Quiroga, L. M.; Schnieder, E.:
Modelling high speed railroad geometry ageing as a discrete-continuous process.
Stochastic Modeling Techniques and Data Analysis International Conference, Chania, Crete, Greece, June 2010.


Forecasting of geometry deterioration of high speed railroads Travelling safely and comfortable on high speed railway lines requires excellent conditions of the whole railway infrastructure in general and of the railroad geometry in particular. The maintenance process required to achieve such excellent conditions is largely complex and expensive, demanding an increased amount of both human and technical resources. Figure 1 shows the measurements of the NL (longitudinal levelling) for a 200 m. track sector for the last 20 years. The NL parameter is representative of the longitudinal mean deviation of the track in respect of the ideal position. By default the value of NL increases with time, reflecting the track geometry deterioration. Thus decrements take place only when some maintenance activity is preformed. If NL exceeds a certain value, the travelling speed on that sector must be reduced. Furthermore, the track geometry maintenance activities need to be planned up to one year in advance. All this makes a reliable forecast of the railway geometry ageing process indispensable for an optimised planning and scheduling of maintenance activities. For this reason the French railway operator SNCF has been measuring periodically the geometrical characteristics of its high speed network since its commissioning, i.e. for more than 20 years now. Figure 1: Longitudinal levelling for a railroad sector. Traditionally, forecasting has been made by simple linear extrapolation of these measurements. In order to improve the forecasting quality and reliability, this paper presents a method for making middle term (i.e. up to one year) predictions of the railway geometry ageing process. The method consists of a combination of interpolation with splines, and filtering and smoothing using the Holtz-Winters technique. Additionally, the Holtz-Winters algorithm parametrisation is optimally tuned by means of the Levenberg-Marquardt procedure for sum of squares minimisation of nonlinear functions. The method is applied on real measurements of a TGV high speed line, and the results are analysed by measuring the prediction errors with different prediction horizons.