Railhead roughness on railways is a cause of noise and vibration. Corrugation (a periodic form of roughness) can grow rapidly and unpredictably, generating high levels of noise and vibration. An emerging technique for monitoring rail roughness is by use of axle-box accelerometers on in-service trains, which can be more cost-effective than conventional inspection methods. Axle-box accelerometers measure the vibration induced by roughness, rather than the roughness itself, and hence require signal processing techniques to translate this vibration into suitable metrics of the railhead condition, such as a wavelength spectrum of roughness. This paper presents progress towards a new stochastic frequency-domain inverse method that derives wavelength-spectra of rail roughness from axle-box acceleration measurements. This method compensates for the effects of vehicle speed and track dynamic behaviour on axle-box acceleration, which have adversely affected previous methods that, for example, rely on calibration on a reference section of track or simply take the RMS of the axle-box acceleration. The practical implications of processing and presenting measurements in the frequency domain are discussed, including the effect of varying vehicle speed and the trade-off between resolution and statistical accuracy. An initial algorithm is proposed and demonstrated through timedomain simulations of a theoretical vehicle-track model. Accurate derivation of roughness from axle-box acceleration will facilitate future development of autonomous monitoring systems fitted to in-service trains that continuously 'map' the condition of a rail network in real time, enabling more efficient and proactive scheduling of rail maintenance
