Finite element model updating is a mature discipline for linear structures, yet its extension to nonlinear regimes remains an open challenge. This paper presents a methodology that combines nonlinear model order reduction (NMOR) based on Taylor-series expansion of the equations of motion with the projection-basis adaptation scheme recently proposed by Hollins et al. [2026] for linear model updating. The structural equations of motion, augmented with proportional (Rayleigh) damping and polynomial stiffness nonlinearity, are recast as a first-order autonomous system whose Jacobian possesses complex eigenvectors forming a biorthogonal basis. Taylor operators of second and third order are derived for the nonlinear internal forces and projected onto the reduced eigenvector basis, yielding a low-dimensional nonlinear reduced-order model (ROM). The Cayley transform, generalised from the real orthogonal to the complex unitary group, parametrises the adaptation of the projection basis so that the ROM mode shapes optimally correlate with experimental measurements. The resulting nonlinear model-updating framework is applied to a representative wingbox panel model. Numerical studies demonstrate that the proposed approach captures amplitude-dependent natural frequencies and modal assurance criterion(MAC) values that a purely linear updating scheme cannot reproduce, while recovering the underlying stiffness parameters with improved accuracy.

翻译：有限元模型修正是线性结构领域成熟的技术，但其向非线性领域的推广仍是一项开放性挑战。本文提出了一种结合两类技术的非线性模型修正方法：基于运动方程泰勒级数展开的非线性模型降阶技术，以及Hollins等[2026]近期提出的适用于线性模型修正的投影基自适应方案。通过引入比例（瑞利）阻尼与多项式刚度非线性项增强的结构运动方程被重构为一阶自治系统，其雅可比矩阵具有构成双正交基的复特征向量。针对非线性内力推导了二阶与三阶泰勒算子，并将其投影到降阶特征向量基上，从而获得低维非线性降阶模型。将凯莱变换从实正交群推广至复酉群，实现了投影基的自适应参数化，使得降阶模型振型与实验测量值达到最优相关。所构建的非线性模型修正框架被应用于典型翼盒面板模型。数值研究表明，该方法能够捕捉纯线性修正方案无法再现的幅值依赖固有频率与模态置信准则值，同时以更高精度恢复底层刚度参数。