## 3 The Proposed New Method MDA-LETCN
### Temporal Feature Extraction Module  
In this paper, the temporal convolution structure is used to extract the time information of generator bearings' degradation process. TCN is a network structure based on CNN, which is composed of causal convolution, dilated convolution, and residual modules, which can learn the temporal features of time series in parallel and avoid leakage. Figure 5 shows the structure of the causal dilated convolutions (CDC) network, which is composed of causal convolution and dilated convolution. Causal convolution learns temporal features based on current and historical information to predict the value at the next moment, that is, using \(\{x_{1},x_{2},\cdots,x_{t}\}\) to predict the value of \(x_{t+1}\). The formula is:  
\[p(x)=\prod_{t=1}^{T}p\{x_{t+1}|x_{1},x_{2},\cdots,x_{t}\} \tag{6}\]  
If only the causal convolution learning temporal feature is relied on, the model needs to build deeper and have a larger convolution kernel size to increase the receptive field to achieve the ideal effect. This results in increased model complexity. To solve this problem,  
Figure 5: MDA-LETCN network structure diagram. the dilated convolution and the combination with causal convolution can greatly reduce the complexity of the model. The receptive field for CDC with expansion rate \(d\) is:  
\[k^{l}=(d-1)\cdot\left(k^{l}_{c}-1\right)+k^{l}_{c} \tag{7}\]  
where \(k^{l}_{c}\) is the convolution kernel of \(l\)-layer causal convolution and \(k^{l}\) is the receptive field size of \(l\)-layer CDC. The final output value of the model depends on the coverage of the model. In order to ensure the low complexity and large receptive field of the model, with each additional layer, the expansion rate of the current layer will increase at the rate of \(b\), and the receptive field width of each layer can also be expressed as:  
\[w=1+\sum_{l=0}^{L-1}{(k-1)\cdot b^{l}}=1+(k-1)\frac{b^{l}-1}{b-1} \tag{8}\]  
where the dilated rate \(d=b^{l}\) and \(l\) represents the number of layers in the model. When inputting layers, \(l=0\) and \(k\) is the size of the convolutional kernel. It is worth noting that dilated convolution can cause voids in the receptive field. To prevent information loss, a residual structure as shown in Figure 6 is added to TCN. This residual structure includes two layers of CDC. After each CDC, the weights are normalized using weight normalization and the ReLU function is used as the activation function to prevent model overfitting. Finally, the result obtained after \(1\times 1\) convolution is added to the results of the two CDC, and the output is:  
\[out=\text{ReLU}(x+f(x)) \tag{9}\]  
where \(f(. )\) represents two CDC-WN-ReLU-Dropout operation transformations. This residual structure not only ensures the integrity of information but also extracts sufficiently long time series features. TCN utilizes CDC and residual structure to extract long-term temporal features of time series but ignores the importance of local features. In this paper, MDA-LETCN adds a local enhancement module to the residual module of TCN, which pays attention to local features while extracting long-term historical information and improves the prediction accuracy of model RUL. LETCN adds a local information enhancement module in the residual module to improve the original \(1\times 1\) convolution to the structure shown in Figure 7. First, the  
Figure 6: CDC structure diagram. features of input signal \(x\) are extracted by the convolution operation with convolution kernels of 3, 5, and 7, respectively. \[o_{i}=conv_{i}(x),i=1,2,3 \tag{10}\]  
Then, the three output signals are spliced according to dimension:  
\[o=\text{concat}(o_{1}+o_{2}+o_{3}) \tag{11}\]  
Next, the features of the three channels are compressed by 1 \(\times\) 1 convolution kernel and integrated by activation function to obtain the weight of each time point:  
\[w=\text{Sigmoid}(conv_{1\times 1}(o)) \tag{12}\]  
Finally, the output of the LERES is:  
Figure 5:0  
The model uses mean square error (MSE) as the loss function, i.e. :  
Figure 5:1