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Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique

机译：非概率凸模型的相关性分析及相应的结构可靠度技术

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摘要

Compared with the probability approach, the non-probabilistic convex model only requires a small amount of samples to obtain the variation bounds of the imprecise parameters, and whereby makes the reliability analysis very convenient and economical. In this paper, we attempt to propose and create a correlation analysis technique mathematically for the non-probabilistic convex model, and based on it develop an effective method to construct the multidimensional ellipsoids on the uncertainty. A marginal convex model is defined to describe the variation range of each uncertain parameter, and a covariance is defined to represent the correlation degree of two uncertain parameters. For a multidimensional problem, the covariance matrix and correlation matrix can be created through all marginal convex models and covariances, based on which the required ellipsoid on the uncertainty can be conveniently achieved. By combining the correlation analysis technique and the reliability index approach, a non-probabilistic reliability analysis method is also developed for uncertain structures. Six numerical examples are presented to demonstrate the effectiveness of the present method.
机译：与概率方法相比，非概率凸模型只需要少量的样本就可以得到不精确参数的变化范围，从而使可靠性分析非常方便和经济。在本文中，我们尝试为非概率凸模型在数学上提出并创建一种相关分析技术，并在此基础上开发了一种在不确定性上构造多维椭球的有效方法。定义了一个边际凸模型来描述每个不确定参数的变化范围，并定义了一个协方差来表示两个不确定参数的相关程度。对于多维问题，可以通过所有边际凸模型和协方差创建协方差矩阵和相关矩阵，在此基础上可以方便地实现不确定性所需的椭球。通过将相关分析技术和可靠性指标方法相结合，还针对不确定结构开发了一种非概率可靠性分析方法。给出了六个数值示例，以证明本方法的有效性。

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  • 来源
    《Computer Methods in Applied Mechanics and Engineering》 |2011年第36期|p.2528-2546|共19页
  • 作者

    C. Jiang; X. Han; G.Y. Lu; J. Liu; Z. Zhang; Y.C. Bai;

  • 作者单位

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha City 410082, PR China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha City 410082, PR China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha City 410082, PR China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha City 410082, PR China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha City 410082, PR China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha City 410082, PR 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

    Convex model; Correlation analysis; Reliability analysis; Non-probabilistic model; Uncertain structures;

    机译：凸模型;相关分析;可靠性分析;非概率模型;不确定的结构;

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