## 1 Introduction  
The interaction between the wheel and the rail gives rise to diverse forms of out-of-round wear on rail vehicle wheels. Operational wear on these wheels can manifest in various types, with the nature of the wear being influenced by the characteristics of the wheel-rail contact forces. Wheel wear can exhibit either uniform patterns or irregular ones [1], with irregular wear comprising both local and continuous wear. Local wear typically results from braking or worn-out treads [2], whereas continuous wear is commonly attributed to polygonization or corrugation [3]. These defects promote negative effects on both the vehicle and the track, increasing maintenance costs. From a railway safety point of view, wheel defects are one of the main causes of accidents, decreasing the reliability of this mode of transport [4]. Polygonal wheels are one of the most common defects in the railway wheel and consist of a periodic variation of the radius of the wheel along the circumference. Its wheel profile results from the superposition of several waves of harmonics characterized by a dominant harmonic order [5]. According to [PERSON] et al. [6], when the amplitude of the defect assumes values above 0.2 mm and wavelengths between 140 mm and the wheel circumference, it is a polygonal wheel defect; otherwise, when the wavelength assumesvalues between 30 and 80 mm, it is considered a corrugation. The excitation frequencies it promotes cause a large fluctuation in the contact forces between the vehicle and the track, resulting in increased vibrations in the system [7; 8]. Polygonal wheels increase the risk of rail breaks, sleeper and track fixing device cracking, axle damage, bearing damage, etc. [9]. It also increases the noise emissions inside and outside the vehicle, decreasing the comfort levels [10]. Depending on the vehicle's characteristics and the type of harmonic order present in a polygonal wheel, the frequency excited by the polygonal damage may cause a resonance effect [11; 12]. Thus, it is desirable to continuously monitor the health status of the wheels to prevent this defect. To monitor the condition of railway systems in service, two approaches are usually used on-board and wayside. These systems can be used to monitor both the infrastructure and the vehicle. In the latter, measuring devices can be installed on the rail and sleepers or in areas surrounding the rail. On the other hand, onboard monitoring systems involve the installation of sensors on the vehicle to gather extensive data from the system consistently. This category encompasses various techniques such as magnetic methods [13], ultrasonic methods [14], acoustic methods [15], and vibration methods [16]. Wayside techniques, depending on the type of sensors employed, include strain gauges [17], fiber optic sensing technology [18], ultrasonic techniques [19], vibration techniques [18], acoustic emission [20], as well as lasers and high-speed cameras [2]. From an economic standpoint, adopting an indirect approach such as Infrastructure to Vehicle (I2V) for wayside detection and classification of wheel defects and Vehicle to Infrastructure (V2I) for onboard systems to detect and classify track defects proves more advantageous. This is due to the capability of a single-section track instrumented to monitor all passing vehicles using a reduced number of sensors, and conversely, a single vehicle's ability to monitor an entire railway line [21]. The application of sensors on the track allows the extraction of a wide range of data regarding all vehicles that circulate on the track, making it possible to monitor several ranges of vehicles with a reduced number of sensors, which does not happen with the onboard system. Recently, machine learning (ML) algorithms were implemented based on dynamic responses, such as artificial neural networks (ANN) [22], deep neural networks (DNN) [23; 24; 25; 26], principal component analysis (PCA) [27], wavelet continuous transform (CWT) [28], and autoregressive (AR) models [29].