Symbolic Regression-Based Modeling for Aerodynamic Ground-to-Flight Deviation Laws of Aerospace Vehicles

The correlation between aerodynamic data obtained from ground and flight tests is crucial in developing aerospace vehicles. This paper proposes methods for modelling this correlation that combine feature extraction and symbolic regression. The neighborhood component analysis (NCA) method is utilized to extract features from the high-dimensional state space and then symbolic regression (SR) is applied to find the concise optimal expression. First, a simulation example of the NASA Twin Otter aircraft is used to validate the NCA and the SR tool developed by the research team in modeling the aerodynamic coefficient deviation between ground and flight due to an unpredictable inflight icing failure. Then, the method and tool are applied to real flight tests of two types of aerospace vehicles with different configurations. The final optimized mathematical models show that the two vehicles’ pitching moment coefficient deviations are related to the angle of attack (AOA) only. The mathematical model built using NCA and the SR tool demonstrates higher fitting accuracy and better generalization performance for flight test data than other typical data-driven methods. The mathematical model delivers a multi-fold enhancement in fitting accuracy over data-driven methods for all fight cases. For UAV flight test data, the average root mean square error (RMSE) of the mathematical model demonstrates a maximum improvement of 37% in accuracy compared to three data-driven methods. For XRLV flight test data, the prediction accuracy of the mathematical model shows an enhancement exceeding 80% relative to Gaussian kernel SVM and Gaussian process data-driven models. The research verifies the feasibility and effectiveness of the data feature extraction combined with the symbolic regression method in mining the correlation law between ground and flight deviations of aerodynamic characteristics. This study provides valuable insight for modeling problems with finite data samples and explicit physical meanings.