## 5 Damage Detection in Wavefield Images Based on NCA-RPCA Algorithm
### Establishment of Lamb Wave Damage Model and Parameter Selection
#### 5.1.3 Algorithm Parameter Selection  
In this experiment, a number of wave damage images with different positions, sizes, and numbers were selected for processing, and all the pictures were processed with a resolution of \(768\times 768\) and the consistent resolution of the pictures is beneficial to unify the processing flow and improve the processing efficiency, as well as facilitating the comparison and output of the results. In order to simulate the actual situation, noise was added to each picture again, and the effect of noise on the outliers was studied by increasing the experiments with different noise densities. In order to further analyze the relationship  
Figure 10: Time-domain waveform of the excitation signal.  
between outliers and noise, the adaptive thresholding method is used, and the noise is processed according to different threshold parameters \"a\". By observing the changes in the number of outliers under different noise density conditions as the threshold \"a\" change, we hope to reveal the correlation between noise density and outliers, as well as the effectiveness of the adaptive thresholding method in dealing with noise, and the experimental results are shown in Figure 12. These experiments will help validate the effectiveness of our algorithm in complex noise environments and provide a more in-depth understanding and guidance for damage recognition in real scenes.  
From Figure 12, an evident trend can be observed: a clear positive correlation exists between noise density and the number of outliers. As the noise density increases, the number of outliers also increases, which is not favorable for subsequent data processing. Excessively low noise density may lead to an overly idealized scenario that does not align with real-world conditions. Thus, noise density is a crucial influencing factor that requires careful selection to ensure the accuracy and reliability of subsequent data processing. In this context, we opted for an intermediate value, selecting a noise density of 0.05 to provide a better simulation of real-world situations.  
After determining an appropriate noise density, the impact of varying the threshold \"a\" on damage detection outcomes was also studied, particularly for images with different locations of damage. In scenarios with higher noise density, increasing the threshold \"a\" can effectively enhance noise removal. Conversely, setting \"a\" too low might overly retain noise,  
Figure 11: Wavefield images of failed grids.  
Figure 12: Relationship curve between different noise densities and the threshold “a” for outliers.  
leading to outcomes that do not align with reality. Therefore, when selecting the value of \"a\", it is necessary to strike a balance between noise reduction and information preservation.  
For the 200 mm \(\times\) 200 mm aluminum plate, 10 defects were selected at different positions (varying both horizontal and vertical coordinates), and their threshold values were defined within a certain range. The results, shown in Figures 13 and 14, reveal that these threshold values for different defect locations exhibit a relatively small and stable fluctuation range, ranging from 0.027 to 0.033. Consequently, by selecting a threshold value of 0.033, excellent identification outcomes can be achieved for various defect locations. This threshold value effectively filters out unwanted interferences while retaining the sparse values of interest, namely, the damaged regions. This finding is of significant importance for the excellent optimization of our algorithm.