Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Archive of Mechanical Engineering

The Journal of Committee on Machine Building of Polish Academy of Sciences

4 Issues per year

CiteScore 2016: 0.44

SCImago Journal Rank (SJR) 2016: 0.162
Source Normalized Impact per Paper (SNIP) 2016: 0.459

Open Access
See all formats and pricing
More options …
Volume 60, Issue 1


Error Analysis and Error Estimates for Co-Simulation in FMI for Model Exchange and Co-Simulation V2.0

Martin Arnold / Christoph Clauss
  • Fraunhofer Institute for Integrated Circuits IIS, Design Automation Division EAS, Zeunerstr. 38, D - 01069 Dresden, Germany
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Tom Schierz
Published Online: 2013-03-27 | DOI: https://doi.org/10.2478/meceng-2013-0005

Complex multi-disciplinary models in system dynamics are typically composed of subsystems. This modular structure of the model reflects the modular structure of complex engineering systems. In industrial applications, the individual subsystems are often modelled separately in different mono-disciplinary simulation tools. The Functional Mock-Up Interface (FMI) provides an interface standard for coupling physical models from different domains and addresses problems like export and import of model components in industrial simulation tools (FMI for Model Exchange) and the standardization of co-simulation interfaces in nonlinear system dynamics (FMI for Co-Simulation), see [10].

The renewed interest in algorithmic and numerical aspects of co-simulation inspired some new investigations on error estimation and stabilization techniques in FMI for Model Exchange and Co-Simulation v2.0 compatible co-simulation environments. In the present paper, we focus on reliable error estimation for communication step size control in this framework.


Złozone multidyscyplinarne modele stosowane w dynamice systemów sa zwykle skonstruowane z podsystemów. Modularna struktura modelu odzwierciedla modularna strukture złozonych systemów technicznych. W zastosowaniach przemysłowych poszczególne podsystemy sa czesto modelowane indywidualnie przy pomocy róznych multidyscyplinarnych narzedzi symulacyjnych. Funkcjonalny interfejs modelowania (Functional Mock-up Interface, FMI) spełnia role standardowego interfejsu do łaczenia modeli fizycznych z róznych dziedzin i pomaga rozwiazac problemy importu i eksportu elementów modelu w przemysłowych narzedziach modelowania (FMI for Model Exchange), lub standaryzacji interfejsów wspólnej stymulacji w dynamice systemów nieliniowych (FMI for Co-Stimulation), por. [10]. Odzywa na nowo zainteresowanie algorytmicznymi i numerycznymi aspektami wspólnej stymulacji, co zainspirowało do podjecia wielu nowych badan nad estymacja błedów i technikami stabilizacji w interfejsie FMI wersji 2.0 w kompatybilnych srodowiskach stymulacji. W prezentowanym artykule autorzy koncentruja sie na wiarygodnej estymacji błedów przy sterowaniu rozmiarem kroku komunikacji w ramach tego interfejsu.

Keywords : multidisciplinary simulation; co-simulation; functional mock-up interface; FMI

  • [1] M. Arnold: Multi-rate time integration for large scale multibody system models. In P. Eberhard, editor, IUTAM Symposium on Multiscale Problems in Multibody System Contacts, pages 1-10. Springer, 2007.Google Scholar

  • [2] M. Arnold: Numerical methods for simulation in applied dynamics. In M. Arnold and W. Schiehlen, editors, Simulation Techniques for Applied Dynamics, volume 507 of CISMCourses and Lectures, p. 191-246. Springer, Wien New York, 2009.Google Scholar

  • [3] M. Arnold: Stability of sequential modular time integration methods for coupled multibody system models. J. Comput. Nonlinear Dynam., 5:031003, 2010.Google Scholar

  • [4] M. Arnold, M. G¨unther: Preconditioned dynamic iteration for coupled differential-algebraic systems. BIT Numerical Mathematics, 41:1-25, 2001.Google Scholar

  • [5] M. Busch: Zur effizienten Kopplung von Simulationsprogrammen. PhD thesis, Universit¨at Kassel, Fachbereich Maschinenbau, 2012.Google Scholar

