## 2 Literature Review  
The Eddy Current Pulsed Thermography (ECPT) system can effectively detect RCF defects in rails. There has been some research regarding the application and development of this system. [PERSON] et al. [9] utilized Pulsed Eddy Current (PEC) technology to effectively detect RCF defects on rails, encompassing both surface and sub-surface anomalies. Additionally, Eddy Current Thermography (ECT), integrating multi-physical field models, exhibits notable advantages including high spatial resolution and sensitivity in detecting subsurface defects. However, challenges remain, particularly in mitigating lift-off [10] arising from variations in cladding thickness or probe motion. Furthermore, it can influence the accuracy of eddy current detection. The presence of lift-off attenuates the strength of the detected signal, leading to a decay in the performance of the sensor [11], thereby necessitating strategies to suppress this effect. Excitation coils play an important role in the ECPT system. [PERSON] et al. [12] utilized linear coils for excitation detection of wind turbine gears, encountering issues related to uneven heating. [PERSON] et al. [13] employed square plane coils to detect artificial and natural cracks on steel blades. Although it facilitated relatively uniform heating, presented challenges related to line of sight occlusion. In [PERSON]'s [14] experiment, it has been demonstrated that in order to obtain a uniform magnetic field in a given area of a Helmholtz coil, the geometry of the coil increases accordingly. However, when using the ECPT method for rail defect detection, the coils can obstruct the detection process, thereby preventing the infrared cameras from obtaining comprehensive images directly above the rail. To address this issue, [PERSON] and [PERSON] [15] devised a novel generation of B-H sensing coils comprising two groups of B-H coils. These coils enable the measurement of magnetic field intensity in different directions, allowing for the analysis of head deflection by comparing measurement results from the two groups. Furthermore, the coils aligned in the same direction are measured in series, thereby effectively enlarging the window area of the coil and enhancing measurement accuracy. Core loop winding is one or more magnetic cores placed in the center of the coil [16], and this configuration offers notable enhancements in both the induction capacity of the coil and the uniformity of heating effects. In a study by [PERSON] and [PERSON] [17], experiments were conducted on spiral coils, revealing that optimal sensitivity for defect detection is achieved when the diameter of the coil is twice the lift-off. The reconstruction of defects has also received attention from researchers. [PERSON] et al. [18] used single-frequency excitation to construct a three-dimensional Pulsed Eddy Current Thermography inspection system. The 3D Pulsed Eddy Current Thermography inspection system has achieved results in detecting multilayer defects. [PERSON] and [PERSON] [19] developed an algorithm from pulsed thermography data to reconstruct 2D as well as 3D defect shapes. [PERSON] et al. [20] extracted the slope inclination feature of the transient temperature distribution to estimate the angle and utilized the maximum temperature amplitude feature to quantify the length and depth of the defects. These investigations are based on testing human-made specimens and lack verification of real cracks. [PERSON] et al. [21] uses skewness to quantify the depth of defects in the real cracks under the ECPT system, effectively reconstructing the depth of defects. [PERSON] et al. [22] evaluated eight spatial and temporal ECPT features on idealized and real RCF cracks. Their results showed that the area-based and kurtosis-based features are suitable for characterizing inclination angles. However, these studies are based on a single excitation frequency and focus only on information such as the depth and angle of the defects, missing the consideration of the number of defect layers.