# Railway Vehicle Wheel Flat Detection with Multiple Records Using Spectral Kurtosis Analysis
## 1 Introduction
[PERSON] and [PERSON] [30] developed a fiber Bragg grating (FGB) method to monitor track-side wheel conditions and detect wheel tread defects. The track-side system with more than 20 fiber Bragg grating sensors installed on the rail allows measuring the bending moments of the rail under a defective wheel. An algorithm is developed to identify potential wheel tread defects using the online-monitored rail responses. The results show that when using the proposed method to process the monitoring data, all the defects were identified, and the results were in accordance with those of the static inspection of the wheelsets. [PERSON] et al. [31] presented a parallelogram mechanism based on the wheel flat detection system to perform the dynamic and quantitative measurement of wheel flats. In their study, the wheel flat could be detected by measuring the change in the vertical displacement of the measuring ruler. The experiments performed in the laboratory showed the effectiveness of the proposed system. The main problem in fault diagnosis is differentiating these fault-related frequencies from the signal spectrum. Since the spectral characteristics of the amplitude modulation component (AM) and the frequency modulation component (FM) are relatively simple and closely related to the fault-related frequencies, the wheel flat information can be disclosed in the spectrum of the AM component and the instant frequency spectrum of the FM component. Therefore, to separate these low-frequency modulation components from the high-frequency carrier signal, a demodulation method can be used [32; 33]. The amplitude envelope and instantaneous frequency of a signal can be adequately estimated by the Hilbert transform [34]. However, the selection of a center frequency and bandpass filter bandwidth poses a challenge to the practical application of these traditional demodulation methods. In fact, the center frequency estimation has a direct influence on the final demodulation result [35]. In other words, extracting the impulsive signal with amplitude modulation is a key preprocessing step before performing the envelope spectrum. Therefore, the critical step is to extract the signal with the highest kurtosis value for each band frequency. One of the innovations of this research is to obtain the center frequency and the bandwidth frequency to apply this information in the envelope spectrum approach to detect a defective wheel. In previous studies, for the successful detection of wheel defects, sensors have been installed along an equivalent wheel perimeter length [21; 36]. However, the study performed by [PERSON] et al. [37] shows that this amount of sensors is not necessary to identify the defective wheel. Installing sensors along an equivalent wheel perimeter length is useful for identifying specific moments when wheel flat impacts occur. Moreover, most previous studies have relied on engineering experiments regarding flat detection rather than sufficient theoretical analysis. With this in mind, this paper established a 3D numerical dynamic model of a vehicle-track coupling system and analyzed the sensitivity and reliability of different sensors and setups to detect wheel flats. A more useful scheme based on multisensor arrays was proposed to capture the abnormal responses caused by wheel flats. A wheel flat recognition methodology was developed using simulated sensor output signals. Another innovation of this research compared to the previous studies from the authors [21; 36; 37] is reducing the number of installed sensors and optimizing their position.