Inverse Identification of Dynamic Wheel-rail Contact Forces

Accurate evaluation of contact forces between wheel and rail is essential in the assessment of vehicle performance and to predict consequences of dynamic vehicle-track interaction. As the contact forces can not be measured directly in the field, one common approach is to measure the strain or acceleration at various positions on a wheel or wheel axle. Based on this data, the forces can be estimated. However, the existing schemes typically involve either a simplified wheel model (neglecting inertia) or, in the case of using more advanced models, imply strong restrictions in terms of the choice of spatial and temporal discretization of the underlying equations of motion. In this work, the vertical contact force is determined by the solution of an inverse problem. A minimization problem is considered in which the time-history of the contact force is sought such that the discrepancy between the predicted and the measured response (strains) is minimized. A particular feature of this formulation is that the discretization of the pertinent state equations in space-time, the sampling instances of the measurements and the parameterization of the sought contact force are all independent of each other. Additionally, the convergence of the spatial and temporal discretization of the model and the time parameterization of the contact force history are investigated. The proposed strategy is firstly evaluated for a simplified 2D disc with focus on the effects of discretization, sensitivity to noise and possible improvements as a result of proper regularization. Effects of considering different measurement outputs for the minimization problem are investigated. In particular, the identification strategy is modified by applying virtual calibration whereby an apparent static load is used as the measurement output, in order to compensate for model and spatial mesh sensitivity. Considering the realistic problem at hand, the rotating wheel is introduced and the measured strains are combined using two Wheatstone bridges to estimate the contact force by the static calibration technique. The inverse identification strategy is adopted for the designed measurement system. Effects of centrifugal and gyroscopic terms in the equation of motion and consequences of noise in the measurement data are evaluated. Finally, the inverse identification strategy is compared to static calibration and a Kalman filtering technique for realistic load cases