## 3 Tunnel Secondary Lining Recognition and Thickness Estimation Model
The architecture of CBAM is depicted in Figure 4. In contrast to the SE (Squeeze-and-Excitation) module, which models only inter-channel dependencies, CBAM concurrently attends to both channel and spatial dimensions, offering superior adaptability for GPR imaging tasks. Furthermore, CBAM features a compact structure and significantly lower computational overhead compared to recent Transformer-based attention mechanisms, making it more suitable for real-time applications with minimal impact on inference latency. In addition, CBAM has been extensively applied across various image classification and object detection benchmarks, demonstrating significant performance improvements. For instance, in the task of marine debris detection, researchers incorporated CBAM into the YOLOv7 model and compared its performance with lightweight coordinate attention mechanisms and self-attention-based Bottleneck Transformers. The results showed that CBAM outperformed the alternatives, achieving an F1 score of 77% for box detection and 73% for mask evaluation [21]. In a separate study on apple leaf disease detection, researchers combined CBAM with the C3 TR module to create the YOLOv5-CBAM-C3 TR model, which demonstrated an 8.25% increase in mAP 0.5 compared to the original YOLOv5 model [22]. These findings further confirm that CBAM significantly enhances the model's ability to focus on target regions. The CAM module compresses the feature map along the spatial dimension to obtain a one-dimensional vector before further processing. During compression along the spatial dimension, both average pooling and max pooling are considered. Average pooling and max pooling are used to aggregate spatial information from the feature map, which is then fed into a shared network to compress the spatial dimensions of the input feature map. The features are summed element-wise to produce the channel attention map. For a GPR image, channel attention focuses on identifying the regions where the secondary tunnel lining is located. Average pooling provides feedback for each pixel on the feature map, whereas max pooling provides gradient feedback only at the locations with the highest responses during backpropagation. The channel attention mechanism can be expressed as \[M_{c}(F)=\sigma(MLP(AvgPool(f))+MLP(MaxPool(F))) \tag{1}\]  
In the equation, the sigmoid activation function is denoted as \(\sigma\). The input feature map is first processed through global max pooling and global average pooling, based on width and height, followed by a multi-layer perceptron (MLP) for each. The features output by the MLP undergo element-wise summation followed by a sigmoid activation, resulting in the final channel attention map. The channel attention map is element-wise multiplied with the input feature map to generate the input features required by the spatial attention module. The SAM module, similar to the CAM module, compresses the channels by applying both average pooling and max pooling along the channel dimension. The MaxPool operation extracts the maximum value along the channel, with the extraction count being the product of height and width. The AvgPool operation extracts the average value along the channel, with the extraction count also being the product of height and width. The feature maps, each with a channel size of 1, are then merged to produce a 2-channel feature map. Through this module, the model is able to focus more effectively on the spatial regions of the tunnel secondary lining, while ignoring background or noise. The spatial attention mechanism can be expressed as  
\[M_{s}(F)=\sigma(f^{7\times 7}[AvgPool(F);MaxPool(F)]) \tag{2}\]  
In the equation, \(\sigma\) denotes the sigmoid activation function, and \(f^{7\times 7}\) represents the convolution operation with a kernel size of \(7\times 7\). The improved CBAM-Bottleneck module employs a two-layer convolutional structure during the feature extraction phase, with Figure 5 illustrating both the C2 fCBAM module and the proposed CBAM-Bottleneck module in this study.