# Train Speed Estimation from Track Structure Vibration Measurements
## 4 Verification of the Train Speed Estimation Method
### Discussions  
Although it is proved that the speeds of all trains can be accurately estimated with unchanged parameters, different threshold condition coefficients and the minimum time difference parameters are also discussed in Table 4 for improving the applicability of the method. It can be seen from the data in Table 4 that the accuracy of train speed estimation is influenced by the threshold condition coefficient and the minimum time difference parameter. Therefore, the results of train speed automatic estimation will be significantly improved if the parameter is selected dynamically and accurately. As the appropriate parameters are related to the train speed, it is necessary to roughly estimate the train speed first to determine the appropriate parameters. Figure 12 shows the minimum time difference parameter on the results of train speed estimation. It can be concluded that the difference decreases notably when the minimum time difference parameter is higher than the time difference of adjacent bogies passing through the measuring site. Therefore, it is necessary to ensure that the minimum time difference parameter is greater than the time difference of adjacent bogies passing through the measuring points. In this paper, there are two types of trains: some of them with eight carriages trains and others with sixteen carriages. The train speed can be roughly estimated by the combination of the total length of the train and the total time of signals. Computer vision will still be a useful application for the problem. The acceleration signal image gives the number of train carriages by the number of closed regions. This method was used in the fields of fish fry counting [23], pest counting [24], cell counting [25], and distinguishing parking spaces [26], and it has achieved good results. Furthermore, displacement signals can be used to estimate train speed as long as a histogram is used instead of a line graph. After rough estimation of train speed, the minimum time difference parameter can be determined as detailed in Section 3.1.2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Train** \\ **Number** \\ \end{tabular}  } & \multirow{2}{*}{**Sensor**} & **Threshold** & **Minimum Time** & **Estimated** \\  & & **Condition** & **Difference** & **Train** & **Time** \\  & & **Coefficient** & **Parameter/s** & **Speed/km-h\({}^{-1}\)** & \\ \hline
9 & A1 & 0.3 & 0.1 & 124.7 & 0.1 \\
9 & A1 & 0.1 & 0.1 & 255.4 & 105.0 \\
9 & A1 &  
As shown in Figure 13, the difference is quite small, as the threshold condition coefficient is equal to 0.4-0.6. When the parameters are higher than 0.6, the number of identified peaks will be significantly reduced. Using this feature, the threshold condition coefficient can be designed to be self-adjusted dynamically. When the threshold condition coefficient is 1, only one peak point can be selected at this time, and more peak points can be selected with decreasing the coefficient. After the train carriage information is obtained, the number \(N\) of train bogies is determined, so the coefficients can be dynamically valued from large to small until \(N\) peak points are selected. Therefore, the coefficients of the method can be easily calibrated based on the numbers of identified bogies and the relationship between minimum time difference parameter and estimated train speed. In addition, after all peak points have been selected, the critical value of the Grubbs criterion can be appropriately tightened to improve the accuracy of recognition. Figure 12: The difference of results of train speed estimation with different minimum time difference parameters. Figure 13: The difference of results of train speed estimation with different threshold condition coefficients. The proposed method can be applied extensively under two conditions. First, the signal waveform of vertical acceleration and displacement produce pronounced peaks when the rail wheels pass through the test site.