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

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.