Nonlinear Model Order Reduction for Coupled Aeroelastic-Flight Dynamic Systems

TL;DR

This paper introduces a systematic nonlinear model order reduction method for coupled aeroelastic-flight systems, achieving significant computational speedups while accurately capturing complex nonlinear dynamics.

Contribution

The proposed approach uses Taylor series expansion and eigenvector projection to reduce system size, validated on diverse aerospace test cases with high accuracy.

Findings

Achieves up to 600x speedup in simulations.

Reduces complex systems from thousands to fewer than ten states.

Second-order Taylor expansion suffices for cubic nonlinearities.

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