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Vine copula-based parametric sensitivity analysis of failure probability-based importance measure in the presence of multidimensional dependencies

机译：基于葡萄的基于概率的参数敏感性分析，在多维依赖性存在下基于失败概率的重要性措施

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摘要

In this paper, we propose derivative-oriented parametric sensitivity indices to investigate the influence of parameter uncertainty on a previously proposed failure probability-based importance measure in the presence of multidimensional dependencies. Herein, the vine copula function, a powerful mathematical tool for modeling variable dependencies, is utilized to establish the joint probability density function (PDF) for multidimensional dependencies. Based on the properties of the copula function, the developed parametric sensitivity indices are decomposed into independent and dependent parts. Using these parts, different types of contributions to the failure probability are identified. By computing the kernel function for each marginal PDF and the copula kernel function for each pair-copula PDF involved in the vine factorization, a general numerical algorithm is developed for estimating separated parametric sensitivity indices. Finally, the feasibility of the proposed indices and numerical solutions is verified through a numerical example and by solving two engineering problems.
机译：在本文中，我们提出了导向导向的参数敏感性指数，以研究参数不确定性对在存在多维依赖性存在下先前提出的基于故障概率的重要性措施的影响。这里，利用用于建模可变依赖性的强大的数学工具，为vine copula函数用于建立用于多维依赖性的联合概率密度函数（PDF）。基于Copula功能的属性，开发的参数敏感性指数被分解成独立和依赖的部件。使用这些部件，识别出对故障概率的不同类型的贡献。通过计算每个边缘PDF的内核函数和用于涉及藤分解中的每对谱的PDF的Copula内核功能，开发了一种通用数值算法，用于估计分离的参数灵敏度指数。最后，通过数值示例验证了所提出的指标和数值解的可行性，并通过解决两个工程问题来验证。

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  • 来源
    《Reliability Engineering & System Safety》 |2021年第11期|107898.1-107898.17|共17页
  • 作者

    Li Haihe; Wang Pan; Huang Xiaoyu; Zhang Zheng; Zhou Changcong; Yue Zhufeng;

  • 作者单位

    Northwestern Polytech Univ Sch Mech Civil Engn & Architecture Xian 710072 Shaanxi Peoples R China;

    Northwestern Polytech Univ Sch Mech Civil Engn & Architecture Xian 710072 Shaanxi Peoples R China;

    Northwestern Polytech Univ Sch Mech Civil Engn & Architecture Xian 710072 Shaanxi Peoples R China;

    Northwestern Polytech Univ Sch Mech Civil Engn & Architecture Xian 710072 Shaanxi Peoples R China;

    Northwestern Polytech Univ Sch Mech Civil Engn & Architecture Xian 710072 Shaanxi Peoples R China;

    Northwestern Polytech Univ Sch Mech Civil Engn & Architecture Xian 710072 Shaanxi Peoples R China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Sensitivity analysis; Importance measure; Vine copula; Multidimensional correlation; Decomposition;

    机译：敏感性分析;重要性措施;藤蔓copula;多维相关;分解;

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