## 4 Simulation Results  
### PI Feature Acquisition  
According to the PEC analytical model, the numerical simulation code was written in MATLAB software to simulate the PEC signal with different relative permeability and verify the thrice subtraction method. In simulations, the height, inner and outer radius of the probe coil were 6 mm, 4 mm and 6 mm, respectively. There were 300 turns of coil. The boundary was set to \(h=20r_{2}=120\) mm. The pulse excitation had a 10 V amplitude, 200 Hz frequency and 50% duty cycle. The time constant of pulse excitation was set to 33 \(\upmu\)s. The excitation signal of pulse voltage is shown in Figure 4. In Figure 5, the difference PEC signals are shown when permeability changes. It can be observed that the difference  
Figure 3: Flow diagram of thrice subtraction method.  
PEC signals integrally decreased when relative permeability decreased. Especially, in the partially enlarged drawing shown in Figure 6, the variation of difference PEC signal is obvious. The results indicated that the difference PEC signals did not show intersection phenomenon and the permeability effect was obvious when permeability changes.  
Under the condition that the rise time of pulse excitation is constant, when excitation pulse frequency increased, the difference PEC signals changed as shown in Figure 7. It was observed that the change of excitation pulse frequency led to the change of excitation pulse period. In experiments, the difference PEC signals were recorded when it was triggered by the rising or falling of pulse excitation. It can be seen that the difference PEC signal did not change in the first half part of the difference PEC  
Figure 4: Pulse excitation voltage signal.  
Figure 5: The difference in PEC signals.  
Figure 6: Partially enlarged drawing.  
signal, as shown in Figure 7a, when the excitation pulse frequency changes at lower excitation pulse frequency. When the pulse frequency was higher, the recorded difference PEC signal in first half part of periodic pulse was incomplete and there was no stationary part in difference PEC signal, as shown in Figure 7b. When the rising time of pulse excitation changed, as shown in Figure 8, it can be observed that the response time of the difference PEC signals to stationary section was shorter.  
By using the thrice subtraction method based on the above difference PEC signals, the thrice subtraction signals could be obtained from the difference PEC signals, as shown in Figure 9. It was observed that the amplitude of thrice subtraction signals was smaller than that in the difference PEC signals. An intersection point phenomenon was exhibited in the thrice subtraction signals, which is called a PI signal feature. It was observed that at the intersection point of thrice subtraction signals, the thrice subtraction signals were independent of permeability effect. The PI feature was immune to permeability change. According to above analyses, it is known that the thrice subtraction signal was affected by excitation pulse frequency and rising time of pulse excitation. Thus, some limits are needed in the application of PI phenomenon. In order to keep the method practical, the excitation pulse frequency should be kept lower when rising time of pulse excitation is longer.  
Figure 8: The difference in PEC signals with different rising times.  
Figure 7: The difference PEC signals with different frequencies. (**a**) lower frequency; (**b**) higher frequency.