# Multi-Scale Rolling Bearing Fault Diagnosis Method Based on Transfer Learning
## 3 Methods
### Overview of the Proposed Model's Architecture
The linear batch normalization-Sigmoid (LBS) block combines a linear layer with batch normalization to fine-tune the feature weights and employs a Sigmoid activation function in the final decision layer to output the probability of fault presence. Pooling layers use max pooling and average pooling to downsample features, aiming to reduce the computational load while preserving key feature information. This ensures that the network maintains sensitivity to important features even after dimension reduction. The structure of MBDCNet is illustrated in Figure 5, primarily comprising three branches. The top branch of the network includes two DBR blocks and a Maxpool layer, tasked with extracting primary features from the input data and emphasizing key features through downsampling. The middle branch starts with a DBR block, uses a DB block for smooth feature extraction, and adds the output of the DB block to the original input of the DBR block, forming a residual connection. This design allows the original features to bypass the processing of two layers and flow directly to the downstream components, helping to alleviate the vanishing gradient problem while preserving the initial feature information. The results are then divided into two pathways: one passes directly through

Figure 4: The pre-training implementation process. a ReLU activation, followed by a DBR block and a DB block, and finally another ReLU activation, each step refining and strengthening the feature representation. The other pathway travels through a DB block, followed by an LBR block and an LBS block, and finally combines with the results of the first path through a weighted sum operation. Another ReLU activation ensures the integration and enhancement of non-linear features, generating the final output for this branch. This structure enables the middle branch to merge features from different processing stages, efficiently analyzing and representing complex signals through residual connections and subsequent feature combinations--vital for bearing fault detection. The bottom branch consists of a DBR block and a Maxpool layer, also focusing on the capture and downsampling of basic features. After processing across the branches, features undergo averaging in an Avgpool layer to integrate a broad range of contextual information, followed by a ReLU activation for additional non-linearity. Then, a linear layer maps the high-dimensional features to the output space, preparing for the final output, which may signify the results of classification or regression tasks. The primary advantage of this multi-branch structure lies in its ability to facilitate collaborative work among different branches. Each branch, while maintaining its unique characteristics, collectively enhances the overall feature extraction capability of the network, and MBDCNet provides robust support for the comprehensive analysis of bearing fault signals through its multi-branch structure and detailed feature learning strategy. Figure 5 clearly demonstrates the hierarchical structure of MBDCNet and the flow of information between its multiple branches. This visual representation not only aids in understanding the unique function of each branch but also shows how they work together to boost the overall performance of the network. In our experimental validation, we will comprehensively assess the performance of MBDCNet on bearing fault datasets, verifying its effectiveness and superiority in practical applications for fault diagnosis tasks. A key feature of the dynamic convolution network proposed in this article is the dynamic generation of convolutional kernel weights through a specially designed fully connected neural network, referred to as \(weight_{net}\), enabling adaptive convolution operations. In this neural network, the channel-wise mean of the input sequence is provided to \(weight_{net}\), the design that aids in extracting the overall features of the input sequence. The \(weight_{net}\) comprises two linear layers and an activation function, as shown in Equation (2).