## 4 Results
### Sample Generation and Evaluation  
In this section, we use the training set in Table 4 to train the ACGAN-SN model. During the training process, the hyperparameters are set as follows: 3000 epochs, learning rate of 0.0002, size 10 batch size, the optimizer is Adam, and the coefficients used for computing the running averages of the gradient and its square are 0.5 and 0.999, respectively. First, the original time\(-\)domain signal is converted into a frequency\(-\)domain signal through FFT, the signal length is reduced from 2048 to 1024 points and then reshaped into a 32 \(\times\) 32 grayscale matrix, and 32 \(\times\) 32 is used as the input of the discriminator and the output size of the generator. Then, the set parameters and data are used to train the ACGAN-SN. Figure 6 shows the transformation curve of the loss function of the discriminator and the generator during the training process, and Figure 7 shows the transformation curve of the classification accuracy of the discriminator and the generator. From the loss results in Figure 6, it can be seen that the discriminator and generator begin to show a decreasing trend of loss after 250 epochs and maintain a steady state between 1000 and 3000 epochs. On the whole, the model reaches the Nash equilibrium at approximately 1000 epochs, which represents the equilibrium state of the generator and discriminator confrontation game at this time. We believe that the generator at 3000 epochs achieves the level of falsehood, that is, it already has the ability to synthesize high-quality fault sample data. It can be seen from the accuracy transformation diagram in Figure 7 that the classification accuracy of the discriminator and generator during the training process fluctuates and rises, which corresponds to the trend in Figure 6. It is proven that the data synthesized by the generator at this time have similar characteristics to the original data, so that the classifier can distinguish the labels corresponding to the synthetic data and the real data. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Sample Class**} & \multicolumn{2}{c}{**Damage**} & \multirow{2}{*}{**Sample Length**} & \multirow{2}{*}{**Training Set**} & \multirow{2}{*}{**Testing Set**} & \multirow{2}{*}{**Label**} \\  & \multicolumn{2}{c}{**Diameter**} & & & & & \\  & \multicolumn{2}{c}{**(Inches)**} & & & & & \\ \hline Majority & Normal & — & 2048 & 100 & 100 & 0 \\ \hline \multirow{8}{*}{Majority} & Ball1 & B0.007 & 2048 & 10 & 100 & 1 \\  & Ball2 & B0.014 & 2048 & 10 & 100 & 2 \\  & Ball3 & B0.021 & 2048 & 10 & 100 & 3 \\  & Inner1 & 10.007 & 2048 & 10 & 100 & 4 \\  & Inner2 & 10.014 & 2048 & 10 & 100 & 5 \\  & Inner3 & 10.021 & 2048 & 10 & 100 & 6 \\  & Outer1 & 00.007 & 2048 & 10 & 100 & 7 \\  & Outer2 & 00.014 & 2048 & 10 & 100 & 8 \\  & Outer3 & 00.021 & 2048 & 10 & 100 & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The details of the bearing dataset. Figure 6: The discrimination loss and generation loss curve of the ACGAN-SN model. The Wasserstein distance is often used to measure the similarity between two distributions, so this paper uses this metric to indirectly observe the training process of the model. The Wasserstein distance transformation diagram is shown in Figure 8. We can see that the Wasserstein distance from 1000 epochs gradually tends to 0. The 10 types of fault data synthesized at this time are compared with the real data, as shown in Figure 9, where the blue curve is the synthetic data and the orange curve is the real data. We can see that the synthetic data are very similar to the real data. In particular, some frequency spectrum lines representing fault features correspond to the real values, which indicates that the synthetic data have some fault frequencies and their multipliers and plays a key role in whether the signal is classified correctly or not.