Transferable scaling function learning method for knowledge embedded aerodynamic database construction

Accurate and complete aerodynamic data is crucial for aircraft performance evaluation; however, constructing high-dimensional, nonlinear aerodynamic databases is costly. To achieve construction of a full-state nonlinear aerodynamic database across different shapes, this paper proposes a transferable scaling function learning (T-SFL) method. The T-SFL method first mines composite function expressions of aerodynamic coefficients from aerodynamic datasets of multiple source domain aircraft by combining symbolic regression and per-shape parameter optimization strategies. The inner function is a scaling function with shape generalization capabilities, and the outer function is an explicit expression of aerodynamic performance with respect to the scaling function. In the database modeling of new-shape aircraft in the target domain, sparse reconstruction of the database is achieved by fine-tuning the parameters of the scaling function through aerodynamic samples. For the high-speed aircraft cases, scaling functions for axial force, normal force, and pitch moment coefficients of HB-2 and sharp cone are extracted through pre-training, and the aerodynamic model is fine-tuned using sparse aerodynamic samples of different configurations (HBS, double ellipsoid, HyTRV waverider). Each aircraft shape only requires 16 state samples to construct a full-state aerodynamic database (with error <4%), and aerodynamic extrapolation can be achieved. For transonic airfoil cases, T-SFL uses data from NACA0012 and NLR7301 to pre-train a scaling function architecture. For RAE2822, the force coefficient model can be fine-tuned and reconstructed based on samples under three typical Mach number conditions (with error <2.5%), verifying the shape generalization ability and state extrapolation ability of the T-SFL method.