## 6 Conclusions  
A power supply is indispensable in daily life, and a crucial element in ensuring its reliability is the transformer. Therefore, its maintenance and prevention of failures through the development and application of accurate methods that timely identify SCTs are imperative. In this regard, this work presents a novel method for SCT fault detection. The proposed method, in summary, utilizes the QSA method within a time-space framework, two statistical indices, and a machine-learning classifier. In this work, it was found that the processing of the current signal and the vibration signals with the QSA method allows for a fast and effective diagnosis, since only 100 samples of the signals are required two achieve 97.55% of accuracy. Thus, the proposed method contributes to minimizing both sample acquisition and processing, using simple operations. These features help to evaluate the transformers in short operating times and prevent the system from being exposed to major faults. It is important to highlight that a larger number of samples increases the accuracy values, 8000 samples being the window size that allows for 99.52% accuracy. Moreover, after testing multiple statistical indices, it was found that \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **Samples** & **Signal Type** & **Statistical Indices** & **Classes** & **Classification** & **Accuracy** \\ \hline Frequency-response analysis [23] & 40,000,000 & Voltage and current & SD & Multiple short cuts & ANN & 0.9 \\ \hline Wavelet-based [24] & 15,360 & Current & Energy & 1-5% short-circuedued winding & — & 1.0 \\ \hline Statistical time features [22] & 30,000 & Vibrations & Entropy, Kurtosis & 0-35 SCTs & SVM & 0.9682 \\ \hline Fractal dimension algorithms [12] & 18,000 & Vibrations & — & 0-35 SCTs & KNN & 0.9962 \\ \hline \multirow{3}{*}{**Quaternion signal analysis (QSA)**} & 100 & & & & 0.9755 \\ \cline{2-6}  & 5000 & Vibrations & SD, VA & 0-35 SCTs & KNN & 0.9914 \\ \cline{1-1} \cline{2-6}  & 8000 & and current & & & 0.9952 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison between the proposed method and others reported in the literature. VA and SD provide suitable patterns to differentiate between SCT conditions, having the advantage of requiring simple mathematical operations for their computation. Finally, although three different classifiers were tested (i.e., KNN, NN, and DT), the best accuracy results were obtained using the KK classifier for all the analyzed window sizes. Despite the obtained promising results, it is important to mention that there are still several opportunities for the future research to overcome some detected shortcomings. For instance, classification results of 87.58% were obtained for the condition of 5 SCTs, which is not a good enough value compared with the other ones obtained, which were higher than 98%. Although this low value is somehow expected since the fault can be considered of low severity and, consequently, the generated signals (current and vibrations) are slightly affected, making difficult the extraction of more useful information, it is fundamental that we continue the research into other methods that can be more effective for incipient damages. The future work will explore the detection of SCTs and other faults in transformers operating under both linear and non-linear loads in order to provide more robust methods. Furthermore, we will explore the application of deep learning techniques in order to enhance diagnostic accuracy, mainly considering incipient damages. Conceptualization and methodology, D.C.-M., M.V.-R. and J.-L.C.-H.; software and formal analysis, J.-L.C.-H., M.V.-R. and D.C.-M.; resources and data curation, M.-A.I.-M. and D.-L.A.-O. ; writing--review and editing, all authors; supervision, project administration, and funding acquisition, M.-A.I.-M., J.P.A.-S., M.V.-R. and D.C.-M. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.