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A self-adaptive finite-step length method based on the inverse tangent function for accurate and efficient structural reliability analysis.

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Title: A self-adaptive finite-step length method based on the inverse tangent function for accurate and efficient structural reliability analysis.
Authors: Xia, Yu1 (AUTHOR) xy@gxust.edu.cn, Hu, Yiying1 (AUTHOR), Kong, Wenzheng1 (AUTHOR), Yu, Yingye1 (AUTHOR)
Source: Engineering Optimization. May2026, Vol. 58 Issue 5, p1511-1547. 37p.
Subjects: Structural reliability, Tangent function, Mathematical optimization, Iterative methods (Mathematics), Engineering, Numerical analysis
Abstract: In first-order reliability estimation, the finite step length (FSL) method can bring improvements, but can only conditionally reduce step length and is restricted by its inability to achieve a self-adaptive step length. Thus, it often fails to balance efficiency, accuracy and robustness. This article proposes a self-adaptive finite-step length method based on the inverse tangent function ITF-FSL) to address the deficiencies of FSL. The proposed method elucidates the nonlinear relationship between the distance of iteration points and the ideal FSL step length. It introduces the inverse tangent function lTF to achieve self-adaptive step length, replacing the fixed one. The parameters involved are discussed. Using the adjustment approach, the proposed method converges stably and efficiently with comparable or superior accuracy. The performance of the method is demonstrated through 10 numerical and engineering examples. Lastly, the optimal parameters of the lTF model are suggested. [ABSTRACT FROM AUTHOR]
Copyright of Engineering Optimization is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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  Data: A self-adaptive finite-step length method based on the inverse tangent function for accurate and efficient structural reliability analysis.
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  Data: <searchLink fieldCode="AR" term="%22Xia%2C+Yu%22">Xia, Yu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> xy@gxust.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Hu%2C+Yiying%22">Hu, Yiying</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Kong%2C+Wenzheng%22">Kong, Wenzheng</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Yu%2C+Yingye%22">Yu, Yingye</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Engineering+Optimization%22">Engineering Optimization</searchLink>. May2026, Vol. 58 Issue 5, p1511-1547. 37p.
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  Data: <searchLink fieldCode="DE" term="%22Structural+reliability%22">Structural reliability</searchLink><br /><searchLink fieldCode="DE" term="%22Tangent+function%22">Tangent function</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Engineering%22">Engineering</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink>
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  Label: Abstract
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  Data: In first-order reliability estimation, the finite step length (FSL) method can bring improvements, but can only conditionally reduce step length and is restricted by its inability to achieve a self-adaptive step length. Thus, it often fails to balance efficiency, accuracy and robustness. This article proposes a self-adaptive finite-step length method based on the inverse tangent function ITF-FSL) to address the deficiencies of FSL. The proposed method elucidates the nonlinear relationship between the distance of iteration points and the ideal FSL step length. It introduces the inverse tangent function lTF to achieve self-adaptive step length, replacing the fixed one. The parameters involved are discussed. Using the adjustment approach, the proposed method converges stably and efficiently with comparable or superior accuracy. The performance of the method is demonstrated through 10 numerical and engineering examples. Lastly, the optimal parameters of the lTF model are suggested. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Engineering Optimization is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1080/0305215X.2025.2517713
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      – Code: eng
        Text: English
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        PageCount: 37
        StartPage: 1511
    Subjects:
      – SubjectFull: Structural reliability
        Type: general
      – SubjectFull: Tangent function
        Type: general
      – SubjectFull: Mathematical optimization
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
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      – SubjectFull: Engineering
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      – SubjectFull: Numerical analysis
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      – TitleFull: A self-adaptive finite-step length method based on the inverse tangent function for accurate and efficient structural reliability analysis.
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            NameFull: Xia, Yu
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            NameFull: Hu, Yiying
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            NameFull: Kong, Wenzheng
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            NameFull: Yu, Yingye
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            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
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            – TitleFull: Engineering Optimization
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