# SCS-JPGD: Single-Channel-Signal Joint Projected Gradient Descent
## 4 Experiments and Results
### Experimental Results  
In this section, we analyze the classification results under four different operating conditions of the CWRU dataset. Specifically, 1730, 1750, 1772, and 1797 represent signal characteristics of the equipment at different speeds, covering various load and fault scenarios. The analysis includes accuracy rates for the raw data and adversarial samples. The experimental results show that the classifier trained with adversarial examples achieved an accuracy rate of over 95% on the test set, and its accuracy on adversarial samples remained above 60%, significantly outperforming the baseline model without adversarial training. Detailed results and comparisons with other adversarial models are presented in Table 2.  
A comparison of the experimental results clearly shows that the SCS-JPGD method significantly outperforms other methods in both classification accuracy and test accuracy on adversarial samples. The core advantage of the SCS-JPGD method lies in its adoption of joint PGD adversarial training, a widely used technique for generating adversarial samples that maximize the disruption of model output through multi-step optimization iterations. This method not only enhances the robustness of the model in the face of adversarial attacks but also ensures that it can effectively resist such attacks in real-world scenarios. Compared to baseline models under different conditions, the SCS-JPGD method shows substantial improvements in classification accuracy and adversarial sample test accuracy. For example, under condition 1730, the classification accuracy of the SCS-JPGD model is 90.34%, and the accuracy for adversarial samples is 66.72%, whereas the baseline model only achieves 79.34% and 4.43%, respectively. Similarly, under condition 1797, the SCS-JPGD model achieves 99.80% classification accuracy and 69.47% accuracy on adversarial samples, demonstrating the model's strong ability to resist adversarial perturbations. In contrast, traditional methods such as the CNN and LeNet models using FGSM, BIM, or PGD adversarial training exhibit poor robustness on adversarial samples. For instance, even with PGD adversarial training, the CNN model's accuracy on adversarial samples is \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameter** & **Value** \\ \hline Learning Rate & 0.003 \\ Training Epochs & 200 \\ Batch Size & 32 \\ Adversarial Training hyperparameters \(\epsilon\) & 0.009 \\ Adversarial Training hyperparameters \(\alpha\) & 0.001 \\ Adversarial Training Iterations & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model hyperparameter setup. only 41.15%, while the LeNet model achieves 58.91%, further confirming the superiority of our method. Additionally, the SCSJPGD method is particularly optimized for the characteristics of single-channel signals, which typically have lower feature dimensions and simpler structures. Existing adversarial attack defense methods are often designed for high-dimensional data or multi-channel signals, leading to suboptimal performance when applied to single-channel signals. SCS-JPGD, through the optimization of its network structure, effectively extracts useful features in low-dimensional signal spaces and maintains strong robustness against adversarial attacks. This targeted optimization ensures that SCS-JPGD achieves significantly better defense performance in simple signals compared to traditional methods. The experimental results presented in Table 2 fully illustrate this advantage. In each condition, the adversarial sample accuracy of the SCS-JPGD method improves by 10% to 20% compared to the baseline models and by over 60% compared to the baseline results without adversarial training, providing strong evidence for the effectiveness and feasibility of this adversarial training approach. These results demonstrate that the SCS-JPGD method has significant advantages in enhancing the robustness of fault diagnosis systems to external perturbations, making it a promising solution.