Skip to main content
SpringerLink
Log in

Data-Driven Reachability Analysis of Digital Twin FMI Models

  • Conference paper
  • First Online:
Leveraging Applications of Formal Methods, Verification and Validation. Practice (ISoLA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13704))

Included in the following conference series:

Abstract

Digital Twins are an emerging technology which makes it possible to couple cyber-physical assets with their virtual representation in real-time. The technology is applicable to a variety of domains and facilitates a more intelligent and dependable system design and operation. In this paper, we address the challenge of analysing Digital Twins by proposing a simulation-based reachability analysis of models based on the Functional Mock-Up Interface standard. The analysis approach uses simulations to obtain the Lipschitz constant of the model which is then used to compute reachable states of the system. The approach also provides probabilistic guarantees on the accuracy of the computed reachable sets that are based on simulations of the system from random initial states.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Julia programming language website - https://julialang.org/.

References

  1. Althoff, M., Frehse, G., Girard, A.: Set propagation techniques for reachability analysis. Annu. Rev. Control Rob. Auton. Syst. 4(1), 369–395 (2021)

    Article  Google Scholar 

  2. Bezanson, J., Edelman, A., Karpinski, S., Shah, V.B.: Julia: a fresh approach to numerical computing. SIAM Rev. 59(1), 65–98 (2017)

    Article  MathSciNet  Google Scholar 

  3. Blochwitz, T., et al.: The functional mockup interface for tool independent exchange of simulation models. In: Proceedings of the 8th International Modelica Conference, pp. 105–114 (2011)

    Google Scholar 

  4. Bogomolov, S., et al.: Guided search for hybrid systems based on coarse-grained space abstractions. Int. J. Softw. Tools Technol. Transfer 18(4), 449–467 (2016)

    Article  Google Scholar 

  5. Bogomolov, S., Forets, M., Frehse, G., Potomkin, K., Schilling, C.: JuliaReach: a toolbox for set-based reachability. In: Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2019, pp. 39–44. Association for Computing Machinery, New York (2019)

    Google Scholar 

  6. Bogomolov, S., et al.: Assume-guarantee abstraction refinement meets hybrid systems. In: Yahav, E. (ed.) HVC 2014. LNCS, vol. 8855, pp. 116–131. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-13338-6_10

    Chapter  Google Scholar 

  7. Bogomolov, S., et al.: Co-simulation of hybrid systems with SpaceEx and Uppaal. In: 11th International Modelica Conference (Modelica 2015), Linköping Electronic Conference Proceedings, pp. 159–169. Linköping University Electronic Press, Linköpings universitet (2015)

    Google Scholar 

  8. Chen, X., Ábrahám, E., Sankaranarayanan, S.: Flow*: an analyzer for non-linear hybrid systems. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 258–263. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39799-8_18

    Chapter  Google Scholar 

  9. Chutinan, A., Krogh, B.H.: Verification of polyhedral-invariant hybrid automata using polygonal flow pipe approximations. In: Vaandrager, F.W., van Schuppen, J.H. (eds.) HSCC 1999. LNCS, vol. 1569, pp. 76–90. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48983-5_10

    Chapter  MATH  Google Scholar 

  10. De Haan, L., Ferreira, A., Ferreira, A.: Extreme Value Theory: An Introduction, vol. 21. Springer, New York (2006). https://doi.org/10.1007/0-387-34471-3

  11. Donzé, A.: Breach, a toolbox for verification and parameter synthesis of hybrid systems. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 167–170. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14295-6_17

    Chapter  Google Scholar 

  12. Donzé, A., Maler, O.: Systematic simulation using sensitivity analysis. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 174–189. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71493-4_16

    Chapter  Google Scholar 

  13. Duggirala, P.S., Mitra, S., Viswanathan, M., Potok, M.: C2E2: a verification tool for Stateflow models. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 68–82. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46681-0_5

    Chapter  Google Scholar 

  14. Fan, C., Qi, B., Mitra, S., Viswanathan, M.: DryVR: data-driven verification and compositional reasoning for automotive systems. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10426, pp. 441–461. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63387-9_22

    Chapter  MATH  Google Scholar 

  15. Fitzgerald, J., Larsen, P.G., Verhoef, M.: Collaborative Design for Embedded Systems. Academic Press (2014). 10, 978-3

