## 4 Fault Diagnosis Results
### Comparative Analysis  
To demonstrate that the WGAN model is the best solution for addressing the data imbalance problem in the vibration signal, a comparative analysis was conducted between the WGAN model and the other methods of ADASYN, SI, and GAN. Table 5 describes the model parameters of the GAN model. The same structure of the discriminator and generator as the WGAN model was used and the corresponding parameters were adjusted by trial and error. Through the parameter optimizing results, it was observed that even though the same discriminator and critic models were utilized, the parameters were completely different according to the type of loss function. Figure 10: (a) Fault diagnosis results for the experimental data only. (b) Fault diagnosis results for the synthetic data. Table 6 shows the number of synthetic data for each method. Basically, the ADASYN algorithm is an oversampling method, which means that it can only generate minority class data, the D1 and D2 cases in this research. Therefore, the total amount of data is different from the other methods. For all the methods, synthetic data instances were randomly divided into 60% and 40% for training and validation while maintaining the proportion of each class. Table 7 shows the fault diagnosis results for the same test dataset as Section 4.2. The accuracy of the WGAN model was the highest result at 91.96%. Also, the experimental data-only case has relatively higher accuracy than the other methods. As mentioned above, this originates from the data imbalance. The majority of the class data was classified properly; thus, the accuracy itself turned out to be high. For precision, ADASYN was the highest, at 77.80%, with a difference of 3.70% compared to the WGAN model. For sensitivity, WGAN had the highest value at 94.39%, which is 3.11% higher than the ADASYN. By comparing the precision and sensitivity of the ADASYN and WGAN, WGAN seems to have a better ability to identify fault states properly. The health state data for ADASYN may be classified more properly than that for WGAN, and this point brought higher precision in ADASYN but lower performance in sensitivity. For the F1 score, ADASYN and WGAN were the highest at 0.81. For overall analysis, the synthetic data generated with SI seems not to be proper for this research because all evaluation metrics were much lower than the other methods. In the case of ADASYN, because of the characteristic of oversampling, real data are contained in the training and validation datasets, while the rest of them are only composed of synthetic data. This could increase the fault diagnosis performance compared with the others. For the ADASYN, GAN, and WGAN cases, the evaluation metrics increased significantly compared to the experimental data case, but the WGAN model showed the best evaluation metrics, which means that the WGAN model can generate signals that contain dynamic characteristics that are the same as real signals. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Healthy** & **Delamination 1** & **Delamination 2** \\ \hline Experimental data only & 800 & 48 & 48 \\ ADASYN & 800 & 793 & 798 \\ SI & 3000 & 3000 & 3000 \\ GAN & 3000 & 3000 & 3000 \\ WGAN & 3000 & 3000 & 3000 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The number of synthetic data for training and validation using the different methods. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Accuracy (\%)** & **Precision (\%)** & **Sensitivity (\%)** & **F1 Score** \\ \hline Experimental data only & 89.29 & 29.76 & 33.33 & 0.31 \\ ADASYN & 90.63 & 77.80 & 91.28 & 0.81 \\ SI & 5.80 & 35.13 & 35.00 & 0.04 \\ GAN & 86.61 & 53.83 & 55.83 & 0.55 \\ WGAN & 91.96 & 74.10 & 94.39 & 0.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Fault diagnosis result of each oversampling and augmentation method.