Nonlinear Model Order Reduction for Coupled Aeroelastic-Flight Dynamic Systems

2026-03-16

AI Summary

This study addresses the computational challenge of efficiently simulating high-dimensional, nonlinear aeroelastic–flight dynamics coupled systems. The authors propose a general nonlinear model order reduction framework that constructs a second-order Taylor expansion of the residual around equilibrium points—sufficient to accurately represent cubic nonlinearities without requiring third-order terms—and employs a bi-orthogonal low-dimensional subspace spanned by the left and right eigenvectors of the Jacobian matrix to achieve an optimal projection. By integrating a matrix-free finite difference approximation, the method avoids dependence on the full-order model’s internal structure. Validated across three test cases of increasing complexity, the approach reduces system dimensionality from thousands to single digits, achieving speedups of up to 600× while accurately capturing strong nonlinear dynamic behaviors such as large deformations exceeding 10% of the wingspan.

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Abstract

A systematic approach to nonlinear model order reduction (NMOR) of coupled fluid-structureflight dynamics systems of arbitrary fidelity is presented. The technique employs a Taylor series expansion of the nonlinear residual around equilibrium states, retaining up to third-order terms, and projects the high-dimensional system onto a small basis of eigenvectors of the coupled-system Jacobian matrix. The biorthonormality of right and left eigenvectors ensures optimal projection, while higher-order operators are computed via matrix-free finite difference approximations. The methodology is validated on three test cases of increasing complexity: a three-degree-of-freedom aerofoil with nonlinear stiffness (14 states reduced to 4), a HALE aircraft configuration (2,016 states reduced to 9), and a very flexible flying-wing (1,616 states reduced to 9). The reduced-order models achieve computational speedups of up to 600 times while accurately capturing the nonlinear dynamics, including large wing deformations exceeding 10% of the wingspan. The second-order Taylor expansion is shown to be sufficient for describing cubic structural nonlinearities, eliminating the need for third-order terms. The framework is independent of the full-order model formulation and applicable to higher-fidelity aerodynamic model

Problem

• nonlinear model order reduction
• aeroelastic-flight dynamics
• coupled fluid-structure systems
• large deformation
• computational efficiency

Innovation

• Nonlinear Model Order Reduction
• Coupled Aeroelastic-Flight Dynamics
• Taylor Series Expansion
• Biorthonormal Projection
• Matrix-Free Finite Difference