## 4 Experimental Study  
Experimental study is conducted to further discuss the feature. Figure 4 illustrates the experimental set-up. Similar to the set-up shown in Section III, a 16 Mn steel step wedge plate with thicknesses of 25.4 mm, 21.5 mm, 20.1 mm, 16.7 mm, and 14.8 mm is used, of which the reference thickness is 25.4 mm, and plates with other thickness are used to simulate the uniform wall thinning. A 40 mm thick plastic plate and a 0.5 mm thick galvanized steel sheet are attached on the 16 Mn steel plate to simulate the insulation and cladding, respectively. A sensor with the parameters shown in Table 1 is placed over the cladding. The sensor lift-off is 5 mm. A square-wave voltage signal is generated by a function generator, and subsequently converted to a current signal and amplified using a power amplifier. The amplified square-wave current signal is provided to the transmitter coil. The induced voltage of the receiver coil is amplified by a preamplifier, then digitized  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{4}{c}{**Transmitter Coil**} & \multicolumn{4}{c}{**Receiver Coil**} \\ \cline{2-9}  & \(r_{\text{1T}}\) **(mm)** & \(r_{\text{2T}}\) **(mm)** & \((l_{\text{2T}}-l_{\text{1}})\) **(mm)** & \(n_{\text{T}}\) & \(r_{\text{1R}}\) **(mm)** & \(r_{\text{2R}}\) **(mm)** & \((l_{\text{2R}}-l_{\text{1}})\) **(mm)** & \(n_{\text{R}}\) \\ \hline
**Values** & 16 & 40 & 34 & 800 & 72 & 76 & 6 & 1200 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the sensor.  
Figure 3: Euclidean distances under different plate thicknesses from analytical calculations.  
using a data acquisition card. A computer is used to display the detection signal. The amplitude, duty cycle, and period of the square-wave current are the same as the ones provided in Section 3.  
All the normalized experimental signals can be obtained by dividing each signal with its own maximum value, and are substituted into Equation (16), where the reference signal \(\Delta U_{\text{norm}}\) is obtained from the 25.4 mm thick plate, while each \(\Delta U_{\text{nor}}\) can be obtained from plates with other thicknesses. The obtained Euclidean distances are presented in Figure 5a, and the errors between the experimental and theoretical results are shown in Figure 5b. As shown in Figure 5b, the maximum relative error is less than 5.0%, which indicates the Euclidean distance obtained by the analytical model is quite accurate. Therefore, the Euclidean distance obtained experimentally is replaced by those calculated from the analytical model in Section 5.  
Furthermore, to illustrate that the feature is viable for thickness measurement, two detection signals with the real thicknesses of 23.5 mm and 18.4 mm are provided. The Euclidean distances between the detection and reference signals are 0.0353 and 0.1820, respectively. The signals obtained from 21.5 mm, 20.1 mm, 16.7 mm, and 14.8 mm thick plates are used as calibration signals, and fitting the curve of the Euclidean distances and the calibration thicknesses with a second order polynomial, a calibration equation is obtained as follows:  
\[d_{1}-d_{2}=54.42x^{2}-48.3x+25.28 \tag{17}\]  
where \(x\) denotes the Euclidean distance, and \((d_{1}-d_{2})\) is the ferromagnetic plate thickness.  
Figure 4: Experimental set-up for PECT: (**a**) The 16 Mn steel step wedge plate. (**b**) experimental schematic diagram.  
Figure 5: Experiment results: (**a**) Euclidean distances. (**b**) relative error of analytical calculations to experiment.  
Substituting the Euclidean distances of the detection signals into Equation (17), the calculated thicknesses are 23.6 mm and 18.3 mm, respectively. The relative errors between calculated and real thicknesses are 0.42% and 0.54%, respectively. This indicates that the feature is feasible for the ferromagnetic plate thickness assessment.