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：针对任意保真度的耦合流固-飞行动力学系统，提出了一种系统性的非线性模型降阶方法。该技术采用泰勒级数展开非线性残差至三阶项，将高维系统投影到由耦合系统雅可比矩阵特征向量构成的小基上。左右特征向量的双正交性确保了最优投影，高阶算子则通过无矩阵有限差分近似计算。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（14个状态缩减至4个）、HALE飞行器构型（2016个状态缩减至9个）以及超柔性飞翼（1616个状态缩减至9个）。降阶模型在精确捕捉非线性动力学（包括超过翼展10%的大幅翼尖变形）的同时实现了高达600倍的计算加速。研究表明，二阶泰勒展开足以描述三次结构非线性，无需保留三阶项。该框架与全阶模型公式无关，适用于更高保真度的气动模型。