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Reliability based design optimization with approximate failure probability function in partitioned design space

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  • Liu, Wang-Sheng
  • Cheung, Sai Hung

Abstract

This paper presents an efficient method for reliability-based design optimization (RBDO), which is robust to complex systems involving computationally expensive numerical models and/or a large number of random variables. This novel method belongs to a type of decoupling approaches in which the failure probability function (FPF) is approximated in the partitioned design space. In the setting of augmented reliability formulation, for a specific design configuration, the failure probability of a system is proportional to the probability density value of design variables conditioned on the failure event, thus transforming FPF approximation into a problem of density estimation. In this paper, we partition the design space into several subspaces and then estimate the density of failure samples in each subspace by binning and constructing regression functions. Sufficient failure samples are efficiently generated in each subspace using Markov Chain Monte Carlo method, which guarantees the accuracy of FPF approximation over there and ultimately over the entire design space. Three illustrative examples involving structural systems subjected to static or dynamic loadings are discussed to demonstrate the efficiency and accuracy of the proposed method.

Suggested Citation

  • Liu, Wang-Sheng & Cheung, Sai Hung, 2017. "Reliability based design optimization with approximate failure probability function in partitioned design space," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 602-611.
    • Handle: RePEc:eee:reensy:v:167:y:2017:i:c:p:602-611
    DOI: 10.1016/j.ress.2017.07.007
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    References listed on IDEAS

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    1. Zhuang, Xiaotian & Pan, Rong & Du, Xiaoping, 2015. "Enhancing product robustness in reliability-based design optimization," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 145-153.
    2. Markus Gasser & Gerhart Schuëller, 1997. "Reliability-Based Optimization of structural systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(3), pages 287-307, October.
    3. 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.
    4. 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.
    5. Shi, Lei & Lin, Shih-Po, 2016. "A new RBDO method using adaptive response surface and first-order score function for crashworthiness design," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 125-133.
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    Cited by:

    1. Yang, Meide & Zhang, Dequan & Jiang, Chao & Han, Xu & Li, Qing, 2021. "A hybrid adaptive Kriging-based single loop approach for complex reliability-based design optimization problems," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    2. Millar, Robert & Li, Hui & Li, Jinglai, 2023. "Multicanonical sequential Monte Carlo sampler for uncertainty quantification," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    3. Jiang, Chen & Qiu, Haobo & Yang, Zan & Chen, Liming & Gao, Liang & Li, Peigen, 2019. "A general failure-pursuing sampling framework for surrogate-based reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 47-59.
    4. Kim, Taeyong & Song, Junho, 2018. "Generalized Reliability Importance Measure (GRIM) using Gaussian mixture," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 105-115.
    5. Rivier, M. & Congedo, P.M., 2022. "Surrogate-Assisted Bounding-Box approach applied to constrained multi-objective optimisation under uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 217(C).

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