# Adaptive Multi-Channel Residual Shrinkage Networks for the Diagnosis of Multi-Fault Gearbox
## 3 Methodology  
### Proposed Adaptive Multi-Channel Residual Shrinkage Block  
(1) Channel attention mechanism: In the general convolution process, all feature information is uniformly extracted, so the representation information in the original signal is easily ignored in the noisy environment. This section describes the channel attention mechanism to improve the performance of the fault diagnosis model. The attention mechanism is added to the channel (convolutional kernel) dimension to obtain the significance of each channel through a fully connected layer (FC). Then weights are assigned to each channel according to the significance level so that the neural network pay attention to the information of a certain channel. This mechanism can promote the information channels that are useful for the current task and suppress the channels that are not very useful for the current task.  
This paragraph describes some specific operations of the attention mechanism. First, the size of the output data obtained after inputting data of size C \(\times\) W \(\times\) 1 to the two convolutional layers is unchanged, and the feature S of size C \(\times\) 1 \(\times\) 1 is obtained by global average pooling (GAP) compression. Then, feature S is divided into two branches, and in branch 1, the feature S does not undergo any transformation. In branch 2, feature S acquires channel-level weights through two FCs. The channel attention coefficients \(w_{c}\) are obtained after the sigmoid activation function as follows:  
\[w_{c}=\sigma(\text{FC}_{2}\cdot\text{ReLU}(\text{FC}_{1}\cdot\eta)) \tag{13}\]  
where \(\eta\) is the feature vector. Finally, as shown in Figure 1, the features from the two branches are multiplied to generate the channel attention feature \(S_{c}\).  
Figure 1: AMC-RSB, where the blue dotted line frame is the channel attention mechanism module.  
(2) Soft threshold: To reduce the noise and improve the diagnostic performance of the network, the basic block inserts a soft threshold function [32] to eliminate irrelevant features of the output through the attention mechanism module. The formula for the soft threshold function is expressed as follows:  
\[y=\begin{cases}\omega+T&\omega\leq-T,\\ 0&-T<\omega\leq T,\\ \omega-T&\omega\geq T.\end{cases} \tag{14}\]  
where \(\omega\) is the input value, and T is the threshold. The idea of a deep residual shrinkage network [7] is used to construct the threshold, which is automatically determined according to the inputs. The threshold value is calculated by a series of matrices from the outputs of two convolution layers and the channel attention mechanism module.  
(3) Adaptive multi-channel residual shrinkage block: The diagnostic model can resist interference, but it is not yet able to extract obvious features in fault signals. A maximum pooling branch is set at the input as a way to extract more obvious features of the input signal. Additionally, since each channel output feature has some ability to characterize the faulty features, weights are set in each branch. These weights are back-propagated to update the values adaptively based on the training of the model. The designed adaptive multi-channel residual shrinkage block (AMC-RSB) is shown in Figure 1.