Novel Approach for Selecting Low-Fidelity Scale Factor in Multifidelity Metamodeling

Abstract

Multifidelity (MF) metamodels have become a popular way to combine a small number of expensive high-fidelity (HF) sample points and many cheap low-fidelity (LF) sample points to make a trade-off between high accuracy and low computational expense. Additive scaling function–based approaches are commonly used for constructing MF metamodels. However, how to select an LF scale factor to improve the accuracy of the MF metamodel is still challenging. This paper proposes a novel approach for selecting an LF scale factor for additive scaling function–based MF metamodeling to improve the accuracy. In the proposed approach, kriging models are constructed for the LF model and scaling function. Because the accuracy of the scaling function metamodel has a significant effect on the accuracy of the MF metamodel, the proposed approach tries to make the scaling function easy to be approximated. A one-dimensional numerical example is adopted to demonstrate the advantages of the proposed approach, and then four multidimensional numerical examples and an engineering case related to aviation are used to illustrate its applicability.