## 5 Damage Detection in Wavefield Images Based on NCA-RPCA Algorithm
### Wavefield Image Damage Identification of Single Defects Based on NCA-RPCA Algorithm
#### 5.2.3 Wavefield Image Damage Identification of Multiple Defects Based on NCA-RPCA Algorithm  
In the process of further demonstrating the effectiveness of the algorithm, we conducted another round of experiments using wavefield damage images. Initially, we changed the positions of the defects and increased their number. This implies that the algorithm needs to face more complex and diverse challenges. We increased the number of defects to two and three, respectively, with each defect having different shapes, sizes, and positions. Among them, one defect was made smaller. After constructing these scenarios, we applied the algorithm for defect detection, and the extracted wavefield damage images are shown in Figure 25.  
Using the adaptive thresholding method to remove noise and irrelevant information, the results are shown in Figures 26 and 27. After the denoising process, the algorithm successfully retained the targeted anomalies for identification. While effectively preserving the desired anomalies, the denoising process contributes to enhancing the algorithm's excellence and stability. By reducing redundant information in the image, the computational complexity of the algorithm is reduced, leading to faster processing speeds. This, in turn, results in improved excellence, especially in real-time or large-scale data processing scenarios.  
Figure 23: The sparse matrix after denoising at the edge of the plate.  
Figure 24: Recognition results in the original image at the edge of the plate.  
The algorithm successfully and accurately identified two distinct defects, one of which was particularly pronounced and featured finer details. This further underscores the remarkable excellence and adaptability of the algorithm in multi-defect detection scenarios. It demonstrates that the algorithm maintains a high detection capability for various types of defects, whether they are larger defects or subtle details, providing precise identification and localization. In real-world engineering scenarios, a variety of complex defects may arise, potentially with varying numbers and types. To evaluate the algorithm's robustness and scalability, as well as its potential to handle multi-defect situations in practical engineering applications, the number of defects was further increased.  
The results demonstrate that the NCA-RPCA algorithm not only performs exceptionally well in detecting single defects but also exhibits outstanding excellence when dealing with multiple defects. Whether facing single or multiple defects, the algorithm is capable of accurately identifying and reliably marking them. Detecting multiple defects is a complex and challenging task, as these defects might possess different shapes, sizes, and locations, and their proximity could introduce interference, increasing the complexity of detection.  
Figure 27: The identification results of two defects (**left**) and three defects (**right**).  
Figure 25: Wavefield damage images for two different defects (**left**); three different defects (**right**).  
However, the algorithm showcases remarkable robustness and adaptability, successfully detecting all defects accurately. This further substantiates the algorithm's reliability and effectiveness in various defect scenarios.