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Two basic problems in reliability-based structural optimization

Author

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  • Norbert Kuschel
  • Rüdiger Rackwitz

Abstract

Optimization of structures with respect to performance, weight or cost is a well-known application of mathematical optimization theory. However optimization of structures with respect to weight or cost under probabilistic reliability constraints or optimization with respect to reliability under cost/weight constraints has been subject of only very few studies. The difficulty in using probabilistic constraints or reliability targets lies in the fact that modern reliability methods themselves are formulated as a problem of optimization. In this paper two special formulations based on the so-called first-order reliability method (FORM) are presented. It is demonstrated that both problems can be solved by a one-level optimization problem, at least for problems in which structural failure is characterized by a single failure criterion. Three examples demonstrate the algorithm indicating that the proposed formulations are comparable in numerical effort with an approach based on semi-infinite programming but are definitely superior to a two-level formulation. Copyright Physica-Verlag 1997

Suggested Citation

  • Norbert Kuschel & Rüdiger Rackwitz, 1997. "Two basic problems in reliability-based structural optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(3), pages 309-333, October.
    • Handle: RePEc:spr:mathme:v:46:y:1997:i:3:p:309-333
    DOI: 10.1007/BF01194859
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    Citations

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    Cited by:

    1. Li, Junxiang & Chen, Jianqiao, 2019. "Solving time-variant reliability-based design optimization by PSO-t-IRS: A methodology incorporating a particle swarm optimization algorithm and an enhanced instantaneous response surface," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    2. Zhang, Xiaobo & Lu, Zhenzhou & Cheng, Kai, 2021. "Reliability index function approximation based on adaptive double-loop Kriging for reliability-based design optimization," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    3. Ahmed, Hussam & Chateauneuf, Alaa, 2014. "Optimal number of tests to achieve and validate product reliability," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 242-250.
    4. Rocchetta, Roberto & Crespo, Luis G. & Kenny, Sean P., 2020. "A scenario optimization approach to reliability-based design," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
    5. Jensen, H.A. & Muñoz, A. & Papadimitriou, C. & Millas, E., 2016. "Model-reduction techniques for reliability-based design problems of complex structural systems," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 204-217.
    6. Benjamin Martin & Marco Correia & Jorge Cruz, 2017. "A certified Branch & Bound approach for reliability-based optimization problems," Journal of Global Optimization, Springer, vol. 69(2), pages 461-484, October.
    7. Zhang, Zheng & Wang, Pan & Hu, Huanhuan & Li, Lei & Li, Haihe & Yue, Zhufeng, 2022. "Efficient reliability-based design optimization for hydraulic pipeline with adaptive sampling region," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    8. Rocchetta, Roberto & Crespo, Luis G., 2021. "A scenario optimization approach to reliability-based and risk-based design: Soft-constrained modulation of failure probability bounds," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    9. Eldred, M.S. & Swiler, L.P. & Tang, G., 2011. "Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1092-1113.
    10. Okoro, Aghatise & Khan, Faisal & Ahmed, Salim, 2023. "Dependency effect on the reliability-based design optimization of complex offshore structure," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    11. Yuan, Xiukai & Lu, Zhenzhou, 2014. "Efficient approach for reliability-based optimization based on weighted importance sampling approach," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 107-114.
    12. Karadeniz, Halil & ToÄŸan, Vedat & Vrouwenvelder, Ton, 2009. "An integrated reliability-based design optimization of offshore towers," Reliability Engineering and System Safety, Elsevier, vol. 94(10), pages 1510-1516.
    13. Jiang, Zhiyuan & Huang, Xianzhen & Wang, Bingxiang & Liao, Xin & Liu, Huizhen & Ding, Pengfei, 2024. "Time-dependent reliability-based design optimization of main shaft bearings in wind turbines involving mixed-integer variables," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    14. Chaudhuri, Anirban & Kramer, Boris & Willcox, Karen E., 2020. "Information Reuse for Importance Sampling in Reliability-Based Design Optimization," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    15. ToÄŸan, Vedat & Karadeniz, Halil & DaloÄŸlu, AyÅŸe T., 2010. "An integrated framework including distinct algorithms for optimization of offshore towers under uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 847-858.

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