# Adaptive Beamforming Damage Imaging of Lamb Wave Based on CNN
## 1 Introduction  
Lamb waves, as an effective tool for damage detection and assessment of plate structures, have the advantages of low attenuation, long propagation distance, and sensitivity to structural surface and internal damage [1, 2]. In order to visualize the damage in structures, many scholars have proposed and developed a large number of Lamb wave imaging methods, such as beamforming [3, 4], phased array imaging [5], and neural network [6] methods. These methods help to identify and assess potential problems in structures more clearly, thereby improving the efficiency and accuracy of detection and monitoring. DAS and MVDR beamforming techniques have been widely used in Lamb wave damage imaging methods. [PERSON] et al. [7] successfully achieved the imaging identification of crack damage in aluminum plates using the DAS method based on a phased array of one-dimensional piezoelectric wafer active sensors. [PERSON] et al. [8] achieved the detection and localization of structural damage using the DAS beamforming method with signals extracted from a network consisting of four sensors only. [PERSON] et al. [9] proposed an improved DAS method, which achieved imaging of impact damage in composite plates byadding windows to the received signals. [PERSON] et al. [10] acquired Lamb wave signals using a completely non-contact method and used an improved DAS algorithm to achieve damage imaging of aluminum plates. Although DAS is a simple and effective damage imaging method, one of its main shortcomings is the poor suppression of undesired interference signals. To improve the performance of Lamb wave damage imaging, [PERSON] et al. [11] introduced the MVDR method to the nondestructive testing of distributed arrays. Subsequently, [PERSON] et al. [12] demonstrated through damage imaging experiments on aluminum plates that the MVDR method can significantly improve the image quality compared to DAS. [PERSON] et al. [13] found that the MVDR method improves the suppression of interfering Lamb modes using uniform rectangular arrays and exhibits higher resolution and better sidelobe and mode suppression. [PERSON] et al. [14] used the MVDR algorithm, which incorporated local signal correlation coefficients as damage features, thereby improving the performance of Lamb wave damage imaging by providing more reliable damage indicators. [PERSON] et al. [15] proposed a weighted sparse decomposition coefficients-based MVDR method and validated it in quasi-isotropic composite laminates. [PERSON] et al. [16] proposed an adaptive diagonal loading MVDR method, which improves the imaging quality of the conventional MVDR method. The above studies have facilitated the application of MVDR methods in the field of Lamb wave SHM. However, the MVDR method requires computing adaptive weights by inverting the covariance matrix, which not only encounters the problem of matrix ill-conditioning but also has high computational complexity, leading to a significant increase in imaging time and making real-time SHM challenging. With the development of machine learning techniques, deep learning networks have been used for damage detection based on ultrasound guided waves [17; 18; 19]. [PERSON] et al. [20] collected the scattering signals of Lamb waves interacting with various types of defects experimentally, obtained the amplitude-frequency characteristics of these signals by using fast Fourier transform, and then utilized these characteristics as inputs to a deep neural network model. This approach established a mapping relationship between the amplitude-frequency characteristics of the scattering signals and the damage locations, thereby achieving accurate defect localization. [PERSON] et al. [21] proposed a sub-wavelength defect super resolution visualization method by using the U-Net network to extract the defect edge information of ultrasound images and achieved subwavelength imaging of defects. [PERSON] et al.