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Structural global reliability assessment considering nonlinear correlation effects by enhanced high-order moment method

考虑非线性相关性影响的结构整体可靠度评估——增**型高阶矩 方法

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Abstract

The global reliability analysis of complex engineering structures considering the correlations between basic random variables remains a challenge, especially for nonlinear correlation problems. In this work, to take into account the influence of nonlinear correlation between random variables, an enhanced high-order moment method is proposed for structural global reliability analysis. Firstly, the traditional Nataf transformation is reviewed, and the generalized Nataf transformation is presented by introducing the Copula theory. Secondly, the corresponding performance functions of global reliability problems are described uniformly by the state variable description method, and the GL2-discrepancy point set is developed for the high-order moments estimation and sensitivity analysis of the state variable. Thirdly, the global reliability of the structures is accurately determined by using the improved maximum entropy method (IMEM). Finally, two examples, including one static and one dynamic, are investigated to demonstrate the accuracy and efficiency of the proposed method and the influence of nonlinear correlation between random variables on the global reliability of the structures, in which the results obtained from the proposed method are compared with Monte Carlo simulation (MCS) method. The results of the examples show the nonlinear correlation between random variables has a significant impact on the global reliability of structures, and the proposed method has fairly high accuracy and efficiency for structural high-order moments estimation and global reliability analysis.

摘要

考虑随机变量间相关性的复杂工程结构整体可靠性分析仍然是一个挑战, 特别是对于非线性相关问题. 该文考虑到随机变量之 间非线性相关的影响, 提出了一种用于结构整体可靠性分析的增**型高阶矩方法. 该文首先回顾了传统的Nataf变换, 进而通过引入 Copula理论提出了广义Nataf变换; 其次, 采用状态变量描述法统一描述整体可靠性问题对应的功能函数, 并发展了基于GL2-偏差点集 的状态变量高阶矩估计和灵敏度分析方法; 再次, 通过改进的最大熵法准确估计了结构整体可靠度; 最后, 通过两个算例验证了所提方 法的准确性和有效性以及考虑随机变量间的非线性相关性对结构整体可靠度影响的必要性. 算例结果与蒙特卡洛模拟方法比较表明, 随机变量间的非线性相关性对结构的整体可靠度有显著影响, 所提方法对结构高阶矩估计和全局可靠度分析具有较高的精度和效率.

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Acknowledgements

This work was supported by the National Key Research and Development Plan of China “Basic Theory and Methods for Resilience Assessment and Risk Control of Transportation Infrastructures” (Grant No. 2021YFB2600500), Natural Science Foundation of Chongqing CSTC (Grant No. 2022NSCQ-MSX4037), and Advanced Talents Incubation Program of the Hebei University (Grant No. 521000981082).

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Authors and Affiliations

  1. College of Civil Engineering and Architecture, Hebei University, Baoding, 071002, China

    Pengyan Song  (宋鹏彦)

  2. School of Transportation Science and Engineering, Harbin Institute of Technology, Harbin, 150040, China

    Tao Wang  (王涛)

  3. Chongqing Research Institute of Harbin Institute of Technology, Harbin Institute of Technology, Chongqing, 401151, China

    Tao Wang  (王涛) & Dagang Lu  (吕大刚)

  4. Key Lab of Structure Dynamic Behavior and Control of China Ministry of Education, Harbin Institute of Technology, Harbin, 150090, China

    Dagang Lu  (吕大刚)

Authors
  1. Pengyan Song  (宋鹏彦)
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  2. Tao Wang  (王涛)
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  3. Dagang Lu  (吕大刚)
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Contributions

Pengyan Song contributed to the investigation, data curation, visualization, software and original draft; Tao Wang contributed to the supervision, methodology, conceptualization, software and reviewing and editing; Dagang Lu contributed to the supervision, resources and funding acquisition.

Corresponding authors

Correspondence to Tao Wang  (王涛) or Dagang Lu  (吕大刚).

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Song, P., Wang, T. & Lu, D. Structural global reliability assessment considering nonlinear correlation effects by enhanced high-order moment method. Acta Mech. Sin. 39, 722356 (2023). https://doi.org/10.1007/s10409-022-22356-x

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