# Application of Lightweight Convolutional Neural Network for Damage Detection of Conveyor Belt
## 2 Principles and Methodology
### Network Structure and Improvement Methods  
MobileNet is an excellent lightweight deep neural network proposed by Google, which includes three versions of V1 [34], V2 [35], and V3 [45]. MobileNet V1 uses depthwise separable convolution instead of standard convolution to achieve feature extraction, which greatly reduces the number of parameters and calculations, making its calculations \(\frac{1}{N}+\frac{1}{D_{k}^{2}}\) times that of standard convolutions. When the input is an RGB image, and the size of the convolution kernel is 3 \(\times\) 3, the calculation amount can be reduced to about 1/9 of the standard convolution. The principle can refer to Figure 1 and Equations (1)-(4). At the same time, the channel number scaling adjustment factor \(\alpha\) and the input image resolution adjustment factor \(\rho\) were introduced to adjust the number of channels in each layer of the network and the input image resolution respectively, to further compress the computational effort, while the parameter amount or calculation amount of the model is positively correlated with \(\alpha^{2}\) and \(\rho^{2}\). The parameter calculation method of depthwise separable convolution and standard convolution can be based on Equations (1)-(4), and at the same time, according to Equation (5), the comparison of the parameters of the two can be obtained. \[N_{\rm 5-params} = \rm D_{k}\times D_{k}\times M\times N_{kernel} \tag{1}\] \[N_{\rm S-cal} = \rm D_{k}\times D_{k}\times M\times N_{kernel}\times D_{F}\times D _{F}\] (2) \[N_{\rm D-params} = D_{k}\times D_{k}\times M+\rm M\times N_{kernel}\] (3) \[N_{\rm D-cal} = D_{k}\times D_{k}\times M\times D_{F}\times D_{F}+\rm M\times N_{ kernel}\times D_{F}\times D_{F}\] (4) \[\frac{N_{D-\rm cal}}{N_{S-cal}} = \frac{D_{k}\times D_{k}\times M\times D_{F}\times D_{F}+\rm M \times N_{kernel}\times D_{F}\times D_{F}}{D_{k}\times D_{k}\times M\times N_{ kernel}\times D_{F}\times D_{F}}=\frac{1}{N_{\rm kernel}}+\frac{1}{D_{k}^{2}} \tag{5}\]  
In the formula, \(N_{\rm S-params}\), \(N_{\rm S-cal}\), means the number of parameters and calculation of standard convolution, \(N_{\rm D-params}\), \(N_{\rm D-cal}\), means the number of parameters and calculation of depthwise separable convolution. \(D_{k}\times D_{k}\times M\) is the kernel size, \(N_{\rm kernel}\) is the number of the kernel, \(D_{k}\times D_{k}\times M\) is the input size. MobilenetV2 continues to use depthwise separable convolution based on MobilenetV1, and uses an inverted residual connection similar to the residual network, as shown in Figure 2. Considering that a large amount of feature information cannot be extracted by applying a convolutional layer to filter low-dimensional tensors, MobilenetV2 uses an expansion convolution layer to obtain a large tensor, uses depthwise convolution to filter the data, and then uses a projection layer to reduce the tensor [35]. By adjusting the low-dimensional tensor, the parameter amount of MobilenetV2 is reduced to about 80% of V1, and the speed is increased by about 33%. Figure 1: The structure comparison of depthwise separable convolution and standard convolution: (**a**) structure of standard convolution (**b**) structure of depthwise separable convolution( It is assumed that the output feature map has the same spatial dimensions as the input and both feature maps are square). MobilenetV3 was designed mainly based on a combination of complementary search techniques, through a combination of hardware-aware network architecture search (NAS) complemented by the NetAdapt algorithm [45]. The former(NAS) is used to search the various modules of the network under the premise of limited calculation and parameter quantity, also called Block-wise Search, and the latter(NetAdapt) is used to fine-tune the network layer after each module is determined; At the same time, it continues the depthwise separable convolution of MobilenetV1 and the bottleneck with the residual structure of MobilenetV2.