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Abstract

The active robust optimization methodology covers a wide range of problem formulations and can support a variety of design optimization activities. In this chapter, two applications from different fields are used to demonstrate how AROPs are formulated and solved for real-world applications. In order to focus on the methodological aspects of the framework instead of the technical issues for each application, the examples are simplified and modelled from first principles.

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Notes

  1. 1.

    In order to be consistent with the notation used throughout this thesis, lower-case j is used instead of the more common upper-case J to denote moment of inertia. As explained in Sect. 2.3.1, lower-case symbols denote deterministic values, while upper-case symbols denote random values. The same rules apply to other notations in this chapter.

  2. 2.

    V, I and L are the universal notations to describe voltage, current and inductance. For clarity, these are used here to describe deterministic values, in contrast to the usual convention of this thesis where capital letters are used to describe random variates.

  3. 3.

    Recall that \(\psi \) denotes a deterministic objective value.

References

  1. Newport Corporation (2012) Vibration Control—Identifying and Controlling Vibrations in the Workplace. http://photonics.com/edu/Handbook.aspx

  2. Salomon S, Avigad G, Goldvard A, Schütze O (2013b) PSA a new scalable space partition based selection algorithm for MOEAs. In: Schütze O, Coello Coello CA, Tantar A-A, Tantar E, Bouvry P, Del Moral P, Legrand P (eds) EVOLVE 2013, vol 175. Advances in Intelligent Systems and Computing. Springer, Berlin, Heidelberg, pp 137–151

    Google Scholar 

  3. McKay MD, Beckman RJ, Conover WJ (1979) Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2):239–245

    MathSciNet  MATH  Google Scholar 

  4. Guzzella L, Amstutz A (1999) CAE tools for quasi-static modeling and optimization of hybrid powertrains. Vehicular Technol IEEE Trans 48(6):1762–1769

    Article  Google Scholar 

  5. Roos F, Johansson H, Wikander J (2006) Optimal selection of motor and gearhead in mechatronic applications. Mechatronics 16(1):63–72

    Article  Google Scholar 

  6. Swantner A, Campbell MI (2012) Topological and parametric optimization of gear trains. Eng Optim 44(11):1351–1368

    Article  Google Scholar 

  7. Mogalapalli SN, Magrab EB, Tsai LW (1992) A CAD System for the Optimization of Gear Ratios for Automotive Automatic Transmissions. Technical report, University of Maryland. http://hdl.handle.net/1903/5299

  8. Yokota T, Taguchi T, Gen M (1998) A solution method for optimal weight design problem of the gear using genetic algorithms. Comput Ind Eng 35(34):523–526

    Article  Google Scholar 

  9. Savsani V, Rao RV, Vakharia DP (2010) Optimal weight design of a gear train using particle swarm optimization and simulated annealing algorithms. Mech Mach Theory 45(3):531–541

    Article  Google Scholar 

  10. Inoue K, Townsend DP, Coy JJ (1992) Optimum design of a Gearbox for low vibration. Int Power Transm Gearing Conf 2:497–504

    Google Scholar 

  11. Li X, Symmons GR, Cockerham G (1996) Optimal design of involute profile helical gears. Mech Mach Theory 31(6):717–728

    Article  Google Scholar 

  12. Osyczka A (1978) An Approach to multicriterion optimization problems for engineering design. Comput Methods Appl Mech Eng 15(3):309–333

    Article  Google Scholar 

  13. Wang H-PH (1994) Optimal engineering design of spur gear sets. Mech Mach Theory 29(7):1071–1080

    Article  Google Scholar 

  14. Thompson DF, Gupta S, Shukla A (2000) Tradeoff analysis in minimum volume design of multi-stage spur gear reduction units. Mech Mach Theory 35(5):609–627

    Article  Google Scholar 

  15. Kurapati A, Azarm S (2000) Immune network simulation with multiobjective genetic algorithms for multidisciplinary design optimization. Eng Optim 33(2):245–260

    Article  Google Scholar 

  16. Deb K, Pratap A, Moitra S (2000) Mechanical component design for multiple ojectives using elitist non-dominated sorting GA. In: Schoenauer M, Deb K, Rudolph G, Yao X, Lutton E, Merelo J, Schwefel H-P (eds) Parallel problem solving from nature PPSN VI SE - 84, vol 1917. Lecture Notes in Computer Science. Springer, Berlin, Heidelberg, pp 859–868

    Chapter  Google Scholar 

  17. Deb K, Jain S (2003) Multi-speed gearbox design using multi-objective evolutionary algorithms. J Mech Des 125(3):609–619

    Article  Google Scholar 

  18. Deb K (2003) Unveiling innovative design principles by means of multiple conflicting objectives. Eng Optim 35(5):445–470

    Article  MathSciNet  Google Scholar 

  19. Li R, Chang T, Wang J, Wei X (2008) Multi-objective optimization design of gear reducer based on adaptive genetic algorithm. In: 12th International conference on computer supported cooperative work in design, 2008. CSCWD 2008, pp 229–233

    Google Scholar 

  20. Krishnan R (2001) Electric motor drives—modeling, analysis. Prentice Hall, And Control. ISBN 0-13-091014-7

    Google Scholar 

  21. Maxon (2014) Maxon Motor online catalog. http://www.maxonmotor.com/maxon/view/catalog/

  22. Branke J, Rosenbusch J (2008) New approaches to coevolutionary worst-case optimization. In: Rudolph G, Jansen T, Lucas S, Poloni C, Beume N (eds) Parallel problem solving from nature PPSN X SE - 15, vol 5199. Lecture Notes in Computer Science. Springer, Berlin, Heidelberg, pp 144–153

    Chapter  Google Scholar 

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Salomon, S. (2019). Case Studies. In: Active Robust Optimization: Optimizing for Robustness of Changeable Products. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-15050-1_5

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