## 4 Training Process and Results  
One hundred twenty experimental and 120 simulated data samples were collected at defect locations of each different concrete beam. The total samples of the experiment and simulation were randomly selected as 70% for training and 30% for validation, with a learning rate of 0.0001 for both datasets. Figure 15 illustrates the fitting curves of validation accuracy and loss over the number of iterations for the CNN model using experimental data in both dimensions. In the one-dimensional CNN training process shown in Figure 15a, compared with frequency domain data, A-scan data exhibits significantly faster convergence speed and lower loss. On the contrary, the two-dimensional CNN training results in Figure 15b show different trends. During the verification process, the accuracy curves of the spectrum and A-scan image almost overlapped. However, the final verification result of the spectrum was slightly higher than that of the A-scan, while its loss was relatively low. Compared with the one-dimensional CNN model, the spectral data achieved better fitting  
Figure 14: Comparison of (**a**) simulated A-scan and (**b**) spectrum of simulated A-scan for three different defect types; (**c**) experimental A-scan and (**d**) spectrum of experimental A-scan for three different defect types. in the two-dimensional CNN model, demonstrating stronger robustness. As the number of iterations increases, spectral data can converge to the optimal state faster. The classification results in this article are visualized in the form of a confusion matrix, which is an important tool for evaluating the performance of classification models. It displays the relationship between the model's predicted results and the actual results in a matrix format. The depth of the colors in the blocks of the confusion matrix is typically used to represent the quantity or proportion of predictions for each category; generally, the darker the color, the higher the quantity or ratio represented in that section. Figures 16 and 17 show the validation results of the confusion matrix obtained after training the numerical simulation data in one-dimensional CNN and two-dimensional CNN, respectively. In the one-dimensional CNN model, the recognition accuracy of different types of defects in the A-scan spectrum is higher than that in the A-scan spectrum. In contrast, the results in the two-dimensional CNN model are exactly the opposite. Overall, the recognition accuracy of the two-dimensional CNN model for different types of defects in the A-scan and A-scan spectrum is significantly higher than that of the one-dimensional CNN model. In the validation results of the one-dimensional CNN model, 8.3% of cracks were identified as non-dense solids, and more than 10% of voids data were identified as non-dense solids. This situation was effectively improved in the validation results of the two-dimensional CNN model. Figure 15: The fitting curves of the training process of two kinds of convolutional networks for (**a**) the one-dimensional CNN and (**b**) the two-dimensional CNN. Figures 18 and 19 show the validation results of the confusion matrix obtained after training the one-dimensional CNN model and the two-dimensional CNN model, respectively. The verification results are very similar to the simulation data, and the recognition accuracy of A-scan data is better than A-scan spectrum data in one-dimensional CNN models, while the recognition accuracy of A-scan spectrum data is higher in two-dimensional CNN models. It is worth mentioning that the validation results of the A-scan spectrum data obtained in the experiment in the one-dimensional CNN model were lower than those of the simulation data, while the validation results of the A-scan spectrum data obtained in the experiment in the two-dimensional CNN model reached 100%. This indicates that compared with one-dimensional data, two-dimensional data can provide richer data information.