In modern engineering practice, there is a steady increase in the need for multi-dimensional global approximations of complex black-box functions involved in today's engineering design problems. Metamodels have been proved to be effective alternatives for analyzing and predicting highly complex original models at a lower computational cost. The Kriging model is valued for its ability to predict the uncertainty of unknown points, which makes it widely used in the active learning methods for global approximation. However, these methods do not extend well to other metamodeling methods. This paper proposes an anisotropic kernel density estimation-based global fit (AKDGF) criterion for the active learning of metamodel. The AKDGF consists of two terms: global exploration dependent on the anisotropic kernel density (AKD) estimation and local development for larger nonlinear regions, which can be combined with various metamodeling methods. The initial sample set should be uniformly distributed in the design space as evenly as possible. Therefore, the uniform design approach is utilized to select the initial sample set for building the metamodel, and the AKDGF selects samples with high expected improvements to the metamodel to update the DOE sequentially. Five numerical examples and three engineering examples are presented to illustrate the proposed method and prove its good performance.

中文翻译：

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一种基于各向异性核密度估计的新型主动学习方法，用于支持工程设计的全局元建模


在现代工程实践中，当今工程设计问题中涉及的复杂黑盒函数的多维全局近似需求稳步增长。元模型已被证明是以较低的计算成本分析和预测高度复杂的原始模型的有效替代方案。Kriging 模型因其预测未知点的不确定性的能力而受到重视，这使其广泛用于全局近似的主动学习方法。然而，这些方法并不能很好地扩展到其他元建模方法。本文提出了一种基于各向异性核密度估计的全局拟合 （AKDGF） 准则，用于元模型的主动学习。AKDGF 由两个术语组成：依赖于各向异性核密度 （AKD） 估计的全局勘探和较大非线性区域的局部发展，可以与各种元建模方法相结合。初始样本集应尽可能均匀地分布在设计空间中。因此，采用统一设计方法来选择用于构建元模型的初始样本集，而 AKDGF 选择对元模型具有高预期改进的样本来依次更新 DOE。文中给出了 5 个数值算例和 3 个工程算例，对所提方法进行了说明并证明了其良好的性能。