Skip to main content
SpringerLink
Log in

Mathematical framework for recursive model-based system design

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, we introduce a mathematical framework that allows the designer to consider more of the proposed ideas and options in conceptual design phase into the design process. The proposed model allows for dynamical relationship between the system’s high-level requirements and the detailed design parameters, where an optimization engine can optimize over the design parameters and variables for a given range in the requirement. This is done by proposing an input/output block structure named recursive design modular (RDM). The output of RDM is the functions that the system supposes to perform at particular level. The input of RDM is the design parameters that control the required behaviour through a set of mapping or transformation.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Boland Jr, R.J.: The process and product of system design. Manag. Sci. 24(9), 887–898 (1978)

    Article  Google Scholar 

  2. Blanchard, B.S., Fabrycky, W.J., Fabrycky, W.J.: Systems Engineering and Analysis. Prentice Hall Englewood Cliffs, New Jersey (1990)

    Google Scholar 

  3. Kroll, E., Condoor, S., Jansson, D.: Innovative Conceptual Design: Theory and Application of Parameter Analysis. Cambridge University Press, Cambridge (2001)

    Book  Google Scholar 

  4. Waldo, J.: On system design. In ACM SIGPLAN Notices, vol. 41, no. 10, pp. 467–480. ACM (2006)

  5. Aronson, J., Liang, T., Turban, E.: Decision Support Systems and Intelligent Systems. Andi, Yoyakarta (2005)

    Google Scholar 

  6. Marston, M., Mistree, F.: A decision-based foundation for systems design: a conceptual exposition. In CIRP 1997 International Design Seminar Proceedings on Multimedia Technologies for Collaborative Design and Manufacturing, pp. 1–11. University of Southern California, Los Angeles, CA (1997)

  7. Kalsi, M., Hacker, K., Lewis, K.: Decision Trade-Offs in Complex Systems Design Using a Conceptual Robustness Approach. In The Third World Congress of Structural and Multidisciplinary Optimization (1999)

  8. Austin-Breneman, J., Honda, T., Yang, M.C.: A study of student design team behaviors in complex system design. J. Mech. Des. 134(12), 124504 (2012)

    Article  Google Scholar 

  9. Senge, P.M.: The fifth discipline. Meas. Bus. Excell. 1(3), 46–51 (1997)

    Article  Google Scholar 

  10. ISO/IEC 15288: Systems and Software Engineering System Life Cycle Processes (2008)

  11. Leontief, W.: Input–Output Economics. Oxford University Press, Oxford (1986)

    Google Scholar 

  12. Friedenthal, S., Moore, A., Steiner, R.: A Practical Guide to SysML: The Systems Modeling Language. Morgan Kaufmann, Burlington (2011)

    Google Scholar 

  13. Estefan, J.A.: Survey of Model-Based Systems Engineering (mbse) Methodologies. Jet Propulsion Laboratory California Institute of Technology Pasadena. California, USA (2008)

  14. Ramos, A.L., Ferreira, J.V., Barceló, J.: Model-based systems engineering: an emerging approach for modern systems. IEEE Trans. Syst. Man Cybern. Part. C Appl. Rev. 42(1), 101–111 (2012)

    Article  Google Scholar 

  15. Weilkiens, T.: Systems Engineering with SysML/UML: Modeling, Analysis, Design. Morgan Kaufmann, Burlington (2011)

    MATH  Google Scholar 

  16. Dori, D.: Object-Process Methodology: A Holistic Systems Paradigm; with CD-ROM, vol. 1. Springer, Berlin (2002)

    Book  MATH  Google Scholar 

  17. Tiller, M.: Introduction to Physical Modeling with Modelica. Springer, Berlin (2001)

    Book  Google Scholar 

  18. Fitzgerald, J., Larsen, P.G., Pierce, K., Verhoef, M., Wolff, S.: Collaborative modelling and co-simulation in the development of dependable embedded systems. In Integrated Formal Methods. pp. 12–26. Springer, Berlin (2010)

  19. Eker, J., Janneck, J.W., Lee, E.A., Liu, J., Liu, X., Ludvig, J., Neuendorffer, S., Sachs, S., Xiong, Y.: Taming heterogeneity-the ptolemy approach. Proc. IEEE 91(1), 127–144 (2003)

