ABSTRACT
In the domain of cyber-physical systems, there is an increasing relevance of data-driven approaches for the learning of hybrid system dynamics. In particular, accurate models have been successfully abstracted from continuous (real-valued) traces and applied for various goals. However, industrial applications involving online modeling or rapid prototyping have two additional requirements: 1) runtime efficiency and 2) the interpretability of the approach and results.
This work adopts a common break down of this learning problem into four steps: 1) trace segmentation, 2) segment clustering, 3) characterization of the dynamics for each cluster (mode) and 4) learning of the overall model of mode transitions. Correspondingly, the bottlenecks in the state-of-the-art approaches are identified and discussed. Then, in a heuristic manner, interpretable and time-efficient algorithms for each of the steps are proposed giving a novel approach named FaMoS. The accuracy and runtime efficiency of the approach are evaluated for several system examples. FaMoS shows very short learning time, while the model’s predictions of system dynamics are close to the ground truth behavior.
- Houssam Abbas, Hans Mittelmann, and Georgios Fainekos. 2014. Formal property verification in a conformance testing framework. In 2014 Twelfth ACM/IEEE Conference on Formal Methods and Models for Codesign (MEMOCODE). IEEE, New York, 155–164.Google ScholarDigital Library
- Rajeev Alur. 2015. Principles of Cyber-Physical Systems. Technical Report. MIT Press.Google Scholar
- R. Alur, T.A. Henzinger, G. Lafferriere, and G.J. Pappas. 2000. Discrete abstractions of hybrid systems. Proc. IEEE 88, 7 (2000), 971–984. https://doi.org/10.1109/5.871304Google ScholarCross Ref
- Fin Hendrik Bahnsen and Goerschwin Fey. 2019. Local Monitoring of Embedded Applications and Devices using Artificial Neural Networks. In Euromicro Conference on Digital System Design (DSD). IEEE, New York, 485–491. https://doi.org/10.1109/DSD.2019.00076Google ScholarCross Ref
- Nathalie Barbosa Roa, Louise Travé-Massuyès, and Victor H. Grisales-Palacio. 2019. DyClee: Dynamic clustering for tracking evolving environments. Pattern Recognition 94 (2019), 162–186.Google ScholarDigital Library
- Omar Ali Beg, Houssam Abbas, Taylor T Johnson, and Ali Davoudi. 2017. Model validation of pwm dc–dc converters. IEEE Transactions on Industrial Electronics 64, 9 (2017), 7049–7059.Google ScholarCross Ref
- Jürgen Beyerer and Oliver Niggemann. 2018. Machine Learning in Automation. At-Automatisierungstechnik 66, 4 (2018), 281–282. https://doi.org/10.1515/auto-2018-0036Google ScholarCross Ref
- Mathias Blumreiter, Joel Greenyer, Francisco Javier Chiyah Garcia, Verena Klös, Maike Schwammberger, Christoph Sommer, Andreas Vogelsang, and Andreas Wortmann. 2019. Towards Self-Explainable Cyber-Physical Systems. CoRR abs/1908.04698 (2019), 6 pages.Google Scholar
- Aaron Bracht, Swantje Plambeck, and Goerschwin Fey. 2024. TUHH-IES/FaMoS-DT: v0.1. https://doi.org/10.5281/zenodo.10657936Google ScholarCross Ref
- Michael S. Branicky. 2005. Introduction to Hybrid Systems. Birkhäuser Boston, Boston, MA, 91–116.Google Scholar
- Andreas Bunte, Benno Stein, and Oliver Niggemann. 2019. Model-Based Diagnosis for Cyber-Physical Production Systems Based on Machine Learning and Residual-Based Diagnosis Models. In Conference on Artificial Intelligence (AAAI). QQQI, Hawaii, USA, 2727–2735.Google Scholar
- François E. Cellier. 1991. Continuous system modeling. Springer, New York.Google Scholar
- Fabio Cremona, Marten Lohstroh, David Broman, Edward A. Lee, and Michael Masin. 2019. Hybrid co-simulation: it’s about time. Software & Systems Modeling 18 (2019), 1655–1679. Issue 3.Google ScholarDigital Library
