## 5 Post Processing of Acoustic Emission Raw Data  
The WPT is applied using the selected mother wavelet db10 and a decomposition level of 3, resulting in 8 packets, which correspond to equally spaced sub-bands of the analyzed frequency range. This level of decomposition has proven to be sufficient to obtain clear and meaningful results, as supported by previous studies [25,27] and as it was previously explained. Moreover, acoustic emission signals typically concentrate most of their energy in the lower frequency bands. Figure 9 shows the frequency analysis of the damage signal shown in Figure 7b. In is because the phenomena associated with damage initiation and progression (such as micro-crack formation or frictional events) generate transient, low-frequency components that are characteristic of the early stages of material degradation. As a result, a decomposition level of 3 captures the most informative part of the signal without introducing unnecessary computational complexity. This choice not only ensures fast and reliable monitoring but also aligns with the configuration used during the mother wavelet selection stage, thus eliminating the need for additional parameter tuning or repeated calculations. This significantly reduces processing time, which is especially advantageous for real-time condition monitoring and early damage detection applications. Figure 8: Confusion matrix of the Ensemble Bagged Trees (case of the db10 mother wavelet). The Daubechies db10 mother wavelet was found to provide the best performance in this scenario. This can be theoretically justified by considering the specific characteristics of both the wavelet and the AE signals generated by fretting fatigue. Daubechies wavelets, including db10, are well-known for their high number of vanishing moments (10 in the case of db10), which confer excellent ability to represent signals with sharp transients and discontinuities. Such properties make db10 particularly suitable for capturing the burst-type AE waveforms that are typical of crack initiation events, characterized by abrupt changes in amplitude and frequency content. Moreover, the compact support of db10 allows efficient localization of signal features in both time and frequency domains, facilitating the extraction of meaningful energy distributions relevant to damage detection. In Figure 10, the cumulative energy as a function of the number of cycles is shown for the complete set of AE signals (i.e., without dividing them into packets as performed previously). In this case, the WPT is applied to each signal as a whole. A significant increase in energy is observed just before 12 million cycles, marked by a red line in Figure 10. It is known from the literature that both failure initiation and final failure are characterized by a high energy level [57]. As it is known that the fracture takes place at the end of the test, the sudden energy increase may mean crack initiation. From a physical standpoint, the abrupt energy increase reflects the rapid release of elastic energy stored in the material as micro-cracks coalesce into a detectable fracture. This stage of crack progression is marked by higher-amplitude and more frequent AE events, which result in a sudden rise in signal energy. Therefore, the increase in energy not only signals the initiation of damage, but also correlates with the intensity of the underlying fracture mechanisms. This observation is consistent with previous works, but with the added benefit that the current method works directly on raw AE data, making it a simpler and faster approach for in-service crack detection. Furthermore, this methodology enables a straightforward procedure for future crack detection tasks: it is only necessary to apply the wavelet-based energy extraction method and monitor for significant changes in cumulative energy over time. The detection does not require signal segmentation, clustering, or manual interpretation, which enhances its applicability in real-time monitoring systems.