A hyperspherical area integral method based on a quasi-Newton approximation for reliability analysis

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering Pub Date : 2024-11-12 DOI:10.1016/j.cma.2024.117533

Jixiang Zhang , Zhenzhong Chen , Ge Chen , Xiaoke Li , Pengcheng Zhao , Qianghua Pan

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引用次数: 0

Abstract

The First-Order Reliability Method (FORM) is renowned for its high computational efficiency, but its accuracy declines when addressing the nNar Limit-State Function (LSF). The Second-Order Reliability Method (SORM) offers greater accuracy; however, its approximation formula can sometimes introduce errors. Additionally, SORM requires extra calculations involving the Hessian matrix, which can reduce its efficiency. To balance efficiency and accuracy, a Hyperspherical Area Integral Method based on a Quasi-Newton Approximation (HAI-QNAM) for reliability analysis is proposed. This method initially employs a quasi-Newton method to determine the Most Probable Point (MPP) of failure, calculate the reliability index, and obtain the approximate Hessian matrix. Then, based on the Curved Surface Integral (CSI) method, the area of the approximate failure domain and the area of the hypersphere are obtained. Using the proportionality of their areas, the failure probability is then calculated. Finally, the proposed method's accuracy and efficiency are validated through examples.

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基于准牛顿近似的超球面面积积分法用于可靠性分析

一阶可靠性方法（FORM）以计算效率高而著称，但在处理 nNar 极限状态函数（LSF）时，其精度会下降。二阶可靠性方法（SORM）的精度更高，但其近似公式有时会引入误差。此外，SORM 还需要进行涉及 Hessian 矩阵的额外计算，这可能会降低其效率。为了在效率和精度之间取得平衡，本文提出了一种基于准牛顿近似的超球面面积积分法（HAI-QNAM），用于可靠性分析。该方法首先采用准牛顿法确定最可能失效点 (MPP)、计算可靠性指数并获得近似赫塞斯矩阵。然后，基于曲面积分法（CSI），得到近似故障域面积和超球面面积。然后利用它们的面积比例关系计算出故障概率。最后，通过实例验证了所提方法的准确性和高效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computer Methods in Applied Mechanics and Engineering 工程技术-工程：综合

CiteScore

12.70

自引率

15.30%

发文量

719

审稿时长

44 days

期刊介绍： Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.