Scaling Function Learning: A sparse aerodynamic data reconstruction method for generalizing aircraft shapes

TL;DR

This paper introduces the Scaling Function Learning (SFL) method, which uses symbolic regression to efficiently generalize aerodynamic data across aircraft shapes and flight conditions with minimal samples.

Contribution

The SFL method enables low-cost, accurate construction of aerodynamic databases by extracting scalable functions, improving data extrapolation and shape generalization in aerodynamics.

Findings

Achieves 1-5% relative error with only 3-4 samples

Successfully generalizes across different aircraft configurations

Demonstrates effective state extrapolation for variable Mach, angle, and Reynolds number

Abstract

Accurate and complete aerodynamic data sets are the basis for comprehensive and accurate evaluation of the overall performance of aircraft. However, the sampling cost of full-state aerodynamic data is extremely high, and there are often differences between wind tunnel conditions and actual flight conditions. Conventional scaling parameter extraction methods can solve the problem of aerodynamic state extrapolation, but hard to achieve data migration and shape generalization. In order to realize the low-cost construction of a full-state nonlinear aerodynamic database, this research proposes the Scaling Function Learning (SFL) method. In SFL method, symbolic regression is used to mine the composite function expression of aerodynamic force coefficient for a relatively complete aerodynamic data set of typical aircraft. The inner layer of the function represents a scaling function. The SFL method was validated on the HB-2 by extracting scaling parameters for axial force coefficients and generalizing the scaling function by releasing its constants. The effectiveness and accuracy of the scaling function are verified using different hypersonic aircraft configurations, such as HBS, double ellipsoid, sharp cone, and double cone missile. The results show that the extracted scaling function has the ability to generalize across states and configurations. With only 3-4 state samples, the aerodynamic database construction of variable Mach number, angle of attack and Reynolds number can be realized, which shows great state extrapolation ability with a relative error of about 1-5%. This research also lays a methodological foundation for parameter space dimensionality reduction and small sample modeling of other complex high-dimensional engineering problems.