Анализ исследований математических основ модельно-ориентированной системной инженерии

Vladimir A. Sukhomlin

doi:10.21638/spbu10.2024.304

Authors

Vladimir A. Sukhomlin Lomonosov Moscow State University, 1, Leninskie Gory, Moscow, 119991, Russian Federation https://orcid.org/0000-0001-9468-7138

DOI:

https://doi.org/10.21638/spbu10.2024.304

Abstract

The article provides an analysis of research into the mathematical foundations of model-based systems engineering (MBSE, Model-Based Systems Engineering). Both the classical mathematical theory of Wymore’s system design and modern research are considered, in particular, the formalization of the semantics of the SysML language using automata theory, the use of category theory as a formal mathematical basis for model-based system design, the study of the possibilities of combining the theoretical basis of Wymore’s systems and the universal Discrete Event System Specification (DEVS) modeling formalism.

Keywords:

systems engineering, model-based systems engineering, finite state machines, semantics of the SysML language, tripartite theory, DEVS modeling, category theory in model-based systems engineering

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References

Литература

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Wymore A. W. Model-based systems engineering. Boca Raton: CRC Press, Inc., 1993. 710 p.

Wach P., Zeigler B. P., Salado A. Conjoining Wymore’s systems theoretic framework and the DEVS modeling formalism: toward scientific foundations for MBSE // Appl. Sci. 2021. N 11. P. 4936. https://doi.org/10.3390/app11114936

Salado A., Wach P. Interpretation discrepancies of SysML state machine: An initial investigation // Proceedings of the 18^th Annual Conference on Systems Engineering Research (CSER). Redondo Beach, CA, USA, 2020. October 8–10. P. 361–370.

Zeigler B. P., Mittal S., Traore M. K. MBSE with/out simulation: State of the art and way forward // Systems. 2018. Vol. 6. N 40. P. 1–18. https://doi.org/10.3390/systems6040040

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Hammami O., Edmonson W. THEFOSE — theoretical foundations of system engineering: A first feedback // Proceedings of the 2015 IEEE International Symposium on Systems Engineering (ISSE). Rome, Italy. 2015. September 28–30. P. 370–374.

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Wymore A. W. Systems movement: autobiographical retrospectives // International Journal of General Systems. 2004. Vol. 33(6). P. 593–610. https://doi.org/10.1080/03081070412331309131

Wymore A. W. Model-based systems engineering: a quick overview // INCOSE International Workshop. Albuquerque, NM. 2007. January 25.

Wymore A. W. Applications of mathematical system theory to system design, modelling and simulation // Winter Simulation Conference Proceedings. 1981. P. 209–219.

Ören T., Zeigler B. P. System theoretic foundations of modeling and simulation: a historic perspective and the legacy of a Wayne Wymore // SIMULATION. 2012. Vol. 88. P. 1033–1046.

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Friedenthal S., Moore A., Steiner R. A practical guide to SysML. 3^rd ed. New York: Morgan Kaufman/Elsevier, 2015. 23 p.

Vaneman W. K. Enhancing model-based systems engineering with the lifecycle modeling language // 2016 Annual IEEE Systems Conference (SysCon). IEEE. Orlando, FL, USA, 2016. P. 1–7.

Graves H., Yvonne B. Using formal methods with SysML in aerospace design and engineering // Annals of Mathematics and Artificial Intelligence. 2011. Vol. 63(1). P. 53–102.

Wacha P., Saladoa A. Can Wymore’s mathematical framework underpin SysML? An initial investigation of state machines // Procedia Computer Science. 2019. Vol. 153. P. 242–249. https://doi.org/10.1016/j.procs.2019.05.076

Mabrok M. A., Ryan M. J. Category theory as a formal mathematical foundation for model-based systems engineering // Appl. Math. Inf. Sci. 2017. Vol. 11. N 1. P. 43–51. https://doi.org/10.18576/amis/110106

Fokkinga M. M. A gentle introduction to category theory — the calculational approach. Utrecht: University of Utrecht, 1992. 72 p.

Hoare C. A. R. Notes on an approach to category theory for computer scientists // Constructive Methods in Computing Science. Berlin; Heidelberg: Springer, 1989. Vol. 55. P. 245–305.

Scott D. S. Relating theories of the lambda calculus // To H. B. Curry: Essays on combinatory logic, lambda calculus and formalism. New York: Academic Press, 1980. P. 403–450.

Rydeheard D. E., Burstall R. M. Computational category theory. Englewood Cliffs: Prentice Hall, 1988. 257 p.

Pierce B. C. Basic category theory for computer scientists. Cambridge: MIT Press, 1991. 114 p.

Reed G. M., Roscoe A., Wachter R. F. Topology and category theory in computer science. Oxford: Oxford University Press, 1991. 402 p.

Herring J., Egenhofer M. J., Frank A. U. Using category theory to model gis applications // 4^th International Symposium on Spatial Data Handling. 1990. Vol. 2. P. 820–829.

