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A classification-pursuing adaptive approach for Gaussian process regression on unlabeled data

机译：一种分类追求未标记数据的高斯过程回归的自适应方法

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摘要

Some areas of mechanical and system engineering such as dynamic systems commonly exhibit highly fluctuating responses over given parametric domains. Therefore, classifying some quantities of interest over the parametric domain for designing new systems turns out to be a highly challenging task. In this context, an innovative adaptive sampling algorithm named Monte Carlo-intersite Voronoi (MiVor) is proposed for design applications based on the classification of one or more continuous quantities of interest useful for parametric studies. In contrast to reliability analysis problems, no probabilistic setting and information is needed. The proposed technique is able to efficiently detect two or more classes of highly imbalanced decision regions and to accurately describe the boundary between these regions in a robust manner. To the best of the authors knowledge it is the first adaptive scheme for classification-pursuing parametric studies that combines information from (potentially) multiple class label outputs and the accompanying continuous values for efficient sampling involving (possibly) multiple class outputs. The resulting surrogates utilize only a small number of observations which are obtained in an active manner. The capabilities of the presented algorithm to provide accurate classification are demonstrated on three dynamic applications with various dimensionality and under consideration of a combination of different first-passage failure scenarios. Comparisons with two regression-based adaptive schemes show that the proposed algorithm outperforms existing methods. For instance, in the case of a quarter-car problem, more than 99% of points are correctly classified using the proposed approach at convergence, whereas less than 80% of reference samples are correctly classified with standard approaches. Similar performances (> 95%) are also obtained with MiVor for a nonlinear oscillator of Duffing's type and a three-degrees-of-freedom mass-spring system with three and six-dimensional parametric spaces respectively.
机译：一些机械和系统工程领域，如动态系统通常表现出对给定参数域的高度波动响应。因此，对用于设计新系统的参数域来分类某些数量的兴趣，结果是一个非常具有挑战性的任务。在这种情况下，提出了一种名为Monte Carlo-Intersite Voronoi（MiVor）的创新自适应采样算法，用于基于对参数研究的一种或多种持续利息的分类来设计应用。与可靠性分析问题相比，不需要概率设置和信息。该提出的技术能够有效地检测两个或更多个高度不平衡的决策区域，并且以稳健的方式精确地描述这些区域之间的边界。据作者所知，它是分类追求参数研究的第一种自适应方案，其将信息与（可能）多个类标签输出和伴随的连续值组合在一起，以便有效采样涉及（可能）多个类输出。所得替代物仅利用以活性方式获得的少量观察结果。在具有各种维度的三种动态应用中，对提供准确分类提供了准确分类的算法的能力，并考虑了不同的第一段失败情景的组合。具有两种基于回归的自适应方案的比较表明，所提出的算法优于现有方法。例如，在四分之一车问题的情况下，使用拟议方法在收敛方面正确分类了99％的点，而小于80％的参考样品是用标准方法正确分类的。对于Duffing的类型的非线性振荡器和三维自由度分别具有三维和六维参数空间的非线性振荡器的弧度也可以获得类似的性能（> 95％）。

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  • 来源
    《Mechanical systems and signal processing》 |2022年第1期|107976.1-107976.21|共21页
  • 作者

    Jan N. Fuhg; Amelie Fau;

  • 作者单位

    Sibley School of Mechanical and Aerospace Engineering Cornell University 921 University Ave Ithaca NY 14853 United States Institute of continuum mechanics Leibniz Universitaet Hannover Appelstraβe 11 30167 Hannover Germany;

    Universite Paris-Saclay ENS Paris-Saclay CNRS LMT - Laboratoire de Mecanique et Technologic 91190 Gif-sur-Yvette France Institute of mechanics and computational mechanics Leibniz Universitaet Hannover Appelstraβe 9a 30167 Hannover Germany;

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  • 正文语种 eng
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  • 关键词

    Adaptive surrogate modeling; Classification; Dynamic systems;

    机译：自适应替代建模;分类;动态系统;

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