## 5 Results Analysis
### Thermal Image Comparison  
Table 1 presents the thermal images of five coils at the peak temperature (using defect 1 as an example). Due to the large total number of frames, only the frame with the highest temperature from each dataset is selected for display. For a specific coil, the heating power remains constant with frequency, but higher frequencies concentrate eddy currents and heat in a shallower area due to the skinkoff effect, leading to a higher maximum temperature on the steel rail surface. The thermal response signals from the steel rail surface are primarily influenced by the excitation frequency and structure of the defects. Table 1 demonstrates the thermal response of defect 1, which is the shallowest single-layer defect in the specimen. All frequencies can effectively heat this defect, and the heat is concentrated more on the rail surface as the frequency increases, resulting in a noticeable increase in the surface's highest temperature above defect 1. Each coil exhibits similar conclusions, differing mainly in field of view and heating uniformity. This analysis is verified in Table 1.  
Figure 7 presents the skewness-based location of a defect within the thermal image (using the excitation frequency of 25 kHz as an example), maintaining the same resolution with the infrared camera of 480 \(\times\) 640. Skewness is a third-order moment statistic that primarily represents the uniformity of the temperature distribution, and thus the highest temperature as well as differences in coils have less effect on it. Throughout the heating process, the defect area will have a rapid warming up and a slower cooling down, resulting in a notably lower negative skewness in the surrounding regions. As a result, the location of the defects can be readily identified in the skewness images. Figure 6: The schema of test piece. Although differences among coils do not affect the locating of defects, they do affect the analysis of the type of defect. Therefore, a suitable coil needs to be selected before analyzing the defect type. As for the helical coil, the dimensions limit the range and  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Excitation** & **Central Trench** & **Linear Coil** & **Helical Coil** & **Square Plane Coil** & **Disc-Shaped Coil** \\ \hline
9 kHz & (a) & (b) & (c) & (d) & (e) \\ \hline
16 kHz & (f) & (g) & (h) & (i) & (i) \\ \hline
25 kHz & (k) & (l) & (m) & (n) & (o)  
strength of the uniform magnetic field that can be generated, which is ineffective for the specimen [17]. Square plane and disc-shaped coils produce an uneven magnetic field with high intensity on the inside edge of the coil, resulting in an inability to effectively heat the entire defect. This can be observed from the skewness image Figure 7. Linear coils are capable of generating a uniform magnetic field over a sufficiently large range, but their coupling to low excitation frequencies is not as effective as that of the central trench plane coil. The central trench plane coil also has the best visibility at the defect area, and hence the following analysis will be based on the central trench plane coil. Table 2 shows the simulation distribution of magnetic flux density and temperature in the cutaway view. As the frequency increases, the penetration distance of the magnetic field and the depth of downward heat transfer become shallower, verifying the skinfold effect. Table 3 compares the simulation and experiment results of defect 1. In the simulation results, the maximum surface temperature increases with frequency, and heat is more concentrated on the defective side of the gap, consistent with the experimental results. The simulated images in both tables are transient images at the end of heating (T = 0.6 s), in the same state as the experimentally captured thermal images.