## 6 Conclusions  
In this work, a procedure to detect crack initiation in a railway axle due to fretting fatigue has been developed. The proposed methodology is based on applying the Wavelet Packet Transform (WPT) to acoustic emission (AE) signals in order to analyze their energy distribution. To ensure the most efficient signal analysis, a selection procedure was conducted to identify the optimal mother wavelet for this application, resulting in the choice of the db10 wavelet, which demonstrated the highest classification performance and best class separation when used with a bagged trees model. This combination yielded not only a high success rate but also a low false alarm rate, making the classification both accurate and reliable.  
Importantly, the energy of the packets was calculated at a decomposition level of 3, which strikes a balance between computational efficiency and feature resolution. This allowed for fast results, while the cumulative energy curve revealed a clear energy increase around 12 million cycles, potentially indicating crack initiation.  
A key advantage of the proposed method lies in its ability to operate directly on raw AE data, avoiding the need for prior clustering or extensive post-processing. The wavelet transform effectively acts as a filter that highlights damage-related signal components, due to its adaptability to transient features typical of crack formation. As a result, the methodology enables automatic and real-time condition monitoring of the axle.  
Moreover, the speed of the method is mainly due to its automated nature, which allows results to be obtained almost immediately. The methodology has been specifically optimized to provide the most reliable results in the shortest possible computation time, making it highly efficient for practical applications.  
Conceptualization, M.Z.; methodology, M.Z.; software, M.Z. and M.C.; validation, M.Z., M.J.G. and C.C.; formal analysis, M.Z.; investigation, M.Z. and M.C.; resources, M.C.; data curation, M.Z.; writing--original draft preparation, M.Z. and M.C.; writing--review and editing, M.Z. and M.C.; visualization, M.Z. and M.C.; supervision, M.C., M.J.G. and C.C.; project administration, M.C.; funding acquisition, M.Z. and M.C. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Figure 10: Cumulative WPT energy of the AE signals.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
**Acknowledgments:** The authors would like to thank [PERSON] and [PERSON] for the given support and the useful discussion and [PERSON] for the active help given to the research. PoliNDT (Interdepartmental Lab for Non-Destructive Testing and Structural Health Monitoring set at Politecnico di Milano) is also acknowledged for providing the acoustic emission equipment. [PERSON] thanks Universidad Carlos III de Madrid for funding the visiting period at Politecnico di Milano to collaborate on the research work through the \"Ayudas para la movilidad de investigadores de la UC3M en centros de investigacion nacionales y extranjeros en sus dos modalidades 2022\" project.  
**Conflicts of Interest:** The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.