Safety evaluation of a vehicle–bridge interaction system using the pseudo-excitation method

A method for analysing the vehicle–bridge interaction system with enhanced objectivity is proposed in the paper, which considers the time-variant and random characteristics and allows finding the power spectral densities (PSDs) of the system responses directly from the PSD of track irregularity. The pseudo-excitation method is adopted in the proposed framework, where the vehicle is modelled as a rigid body and the bridge is modelled using the finite element method. The vertical and lateral wheel–rail pseudo-excitations are established assuming the wheel and rail have the same displacement and using the simplified Kalker creep theory, respectively. The power spectrum function of vehicle and bridge responses is calculated by history integral. Based on the dynamic responses from the deterministic and random analyses of the interaction system, and the probability density functions for three safety factors (derailment coefficient, wheel unloading rate, and lateral wheel axle force) are obtained, and the probabilities of the safety factors exceeding the given limits are calculated. The proposed method is validated by Monte Carlo simulations using a case study of a high-speed train running over a bridge with five simply supported spans and four piers.