## 4 Selection of the Mother Wavelet
In this study, all the available models within the app were trained using the same dataset, and their performance was compared based on accuracy. The model that achieved the highest success rate (i.e., classification accuracy) was the Ensemble Bagged Trees, which was, therefore, selected for further analysis. This model is also used to generate the comparison results presented in Table 2.  
Ensemble methods like Bagged Trees improve predictive performance by combining multiple weak learners (in this case, decision trees) into a strong overall model [55; 56]. Decision trees are intuitive, tree-structured models used to assign class labels based on input features. However, a single decision tree may be prone to overfitting or high variance. The concept of \"bagging\" (bootstrap aggregating) helps mitigate this by creating several random subsets of the training data (with replacement), training an individual tree on each subset, and then averaging the predictions of all trees. This aggregation process enhances robustness and overall accuracy compared to a single decision tree. Figure 5: Mean energy of the packets for each selected signal and change point. Figure 6: DEV evolution of different families of mother wavelets: (**a**) Daubechies, Coiflets and Symlets; (**b**) DEV (%). The choice to select the model with the highest accuracy is justified by the fact that accuracy is a widely accepted performance metric for classification tasks, especially when the dataset is balanced and the goal is to maximize correct classification across all classes. In this context, accuracy provides a reliable indication of the model's generalization capability. The mother wavelet with the highest success rate will be the optimal for the study case. Then, according to the highest success rates, db10 has been chosen as the optimal mother wavelet for this application, and it will be used in a further analysis to detect damage. In Figure 7a, the mother wavelet db10 is shown, and in Figure 7b, an example of a typical AE burst signal is represented. It can be seen that both functions are very similar. In Figure 7a, the time-domain representation of the db10 mother wavelet is shown, while Figure 7b displays a typical acoustic emission (AE) burst signal acquired during the test. Although the two functions are not identical, they share key morphological features that justify the suitability of db10 for this application. Both exhibit short-duration, asymmetric waveforms with rapid rise times, followed by decaying oscillations, a typical signature of transient, burst-type signals. The db10 wavelet, with its 10 vanishing moments and compact support, offers high time-frequency localization and is capable of representing signals with sharp transients and abrupt changes. This structural similarity facilitates the projection of AE signals onto the wavelet basis, enhancing the concentration of energy in a small number of coefficients during the WPT. Consequently, db10 allows efficient feature extraction and signal representation, particularly for damage-related AE events that manifest as short, high-energy bursts. The confusion matrix of the model is shown in Figure 8. It reveals a high classification performance for both classes. Specifically, for class 0, the true positive rate (TPR) is 97.5%, meaning that the model correctly identifies 97.5% of the signals belonging to this class, while the false negative rate (FNR) is only 2.5%. Similarly, for class 1, the TPR is 95.6%, and the \begin{table}
\begin{tabular}{c c} \hline
**Mother Wavelet** & **Success Rate (\%)** \\ \hline Db10 & 96.8 \\ Coif4 & 95.6 \\ Coif5 & 96.4 \\ Sym6 & 95.6 \\ Sym8 & 95.7 \\ Sym9 & 96.0 \\ Sym10 & 95.7 \\ \hline \end{tabular}
\end{table} 
Table 2: Success rate of Ensemble Bagged Trees model for the preselected mother wavelets. Figure 7: Similarity of mother wavelet function to AE events: (**a**) Mother wavelet db10; (**b**) Example of AE burst signal. FNR is 4.4%.