Abstract
The accuracy of the result of a co-simulation is dependent on the correct initialization of all the simulation units. In this work, we consider co-simulation where the simulation units are described as Functional Mock-up Units (FMU). The Functional Mock-up Interface (FMI) specification specifies constraints to the initialization of variables in the scope of a single FMU. However, it does not consider the initialization of interconnected variables between instances of FMUs. Such interconnected variables place particular constraints on the initialization order of the FMUs.
The approach taken to calculate a correct initialization order is based on predicates from the FMI specification and the topological ordering of both internal connections and interconnected variables. The approach supports the initialization of co-simulation scenarios containing algebraic loops using fixed point iteration. The approach has been realized as a plugin for the open-source INTO-CPS Maestro 2 Co-simulation framework. It has been tested for various scenarios and compared to an existing Initializer that has been validated through academic and industrial application.
We are grateful to the Poul Due Jensen Foundation, which has supported the establishment of a new Centre for Digital Twin Technology at Aarhus University. Finally, we thank the reviewers for the thorough feedback.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Currently in alpha https://github.com/INTO-CPS-Association/maestro/tree/2.0.0-alpha.
- 2.
5 iterations is the default in our approach. This number is based on experience.
- 3.
- 4.
References
Amálio, N., Payne, R., Cavalcanti, A., Woodcock, J.: Checking SysML models for co-simulation. In: Ogata, K., Lawford, M., Liu, S. (eds.) ICFEM 2016. LNCS, vol. 10009, pp. 450–465. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-47846-3_28
Arnold, M., Clauß, C., Schierz, T.: Error analysis and error estimates for co-simulation in FMI for model exchange and co-simulation v2.0. In: Schöps, S., Bartel, A., Günther, M., ter Maten, E.J.W., Müller, P.C. (eds.) Progress in Differential-Algebraic Equations. DEF, pp. 107–125. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44926-4_6
Bastian, J., Clauß, C., Wolf, S., Schneider, P.: Master for co-simulation using FMI. In: 8th International Modelica Conference, pp. 115–120. Linköping University Electronic Press, Linköpings universitet (2011). https://doi.org/10.3384/ecp11063115
Blockwitz, T., et al.: Functional mockup interface 2.0: the standard for tool independent exchange of simulation models. In: 9th International Modelica Conference, pp. 173–184. Linköping University Electronic Press (2012). https://doi.org/10.3384/ecp12076173
Broman, D., et al.: Composition of FMUs for Co-Simulation. Technical report, University of California, Berkeley (2013). http://www.eecs.berkeley.edu/Pubs/TechRpts/2013/EECS-2013-153.html
Évora Gómez, J., Hernández Cabrera, J.J., Tavella, J.P., Vialle, S., Kremers, E., Frayssinet, L.: Daccosim NG: co-simulation made simpler and faster. In: The 13th International Modelica Conference, Regensburg, Germany, March 4–6, 2019, pp. 785–794, February 2019. https://doi.org/10.3384/ecp19157785
FMI.: Functional Mock-up Interface for Model Exchange and Co-Simulation (2014). https://fmi-standard.org/downloads/
Gomes, C., Denil, J., Vangheluwe, H.: Causal-block diagrams: a family of languages for causal modelling of cyber-physical systems. Foundations of Multi-Paradigm Modelling for Cyber-Physical Systems, pp. 97–125. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-43946-0_4
