An investigation into model extrapolation and stability in the system identification of a nonlinear structure

Estimating a nonlinear model from experimental measurements of a vibrating structure remains a challenge, despite huge progress in recent years. A major issue is that the dynamical behaviour of a nonlinear structure strongly depends on the magnitude of the displacement response. Thus, the validity o...

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Vydané v:Nonlinear dynamics Ročník 111; číslo 19; s. 17653 - 17665
Hlavní autori: Anastasio, D., Marchesiello, S., Gatti, G., Gonçalves, P. J. P., Shaw, A. D., Brennan, M. J.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Dordrecht Springer Netherlands 01.10.2023
Springer Nature B.V
Predmet:
Aerospace engineering
Amplitudes
Approximation
Automotive Engineering
Broadband
Cantilever beams
Classical Mechanics
Control
Dynamical Systems
Engineering
Excitation
Extrapolation
Geometric nonlinearity
Identification
Investigations
Magnets
Mechanical Engineering
Motion stability
Original Paper
Random noise
Range of motion
State space models
System identification
Validity
Vibration
Extrapolation
Interpolation
Stability
Data-driven
Nonlinear system identification
ISSN:0924-090X, 1573-269X
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Shrnutí:Estimating a nonlinear model from experimental measurements of a vibrating structure remains a challenge, despite huge progress in recent years. A major issue is that the dynamical behaviour of a nonlinear structure strongly depends on the magnitude of the displacement response. Thus, the validity of an identified model is generally limited to a certain range of motion. Also, outside this range, the stability of the solutions predicted by the model are not guaranteed. This raises the question as to how a nonlinear model derived using data from relatively low amplitude excitation can be used to predict the dynamical behaviour for higher amplitude excitation. This paper focuses on this problem, investigating the extrapolation capabilities of data-driven nonlinear state-space models based on a subspace approach. The experimental vibrating structure consists of a cantilever beam in which magnets are used to generate strong geometric nonlinearity. The beam is driven by an electrodynamic shaker using several levels of broadband random noise. Acceleration data from the beam tip are used to derive nonlinear state-space models for the structure. It is shown that model predictions errors generally tend to increase when extrapolating towards higher excitation levels. Furthermore, the validity of the estimated nonlinear models become poor for very strong nonlinear behaviour. Linearised models are also estimated to have a complete view of the performance of each candidate model for each level of excitation.
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-023-08770-7