## 3 Proposed Method
### Lightweight Convolution and Attention Network for Damage Detection
#### 3.2.2 Lightweight Feature-Extraction Module  
As shown in Figure 4, following the convolution layer, there are three designed LFE modules, and the proposed LFE module is constructed by three main parts, which are group convolution, depthwise separable convolution, and channel shuffle. Different convolution operations are shown in Figure 5. The solid line between the input and output features represents the convolution operation. Suppose the input features are \(\mathbf{F}_{1}\in\mathbb{R}^{C_{1}\times W_{1}\times H_{1}}\), The output features are \(\mathbf{F}_{2}\in\mathbb{R}^{C_{2}\times W_{2}\times H_{2}}\), and only a single convolution kernel of size \(\mathbf{K}\in\mathbb{R}^{C_{2}\times k\times k}\) is used. The bias of the convolution layer is set to false. Then, the parameters of conventional convolution in Figure 5a is  
\[params_{cc}=k\times k\times C_{1}\times C_{2}=k^{2}C_{1}C_{2}, \tag{2}\]  
The floating-point operations (FLOPs) are  
\[FLOPs_{cc}=(2\times k^{2}\times C_{1}-1)\times C_{2}\times W_{2}\times H_{2}=(2 k^{2}C_{1}-1)C_{2}W_{2}H_{2}. \tag{3}\]  
Figure 4: The architecture of LCANet for damage recognition. Figure 5: Mechanism of different convolution and channel shuffling. For the group convolution in Figure 5b, the input features are divided into \(g\) groups, and the number of convolution kernels in each group is equal to the number of output channels in its group. Thus, the number of group convolution parameters is  
\[params_{gc}\&=k\times k\times\frac{C_{1}}{g}\times\frac{C_{2}}{g}\times g=\frac{k ^{2}C_{1}C_{2}}{g}, \tag{4}\]  
and its floating-point operation (FLOP) is  
\[FLOPs_{gc}=(2\times k^{2}\times\frac{C_{1}}{g}-1)\times\frac{C_{2}}{g}\times g \times W_{2}\times H_{2}=(2k^{2}\frac{C_{1}}{g}-1)C_{2}W_{2}H_{2}, \tag{5}\]  
The parameters of group convolution are \(\frac{1}{g}\) of those of conventional convolution operation. Furthermore, when the \(g\) of group convolution is equal to the number of input and output channels \(C_{1}=C_{2}=g\), it would become depthwise convolution as shown in Figure 5c. The number of depthwise convolution parameters is  
\[params_{dc}\&=k\times k\times\frac{C_{1}}{g}\times\frac{C_{2}}{g}\times g=k^{ 2}C_{1}, \tag{6}\]  
and  
\[FLOPs_{dc}=(2\times k^{2}\times\frac{C_{1}}{g}-1)\times\frac{C_{2}}{g}\times g \times W_{2}\times H_{2}=(2k^{2}-1)C_{1}W_{2}H_{2}. \tag{7}\]  
The processing of features by a conventional convolution can be divided into a spatial part and a channel part. The spatial part is represented by the variation of feature map length and width, and the channel part is represented by the increase or decrease of the number of channels. Depthwise convolution and group convolution can deal with the spatial part and the channel part, respectively. Therefore, these two convolutions comprise a depthwise separable convolution that can replace the conventional convolution as shown in Figure 5d. The number of depthwise separable convolution parameters is  
\[params_{dc}\&=\frac{k^{2}C_{1}C_{2}}{g}+1\times 1\times C_{1}=\frac{k^{2}C_{1}C_{ 2}}{g}+C_{1}, \tag{8}\]  
where \(1\times 1\) is the convolution kernel for group convolution. In the proposed LFE module, we use two group convolutions and a depthwise convolution as shown in \[params_{cc}=k\times k\times C_{1}\times C_{2}=k^{2}C_{1}C_{2}, \tag{2}\]0 Moreover, the kernel of depthwise convolution is set to \(3\times 3\) and the convolution kernel of group convolutions is set to \(1\times 1\). The input feature is \(\mathbf{F}_{CC}\in\mathbb{R}^{C_{1}\times W_{1}\times H_{1}}\), and the convolution layer can be represented as  
\[params_{cc}=k\times k\times C_{1}\times C_{2}=k^{2}C_{1}C_{2}, \tag{2}\]1  
where \(\mathbf{F}_{LC}\in\mathbb{R}^{C_{2}\times\frac{W_{1}}{2}\times\frac{H_{1}}{2}}\) is the output of the lightweight convolution layer. In addition, although the use of group convolution can make the model lighter, but the grouping mechanism leads to the inability to communicate the channels between groups, which would further affect the network learning ability.