# SCS-JPGD: Single-Channel-Signal Joint Projected Gradient Descent
## 3 Methods  
In modern fault diagnosis systems, the interference from external adversarial attack signals has become a critical factor affecting model performance. Especially in high-risk environments, such interference may lead to severe misjudgments, thus impacting the accuracy and reliability of fault diagnosis. The vulnerability of models to adversarial attacks is often closely related to the distribution characteristics of the data, particularly when there are poor or uneven data distributions in high-dimensional spaces, where models tend to exhibit instability when faced with small perturbations. Existing diagnostic methods often lack sufficient robustness in the face of adversarial attacks, making it challenging to effectively cope with complex attack patterns. Most current adversarial attack defense methods are designed for high-dimensional or multi-channel signals, and traditional methods may fail to effectively address adversarial attacks when applied to single-channel signals, which typically exhibit simpler structures and lower feature dimensions. To address this issue, this paper proposes a Joint PGD Adversarial Training Method for Single-Channel Signals (SCS-JPGD), which combines adversarial sample training with gradient optimization techniques to enhance the model's robustness when facing external attack signals. Figure 1 illustrates the overall framework proposed in this work. The model network structure and SPGD attack model operations are shown in Figure 2. The design of this neural network model aims to strengthen the defense capabilities against adversarial attacks, particularly optimized for single-channel signals. When processing such signals, which typically have relatively simple input data and low feature dimensions, the model must effectively extract hierarchical features from the signals while maintaining strong robustness to counteract adversarial sample attacks. To achieve this, the model extracts multi-level features of the input signal through three convolutional layers. In the case of single-channel signals, the convolutional layers effectively capture local patterns and spectral features within the signal, which are crucial for subsequent classification tasks. Each convolutional layer is followed by a batch normalization layer to stabilize the training process, ensure stable gradient propagation, and enhance training convergence speed. The ReLU activation function introduces nonlinearity, enabling the model to capture complex signal features. To prevent overfitting and  
Figure 1: Overall Methodology Framework Design Diagram. improve the model's generalization ability, especially when the dataset is small, a dropout layer is applied after each convolutional layer. The dropout strategy randomly drops some of the connections between neurons, effectively mitigating overfitting and enhancing the model's robustness when facing unseen adversarial samples. Additionally, the max-pooling operation reduces the size of the feature maps, decreasing computational complexity while improving the model's tolerance to input signal perturbations, further strengthening the defense against adversarial attacks. The model flattens the output of the convolutional layers into a one-dimensional vector and then passes it through fully connected layers for the final classification prediction. This design ensures that the features extracted from the convolutional layers are effectively mapped to specific class labels, providing predictions for four different categories. Overall, this network structure, by integrating the convolutional layers, batch normalization, dropout, and pooling operations, effectively enhances the feature representation capability of single-channel signals and strengthens the model's defense capabilities in adversarial attack environments.