Gomes, C., Lucio, L., Vangheluwe, H.: Semantics of co-simulation algorithms with simulator contracts. In: 2019 ACM/IEEE 22nd International Conference on Model Driven Engineering Languages and Systems Companion (MODELS-C) (2019). https://doi.org/10.1109/models-c.2019.00124
Gomes, C., Thule, C., Lúcio, L., Vangheluwe, H., Larsen, P.G.: Generation of co-simulation algorithms subject to simulator contracts. In: Camara, J., Steffen, M. (eds.) SEFM 2019. LNCS, vol. 12226, pp. 34–49. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-57506-9_4
Gomes, C., et al.: HintCO - hint-based configuration of co-simulations. In: International Conference on Simulation and Modeling Methodologies, Technologies and Applications, pp. 57–68 (2019). https://doi.org/10.5220/0007830000570068
Gomes, C., Thule, C., Broman, D., Larsen, P.G., Vangheluwe, H.: Co-simulation: a survey. ACM Comput. Surv. 51(3), 1–33, Article 49 (2018). https://doi.org/10.1145/3179993
JIProlog: JIProlog, October 2016. http://www.jiprolog.com. Accessed 20 Aug 2020
Kübler, R., Schiehlen, W.: Two methods of simulator coupling. Math. Comput. Model. Dyn. Syst. 6(2), 93–113 (2000). https://doi.org/10.1076/1387-3954(200006)6:2;1-M;FT093
Miyazawa, U.Y.A., Woodcock, U.J.: Integrated tool chain for model-based design of CPSs foundations of the SysML profile for CPS modelling (2016). https://www.semanticscholar.org/paper/INtegrated-TOol-chain-for-model-based-design-of-of-Miyazawa-Woodcock/3042572251aba18ab21ced9cc2fb49223dea2a2c. Accessed 13 Nov 2020
Palensky, P., Van Der Meer, A.A., Lopez, C.D., Joseph, A., Pan, K.: Cosimulation of intelligent power systems: fundamentals, software architecture, numerics, and coupling. IEEE Ind. Electron. Mag. 11(1), 34–50 (2017). https://doi.org/10.1109/MIE.2016.2639825
Robby Hatcliff, J., Belt, J.: Model-based development for high-assurance embedded systems. In: Margaria, T., Steffen, B. (eds.) Leveraging Applications of Formal Methods, Verification and Validation. Modeling, pp. 539–545. Lecture Notes in Computer Science, Springer International Publishing (2018). https://doi.org/10.1007/978-3-030-03418-4_32
Scala: The Scala Programming Language, August 2020. https://www.scala-lang.org. Accessed 19 Aug 2020
Schramm, D., Hiller, M., Bardini, R.: Force components. Vehicle Dynamics, pp. 207–224. Springer, Heidelberg (2018). https://doi.org/10.1007/978-3-662-54483-9_9
Tarjan, R.: Depth-first search and linear graph algorithms. SIAM J. Comput. 1(2), 146–160 (1972). https://doi.org/10.1137/0201010
Thule, C., Lausdahl, K., Gomes, C., Meisl, G., Larsen, P.: Maestro: the INTO-CPS co-simulation framework. Simul. Model. Pract. Theor. 92, 45–61 (2019). https://doi.org/10.1016/j.simpat.2018.12.005
Thule, C., et al.: Towards reuse of synchronization algorithms in co-simulation frameworks. In: Camara, J., Steffen, M. (eds.) SEFM 2019. LNCS, vol. 12226, pp. 50–66. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-57506-9_5
Z3prover: z3, September 2020). https://github.com/Z3Prover/z3/wiki. Accessed 13 Sept 2020
Acknowledgements
We would like to thank Stefan Hallerstede, Christian Møldrup Legaard, and Peter Gorm Larsen for providing valuable input to this paper and the developed plugin.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Hansen, S.T., Thule, C., Gomes, C. (2021). An FMI-Based Initialization Plugin for INTO-CPS Maestro 2. In: Cleophas, L., Massink, M. (eds) Software Engineering and Formal Methods. SEFM 2020 Collocated Workshops. SEFM 2020. Lecture Notes in Computer Science(), vol 12524. Springer, Cham. https://doi.org/10.1007/978-3-030-67220-1_22
Download citation
DOI: https://doi.org/10.1007/978-3-030-67220-1_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-67219-5
Online ISBN: 978-3-030-67220-1
eBook Packages: Computer ScienceComputer Science (R0)