# Adaptive Beamforming Damage Imaging of Lamb Wave Based on CNN
## 5 Conclusions  
A deep-learning-based improved Lamb wave adaptive DAS beamforming imaging method is proposed. This method employs a compact, CNN-model-based beamforming architecture that significantly enhances the speed, resolution, and SNR of Lamb wave damage imaging. The CNN method directly maps the delayed Lamb wave input signals from each channel into adaptive beamforming weight vectors through the network model, avoiding the need for the inverse calculation of weight vectors by inverting the covariance matrix of the delayed signals, as required in the MVDR method.  
Through numerical simulations and experiments, single and double damages in aluminum plates were imaged using the proposed CNN-weighted adaptive DAS beamforming method, as well as the traditional DAS and MVDR methods. A comparative analysis was conducted on the quality of damage imaging, transverse damage index profiles at the damage sites, and quantitative comparisons of the API and SNR. The results show that the resolution and SNR of the CNN-based method can approach or match those of the MVDR method, while being significantly better than those of the DAS method. Specifically, the CNN-based method exhibits a narrower main lobe width and lower side lobe levels, with superior quantitative metrics, such as those of API and SNR, compared to the DAS method. In the experiments with three preset damages, the CNN method achieved an API that was only one-third of that obtained by the DAS method, while also attaining an SNR nearly 40 dB higher than that of the DAS method. Since the constructed CNN network establishes a nonlinear mapping relationship between the input and the output during the training stage, the trained model can quickly predict the weighting parameter for various channels during the testing stage.  
The CNN-based adaptive Lamb wave beamforming technique effectively addresses the computational inefficiency and real-time challenges of conventional MVDR methods, whilst preserving high-resolution and high-SNR imaging capabilities. This advancement facilitates rapid, precise damage imaging, thereby enhancing real-time SHM efficacy. Despite achieving a notable balance between imaging efficiency and quality, the proposed CNN approach currently underperforms compared to the MVDR method in imaging quality. Future research will focus on expanding the model's application to complex structures and analyzing how model architecture and parameter choices affect imaging quality, with the goal of improving the imaging results' SNR and API.  
Conceptualization, G.X., B.X. and Y.L.; methodology, G.X., B.X. and Y.L.; software, R.S. and Z.Z.; validation, S.Z., C.X. and Z.Z.; formal analysis, R.S. and G.X.; investigation, R.S., Z.Z. and G.X.; resources, R.S. and Z.Z.; data curation, R.S. and Z.Z.; writing--original draft preparation, R.S. and Z.Z.; writing--review and editing, S.Z., C.X., G.X. and B.X.; visualization, R.S., G.X. and Z.Z.; supervision, G.X. and C.X.; project administration, B.X. and S.Z.; funding acquisition, B.X. and S.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (NNSFC), grant numbers 62071205 and 62271235; the Research Innovation Program for College Graduates of Jiangsu Province, grant number KYLX15_1045; and the Foundation of State Key Laboratory of Dynamic Testing Technology, grant number 2022-SYSJJ-10.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
Thanks to [PERSON] and his team for their support in providing the experimental platform for the completion of this paper.