Comparative Study on Parameter Estimation Methods for Multi-fidelity Co-kriging Modeling

As a well-known multi-fidelity modeling technique, the co-kriging method combining the data from two or more models with different levels of fidelity to efficiently construct a metamodel has gained increasing attention to save the computational cost. Although the existing multi-fidelity co-kriging modeling approaches utilize the data from all models for response prediction, most of those methods only utilize the correlation of the data from two models with adjacent fidelities or from the same model in estimating the unknown hyper-parameters for model construction. Therefore, an enhanced co-kriging method utilizing the covariance of all observed data is developed in this paper to improve the prediction accuracy, in which the hyper-parameters are estimated altogether by maximizing a unified likelihood function. The results from the comparative studies show that the proposed co-kriging method is evidently more accurate than some existing popular approaches, demonstrating its effectiveness and relative merits.