## 6 Conclusions  
A procedure for the continuous monitoring of rail corrugation along a metro line has been proposed. It is based on acceleration measurements performed by axlebox accelerometers mounted on a commercial vehicle. A single vehicle equipped with this measurement system allows to collect data on the rail conditions along the whole line several times per day. The output of the monitoring system is the estimate of the power spectra of rail irregularity. This helps in promptly identifying specific locations where corrugation is developing and to schedule rail grinding operations only when and where they are strictly necessary. The estimation of the rail roughness from axlebox acceleration measurements requires the knowledge of the transfer function of the measurement system, which relates the input rail irregularity to the measured acceleration. It was calculated by studying the vertical dynamics of the wheel-rail interaction with a linearised model in the frequency domain. Two different approaches for the characterisation of the wheel dynamics have been proposed. The first state-of-the-art approach is used in the HRSCA measurement system and considers the wheel as a point mass, while in the proposed methodology the  
Figure 13: Roughness Level in the 30–100 mm wavelength band: (**a**) left rail; (**b**) right rail. dynamic behaviour of the wheel is derived by considering the wheelset as a flexible body. The track dynamics is characterised by using an analytical model validated experimentally. The transfer functions calculated with the two approaches are similar at low frequencies, at which the dynamics of the wheel-rail interaction is mainly determined by the wheel mass, and therefore the point mass assumption is reasonable. At higher frequencies, the track dynamics becomes predominant, and neglecting the wheelset flexibility leads to an overestimation of the rail irregularity. In this frequency range the transfer function derived with the flexible wheelset model amplifies the irregularity at the natural frequencies of its mode shapes. This eases the identification of the corrugated track section, since it is common that corrugation tends to form at wavelengths related to the natural frequencies of the wheelset by the vehicle speed. The transfer functions of the HRSCA measurement system and of the proposed one were used to estimate the power spectrum of rail irregularity in terms of Roughness Level (within the 30-100 mm and 100-300 mm wavelength bands of Standard EN 13231-3) on a track section of a subway line between two stations. The results indicate the presence of corrugation on the low rail of both the curves in the 100-300 mm wavelength band, which was confirmed by in-field observations. The flexible wheelset model shows a higher RL in the 100-300 mm wavelength band with respect to the point mass mode, indicating that the proposed measurement system is more sensible for finding the presence of rail corrugation. Moreover, a fast corrugation development is observed on the low rail of a curve of the analysed site. On the contrary, in the 30-100 mm wavelength band, in which no corrugation is observed, the point mass model leads to an overestimation of the RL with respect to that proposed along the whole track section. The proposed methodology can be used for the continuous monitoring of rail corrugation at service speed, and it is effective in identifying those sections where corrugation is developing and rail grinding becomes necessary. However, a relatively high Roughness Level is also estimated on the high rail of the corrugated curves. This is related to the fact that the axleboxes of the same wheelset are assumed to be dynamically decoupled. This is a strong assumption because the irregularity of a rail induces wheelset vibrations that are also measured by sensors on the opposite side. A more refined model of the wheel-rail interaction that considers this dynamic coupling is needed for a more accurate estimation. Conceptualization, E.D.G. and C.S.