- Paul Cull, Mary Flahive, and Robby Robson. 2005. Matrix Difference Equations. Springer, New York, Chapter 7, 392.Google Scholar
- Dario Della Monica, Giovanni Pagliarini, Guido Sciavicco, and Ionel Eduard Stan. 2023. Decision Trees with a Modal Flavor. In Advances in Artificial Intelligence (AIxIA), Agostino Dovier, Angelo Montanari, and Andrea Orlandini (Eds.). Springer-Verlag, Berlin, Heidelberg, 47–59.Google Scholar
- Mark Gold. 1967. Language identification in the limit. Information and Control 10, 5 (1967), 447–474.Google ScholarCross Ref
- Nemanja Hranisavljevic, Alexander Maier, and Oliver Niggemann. 2020. Discretization of hybrid CPPS data into timed automaton using restricted Boltzmann machines. Engineering Applications of Artificial Intelligence 95 (2020), 103826. https://doi.org/10.1016/j.engappai.2020.103826Google ScholarCross Ref
- Malte Isberner, Falk Howar, and Bernhard Steffen. 2014. The TTT Algorithm: A Redundancy-Free Approach to Active Automata Learning. In Runtime Verification. Springer International Publishing, Cham, 307–322.Google Scholar
- Pranav Srinivas Kumar, William Emfinger, and Gabor Karsai. 2015. A testbed to simulate and analyze resilient cyber-physical systems. In 2015 International Symposium on Rapid System Prototyping (RSP). IEEE, New York, 97–103. https://doi.org/10.1109/RSP.2015.7416553Google ScholarCross Ref
- Edward A. Lee. 2016. Fundamental Limits of Cyber-Physical Systems Modeling. ACM Transactions on Cyber-Physical Systems 1, 1 (2016), 26 pages. https://doi.org/10.1145/2912149Google ScholarDigital Library
- Scott Linderman, Matthew Johnson, Andrew Miller, Ryan Adams, David Blei, and Liam Paninski. 2017. Bayesian Learning and Inference in Recurrent Switching Linear Dynamical Systems. In Proceedings of the 20th International Conference on Artificial Intelligence and Statistics(Proceedings of Machine Learning Research, Vol. 54), Aarti Singh and Jerry Zhu (Eds.). PMLR, Palermo, 914–922. https://proceedings.mlr.press/v54/linderman17a.htmlGoogle Scholar
- Changliu Liu, Tomer Arnon, Christopher Lazarus, Clark W. Barrett, and Mykel J. Kochenderfer. 2019. Algorithms for Verifying Deep Neural Networks. CoRR abs/1903.06758 (2019), 161 pages. arXiv:1903.06758Google Scholar
- Lennart Ljung. 1986. System Identification: Theory for the User. Prentice-Hall, Inc., Upper Saddle River, NJ, USA.Google ScholarDigital Library
- Wei-Yin Loh. 2011. Classification and regression trees. WIREs Data Mining and Knowledge Discovery 1, 1 (2011), 14–23. https://doi.org/10.1002/widm.8Google ScholarCross Ref
- Estrella Lucena-Sanchez, Guido Sciavicco, and Ionel Eduard Stan. 2020. Symbolic Learning with Interval Temporal Logic: theCase of Regression. In Workshop on Artificial Intelligence and Formal Verification, Logics, Automata and Synthesis (OVERLAY). CEUR, Bozen Bolzano, 5–10.Google Scholar
- J. Lunze and F. Lamnabhi-Lagarrigue. 2009. Handbook of Hybrid Systems Control: Theory, Tools, Applications. Cambridge University Press, Cambridge. https://books.google.de/books?id=pPLRV3ehMVICGoogle Scholar
- Alexander Maier. 2014. Online Passive Learning of Timed Automata for Cyber-Physical Production Systems. In International Conference on Industrial Informatics (INDIN). IEEE, Porto Alegre, Brazil, 60–66.Google Scholar
- Meinard Müller. 2007. Dynamic Time Warping. Springer-Verlag, Heidelberg, Chapter 4, 69–84.Google Scholar
- Oliver Niggemann and Volker Lohweg. 2015. On the Diagnosis of Cyber-Physical Production Systems - State-of-the-Art and Research Agenda. In Twenty-Ninth Conference on Artificial Intelligence (AAAI-15). AAAI, Austin, Texas, USA, 8 pages.Google Scholar
- Oliver Niggemann and Stephan Myschik. 2022. DTEC - (K)ISS – Künstliche Intelligenz für die Diagnose der ISS. https://dtecbw.de/home/forschung/hsu/projekt-kiss.Google Scholar