    Google Scholar 

  16. Frehse, G., et al.: SpaceEx: scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_30

    Chapter  Google Scholar 

  17. Fritzson, P., et al.: OpenModelica - a free open-source environment for system modeling, simulation, and teaching. In: 2006 IEEE Conference on Computer Aided Control System Design, pp. 1588–1595 (2006)

    Google Scholar 

  18. Geretti, L., et al.: ARCH-COMP20 category report: continuous and hybrid systems with nonlinear dynamics. In: Frehse, G., Althoff, M. (eds.) ARCH20, 7th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH20). EPiC Series in Computing, vol. 74, pp. 49–75. EasyChair (2020)

    Google Scholar 

  19. Girard, A., Pappas, G.: Approximate bisimulations for nonlinear dynamical systems. In: Proceedings of the 44th IEEE Conference on Decision and Control, pp. 684–689 (2005)

    Google Scholar 

  20. Gomes, C., Thule, C., Broman, D., Larsen, P.G., Vangheluwe, H.: Co-simulation: a survey. ACM Comput. Surv. 51(3) (2018)

    Google Scholar 

  21. Hu, H., Fazlyab, M., Morari, M., Pappas, G.J.: Reach-SDP: reachability analysis of closed-loop systems with neural network controllers via semidefinite programming (2020)

    Google Scholar 

  22. Huang, C., Fan, J., Li, W., Chen, X., Zhu, Q.: ReachNN: reachability analysis of neural-network controlled systems (2019)

    Google Scholar 

  23. Jensen, P.G., Larsen, K.G., Legay, A., Nyman, U.: Integrating tools: co-simulation in UPPAAL using FMI-FMU. In: 2017 22nd International Conference on Engineering of Complex Computer Systems (ICECCS), pp. 11–19 (2017)

    Google Scholar 

  24. Kapinski, J., Krogh, B.H., Maler, O., Stursberg, O.: On systematic simulation of open continuous systems. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 283–297. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36580-X_22

    Chapter  MATH  Google Scholar 

  25. Kazemi, M., Perez, M., Somenzi, F., Soudjani, S., Trivedi, A., Velasquez, A.: Translating omega-regular specifications to average objectives for model-free reinforcement learning. In: Proceedings of the 21st International Conference on Autonomous Agents and Multiagent Systems, pp. 732–741 (2022)

    Google Scholar 

  26. Kazemi, M., Soudjani, S.: Formal policy synthesis for continuous-state systems via reinforcement learning. In: Dongol, B., Troubitsyna, E. (eds.) IFM 2020. LNCS, vol. 12546, pp. 3–21. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-63461-2_1

    Chapter  Google Scholar 

  27. Lamport, L.: Specifying Systems: The TLA+ Language and Tools for Hardware and Software Engineers. Addison-Wesley Longman Publishing Co., Inc., Boston (2002)

    Google Scholar 

  28. Larsen, P.G., et al.: Integrated tool chain for model-based design of cyber-physical systems: the INTO-CPS project. In: 2nd International Workshop on Modelling, Analysis, and Control of Complex CPS (CPS Data), pp. 1–6 (2016)

    Google Scholar 

  29. Lavaei, A., Somenzi, F., Soudjani, S., Trivedi, A., Zamani, M.: Formal controller synthesis for continuous-space MDPs via model-free reinforcement learning. In: 2020 ACM/IEEE 11th International Conference on Cyber-Physical Systems (ICCPS), pp. 98–107. IEEE (2020)

    Google Scholar 

  30. Lavaei, A., Soudjani, S., Abate, A., Zamani, M.: Automated verification and synthesis of stochastic hybrid systems: a survey. arXiv preprint arXiv:2101.07491 (2021)

  31. Mohajerin Esfahani, P., Sutter, T., Lygeros, J.: Performance bounds for the scenario approach and an extension to a class of non-convex programs. IEEE Trans. Autom. Control 60(1), 46–58 (2015)

    Article  MathSciNet  Google Scholar 

  32. Nghiem, T., Sankaranarayanan, S., Fainekos, G., Ivancić, F., Gupta, A., Pappas, G.J.: Monte-Carlo techniques for falsification of temporal properties of non-linear hybrid systems. In: Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2010, pp. 211–220. Association for Computing Machinery, New York (2010)

