## 1 Introduction  
The railway transportation has a rapid growth worldwide, railway safety is a subject of high interest in the research field. Railway axles are one of the most critical elements in railway transportation systems, and failures such as a cracked axle can lead to the derailment and probably human and economic losses. Therefore, the early detection of faults in railway axles is crucial in railway safety [1, 2]. The ultrasound technique can be used to perform condition monitoring over railway axles; however, its disadvantage is that it does not provide continuous information between different tests; therefore,it is not possible to detect fast-growing faults [3]. Other techniques that involve variables, such as temperature [4], acoustics [5], and acoustic emission [1], have been used for the continuous monitoring of faults on railway axles. However, vibration signal monitoring has become the most common monitoring technique due to its high reliability. Fault diagnosis based on vibration signals enables early fault detection, online condition monitoring, and when combined with different signal processing methods and artificial intelligence, better diagnostic results are obtained [6; 7; 8]. Fault diagnosis based on vibration signals with a data-driven approach is generally accomplished in four phases: (a) acquisition and conditioning of the vibration signal, (b) extraction of features, also called condition indicators, (c) selection of features, and (d) classification. After acquisition and conditioning of the vibration signal, in the feature extraction phase, we study the change of the signal behavior that can be an indicator of the fault condition. The study of these changes in the signal can be focused on the time, frequency or time-frequency domains. From these domains, condition indicators (CIs) or features can be extracted, which allows monitoring or detecting different faults [9]. The evaluation of the CIs has been widely studied, leading to achieve good results in the detection of faults in the railway axles. In the time-frequency domain, the energy calculated by means of Wavelet Packet Transform (WPT) has been used, allowing crack detection with excellent results [10; 11]. The above-mentioned works only measured vibrations in the railway axle and bearings in insulation, without the bogie. The work developed by [PERSON] et al. [7] (which is the same case of study of the present work), used real railway axles installed in a real Y21 bogie, where the vibration signals from six accelerometers were processed by means of the WPT energy. The feature selection stage was carried out by means of a visual analysis, the energy packages were selected to increase their values with the depth of the crack, and the packages varied with the change of speed. In the classification stage, a radial-basis function-based artificial neural network was used with 32 inputs corresponding to the selected energy packets, the load and speed values; the two possible outputs of the network were healthy or cracked conditions. This work highlighted that the six accelerometers provide important information for detection and better results are achieved at certain speeds. A recent work, over this same case, presented by [PERSON] at al. [12] evaluated the signals from the six accelerometers; thirty features from the time-domain signal were extracted, then, feature selection was applied, and finally the classification was implemented through a random forest classifier. The best accuracy in the classification was found with ten features, extracted from vibration signals measured with the accelerometers located in the longitudinal direction. The results in this work also show that features such as Wilson Amplitude (WAMP), Wave length (WL), Zero crossing (ZC), Slope Sign Change (SSC), mean, Energy Operator (EO), and the skewness are well-suitable to handle the fault classification. On the other hand, vibrations signals by nature exhibit random behavior in a wide range of applications.