is found that the FRA signature shows a variation between 1 kHz and 300 kHz due to broken bars in the squirrel cage induction motor. However, the investigation in this paper is based on the rotor position, and there is no FRA interpretation methodology presented. The application of FRA to diagnose TPIMs has also been proposed in [23; 24; 25; 26; 27]. In [23; 24], the FRA results were analyzed based on the assessment factor E12. The other studies did not propose an interpretation methodology [26]. There were other studies on reliable diagnostic methods for rotating machines [28; 29; 30]. Ref. [28] presented healthy and faulty models for the induction motor through simulation and experimental analyses. The studies presented in [29; 30] investigated the application of the FRA method to detect failures in the stator winding of the induction motor. In [30], the online application of FRA was proposed. Results revealed the high accuracy of the FRA technique to detect winding SC faults of low levels. Regardless of these research efforts in the literature, there was still a lack of full understanding of the interpretation of the FRA signatures for rotating machines. This study takes a further step to investigate and employ various statistical indicators to understand the effect of SC faults on the FRA signature of three-phase induction motors. Given the graphical comparison nature of the technique, several studies presented various statistical coefficients to quantify the difference between the measured FRA signatures [31; 32]. A survey was conducted to assess the applicability of using statistical indicators to evaluate the variations among the measured FRA signatures [32]. Among them, correlation coefficient (CC), mean squared error (MSE), the absolute sum of logarithmic error (ASLE), and comparative standard deviation (CSD) as listed in Table 2 show high sensitivity to changes in the FRA signatures. The CC is recommended by the IEEE standard \begin{table}
\begin{tabular}{c c c c} \hline
**Test** & **Detected Component** & **Purpose of Test** & **References** \\ \hline Partial discharge (PD) & & Partial discharges, insulation & \\  & & degradation & \\ \hline Tan \(\delta\) & & Partial discharges, insulation & \\  & & degradation & \\ \hline Vibration test & Shaft or bearing, rotor winding & The shaft or bearing vibration & [8] \\ \hline Voltage withstand & & Voltage withstand & [9] \\ \hline Winding and insulation resistance & stator windings & High contact resistance and poor & [10] \\ \hline Pole drop testing & & & \\ \hline Frequency response analysis & & Turns-turn faults & [11; 12] \\ \hline Dielectric response analysis & & & \\ \hline \end{tabular}
\end{table}