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A second order SAP algorithm for risk and reliability based design optimization

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  • Torii, A.J.
  • Lopez, R.H.
  • Miguel, L.F.F.

Abstract

This paper presents a decoupling approach for the efficient solution of Risk Optimization (RO) and Reliability Based Design Optimization (RBDO) problems. The proposed approach, SAP2nd, is a Sequential Approximate Programming (SAP) technique including second order terms obtained with the BFGS (Broyden-Fletcher-Goldfarb-Shanno) approximation for the Hessian. A first advantage of SAP2nd is that any reliability analysis method can be employed for the evaluation of the probabilities of failure and its sensitivities. Here, Polynomial Chaos Expansion (PCE) is employed for this purpose. Several benchmark problems are solved to study the efficiency, robustness and accuracy of SAP2nd. It is demonstrated that the inclusion of second order terms leads to: (i) a much more stable algorithm in comparison to a first order SAP algorithm, i.e. it was able to avoid convergence issues arising from cycling, and (ii) a more efficient algorithm since SAP2nd reduced the computational effort, in both RO and RBDO problems, when compared to the coupled PCE algorithm previously proposed by the authors. The use of PCE for the evaluation of the probabilities of failure and its sensitivities allowed SAP2nd to achieve much more accurate results when compared to FORM based approaches, requiring the same order of computational effort. Finally, SAP2nd using PCE for reliability and sensitivity analysis is well suited for RO and RBDO problems where the drawbacks of FORM based approaches prevail, especially cases with highly nonlinear limit state function and non Gaussian random variables.

Suggested Citation

  • Torii, A.J. & Lopez, R.H. & Miguel, L.F.F., 2019. "A second order SAP algorithm for risk and reliability based design optimization," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    • Handle: RePEc:eee:reensy:v:190:y:2019:i:c:22
    DOI: 10.1016/j.ress.2019.106499
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    References listed on IDEAS

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    1. Shan, Songqing & Wang, G. Gary, 2008. "Reliable design space and complete single-loop reliability-based design optimization," Reliability Engineering and System Safety, Elsevier, vol. 93(8), pages 1218-1230.
    2. 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.
    3. 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:

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    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. Van Huynh, Thu & Tangaramvong, Sawekchai & Do, Bach & Gao, Wei & Limkatanyu, Suchart, 2023. "Sequential most probable point update combining Gaussian process and comprehensive learning PSO for structural reliability-based design optimization," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    4. 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).
    5. 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).
    6. Carlon, André Gustavo & Kroetz, Henrique Machado & Torii, André Jacomel & Lopez, Rafael Holdorf & Miguel, Leandro Fleck Fadel, 2022. "Risk optimization using the Chernoff bound and stochastic gradient descent," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    7. Peng, Yongbo & Ma, Yangying & Huang, Tianchen & De Domenico, Dario, 2021. "Reliability-based design optimization of adaptive sliding base isolation system for improving seismic performance of structures," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    8. Shi, Yan & Lu, Zhenzhou & Huang, Hongzhong & Liu, Yu & Li, Yanfeng & Zio, Enrico & Zhou, Yicheng, 2022. "A new preventive maintenance strategy optimization model considering lifecycle safety," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    9. Jiang, Chen & Qiu, Haobo & Gao, Liang & Wang, Dapeng & Yang, Zan & Chen, Liming, 2020. "EEK-SYS: System reliability analysis through estimation error-guided adaptive Kriging approximation of multiple limit state surfaces," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    10. 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).
    11. Ling, Chunyan & Lu, Zhenzhou & Zhang, Xiaobo, 2020. "An efficient method based on AK-MCS for estimating failure probability function," Reliability Engineering and System Safety, Elsevier, vol. 201(C).

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