How to Shape Noise Spectra for Continuous System Simulation

Andreas Klöckner
DLR German Aerospace Center, Institute of System Dynamics and Control, Weßling, Germany,

Andreas Knoblach
DLR German Aerospace Center, Institute of System Dynamics and Control, Weßling, Germany,

Andreas Heckmann
DLR German Aerospace Center, Institute of System Dynamics and Control, Weßling, Germany,

Ladda ner artikelhttp://dx.doi.org/10.3384/ecp15118411

Ingår i: Proceedings of the 11th International Modelica Conference, Versailles, France, September 21-23, 2015

Linköping Electronic Conference Proceedings 118:44, s. 411-418

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Publicerad: 2015-09-18

ISBN: 978-91-7685-955-1

ISSN: 1650-3686 (tryckt), 1650-3740 (online)


Noise for continuous-time system simulation is relevant for many applications, where time-domain results are required. Simulating such noise raises the need to consistently shape the frequency content of the signal. However, the methods for this task are not obvious and often state space implementations of form filters are approximated. In this paper, we address the problem with a new method relying on directly using the specified power spectral density for a convolution filter. For the example of railway track irregularities, we explain how to derive the required filters, implement them in the open-source Noise library, and verify the results. The new method produces correct results, is very simple to use, and enables new features for time simulation of physical systems.


Noise; power spectral density; track irregularity


EASA CS-25. Certification specifications and acceptable means of compliance for large aeroplanes, 2013.

Fritz Frederich. Die Gleislage aus fahrzeugtechnischer Sicht. ZEV–Glasers Annalen, pages 108–1984, 1984.

Joachim Haase, S Wolf, and C Clauß. Monte carlo simulation with modelica. In 6th International Modelica Conference, pages 601–604, Bielefeld, Germany, 2008.

H.D. Joos, J. Bals, G. Looye, K. Schnepper, and A. Varga. A multiobjective optimisation-based software environment for control systems design. In Conference on Computer-Aided Control Systems Design. IEEE, 2002.

Andreas Klöckner, Franciscus L. J. van der Linden, and Dirk Zimmer. Noise generation for continuous system simulation. In Hubertus Tummescheit and Karl-Erik Årzén, editors, Proceedings of the 10th International Modelica Conference, number 96 in Linköping Electronic Conference Proceedings, pages 837–846, Lund, Sweden, March 10-12 2014. Modelica Association and Linköping University Electronic Press. doi: 10.3384/ECP14096837. ISBN: 978-91-7519-380-9. ISSN: 1650-3686. eISSN: 1650-3740.

K. Knothe and S. Stichel. Schienenfahrzeugdynamik. Springer, Berlin, 2003.

Hans Wolfgang Liepmann. On the application of statistical concepts to the buffeting problem. Journal of the Aeronautical Sciences (Institute of the Aeronautical Sciences), 19(12), 1952. doi: 10.2514/8.2491.

Alexander Pollok, Dirk Zimmer, and Francesco Casella. Fractionalorder modelling in modelica. accepted and to be presented at the 11th International Modelica Conference, 2015.

K. Popp and W. Schiehlen. Ground Vehicle Dynamics. Springer, 2010.

SIMPACK Time Excitations Catalogue. SIMPACK, 24th September 2003. SIMDOC v8.607.

Franciscus L. J. van der Linden, Andreas Klöckner, and Dirk Zimmer. Effects of event-free noise signals on continuous-time simulation perfomance. In Felix Breitenecker, Andreas Kugi, and Inge Troch, editors, 8th Vienna International Conference on Mathematical Modelling, volume 8 of Mathematical Modelling, pages 280–285, Vienna, Austria, 2015. IFAC-PapersOnLine. doi: 10.3182/20150218-3-AU-30250.

Sebastiano Vigna. Further scramblings of marsaglia’s xorshift generators. CoRR, abs/1404.0390, 2014. URL http://arxiv.org/abs/1404.0390. Code available
at http://xorshift.di.unimi.it/.

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