Co-simulation with communication step size control in an FMI compatible master algorithm

Tom Schierz; Martin Arnold; Christoph Clauß

Title:

Author:

Tom Schierz: Martin Luther University Halle-Wittenberg, NWF II - Institute of Mathematics, Halle (Saale), Germany Martin Arnold: Martin Luther University Halle-Wittenberg, NWF II - Institute of Mathematics, Halle (Saale), Germany Christoph Clauß: Fraunhofer Institute for Integrated Circuits IIS, Design Automation Division EAS, Dresden, Germany

DOI:

10.3384/ecp12076205

Download:

Full text (pdf)

Year:

2012

Conference:

Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany

Issue:

076

Article no.:

020

Pages:

205-214

No. of pages:

Publication type:

Abstract and Fulltext

Published:

2012-11-19

ISBN:

978-91-7519-826-2

Series:

Linköping Electronic Conference Proceedings

ISSN (print):

1650-3686

ISSN (online):

1650-3740

Publisher:

Linköping University Electronic Press; Linköpings universitet

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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 modeled 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). In November 2011; the third beta version of FMI for Model Exchange and Co-Simulation v2.0 was released that supports advanced numerical techniques in co-simulation like higher order extrapolation and interpolation of subsystem inputs; step size control including step rejection and Jacobian based linearly implicit stabilization techniques. Well known industrial simulation tools for applied dynamics support Version 1.0 of this standard and plan to support the forthcoming Version 2.0 in the near future; see the "Tools" tab of website http://www.functional-mockup-interface.org/ for up-to-date information. 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. The present paper extends recent results from [ArnoldClaussSchierz12] on reliable error estimation and communication step size control in the framework of FMI for Model Exchange and Co-Simulation v2.0. Based on a strict mathematical analysis; we study the asymptotic behaviour of the local error and two error estimates that may be used to adapt the communication step size automatically to the changing solution behaviour during time integration. These theoretical results are illustrated by numerical tests for a (linear) quarter car model and provide a basis for future investigations with more complex coupled engineering systems.

Keywords: FMI; error estimation; step size control

Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany

Author:

Tom Schierz, Martin Arnold, Christoph Clauß

Title:

Co-simulation with communication step size control in an FMI compatible master algorithm

DOI:

http://dx.doi.org/10.3384/ecp12076205

References:

[1] M. Arnold. Stability of sequential modular time integration methods for coupled multibody system models. J. Comput. Nonlinear Dynam.; 5:031003; 2010. doi: 10.1115/1.4001389.

[2] M. Arnold; T. Blochwitz; C. Clauß; T. Neidhold; T. Schierz; and S. Wolf. FMI-for-CoSimulation. In The International Journal of Multiphysics. Special Edition: Multiphysics Simulations. Advanced Methods for Industrial Engineering. Selected contributions from 1st Fraunhofer Multiphysics Conference; pages 345–356; Brentwood; Essex; UK; 2011. Multi-Science Publishing Co. Ltd.

[3] M. Arnold; C. Clauß; and T. Schierz. Numerical aspects of FMI for Model Exchange and Co-Simulation v2.0. In P. Eberhard and P. Ziegler; editors; Proc. of The 2nd Joint International Conference on Multibody System Dynamics; Stuttgart; Germany; May 29 - June 1; 2012; ISBN 978-3-927618-32-9; 2012.

[4] J. Bastian; C. Clauß; S. Wolf; and P. Schneider. Master for Co-Simulation Using FMI. In C. Clauß; editor; Modelica Association; Linköping: 8th International Modelica Conference 2011 : Dresden; Germany; 20-22 March 2011; Dresden: Fraunhofer IIS / EAS; 2011.

[5] M. Busch and 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 Joint International Conference on Multibody System Dynamics; May 25–27; 2010; Lappeenranta; Finland; 2010.

[6] C. Clauß; M. Arnold; T. Schierz; and J. Bastian. Master zur Simulatorkopplung via FMI. In X. Liu-Henke; editor; Tagungsband der ASIM/GI-Fachgruppen STS und GMMS; Wolfenbüttel; 23.02.-24.02.2012; Ostfalia Hochschule für Angewandte Wissenschaften; Wolfenbüttel; 2012.

[7] P. Deuflhard and A. Hohmann. Numerical Analysis in Modern Scientific Computing: An Introduction. Number 43 in Texts in Applied Mathematics. Springer; 2nd edition; 2003.

[8] FMI. The functional mockup interface. http://www.functional-mockup-interface.org/.

