## 3 Similarity Measurement Based Feature  
As indicated above, the original signal, \(\Delta U\), could be decomposed into two terms \(\Delta U_{1}\) and \(\Delta U_{2}\), where \(\Delta U_{1}\) is the cladding-induced interference, and \(\Delta U_{2}\) contains the information regarding the plate thickness. For \(\Delta U_{1}\), differential methods or similarity measurement methods could be used to eliminate it. However, the differential method is always used as a pre-processing method [8; 9; 10; 11; 12]. It cannot obtain the thickness measurement feature directly. Therefore, the similarity measurement method is selected herein. In addition, as \(\Delta U_{2}\) is approximately inversely proportional to the insulation thickness and sensor lift-off, \((l_{1}+d_{2}-d_{3})\) can be reduced by dividing two signals. Normalization method is used to eliminate the influence of interfering factors. Then a feature based on the similarity measurement of the normalized PECT signal is proposed in this study.  
The similarity of the signals is always measured by the distance information. It could be calculated through the Euclidean distance, angular separation, correlation coefficient et al. In this paper, the Euclidean distance is used. Then, the feature could be calculated as follows:  
\[Dis=\sqrt{\sum(\Delta U_{\text{norr}}-\Delta U_{\text{nor}})^{2}} \tag{16}\]  
where \(Dis\) is the Euclidean distance, \(\Delta U_{\text{norr}}\) is the normalized reference signal, and \(\Delta U_{\text{nor}}\) is the normalized calibration signal or the detection signal. Moreover, the reference signal is the signal of the defect-free plate, the calibration signal is the signal of the plate with a known thickness, and the detection signal is the signal of the detected plate.  
To examine the feature details, a 16 Mn steel step wedge plate is used. The thicknesses of the 16 Mn steel step wedge plate are 25.4 mm, 21.5 mm, 20.1 mm, 16.7 mm, and 14.8 mm. The thicknesses of the insulation and the cladding located above the plate are 40 mm and 0.5 mm, respectively. The cladding is composed of galvanized steel sheet (GS cladding). The sensor parameters are listed in Table 1. The lift-off of the sensor is 5 mm, and the amplitude, duty cycle, and period of the square-wave current are 4 A, 50%, and 1 s, respectively. Moreover, the signals of the 16 Mn steel plate are calculated based on the analytical model described in Section 2.1. In the calculation, the relative magnetic permeability and conductivity of the 16 Mn steel plate are 500 and 1.6 MS/m, respectively, and those of the GS cladding are 300 and 2.0 MS/m, respectively. As \(\Delta U\) shown in Equation (1) is expressed as an integral of Bessel functions which is cumbersome and complex, the truncated region eigenfunction expansion (TREE) method presented in [26] is applied to calculate the signals.  
The calculated normalized signal obtained from the 25.4 mm thick plate is used as the reference signal \(\Delta U_{\text{norr}}\), and those obtained from the 21.5 mm, 20.1 mm, 16.7 mm, and 14.8 mm thick plates are used as the calibration signals \(\Delta U_{\text{nor}}\). Substituting \(\Delta U_{\text{norr}}\) and \(\Delta U_{\text{nor}}\) into Equation (15), Dis are obtained. The results are shown in Figure 3. It shows that the plate thickness is monotonically related to the Euclidean distances, then it can be used for thickness measurement.