A stochastic dynamic model of train-track-bridge coupled system based on probability density evolution method

An innovative stochastic dynamic model of a 3D train-track-bridge coupled system (TTBS) with refined wheel/rail interaction is established for a high-speed railway based on the random theory of probability density evolution method (PDEM). The multi-coupling effect of excitations can be simultaneously input into the new model, e.g. random track irregularity, random vehicle loads, stochastic system parameters, et al. Moreover, a new approach, named “Number theoretic method of multi-target probability functions” (NTM-mp), is developed to obtain the discrete point sets of multidimensional random parameters in hypercube space, aims to solve the point design of system uncertainty. The stochastic harmonic function (SHF) is applied to generate representative random track irregularity samples. The results of TTBS got by PDEM are verified with several typical case studies for its efficiency and reliability, which are the deterministic results in the representative publication, the Monte Carlo method (MCM) results, and the field testing results on the high-speed railway. At last, a typical case study of TTBS on a high-speed railway is presented for numerical analysis. Discussions and significant conclusions on the random dynamic responses are presented.