Rising III H., Tabatabai A. Application of category theory and cognitive science to design of semantic descriptions for content data. US Patent 7,319,951. 2008. January 15.

Williamson K., Healy M., Barker R. Industrial applications of software synthesis via category theorycase studies using specware // Automated Software Engineering. 2001. Vol. 8. N 1. P. 7–30.

Fiadeiro J. L. Categories for software engineering. Berlin: Springer, 2005. 250 p. https://doi.org/10.1007/b138249

Kovalyov S. Modeling aspects by category theory // Proceedings 9^th Workshop on Foundations of Aspect-Oriented Languages. Rennes, France, 2010. P. 63–68.

Diskin Z., Maibaum T. Category theory and model-driven engineering: from formal semantics to design patterns and beyond // Proceedings of ACCAT 2012 EPTCS 93. 2012. P. 1–21.

Luzeaux D. A formal foundation of systems engineering // Complex Systems Design & Management. Cham: Springer, 2015. P. 133–148.

Vidalie J. Category theory for consistency between multilevel system modeling (MBSE) and safety (MBSA). Paris: Universite Paris-Saclay, 2023. 203 p.

Atkinson C., Kuhne T. Model-driven development: a metamodeling foundation // IEEE Software. 2003. Vol. 20. N 5. P. 36–41.

Spivak D. I., Kent R. E. Ologs: a categorical framework for knowledge representation // PLoS One. 2012. Vol. 7. N 1. P. e24274.

Engel A., Mordecai Y. Systems engineering using category theory // Systems Science for Engineers and Scholars. 2024. P. 63–68. https://doi.org/10.1002/9781394211678.ch18

Breiner S., Subrahmanian E., Sriram R. D. Category theory // Handbook of Model-Based Systems Engineering. Cham: Springer, 2022. P. 1–41. https://doi.org/10.1007/978-3-030-27486-385-1

Myers D. J. Categorical systems — theory. 2023. URL: http://davidjaz.com/Papers/DynamicalBook.pdf (accessed: November 14, 2023).

NAFEMS: Systems modeling & simulation working group. URL: https://www.nafems.org/community/working-groups/systems-modeling-simulation/ (accessed: April 13, 2021).

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Mesarovic M., Takahara Y. General systems theory: Mathematical foundations. London, Academic Press, 1975, 268 p.

Mesarovic M., Takahara Y. Abstract systems theory. New York, Springer, 1989, 439 p.

Wymore A. W. A Mathematical theory of systems engineering: The elements. New York, John Wiley & Sons Publ., 1967, 353 p.

Wymore A. W. Model-based systems engineering. Boca Raton, CRC Press, Inc., 1993, 710 p.

Wach P., Zeigler B. P., Salado A. Conjoining Wymore’s systems theoretic framework and the DEVS modeling formalism: toward scientific foundations for MBSE. Appl. Sci., 2021, no. 11, p. 4936. https://doi.org/10.3390/app11114936

Salado A., Wach P. Interpretation discrepancies of SysML state machine: An initial investigation. Proceedings of the 18^th Annual Conference on Systems Engineering Research (CSER). Redondo Beach, CA, USA, 2020, October 8–10, pp. 361–370.

Zeigler B. P., Mittal S., Traore M. K. MBSE with/out simulation: State of the art and way forward. Systems, 2018, vol. 6, no. 40, pp. 1–18. https://doi.org/10.3390/systems6040040

INCOSE. Future of systems engineering (FuSE). Available at: https://www.incose.org/about-systems-engineering/fuse (accessed: June 9, 2020).

Rousseau D. The theoretical foundation(s) for systems engineering? Response to Yearworth. Syst. Res. Behav. Sci., 2020, vol. 37, pp. 188–191.

NSF. Workshop: Investigation of the theoretical foundations in systems engineering. Available at: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1548480 (accessed: April 9, 2024).

NSF. Workshop: The science of systems engineering. Available at: https://nsf.gov/awardsearch/showAward?AWD_ID=1447031 (accessed: June 9, 2020).

Hammami O., Edmonson W. THEFOSE — Theoretical foundations of system engineering: A first feedback. Proceedings of the 2015 IEEE International Symposium on Systems Engineering (ISSE). Rome, Italy, 2015, September 28–30, pp. 370–374.

Collopy P. D. Systems engineering theory: What needs to be done. Proceedings of the 2015 Annual IEEE Systems Conference (SysCon). Vancouver, Canada, 2015, April 13–16, pp. 536–541.

INCOSE. INCOSE system engineering vision. 2025, July. 2014. Available at: https://www.incose.org/docs/default-source/aboutse/se-vision-2025.pdf?sfvrsn=4&sfvrsn=4 (accessed:linebreak November 12, 2020).

Estefan J. A. Survey of model-based systems engineering (MBSE) methodologies. INCOSE MBSE Focus Group, 2008. Available at: https://www.omgsysml.org/MBSE_Methodology_Survey_RevB.pdf (accessed: November 14, 2023).

