## 6 Simulation Evaluation Results  
The data set includes 180 data samples covering 10 crack depths and 15 angles and is divided into 150 training samples and 30 test samples. The input parameter number of the SVM model is 7, and the output parameter number of the SVM model is 10 depths and 15 angles in this paper, so there must be at least 1720 samples for training if a feed-forward neural network with nine hidden layers is used. Therefore, the number of samples in this work for training satisfies the quantity for small samples.  
To show the linear relationship between feature parameters and crack depths and angles, seven feature parameters selected in this paper of 150 training samples are converted to one-dimensional data of 150 training samples adopting the KPCA method.  
KPCA is a widely used method in data dimension reduction. This method can minimize the loss of information while compressing the data and retain the overall characteristics of all feature parameters. In this paper, the KPCA method is adopted to convert seven feature parameters to one KPCA parameter, which can show the overall relationship between the selected parameters and the crack geometry information.  
Figure 16 shows the 3D map with depth as the \(X\) axis, angle as the \(Y\) axis, and the normalized feature parameter as the \(Z\) axis.  
Figure 16: Three-dimensional map of depth and angle versus feature parameter.  
Figure 15: SVM prediction error differences between A and B.  
In Figure 16, when the depths and angles increase, the feature parameter gradually decreases. There is a good correlation between the feature parameter and the crack depths and angles. Therefore, the feature parameters are suitable for the SVM model to predict the crack depths and angles.  
Using the feature parameters, the depth and angle prediction results and the actual depth and angle sequences are shown in Figure 17.  
Figure 17 shows that the correct rate of crack depth prediction in the depth range of 0.2-0.6 mm reached 100%. All error values are only one depth step. Figure 17c,d show that the accuracy of angle prediction reached 100% in the angle range of 22.5-70\({}^{\circ}\), 90-120\({}^{\circ}\), and 135-150\({}^{\circ}\). The prediction results of depth and angle error sequence diagrams using different numbers of parameters are shown in Figures 18 and 19.  
Figure 18: SVM depth prediction errors.  
In Figures 18 and 19, the five parameters in (a) are the seven selected parameters except for the Tr wave WP entropy and Rr wave WP energy peak. The nine parameters in (c) are the seven selected parameters, Tr wave WP coefficient peak, and Rr wave WP coefficient peak. The depth and angle classification errors of this paper using the seven-parameter SVM model are shown in Figures 18b and 19b, respectively.  
In Figures 18a-c and 19a-c, the depth and angle prediction errors using five, seven and nine feature parameters are shown, respectively. In Figure 18a-c, the error numbers are eight, four, and six, respectively. Figure 19a-c also show that the prediction angle errors using the seven parameters in (b) are the smallest. The results show that the seven chosen parameters have the best ability for evaluating oblique crack depths and angles, which also verifies the correctness of the proposed feature parameter selection standards. Therefore, this article selects these seven feature parameters to  
The 110 groups of experimental data containing eleven angles (30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), 70\({}^{\circ}\), 80\({}^{\circ}\), 90\({}^{\circ}\), 100\({}^{\circ}\), 110\({}^{\circ}\), 120\({}^{\circ}\), 135\({}^{\circ}\), 150\({}^{\circ}\)) were randomly selected; 88 groups were selected as the training set, and the remaining 22 groups were selected as the test set. Sixty groups of experimental data of six depths (0.1-0.6 mm) were randomly chosen; 48 groups were selected as the training set, and the remaining 12 groups were selected as the test set. The experimental data were a set of small samples applicable for the quantity of the SVM method.