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<p>The first-order reliability method presents a linear approximation of the limit state function based on Taylor expansion. In the high degrees of nonlinearity, this approximation may be inaccurate or lead to instability in the computation of the reliability index. The second-order reliability method improves the accuracy by approximating a quadratic polynomial but at the expense of computational complexity. This paper introduces a novel numerical approach to estimate the reliability index by approximating the limit state function with a quartic polynomial. To reduce the complexity, specific coefficients are defined as alternatives to the Hessian matrix in the Taylor expansion. The proposed method enhances the accuracy of the first-order reliability method while maintaining low complexity. In addition, to efficiently mitigate the potential chaotic behavior of estimation, a chaos control criterion is applied. To investigate the accuracy and efficiency of the proposed method, various mathematical and structural examples are employed.</p>

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A Novel Structural Reliability Method Based on Quartic Polynomial Approximation of Limit State Function and Chaos Control Concept

  • 期刊论文

  • 发表日期：

    2025年11月4日

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  • Mohammad Amin Roudak,
  • Melika Farahani,
  • Sepideh Badiezadeh,
  • Mobina Amiri Beirami,
  • Sheida Kiashemshaki

摘要

The first-order reliability method presents a linear approximation of the limit state function based on Taylor expansion. In the high degrees of nonlinearity, this approximation may be inaccurate or lead to instability in the computation of the reliability index. The second-order reliability method improves the accuracy by approximating a quadratic polynomial but at the expense of computational complexity. This paper introduces a novel numerical approach to estimate the reliability index by approximating the limit state function with a quartic polynomial. To reduce the complexity, specific coefficients are defined as alternatives to the Hessian matrix in the Taylor expansion. The proposed method enhances the accuracy of the first-order reliability method while maintaining low complexity. In addition, to efficiently mitigate the potential chaotic behavior of estimation, a chaos control criterion is applied. To investigate the accuracy and efficiency of the proposed method, various mathematical and structural examples are employed.