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HLRF-BFGS-Based Algorithm for Inverse Reliability Analysis

机译：基于HLRF-BFGS的逆可靠性分析算法

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摘要

This study proposes an algorithm to solve inverse reliability problems with a single unknown parameter. The proposed algorithm is based on an existing algorithm, the inverse first-order reliability method (inverse-FORM), which uses the Hasofer Lind Rackwitz Fiessler (HLRF) algorithm. The initial algorithm analyzed in this study was developed by modifying the HLRF algorithmin inverse-FORM using the Broyden-Fletcher-Goldarb-Shanno (BFGS) update formula completely. Based on numerical experiments, this modification was found to be more efficient than inverse-FORM when applied to most of the limit state functions considered in this study, as it requires comparatively a smaller number of iterations to arrive at the solution. However, to achieve this higher computational efficiency, this modified algorithm sometimes compromised the accuracy of the final solution. To overcome this drawback, a hybrid method by using both the algorithms, original HLRF algorithm and the modified algorithm with BFGS update formula, is proposed. This hybrid algorithm achieves better computational efficiency, compared to inverse-FORM, without compromising the accuracy of the final solution. Comparative numerical examples are provided to demonstrate the improved performance of this hybrid algorithm over that of inverse-FORM in terms of accuracy and efficiency.
机译：这项研究提出了一种算法来解决具有单个未知参数的逆可靠性问题。所提出的算法基于现有算法逆一阶可靠性方法（inverse-FORM），该方法使用了Hasofer Lind Rackwitz Fiessler（HLRF）算法。通过使用Broyden-Fletcher-Goldarb-Shanno（BFGS）更新公式完全修改反形式的HLRF算法，开发出了本研究中分析的初始算法。根据数值实验，发现将这种修改应用于本研究中考虑的大多数极限状态函数时，其效率要优于逆格式，因为它需要相对较少的迭代次数即可得出解。但是，为了获得更高的计算效率，这种修改后的算法有时会损害最终解决方案的准确性。为了克服这个缺点，提出了一种同时使用原始HLRF算法和带BFGS更新公式的改进算法的混合方法。与逆格式相比，此混合算法可实现更好的计算效率，而不会影响最终解决方案的准确性。提供了比较数值示例，以证明该混合算法在准确性和效率方面优于逆格式。

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  • 来源
    《Mathematical Problems in Engineering》 |2017年第7期|4317670.1-4317670.15|共15页
  • 作者

    Ramesh Rakul Bharatwaj; Mirza Olivia; Kang Won-Hee;

  • 作者单位

    Univ Western Sydney, Sch Comp Engn & Math, Penrith, NSW 2747, Australia;

    Univ Western Sydney, Sch Comp Engn & Math, Penrith, NSW 2747, Australia;

    Univ Western Sydney, Sch Comp Engn & Math, Penrith, NSW 2747, Australia;

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