A novel multi-fidelity surrogate modeling framework integrated with sequential sampling criterion for non-hierarchical data

Multi-fidelity surrogate model (MFSM) methods have attracted significant attention recently in the field of engineering design by combining the information from high-cost high-fidelity (HF) data and low-cost low-fidelity (LF) data, which realizes the trade-off between computational expense and prediction accuracy. However, the widely used autoregressive framework assumes that the fidelity of multiple LF data can be clearly sorted (i.e., hierarchical LF data), which is inconsistent with many actual situation. Fusing the linear combination of multiple LF models with HF data is a widely used non-hierarchical fusion framework as its relatively computational simplicity. However, it may lead to the accuracy of MFSM decrease as the number of LF models increase. Thus, a novel MFSM framework is proposed to focus on non-hierarchical LF data. Specifically, the relationship between HF and LF is utilized to build multiple bi-fidelity surrogate models, and the weighted-sum of multiple bi-fidelity models is used as the final MFSM. In our work, hierarchical Kriging (HK) model is used as bi-fidelity model and three weight setting methods are provided. Moreover, a sequential sampling criterion adapted to the multi-fidelity model is proposed to further improve the accuracy. Seven numerical functions and an engineering case are used to demonstrate the performance of the proposed method by comparing with three other MFSMs (VWS-MFS, LR-MFS and NHLFCK). The results show that the proposed model under the new framework is superiority in both accuracy and robustness, and the corresponding sequential sampling criterion effectively improve the accuracy of the model.