Adaptive Sequential Infill Sampling Method for Experimental Optimization with Multi-Fidelity Hamilton Kriging Model

Experimental optimization with surrogate models has received much attention for its efficiency recently in predicting the responses of the experimental optimum. However, with the development of multi-fidelity experiments with surrogate models such as Kriging, the traditional expected improvement (EI) in efficient global optimization (EGO) has suffered from limitations due to low efficiency. Only high-fidelity samples to be used in optimizing Kriging surrogate models are infilled, misleading the sequential sampling method in low-fidelity data sets. This recent theory based on multi-fidelity sequential infill sampling methods has gained much attention for balancing the selection of high- or low-fidelity data sets, but ignores the efficiency of sampling in experiments. This article proposes an Adaptive Sequential Infill Sampling (ASIS) method based on Bayesian inference for a multi-fidelity Hamilton Kriging model in the use of experimental optimization, aiming to address the efficiency of sequential sampling. The proposed method is demonstrated by two numerical simulations and one practical aero-engineering problem. The results verify the efficiency of the proposed method over other popular EGO methods in surrogate models, and ASIS can be useful for any other reliability engineering problems due to its efficiency.