## 4 Experimental Study  
### Experimental Setup  
(1) ECPTT Configuration  
The ECPTT system includes an induction heating device, an excitation coil, a test specimen, an infrared thermal imaging camera, a water-cooling device, and a PC, as shown in Figure 3. The water-cooling device utilizes the hydrological cycle to lower the temperature of the coil and eliminates the influence of the coil's thermal resistance on the detection effect. This experiment uses multi-frequency excitation to induce different heating depths. In this study, 9 kHz, 16 kHz, and 25 kHz excitation frequencies are applied to detect multi-layer RCF defects. Different excitation frequencies lead to different heating depths, and thus the defects can be analyzed layer by layer through the thermal response of different excitation frequencies. The excitation current is set at 45 A. To ensure consistent input power of different excitation frequencies, the coil turn ratios corresponding to 9 kHz, 16 kHz, and 25 kHz are set at 46, 37, and 33, and the coil current are 2070 A, 1665 A, and 1485 A, respectively. The heating duration is 600 ms. The Flir 655 SC infrared camera made by FLIR System Inc. (Wilsonville, OR, USA) is utilized to record the heating process of the RCF cracks.  
Figure 3: Experimental device.  
Figure 4a shows the helical coil positioned perpendicular to the specimen, generating an excitation magnetic field distributed in a spiral pattern within the specimen. Helical coils offer advantages such as the ability to produce a uniform magnetic field of consistent strength and simplicity in construction, as well as facilitating closed magnetic circuits. However, similar to Helmholtz coils, they require increased sizes to achieve a broader range of uniform magnetic fields. Empirical investigations by [PERSON] and [PERSON] [17] indicate that the heating effect of helical coils is not particularly pronounced. Additionally, optimal heating efficiency and detection sensitivity are observed only when the multi-turn helical coil is elevated to a height equal to half of its radius.  
Figure 4b shows the disc-shaped coil and Figure 4c shows the square plane coil. These coils are juxtaposed for comparative analysis owing to their similar geometric profiles. Figure 4d shows the linear coil, renowned for its exceptional linearity and measurement accuracy, making it a staple in various experimental contexts. Furthermore, linear coils find utility in applications such as generating excitation for detecting false soldering in SMD circuit boards [24] and assessing changes in material properties [12], and while linear coils afford a comprehensive field of view during excitation generation, their heating efficacy is often suboptimal and lacks uniformity. Figure 4e shows the center trench plane coil.  
Figure 5 illustrates the five types of coils utilized in the experiment.  
Coils can shade the defect part of a rail and may have the uniformity of heating. The viewing angle shown in Figure 5 is also the view angle of the infrared camera. Coils a, b, and c shade the defect part of the rail as shown in Figure 5, thus affecting the infrared camera's recording of the thermal response. The uniformity of coil heating also affects the quality of defect heating. If coil heating is not sufficiently uniform within the defect space, defects of the same depth and number of layers may exhibit different thermal responses at different locations, complicating the analysis of experimental results.  
In this experiment, the center trench plane coil ensures unobstructed visibility of defect in the thermal images as well as the heating uniformity, and this coil couples best with low excitation frequencies such as 9 kHz.