Determination of longitudinal profile of railway track using vehicle-based inertial readings

The longitudinal profile of a railway track excites a dynamic response in a train which can potentially be used to determine that profile. A method is proposed in this paper for the determination of the longitudinal profile through an analysis of bogie vertical accelerations and angular velocities resulting from the train/track dynamic interaction. The cross-entropy optimisation technique is applied to determine the railway track profile elevations that generate a vehicle response which best fits the measured dynamic response of a railway carriage bogie. Numerical validation of the concept is achieved by using a two-dimensional quarter-car dynamic model, representing a railway carriage and bogie, traversing an infinitely stiff profile. The concept is further tested by the introduction of a two-dimensional car dynamic vehicle model and a three-layer track model to infer the track profile in the longitudinal direction. Both interaction models are implemented in Matlab. Various grades of track irregularity are generated which excite the vehicle inducing a dynamic response. Ten vertical elevations are found at a time which give a least squares fit of theoretical to measured accelerations and angular velocity. In each time step, half of these elevations are retained and a new optimisation is used to determine the next 10 elevations along the length of the track. The optimised elevations are collated to determine the overall longitudinal profile over a finite length of railway track.