## 4 Results and Discussion
### On of the Performance in Each Class  
To further analyze the above results, the recall indicator of each fault class is studied. As it is shown in Figure 11, the recall indicator in the RF-i model of the health state reaches 100% while, for the other three faulty classes, comes down to 63.88% in gear pitting; 84.3% in gear broken tooth, and 63.35% in gear cracking for an average of 77.88%. This clearly shows the effect of the unbalanced data set. For RF-GAN, the recall indicator in each class is 99.53%, 99.73%, 99.63%, and 99.87%, respectively. In RF-GAN1, the recall indicator in each class is 98.63%, 98.67%, 98.28%, and 95.40%, respectively. For the RF-GAN2 model, the recall indicator in each class is 99.30%, 93.08%, 98.15%, and 90.08%, respectively. The high recall indicators are due to the existence of sufficient examples in each class. This is also visible in the recall of SMOTE.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Pair** & \(p\)**-Value** & **Winner** \\ \hline RF-i vs. RF-b2 & 8.857 \(\times\) 10\({}^{-5}\) & RF-b2 \\ RF-i vs. RF-GAN & 8.857 \(\times\) 10\({}^{-5}\) & RF-GAN \\ RF-i vs. RF-GAN1 & 8.857 \(\times\) 10\({}^{-5}\) & RF-GAN1 \\ RF-i vs. RF-GAN2 & 8.857 \(\times\) 10\({}^{-5}\) & RF-GAN2 \\ RF-i vs. SMOTE & 8.857 \(\times\) 10\({}^{-5}\) & SMOTE \\ RF-b2 vs. RF-GAN & 8.857 \(\times\) 10\({}^{-5}\) & RF-GAN1 \\ RF-b2 vs. RF-GAN2 & 8.857 \(\times\) 10\({}^{-5}\) & RF-GAN2 \\ RF-b2 vs. SMOTE & 1.204 \(\times\) 10\({}^{-5}\) & SMOTE \\ RF-GAN vs. RF-GAN1 & 0.079 & – \\ RF-GAN vs. RF-GAN2 & 8.857 \(\times\) 10\({}^{-5}\) & RF-GAN \\ RF-GAN vs. SMOTE & 8.857 \(\times\) 10\({}^{-5}\) & RF-GAN \\ RF-GAN1 vs. RF-GAN2 & 8.845 \(\times\) 10\({}^{-5}\) & RF-GAN1 \\ RF-GAN1 vs. SMOTE & 8.844 \(\times\) 10\({}^{-5}\) & RF-GAN1 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Wilcoxon _posthoc_ pairwise tests for the different scenarios.  
The fit score is another metric that can be used to compare the relative performance of the different scenarios in each class. From Figure 12, one can see that the performance of RF-i as measured by the F1-score is 70.38% in fault A, 77.54% in fault B, 90.03% in fault C, and 76.49% in fault D. The performance of RF-b2 in each faulty condition is 91.05% in fault A, 92.25% in fault B, 96.50% in fault C and 94.3% in fault D, respectively. The performance of RF-GAN is 98.52% in fault A, 98.83% in fault B, 95.66% in fault C and 95.23 in fault D. The performance of RF-GAN1 is 98.55% in fault A, 98.95% in fault B, 96.87% in fault C and 96.62 in fault D. The performance of RF-GAN2 is 95.70% in fault A, 96.54% in fault B, 90.01% in fault C, and 94.57% in fault D. For SMOTE, the performance is 89.72% in fault A, 93.08% in fault B, 97.56% in fault C, and 95.28% in fault D.  
For completeness, the confusion matrices are presented in Figure 13. All these matrices consider the 6000 test observations as per Table 2. For RF-i (Figure 13a), one can see a high number of misclassifications in non-healthy states due to the unbalanced training set. These misclassifications are strongly reduced (especially in the GAN-based scenarios) when enough data are generated and used for training.