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M. Tiefenbacher, M. Kozek:
"Black Box Identification of Wheel Forces of a Railway Vehicle Using Asynchronously sampled Data";
Poster: 6th Vienna Mathmod 09, Vienna; 2009-02-11 - 2009-02-13; in: "Proceedings of the 6th Mathmod Vienna 09", Argesim Report, Abstract Volume, No. 34 (2009), ISBN: 978-3-901608-34-6.

Data-based techniques are widely used for identification purposes of dynamic systems. In case of a limited number of measurement channels, signals are divided into multiple measurement systems, which are utilized for data recording. As identification algorithms require synchronously and uniformly sampled data in terms of independently measured input and output data, a synchronization process becomes necessary. The aim of this investigationwas to identify a dynamic model, which describes the relation between track geometry and vertical wheel forces of a railway car. Track geometry and wheel forces have been recorded of different railway cars by independent measurement setups. In addition to the well established cross-correlation method a linear model-based iterative algorithm was used
to enhance synchronization of data sets as well as model quality. Subsequently, artificial neural networks (NARX) were trained to improve prediction quality and synchronization of the data sets.
Data sets are recorded in spatial domain according to the wheel circumference. Thus, approximation of rolling radii by the nominal value and the non-linear shaped running tread leads to non-uniformly and asynchronously sampled input and output data. Since both data sets are distorted, the geometric
track signals, gauge and cant, are assumed to be free of any distortions and jitter due to the measurement principle. The corresponding output signal, which is shifted to the input by a relative shift function, is the difference of vertical wheel-forces.
The relative shift function can be split up into a constant, a linear and a zero-mean non-linear term. The constant shift is caused by independent starting points of the measurement setups or dead-time. Cross-Correlation methods cannot distinguish between these cases. Additionally, a left shift (acausal) in consequence of the measuring setup can be detected. The linear shift component leads on average to a relative shift of the wavelengths of the output and input data respectively. Thus, a biased model would be identified. In order to avoid large errors of the identified model poles, the linear relative shift between input and output primerily has to be removed by cross-correlation. The model-based iterative algorithm is performed in two steps. First, a model, which is capable of reproducing the input-output dynamics on average (prediction error method) is identified. Next, a windowed cross-correlation function between output and simulated output is calculated and the detected shift is corrected by resampling the output data by applying cubic-splines. The model-based iterative algorithm enhances the synchronizity of the data sets compared to the cross-correlation method as a result of strongly pronounced extrema in the cross-correlation function caused by the high frequency content in the simulated and measured output. A high-order output error model was identified, which leads to high prediction quality in the low and middle frequency range. The model predicated on the presented algorithm outperfoms other models, which are identified by application only cross-correlation techniques in the prediction quality by cross-validation. Artificial Neural
Networks show no enhancement regarding prediction accuracy compared to linear models.