# Imbalanced Diagnosis Scheme for Incipient Rotor Faults in Inverter-Fed Induction Motors
## 7 Conclusions  
This article reviews and applies several resampling techniques for diagnosing rotor faults in line-fed and inverter-fed induction motors. These resampling techniques are SMOTE extensions and produce synthetic observations belonging to the minority fault class for balancing training sets and improving the synthetic data generation according to boundary area behavior. The evaluation of the classifier performance with the metrics \(AUC\) and \(G_{mean1}\) metrics shows that for the highest fault severity of the broken rotor bar fault (R5), all resampling techniques considered have similar behavior, which implies that in terms of performance, any of them can obtain successful diagnostic results independent of the motor power supply and the imbalanced ratio analyzed. Therefore, by incorporating any of these oversampling techniques into the diagnosis methodology to predict the rotor's condition, it is possible to construct a more precise and robust diagnosis of the rotor faults of inverter-powered induction motors with small and unbalanced data. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Classifier** & **Supply** & \begin{tabular}{c} **Case** \\ **Number** \\ \end{tabular} & **Severity** & \begin{tabular}{c} **Imbalance** \\ **Ratio (IR)** \\ \end{tabular} & **AUC (\%)** & \(p\)**-Value** & **Gmean1 (\%)** \\ \hline \multirow{9}{*}{SVM} & Line-fed & 1 & R3 & 12 & \(97\pm 2.55\) & 0.085 & \(98\pm 1.58\) \\  & Line-fed & 2 & R3 & 7 & \(97\pm 2.52\) & 0.251 & \(97\pm 2.63\) \\  & Line-fed & 3 & R3 & 3 & \(97\pm 1.36\) & 0.651 & \(97\pm 2.14\) \\  & Line-fed & 4 & R5 & 12 & \(100\pm 0.00\) & 0.156 & \(100\pm 0.00\) \\  & Line-fed & 5 & R5 & 7 & \(100\pm 0.00\) & 0.746 & \(100\pm 0.00\) \\  & Line-fed & 6 & R5 & 3 & \(100\pm 0.00\) & 0.365 & \(100\pm 0.00\) \\  & Inverter & 7 & R3 & 12 & \(97\pm 2.11\) & 0.711 & \(97\pm 2.77\) \\  & Inverter & 8 & R3 & 7 & \(96\pm 1.23\) & \textless{}0.01 & \(97\pm 2.98\) \\  & Inverter & 9 & R3 & 3 & \(96\pm 2.58\) & \textless{}0.01 & \(97\pm 2.73\) \\  & Inverter & 10 & R5 & 12 & \(100\pm 0.00\) & 0.411 & \(100\pm 0.00\) \\  & Inverter & 11 & R5 & 7 & \(100\pm 0.00\) & 0.709 & \(100\pm 0.00\) \\  & Inverter & 12 & R5 & 3 & \(100\pm 0.00\) & 0.177 & \(100\pm 0.00\) \\ \hline \multirow{9}{*}{AdaBoost} & Line-fed & 1 & R3 & 12 & \(97\pm 1.23\) & 0.785 & \(98\pm 1.42\) \\  & Line-fed & 2 & R3 & 7 & \(97\pm 2.58\) & 0.150 & \(97\pm 2.40\) \\  & Line-fed & 3 & R3 & 3 & \(98\pm 1.32\) & 0.255 & \(98\pm 1.84\) \\  & Line-fed & 4 & R5 & 12 & \(100\pm 0.00\) & 0.456 & \(100\pm 0.00\) \\  & Line-fed & 5 & R5 & 7 & \(100\pm 0.00\) & 0.606 & \(100\pm 0.00\) \\  & Line-fed & 6 & R5 & 3 & \(100\pm 0.00\) & 0.865 & \(100\pm 0.00\) \\  & Inverter & 7 & R3 & 12 & \(97\pm 1.10\) & 0.545 & \(97\pm 2.66\) \\  & Inverter & 8 & R3 & 7 & \(97\pm 1.23\) & \textless{}0.01 * & \(97\pm 2.09\) \\  & Inverter & 9 & R3 & 3 & \(98\pm 2.58\) & \textless{}0.01 * & \(97\pm 2.09\) \\  & Inverter & 10 & R5 & 12 & \(100\pm 0.00\) & 0.811 & \(100\pm 0.00\) \\  & Inverter & 11 & R5 & 7 & \(100\pm 0.00\) & 0.811 & \(100\pm 0.00\) \\ k-NN & \
\begin{tabular}{c} \(\ast\) \\ \end{tabular} &
\begin{tabular}{c} Outcome of the test from pairwise performance where MWMOTE outperforms the rest. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Classification results with feature selection and oversampling with SLSMOTE, RLSSMOTE, and MWMOTE. In addition, from this experimental study, the authors observed that one area of exploration is the application of these oversampling methods to more incipient rotor breakages, where the feature differences regarding the healthy class are much more reduced. Conceptualization, I.M.-D. and D.M.-S.; data curation, I.M.-D.; methodology, I.M.-D. and D.M.-S.; software, T.G.-C.; validation, D.M.-S. and T.G.-C.; writing--original draft, I.M.-D.; writing--reviewing and editing, D.M.-S. and O.D.-P. All authors have read and agreed to the published version of the manuscript. This research was partially funded by the University of Valladolid. Not applicable.