While many studies have been used onboard monitoring methods to detect train wheel defects, this paper aims to extract damage features from vibrational signals obtained by the wayside monitoring system. To provide an appropriate tool for the decomposition of experimental nonstationary vibration signals containing impacts, an analytical amplitude-based signal decomposition method is provided. A two-axle motor car with a flat wheel defect is studied at different operating conditions. Vibrational signals arising from wheel-rail interactions are gathered by the Wayside Data Collection Setup (WDCS) with five piezoelectric accelerometers. The tests are performed at the constant speeds of 10, 20, 30, and 40 km/h. The acquired signals are decomposed by the Multi-channel Singular Spectrum Analysis (MSSA) into the contributing components. Based on the results, increases in the amplitudes of the second reconstructed components (RCs) of the vibrational signals sensed by all the accelerometers can be observed at a specific time instance as a repeating pattern. Similar patterns are obtained at different motor car positions relative to the measurement area, as well as different motor car speeds. To verify the consistency of the second RCs, the crest factors are obtained for all the angular positions. The results show sudden increases in the crest factor at a fixed angular position that indicate the existence of a defect at that specific angular position of the wheel.