# Research on Wheel Flat Recognition Based on Wayside Wheel-Rail Force
## 5 Field Test and Discussion  
To validate the reliability of the identification algorithm, the developed Train Operation State Detection System (TODS) was deployed on an operational railway line. The test site is located approximately 2 km from the Suning North Station of the Shuohuang Heavy-Haul Railway, where the average passing vehicle speed is around 40 km/h. The TODS  
Figure 16: Main steps of the wheel flat length calculation process. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Speed**} & \multicolumn{4}{c}{**Empty State**} & \multicolumn{4}{c}{**Loaded State**} \\ \cline{2-9}  & _a1_ & _b1_ & _c1_ & **R2** & _a2_ & _b2_ & _c2_ & _d2_ & **R2** \\ \hline
10 km/h & 347\_31 & \(-\)4.59 & 51,859.01 & 0.11179 & \(-\)9.06 & 0.46 & \(-\)0.01 & 151,928.64 & 0.86765 \\
20 km/h & 7142.32 & \(-\)4.47 & \(-\)25,553.03 & 0.99985 & 4608.56 & 40.76 & \(-\)0.01 & 116,433.04 & 0.99775 \\
30 km/h & 6182.02 & 36.77 & \(-\)27,859.61 & 0.99948 & 4119.41 & 283.03 & \(-\)2.26 & 103,812.61 & 0.99952 \\
40 km/h & 3295.36 & 72.93 & \(-\)2877.44 & 0.99922 & 8906.73 & 295.85 & \(-\)2.35 & 51482.71 & 0.99744 \\
50 km/h & 1414.32 & 79.24 & 19,869.62 & 0.99914 & 3402.04 & 536.77 & \(-\)4.13 & 857,070.04 & 0.99717 \\
60 km/h & 515.38 & 71.54 & 39,936.31 & 0.99381 & \(-\)1441.68 & 516.16 & \(-\)3.12 & 123,085.14 & 0.99794 \\
70 km/h & 3155.03 & 23.98 & 16,795.12 & 0.9879 & \(-\)12,913.77 & 809.08 & \(-\)5.66 & 215,367.14 & 0.99839 \\
80 km/h & 6407.69 & \(-\)24.34 & \(-\)22,307.21 & 0.99982 & \(-\)26,291.14 & 1290.74 & \(-\)10.03 & 316,469.57 & 0.99805 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fitting curve coefficient (for empty state(0 t load)/loaded state(80 t load)). wheel-rail impact detection system was installed on the upstream track, focusing on fully loaded trains. Shear strain gauges were strategically mounted on both the left and right rails to measure wheel-rail forces. The installation encompasses 14 rail spans. Each measuring point consists of four strain gauges, which are combined through a bridge circuit to form one measuring point. One rail span has two measuring points (one on the left and one on the right), utilizing a total of 28 strain gauge channels. Additionally, a proximity switch was affixed to one side of the rail, serving as a trigger to accurately record the precise moments when wheels enter and exit the detection zone. Table 4 details the key parameters of the strain gauges and proximity switch, while Figure 17 illustrates the actual installation configuration. Figure 18a depicts the wheel-rail force signal captured by a single vertical force measurement channel of the TODS. Notably, each peak in the figure represents the wheel-rail force exerted when a wheel traverses the load-measuring bridge; these peaks correspond to individual wheels rather than continuous, discrete forces from a single wheel across different spatial positions. As a result, the time intervals between successive wheel-rail force \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Strain Gauge** & \multicolumn{3}{c}{**Proximity Switch**} \\ \hline Size & 10 mm \(\times\) 4.6 mm & Thread type & M30 \(\times\) 1.5 \\ Coefficient of thermal expansion & 10.8 \(\times\) 10\({}^{-6}\)/K & Switching frequency & \(\leq\)90 Hz \\ Operating temperature range & \(-\)30\(-\)40 \({}^{\circ}\)C & Delay response & \(\leq\)6 \(\times\) 10\({}^{-5}\) ms \\ Maximum permissible effective & & 13 V & [Us] rated supply voltage & 12–24 V DC \\ bridge voltage & & & \\ Nominal resistance & 120 \(\Omega\) & [Sn] nominal sensing distance & 40 mm \\ GF & 1.8 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The relevant parameters of the strain gauge and proximity switch. Figure 17: TODS field installation effect of wheel–rail impact detection system. signals are irregular. Leveraging the known inter-wheel distance of 1.83 m within a bogie, the vehicle's running speed was calculated to be 59.89 km/h.