Keywords: stochastic modelling, track geometry, random process, polynomial chaos expansion.

The dynamic behaviour of the trains is mainly induced by the track geometry. To characterize this behaviour, it is however difficult to simulate runs on the whole railway network as well as to find a portion of track that is representative of the network. The work presented here therefore aims at building representative track geometry using a stochastic modelling. This modelling, which has to integrate the statistical and spatial variabilities and dependencies, is a key issue when using simulation for conception, maintenance or certification purposes.

The track geometry, made up of straight lines and curves at its construction, is gradually damaged and regularly subjected to maintenance operations during its lifecycle. The irregularities appearing are of four types: vertical and horizontal alignment irregularities on the one hand, gauge and cross level irregularities on the other hand. These irregularities are characterized by a short wavelength evolution (between 3 and 150 meters) whereas the geometry of new tracks is characterized by long wavelengths. Moreover, they may be very different from one track to an other, from one country to an other, depending on the physical properties of the track substructures, on the traffic conditions (number and type of trains) and on the geographical locations (which can be correlated with weather conditions).

To model this variability, a local-global approach is proposed; this means that a whole track of length S is built from the concatenation of N track portions of length s. Each portion is then one realization of a stochastic model.

The first step is therefore to find the optimal length, which premits preservation of the maximum of the frequency and spatial information of the track irregularities. The irregularity vector (gathering the four types of irregularity) is then considered as a stochastic process of the optimal length. From a set of portions of the same stochastic and spatial properties, the correlation matrix of the process can be computed. According to the Karhunen-Loève expansion theory [1], the irregularity vector is then projected on a determinist orthonormal basis. At last, the projection coefficients, which are random values, are expanded on a polynomial chaos basis [2].

Finally, the track stochastic model allows the generation of representative and realistic railway tracks that can be used in any determinist railway dynamic code.

1

O.P. Le Maître, O.M. Knio, "Spectral Methods for Uncertainty Quantification", Springer, 2010. doi:10.1007/978-90-481-3520-2

2

C. Soize, "Identification of high-dimension polynomial chaos expansions with random coefficients for non-gausian tensor-valued random fields using partial and limited experimental data", Computer Methods in Applied Mechanics and Engineering, 199, 2150-2164, 2010. doi:10.1016/j.cma.2010.03.013

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