## 4 Experimental Results
### Defect Shape Mapping Based on C-scan Imaging  
C-scan imaging software, which refers to the data acquisition software written in VC++ language, includes parameter setup, feature extraction, data acquisition, data matrix formation, data processing, and a C-scan image display. First, the excitation pulse parameters were configured in the parameter setup. In this experiment, the excitation pulse was 7.5 V in amplitude, 5 ms in pulse duration, and 100 Hz in frequency. Then, the transient response signal measured from the _By_ pickup coil was sampled by data acquisition. Next, during feature extraction, the peak amplitude of the _By_ transient response signal was picked up as a feature of the C-scan imaging. In data matrix formation, the coordinates of scanning points were determined and the C-scan data matrix was formed. Peak wave and transient response signals may be disturbed by unknown noise, which may lead to potential misjudgment of imaging results. With the help of the \"wden\" function in MATLAB, the C-scan data matrix was denoised through wavelet analysis. Finally, the data matrix was transformed to a colority matrix, and the C-scan images of the scanned area formed in step with the C-scan images display. Finally, defect shape mapping could be obtained by analyzing the C-scan images. As described above, the data matrix needed to be denoised, and we propose wavelet analysis to denoise the C-scan data matrix during data processing. Wavelet analysis is an effective technique in signal processing, and the analysis is done in both time and frequency domains. First, the transverse data in the original C-scan data matrix was denoised. Next, the longitudinal data in the C-scan data matrix was denoised. Finally, the denoised C-scan data was transformed into a colority matrix. Figures 6 and 7 display the efficiency of a two-dimensional wavelet filter, respectively showing the original C-scan contour image and the C-scan imaging results after the process of the first defect. As expected, the denoising result was clearer than the original image. Figure 6: The original C-scan contour images of defect 1. C-scan contour images of defects 1, 2, and 3 in the direction of magnetic flux are respectively shown in Figures 8-10. C-scan contour images of defects one, two, and three in the direction of the exciting current are respectively shown in Figures 11-13. The horizontal axis represents the scanning path, with a distance between the two adjacent scanning paths of 1 mm. The vertical axis represents the scanning time, with the color bar representing the voltage amplitude. In Figures 8-13, two crest areas and two trough areas appear on the defect's four corners in every C-scan contour image, which is consistent with the analysis in Section 3.1. Defects can be clearly identified and the defect's shape can be imagined by the two crests and two troughs in the C-scan contour images. Figure 8: C-scan outline images of defect 1 in the direction of magnetic flux. Figure 7: C-scan images of defect 1 after a two-dimensional filter. Figure 10: C-scan outline images of defect 3 in the direction of magnetic flux. Figure 9: C-scan outline images of defect 2 in the direction of magnetic flux. In addition, the length of the defects can be effectively evaluated from the C-scan outline images. As shown in Figure 8, the time between the maximum and minimum values on the C-scan image corresponds to the instants when the sensor entered and left the defect angle. Defect length can be measured by the formula \(L=v\times\Delta t=v\times(t_{2}-t_{1})\). Here, \(L\) is the estimated length of the defect, \(v\) is the scanning speed of the sensor, \(\Delta t\) is the time difference, \(t_{2}\) is the time when the sensor leaves the defect corner, and \(t_{1}\) is the time when the sensor enters the defect corner. Figure 11: C-scan outline images of defect 1 in the direction of the exciting current. Figure 12: C-scan outline images of defect 2 in the direction of the exciting current. The scan speed was 0.06 m/s in this experiment.