# Acoustic Roughness Measurement of Railhead Surface Using an Optimal Sensor Batch Algorithm
## 3 Field Test and Results  
We conducted a measurement test of a field track using the calculated optimal sensor positions to verify the results. The test measured acoustic roughness of the operating rail track surface using constant speed control with the ARCer [24] shown in Figure 7. The new ARCer featured a real-time operating system, speed controller, rotary encoder to measure distance, and wireless data communication. ARCer had a wheelbase of 716 mm, front and rear drive wheels 100 mm in diameter, a maximum driving speed of 4 m/s, a measurement speed of 0.5 m/s, and the capability for up to three sensors in adjustable positions (see Figure 7). Measurement and analysis of the longitudinal rail surface roughness conformed to the standard presented in EN 15610:2019 [12]. The first field test was conducted on a track inside tunnel \"Y\" that had abrasion wear and corrugation in some track sections (see Figure 8). We measured every 10 m of two sections of the track in the tunnel using ARCer. The first section A as shown in Figure 8b has a corrugated railhead surface of 65 mm wavelength. The first section A as shown in Figure 8c has a normal worn railhead surface. Figure 6: Minimized residual results with two sensors focused on a periodic wavelength in the chord offset synchronization method. Figure 7: Auto Rail Checker (ARCer) with two displacement sensors and the detailed structure of the sensor; S1 and S2 are the position of the first and second sensor (Adapted and modified from [17]). The positions of the sensors attached to the measurement system were \(d_{1}\) = 222 mm, \(d_{2}\) = 327 mm, and \(d_{3}\) = 432 mm for three sensors and \(d_{1}\) = 255 mm and \(d_{2}\) = 380 mm for two sensors. The positions of the two sensors did not mitigate the wavelength level at \(\lambda\) = 0.314 m associated with wheel diameter of the measurement system. Figures 9 show the logitudinal rail surface roughness of the track \"Y\" for the two track sections, which are illustrated in Figure 8b,c. The section A shows larger deviation in measured roughness because of the developed corrugation. Figure 10 shows the spectrum of acoustic roughness of the rail surface obtained through the acoustic roughness values measured by the two and three sensors and the frequency analysis. While there is high peak at the corrugated wavelength of 0.065 m in Figure 10a, there is no peak at the smooth railhead surface in Figure 10b except the wheel diameter related wavelength of 0.314 m. Although the field measurements of the two track sections match in most rolling noise wavelengths, the acoustic roughness value showed a gap of more than 6 dB at the wavelength \(\lambda\) = 0.314 m associated with wheel diameter. To compensate for the measurement error at this wavelength, we used new sensor positions to verify the results. Figure 8: Railway track field experiment; (**a**) Tunnel track “Y”, (**b**) Corrugated rail section A, (**c**) Normal rail section B.  
Figure 9: Rail surface roughness of track sections in tunnel “Y”. We also conducted a field test on the second track (\"Z\" track), which had no abrasion wear or corrugation, to directly check the measured value of the wheel and verify the measurement results of the proposed optimal two sensors. The test used the same two- and three-sensor positions as in the previous test and used an additional two optimum sensor positions (\(d_{1}\) = 230 mm and \(d_{2}\) = 380 mm) to compare. Figure 11 shows the measured section and rail, while Figure 12 shows the results of the spectrum analysis of acoustic roughness using three different algorithms. As shown in Figure 12, when the optimization algorithm is used, the spectrum level at \(\lambda\) = 0.314 m, the wavelength associated with wheel diameter, converged in the same way as the three sensor-based algorithm. The results of the field tests of these two sections verified that the proposed batch algorithm using two sensors could generate the same level of measurement accuracy as using three sensors. Figure 11: Field experiment on “Z” track.