The polynomial response surface model (RSM) is a standard model in aerodynamic coefficient modeling. Real-time collected aerodynamic data are strongly correlated. Estimating the parameters of RSM by conventional least-square regression methods will yield significant errors since the regression matrix is ill-posed. A polynomial RSM based on multivariate orthogonal functions proposed here can overcome such a shortcoming and improve RSM's accuracy by iterating real-time data on the R matrix of the QR decomposed regression matrix. Moreover, RSM is further simplified by introducing Predicted Squared Error (PSE) and the R² coefficient to eliminate negligible items so that the over-fitting of the model is avoided. Part of the aerodynamic data of an F-16 wind tunnel test is interpolated with the spline function to obtain complete experimental data. The real-time data acquisition process is simulated by inputting data one by one to verify the effectiveness and real-time performance of the experimental algorithm. The multivariate orthogonal function modeling method is used to establish six models of dimensionless aerodynamic coefficients of the target aircraft, and the real-time performance of the modeling process is analyzed. Results show that the polynomial RSM based on multivariate orthogonal functions has a good predictive capability for real-time data. Meanwhile, the time consumption of each step in the modeling process is milliseconds, indicating that the method can establish the real-time modeling of the nonlinear aerodynamic coefficients of target aircraft.

Aerodynamic analysis of aircraft design often requires a large amount of high-fidelity (HF) aerodynamic data to improve the performance of aircraft design. However, the acquisition cost is very high. In order to alleviate the contradiction between modeling cost and accuracy, this paper constructs a multi-fidelity aerodynamic data fusion model by associating data with different fidelity. Furthermore, an optimal correlation point selection method and a uniformly enhanced sequential sampling method are proposed to achieve the efficient initialization and fastest convergence of variable-fidelity models based on co-Kriging. As a validation, standard numerical examples are selected to carry out modeling study, and the accuracy of the method is checked by comparing the statistical variables. Finally, the framework is successfully applied in the transonic aerodynamic engineering case of the NACA0012 airfoil. The results show that compared with the traditional model, the proposed method can greatly improve the convergence accuracy and modeling efficiency of the variable-fidelity model with only a small number of high-fidelity samples, which effectively reduces the sampling cost. Compared to the high-fidelity single precision sequence modeling, the error can be reduced by more than a half.