# Review on Rail Damage Detection Technologies for High-Speed Trains
## 3 Non-Destructive Testing Methods for High-Speed Train Rails
### LiDAR Detection Methods  
In the research and application of non-destructive testing for surface defects on railway tracks, in addition to the laser ranging detection method, another method is to use the laser ground-penetrating radar (GPR) detection method, which mainly uses a radio wave source to generate electromagnetic energy pulse waves on the detected railway track surface (Figure 12). The electromagnetic energy pulse waves are transmitted in different material media, accompanied by reflection between contact surfaces, and finally, the reflected energy is received and analyzed [58]. Therefore, laser ground-penetrating radar can map the surface structure of railway tracks and the underground conditions of railway track structures. Figure 11: Laser ranging detection system. The collected rail surface data information is processed through relevant algorithms and serialized to achieve the non-destructive testing of rail surface quality. The commonly used processing algorithms include machine learning algorithms, such as artificial neural network (ANN) algorithms and CNNs [59]. The clustering algorithm is commonly used in the field of LiDAR obstacle detection. Its principle is to divide the sample into multiple categories, with the similarity between points within the same category as high as possible and the similarity between different categories as low as possible, in order to reveal the distribution of data. The commonly used clustering algorithms include Density-Based Spatial Clustering of Applications with Noise (DBSCAN), the K-means clustering algorithm, and the Euclidean clustering algorithm. The DBSCAN algorithm is a clustering algorithm based on data density features which can cluster point cloud data of any shape. [PERSON] et al. improved the traditional DBSCAN algorithm by setting an adaptive clustering neighborhood radius that varies according to the target distance, which improved the accuracy of obstacle detection [60]. [PERSON] et al. proposed an adaptive DBSCAN algorithm, which selects representative core points and adaptive clustering radii to achieve the fast and accurate clustering of obstacles with different densities [61]. [PERSON] et al. designed the coplanar threshold as an additional clustering condition, where the clustering threshold is automatically adjusted to adapt to the local distribution of samples in the input dataset without the need to adjust the parameters [62]. The method based on a ground grid usually involves projecting a 3D point cloud onto a 2.5D grid map. A 2.5D grid map, also known as an elevation map, stores the height information of point clouds. [PERSON] et al. extended the elevation map by combining the average height within the grid and the voxel-based object model of the point cloud, and the resulting model is also applicable to path planning [63]. [PERSON] et al. first clustered the three-dimensional point cloud into grids based on gradients and finally used cubic B-spline curves for smooth fitting and the segmentation of the ground. [PERSON] et al. used local geometric features of three-dimensional data to segment the ground and objects, achieving good segmentation results in urban environments including smooth and curved road surfaces [64]. The method based on plane fitting usually utilizes the three-dimensional information of the original point cloud data to construct a ground model and distinguishes ground points based on the degree of matching between each point and the model. [PERSON] et al. proposed an extended Gaussian regression method to fit the ground, utilizing non-stationary covariance functions to locally adapt to terrain data structures [65]. [PERSON] et al. proposed a probabilistic technique based on Gaussian processes which more reliably predicts the elevation of unseen locations than  
Figure 12: Laser radar detection method. other methods while estimating the uncertainty of predictions [66]. [PERSON] et al.