## 2 Principles of Eddy Current Testing and Probe Design
### Probe Design
#### 2.2.2 Probe Parameter Determination Method
Finally, the number of levels with the largest A value for every factor is selected to achieve the experimental goal. Considering the geometric structure of the probe, the parameters of the excitation coils will affect the parameters of the detection coil. Therefore, in the process of determining the parameters, the parameters of the excitation coils are prioritized. Furthermore, to ensure the uniformity of the generated magnetic field, the dual excitation coils use the same set of parameters. 1. Determination method of excitation coil parameters;  
The magnetic flux density not only affects the generation of eddy currents but also directly relates to the distribution and intensity of the eddy currents in the conductor [28]. A higher magnetic flux density can make the changes in the detection signal caused by defects more significant, thereby affecting the detection sensitivity. Therefore, in the determination of the excitation coil parameters, the magnetic flux density (\(B\)) at a fixed point in the CFRP sample is chosen as the evaluation criterion, and the y in Equation (4) is replaced by the magnetic flux density (\(B\)). The relationship between the excitation coil size, the distance between the two excitation coils, and the magnetic flux density is studied. By changing the coil parameters, the magnetic flux density is indirectly controlled. The objective function for excitation coil parameter determination is shown as follows:  
\[maxB(D_{\text{e}},H_{\text{e}},K_{\text{e}},S_{\text{e}},N_{\text{e}}), \tag{6}\]  
where \(B\) represents the magnetic flux density, \(D_{\text{e}}\) is the width of the excitation coil winding, \(H_{\text{e}}\) is the height of the excitation coils, \(K_{\text{e}}\) is the thickness of the excitation coil bundle, \(S_{\text{e}}\) is the distance between the two excitation coils, and \(N_{\text{e}}\) is the number of turns in the excitation coils. 2. Determination method for detection coil parameters. After determining the parameters of the excitation coils, it is necessary to choose a suitable evaluation criterion to determine the parameters of the detection coil. This involves applying an alternating current to the excitation coils of a known size to induce a magnetic field in the CFRP sample. Following this, the impact of changes in detection coil parameters on the evaluation criterion will be studied. The detection voltage change rate is used to represent the relative change between the voltage signal when delamination is present in the CFRP sample and when there is no delamination present. It is a normalized value, and a higher detection voltage change rate indicates a more significant relative change between the voltage signals with and without delamination. This means that the probe is more sensitive to delamination. Therefore, in the determination of the detection coil parameters, the detection voltage change rate (\(C\)) is selected as the evaluation criterion, and the y in Equation (4) is replaced by the rate of change of the detection voltage difference \(C\). This implies selecting a representative delamination and detecting it with detection coils of different sizes to study the influence of various factors of the detection coils on the voltage detection change rate of this defect. The equation for calculating the voltage detection change rate is as follows:  
\[C=\frac{V_{\text{defect}}-V_{\text{nodefect}}}{V_{\text{nodefect}}}, \tag{7}\]  
where \(V_{\text{defect}}\) is the voltage measured by the detection coil when there is a delamination, and \(V_{\text{nodefect}}\) is the voltage measured by the detection coil when there is no delamination. The objective function for determining the detection coil parameters is shown in Equation (8):  
\[maxC(D_{\text{r}},H_{\text{r}},K_{\text{r}},N_{\text{r}}), \tag{8}\]  
where \(D_{\text{r}}\) is the width of the detection coil, \(H_{\text{r}}\) is the height of the detection coil, \(K_{\text{r}}\) is the thickness of the detection coil winding, and \(N_{\text{r}}\) is the number of turns of the detection coil.