## A new approach for the modeling of railway track geometry deterioration

Travelling safely and comfortably on high speed railway lines requires excellent conditions of the whole railway infrastructure in general and of the railway track geometry in particular. Deterioration of track geometry is characterized by the development of different representative parameters like, for example, the levelling of the track (the longitudinal (NL) and transversal (NT) levelling indicators). We dispose a real dataset of a part of a high speed railway track that was already studied by Mercier et al. [3]. The two indicators (NL and NT) are modeled separately through a new degradation model. This new approach is to consider the degradation as the sum of a gamma process and Brownian motion, independent of the gamma process [1]. Using the real dataset we estimate the model parameters using the method of moments. Then we compare our results with other estimators that already exist in literature. Moreover we construct the confidence intervals of each model parameter. These intervals are useful to select a model between the gamma process, the Brownian motion with positive drift and the perturbed gamma process. Based on the first model cited in [1], we assume that covariates act only on the gamma process part involved in our degradation model and they are integrated to modify the time scale [2]. A direct application on the real dataset is to model an indicator relatively to the other.

Laurent Bordes, Christian Paroissin, Ali Salami