Adaptive multi-fidelity sampling for CFD-based optimisation via radial basis function metamodels

The paper presents a study on four adaptive sampling methods of a multi-fidelity (MF) metamodel, based on stochastic radial basis functions (RBF), for global design optimisation based on expensive CFD computer simulations and adaptive grid refinement. The MF metamodel is built as the sum of a low-fidelity-trained metamodel and an error metamodel, based on the difference between high- and low-fidelity simulations. The MF metamodel is adaptively refined using dynamic sampling criteria, based on the prediction uncertainty in combination with the objective optimum and the computational cost of high- and low-fidelity evaluations. The adaptive sampling methods are demonstrated by four analytical benchmark and two design optimisation problems, pertaining to the resistance reduction of a NACA hydrofoil and a destroyer-type vessel. The performance of the adaptive sampling methods is assessed via objective function convergence.