# Railway Track Monitoring Using Train Measurements: An Experimental Case Study
## 1 Introduction
Several researchers have proposed using inertial measurements to find the railway track stiffness profile. [PERSON] et al. [18] propose the use of drive-by measurements to detect railway track stiffness variation while using an optimization algorithm. Although their method provides good accuracy, it is computationally expensive and it has not been confirmed by experimental data. [PERSON] et al. [19] use on-train measurements to identify changes in track support stiffness. [PERSON] et al. [17] propose a method that uses a Fourier transform to find the rail profile while using vertical accelerations that were measured on a passing train. [PERSON] et al. [11] employ an inverse technique to find the longitudinal track profile using inertial measurements from an in-service train. The track longitudinal profile that generated the vehicle model responses that best match the measured responses is found using the Cross Entropy optimization technique. [PERSON] et al. [24] develop a portable condition monitoring system for track, which is integrated into an in-service train. In this method, the rail irregularities can be estimated from the vertical and lateral accelerations of the car body. [PERSON] et al. [25] use a Kalman Filter to solve an inverse problem, showing the possibility of only estimating the track irregularities from car-body motions. [PERSON] et al. [26] present an approach that uses acceleration measurements from smartphones inside in-service trains for the assessment of the structural performance and geometrical degradation of railway tracks. They obtain cross-correlation values of greater than 0.85 between \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Category number** & **Monitoring Purpose** & **Example** & **Literature** \\ \hline
1 & Track components & Crossings, joints, turnout frogs, squats etc. & [12; 13; 14; 15; 16] \\
2 & Track profile & Stiffness profile, elevation profile & [17; 18; 11; 19] \\
3 & Others & Track replacement, tamping, rail bump and rail surface irregularities & [20; 21; 22; 23] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The main track parameters for drive-by monitoring using inertial measurements. the standard deviations of the longitudinal level and the vertical accelerations measured on-board a passenger train on an 11 km stretch of railway. [PERSON] and [PERSON] [20] use wavelet transforms of acceleration responses to a passing train to identify any railway track irregularities. They use a simple model and do not consider track stiffness. [PERSON] et al. [22] propose the application of the Hilbert transform to the measured signals from the axle box of an operational train. They show that decomposing the signals while using the Hilbert transform has the potential to find track irregularities. Recently, [PERSON] et al. [23] propose an energy-based approach for track change monitoring. They plot the average energy of the measured acceleration in the space domain in a contour plot. A feature detection method is proposed to find changes in the contour plot, which can be indicators of faults on the track. In another study, [PERSON] et al. [27] show that in some parts of the track, the train is more excited which creates bumps in the measured acceleration signals. They suggest that changes in the sizes of the bumps in consecutive runs are indicative of changes to the track. Although energy-based methods have shown good potential for railway track monitoring while using multiple passes, there are several challenges that need to be overcome. The first one is the method of representing the average energy of signals. The current method that was proposed by [PERSON] et al. [23] estimates the energy by summing the amplitudes of the acceleration signal over a pre-specified window. This method might not be accurate if the window length is not well defined. Another important challenge is the influence of train forward speed to the amplitude of the measured signals. There is usually considerable speed variation in multiple train passes over the same route.