Statistical inverse problems for non-Gaussian vector valued random fields with a set of experimental realizations

G. Perrin (1, 2, 3) , Christian Soize (1) , Denis Duhamel (2, 4) , C. Fünfschilling (3)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
2 navier umr 8205 - Laboratoire Navier
3 SNCF - Direction de l'Innovation et de la Recherche
4 Dynamique des structures et identification

The railway track irregularities, which is a four dimensions vector-valued random field, are the main source of excitation of the train. At first, using a revisited Karhunen-Loève expansion, the considered random field is approximated by its truncated projection on a particularly well adapted orthogonal basis. Then, the distribution of the random vector that gathers the projection coefficients of the random field on this spatial basis is characterized using a polynomial chaos expansion. The dimension of this random vector being very high (around five hundred), advanced identification techniques are introduced to allow performing relevant convergence analysis and identification. Based on the stochastic modeling of the non- Gaussian non-stationary vector-valued track geometry random field, realistic track geometries, which are representative of the experimental measurements and representative of the whole railway network, can be generated. These tracks can then be introduced as an input of any railway software to characterize the stochastic behavior of any normalized train.

Mots clés: uncertainty quantification; statistical inverse problems; non-Gaussian vector-valued random fields; experimental realizations

Domaines: Mécanique [physics.med-ph]; Probabilités [math.PR]; Statistiques [math.ST]

G. Perrin, Christian Soize, Denis Duhamel, C. Fünfschilling. Statistical inverse problems for non-Gaussian vector valued random fields with a set of experimental realizations. ICOSSAR 2013, 11th International Conference on Structural Safety and Reliability, Columbia University, Jun 2013, New-York, United States. pp.1-7. ⟨hal-00806417⟩