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

翻译：本文提出了一种针对任意精度耦合流体-结构-飞行动力学系统的非线性模型降阶（NMOR）系统化方法。该技术采用非线性残差在平衡态附近的泰勒级数展开，保留至三阶项，并将高维系统投影到耦合系统雅可比矩阵特征向量构成的小型基上。左右特征向量的双正交性确保了投影的最优性，而高阶算子则通过无矩阵有限差分近似进行计算。该方法在三个复杂度递增的测试案例中得到验证：具有非线性刚度的三自由度翼型（状态从14维降至4维）、HALE飞机构型（状态从2,016维降至9维）以及大柔性飞翼（状态从1,616维降至9维）。降阶模型实现了高达600倍的计算加速，同时精确捕捉了非线性动力学行为，包括超过翼展10%的大尺度机翼变形。研究表明二阶泰勒展开足以描述三次结构非线性，从而无需三阶项。该框架独立于全阶模型表述形式，适用于更高精度的气动模型。