# Adaptive Beamforming Damage Imaging of Lamb Wave Based on CNN
## 4 Discussion and Analysis of Results
### Simulation Results and Analysis  
In order to compare and validate the damage imaging performance of the proposed CNN method, Figure 6 give the imaging results for single damage. Figure 6a,c,e are all 2D planar images of the imaging, while (b), (d), and (f) are the corresponding 3D images; (a) and (b) correspond to the DAS method, (c) and (d) correspond to the MVDR method, and (e) and (f) correspond to the CNN method. The magnitudes of the results in the figures are normalized by their respective maxima, and the damage locations are marked by white circles. Figure 5: Simulated 100 random damage locations. Figure 6: Imaging results of three imaging methods on single-damage simulation data: (**a**) DAS, 2D, (**b**) DAS, 3D, (**c**) MVDR, 2D, (**d**) MVDR, 3D, (**e**) CNN, 2D, (**f**) CNN, 3D. A comparative analysis of the imaging results shown in Figure 6a,c,e reveals that all three methods achieved accurate damage localization. However, the damage area identified by the DAS method exhibited a notably larger spatial extent beyond the marked boundaries, whereas the damage regions reconstructed by both the MVDR and CNN methods were confined within the marked boundaries. As demonstrated in the 3D intensity distributions (Figure 6b,d,f), the MVDR and CNN methods produced significantly sharper focal peaks compared to the DAS method. Specifically, the MVDR results were nearly noise-free, while the CNN method introduced minimal noise--both of which were substantially lower than the noise levels observed in the DAS results. These findings indicate that the proposed CNN-based method achieved imaging performance comparable to the MVDR method and significantly outperformed the DAS method. The CNN framework effectively suppressed most background noise in the images, resulting in a more compact and precise representation of the damage region. Quantitative comparisons from Table 1 indicate that the MVDR method achieved the smallest API and the highest SNR. Specifically, the CNN method achieved an API that was approximately one-ninth that of the DAS method, with an SNR that was about 70 dB higher. To further compare the results of the three methods, the pixel intensity profiles along the horizontal line at the pre-damaged position y = 150 mm are plotted in Figure 7. The comparison shows that all three methods achieved their maximum values at x = 0 mm, confirming that the damage localization accurately corresponded to the pre-damaged position. However, both the CNN and MVDR methods exhibited sharper amplitude distribution curves, indicating that the CNN method had a narrower main lobe width and lower side lobe levels compared to the DAS method. Therefore, the CNN method outperformed the DAS method in terms of narrowing the main lobe width, suppressing background noise, and reducing side lobe levels. Figure 8 presents the dual-damage imaging results, demonstrating that all three methods accurately identified and localized the two damages. Similar to the single-damage scenario, the damage areas reconstructed by the DAS method (Figure 8a) extended beyond the marked boundaries, whereas those from the MVDR and CNN methods (Figure 8c,e) \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**DAMAGE**} & \multicolumn{3}{c}{**API**} & \multicolumn{3}{c}{**SNR (dB)**} \\ \cline{2-7}  & **DAS** & **MVDR** & **CNN** & **DAS** & **MVDR** & **CNN** \\ \hline \((0,150)\) & 36.50 & 2.32 & 4.16 & 19.58 & 121.12 & 95.62 \\ \((-20,180)\) & 38.26 & 2.62 & 4.68 & 21.41 & 120.28 & 89.08 \\ \((20,130)\) & 35.32 & 2.26 & 5.03 & 20.35 & 119.53 & 93.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Quantitative analysis and comparison of evaluation metrics for simulated imaging results. Figure 7: Transverse damage index profiles at y = 150 mm for different imaging methods based on simulation data: (**a**) full view, (**b**) zoom-in view. remain confined within the marked regions.