Wymore A. W. Systems movement: autobiographical retrospectives. International Journal of General Systems, 2004, vol. 33(6), pp. 593–610. https://doi.org/10.1080/03081070412331309131

Wymore A. W. Model-based systems engineering: a quick overview. INCOSE International Workshop. Albuquerque, NM, 2007, January 25.

Wymore A. W. Applications of mathematical system theory to system design, modelling and simulation. Winter Simulation Conference Proceedings, 1981, pp. 209–219.

Ören T., Zeigler B. P. System theoretic foundations of modeling and simulation: a historic perspective and the legacy of a Wayne Wymore. SIMULATION, 2012, vol. 88, pp. 1033–1046.

Object Management Group. System modeling language. 2016. Available at: http://www.omgsysml.org/ (accessed: December 19, 2016).

Friedenthal S., Moore A., Steiner R. A practical guide to SysML. 3^rd ed. New York, Morgan Kaufman/Elsevier Publ., 2015, 23 p.

Vaneman W. K. Enhancing model-based systems engineering with the lifecycle modeling language. Annual IEEE Systems Conference (SysCon). Orlando, FL, USA, 2016, pp. 1–7.

Graves H., Yvonne B. Using formal methods with SysML in aerospace design and engineering. Annals of Mathematics and Artificial Intelligence, 2011, vol. 63(1), pp. 53–102.

Wacha P., Saladoa A. Can Wymore’s mathematical framework underpin SysML? An initial investigation of state machines. Procedia Computer Science, 2019, vol. 153, pp. 242–249. https://doi.org/10.1016/j.procs.2019.05.076

Mabrok M. A., Ryan M. J. Category theory as a formal mathematical foundation for model-based systems engineering. Appl. Math. Inf. Sci., 2017, vol. 11, no. 1, pp. 43–51. https://doi.org/10.18576/amis/110106

Fokkinga M. M. A gentle introduction to category theory — the calculational approach. Utrecht, University of Utrecht Press, 1992, 72 p.

Hoare C. A. R. Notes on an approach to category theory for computer scientists. Constructive Methods in Computing Science. Berlin, Heidelberg, Springer, 1989, vol. 55, pp. 245–305.

Scott D. S. Relating theories of the lambda calculus. To H. B. Curry: Essays on combinatory logic, lambda calculus and formalism. New York, Academic Press, 1980, pp. 403–450.

Rydeheard D. E., Burstall R. M. Computational category theory. Englewood Cliffs, Prentice Hall Press, 1988, 257 p.

Pierce B. C. Basic category theory for computer scientists. Cambridge, MIT Press, 1991, 114 p.

Reed G. M., Roscoe A., Wachter R. F. Topology and category theory in computer science. Oxford, Oxford University Press, 1991, 402 p.

Herring J., Egenhofer M. J., Frank A. U. Using category theory to model gis applications. 4^th International Symposium on Spatial Data Handling, 1990, vol. 2, pp. 820–829.

Rising III H., Tabatabai A. Application of category theory and cognitive science to design of semantic descriptions for content data. US Patent 7,319,951, 2008, January 15.

Williamson K., Healy M., Barker R. Industrial applications of software synthesis via category theorycase studies using specware. Automated Software Engineering, 2001, vol. 8, no. 1, pp. 7–30.

Fiadeiro J. L. Categories for software engineering. Berlin, Springer, 2005, 250 p. https://doi.org/10.1007/b138249

Kovalyov S. Modeling aspects by category theory. Proceedings of 9^th Workshop on Foundations of Aspect-Oriented Languages. Rennes, France, 2010, pp. 63–68.

Diskin Z., Maibaum T. Category theory and model-driven engineering: from formal semantics to design patterns and beyond. Proceedings of ACCAT 2012 EPTCS 93, 2012, pp. 1–21.

Luzeaux D. A formal foundation of systems engineering. Complex Systems Design & Management. Cham, Springer, 2015, pp. 133–148.

Vidalie J. Category theory for consistency between multilevel system modeling (MBSE) and safety (MBSA). Paris, Universite Paris-Saclay Press, 2023, 203 p.

Atkinson C., Kuhne T. Model-driven development: a metamodeling foundation. IEEE Software, 2003, vol. 20, no. 5, pp. 36–41.

Spivak D. I., Kent R. E. Ologs: a categorical framework for knowledge representation. PLoS One, 2012, vol. 7, no. 1, p. e24274.

Engel A., Mordecai Y. Systems engineering using Category theory. Systems Science for Engineers and Scholars, 2024, pp. 63–68. https://doi.org/10.1002/9781394211678.ch18

Breiner S., Subrahmanian E., Sriram R. D. Category theory. Handbook of Model-Based Systems Engineering. Cham, Springer, 2022, pp. 1–41. https://doi.org/10.1007/978-3-030-27486-3_85-1

Myers D. J. Categorical systems — theory. 2023. Available at: http://davidjaz.com/Papers/DynamicalBook.pdf (accessed: November 14, 2023).

NAFEMS: Systems modeling & simulation working group. Available at: https://www.nafems.org/community/working-groups/systems-modeling-simulation/ (accessed: April 13, 2021).