A sequential multi-fidelity surrogate model-assisted contour prediction method for engineering problems with expensive simulations

The problem of locating a contour widely exists in the engineering product design, such as the constrained optimization problem, reliability analysis, and so on. The surrogate model-assisted contour prediction methods have gained more attention lately because they can alleviate the computational burden significantly compared with the traditional simulation-based approaches. Representatively, the method built on the expected improvement (EI) infill criterion can allocate a contour from expensive simulations by refining the Kriging model with high-fidelity (HF) samples sequentially. Recently, the multi-fidelity (MF) Kriging model has gained remarkable attention because it integrates the accurate but costly HF model and cheap but biased low-fidelity (LF) model to provide an accurate prediction of the original black-box system. To facilitate the usage of the MF Kriging model in the contour prediction, a novel sequential multi-fidelity surrogate model-assisted contour prediction method is developed in this work. First, an extended expected improvement (EEI) infill criterion is developed to overcome the shortcoming of the original EI criterion on determining the locations and fidelity level of new samples. The developed EEI criterion can quantify the improvement of a sample from different fidelities over the contour of interest by considering the relative correlation between different fidelities. Second, considering the significant effect of the high-to-low simulation cost ratio on the MF Kriging model, the proposed approach selects an HF sample or several LF samples with equivalent computational resources to refine the MF Kriging model in each cycle according to their total improvements to the contour of interest. To this end, the EEI criterion is further revised combining a parallel strategy to generate the LF samples. The performance of the proposed approach is tested on three numerical examples with different complexities and an engineering case. The results show that the proposed approach has better efficiency, prediction accuracy, and robust performance compared with several state-of-the-art methods.