###### Abstract  
Structural damage identification has been one of the key applications in the field of Structural Health Monitoring (SHM). With the development of technology and the growth of demand, the method of identifying damage anomalies in plate structures is increasingly being developed in pursuit of accuracy and high efficiency. Principal Component Analysis (PCA) has always been effective in damage identification in SHM, but because of its sensitivity to outliers and low robustness, it does not work well for complex damage or data. The effect is not satisfactory. This paper introduces the Robust Principal Component Analysis (RPCA) model framework for the characteristics of PCA that are too sensitive to the outliers or noise in the data and combines it with Lamb to achieve the damage recognition of wavefield images, which greatly improves the robustness and reliability. To further improve the real-time monitoring efficiency and reduce the error, this paper proposes a non-convex approximate RPCA (NCA-RPCA) algorithm model. The algorithm uses a non-convex rank approximation function to approximate the rank of the matrix, a non-convex penalty function to approximate the norm to ensure the uniqueness of the sparse solution, and an alternating direction multiplier method to solve the problem, which is more efficient. Comparison and analysis with various algorithms through simulation and experiments show that the algorithm in this paper improves the real-time monitoring efficiency by about ten times, the error is also greatly reduced, and it can restore the original data at a lower rank level to achieve more effective damage identification in the field of SHM. L +
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structural health monitoring research. It involves exciting certain forms of Lamb waves in plate-like structures through an integrated advanced sensor network within the structure. The collected responses are then analyzed to monitor the structural condition and assess any damages. These waves have been widely used to determine surface defects in SHM and large metal structures. Lamb waves exhibit diverse propagation characteristics in complex structures, making them suitable for monitoring various types of structural damages, including fatigue cracks, corrosion, impacts, and collisions. Moreover, their long-range propagation enables scanning the entire structure through localized excitation, resulting in a wide detection range. By monitoring and analyzing Lamb waves, it becomes possible to identify and locate damages, such as internal defects and cracks within the structure. Additionally, the technique allows for the assessment of the remaining useful life of the structure, providing essential information for maintenance and repair decisions. Many Lamb wave-based methods for damage identification rely on obtaining complete acoustic wavefield data across the structure. These data help describe how the guided waves propagate in time or frequency and, ultimately, how they interact with defects [8]. The wavefield can be driven and sensed using various techniques, such as those based on piezoelectric transducers or scanning laser Doppler vibrometers [9; 10]. However, wavefield imaging demands the collection of a large amount of data. Additionally, even in a laboratory setting, measurements should be repeated frequently and then averaged to mitigate the influence of noise. In the past, many damage identification techniques suffered from high computational complexity and low time efficiency. Therefore, new identification methods were introduced. Principal Component Analysis (PCA) seeks a small set of variables (low-rank) that contain as much information as possible from the original complete variable set [11]. Previous research results have shown that PCA achieves good excellence in SHM for damage detection [12; 13; 14; 15]. For example, ref. [12] describes moving PCA on vibration data.