# Railway Track Monitoring Using Train Measurements: An Experimental Case Study
## 4 Forward Speed of the Train
### Energy Scaling Using Forward Speed  
Even when data with speed less than 50 km/h are removed from the dataset, there is high influence of speed on signal energy. In some cases, this variability might cause fluctuations in calculated energy and it might de-emphasize the features caused by track faults. For example, the acceleration signals for two consecutive passes, Passes 19 and 20, are shown in Figure 8a for the zone, 3000 to 5000 m. Figure 8b shows the train forward speeds corresponding to these two passes. Figure 8c shows the PF5 of these two signals. The forward train speed of Pass 19 is about 30% less that Pass 20 in the range from 3000 to 3200 m, but it is increasing and catches up with the speed of Pass 20 at about 4000 m. There are two distance ranges in the signals where high energy levels are present; 3000 to 3100 m and 3800  
Figure 6: Comparison of the raw acceleration, Peak 4, Peak 5, and average energy.  
Figure 7: Forward speed of the first five passes.  
to 4000 m. Figure 8c shows that there is a considerable difference in the energy of signals at the first range, while both of the signals give almost similar levels of energy for the second one. This shows that a higher forward speed creates a higher energy at the same section of track, with the lower speed of Pass 19 de-emphasizing the peak around 3000 to 3100 m.  
The influence of forward speed on the signal amplitude is clearly not desirable for drive-by railway track monitoring.  
A scaling method is proposed in order to minimize the effect of forward speed. Several scaling methods (linear, quadratic, etc.) were tested and showed a nonlinear relationship between the energy of vertical acceleration responses and the train forward speeds (horizontal speed). However, a linear scaling method is adopted, as it gives a reasonable performance while being simple and easy to apply. The linear scaling factor corrects the signal energy while using the corresponding train forward speed. To get consistent amplitudes for different passes at different speeds, a scaling factor using the train forward speed is applied:  
\[\text{amp}_{sc}(x)=\frac{v_{av}}{v(x)}\text{amp}(x) \tag{5}\]  
where \(\text{amp}_{sc}(x)\) is the scaled amplitude at location \(x\), \(v_{av}\) is an arbitrary average speed used as a baseline for all passes (taken to be 80 km/h here), \(v(x)\) is the speed of the train at location \(x\), and \(\text{amp}(x)\) is the amplitude obtained from the PD algorithm. Figure 9 shows the scaled PF4 for both passes 19 and 20 while using \(v_{av}=80\) km/h. Except for the first peak around 3020 m, the peaks are more consistent in the scaled PF4 for these passes.  
Figure 8: Two sample signals, (**a**) the accelerations, (**b**) the forward speed, and (**c**) the energy level (PF 4).  
Figure 9: The scaled energy level for two sample signals (PF 4).  
There are several factors (e.g., change in the total mass of the train, temperature change, etc.) that impact the energy levels. However, the focus of this study is more on the impact of vehicle forward speed and the other data were not measured during the experiment.