Nonlinear Model Updating of Aerospace Structures via Taylor-Series Reduced-Order Models

TL;DR

This paper introduces a nonlinear model updating method for aerospace structures using Taylor-series reduced-order models, effectively capturing amplitude-dependent dynamics and improving parameter accuracy.

Contribution

It combines nonlinear model order reduction with projection-basis adaptation, extending linear model updating techniques to nonlinear regimes.

Findings

Captures amplitude-dependent natural frequencies.

Improves accuracy of stiffness parameter estimation.

Outperforms purely linear updating schemes.

Abstract

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.