## 5 Feature Parameter Selection
### Correlation Coefficients between Geometric Information and Feature Parameters  
Figure 13 shows a scatter plot of the root mean square of reflected waves in Part B and the transmission coefficients in Part C of Section 4. Their correlation coefficients versus depth are \(0.329\) and \(-0.952\), respectively. When the correlation coefficient reaches \(1\), it is a completely positive correlation; when it reaches \(-1\), it is a completely negative correlation. Figure 12: (a) Scatter plot of WP coefficient peaks; (b) scatter plot of WP energy peaks; (c) scatter plot of WP entropy. Figure 13: _Cont._  
Comparing Figure 13a,b, a greater linear relationship between transmission coefficient and depth is reflected by the larger correlation coefficient than that for the root mean square. Thus, the transmission coefficient is a better feature parameter to classify different depths. The prediction errors using the root mean square and transmission coefficient as feature parameters in the SVM model to realize depth classification are shown in Figure 14.  
In Figure 14, the prediction errors of the transmission coefficient in (b) are lower than those of the root mean square in (a). The feature parameter with a higher correlation coefficient with the crack depth is included in the SVM model, and lower prediction errors are obtained. Therefore, the transmission coefficient has a better prediction ability to evaluate the crack depth by the SVM method. This result proves that the correlation coefficient between feature parameters and predicted geometric information is a selection standard to select suitable feature parameters for the SVM model. According to this selection standard, the correlation coefficients between the feature parameters and the crack depths and angles are shown in Tables 2 and 3, respectively. The higher correlation coefficients (absolute value > 0.6) in the tables are shown in red for clarity. Figure 14: (**a**) SVM prediction error with the root mean square of the Rr wave; (**b**) SVM prediction error with transmission coefficient. Figure 13: (**a**) Scatter plot of the root mean squares of reflected waves. (**b**) Scatter plot of transmission coefficients. In total, seven feature parameters are chosen in this paper, as shown in Table 2. In Table 2, the transmission coefficient, transmitted wave peak, deconvolution sum, and Tr wave WP entropy have absolute correlation coefficients greater than 0.8 with the crack depth, which shows an excellent ability to evaluate the crack depth according to the correlation coefficient standard. The reflection coefficient, the root mean square of the reflected wave, and Rr wave WP energy peak have a good correlation with the angle. They are chosen as feature parameters for crack angle evaluation. The Rr wave WP energy peak has a correlation coefficient of \(-\)0.433, which is less than 0.6 at angles of 90-180\({}^{\circ}\). The angle evaluation in this paper involves two parts: 0-90\({}^{\circ}\) and 90-180\({}^{\circ}\). Although the Rr wave WP energy peak has a low correlation with angles of 90-180\({}^{\circ}\), it can still be a feature parameter for the angle evaluation because it has a good correlation with angles of 0-90\({}^{\circ}\). In Table 3, the Tr wave WP coefficient peak and Tr wave WP energy peak have absolute correlation coefficients below 0.6. According to the correlation coefficient standard, these feature parameters are not chosen for the SVM model for crack depth and angle evaluation. Notably, the Rr wave WP coefficient peak and Rr wave WP entropy have a correlation value above 0.6 at angles of 0-90\({}^{\circ}\). However, they are not selected as feature parameters because these two parameters have low correlation with angles of 90-180\({}^{\circ}\), and the correlation with angles of 0-90\({}^{\circ}\) is not sufficiently high. Another important reason is expounded in the following section: the correlation coefficients among the feature parameters as another selection standard must be considered and discussed.