# Enhanced Nondestructive Testing Using Pulsed Eddy Current and Electromagnetic Ultrasonic Techniques
## 4 Composite Detection Probe Optimization  
Given the complexity of calculating the relationship between the received signal, the excitation signal, the coil structure, and other parameters of the composite sensor, this study employed the finite-element simulation software COMSOL 6.2 to simulate and model the composite detection probe. The aim was to enhance the probe's energy conversion efficiency. To expedite the simulation process, a two-dimensional axisymmetric model of the compound detection probe was developed, as shown in Figure 5.  
Figure 4: Schematic of the detection ranges of pulsed eddy currents and electromagnetic ultrasound. Figure 5: Simulation model of composite detector. Figure 3: Composite sketch of pulsed eddy current and electromagnetic ultrasonic testing system layer. The geometric model includes an air zone with a radius of 200 mm, an aluminum plate with a diameter of 80 mm \(\times\) 10 mm, and an aluminum plate with a diameter of 2 mm \(\times\) 0.1 mm. In practice, a PCB coil is used as the excitation coil to maintain consistent coil distances. Therefore, the model utilizes 30 rectangular PCB spiral coils, each with 30 turns. The space between the lower surface of the permanent magnet and the upper surface of the aluminum plate is 2 mm, and the space between the coil and the aluminum plate is 1 mm. The electrical conductivity of the PCB material is considered to be 0, so the PCB material can be treated as air except for the coil. The specific parameters of the permanent magnet, coil, and material are shown in Table 1.  
To facilitate enhanced detection signal observation, the simulation model incorporates a two-layer coil structure consisting of one transmitter and one receiver. \[i(t)= \begin{cases}I_{0}(1-\cos\frac{2\pi ft}{n})\cos(2\pi f),&0\leq t\leq\frac {n}{f}\\ 0&t\geq\frac{n}{f}\end{cases} , \tag{6}\]  
When \(n\) = 4, the waveform of the current excitation signal is as depicted in Figure 6.  
In this paper, each wavelength is divided into six grids. The formula for calculating the wavelength of an ultrasonic wave is  
\[\lambda=\frac{v_{s}}{f} \tag{7}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Name** & **Numerical Value** \\ \hline Remanence strength of permanent magnet & 1.2 T \\ Permanent magnet size & 15 mm length \(\times\) 30 mm height \\ Excitation and receiving coil material & copper \\ Electrical conductivity of excitation and receiving coils & 5.998 \(\times\) 10\({}^{7}\) S/m \\ Cross-sectional area of coil & 0.203 mm \(\times\) 0.035 mm \\ Material to be tested & aluminium \\ Material conductivity & 3.774 \(\times\) 10\({}^{7}\) S/m \\ Material density & 2700 kg/m\({}^{3}\) \\ Material size & 80 mm \(\times\) 10 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation model parameters. Figure 6: Current-excited signal waveform. where \(\lambda\) represents the wavelength of the ultrasonic wave, \(v_{s}\) represents the shear wave velocity, and \(f\) represents the frequency. The velocity \(v_{s}\) is mainly related to the properties of the propagation medium itself:  
\[v_{s}=\sqrt{\frac{E}{\rho}\cdot\frac{1}{2(1+\sigma)}} \tag{8}\]  
Here, \(E\) represents the Young's modulus of the medium, \(\sigma\) is the shear modulus of the aluminum plate, and \(\rho\) stands for the density of the medium. Based on the material parameters of the aluminum plate specified in the model, the propagation velocity of shear waves in the aluminum plate is approximately 3122 m/s. Consequently, when meshing the aluminum in the model, the maximum cell size should not exceed 520/\(f\). The ultrasonic propagation process and detection signal at different times after the introduction of a 2 mm \(\times\) 0.1 mm internal defect in the aluminum plate are depicted in Figures 7 and 8. As shown in Figure 7, the reflection of the ultrasonic wave becomes apparent as it encounters the internal defect or reaches the bottom of the aluminum plate.