## 2 Deep Learning Based Underground Pipeline Target Recognition Using 3-Dimensional GPR Data
### Deep Learning Model  
#### 2.4.1 2.5D-CNN  
Nowadays, deep learning is developing rapidly, and various neural network structures are emerging one after another, but these structures often take 2D images as input. For three-dimensional images, in order to effectively use the mature deep learning neural network structures, the three-dimensional ground-penetrating radar data of multiple acquisition channels in parallel can be equated into multiple color channels as in the case of RGB three-channel color images, and the convolution kernels with the same depth as the channels are used for feature extraction and then accumulated in each layer, as shown in Figure 9. Since this approach still follows the pattern of 2D images for feature extraction, this approach is denoted as 2.5D-CNN to distinguish it from 2D-CNN and 3D-CNN.  
In this paper, we refer to the multilayer network structure of AlexNet, which is widely used in image classification and recognition, and improve it by adapting the 2.5D-CNN neural network structure as shown in Figure 10.  
A single 3D dataset with a size of (20, 40, 45) is used as the input, and the first layer of 8 (3, 3) convolution kernels is used to perform the 2D convolution operation. Then batch normalization is applied to normalize each batch of training data, and then the ReLU activation function is used to complete the nonlinear transformation of the data. The second layer is a two-dimensional convolution operation with 16 (3, 3) convolution kernels, also using batch normalization and the ReLU activation function and a (2, 2) maximum pooling operation. The third layer is a 2-D convolution operation with 32 (3, 3) convolution kernels, and the rest of the parameters and steps are the same as in the first layer. The fourth layer is a 2-D convolution operation with 64 (3, 3) convolution kernels, using the same batch normalization, ReLU activation function, and pooling as in the second layer, and a 0.2 Dropout, which randomly removes some of the hidden neurons during training to reduce training time and overfitting. The extracted features are then flattened by the Flatten layer and fed into the next layer of the fully connected network, which is output by Softmax classification.  
After validation, the training hyperparameters are adjusted to a Batch Size of 10, with 10 training iterations and a learning rate of 0.0001. The previously generated dataset is used,  
Figure 10: Neural network structure adopted by 2.5D-CNN.  
Figure 9: Feature extraction with 2.5D-CNN convolutional kernel.  
with four classifications: A longitudinal pipeline, a transverse pipeline, an underground cavity, and no target. The training and validation sets were assigned in the ratio of 4:1, and the recognition accuracy and loss curves obtained from the iterations are shown in Figure 11. It can be seen that the accuracy and loss function gradually stabilize after four training iterations, and the training and validation results are basically consistent without any obvious overfitting.  
The model parameters of 2.5D-CNN iterations of up to 10 cycles are taken to test the recognition of real data, as shown in Figure 12. For visualization, the confusion matrix of real and predicted labels is represented in the form of a heat map, and the four classifications (longitudinal pipeline, transverse pipeline, void, and no target) are replaced by labels 0 to 3, respectively. It can be seen that there are 18 misclassifications among 416 data samples. Four samples of classification 0 (longitudinal pipeline) are misidentified as classification 1 (transverse pipeline) and one sample is misidentified as classification 3 (void); six samples of classification 3 (void) are misidentified as classification 0 (longitudinal pipeline) and seven samples are misidentified as classification 1 (transverse pipeline).