A multi-fidelity surrogate modeling method based on variance-weighted sum for the fusion of multiple non-hierarchical low-fidelity data

Multi-fidelity (MF) surrogate models have been widely adopted in simulation-based engineering design problems to reduce the computational cost by fusing data with diverse fidelity levels. Most of the MF modeling methods only apply to the problems with hierarchical low-fidelity (LF) models. However, the LF models obtained from different simplification approaches often vary in fidelity levels throughout the design space, namely, the multiple LF models are non-hierarchical. To address this challenge, a MF surrogate modeling method based on variance-weighted sum (VWS-MFS) is developed to flexibly handle multiple non-hierarchical LF data in this work. Firstly, each set of the non-hierarchical LF data is allocated diverse weights according to uncertainties quantified by variances of constructed Kriging models, which enables all the LF data to be fused and contribute to the trend function reflecting the response trend of the true model. Secondly, for more precise scaling factor between HF and LF models and mean square error (MSE) estimation, an improved hierarchical kriging (IHK) model is introduced to construct the MF surrogate model enabling the LF model scaled by a varied scaling factor to capture the characteristics of the HF model. The performance of the proposed VWS-MFS method is compared to three MF surrogate models through several numerical examples and one engineering case. Results show that the proposed method provides more accurate MF surrogate models under the same computational cost. Additionally, the proposed method saved the computational cost by more than 59.61% with the same model accuracy compared to the Kriging model built with HF data for the engineering case.