A numerical framework for load identification and regularization with application to rolling disc problem

Indirect identification methods are applied when direct measurement is unfeasible. One example is the measurement of the contact force between wheel and rail in railway traffic. This paper focuses on optimization-based methods for the identification of contact forces with the aim of developing a reliable and robust load identification scheme. A particular issue discussed here is the choice of discretization in space-time, enabling the sampling instances of the measurements, the parameterization of the sought input and the discretization of the pertinent state equations to be decoupled, in contrast to traditional methods such as, e.g. dynamic programming. In the present preliminary study where a 2-D disc is considered as a representative of a train wheel, a radial concentrated force rotates around the disc\u27s perimeter, representing the contact force acting on the rim of the wheel, while radial strains are measured on a set of points corresponding to the strain gauges position. The strain history data is then used in the identification procedure where the applied force is sought to minimize the discrepancy between the predicted and measured strain history. In particular the convergence of the results with respect to the temporal discretization of the model and the time parameterization of the sought loading history are investigated under the influence of noise. It is seen that choosing a discretization of the sought load that is coarser than that of the state variable gives a more robust scheme. The traditional Tikhonov regularization can also be added within the current framework. Furthermore, with the aid of a sensitivity analysis, the influence of measurement noise can be quantified