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Sequential optimization and moment-based method for efficient probabilistic design

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Abstract

To increase the range of applicability of decoupling strategies for reliability-based design optimization (RBDO), a sequential optimization and moment-based reliability assessment (SOMRA) is proposed. In this approach, a moment method based on the univariate dimension reduction method (UDRM) and probability density function (PDF) estimation is employed. Meanwhile, a corresponding mathematical model and a PDF-based method of calculating the shifting scalar are developed to decouple the reliability assessment from the optimization process. The shifting scalar is corrected according to the nonlinear degree of the limit state surface of the performance function before reconstructing the mathematical model for the next iteration of optimization. This approach uses statistical moments to check whether the constraints are active, and rather than assessing the reliability and calculating the shifting scalars for all constraints, only the active constraints are considered for the PDF estimation and shifting scalar calculation. Three numerical examples and an automobile crashworthiness lightweight design problem are presented to demonstrate the effectiveness of the proposed method.

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Data availability statement

The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Funding

This study was funded by the National Natural Science Foundation of China (No. U1664252) and the National Key Research and Development Program of China (No. 2016YFB0101700).

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, People’s Republic of China

    Zhenhu Wang, Hao Li, Ziming Chen, Luoxing Li & He Hong

  2. College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, People’s Republic of China

    Zhenhu Wang, Hao Li, Ziming Chen, Luoxing Li & He Hong

Authors
  1. Zhenhu Wang
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  2. Hao Li
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  3. Ziming Chen
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  4. Luoxing Li
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  5. He Hong
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Corresponding author

Correspondence to Luoxing Li.

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The authors declare that they have no conflict of interest.

Replication of results

The corresponding codes can be obtained in the supplementary material. Only the codes for numerical example 1.1 are given because differences exist only for the functions of constraints and objections.

Figures 1 and 3 are created with Microsoft Visio 2013. Figures 2 and 10 are created with AutoCAD 2014. Figures 4, 5, 6, 7, 8, 9, 11, and 13 are created with Origin9.0. Figure 12 is created with HyperView14.0.

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Responsible Editor: Mehmet Polat Saka

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Cite this article

Wang, Z., Li, H., Chen, Z. et al. Sequential optimization and moment-based method for efficient probabilistic design. Struct Multidisc Optim 62, 387–404 (2020). https://doi.org/10.1007/s00158-020-02494-7

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  • DOI: https://doi.org/10.1007/s00158-020-02494-7

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