[9] E. Hairer; S.P. Nørsett; and G. Wanner. Solving Ordinary Differential Equations. I. Nonstiff Problems. Springer–Verlag; Berlin Heidelberg New York; 2nd edition; 1993.

[10] K. Jackson. A survey of parallel numerical methods for initial value problems for ordinary differential equations. IEEE Transactions on Magnetics; 27:3792–3797; 1991. doi: 10.1109/20.104928.

[11] R. Kübler. Modulare Modellierung und Simulation mechatronischer Systeme. Fortschritt-Berichte VDI Reihe 20; Nr. 327. VDI–Verlag GmbH; Düsseldorf; 2000.

[12] R. Kübler and W. Schiehlen. Two methods of simulator coupling. Mathematical and Computer Modelling of Dynamical Systems; 6:93–113; 2000. doi: 10.1076/1387-3954(200006)6:2;1-M;FT093.

[13] Modelisar. Functional Mock-up Interface for Model Exchange and Co-Simulation v2.0 Beta 3. http://www.functional-mockup-interface.org/specifications/FMI_for_ModelExchange_and_CoSimulation_v2.0_Beta3.pdf; November 2011.

[14] Modelisar. Functional Mock-up Interface for Co-Simulation. http://www.functional-mockup-interface.org/specifications/FMI_for_CoSimulation_v1.0.pdf; October 2010.

[15] H. Olsson. Private communication within FMI 2.0 development; June 2011.

Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany

Author:

Tom Schierz, Martin Arnold, Christoph Clauß

Title:

Co-simulation with communication step size control in an FMI compatible master algorithm

DOI:

https://doi.org10.3384/ecp12076205

Note: the following are taken directly from CrossRef

Citations:

Severin Sadjina, Lars T. Kyllingstad, Stian Skjon & Eilif Pedersen (2017). Energy conservation and power bonds in co-simulations: non-iterative adaptive step size control and error estimation. Engineering with Computers, 33(3): 607. DOI: 10.1007/s00366-016-0492-8

Fabio Cremona, Marten Lohstroh, David Broman, Edward A. Lee, Michael Masi & Stavros Tripakis (2019). Hybrid co-simulation: it’s about time. Software & Systems Modeling, 18(3): 1655. DOI: 10.1007/s10270-017-0633-6

Peter Palensky, Arjen A. Van Der Meer, Claudio David Lopez, Arun Josep & Kaikai Pan (2017). Cosimulation of Intelligent Power Systems: Fundamentals, Software Architecture, Numerics, and Coupling. IEEE Industrial Electronics Magazine, 11(1): 34. DOI: 10.1109/MIE.2016.2639825

C. Le Brun, E. Godoy, D. Beauvois, G. Le Pach & R. Noguera (2014). Modeling and Analysis of a Turbojet Fuel System. International Journal of Computer Theory and Engineering, 6(3): 260. DOI: 10.7763/IJCTE.2014.V6.872

Martin Busch (2016). Continuous approximation techniques for co-simulation methods: Analysis of numerical stability and local error. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 96(9): 1061. DOI: 10.1002/zamm.201500196

Alessandro Vittorio Papadopoulo & Alberto Leva (2014). Automating efficiency-targeted approximations in modelling and simulation tools: dynamic decoupling and mixed-mode integration. SIMULATION, 90(10): 1158. DOI: 10.1177/0037549714547296

Jarkko Rahikainen, Francisco Gonzále & Miguel Ángel Naya (2020). An automated methodology to select functional co-simulation configurations. Multibody System Dynamics, 48(1): 79. DOI: 10.1007/s11044-019-09696-y

Dag Fritzson, Robert Brau & Jan Hartford (2018). Composite modelling in 3-D mechanics utilizing Transmission Line Modelling (TLM) and Functional Mock-up Interface (FMI). Modeling, Identification and Control: A Norwegian Research Bulletin, 39(3): 179. DOI: 10.4173/mic.2018.3.4

Veronika Brandstette & Jan Christoph Wehrstedt (2018). A Framework for Multidisciplinary Simulation of Cyber-Physical Production Systems. IFAC-PapersOnLine, 51(11): 809. DOI: 10.1016/j.ifacol.2018.08.418

Severin Sadjin & Eilif Pedersen (2020). Energy conservation and coupling error reduction in non-iterative co-simulations. Engineering with Computers, 36(4): 1579. DOI: 10.1007/s00366-019-00783-4

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