## 4 Experimentation and Results
### Results for the Transient State  
Once the noise of the vibration signal has been reduced, the comb filter is applied to eliminate the harmonic content of the signal; therefore, only the frequency components that emerge during the transformer energization are retained, facilitating the diagnosis of SCT conditions in the transformer during this regimen.  
Figures 7 and 8 display the time-frequency representations of the vibration signals for each SCT condition, both without and with the comb filter, respectively. In Figure 7, it is evident that the harmonic content increases throughout the time-frequency plane relative to the fault severity, being somehow lower in Figure 7a (0 SCTs) and higher in Figure 7g (30 SCTs). It is worth noting that the straight lines which are observed in the time-frequency plane represent constant frequency components (i.e., harmonic components); although the magnitudes of these components are indicated by a color scale, their specific values are not taken into account in this work since they are quantified in a global manner by the proposed indices. On the other hand, as can be seen, most of the stationary content has been removed (see Figure 8), leaving only the transient components, as depicted by the white arrows. It is also observed that the transient frequency content increases relative to the fault severity, being somehow lower in Figure 8a (0 SCTs) and higher in Figure 8g (30 SCTs). In  
Figure 5: Vibration signals: (**a**) Vx, (**b**) Vy, and (**c**) Vz.  
order to characterize the impact of the SCTs on the vibration signals during the transformer energization, the _ENE_ index is computed according to Equation (7). In general, the _ENE_ index can be interpreted as the sum of all the nonzero frequency components present in the time-frequency plane.  
Figure 9 shows the boxplot results for the _ENE_ index in all of the transformer conditions. Each boxplot summarizes the results for the 100 tests of each SCT condition. Each subfigure corresponds to one axis (Vx, Vy, and Vz). In order to have the same reference in the three axes, the values are normalized, with the 0 SCTs condition serving as the baseline, resulting in an index value of 1 for that condition. This approach can be useful for establishing a reference in different transformers. In Figure 9, it is observed that the _ENE_ index increases in accordance with the severity of damage in the three vibration axes (see the red arrows), making it a valuable feature for fault severity detection. From a visual inspection, the results for the X-axis exhibit a more proportional trend relative to the fault severity. For a more quantitative understanding, Table 1 presents the average values of the _ENE_ index for each axis.  
Figure 6: Time domain and its time–frequency representation for (a) a noisy vibration signal and (b) a denoised vibration signal.  
Figure 7: Time–frequency representation for the vibration signals without the comb filter: (**a**) 0 SCTs, (**b**) 5 SCTs, (**c**) 10 SCTs, (**d**) 15 SCTs, (**e**) 20 SCTs, (**f**) 25 SCTs, and (**g**) 30 SCTs.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & & & & & \\ \hline
**Signal** & **0** & **5** & **10** & **15** & **20** & **25** & **30** \\ \hline Vx & 1 & 1.0787 & 1.1394 & 1.3116 & 1.3564 & 1.8395 & 2.7043 \\ \hline Vy & 1 & 0.9002 & 1.2071 & 1.2624 & 1.2409 & 1.8031 & 1.8108 \\ \hline Vz & 1 & 1.0071 & 1.0095 & 1.0291 & 1.0341 & 1.0795 & 1.0709 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Average _ENE_ values for the different SCTs conditions.