Multi-fidelity uncertainty analysis in CFD using hierarchical Kriging

Multi-fidelity uncertainty analysis method is a potential technique to speed up the process of uncertainty quantification (UQ) when an expensive computational simulation is involved. In this paper, we investigate the capability of hierarchical Kriging (HK) method for multi-fidelity uncertainty analysis, especially for application in computational fluid dynamics (CFD). Besides the conventional HK, we also enhanced the HK method by utilizing polynomial chaos expansion (PCE) and the ensemble of Kriging and PCE as the low-fidelity surrogate model. We also extend the formulation of HK so that it could use polynomial scaling function to further enhance the approximation capability of HK. The MF framework was firstly demonstrated on the multi-fidelity Branin and Ishigami function. Computational study on two CFD test problems was performed and the result was compared with ordinary Kriging, PCE, and multi-fidelity PCE. In light of our investigation, we found that using the ensemble of PCE and Kriging as the low-fidelity surrogate model is a better and more robust way to deal with various problems in UQ instead of using just one type of surrogate model for HK. The HK framework is also more efficient than the multi-fidelity PCE which relies on a simple correction function. Results on common research model and RAE 2822 problems reveal the remarkable efficiency of HK for UQ in real-world CFD-based problems with multi-fidelity simulation. On the RAE 2822 problem, the use of first order polynomial scaling function is needed in order to make the HK more efficient than the single-fidelity surrogate.