Hierarchical Clustering Weighted Gaussian Process Regression Low-Fidelity Model and Application in Airfoil Drag Coefficients Prediction

Multi-fidelity modeling is a common approach for predicting the drag coefficient of airfoil, offering high accuracy and low computational cost. Low-fidelity data are acquired by simplifying high-fidelity models. However, existing multi-fidelity modeling techniques fail to consider the relative importance of different low-fidelity samples and treat them uniformly, which reduces the accuracy of multi-fidelity models. To effectively utilize different low-fidelity samples, this paper proposes a hierarchical clustering weighted Gaussian process regression (HCWGPR) low-fidelity model and applies it to the multi-fidelity modeling of the airfoil drag coefficient. First, principal component analysis is used to extract the key information of low-fidelity samples. Then, empirical mode decomposition is employed to decompose the key information into high-frequency energy fluctuations and low-frequency feature vectors. Next, a hierarchical clustering weight calculation algorithm based on high-frequency energy differences and low-frequency feature similarity is proposed to assign weights to low-fidelity samples. Finally, a weighted Gaussian process regression framework is used to construct the HCWGPR. A Gaussian process regression is also adopted as a discrepancy model. The effectiveness of the proposed method is verified by 9 sets of analytical test cases and the drag coefficient prediction of 6 airfoils.