Extended Co-Kriging interpolation method based on multi-fidelity data

The common issue of surrogate models is to make good use of sampling data. In theory, the higher the fidelity of sampling data provided, the more accurate the approximation model built. However, in practical engineering problems, high-fidelity data may be less available, and such data may also be computationally expensive. On the contrary, we often obtain low-fidelity data under certain simplifications. Although low-fidelity data is less accurate, such data still contains much information about the real system. So, combining both high and low multi-fidelity data in the construction of a surrogate model may lead to better representation of the physical phenomena. Co-Kriging is a method based on a two-level multi-fidelity data. In this work, a Co-Kriging method which expands the usual two-level to multi-level multi-fidelity is proposed to improve the approximation accuracy. In order to generate the different fidelity data, the POD model reduction is used with varying number of the basis vectors. Three numerical examples are tested to illustrate not only the feasibility and effectiveness of the proposed method but also the better accuracy when compared with Kriging and classical Co-Kriging.