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Reliability-based design optimization using a family of methods of moving asymptotes

Abstract

In this study, an effective method for reliability-based design optimization is proposed enhancing sequential optimization and reliability assessment (SORA) method by a family of methods of moving asymptotes (MMA) approximations. In SORA, reliability estimation and deterministic optimization are performed sequentially. And the sensitivity and function value of probabilistic constraint at the most probable point (MPP) are obtained in the process of finding reliability information. In this study, a family of MMA approximations are constructed by utilizing the sensitivity and function value of the probabilistic constraint at the MPP. So, no additional evaluation of the probabilistic constraint is required in constructing MMA approximations. Moreover, no additional evaluation of the probabilistic constraint is required in the deterministic optimization of SORA by using a family of MMA approximations. The efficiency and accuracy of the proposed method were verified through numerical examples.

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References

  1. Bruyneel M, Duysinx P, Fleury C (2002) A family of MMA approximations for structural optimization. Struct Multidisc Optim 24:264–276

  2. Chen X, Neil DJ (1997) Reliability based structural design optimization for practical applications. In: AIAA-97-1403, pp 2724–2732

  3. Du X, Chen W (2004) Sequential optimization and reliability assessment method for efficient probabilistic design. ASME J Mech Design 126:225–233

  4. Fleury C, Braibant C (1986) Structural optimization: a new dual method using mixed variables. Int J Numer Methods Eng 23:409–428

  5. Golinski J (1970) Optimal synthesis problems solved by means of nonlinear programming and random methods. ASME J Mech Des 5(4):287–309

  6. Haldar A, Mahadevan S (2000) Reliability assessment using stochastic finite element analysis. Wiley, New York

  7. Hasofer AM, Lind NC (1974) Exact and invariant second moment code format. J Eng Mech ASCE 100:111–121

  8. Ju BH, Lee BC (2008) Reliability-based design optimization using a moment method and kriging metamodel. Eng Optim 40(5):421–438

  9. Kaymaz I (2005) Application of kriging method to structural reliability problems. Struct Saf 27:133–151

  10. Kharmanda G, Mohamed A, Lemaire M (2002) Efficient reliability-based design optimization using a hybrid space with application to finite element analysis. Struct Multidisc Optim 24:233–245

  11. Kuschel N, Rackwitz R (2000) A new approach for structural optimization of series systems. Appl Stat Prob 2(8):987–994

  12. Lee TW, Kwak BM (1987–1988) A reliability-based optimal design using advanced first order second method. Mechan Struct Mach 15(4):523–542

  13. Lee JJ, Lee BC (2005) Efficient evaluation of probabilistic constraints using an envelope function. Eng Optim 37(2):185–200

  14. Lee IJ, Choi KK, Gorsich D (2009) Sensitivity analysis of FORM-based and DRM-based performance measure approach for reliability-based design optimization. Int J Numer Methods Eng. doi:10.1002/nme.2752

  15. Mohsine A, Kharmanda G, El-Hami A (2006) Improved hybrid method as a robust tool for reliability-based design optimization. Struct Multidisc Optim 32:203–213

  16. Rackwitz R, Fiessler B (1978) Structural reliability under combined random load sequence. Comput Struct 9:489–494

  17. Rosenblatt M (1952) Remarks on a multivariate transformation. Ann Math Stat 23(3):470–472

  18. Svanberg K (1987) The method of moving asymptotes-a new method for structural optimization. Int J Numer Methods Eng 24:359–373

  19. Svanberg K (2002) A class of globally convergent optimization methods based on conservative convex separable approximations. Soc Ind Appl Math 12(2):555–573

  20. Svanberg K (2007) MMA and GCMMA, versions September 2007. http://www.math.kth.se/~krille/gcmma07.pdf. Accessed 20 March 2009

  21. Tu J, Choi KK, Park YH (1999) A new study on reliability based design optimization. J Mech Design ASME 121:557–564

  22. Yang RJ, Gu L (2004) Experience with approximate reliability-based optimization methods. Struct Multidisc Optim 26:152–159

  23. Yang RJ, Chuang C, Gu L, Li G (2005) Experience with approximate reliability-based optimization method II: an exhaust system problem. Struct Multidisc Optim 29:488–497

  24. Youn BD, Choi KK, Park YH (2003) Hybrid analysis method for reliability-based design optimization. J Mech Design 125:221–232

  25. Youn BD, Choi KK, Du L (2005a) Adaptive probability analysis using an enriched hybrid mean value method. Struct Multidisc Optim 29:134–148

  26. Youn BD, Choi KK, Du L (2005b) Enriched performance measure approach for reliability-based design optimization. AIAA J 43(4):874–884

  27. Zhang WH, Fleury C (1997) A modification of convex approximation methods for structural optimization. Comput Struct 64(1–4):89–95

  28. Zillober C (1993) A globally convergent version of the method of moving asymptotes. Struct Optim 6:166–174

  29. Zou T, Mahadevan S (2006) A direct decoupling approach for efficient reliability-based design optimization. Struct Multidisc Optim 31:190–200

  30. Zuo KT, Chen LP, Zhang YQ, Yang J (2007) Study of key algorithms in topology optimization. Int J Adv Manuf Technol 32:787–796

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Correspondence to Tae Min Cho.

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Cho, T.M., Lee, B.C. Reliability-based design optimization using a family of methods of moving asymptotes. Struct Multidisc Optim 42, 255–268 (2010). https://doi.org/10.1007/s00158-010-0480-3

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Keywords

  • Reliability-based design optimization
  • Method of moving asymptotes
  • Most probable point
  • Sequential optimization and reliability assessment method