# MTC-GAN Bearing Fault Diagnosis for Small Samples and Variable Operating Conditions
## 4 Experimental Validation
### Model Testing

Table 4: Datasets for the proposed fault diagnosis scheme. \begin{table}
\begin{tabular}{l c} \hline \hline \multicolumn{2}{l}{**Hyperparameter**} & **Value** \\ \hline Generator Learning Rate & 0.0002 \\ Discriminator Learning Rate & 0.0002 \\ Batch Size & 4 \\ Number of Epochs & 500 \\ Noise Dimension & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Hyperparameter settings for the MTC-GAN model. After confirming the initial accuracy of the discriminator under small sample imbalanced data conditions, additional training samples were generated using the generator of the MTC-GAN for data augmentation. The trained discriminators were extracted and directly applied to the test set for fault classification. Unlike traditional GANs, MTC-GAN does not combine the generated high-quality samples with real samples for additional classifier training after training is complete. Instead, it internally and dynamically inputs additional generated samples during the training process. As an example, the classification accuracy curve for bearing under the 1797 rpm operating condition is shown in Figure 7. The figure shows the number of samples generated by MTC-GAN in each training round after starting to generate extra generated samples and the specific impact of these samples on the accuracy of the final test set. As can be seen in Figure 7, after the MTC-GAN model is initially trained and reaches a steady state, the generator gradually acquires more data features. When the quality score of the data generated by the model reaches the agreed scoring threshold (MSE < 0.02, SSIM > 0.90), the model starts to generate high-quality additional samples. The introduction of additional samples begins after the model has steadily generated high-quality samples. This not only ensures the quality and diversity of the training data but also optimizes the model's adaptability and stability in complex data environments. As the number of samples added in each round increases, the accuracy of the model on the test set shows an upward trend. Specifically, when the number of additional samples generated per round is two, the model can achieve an accuracy of approximately 96% within the specified number of training rounds. When this number is increased to four, the accuracy further improves to about 98%. Although these increases are significant, they are not as rapid and stable as when the number of additional samples generated per round is six. With six additional samples per round, the model performs best on the test set, achieving 100% accuracy. Additionally, to further analyze the performance of the MTC-GAN model during training, Figure 8 shows the loss curves of the generator and discriminator. From the curves, it can be observed that in the early stages of training, the discriminator's loss drops rapidly while the generator's loss rises. This indicates that the discriminator is initially able to effectively distinguish between real and generated data, whereas the generator has not yet produced high-quality samples. As the training progresses, the generator's loss  
Figure 7: Test set accuracy curves with different numbers of additional generated samples at 1797 rpm. gradually decreases while the discriminator's loss increases slowly, suggesting that the generator is learning to create more realistic data and gradually deceiving the discriminator. After approximately 300 epochs, the loss values for both the generator and discriminator stabilize, indicating that the adversarial training has reached a relatively balanced state, with further convergence in the loss values. Around 350 epochs, the quality of the data generated by the generator reaches the pre-defined evaluation thresholds, and additional samples are generated. As more training samples are introduced, the generator learns to capture more diverse features and characteristics, reducing the discrepancy with the real data, leading to a rapid convergence of the loss, which then fluctuates within a smaller range.