    Google Scholar 

  33. Ray, R., Gurung, A., Das, B., Bartocci, E., Bogomolov, S., Grosu, R.: XSpeed: accelerating reachability analysis on multi-core processors. In: Piterman, N. (ed.) HVC 2015. LNCS, vol. 9434, pp. 3–18. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-26287-1_1

    Chapter  Google Scholar 

  34. Salamati, A., Lavaei, A., Soudjani, S., Zamani, M.: Data-driven safety verification of stochastic systems via barrier certificates. In: Proceedings of the 7th IFAC Conference on Analysis and Design of Hybrid Systems (ADHS), vol. 54, no. 5, pp. 7–12 (2021)

    Google Scholar 

  35. Esmaeil Zadeh Soudjani, S., Majumdar, R., Nagapetyan, T.: Multilevel Monte Carlo method for statistical model checking of hybrid systems. In: Bertrand, N., Bortolussi, L. (eds.) QEST 2017. LNCS, vol. 10503, pp. 351–367. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66335-7_24

    Chapter  MATH  Google Scholar 

  36. Tabuada, P.: Verification and Control of Hybrid Systems: A Symbolic Approach. Springer, New York (2009). https://doi.org/10.1007/978-1-4419-0224-5

  37. Tao, F., Zhang, H., Liu, A., Nee, A.Y.C.: Digital twin in industry: state-of-the-art. IEEE Trans. Industr. Inf. 15(4), 2405–2415 (2019)

    Article  Google Scholar 

  38. Tempo, R., Calafiore, G., Dabbene, F.: Randomized Algorithms for Analysis and Control of Uncertain Systems: with Applications. Springer, London (2012). https://doi.org/10.1007/b137802

  39. The MathWorks: Simulink User’s Guide (2021)

    Google Scholar 

  40. Thule, C., Gomes, C., Lausdahl, K.G.: Formally verified FMI enabled external data broker: RabbitMQ FMU. In: Proceedings of the 2020 Summer Simulation Conference. SummerSim 2020. Society for Computer Simulation International, San Diego (2020)

    Google Scholar 

  41. Weng, T.W., et al.: Evaluating the robustness of neural networks: an extreme value theory approach. In: International Conference on Learning Representations (2018)

    Google Scholar 

  42. Wood, G., Zhang, B.: Estimation of the Lipschitz constant of a function. J. Global Optim. 8(1), 91–103 (1996)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We would like to thank Thomas Helyer for his contributions in the early stages of this research. This work was partially supported by the Air Force Office of Scientific Research under award no. FA2386-17-1-4065. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the United States Air Force.

Author information

Authors and Affiliations

  1. School of Computing, Newcastle University, Newcastle upon Tyne, UK

    Sergiy Bogomolov, John Fitzgerald, Sadegh Soudjani & Paulius Stankaitis

Authors
  1. Sergiy Bogomolov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John Fitzgerald
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sadegh Soudjani
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Paulius Stankaitis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paulius Stankaitis .

Editor information

Editors and Affiliations

  1. University of Limerick, CSIS and Lero, Limerick, Ireland

    Tiziana Margaria

  2. TU Dortmund, Dortmund, Germany

    Bernhard Steffen

Appendix A

Appendix A

See Fig. 6.

Fig. 6.
figure 6

Reachable set comparison of the 3D linear system \(\textbf{A} = [1 \; -1 \; 0; \;1 \; -1 \; 3; \; -1 \; 2 \; -1] \) with initial region \([0,0.1]\times [0,0.1]\times [0,0.1]\): (a, b, c) 1000 samples and maximum function, (d) accuracy plot over time

Full size image
Table 1. The summary of results from Subsect. 5.1: variation of the average error between a true and sampled Lipschitz constant values over time for stable and unstable linear system.
Full size table

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bogomolov, S., Fitzgerald, J., Soudjani, S., Stankaitis, P. (2022). Data-Driven Reachability Analysis of Digital Twin FMI Models. In: Margaria, T., Steffen, B. (eds) Leveraging Applications of Formal Methods, Verification and Validation. Practice. ISoLA 2022. Lecture Notes in Computer Science, vol 13704. Springer, Cham. https://doi.org/10.1007/978-3-031-19762-8_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-19762-8_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-19761-1

  • Online ISBN: 978-3-031-19762-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation