Polygonal wheels are one of the most common defects in train wheels, causing a reduction in comfort levels for passengers and a higher degradation of vehicle and track components. With the aim of contributing to the safety and reliability of railway transport, this paper presents the development of an innovative methodology for classifying polygonal wheels based on a wayside system. To achieve that, a numerical train-track interaction model was adopted to simulate the passage of a freight train over a virtual wayside monitoring system composed of a set of accelerometers installed on the rails. Then, the acquired acceleration time series was transformed to a frequency domain using a Fast Fourier transform (FFT), and on this data, damage-sensitive features were extracted. The features based on Principal Component Analysis (PCA) showed great sensitivity to the harmonic order, while the ones based on Continuous Wavelet Transform (CWT) model showed great sensitivity to the defect amplitude. One step further, all features are merged using the Mahalanobis distance in order to obtain a damage index strongly correlated with the polygonal defect. Finally, a cluster analysis allowed the automatic classification of polygonal wheels, according to the harmonic order (harmonic-based) and defect amplitude (amplitude-based). The proposed methodology demonstrated high efficiency in identifying different types of polygonal wheels using a minimum layout of two sensors.