# SCS-JPGD: Single-Channel-Signal Joint Projected Gradient Descent
## 4 Experiments and Results
### Analysis of Results  
In Figures 4 and 5, we present the comparison of vibration signals under four different operating conditions: 1730, 1750, 1772, and 1797. The signals under each condition include four types of faults: Normal, Ball Fault (ball), Inner Race Fault (InnerRace), and Outer Race Fault (OuterRace). These figures help us deeply analyze the changes in the raw signals and adversarial sample signals under different operating conditions and assess the impact of adversarial attacks on the model's performance. In Figure 4, the left subfigure (a) shows the vibration signal comparison under operating condition 1730. This condition typically represents signal characteristics under low-load conditions, with relatively smooth signals and smaller amplitudes. The signal features of the four fault types are distinctly distinguishable, with the Ball Fault (ball) and Inner Race Fault (InnerRace) signals exhibiting more significant fluctuations. The adversarial sample signals are similar to the raw signals, but some disturbances appear in specific regions, especially during the rise and fall phases of the signal, which could be caused by the adversarial attack. The right subfigure (b) shows the vibration signal under operating condition 1750. In this condition, the load slightly increases, and the signal exhibits more \begin{table}
\begin{tabular}{l c c} \hline \hline
**Model** & **Accuracy** & **Adversarial Test Accuracy** \\ \hline LeNet & 95.96\% & 60.20\% \\ AlexNet & 93.01\% & 56.76\% \\ ResNet-18 & 96.45\% & 64.36\% \\ CNN (ours) & 99.80\% & 69.47\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Test results of different architectures. Figure 4: Comparison of vibration signals under 1730 and 1750. (**a**) Comparison of vibration signals under 1730. (**b**) Comparison of vibration signals under 1750.  
complex variations with larger amplitudes and richer frequency components. Although there are some disturbances in the adversarial sample signals at certain details, they retain the main features of the four fault types and are able to differentiate the different fault types quite well. In Figure 5, the left subfigure (a) shows the vibration signals under operating condition 1772. In this condition, the signal exhibits characteristics under high-load conditions, with larger amplitudes and richer frequency components. The differences between the four fault types in the signal remain clear, especially in the fluctuations of the Ball Fault (ball) and Inner Race Fault (InnerRace). The disturbances in the adversarial sample signals are relatively weak, and the overall signal features are largely preserved. The right subfigure (b) shows the vibration signal under operating condition 1797. This condition represents a nearly full load, with more intense signal variations, containing more high-frequency components and amplitude changes. The adversarial sample signals show more significant fluctuations in this condition, especially in the high-frequency parts, where the disturbances are noticeable, but the basic features of the four fault types can still be distinguished. Figures 6 and 7 show the t-SNE plots of the baseline model and the adversarially trained model after 20 iterations of adversarial training, respectively. Figure 6 displays the results under clean data, while Figure 7 shows the results under adversarial samples. From Figure 6, it can be seen that some clusters initially overlap, but the classification performance is still acceptable. As adversarial training progresses, the clusters no longer overlap and are distinctly separated, demonstrating that, with adversarial training, the model improves in classifying the data as the epochs increase. In the adversarial sample testing process, we observed that initially, the overlap between clusters was severe, and the  
Figure 5: Comparison of vibration signals under 1772 and 1797. (**a**) Comparison of vibration signals under 1772. (**b**) Comparison of vibration signals under 1797.  
model hardly contributed to classification.