Dual-sampling based co-kriging method for design optimization problems with multi-fidelity models

To improve the efficiency and quality of simulation-driven design optimization, metamodel-based design and optimization (MBDO) technologies have been widely employed. In this paper, a novel dual-sampling based Co-Kriging method, notated as DS-CoKriging, is proposed to effectively solve the expensive design optimization problems with multi-fidelity simulation models. In DS-CoKriging, expensive data from high-fidelity simulation models are integrated with the cheap ones from low-fidelity simulation models to create an accurate Co-Kriging metamodel with moderate cost, and the Co-Kriging metamodel is gradually updated by sequentially sampling based on a dual-sampling approach during the optimization. Different from expected improvement (EI) criterion oriented sampling approach, the proposed dual-sampling approach consists of two sub-sampling processes, i.e., trust region based sampling and mean square error (MSE) prediction based sampling, to balance the global exploration and local exploitation effectively. The procedure of DS-CoKriging and the algorithm of dual-sampling approach are first presented. Then a numerical benchmark problem is used to demonstrate the merits of the proposed method compared with EI criterion based Co-Kriging method. Finally, DS-CoKriging is applied in an all-electric propulsion geostationary Earth orbit (GEO) transfer design optimization problem. The results show that the total transfer time is successfully reduced by 12 days after optimization. Moreover, DS-CoKriging method significantly reduces the computational cost by 43.6% compared with that of simply optimizing the expensive high-fidelity simulation model, which illustrates the effectiveness and practicality of the proposed DS-CoKriging in solving real-world engineering design optimization problems.