Stochastic prediction of high-speed train dynamics to long-term evolution of track irregularities

•New stochastic model for long-time prediction of railway track irregularities.•Nonlinear stochastic dynamics of high-speed trains with model uncertainties.•Nonstationary and non-Gaussian ARMA model for the long-time-prediction model.•Identification and validation of the stochastic model with experimental data. There is a great interest to predict the long-term evolution of the track irregularities for a given track stretch of the high-speed train network, in order to be able to anticipate the start off of the maintenance operations. In this paper, a stochastic predictive model, based on big data made up of a lot of experimental measurements performed on the French high-speed train network, is proposed for predicting the statistical quantities of a vector-valued random indicator related to the nonlinear dynamic responses of the high-speed train excited by stochastic track irregularities. The long-term evolution of the vector-valued random indicator is modeled by a discrete non-Gaussian nonstationary stochastic model (ARMA type model), for which the coefficients are time-dependent. These coefficients are identified by a least-squares method and fitted on long time, using experimental measurements. The quality assessment of the stochastic predictive model is presented, which validates the proposed stochastic model.