A multi-fidelity surrogate modeling approach for incorporating multiple non-hierarchical low-fidelity data

Multi-fidelity (MF) surrogate models have been widely used in simulation-based design problems to reduce the computational cost by integrating the data with different fidelity levels. Most of the existing MF modeling methods are only applicable to the problems with hierarchical low-fidelity (LF) models, namely the fidelity levels of multiple LF models can be identified. However, the fidelity levels of the LF models that are obtained from different simplification methods often vary over the design space. To address this challenge, a non-hierarchical Co-Kriging modeling (NHLF-Co-Kriging) method that can flexibly handle multiple non-hierarchical LF models is developed in this work. In the proposed method, multiple LF models are scaled by different scale factors, and a discrepancy model is utilized to depict the differences between the HF model and the ensembled LF models. To make the discrepancy Gaussian process (GP) model easy to be fitted, an optimization problem whose objective is to minimize the second derivative of the prediction values of the discrepancy GP model is defined to obtain optimal scale factors of the LF models. The performance of the NHLF-Co-Kriging method is compared with the extended Co-Kriging model and linear regression MF surrogate model through several analytical examples and an engineering case. Results show that the proposed method selects more reasonable scale factors for the multiple LF models and provides more accurate MF surrogate models under a limited computational budget.