## 3 Finite Element Modeling and Probe Parameter Determination
### Determination of Probe Parameters  
#### 3.2.1 Determination of Excitation Coil Parameters  
The design of an orthogonal experiment mainly considers the factors of the experiment and the levels of each factor. According to the previous analysis, the factors that need to be determined for the excitation coils are \(D_{\mathrm{e}}\), \(H_{\mathrm{e}}\), \(K_{\mathrm{e}}\), \(S_{\mathrm{e}}\), and \(N_{\mathrm{e}}\). According to the skin effect, in high-frequency AC circuits, current does not flow evenly across the entire cross-section of the conductor but instead concentrates more near the surface. To ensure stable efficiency in signal transmission, when making coils, keeping the wire radius smaller than the skin depth at the excitation frequency can effectively increase the current density within the wire cross-section, reduce resistance, and thereby ensure probe performance. The coil winding wire usually requires copper-enamel wire with a diameter of 0.2 mm or less. In this study, the selected excitation frequency is 1 MHz, and at this frequency, the skin depth of copper wire is 0.06 mm. Therefore, choose a copper-enamel wire with a diameter of 0.1 mm to wind the probe. After the wire diameter is determined, the relationship between \(N_{\mathrm{e}}\), \(H_{\mathrm{e}}\), and \(K_{\mathrm{e}}\) is as follows:  
\[K_{\mathrm{e}}H_{\mathrm{e}}=0.01N_{\mathrm{e}} \tag{11}\]  
Therefore, in the orthogonal experiment, only four independent factors need to be considered (\(D_{\mathrm{e}}\), \(H_{\mathrm{e}}\), \(K_{\mathrm{e}}\), and \(S_{\mathrm{e}}\)). The simplified objective function is as follows:  
\[maxB(D_{\mathrm{e}},H_{\mathrm{e}},K_{\mathrm{e}},S_{\mathrm{e}}) \tag{12}\]  
In order to comprehensively and effectively understand the primary and secondary effects of each factor with as few experimental trials as possible, an orthogonal experiment with four (\(2^{2}\)) levels is chosen for each factor in the process of determining coil parameters. The lateral dimensions of delamination are typically above 10 mm, making them relatively large defects. Therefore, slightly larger excitation coils should be chosen to induce a larger magnetic field inside the CFRP sample. Specifically, the inner diameter of the excitation coils should be greater than half of the lateral dimensions of the delamination. However, if the coil size is too large, it can indeed affect the sensitivity of the probe. This means that when the defect size changes, the probe may not be as sensitive to those changes. Therefore, the selected four levels need to cover the characteristics of both large and small coils to achieve a comprehensive and systematic study of coil parameters, thus achieving the design objectives. The four levels chosen for each factor are shown in Table 1.  
Figure 7: Delamination detection scanning path.  
In Table 2, the \(T_{Z}\) of each factor is greater than the \(T_{Z}\) of the reference factor \(X_{\rm e}\). This indicates that each factor at the selected levels has a significant effect on magnetic flux density, proving the rationality of the experiment. The influence of the four factors on magnetic flux density is: \(D_{\rm e}>S_{\rm e}>H_{\rm e}>K_{\rm e}\). According to the experimental results in Table 2, the number of levels with the largest A value for every factor is selected to increase the magnetic flux density and consequently enhance the signal amplitude in the sample. Thus, the combination \(D_{\rm e3}H_{\rm e3}K_{\rm e4}S_{\rm e1}\) is determined by the geometry parameters of the excitation coils.