Multi-fidelity Modeling via Regression-Based Hierarchical Kriging

Advances in computational technology have enabled engineers to obtain large amounts of data efficiently. However, generating datasets from a single source is still burdensome and inefficient, so there have been many studies on data fusion techniques using multiple sources of data: e.g., low-fidelity data from computational fluid dynamics simulations and high-fidelity data from wind tunnel experiments. The hierarchical Kriging surrogate model is one of these data fusion methods which is known to be simple, robust, and accurate. It is based on the Kriging surrogate model, which predicts quantities of interest using an accumulated database based on the interpolation method. However, serious problems arise when it is built based on the noisy datasets for the following reasons: 1) noise in the dataset induces ill-conditioned correlation matrix; and 2) errors at lower-fidelity levels due to the noise accumulate as the fidelity level increases, adversely affecting the accuracy of the final model. These issues can be mitigated by a method called regression-based Kriging, which incorporates the adaptive regression factor (nugget) to the correlation matrix. This paper extends the corresponding regression technique to the hierarchical Kriging surrogate model, which will be called regression-based hierarchical Kriging. Considering that data fusion methods synthesize data with different fidelity levels to build a surrogate model efficiently, the regression-based hierarchical Kriging model can consider the different degrees of noise at each fidelity level. Herein, this model is demonstrated with several numerical examples with artificial noise and is finally validated with real engineering problem. These examples show that the proposed method has better performance than interpolation-based hierarchical Kriging when trained with the noisy data.