Parametric Nonlinear Volterra Series via Machine Learning: Transonic Aerodynamics

TL;DR

This paper presents a machine learning-based method to model unsteady transonic aerodynamics using Volterra series, capturing nonlinear effects and enabling efficient interpolation across parameter spaces for improved aerodynamic predictions.

Contribution

It introduces a novel approach combining Volterra series with machine learning to model nonlinear transonic aerodynamics and interpolate kernel coefficients across parameters.

Findings

Including second-order kernels improves accuracy for nonlinear responses.

Neural networks effectively interpolate kernel coefficients.

Method achieves sufficient accuracy for conceptual design applications.

Abstract

This study introduces an approach for modeling unsteady transonic aerodynamics within a parametric space, using Volterra series to capture aerodynamic responses and machine learning to enable interpolation. The first- and second-order Volterra kernels are derived from indicial aerodynamic responses obtained through computational fluid dynamics, with the second-order kernel calculated as a correction to the dominant linear response. Machine learning algorithms, specifically artificial neural network and Gaussian process regression, are used to interpolate kernel coefficients within a parameter space defined by Mach number and angle of attack. The methodology is applied to two and three dimensional test cases in the transonic regime. Results underscore the benefit of including the second-order kernel to address strong nonlinearity and demonstrate the effectiveness of neural networks. The approach achieves a level of accuracy that appears sufficient for use in conceptual design.