# Condition Monitoring of Railway Tracks from Car-Body Vibration Using a Machine Learning Technique
## 4 Track Fault Detection Using Machine Learning
### Feature Extraction of Track Faults from Car-Body Vibration  
Track irregularities can be used as an index for managing track conditions. The types of track irregularities include longitudinal level irregularities that indicate vertical rail displacement, alignment irregularities that indicate lateral rail displacement, and cross level irregularities that indicate a difference in the elevation of the left and right rails. Because a high degree of correlation exists between these track irregularities and car-body vibrations, the magnitude of car-body vibrations can be an effective method to determine track conditions [12; 13]. The track-condition monitoring system can automatically collect the vertical and lateral accelerations and the roll rate of the car body during travel to detect any longitudinal level irregularities, alignment irregularities, and cross level irregularities. To identify different types of track faults by using machine-learning techniques, it is necessary to extract the features of each type of track irregularity from the car-body vibrations that occur when travelling on a faulty track. The data obtained by learning the extracted features can be used to construct a training model. Subsequently, if unknown car-body vibration data are input to the model, the type of track irregularity and its degradation level can be identified. As shown in Figure 5, we created a baseline track geometry for an assumed regional railway line and a track geometry with increased track irregularities. We subsequently performed a travel simulation by using a track for which all the longitudinal level irregularities, alignment irregularities, and cross level irregularities were within the normal range, and also by using a track for which one type of irregularity was abnormal. Degraded track is generated by the power spectral density of track where the standard deviation becomes twice as large as the normal track. The travelling distance was 1000 m and the travelling speed was 60 km/h. Figure 4: Vehicle model. The acceleration root mean square (RMS) is closely linked to the general health of the running gear and track [12]. Therefore, the acceleration RMS can be used as the primary index to predict the track condition. First, we need to obtain localised RMS values over short time intervals with a small window size to obtain the relationship between track condition and position. The RMS value may be obtained from measured values over a short time segment according to  
\[x_{rms}^{i}=\sqrt{\frac{1}{N}\sum_{j=i}^{i+N-1}x_{j}^{2}}, \tag{1}\]  
where \(x_{j}\) is the measured vertical acceleration, lateral acceleration or roll angular velocity of car-body and \(N\) denotes the sliding window size. Track irregularities include longitudinal level irregularities, alignment irregularities, and cross level irregularities. In order to assess the irregularities, we determine the RMS values of vertical acceleration, lateral acceleration, and roll rate measured by the compact-sized on-board sensing device. We compute RMS values by using \(N=4\) and a sampling frequency of 82 Hz. The number \(N\) should be optimised based on the analysis of collected measurement data as the future work. Figure 6 shows the results of car-body vibration calculations, which indicate that longitudinal level and alignment irregularities influence the vertical and lateral accelerations, respectively, while cross level irregularities influence both the lateral acceleration and roll rate. The maximum RMS values for the vertical acceleration, lateral acceleration, and roll rate were calculated for each 10 m section. The section length 10 m is decided based on the consideration of GNSS error. Figure 7 shows a feature space created by plotting these values in three dimensions. As shown, four clusters are present, representing a normal track, and abnormal tracks with longitudinal level, alignment, and cross level irregularities. It is obvious that such a feature space could be used as training data for machine learning to enable track conditions to be identified.