A novel active learning method based on the anisotropic kernel density estimation for global metamodeling in support of engineering design

Abstract

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.