## 4 Evaluation and Discussion
### Case Study  
As shown in Figure 8, in the correlation heatmap view of AE data from both sides of the recessed material, the closer the value in the red blocks is to 0, the weaker the correlation between the two features, and conversely, the stronger the correlation. By clicking on a block, the AE event relationships between the two features in the feature detail view is displayed. It can be observed that features such as \"peak_volt\" and \"RMS\" exhibit a strong correlation. We select features with weak correlations for principal component analysis. By selecting AE features (frequency, duration, peak_volt, rise_time, and peak_frequency) to compare with the lower panel and clicking the PCA button, we can observe which feature is more dominant in the PCA view. As shown in Figure 8, the peak_volt feature, with a max value of 0.7 points, from both recessed materials is the most dominant. The frequency of 0.69 is closer. Furthermore, by selecting the peak_volt feature and frequency feature for clustering, clustering views can be obtained, as shown in Figure 9, where the trend of AE events can be seen. As shown in Figure 9, the change points in the multiple-line plots represent anomalous variations in AE events (the red box area). We can save and evaluate the current clustering features by clicking the CO-AE button, resulting in an SC value of 0.81 and an Xie-Beni value of 2.49, respectively, indicating good clustering performance. Upon observing the anomalous variation in the force loading, we select the anomalous points within the range of 0.2-0.3 for further analysis. By clicking the \"choose\" button in Figure 9 and entering the force loading value of 0.23 or 0.25, five pattern plots are generated in the Dividing Point I view. Examining these plots reveals a distinct red state on the outer arc in one plot, indicating that severe material damage occurred near a force stroke of 0.23. The clustering results of two kinds of AEs show that material damage occurs near a force loading of 0.23, and the trend of damage events can be seen from the subsequent AE curves. Figure 8: AE feature analysis of center side concave material. Among ‘frequency’, ‘duration’, ‘peak_volt’, ‘rise_time’, and ‘peak_frequency’ features, ‘peak_volt’ scored the highest in the principal component analysis. Figure 9: Comparison of AE events under two clustering methods. The results show the initial damage state of the material occurred at a force loading of 0.23. (**a**) is the result of the K-means++  
method for 3-clustering of AE data. (**b**) is the result of the FCM method for 4-clustering of AE data. The blank star in (**a,b**) is the clustering center of the horizontal dotted line closest to it. And these four lines are trend lines for clustering of AE events generated based on the values of the set clustering method. The dots and dotted lines of each color correspond to same color, indicating the clustering trend of a type of AE event. (**c**) is the glyph plots of Dividing Point I when the force loading is 0.23. (**d**) is the glyph plots of Dividing Point I when the force loading is 0.25. In the following, we examine the characteristics of material damage during the second phase using DIC data. By observing the changes in the DIC images, more intuitive information on deformation trends can be obtained. As shown in Figure 10, by examining the colored feature views of \(U\), \(V\), \(E_{xx}\), \(E_{xy}\), and \(E_{yy}\), the corresponding material damage features can be identified in each image. Increasing the force loading value to 1 reveals significant deformation in the \(E_{yy}\) direction (see Figure 10). Compared with the \(E_{xx}\) direction change process, when the force loading is 0.8, 0.95, and 0.98 (see Figure 11a-c), the image shows that the material has been severely damaged at a loading of 0.95-0.98. The red feature view shows the obvious morphological change of damage in the two concave parts of the material, and the white area in the green and blue views also verifies this.