# Acoustic Roughness Measurement of Railhead Surface Using an Optimal Sensor Batch Algorithm
## 1 Introduction  
The noise and vibration from train operations create noise pollution for residents living near rail tracks, gradually deforms rail track structures, and increase maintenance costs. Therefore, accurate measurement of railway noise provides the essential data needed to analyze and predict such noise and helps to monitor and preventively manage track conditions. Railway noise can be classified into traction, rolling, and aerodynamic noise. While aerodynamic noise is generated by friction of the front head, body, pantograph, and space between cars with air during high-speed operation, traction noise is caused by a power source such as an engine, traction motor, rolling fans, and equipment installed under the car body [1]. Rolling noise is generated by unevenness of the wheel/rail running surface. Rolling noise is also the most important source of noise at the speed domain of 30-250 km/h, which is the typical operating speed of urban train [2]. Relatively, the impact of traction noise is greatest at low speeds while the impact of aerodynamic noise becoming greatest at higher speeds. As shown in the TWINS model [3; 4] in Figure 1, rolling noise is based on the theory that irregularities of the wheel and rail running surfaces cause the wheel and rail to vibraterelative to one another; these vibrations are transmitted through the structures and thereby, radiate noise [4; 5; 6; 7]. As such, measuring, analyzing, and predicting rolling noise caused by contact surface irregularity is critical to managing railway noise related to train operations [8; 9]. In this, the accurate measurement system is critical and also main focus of this paper. The surface irregularities (\"roughness\") of a railway track can be expressed as a function of wavelength, with each wavelength related to the frequency generated by the noise according to speed. Irregularities with a wavelength \(\lambda\) (in m) produce excitation at a frequency \(f=V/\lambda\), where V is the train speed in m/s. Therefore, for a frequency range 100-5000 Hz, and normal train speeds (50-160 km/h), roughness with wavelengths approximately 3-450 mm needs to be measured [3]. The wavelength of acoustic roughness related to rolling noise increases with the speed of the train on the rail. A rail surface with a long wavelength generates dynamic stress and causes structure-born noise (0 Hz-100 Hz), while the relatively short wavelength on the rail surface, defined by rail surface irregularity or acoustic roughness of the rail is the main cause of air-born noise (30 Hz-5 kHz) transmitted from a high-frequency domain to the air [10]. The purpose of this paper was to measure acoustic roughness amplitude (0.1-100 \(\upmu\)m) at the frequency band of 500-2000 Hz for general urban train operational speeds (50-120 km/h) and their wavelength of 7-70 mm. International standards specify the wavelength ranges used in measurement of acoustic roughness and prediction of rolling noise to be 3.15-630 mm (EN ISO 3095) [11], 3.15-250 mm (EN 15610) [12], and 10-1000 mm (EN 13231-3) [13]. Various mobile measurement systems are available to measure acoustic roughness and analyze rolling noise. Measurement of rail surface roughness uses an acceleration sensor installed on a mobile platform [14] or displacement sensor fixed on a platform, which is generally mounted on a trolley-type mobile measurement system [15]. Other methods include a fixed system installed on a rail to move non-contact sensors, such as a laser displacement sensor. The recently developed method using a displacement sensor in contact with rail surface measures relative displacement from upper platform to rail surface to observe displacement fluctuations caused by surface unevenness when the measurement system platform moves while maintaining a specific height from the surface and converting those fluctuations into rail surface roughness.