###### Abstract  
To intelligently and quickly verify the depths and angles of oblique surface cracks using the laser ultrasound technique, a crack geometry information evaluation method using a support vector machine (SVM) is proposed. The relationships between several parameters--which are based on transmitted waves and reflected waves containing crack geometry information in the time domain, frequency domain and time-frequency domain, and crack size--are presented in detail. To decide which feature parameters are involved in the SVM model, two selection standards are proposed according to the correlations between feature parameters and crack size and between the feature parameters themselves. Finally, a seven-feature-parameter SVM model which has an excellent ability to classify oblique crack depths and angles is built. The results of simulations using the finite element method (FEM) and experimental data show that seven parameters based on the SVM model are available for the oblique surface crack depth and angle evaluation and can be used to nondestructively detect natural cracks. laser ultrasound; support vector machine method; two selection standards; oblique crack +
Footnote †: journal: Applied Sciences  
staggered lasers excited ultrasonic waves at two sides of a rail. Because the receiving time is related to the crack position, by forming two detection images of the crack, this method improves the laser ultrasound's sensitivity to crack widths. [PERSON] [3] found that the arrival times of these scattered waves were related to crack depth and could be used to measure crack depth by analyzing the intersection within the ultrasound propagation using the FEM. All of these studies in the time domain are in the early stage of nondestructive detection, and attention is extended to the analysis in the frequency domain. Second, regarding the frequency domain methods, [PERSON] [4] and [PERSON] [5] used the reflection coefficient and transmission coefficient in the frequency domain to evaluate the crack depth. [PERSON] [6] adopted the critical frequency at which the threshold phenomenon occurred due to the energy transformation of transmission and reflection Rayleigh waves to determine the size of subwavelength surface cracks. [PERSON] [7] developed a practical algorithm to increase the time resolution of an ultrasonic system to inspect pipeline girth welds via deconvolution with autoregressive spectral extrapolation. The referenced studies [4; 5; 6; 7] are analyses in the frequency domain, and these developments helped researchers find more information in the ultrasound waves in addition to the time domain. To obtain a more comprehensive description of crack size, characteristic parameters in the time-frequency domain are also employed. [PERSON] [8] proposed a new feature extraction algorithm based on the wavelet packet algorithm. The algorithm extracts the wavelet packet decomposition coefficients of the denoised signal as characteristic data to quantitatively classify the ultrasonic echo data. [PERSON] [9] used the wavelet packet transformation (WPT) to decompose the original laser ultrasound signal and analyzed the energy attenuation in the time-frequency domain. After the analysis of the reconstructed signals, the characterization's accuracy is improved. This research provided strong support that more information on crack size can be found using WPT analysis. [PERSON] [10] proposed a method based on the wavelet packet transform and singularity value decomposition (WPT-SVD) to extract features from laser ultrasound signals and gauge the depth of surface-breaking cracks. These studies [8; 9; 10] have involved time-frequency domain analysis and have shown its great potential for nondestructive detection. In summary, there is considerable useful information for research in the time domain, frequency domain, and time-frequency domain. Due to all of their previous work, the method of combining and integrating information from different domains to obtain the most comprehensive analysis is introduced to researchers.