## 2 Principles of Eddy Current Testing and Probe Design
### Probe Design
#### 2.2.2 Probe Parameter Determination Method  
Coil size directly affects the results of CFRP eddy current testing [24]. Generally, smaller coils have higher spatial resolution and better sensitivity to small defects (such as cracks). However, overly small coils can result in weak detection signals, which may drown out the defect signal in noise, ultimately leading to the inability to obtain useful defect information. Larger coils can generate deeper eddy current penetration depths, which are advantageous for detecting larger defects (such as delamination). However, excessively large coils during scanning may lead to significant differences between the detected defect edges and the actual defect edges, thereby increasing the difficulty in detecting defect edges. This study aims to design a probe with high sensitivity specifically for delamination. Therefore, it is necessary to comprehensively consider coil size to determine a set of suitable probe parameters. The orthogonal experiment is a research method for studying multiple factors and levels of experiments. It can comprehensively and effectively explore the influence of multiple factors on a relatively small experimental scale [25]. When conducting an orthogonal experiment, first identify the factors and levels to be studied, and then select an appropriate orthogonal array to design the experimental plan. During the experiment, different levels of each factor are combined into experimental conditions and grouped according to the orthogonal array to ensure that each level of each factor appears in a relatively equal proportion with every level of other factors. Next, execute the experiments one by one according to the experimental plan, recording the experimental results for each group of conditions. Finally, evaluate the influence of each factor on the target variable using statistical analysis methods and determine the optimal combination of factors to achieve the optimization goals. In the process of determining probe parameters, there are many influencing factors. To reduce the number of blind tests and improve experimental efficiency, orthogonal experimental methods and finite element analysis are used to determine the probe parameters. To ensure the orthogonality of the experiment, the number of levels for each factor is typically chosen as 2 m, where m is a positive integer. To assess the influence of each factor on the evaluation criteria, range analysis is conducted on the results of orthogonal experiments. This involves calculating the average value \(A_{ZJ}\) and the range \(T_{Z}\):  
\[A_{ZJ}=\frac{\sum\limits_{i=1}^{n}y_{ Zi}}{m}, \tag{4}\]  
\[T_{Z}=R_{\text{max}z}-R_{\text{min}z}, \tag{5}\]  
Figure 3: Eddy current path in the CFRP sample under different excitations: (a) the current direction in the two excitation coils is same; (b) the current direction in the two excitation coils is opposite. where \(i\) is the test number, \(Z\) is the influencing factor, \(N\) is the number of levels in the orthogonal experiment, \(J=1,2,\ldots\) N, \(y\) is the evaluation index, and \(n\) is the number of experiments. \(R_{maxZ}=\) max \(\{A_{Z1},A_{Z2}\ \ldots\.\ A_{Z}\}\), \(R_{minZ}=\) min \(\{A_{Z1},A_{Z2}\ \ldots\.\ A_{Z}\}\). The range \(T_{Z}\) can be used to analyze the degree of influence of each factor on the evaluation criterion. The larger the \(T_{Z}\), the more significant the influence of factor \(Z\) on the evaluation criterion [26]. In the range analysis, the average value \(A_{Zj}\) when \(J=1,2,\ldots\) N describes the effect of the factor \(Z\) on the test result. By selecting a reference factor \(X\) (with no need to set levels) and considering its extreme values as the benchmark for the experiment, we can test whether other factors have a significant impact on the evaluation criterion. If the extreme value of a certain factor exceeds the extreme value of \(X\), it indicates that this factor has a significant impact on the evaluation criterion, thereby validating the rationality of the designed experiment [27].