## 4 Results and Discussion  
This paper uses the track geometry data from 2016 to 2018 to train and test the proposed detection framework. The inspections of low-temperature months (January to March) and high-temperature  
Figure 10: Final architecture of the convolutional neural network (CNN) detection model.  
months (July to August) of each year are combined in pairs to construct an image dataset. Each inspection contains 315 km of track geometry data, which is much longer than the arching wavelength (less than 10 m). The inspection line passes through different substructures and external environment, so the samples cover waveform characteristics of various conditions. Moreover, the combinations of different inspections can include different degrees of arching from the initial stage to the later stage. Therefore, the dataset contains sufficient features and can meet the need for model training and verification.  
According to the data conversion and augmentation method in Section 3.1, the dataset is constructed including 11896 arching images. On this basis, five subsets are used for the research, as shown in Table 2. As for the training and validation sets, each subset has a different pattern ratio and sample scale, and the proportion of training and validation is 5:1. Subset 2 is a balanced set that provides an equivalent proportion for each type, whereas other subsets are imbalanced sets for comparison studies. Compared with Subset 2, all arching samples used for training and validation in Subset 1 are original images without augmentation operation. Subset 3 and Subset 4 have the same sample size as Subset 2 in training and validation set, but the ratio of \"Arching\" to \"Normal\" is 1:3 and 1:6, respectively. The total number of training and validation samples for Subset 5 is twice that of Subset 3, whereas the pattern ratio is the same. Besides, different subsets share the same testing set containing 11896 images, in which the samples in training and validation sets are filtered out.  
The model is implemented on the python Tensorflow (1.10.1) deep learning framework. Three error metrics, including Precision, Recall, and F\({}_{1}\)-score, are mainly employed to optimize the model structure and assess the model performance. They are defined as follows.  
\[\text{Precision}=\text{TP}/(\text{TP}+\text{FP})\times 100\% \tag{7}\]  
\[\text{Recall}=\text{TP}/(\text{TP}+\text{FN})\times 100\% \tag{8}\]  
\[\text{F}_{1}-\text{score}=2\times\text{Precision}\times\text{Recall}/(\text{ Precision}+\text{Recall}) \tag{9}\]  
where TP (i.e., True Positive) represents the number of the arching samples that are correctly detected as \"Arching\"; FP (i.e., False Positive) represents the number of the normal samples that are incorrectly detected as \"Arching\"; FN (i.e., False Negative) represents the number of the arching samples that are incorrectly detected as \"Normal\". Precision reflects the proportion of the actual arching samples in detected \"Arching\" samples. Recall reflects the proportion of the correctly detected samples in actual arching samples. F\({}_{1}\)-score is the harmonic mean of Precision and Recall, which indicates the overall accuracy of the arching detection model.