- Oliver Niggemann, Benno Stein, Asmir Vodencarevic, Alexander Maier, and Hans Kleine Büning. 2012. Learning Behavior Models for Hybrid Timed Systems. AAAI Conference on Artificial Intelligence 26, 1 (2012), 1083–1090. https://doi.org/10.1609/aaai.v26i1.8296Google ScholarCross Ref
- Oliver Niggemann, Stefan Windmann, Soeren Volgmann, Andreas Bunte, and Benno Stein. 2014. Using Learned Models for the Root Cause Analysis of Cyber-Physical Production Systems. In DX. Research Gate, Graz, 8 pages.Google Scholar
- Swantje Plambeck, Lutz Schammer, and Gorschwin Fey. 2022. On the Viability of Decision Trees for Learning Models of Systems. In Asia and South Pacific Design Automation Conference (ASP-DAC). IEEE, New York, 696–701. https://doi.org/10.1109/ASP-DAC52403.2022.9712579Google ScholarDigital Library
- Iman Saberi, Fathiyeh Faghih, and Farzad Sobhi Bavil. 2021. A Passive Online Technique for Learning Hybrid Automata from Input/Output Traces. ACM Transactions on Embedded Computing Systems 22, 1 (2021), 1–24. https://doi.org/10.1145/3556543Google ScholarDigital Library
- Habiba Muhammad Sani, Ci Lei, and Daniel Neagu. 2018. Computational Complexity Analysis of Decision Tree Algorithms. In International Conference on Artificial Intelligence. Springer International Publishing, Cham, 191–197.Google Scholar
- Guido Sciavicco and Ionel Eduard Stan. 2020. Knowledge Extraction with Interval Temporal Logic Decision Trees. In International Symposium on Temporal Representation and Reasoning (TIME). Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 9:1–9:16.Google Scholar
- Shai Shalev-Shwartz and Shai Ben-David. 2014. Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9781107298019Google ScholarCross Ref
- Bernhard Steffen, Falk Howar, and Maik Merten. 2011. Introduction to Active Automata Learning from a Practical Perspective. Springer, Berlin, Heidelberg, 256–296. https://doi.org/10.1007/978-3-642-21455-4_8Google ScholarCross Ref
- Henrik Steude, Alexander Windmann, and Oliver Niggemann. 2022. Learning Physical Concepts in CPS: A Case Study with a Three-Tank System. IFAC-PapersOnLine 55, 6 (2022), 15–22. https://doi.org/10.1016/j.ifacol.2022.07.099Google ScholarCross Ref
- Paulo Tabuada, Sina Yamac Caliskan, Matthias Rungger, and Rupak Majumdar. 2014. Towards Robustness for Cyber-Physical Systems. IEEE Trans. Automat. Control 59, 12 (2014), 3151–3163. https://doi.org/10.1109/TAC.2014.2351632Google ScholarCross Ref
- The MathWorks Inc.2023. MATLAB (R2023b).Google Scholar
- Charles Truong, Laurent Oudre, and Nicolas Vayatis. 2020. Selective review of offline change point detection methods. Signal Processing 167, 4 (2020), 20 pages. https://doi.org/10.1016/j.sigpro.2019.107299Google ScholarDigital Library
- Henning Urbat and Lutz Schröder. 2020. Automata Learning: An Algebraic Approach. In ACM/IEEE Symposium on Logic in Computer Science. ACM, New York, 900–914. https://doi.org/10.1145/3373718.3394775Google ScholarDigital Library
- Amaury Vignolles, Elodie Chanthery, and Pauline Ribot. 2022. Hybrid Model Learning for System Health Monitoring. In Symposium on Fault Detection, Supervision and Safety for Technical Processes (SAFEPROCESS). Science Direct, Pafos, 7–14.Google Scholar
- Xiaodong Yang, Omar Ali Beg, Matthew Kenigsberg, and Taylor T. Johnson. 2022. A Framework for Identification and Validation of Affine Hybrid Automata from Input-Output Traces. ACM Transactions on Cyber-Physical Systems 6, 2 (2022), 1–24. https://doi.org/10.1145/3470455Google ScholarDigital Library
Index Terms
- FaMoS– Fast Model Learning for Hybrid Cyber-Physical Systems using Decision Trees
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