Multi-fidelity expected improvement based on multi-level hierarchical kriging model for efficient aerodynamic design optimization

To reduce the computational burden of aerodynamic design optimization, a multi-fidelity expected improvement (MFEI) method is developed, based on the error analysis of a multi-level hierarchical kriging (MHK) model for accelerating optimization convergence. By maximizing the MFEI function, a new sample of arbitrary fidelity level is determined to ameliorate the accuracy of the MHK model, and convergence to the high-fidelity optimum is ensured. The proposed optimization method based on MFEI and MHK is demonstrated by two analytical function cases and verified by two aerodynamic design optimizations: drag minimizations of an RAE2822 aerofoil and an ONERA M6 wing in transonic flows. It is shown that the MFEI method tends to infill more gainful samples of lower fidelities during optimization, so fewer highest-fidelity samples are required. This confirms that the proposed method can obtain optimal results within a limited computational budget and is more efficient than the existing single-fidelity or two-fidelity methods.