# Evaluation of Measurement Strategy for Track Side Monitoring of Railway Wheels
## 4 Results and Discussion  
Table 3 depicts the results of the reproducibility measurement where the manual measurement system was tested by two different operators on wheel HP6448. The average value of the mean and the standard deviation for both operators is presented as \(\mu_{3}\) and \(\sigma_{3}\) \begin{table}
\begin{tabular}{c c} \hline \hline
**Wheel Number** & **Measurements** \\ \hline Wheel 1 & 8 \\ Wheel 2 & 9 \\ Wheel 3 & 9 \\ Wheel 4 & 10 \\ Wheel 5 & 9 \\ Wheel 6 & 9 \\ Wheel 7 & 10 \\ Wheel 8 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Number of wheel profile measurements used for each wheel captured using automatic wheel profile measurement system. Figure 3: The automatic wheel profile measurement system with its two units located in the southern part of the Iron Ore Line in Sweden. respectively, in the rightmost column. From the table below it is evident that the mean value of all four parameters calculated for the measurements carried out by the two operators was similar, with a standard deviation of 0.6. The repeatability of the handheld equipment is well in accordance with the manufacturer value. For further studies only the measurements carried out by one of the operators were used. Figure 4 depicts the wheel profile measurement performed using the handheld measurement system along the circumference of the wheel HP6448 by one of the operators. The right graph shows a zoomed part of the wheel profile where the difference between the individual measurements is clearly visible. Figure 5 depicts the box plot, and Table 4 represents the statistical parameters such as mean, standard deviation, and range for the four-wheel parameters estimated for different wheels. Each wheel was measured at 35 different positions along the wheel circumference by the same operator with a gap of 100 mm between each position. The mean value for flange height increased with respect to the running distances of the wheel (running distances of the wheels are depicted in Table 1). Wheel HP9709 with an age of over 400,000 km (running distance) exhibited higher values of flange height, flange slope, and hollow wear than when compared to the relatively new wheel HP8628. The box plot shows that there are variations in all four estimated parameters when measured at different positions within the same wheel. The spread in the parameter was comparatively smaller for relatively newer wheels. Figure 4: Wheel profile plots of 35 measurements for wheel HP6448. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Operator 1**} & \multicolumn{2}{c}{**Operator 2**} & \multicolumn{2}{c}{**Operator 1 and 2**} \\ \cline{2-7}
**Parameter** & \(\mu_{1}\) & \(\sigma_{1}\) & \(\mu_{2}\) & \(\sigma_{2}\) & \(\mu_{3}\) & \(\sigma_{3}\) & \\  & **(mm)** & **(mm)** & **(mm)** & **(mm)** & **(mm)** & **(mm)** & **100 \(\times\) 3/\(\mu_{3}\)** \\ \hline Sh & 35.122 & 0.002996 & 35.039 & 0.001409 & 35.0805 & 0.00220 & 0.00628 \\ Sd & 26.348 & 0.001876 & 26.293 & 0.002681 & 26.3205 & 0.00228 & 0.00866 \\ qR & 11.197 & 0.000921 & 11.159 & 0.000789 & 11.1780 & 0.00086 & 0.00765 \\ Th & 1.181 & 0.000459 & 1.195 & 0.000845 & 1.1880 & 0.00065 & 0.05488 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean values and standard deviations of measured wheel parameters (wheel HP6448) for two different measurement operators. Figure 5: Box plot for the four parameters for different wheels measured using the handheld equipment: (**a**) flange height, (**b**) flange width, (**c**) flange slope, (**d**) hollow wear. The \(X\)-axis for all four plots shows the wheel ID for the studied wheel. The highest mean value, standard deviation, and range for flange height (Sh) was observed for wheel HP9709, which had the highest running distance, over four hundred thousand kilometers. The average standard deviation of flange height over all the wheels recorded was 0.1 mm around the mean value, and the average range (difference between maximum and minimum value) was 0.4 mm.