## 5 Feature Parameter Selection
### Correlation Coefficients among Feature Parameters  
The SVM algorithm in this article is a multiparameter algorithm, so the correlations with crack geometry information and the correlations among the parameters should be considered. The correlation coefficients among the selected feature parameters are shown in Table 4.  
In Table 4, the smallest value of 0.004 is the correlation between the transmission coefficient and the Rr wave WP energy peak. The transmission coefficient is a feature parameter of transmission waves in the frequency domain; however, the Rr wave WP energy peak is a feature parameter of reflected waves in the time-frequency domain. Because the frequency domain and time-frequency domain are two different domains and the transmitted waves and reflected waves are uncorrelated, the transmission coefficient and Rr wave WP energy peak have the lowest correlation value. Therefore, the correlation \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Depth** & **Angle (0–90\({}^{\circ}\))** & **Angle (90–180\({}^{\circ}\))** \\ \hline Transmission coefficient & \(-\)0.952 & \(-\)0.132 & 0.140 \\ Transmitted wave peak & \(-\)0.911 & \(-\)0.196 & 0.186 \\ Deconvolution sum & \(-\)0.897 & \(-\)0.062 & 0.230 \\ Tr wave WP entropy & \(-\)0.829 & \(-\)0.312 & 0.080 \\ Reflection coefficient & 0.238 & 0.852 & 0.667 \\ Root mean square of reflected wave & 0.329 & 0.766 & 0.712 \\ Rr wave WP energy peak & 0.116 & \(-\)0.784 & \(-\)0.443 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Selected correlation coefficients. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Depth** & **Angle (0–90\({}^{\circ}\))** & **Angle (90–180\({}^{\circ}\))** \\ \hline Tr wave WP coefficient peak & \(-\)0.105 & 0.316 & \(-\)0.337 \\ Tr wave WP energy peak & 0.592 & 0.279 & \(-\)0.066 \\ Rr wave WP coefficient peak & 0.066 & \(-\)0.654 & \(-\)0.137 \\ Rr wave WP entropy & \(-\)0.104 & 0.734 & 0.487 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Other correlation coefficients for contrast. coefficients in different domains or determined by different wave generation methods are small. This result also suggests that a comprehensive analysis is required in the parameter extraction process to obtain higher accuracy. There is another reason for not choosing the Rr wave WP coefficient peak and Rr wave WP entropy as feature parameters. As discussed in Part A, the Rr wave WP coefficient peak and Rr wave WP entropy are not included in the SVM model partly due to their low correlation with angles of 90-180\({}^{\circ}\). However, another reason is that these two feature parameters have a high correlation with the Rr wave WP energy peak, which has been selected as a feature parameter for the SVM model. The correlation coefficients of the Rr wave, WP coefficient peak, and Rr wave WP entropy with the Rr wave WP energy peak are shown in Table 5.  
In Table 5, the correlation coefficient between the Rr wave WP coefficient peak and the Rr wave WP energy peak is 0.770, and the correlation coefficient between the Rr wave WP entropy and the Rr wave WP energy peak is \(-\)0.976. Compared to Table 4, the values of these two correlation coefficients are sufficiently high to exclude the Rr wave WP coefficient peak and Rr wave WP entropy as feature parameters. To further expound the necessity of the selection standard using correlation coefficients among the feature parameters, we assume that the transmission coefficient is selected as a feature parameter in the SVM model to evaluate the crack depth. The deconvolution sum and Tr wave WP entropy are analyzed as other potential feature parameters for the SVM model. The correlation coefficient between transmission coefficient and deconvolution sum is 0.951, and the correlation coefficient between the transmission coefficient and Tr wave WP entropy is 0.811. The differences between their SVM prediction errors are shown in Figure 15.  
In Figure 15, the SVM model, which uses the transmission coefficient and deconvolution sum as the feature parameters, is defined as A.