Model-based estimation of rail roughness from axle box acceleration

Monitoring rail roughness in the railway network allows directing grinding actions to where they are needed to reduce rolling noise and large wheel/rail forces. To be able to measure rail roughness on a large scale, indirect measurements onboard railway vehicles have to be carried out. Existing methods use either axle box acceleration (ABA) or under-coach noise measurements to monitor the rail roughness indirectly. The two main challenges with rail roughness estimation from vibroacoustic signals measured onboard vehicles are to separate wheel and rail roughness and to take into account varying track dynamics in the railway network. Both questions have not yet been addressed sufficiently. In this paper, an enhanced method for estimating rail roughness from ABA is presented. In contrast to all existing methods in the literature, the presented method operates in the time domain. A time-domain method has the advantage that the spatial variations of roughness become visible and paves the way for the detection of localized defects such as squats or deteriorated welds. The method is based on a previously developed time-domain model for high-frequency wheel/rail interaction and estimates the time series of the roughness from the time series of ABA. In a first step, the time series of the contact force is calculated from the axle box acceleration using a Least Mean Square algorithm for source identification. In a second step, the combined wheel/rail roughness is obtained from the contact force based on a non-linear Hertzian contact model and a convolutional approach to determine wheel and rail displacement. Separation of wheel and rail roughness is possible by cycle-averaging the contact force over a distance corresponding to the wheel perimeter and performing the second step separately for the part of the contact force originating from the wheel and the rail roughness, respectively. The method was tested for simulated ABA obtained from measured wheel and rail roughness. In the relevant wavelength range from 0.5 m to 5 mm, the rail roughness could be estimated with good accuracy for known track dynamics. Overall, deviations in 1/3-octave bands between estimated and actual roughness were below 1 dB. Only for low rail roughness, higher deviations of less than 2.6 dB occurred around the pinned-pinned resonance frequency. Uncertainties in the track parameters affect the roughness estimation, where the most critical parameter is the rail pad stiffness. A deviation of 20% in rail pad stiffness leads to deviations in the rail roughness of up to 3.5 dB in single 1/3-octave bands. The results illustrate the need to extend the method for the simultaneous extraction of track parameters and roughness from measured axle box acceleration