## 4 Design of CNN-BLS Tremor Filter
### Algorithm of CNN-BLS
#### 4.1.2 Structure of Our CNN-BLS Network  
In Figure 7, the internal algorithm of the designed tremor filter is shown and the algorithm of our designed network is given in Algorithm 1, where \(\gamma\) represents the number of feature maps, \(\delta\) represents the number of enhancement nodes and \(f^{(\gamma)}(\cdot)\) represents the output of the \(\gamma\)-th pooling layer. We point out that the primary network framework is the  
Figure 6: Network structure of BLS. BLS. Since the original BLS does not extract time feature sequences well, the network fuses a simple CNN with a lateral connection approach [38]. ```
Input: Training data \(G=[x,y,z]\); Number of feature nodes and enhancement nodes \(N_{1}\), \(N_{2}\); Number of additional feature mapping nodes and additional enhancement nodes \(m_{1}\), \(m_{2}\). Output: The weight parameters of output layer \(W\). Preprocess data \(G\); foreach\(i=1\); \(i\leq\gamma\)do  Calculate the feature sequences by Equation (15);  Set the feature node layer \(Z^{\gamma}=[Z_{1},\ldots,Z_{\gamma}]\); foreach\(j=1\); \(j\leq\delta\)do  Random \(W_{c_{j}}\) and \(\beta_{c_{j}}\); calculate the enhancement nodes by Equation (17);  Obtain the input layer \(I\) by Equation (18);  Obtain the connection weights by Equation (19); while the training error threshold is not satisfied do if\(m_{1}\) feature nodes are addedthen  Calculate \(\Xi_{\gamma+1}=f^{(\gamma+1)}(GW_{conv_{\gamma+1}})\); Random \(\Delta W_{i}\), \(\Delta\beta_{i}\), \(i=1,\ldots,\delta\);  Calculate \(\Delta H_{\gamma+1}\) and \(I\!I_{\gamma+1}\) by Equations (21) and (22); Update \(\big{(}I\!I_{\gamma+1}\big{)}^{+}\) and \(W_{\gamma+1}\) by Equations (23) and (25); \(\gamma=\gamma+1\); if\(m_{2}\) enhancement nodes are addedthen  Random \(W_{c_{\delta+1}}\), \(\beta_{c_{\delta+1}}\); Obtain the input layer \(I\!I^{\delta+1}\) by Equation (26); Update \(W^{\delta+1}\) by Equation (27); \(\delta=\delta+1\);
```  
**Algorithm 1**Convolutional Broad Learning Filter Algorithm: Increment of Feature Mapping Nodes and Enhancement Nodes. The input data \(G=[x,y,z]\) are sent to the convolutional network layer, which contains \(\gamma\) convolution and pooling process and can yield some feature sequences concerning the input. In Figure 8, the convolution and pooling operation process is given. Firstly, the input time series can form the feature maps. The process uses auto-padding to generate a \(3\times 3\) feature map of the same size as the convolution kernel. Then, the feature map can  
Figure 7: Network structure of CNN-BLS. be mapped as feature series based on the max pooling. Finally, through the process of convolution and pooling, the \(i\)-th feature sequence \(\vec{z_{i}}\) is represented as  
\[\vec{z_{i}}=f^{(i)}(GW_{conv_{i}}),i=1,\ldots,\gamma, \tag{15}\]  
where \(W_{conv_{i}}\) is the kernel weight of the i-th convolution layer and \(f^{(i)}(\cdot)\) represents the output of the \(i\)-th pooling layer. Denote \(\gamma\) feature sequences as network feature nodes, and they are written as  
\[Z^{\gamma}=[\vec{z_{1}},\ldots,\vec{z_{\gamma}}]=[Z_{1},\ldots,Z_{\gamma}]. \tag{16}\]  
Similar to the Equations (10)-(14), the \(\delta\) enhancement nodes can be generated by \(Z^{\gamma}\) and they can be written as  
\[H_{j}=\xi\Big{(}Z^{\gamma}W_{ej}+\beta_{ej}\Big{)},\quad j=1,\ldots,\delta. \tag{17}\]  
Our designed network input layer can be written as  
\[I\!I=\big{[}\;Z_{i}\;|\;H_{j}\;\big{]},\;i=1,\ldots,\gamma,\,j=1,\ldots,\delta. \tag{18}\]  
We have  
\[W=(\lambda E+(I\!I)^{T}I\!I)^{-1}(I\!I)^{T}Y. \tag{19}\]  
**Remark 2**. : _We point out that the BLS filter shows the capacity to cancel tremor is unpowerful because the feature extraction part may not effectively obtain corresponding feature maps. Hence, the above work shows our employed CNN to replace the SAE of BLS._  
To enrich the feature extraction process of the network, we propose an approach concerning multi-scale extraction. In other words, it can be defined as a feature fusion method.