## 3 Pressure Relief Hole Identification Model Based on Improved Faster R-CNN
### Design of Lightweight CNN  
In 2016, the SqueezeNet model was proposed by [PERSON] and [PERSON] It is a lightweight CNN which can reach the accuracy of the AlexNet level, while the parameters are only 1/50 of AlexNet, reducing the complexity of the network and ensuring the accuracy. The structure of the SqueezeNet model is shown in Figure 4. SqueezeNet starts from the convolution layer 1 (conv1) with a convolution kernel of 7 \(\times\) 7 and a step size of 2. Then, eight fire modules are set between convolution layer 1 (conv1) and convolution layer 10 (conv10). Each fire module contains two convolution layers, namely squeezer and expand. The convolution kernel of conv10 is 1 \(\times\) 1 and the step size is 1. After the convolution layer 10, there is a global average pooling layer, which is sent to the softmax layer after global average pooling. The softmax layer is used to classify the images and output the results. Among them, the max-pooling layer is inserted between conv1 and fire2, fire4, fire5, fire8, and fire9. The step size of this layer is uniformly set to 2, and the convolution kernel is set  
Figure 3: Generation model of a pressure relief hole image based on improved SinGAN.  
to \(3\times 3\). Before being sent to fire9 for processing, the size of the feature map is \(1/16\) of that before being sent to conv1.  
In order to improve the applicability of the SqueezeNet model to the pressure relief holes images in coal mines, this paper optimizes and adjusts its structure, and also designs an improved SqueezeNet network, as shown in Figure 5.  
Figure 4: Structure of the SqueezeNet model.  
Figure 5: Optimization of SqueezeNet network structure.  
The detailed optimization processes of SqueezeNet are as follows. The image input size is resized to a fixed scale. The side length of the convolution kernel of the first convolution layer is changed to 3, the sliding interval of the filter is 1, and the number of final output channels is modified to 64. conv2 is added after conv1, the convolution kernel size is also 3 \(\times\) 3, and the step size is 1. After the second convolution layer, the second fire module, the fourth fire module, and the eighth fire module, a maximum pooling layer is added, and the side length and step size of the convolution kernel are both 2. A ROI pooling layer is added after fire10, and then the fire11 and fire12 modules are added before the pooling layer. The original conv10 is replaced by fc13 (fc means full connection layer), fc14 is added after fc13, and then the full connection layers are added on the left and right, respectively. The left full connection layer is used for hole target classification, and the right full connection layer is used for location regression. In addition, a layer of Batch Normalization (BN) is added after each convolution layer (including the convolution layer in the fire module).  
The purpose of adding a BN layer is to normalize the data, as shown in Equation (5). After normalization, the data need to be translated and zoomed, as shown in Equation (6). When training the model, each batch of training should be based on the parameters of mini_batch, that is, each mini_batch parameter should be processed according to Equations (5) and (6).  
\[E[x]=\frac{1}{n}\sum_{i=1}^{n}x_{i}, \tag{3}\]  
\[Var[x]=\frac{1}{n}\sum_{i=1}^{n}(x_{i}-E[x])^{2} \tag{4}\]  
\[\hat{x}_{i}=\frac{x_{i}-E[x]}{\sqrt{Var[x]+\epsilon}} \tag{5}\]  
\[y_{i}=BN_{\gamma\hat{\beta}}(x_{i})=\gamma\hat{x}_{i}+\beta \tag{6}\]  
where \(n\) is the number of parameters of mini_batch, \(i\) is the index number of data, \(E[x]\) represents the average value, \(Var[x]\) represents the variance, \(\hat{x}_{i}\) is the data after BN operation, and \(y_{i}\) is the result of translation and reduction after BN operation. \(\beta\) and \(\gamma\) represent the learning parameters and \(\epsilon\) represents the subtle invariant. When \(\epsilon\) is ignored, the normalized data will be transformed into the standard normal distribution with a mean of 0 and a variance of 1.