## 3 Materials and Methods
### Visual Design Method  
#### 3.3.1 AE Analysis Views  
Building on expert insights, we design a procedure specifically designed for AE feature analysis, beginning with the representation of correlations between various sound signal features, for which we used [PERSON]'s correlation coefficient (as shown in Equation (3)) to measure the correlation. The method first selects a few representative features used for PCA dimensionality reduction, it then clusters the high-dimensional features based on the principal component coefficients to obtain the clustering results. Finally, by comparing the results of multiple clusters, the accuracy of the damage pattern recognition is improved. \[r_{xy}=\frac{\sum_{i=1}^{n}(x_{i}-\overline{x})(y_{i}-\overline{y})}{\sqrt{ \sum_{i=1}^{n}(x_{i}-\overline{x})^{2}}\sqrt{\sum_{i=1}^{n}(y_{i}-\overline{y })^{2}}} \tag{3}\]  
To visualize feature relationships, we design a correlation matrix in the form of a feature correlation heatmap (Figure 5a) to show the correlation between all pairs of features, with darker squares indicating stronger correlations between features. Users can click on any independent small square to generate a scatter histogram in the feature detail view (Figure 5b) and examine the detailed distribution of any pair of features. After comparing and analyzing the importance of each feature, the preliminary feature selection is complete, and users can interactively add or remove corresponding features by clicking checkboxes to further reduce the dimensionality of the feature set using PCA. In the PCA view (Figure 5c), the size of the principal component coefficients is still represented by color depth, and we also list the cumulative contribution rate under different numbers of principal components in the lower half. Finally, we can select the most representative features in the AE feature set for the clustering analysis (Figure 5d). Before obtaining the clustering results, we allow users to select two effective clustering methods and specify different numbers of clusters and iteration times. We implemented two clustering methods, one of which is the fuzzy C-means (FCM) algorithm, frequently used in previous studies. Since traditional K-means clustering is highly dependent on the selection of initial cluster centers, we also adopted another clustering method, K-means++, which improves the selection of initial centroids for the K-means algorithm. The core idea of K-means++ is that when selecting a new cluster center, the farther a point is from the existing centers, the higher the probability of it being chosen as a new cluster center. In the clustering view, the scatter plots corresponding to each category are distinguished by different colors, and we draw line graphs for the number of interval scatter plots for each category. By showing the trend of changes in the number of scatter plots for each category, potential damage patterns can be identified. To overcome the difficulties experts face in understanding and comparing the quality and effectiveness of different clustering results through visualizations, distinct evaluation metrics are selected for the two clustering algorithms. We chose the Xie-Beni index as the effectiveness evaluation index of the FCM algorithm, with smaller values indicating better clustering effects (as shown in Equation (4)). Figure 5: AE feature analysis visualization. **(a)** Feature correlation heatmap: displays the correlation between acoustic emission data features; **(b)** feature detail view: illustrates the relationship between two specific features; **(c)** PCA view: conducts principal component analysis on the features; **(d)** clustering view: analyzes the clustering of acoustic emission events under force loading conditions. The blank star in **(d)** 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.