## 1 Introduction  
Ensuring proper maintenance of a railway axle is crucial, as it is a key safety component. Detecting fatigue cracks, able to quickly propagate to failure in axles during service, is currently one of the most significant research areas in the railway field. Nevertheless, according to relevant standards [1, 2], axle design still follows the traditional fatigue limit concept with the consequence that initiation and propagation of cracks, along with failures, are still observed from time to time. This work addresses the phenomenon of fretting fatigue damage [3, 4, 5, 6] in railway axles, which refers to the repeated micro-sliding between two contacting surfaces in a press-fit connection, caused by applied loads and vibrations. Damage, then, starts with the onset of wear and gradually progresses to the formation of microcracks. These can develop into larger surface cracks that may propagate, depending on the applied load, leading to a significant reduction in fatigue life [3,7,8]. In railway wheelsets, this phenomenon can lead to unexpected early failures, typically occurring at the interfaces between the axle and the press-fitted wheels, brakes, or gear wheels [9,10]. For this reason, various approaches have been proposed over time to address refetting fatigue in railway axles [11], including design modifications and maintenance operations based on non-destructive testing (NDT) techniques during service interruptions [12]. However, the current trend favors condition-based monitoring, as it enables real-time or on-demand structural health monitoring (SHM) tools and methods to be applied without interrupting service or disassembling the axles, resulting in cost savings. At present, only a limited number of studies focuses on SHM applied to railway axles. These studies, in terms of methodological approach, primarily utilize acoustic emission (AE) [13, 14, 15, 16, 17], low frequency vibrations [18], high frequency vibrations [19] and automated ultrasonic testing (UT) [20,21]. The only found research specifically addressing refetting fatigue damage monitored through AE is research work by the current authors [22]. The advantages of AE [23] lie in its proven effectiveness across various technical fields and its use of compact, easy-to-handle equipment. However, its main drawback is the vast amount of data generated, which must be managed and interpreted, as not all recorded signals are related to damage developing in the material. Therefore, clustering and classification techniques are typically required to interpret and extract useful data [22,24]. From the point of view of signal processing for the case at hand, numerous studies have explored and applied wavelet techniques to detect damage in various applications [25, 26, 27], some of which are specifically tailored for analyzing AE signals [28, 29, 30, 31]. These approaches are particularly effective for analyzing AE signals associated with the damage initiation phase (static or cyclic plasticity leading to initial material cracking) and the final failure phase (rapid and unstable crack propagation). Both stages are typically marked by high-energy AE events, whereas the stable propagation phase is known to be much more silent [32,33]. A beneficial outcome is that, during the initiation and final failure stages, AE signals related to noise or other non-failure phenomena generally have minimal impact on the overall energy trend of AE events [34]. This is why the acquired waveforms can often be analyzed directly without the need to first classify or cluster out unwanted signals. The Wavelet Packet Transform (WPT) is one of the most widely used tools in defect detection, often relying on the energy content of signals. Additionally, a key advantage of wavelet-based techniques is their ability to function as a filtering process, enhancing the signal-to-noise ratio and enabling the extraction of features from complex signals.