Expert's experience-informed hierarchical kriging method for aerodynamic data modeling

Data-driven models, such as kriging, have gained popularity in aerospace engineering due to their capability of predicting multidimensional, nonlinear aerodynamic characteristics of an aircraft. However, they are still suffering from the problem associated with poor extrapolation capability and physical interpretability, which in turn has great impacts on aerodynamic performance and flight safety. To address this problem, this article proposes to incorporate an empirical aerodynamic model obtained from expert's understanding of aerodynamics in the fitting process of a kriging model. First, empirical aerodynamic models based on expert's understanding and experience are derived. Second, the regression term of a kriging model is replaced by the expert's experience-informed model so that the global trend can be consistent with physical laws and provides extra knowledge in the subregion(s) without training data, especially for the extrapolation region(s). Finally, the expert's experience-informed hierarchical kriging (EEI-HK) model is built in a sequential way. The proposed method is validated with analytical test examples and demonstrated by aerodynamic data modeling of an AGARD-B missile and an FDL-5A hypersonic flight vehicle. Results show that, compared with ordinary and universal kriging models, the proposed EEI-HK model can dramatically improve the prediction accuracy in the extrapolation domain and slightly enhance the interpolation accuracy, with assistance from physical information provided by an empirical model. In consequence, it can be a promising approach for aerodynamic data extrapolation and saving the cost of establishing an aerodynamic database.