A new cokriging method for variable-fidelity surrogate modeling of aerodynamic data

Cokriging is a statistical interpolation method for the enhanced prediction of a less intensively sampled primary variable of interest with assistance of intensively sampled auxiliary variables. In the geostatistics community it is referred to as two- or multi-variable kriging. In this paper, a new cokriging method is proposed and used for variable-fidelity surrogate modeling of aerodynamic data obtained with an expensive high-fidelity CFD code, assisted by data computed with cheaper lower-fidelity codes or by gradients computed with an adjoint version of the high-fidelity CFD code, or both. A self-contained derivation as well as the numerical implementation of this new cokriging method is presented and the comparison with the autoregressive model of Kennedy and O'Hagan is discussed. The developed cokriging method is validated against an analytical problem and applied to construct global approximation models of the aerodynamic coefficients as well as the drag polar of an RAE 2822 airfoil based on sampled CFD data. The numerical examples show that it is efficient, robust and practical for the surrogate modeling of aerodynamic data based on a set of CFD methods with varying degrees of fidelity and computational expense. It can potentially be applied in the efficient CFD-based aerodynamic analysis and design optimization of aircraft.