## 5 Results Analysis
### Quantitative Analysis
It shows that sweeping excitation frequency is beneficial for detecting defects with different layers. 3 Discussion  
Based on the analysis, defects with different properties exhibit different characteristics under swept-frequency excitation. In this experiment, the infrared camera records the temperature of the defect surface. The temperature of the defect surface is mainly influenced by the depth of heating and the structure of the defect. The depth of heating depends directly on the excitation frequency due to the skinfold effect. The structural factors of defects are mainly the depth and number of layers that can affect the temperature of the defect surface. For single-layer defects of different depths, the defect can be heated effectively under three excitation frequencies when it is shallow. Due to the constant power, the heat will concentrate more on the defective surface as the frequency rises, and thus the temperature of the defect surface increases significantly when the frequency is increased. However, only the 9 kHz excitation frequency can effectively heat the deep defect, and even if the higher excitation frequency concentrates more heat on the defective surface, it lacks the heat that the defect gives off when it is effectively heated, and hence the temperature change in the  
Figure 10: Temperature variation diagram of defects with different depths. deep defect surface is not much different from the lower excitation frequency. Therefore, the variation in TSR values with frequency is significant for shallow defects and insignificant for deep defects. This analysis can be verified by comparing the images in Figure 10.  
For multi-layer defects, the number of layers that can be heated varies with excitation frequencies. If the defect is heated at a low frequency, all layers can be heated efficiently. For single-layer defects, most of the heat is concentrated on a single defect. However, for multi-layer defects, the heat is distributed to defects in different layers, which results in the first-layer defect receiving significantly less energy than the single-layer defect. Therefore, the maximum temperature of a single-layer defect surface will be significantly higher than those of double- and triple-layer defects. Comparatively, a higher excitation frequency led to a shallower penetration depth of the magnetic field, which can only effectively heat up to the first layer of defects. Single-layer defects have the rail material underneath them, while multi-layer defects have other layers of defects underneath the first layer of defects. Since the defects are filled with air, which has a lower thermal conductivity than the rail material, deeper defects in a multi-layer defect prevent the first layer of the defect from dissipating heat downward, resulting in a significant increase in the surface temperature of the multi-layer defect. This leads to a mutation in the maximum surface temperature of the multi-layer defects between two excitation frequencies. In this experiment, the double-layer defect has the mutation in the maximum surface temperature from the excitation frequency  
Figure 11: Temperature variation diagram of defects with different layers. of 9 kHz to 16 kHz, while the triple-layer defects have the mutation in the maximum surface temperature from the excitation frequency of 16 kHz to 25 kHz. This analysis can be verified by comparing the images and TSR values in Figure 11.  
In this experiment, the lowest excitation frequency selected is 9 kHz, providing sufficient heating depth to reach the deepest defects in the experimental specimens. Three excitation frequencies are selected for effectively identifying the three layers of defects in the specimen. In practice, a wider range of excitation frequencies should be selected to detect potential defects in rails, reducing the impact of detection limits on the detection effects. This experiment uses manual specimens, and thus the defect locating based on skewness is accurate enough.