IDEAS home Printed from https://ideas.repec.org/a/sae/risrel/v235y2021i2p209-229.html
   My bibliography  Save this article

An improved first order reliability method based on modified Armijo rule and interpolation-based backtracking scheme

Author

Listed:
  • Sheng-Tong Zhou
  • Di Wang
  • Qian Xiao
  • Jian-min Zhou
  • Hong-Guang Li
  • Wen-Bing Tu

Abstract

Hasofer-Lind and Rackwtiz-Fiessler (HLRF) method is an efficient iterative algorithm for locating the most probable failure point and calculating the first order reliability index in structural reliability analysis. However, this method may encounter numerical instability problems for high nonlinear limit state function (LSF). In this paper, an improved HLRF-based first order reliability method is developed based on a modified Armijo line search rule and an interpolation-based step size backtracking scheme to improve the robustness and efficiency of the original HLRF method. Compared with other improved HLRF-based methods, the proposed method can not only guarantee the global convergence but also adaptively estimate some sensitive algorithm parameters, such as initial step size, step-size reduction coefficient, using the current known iterative information. Ten selected examples with high nonlinear LSFs are used to compare the robustness and efficiency of the proposed method with the original HLRF method and the improved HLRF (iHLRF) method. Results indicate that the proposed method is not only more computationally efficient but also less sensitive to the remaining user-defined algorithm parameters than the iHLRF method.

Suggested Citation

  • Sheng-Tong Zhou & Di Wang & Qian Xiao & Jian-min Zhou & Hong-Guang Li & Wen-Bing Tu, 2021. "An improved first order reliability method based on modified Armijo rule and interpolation-based backtracking scheme," Journal of Risk and Reliability, , vol. 235(2), pages 209-229, April.
    • Handle: RePEc:sae:risrel:v:235:y:2021:i:2:p:209-229
    DOI: 10.1177/1748006X20959894
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/1748006X20959894
    Download Restriction: no
    File URL: https://libkey.io/10.1177/1748006X20959894?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Z. J. Shi & J. Shen, 2005. "New Inexact Line Search Method for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 127(2), pages 425-446, November.
    2. Keshtegar, Behrooz & Chakraborty, Subrata, 2018. "An efficient-robust structural reliability method by adaptive finite-step length based on Armijo line search," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 195-206.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Keshtegar, Behrooz & Kisi, Ozgur, 2018. "RM5Tree: Radial basis M5 model tree for accurate structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 49-61.
    3. Ping Hu & Xu-Qing Liu, 2013. "A Nonmonotone Line Search Slackness Technique for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 773-786, September.
    4. Vieira, Douglas Alexandre Gomes & Lisboa, Adriano Chaves, 2014. "Line search methods with guaranteed asymptotical convergence to an improving local optimum of multimodal functions," European Journal of Operational Research, Elsevier, vol. 235(1), pages 38-46.
    5. Shi, Zhenjun & Wang, Shengquan, 2011. "Nonmonotone adaptive trust region method," European Journal of Operational Research, Elsevier, vol. 208(1), pages 28-36, January.
    6. Keshtegar, Behrooz & Chakraborty, Souvik, 2018. "Dynamical accelerated performance measure approach for efficient reliability-based design optimization with highly nonlinear probabilistic constraints," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 69-83.
    7. Long, Jiancheng & Szeto, W.Y., 2019. "Congestion and environmental toll schemes for the morning commute with heterogeneous users and parallel routes," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 305-333.
    8. Zhiguang Zhang, 2010. "A New Method for Unconstrained Optimization Problem," Modern Applied Science, Canadian Center of Science and Education, vol. 4(10), pages 133-133, October.
    9. Antoine Soubeyran, 2022. "Variational rationality. Self regulation success as a succession of worthwhile moves that make sufficient progress," Working Papers hal-04041238, HAL.
    10. Abdollahi, Azam & Amini, Ali & Hariri-Ardebili, Mohammad Amin, 2022. "An uncertainty-aware dynamic shape optimization framework: Gravity dam design," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    11. Antoine Soubeyran, 2023. "Variational rationality. Self regulation success as a succession of worthwhile moves that make sufficient progress," AMSE Working Papers 2307, Aix-Marseille School of Economics, France.
    12. Zhang, Qiang & Liu, Jijun, 2024. "On fluorophore imaging by nonlinear diffusion model with dynamical iterative scheme," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 533-549.
    13. Jing, Zhao & Chen, Jianqiao & Li, Xu, 2019. "RBF-GA: An adaptive radial basis function metamodeling with genetic algorithm for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 42-57.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:risrel:v:235:y:2021:i:2:p:209-229. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.