# Multi-Scale Rolling Bearing Fault Diagnosis Method Based on Transfer Learning
## 3 Methods
### Overview of the Proposed Model's Architecture  
In practical bearing fault diagnosis applications, acquiring large-scale and comprehensively labeled datasets is often challenging. In this context, transfer learning emerges as an effective strategy, utilizing knowledge learned in the source domain (such as different types of bearings or datasets under various operating conditions) to significantly enhance the model performance in the target domain, even with limited data types. The primary advantage of this approach lies in enhancing the model's generalization capability, reducing the training time and computational resource requirements, and improving the adaptability to new application scenarios. Accordingly, this paper proposes a bearing fault diagnosis method based on transfer learning. Its overall architecture encompasses four key components: data acquisition, model pre-training, transfer, and the visualization of the fault diagnosis results, as illustrated in Figure 3. Specifically, in the data acquisition phase, the method initially involves the preprocessing of raw data collected by sensors, identifying bearing fault vibration signals under different operating conditions, and dividing the dataset, while defining the scope of the source and target domain data. Subsequently, the designed MBDCNet is used for pre-training on these data, during which the model learns and saves key weight parameters, laying a solid foundation for the subsequent transfer phase, as depicted in Figure 4.  
Subsequently, we migrate these parameters to the target domain and fine-tune them, as shown in Algorithm 1. Lastly, the fault diagnosis results are visualized for presentation. ```
0: configuration parameters: \(args\), number of fault types: \(types\)
0: the health state of the bearing. 1: Load datasets and divide target domain dataset into training and validation sets. 2: Load the model: \(model_{f}=MBDCNet(args)\); \(model_{c}=MBDCNet(args)\)
3: Load pre-trained parameters saved from the model. 4: Define the optimizer and learning rate. 5: Define the loss function. 6:for\(epoch=0\) to \(epochs-1\)do
7:for each batch in the dataset do
8: Compute loss function for the source domain: \(L_{s}=-\frac{1}{N}\sum\limits_{i=1}^{N}(1-p_{i})^{2}\log(p_{i})-\sum\limits_{ i=1}^{C}y_{i}\log(\hat{y_{i}}



Figure 3: Overall framework structure of the proposed model. ### Feature Extraction Method Based on MBDCNet

In our research, we develop a novel multi-branch convolutional neural network architecture named MBDCNet, optimized specifically for the task of bearing fault feature extraction. The essence of this architecture lies in its multi-branch parallel processing mechanism, where each branch independently captures and analyzes different levels of features in the data. This enables the network to comprehensively handle complex signals, enhancing its adaptability to the complexity and diversity of bearing fault signals. The core components of MBDCNet include the dynamic convolution-batch normalization-ReLU (DBR) block, which integrates a dynamic convolution layer to dynamically adjust weights according to the input signal's characteristics. It includes a batch normalization layer to reduce internal covariate shift, speeding up training, and a ReLU activation function to introduce non-linearity, boosting the model's ability to capture complex non-linear relationships. Additionally, the dynamic convolution-batch normalization (DB) block deepens the feature hierarchy with additional dynamic convolution and batch normalization steps, enhancing the model's sensitivity to subtle signal differences. The linear batch normalization-ReLU (LBR) block applies linear transformations to strengthen feature learning, uses batch normalization to stabilize the learning process, and incorporates a ReLU activation function to further enhance feature abstraction.