    Article  Google Scholar 

  20. Ptolemaeus, C.: System Design, Modeling, and Simulation: Using Ptolemy II. Ptolemy. org (2014)

  21. Suh, N.P., Sekimoto, S.: Design of thinking design machine. CIRP Ann. Manuf. Technol. 39(1), 145–148 (1990)

    Article  Google Scholar 

  22. Suh, N.: Axiomatic Design: Advances and Applications. MIT-Pappalardo Series in Mechanical Engineering. Oxford University Press, Oxford (2001)

    Google Scholar 

  23. Wymore, A.: Model-Based Systems Engineering ser. Systems Engineering. Taylor & Francis, New York (1993)

    Google Scholar 

  24. Kulak, O., Cebi, S., Kahraman, C.: Applications of axiomatic design principles: a literature review. Expert Syst. Appl. 37(9), 6705–6717 (2010)

    Article  Google Scholar 

  25. Bae, S., Lee, J.M., Chu, C.N.: Axiomatic design of automotive suspension systems. CIRP Ann. Manuf. Technol. 51(1), 115–118 (2002)

    Article  Google Scholar 

  26. Thielman, J., Ge, P.: Applying axiomatic design theory to the evaluation and optimization of large-scale engineering systems. J. Eng. Des. 17(1), 1–16 (2006)

    Article  Google Scholar 

  27. Helander, M.G.: Using design equations to identify sources of complexity in human-machine interaction. Theor. Issues Ergon. Sci. 8(2), 123–146 (2007)

    Article  Google Scholar 

  28. Kim, D.-E., Chung, K.-H., Cha, K.-H.: Tribological design methods for minimum surface damage of hdd slider. Tribol. Int. 36(4), 467–473 (2003)

    Article  Google Scholar 

  29. Kulak, O., Kahraman, C.: Fuzzy multi-attribute selection among transportation companies using axiomatic design and analytic hierarchy process. Inf. Sci. 170(2), 191–210 (2005)

    Article  MATH  Google Scholar 

  30. Kulak, O., Kahraman, C.: Multi-attribute comparison of advanced manufacturing systems using fuzzy vs. crisp axiomatic design approach. Int. J. Prod. Econ. 95(3), 415–424 (2005)

    Article  Google Scholar 

  31. Cebi, S., Kahraman, C.: Extension of axiomatic design principles under fuzzy environment. Expert Syst. Appl. 37(3), 2682–2689 (2010)

    Article  Google Scholar 

  32. Cloutier, R., Muller, G., Verma, D., Nilchiani, R., Hole, E., Bone, M.: The concept of reference architectures. Syst. Eng. 13(1), 14–27 (2010)

    Google Scholar 

  33. Migdalas, A., Pardalos, P., Värbrand, P.: Multilevel Optimization: Algorithms and Applications. Nonconvex Optimization and Its Applications. Springer, Berlin (1998)

    Book  MATH  Google Scholar 

  34. Siljak, D., Sundareshan, M.: A multilevel optimization of large-scale dynamic systems. IEEE Transactions on Automatic Control 21(1), 79–84 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  35. Frandi, E., Papini, A.: Coordinate search algorithms in multilevel optimization. Optim. Methods Softw. 29(5), 1020–1041 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  36. Pettersson, H., Rodiouchkina, M., Micklow, G., et al.: Multidisciplinary Design Optimization for Automotive Design Systems. SAE Technical Paper. Tech. Rep. (2015)

  37. Sarker, R., Elsayed, S., Ray, T.: Differential evolution with dynamic parameters selection for optimization problems. IEEE Trans. Evol. Comput. 18(5), 689–707 (2014)

    Article  Google Scholar 

  38. Storn, R., Price, K.: Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  39. Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186(2), 311–338 (2000)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering and Information Technology, University of New South Wales, Australian Defence Force Academy, Canberra, ACT, 2600, Australia

    Mohamed A. Mabrok, Saber Elsayed & Michael J. Ryan

  2. Faculty of Computers and Informatics, Zagazig University, Zagazig, Egypt

    Saber Elsayed

  3. Mathematics Department, Faculty of Science, Suez Canal University, Ismailia, Egypt

    Mohamed A. Mabrok

Authors
  1. Mohamed A. Mabrok
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Saber Elsayed
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael J. Ryan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamed A. Mabrok.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mabrok, M.A., Elsayed, S. & Ryan, M.J. Mathematical framework for recursive model-based system design. Nonlinear Dyn 84, 223–236 (2016). https://doi.org/10.1007/s11071-015-2418-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-015-2418-1

Keywords

Search

Navigation