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

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.

Figures (13)

• Figure 1: Schematic diagrams of the experimental wingbox panel showing geometry, dimensions, sensor and shaker locations. Reproduced from hollins2026projection.
• Figure 2: FE mesh and substructure definitions of the wingbox panel. Different colours correspond to different substructures; blue spheres indicate sensor locations. Reproduced from hollins2026projection.
• Figure 3: Initial MAC matrix for the wingbox panel. Rows: FE model natural frequencies (Hz); columns: experimental natural frequencies (Hz). Diagonal values (bold) range from 0.863 to 0.997, indicating good but imperfect correlation. Modes 4 and 5 show the lowest MAC and largest frequency discrepancies. Data from hollins2026projection, Table 2.
• Figure 4: FOM time histories at sensor 1 for increasing cubic stiffness: $K_{nl} = 0$ (linear), $10^6$, $10^7$, and $10^8$ N/m$^3$. Initial condition: first mode shape, $A = 0.01$ m.
• Figure 5: Dominant frequency vs. cubic stiffness $K_{nl}$.