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

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  • 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
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    References listed on IDEAS

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    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.
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