  • [6] M. Busch, B. Schweizer: Numerical stability and accuracy of different co-simulation techniques: Analytical investigations based on a 2-DOF test model. In Proc. of The 1st JointInternational Conference on Multibody System Dynamics, May 25-27, 2010, Lappeenranta, Finland, 2010.Google Scholar

  • [7] C. Clauß, M. Arnold, T. Schierz, J. Bastian: Master zur Simulatorkopplung via FMI. In X. Liu-Henke, editor, Tagungsband der ASIM/GI-Fachgruppen STS und GMMS, Wolfenb¨uttel,23.02.-24.02.2012, Wolfenb¨uttel, 2012. Ostfalia Hochschule f¨ur Angewandte Wissenschaften.Google Scholar

  • [8] T.H. Cormen, C.E. Leiserson, R.L. Rivest, C. Stein: Introduction to Algorithms. The MIT Press, Cambridge, MA, 2nd edition, 2001.Google Scholar

  • [9] P. Deuflhard, A. Hohmann: Numerical Analysis in Modern Scientific Computing: An Introduction.Google Scholar

  • Number 43 in Texts in Applied Mathematics. Springer, 2nd edition, 2003.Google Scholar

  • [10] FMI: The Functional Mockup Interface. https://www.fmi-standard.org/.Google Scholar

  • [11] E. Hairer, G. Wanner: Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems. Springer-Verlag, Berlin Heidelberg New York, 2nd edition, 1996.Google Scholar

  • [12] S. Knorr: Multirate-Verfahren in der Co-Simulation gekoppelter dynamischer Systeme mit Anwendung in der Fahrzeugdynamik. Master Thesis, University Ulm, Faculty of Mathematics and Economics, 2002.Google Scholar

  • [13] R. K¨ubler: Modulare Modellierung und Simulation mechatronischer Systeme. Fortschritt- Berichte VDI Reihe 20, Nr. 327. VDI-Verlag GmbH, D¨usseldorf, 2000.Google Scholar

  • [14] R. K¨ubler, W. Schiehlen: Two methods of simulator coupling. Mathematical and ComputerModelling of Dynamical Systems, 6:93-113, 2000.Google Scholar

  • [15] Modelica Association Project FMI: Functional Mockup Interface for Model Exchange and Co-Simulation v2.0 beta 4. https://www.fmi-standard.org/downloads, August 2012.Google Scholar

  • [16] H. Olsson: Private communication, June 2011.Google Scholar

  • [17] P. Popp, W.O. Schiehlen: Ground Vehicle Dynamics. Springer-Verlag, Berlin Heidelberg, 2010.Google Scholar

  • [18] T. Schierz, M. Arnold: Stabilized overlapping modular time integration of coupled differentialalgebraic equations. Applied Numerical Mathematics, 62:1491-1502, 2012.Web of ScienceGoogle Scholar

  • [19] T. Schierz, M. Arnold, C. Clauß: Co-Simulation with communication step size control in an FMI compatible master algorithm. In M. Otter and D. Zimmer, editors, Proc. of the 9th International Modelica Conference, September 3-5, 2012, Munich, Germany, 2012.Google Scholar

  • [20] W. Walter: Ordinary Differential Equations. Number 182 in Graduate Texts in Mathematics.Google Scholar

  • Springer, 1998.Google Scholar

About the article

Published Online: 2013-03-27

Published in Print: 2013-03-01

Citation Information: Archive of Mechanical Engineering, Volume 60, Issue 1, Pages 75–94, ISSN (Print) 0004-0738, DOI: https://doi.org/10.2478/meceng-2013-0005.

Export Citation

This content is open access.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Severin Sadjina, Lars T. Kyllingstad, Stian Skjong, and Eilif Pedersen
Engineering with Computers, 2017, Volume 33, Number 3, Page 607
Yisheng Zou, Guofu Ding, Weihua Zhang, Jian Zhang, Shengfeng Qin, and John Kian Tan
Chinese Journal of Mechanical Engineering, 2016, Volume 29, Number 6, Page 1074
W. Stuart Dols, Liangzhu (Leon) Wang, Steven J. Emmerich, and Brian J. Polidoro
Journal of Building Performance Simulation, 2015, Volume 8, Number 5, Page 326

Comments (0)

Please log in or register to comment.
Log in