# Train Wheel Condition Monitoring via Cepstral Analysis of Axle Box Accelerations
## 6 Conclusions  
The early detection of wheel defects is an important asset management and maintenance task. Wheel vibrations are excited by the imperfections of the wheel and rail and hence contain information on the health status of both assets. These vibrations can be measured by means of ABA sensors.  
In this paper, a promising methodology, the cepstrum analysis, was tested for the application to wheel condition monitoring. The cepstrum is powerful in revealing periodic signals and separating them from the rest of the signal. This makes the cepstrum particularly interesting for wheel monitoring. The vibration signal excited by the wheel profile is periodic with respect to the wheel circumference. This periodicity changes with the rotational frequency of the wheel and hence depends on the speed of the train. This dependency can be compensated for by transforming the ABA data from the time to the spatial domain. To accomplish that, accurate speed information is necessary, which was obtained by fusing IMU and (E)GNSS data. The cepstral analysis was then performed in the spatial domain. The obtained cepstrum itself is then in a spatial domain, which we called navewumber domain to highlight the inverse relation to the wavenumber. The periodicity of the ABA signal excited by the wheel is then represented by a peak in the cepstrum at a wavenumber equal to the wheel circumference. The position of the peak precisely indicates the wheel circumference and can therefore be used to monitor the wheel diameter. The amplitude of this peak provides a measure of the relative contribution of the wheel to the combined wheel-rail roughness. The cepstral wheel monitoring approach presented here requires neither extensive hyperparameter testing nor training data. Ground truth data might be used to define hard thresholds for the detection of certain track defects. However, we think that it is more reasonable and also sufficient to monitor changes in the cepstral features and thus detect deviations from the normal behavior that can be related to wheel defects.  
Through the analysis of experimental data, we could show that the cepstrum analysis is robust under varying operating conditions.  
From these findings we conclude that cepstral analysis of ABA data is a powerful methodology to monitor the wear-related reduction of the wheel circumference and to detect and monitor the evolution of wheel surface defects.  
Conceptualization, B.B.; methodology, B.B.; software, B.B., J.H., T.N. and M.R.; validation, B.B., J.H. and T.N.; formal analysis, T.N.; investigation, B.B.; data curation, J.H.; writing--original draft preparation, B.B.; writing--review and editing, J.H. and M.R.; visualization, B.B.; supervision, B.B.; project administration, M.R. All authors have read and agreed to the published version of the manuscript.  
This project has received funding from the European GNSS Agency under the European Union's Horizon 2020 research and innovation program under grant agreement No. 776402.  
Not applicable.  
Restrictions apply to the availability of these data. Data was obtained in collaboration with the Osterreichische Bundesbahnen (OBB, Vienna, Austria) and are available on request from the corresponding author only with permission of the OBB.  
We would like to thank the OBB for providing the measurement train and for guidance and support during the measurement campaign. We would like to thank the two anonymous reviewers for their valuable comments and advice, which helped to improve the manuscript.  
The authors declare no conflict of interest.