## 3 Fault Diagnosis Transfer Model
### Basic Theory of CRU  
Following feature extraction by the \(y\)th feature extraction module, the output is then input into the channel reconstruction unit (CRU). The CRU depicted in Figure 3 was proposed by [PERSON] et al. (2017). Unlike standard convolution, the CRU employs splitting, transforming, and reconstruction strategies.  
The first step is the splitting strategy, which divides the pass into two parts, the \(\alpha C\) and \((1-\alpha)C\) channels, as depicted in Figure 3. Here, \(0<\alpha<1\) is the splitting ratio.  
Figure 3: Structure of CRU.  
The channels of feature mapping are subsequently compressed using \(1\times 1\) convolution to improve the efficiency of computation. Following splitting, the feature channel is squeezed, and the squeezing ratio \(\tau\) is 2. Following splitting and squeezing, the feature \(X=p\left(BN\left(X_{D,y_{cov}}^{i}\right)\right)\) from the feature module is divided into the upper portion \(X_{up}\) and the lower portion \(X_{low}\), and then enters into the transformation stage, where \(X_{up}\) is inputted into the upper transformation stage. In the upper transformation stage, group-by-group convolution (GWC) [28] and point-by-point convolution (PWC) are used instead of a convolution operation to extract deep information. The \(k\times 1\) GWC and \(1\times 1\) PWC operations are performed on the upper part of the output. After that, the outputs are summed to form the merged feature \(Y_{1}\). The upper transform stage can be expressed by Equation (8).  
\[Y_{1}=GX_{up}+P_{1}X_{up} \tag{8}\]  
where \(G\in R^{\frac{4G}{\tau}\times k\times 1\times c}\) and \(P_{1}\in R^{\frac{4G}{\tau}\times 1\times 1\times c}\) are the relevant parameters of GWC and PWC.  
\(X_{low}\) is input into the lower transform stage to generate features with shallow hidden details using the \(1\times 1\) PWC operation. This serves as a complement to the rich features generated earlier. Utilizing \(X_{low}\) allows for the generation of additional features without incurring extra costs. Finally, the newly generated features and the reused features are concatenated to form the feature \(Y_{2}\). The lower transformation stage formula is shown in Equation (9):  
\[Y_{2}=P_{2}X_{low}\cup X_{low} \tag{9}\]  
where \(P_{2}\in R^{\frac{(1-a)C}{\tau}\times 1\times 1\times(1-\frac{1-a}{\tau})c}\) represents the relevant parameters of the lower input PWC.  
After the transformation, the output features \(Y_{1}\), \(Y_{2}\) of the upper and lower transformation stages are fused using the simplified Sknet method [29], as depicted in the fusion section in Figure 3. Global average pooling is applied to collect the global spatial message for \(S_{m}\), which is computed as in Equation (10).  
\[S_{m}=Pooling(Y_{m})=\frac{1}{L}\underset{i=1}{\overset{L}{\sum}}Y_{c}(i),m=1,2 \tag{10}\]  
\[\beta_{1}=\frac{e^{s_{1}}}{e^{s_{1}+e^{s_{2}}}},\beta_{2}=\frac{e^{s_{2}}}{e^ {s_{1}+e^{s_{2}}}},\beta_{1}+\beta_{2}=1 \tag{11}\]  
The global up-channel descriptions \(S_{1}\) and global down-channel descriptions \(S_{2}\) are then stacked together, and a channelized soft attention operation is used to generate the feature importance vectors \(\beta_{1}\) and \(\beta_{2}\). Finally, the up-channel descriptions \(S_{1}\) are combined with the down-channel descriptions \(S_{2}\) by combining the upper feature \(Y_{1}\) and lower feature \(Y_{2}\) by channel to obtain the channelized refinement feature \(Y\), as shown in Equations (11) and (12).  
\[Y=\beta_{1}Y_{1}+\beta_{2}Y_{2} \tag{12}\]  
The result of the final processing of the features input from the feature module by the channel reconstruction unit can be expressed as Equation (13).  
\[X_{y,out}^{i}=CRU\Big{[}p\Big{(}BN\Big{(}X_{D,y_{cov}}^{i}\Big{)}\Big{)}\Big{]} \tag{13}\]