In track diagnostics, an important issue is the study of the effects of vehicle wheel and rail contact. Often, for technical reasons, it is not possible to obtain a complete set of measurement data useful for assessing rail deformations resulting from the impact of a rail vehicle on the track, which is why mathematical modeling supports experimental research. The effects of vehicle wheel and rail contact can be modeled by reducing the studied system to a 2-D field problem and determining the field sources. This is a problem of field source identification. In the case of physical fields described by a non-homogeneous second-order partial differential equation (Poisson equation), effective numerical methods for field source identification can be applied. Because the identification problem in the modeling of dynamic systems is an inverse problem belonging to the class of ill-posed problems, the obtained solutions may be unstable. The paper presents in detail various useful ways to stabilize the results, which must be used to supplement numerical methods for field source identification.INVERSE PROBLEMS MODELLING IN DIAGNOSTICS OF THE RAILWAY TRACT
Abstract
In the diagnostics of the track an important issue is to study the effects of contact wheels and rails. Often, for technical reasons, it is impossible to obtain a complete set of measurement data useful in assessing the rail deformation caused by the impact of rail vehicle on the track and therefore the mathematical modeling supports experimental research.
The effects of contact wheels and rails can be modelled by treatment of the studied system as a field issue of 2-D system and determining sources of the field. This is a matter of identifying sources of fields. In the case of physical fields described inhomogeneous partial differential equation of second order (Poisson equation) can be used efficient numerical methods for the identification of sources of fields. For this reason, that in the modelling of dynamical systems identification problem is the inverse problem in the class containing the incorrectly formulated problem, the obtained solutions may be unstable. In this paper various useful ways to stabilize the results which must be supplemented by numerical methods for the identification of sources of fields. (…)
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Source: Logistyka Magazine 2/2010