Using reduced-order models to optimise the dynamics of nonlinear systems

Abstract

Currently, the demand for modelling complex flexible structures, which typically exhibit geometric nonlinearities and large-amplitude responses, is growing significantly. However, direct dynamic simulations of these structures in finite-element (FE) software are often computationally prohibitive. To alleviate the computational burden, reduced-order modelling can construct low-dimensional models which capture the salient dynamics of the original full-order model. The aim of this thesis is to further the understanding of a category of indirect methods for reduced-order modelling- force-based methods- which are suitable for FE models generated in commercial software. These methods utilise static datasets from static FE analyses to construct ROMs through a fitting procedure. In this thesis, both the accuracy and computational efficiency of force-based ROMs are discussed in detail for parameter-dependent problems, particularly in the context of optimisation. First, an algorithm is proposed to ensure the fitting accuracy of a ROM within a specified range. It is shown that this algorithm can identify the static dataset in a meaningful way. The resulting ROMs can achieve high fitting accuracy whilst requiring only a limited number of static FE analyses, thereby reducing the computational costs of ROM construction. Then, force-based ROMs are applied to parameter-dependent problems. A parameter analysis is conducted on a wing-inspired FE model with varying physical parameters. By considering the characteristics of these parameters, it is shown that only parameters associated with conservative terms in the FE model’s governing equations require ROM reconstruction, whereas nonconservative parameters do not. Using this FE model, it is demonstrated that force-based ROMs maintain relatively high computational cost compared with dynamic FE simulations, even when including the cost of ROM construction. Finally, force-based ROMs are extended to an optimisation framework. A computationally efficient algorithm is developed to handle qualitative changes in dynamics resulting fromvariations in physical parameters. Using this algorithm, it is shown that force-based ROMs can not only identify the correct optimal solution but also achieve significant computational advantages for both individual parameter point computation and the overall optimisation process. i

Date of Award	20 Jan 2026
Original language	English
Awarding Institution	University of Bristol
Supervisor	Tom L Hill (Supervisor) & Simon A Neild (Supervisor)