## 5 Case Study  
The method was applied to the civil engineering works of the underground section of the Xiong'an New Area of the Beijing-Xiong'an High-Speed Railway. The scope of the project encompasses multiple complex structural elements, including railway embark  
Figure 9: Schematic diagram of intersection detection: (**a**) Process of Detecting Neighboring Intersections (Nearest Intersection); (**b**) Extracted Intersection Image (Red Box Indicates Identified Intersections).  
ments, bridges, tunnels, and stations, with a total length of approximately 24.838 km and a transverse width of 135 m. Given the extensive use of reinforced rebar mesh structures in the project, ensuring that the spacing distribution of the rebar mesh adheres to relevant standards and regulations is a crucial aspect of quality assurance. Through the automated detection of rebar mesh spacing, the efficient and precise verification of reinforcement layout can be achieved, reducing the errors associated with manual inspections and ensuring that the construction quality meets regulatory requirements.  
In the detection of rebar mesh spacing, an improved U-Net model was employed for semantic segmentation. The model was trained using hardware configurations including GPU: RTX 4060 and CPU: Intel Core i9-14900K. The enhanced U-Net model was utilized, with model weights pre-trained on the ImageNet dataset, thereby leveraging the advantages of transfer learning to ensure that satisfactory performance could be achieved in fewer training iterations. During the training process, the random seed was set to 11 to ensure the reproducibility of the experimental results. The batch size was set to 10, which was adjusted to fit the memory constraints of the hardware while maintaining the stability of the training process. Regarding the optimization strategy, a cosine annealing learning rate schedule was applied. This scheduling method allows the learning rate to gradually decrease during training, with a more significant reduction as convergence approaches, helping to prevent overfitting and accelerating the final convergence process. The maximum learning rate was set to 1e-4, and the minimum learning rate to 1e-6, ensuring rapid convergence in the early stages of training while allowing for more refined model learning in the later stages. The Adam optimizer was employed, with a momentum parameter set to 0.9. The Adam optimizer, known for its adaptive learning rate capabilities, was chosen to further enhance model training efficiency.  
The training process consisted of 100 epochs, with the training results shown in Figure 4a. Finally, an intersection detection algorithm was employed. This algorithm enables the automatic identification of intersections within the rebar mesh and the precise calculation of mesh spacing based on a predefined threshold. The automatic selection of the threshold is guided by the model's training outcomes and the actual detection performance. It can be flexibly adjusted according to different environmental conditions, operating states, and precision requirements. Typically, the threshold is set to 20% of the maximum distance within the filter area, thereby enabling the accurate detection of rebar mesh spacing as depicted in Figure 10. The application results indicate that for regularly distributed rebar mesh structures, the accuracy of spacing detection exceeds 90% when compared to the true values. It should be noted that this accuracy is based on images captured under the condition of correct shooting, where the camera is perpendicular to the target and the distance is between 0.5 and 2 m. This shooting strategy helps reduce the impact caused by the angle and depth of the rebar mesh on the calculations.  
Figure 10: _Cont._