## 5 Conclusions  
Vibration analysis for fault detection in transformers is one of the most employed methods. In this work, a novel methodology for diagnosing SCTs in transformers in both operating regimes (i.e., transient and steady state) by using vibration signals is proposed. This approach is experimentally validated using a modified transformer subjected to various levels of fault severity (i.e., 0-healthy, 5, 10, 15, 20, 25, and 30 SCTs), resulting in accuracy average values of 90% in both operating conditions. For the transient state, a minimum value of 81.8% (20 SCTs) and a maximum of 96.7% (30 SCTs) are obtained; on the contrary, for the steady state, these values correspond to a minimum of 87.1% (10 SCTs) and a maximum of 96.6% (0 SCTs). Despite the inherent properties of vibration signals, i.e., high-level noise and nonstationary properties, the adroit integration or various signal processing stages in the proposed method allows for several advantages. The noise rejection stage effectively reduces components that are not of interest and mitigates negative effects during the estimation of harmonic components using STFT and FT. Furthermore, this proposal does not necessitate complex time-frequency kernels or techniques, since the proposed approach allows the resolution limitations of STFT to be disregarded due to the energy conservation (Parseval's theorem) and the use of the _ENE_ and _THD_ indices, which are calculated based on the energy parameters of the signal. Additionally, the comb filter facilitates the removal of steady state components, enabling a focused analysis on transient components related to faults. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Reference** & \begin{tabular}{c} **Signal Processing** \\ **Methods** \\ \end{tabular} & **Analyzed State** & \begin{tabular}{c} **Number of** \\ **Sensors** \\ **Employed** \\ \end{tabular} & **Detected Faults** & **Severity Levels** & \
\begin{tabular}{c} **Automatic** \\ **Diagnosis** \\ \end{tabular} \\ \hline Proposal &
\begin{tabular}{c} Wavelet \\ denoising and \\ FT-based \\ methods \\ \end{tabular} & Transient and & 1 & SCTs & 6 & ANNs \\ \hline
[3] & \
\begin{tabular}{c} Electromagnetic \\ force analysis \\ \end{tabular} & Steady & 5 &
\begin{tabular}{c} Winding \\ loosening \\ \end{tabular} & 3 & \(-\) \\ \hline
[13] & \
\begin{tabular}{c} Empirical wavelet \\ transform and HT \\ \end{tabular} & Transient and & 2 &
\begin{tabular}{c} Winding \\ deformation \\ \end{tabular} & 3 & \(-\) \\ \hline
[19] & \begin{tabular}{c} CEEMDAN and \\ multiscale \\ dispersion \\ entropy \\ \end{tabular} & Steady & 1 & \
\begin{tabular}{c} Winding and core \\ loosening \\ \end{tabular} & 1 &
\begin{tabular}{c} Density peaks \\ clustering \\ \end{tabular} \\ \hline
[20] & \
\begin{tabular}{c} VMD and WT \\ \end{tabular} & Steady & 1 &
\begin{tabular}{c} Winding \\ deformation \\ \end{tabular} & 3 & CNN \\ \hline
[21] &
\begin{tabular}{c} NMD and \\ HT-based RMS \\ \end{tabular} & Transient and & 1 & SCTs & 6 & FLS \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of the proposed methodology against other relevant methodologies that use vibration signals for winding faults in transformers. The _ENE_ and _THD_ indices, combined with the proposed signal processing techniques (i.e., wavelet denoising, comb filter-based filtering, and Fourier-based transformations), have proven to be effective indicators of fault severity, as their values somehow increase with the severity of the fault. This suggests their potential applicability to other transformers. In future work, the detection of SCTs in the transformer operating with linear and nonlinear loads will be explored. Additionally, more sophisticated machine learning and deep learning-based models will be researched to further enhance the accuracy of the diagnosis.