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：有限元模型更新在线性结构领域已是一项成熟技术，但其向非线性领域的扩展仍是开放式挑战。本文提出一种方法，将基于运动方程泰勒级数展开的非线性模型降阶技术与Hollins等人[2026]近期针对线性模型更新提出的投影基适应方案相结合。通过引入比例（瑞利）阻尼和多项式刚度非线性，将结构运动方程重构为具有复特征向量构成双正交基的一阶自治系统。推导了非线性内力的二阶与三阶泰勒算子，并将其投影至降维特征向量基，构建出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，参数化表征投影基的适应过程，使降阶模型模态振型与实验测量值达到最优相关。所提出的非线性模型更新框架被应用于典型翼盒面板模型。数值研究表明，该方法能够捕获纯线性更新方案无法复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。