Keywords: stochastic model, geometrical track quality, degradation rate, Dagum distribution.

For the development of maintenance tools that enable the optimization of the infrastructure asset management, the geometrical track degradation process has to be fully understood. The variables that influence the degradation process, such as the initial geometrical quality; the degradation rate; the recovery after maintenance are random. Modelling the geometrical rail track degradation by probabilistic models is not common. One of the reasons may be the lack of historical data related to the geometrical quality of tracks for research purposes.

The geometrical track degradation is characterized by the evolution over time (or tonnage) of several parameters such as the longitudinal level, the alignment, the gauge, the twist and the cross level. Dynamic track inspections enable the monitoring of the track geometrical quality which is essential to ensure track availability and reliability, passenger safety and comfort and also energy efficiency. The track geometrical quality is guaranteed by performing condition-based maintenance and renewal actions during the life of the track and for that it is crucial to understand the geometrical track degradation process.

In this paper, the geometrical track degradation process of 169.4 km (around 50%) of the Portuguese Railway Northern Line that links Lisbon to Porto is characterized by a stochastic model. Fifty two probabilistic distributions are tested such as the exponential, the gamma, the Weibull, the logistic, the lognormal, the log-logistic, the Dagum, the Burr, etc. The fitting process is done for twenty one time intervals of ninety days, the usual interval between inspections in this railway line. The track quality is evaluated considering exclusively the longitudinal level (disregarding the other four parameters) because:

1. the longitudinal level is the parameter that progresses more rapidly over time than the others;
2. the number of records per geometrical parameter is very high which makes their analysis time-consuming.

In the stretches considered the maximum permissible train speed is higher than 160 km/h but lower than 220 km/h. During the data analysis a good consistency was found.

This paper shows that the degradation rate of standard deviation of the longitudinal level is similar for both rails. Another important achievement of this work is that the extreme value distributions, such as the General Extreme Value, the Pareto, the Dagum, the Gamma or the Weibull distributions, can provide good fitting to real data, in terms of the standard deviation of the longitudinal level in rail stretches of 200 m of length.

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