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Kriging-Based Reliability-Based Design Optimization Using Single Loop Approach

  • Hongbo ZhangEmail author
  • Younes Aoues
  • Hao Bai
  • Didier Lemosse
  • Eduardo Souza de Cursi
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)

Abstract

Reliability-Based Design Optimization (RBDO) is a powerful tool in engineering structural design, it tries to find a balance between cost and reliability for structural designs under uncertainty. Several RBDO formulations are developed to solve the RBDO problem, such as double loop methods, single loop methods, and decoupled methods. Despite, these new formulations of RBDO, they are unable to deal for engineering complex problems, due to the computational cost. The Kriging surrogate has been widely used to replace the time-consuming mechanical constraints. In this paper, a single loop RBDO approach (SLA) is coupled with the Kriging surrogate, the most probable points (MPP) of each loop are used as new sample points to update the Kriging model. The Kriging-SLA is running iteratively until it reaches the converge criteria. Compared with other sampling methods, this method can be started with very few training points and converges to the right minimum very efficiently. 2 benchmark examples are used to demonstrate this method.

Keywords

Reliability-based optimization Single loop approach Kriging surrogate Adaptive sampling 

References

  1. 1.
    Chen, Z., Qiu, H., Gao, L., Li, X., Li, P.: A local adaptive sampling method for reliability-based design optimization using kriging model. Struct. Multidiscip. Optim. 49(3), 401–416 (2014)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Cheng, G., Xu, L., Jiang, L.: A sequential approximate programming strategy for reliability-based structural optimization. Comput. struct. 84(21), 1353–1367 (2006)CrossRefGoogle Scholar
  3. 3.
    Cho, T.M., Lee, B.C.: Reliability-based design optimization using convex linearization and sequential optimization and reliability assessment method. Struct. Saf. 33(1), 42–50 (2011)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Du, X., Chen, W.: Sequential optimization and reliability assessment method for efficient probabilistic design. American Society of Mechanical Engineers (2002)Google Scholar
  5. 5.
    Dubourg, V., Sudret, B.: Meta-model-based importance sampling for reliability sensitivity analysis. Struct. Saf. 49, 27–36 (2014)CrossRefGoogle Scholar
  6. 6.
    Enevoldsen, I., Sørensen, J.D.: Reliability-based optimization in structural engineering. Struct. Saf. 15(3), 169–196 (1994)CrossRefGoogle Scholar
  7. 7.
    Forrester, A., Sobester, A., Keane, A.: Engineering Design via Surrogate Modelling: A Practical Guide. Wiley (2008)Google Scholar
  8. 8.
    Lee, I., Choi, K., Du, L., Gorsich, D.: Dimension reduction method for reliability-based robust design optimization. Comput. Struct. 86(13–14), 1550–1562 (2008)CrossRefGoogle Scholar
  9. 9.
    Lee, T.H., Jung, J.J.: A sampling technique enhancing accuracy and efficiency of metamodel-based RBDO: constraint boundary sampling. Comput. Struct. 86(13–14), 1463–1476 (2008)CrossRefGoogle Scholar
  10. 10.
    Liang, J., Mourelatos, Z.P., Tu, J.: A single-loop method for reliability-based design optimization. American Society of Mechanical Engineers (2004)Google Scholar
  11. 11.
    Lv, Z., Lu, Z., Wang, P.: A new learning function for kriging and its applications to solve reliability problems in engineering. Comput. Math. Appl. 70(5), 1182–1197 (2015)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Madsen, H., Hansen, P.F.: A comparison of some algorithms for reliability based structural optimization and sensitivity analysis, pp. 443–451. Springer (1992)Google Scholar
  13. 13.
    Rasmussen, C., Williams, C.: Gaussian processes for machine learning. MIT Press (2006)Google Scholar
  14. 14.
    Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and analysis of computer experiments. Statistical science, pp. 409–423 (1989)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Tu, J., Choi, K.K., Park, Y.H.: A new study on reliability-based design optimization. J. Mech. Des. 121(4), 557–564 (1999)CrossRefGoogle Scholar
  16. 16.
    Zhang, J., Xiao, M., Gao, L.: An active learning reliability method combining kriging constructed with exploration and exploitation of failure region and subset simulation. Reliab. Eng. Syst. Saf. (2019)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Hongbo Zhang
    • 1
    Email author
  • Younes Aoues
    • 1
  • Hao Bai
    • 1
  • Didier Lemosse
    • 1
  • Eduardo Souza de Cursi
    • 1
  1. 1.Normandie Univ, INSA Rouen Normandie, LMNRouenFrance

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