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Design Improvement for Complex Systems with Uncertainty

Author

Listed:
  • Yue Chen

    (School of Statistics, Capital University of Economics and Business, Beijing 100070, China)

  • Jian Shi

    (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100864, China
    School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China)

  • Xiao-Jian Yi

    (School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100811, China)

Abstract

The uncertainty of the engineering system increases with its complexity, therefore, the tolerance to the uncertainty becomes important. Even under large variations of design parameters, the system performance should achieve the design goal in the design phase. Therefore, engineers are interested in how to turn a bad design into a good one with the least effort in the presence of uncertainty. To improve a bad design, we classify design parameters into key parameters and non-key parameters based on engineering knowledge, and then seek the maximum solution hyper-box which already includes non-key parameters of this bad design. The solution hyper-box on which all design points are good, that is, they achieve the design goal, provides target intervals for each parameter. The bad design can be turned into a good one by only moving its key parameters into their target intervals. In this paper, the PSO-Divide-Best method is proposed to seek the maximum solution hyper-box which is in compliance with the constraints. This proposed approach has a considerably high possibility to find the globally maximum solution hyper-box that satisfies the constraints and can be used in complex systems with black-box performance functions. Finally, case studies show that the proposed approach outperforms the EPCP and IA-CES methods in the literature.

Suggested Citation

  • Yue Chen & Jian Shi & Xiao-Jian Yi, 2021. "Design Improvement for Complex Systems with Uncertainty," Mathematics, MDPI, vol. 9(11), pages 1-20, May.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1173-:d:560271
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    References listed on IDEAS

    as
    1. Yue Chen & Jian Shi & Xiao-jian Yi, 2020. "A New Reliable Operating Region Design Method," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, February.
    2. Yue Chen & Jian Shi & Xiao-jian Yi, 2020. "A Globally Optimal Robust Design Method for Complex Systems," Complexity, Hindawi, vol. 2020, pages 1-25, May.
    3. Remigijus Paulavičius & Lakhdar Chiter & Julius Žilinskas, 2018. "Global optimization based on bisection of rectangles, function values at diagonals, and a set of Lipschitz constants," Journal of Global Optimization, Springer, vol. 71(1), pages 5-20, May.
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