## 1 Introduction
Among them, artificial neural networks and deep neural network algorithms have been applied in diverse areas through the years. Although there are many studies in the literature on identifying polygonal damage, most of them are based on onboard approaches. Preferably, the sensors are located in the axle boxes to better capture the excitation frequencies induced by the polygonal wheels. Positioning the sensors in a location close to the damage allows the acquisition of a signal with a high correlation with damage. However, some factors cause signal interference, such as track irregularities, whose defect periodicities or wavelengths may coincide with that of the wheel, excitations in nearby components, and noise [30]. Therefore, for polygonal wheel identification, signal processing techniques are normally used to mitigate interference in the signal. [PERSON] et al. [31] present a numerical work based on processing the axle-box vibration acceleration signals using empirical mode decomposition (EMD) and Wigner-Ville distribution (WVD) techniques to identify the polygonal wheels. [PERSON] [30] proposed a method to detect polygonal wheel damage based on an iterative modified discrete Fourier transform, being promising for estimating the amplitude of the defect. [PERSON] [32] proposed a novel quantitative detection method for polygonal wheels under non-stationary conditions based on an adaptive chirp mode decomposition (ACMD) approach. [PERSON] et al. [33] conceived a novel method to identify polygonal wheels consisting of combining variational mode decomposition (VMD) with the Fast independent component analysis (FastICA), achieving better accuracy in damage identification. [PERSON] et al. [23], using vertical axle box accelerations developed a deep learning model for wheel out-of-roundness (OOR) diagnosis. The authors used three different features (wavelet transform (WT) spectrum, deep learning model, and Fast Fourier transform spectrum) to feed the neuronal network, obtaining results with greater accuracy when using the three features simultaneously. [PERSON] et al. [34; 35] proposed a Multislice Time-Frequency Image Entropy and an activated time-domain image combined with a deep neural network for wheel OOR diagnosis and wheel flat detection, respectively. Both works reveal very good results under ideal and complex real-world scenarios. Regarding wayside monitoring, the most common wheel monitoring systems are wheel impact load detectors (WILDs). They measure the rail response such as strain [36; 37; 38; 39] and vibration [40; 41], by a single or multiple sensors to estimate the condition of the wheels. [PERSON] et al. [36] used strain gauges installed on the rail to determine the wheel-rail impact force, thus assessing the condition of the wheels. [PERSON] et al. [39] proposed a fusion method to associate the samples collected by multiple strain gauges. [PERSON] et al. [40] proposed a method based on the statistical processing of vibration signals to characterize the state of the wheels according to established vibration limits using data acquired by accelerometers installed on the rail. More recently, automatic methodologies based on machine learning have been implemented, with very good results in detecting wheel flat and polygonal wheels [17; 27; 29]. [PERSON] et al. [42] established a reliable damage index for diagnosing wheel defects in real-time based on Hidden Markov Model (HMM) and processing the signal using a Short-time Fourier Transform (STFT). These works follow unsupervised methodologies and typically involve feature extraction using data measured on the track from accelerometers and strain gauges. Concerning polygonal wheels, the reported literature on automatic polygonal wheel identification using a wayside system has been limited so far, and none of them can classify the severity of this defect. In this context, the present research aims to design an unsupervised methodology with machine learning (ML) algorithms to classify polygonal wheels according to the harmonic order and amplitude of the defect.