Reduced-Order Modelling of Flutter Oscillations Using Normal Forms and Scientific Machine Learning

Lee, K.H.; Barton, David A. W.; Renson, Ludovic

doi:10.1007/978-3-030-81162-4_5

Cited by 6 publications

(12 citation statements)

References 13 publications

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“…Figure 6 shows the branches of the identified limit cycles/near-periodic solutions with an additive stochastic moment with standard deviations σ = 0, 0.02 and 0.04 using the model given in (18). The crosses corresponding to the 'measurement data' indicate the average amplitude of the near-periodic solutions of the observed stochastic system, whereas the limit cycles of the UDE model were obtained by numerical collocation considering the deterministic part of the model only.…”

Section: Simulations With Process Noisementioning

confidence: 99%

“…In this section, we present the algorithm used for the numerical simulation of the fluttering aerofoil. This is an extended version of the algorithm presented in [18] by Lee et al, capable of finding limit cycles in autonomous system. However, due to the limitations of the experimental rig, limit cycles are only tracked for a number of fixed airspeeds while we implement a full continuation using the airspeed as bifurcation parameter.…”

Section: A Coefficient Matrices Of the Flutter Modelmentioning

confidence: 99%

“…with F = (F ctrl 0 0) T . To consider process noise, we apply the same extension to the SDE in (18).…”

Section: A Coefficient Matrices Of the Flutter Modelmentioning

confidence: 99%

“…The technique of controlbased continuation (CBC), introduced in [14] is capable of tracing both stable and unstable limit cycles in physical experiments. The method has been adapted to deal with random perturbations/process-noise in the experiment [15,16], it has been also extended to provide information on stability (without turning the controller off) [17], and it has been made capable of tracing selfexcited vibrations in autonomous systems [18]. Having the additional information about the unstable solutions has significant merits in modelling and parameter identification problems.…”

Section: Introductionmentioning

confidence: 99%

“…In context of nonlinear systems, there is often an interest to find the so-called normal forms: minimalistic models with the bifurcation diagram characteristic to the observed phenomenon. In their study, Lee et al [18] used machine learning techniques to identify the transformation from physical to normal coordinates of a Hopf bifurcation for aeroelastic flutter based on measurement data. The aim of our investigation is similar in the sense that we reconstruct measured bifurcation diagrams of nonlinear systems: an aerofoil undergoing flutter and an electrodynamical oscillator.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Using scientific machine learning for experimental bifurcation analysis of dynamic systems

Beregi¹,

Barton²,

Rezgui³

et al. 2021

Preprint

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Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and reality through measurement data. Our exploratory study focuses on training universal differential equation (UDE) models for physical nonlinear dynamical systems with limit cycles: an aerofoil undergoing flutter oscillations and an electrodynamic nonlinear oscillator. We consider examples where training data is generated by numerical simulations, whereas we also employ the proposed modelling concept to physical experiments allowing us to investigate problems with a wide range of complexity. To collect the training data, the method of controlbased continuation is used as it captures not just the stable but also the unstable limit cycles of the observed system. This feature makes it possible to extract more information about the observed system than the standard, open-loop approach would allow. We use both neural networks and Gaussian processes as universal approximators alongside the mechanistic models to give

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Section: Simulations With Process Noisementioning

confidence: 99%

Section: A Coefficient Matrices Of the Flutter Modelmentioning

confidence: 99%

“…with F = (F ctrl 0 0) T . To consider process noise, we apply the same extension to the SDE in (18).…”

Section: A Coefficient Matrices Of the Flutter Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Using scientific machine learning for experimental bifurcation analysis of dynamic systems

Beregi¹,

Barton²,

Rezgui³

et al. 2021

Preprint

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Bayesian Local Surrogate Models for the Control-Based Continuation of Multiple-Timescale Systems

Blyth

Marucci

Renson

2021

NODYCON Conference Proceedings Series

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Nonlinear analysis of the delayed tyre model with control-based continuation

Beregi

2022

Nonlinear Dyn

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In this study, the numerical bifurcation analysis of a shimmying wheel is performed with a non-smooth, time-delayed model of the tyre-ground contact. This model is capable of reproducing the bistable behaviour often observed in experiments: a stable equilibrium and a stable periodic orbit coexisting for the same set of system parameters, that the simpler quasi-steady tyre models fail to capture. In the bistable parameter domain, there also exists an unstable periodic orbit within the separatrix between the domains of attractions of the two stable steady-state solutions. Although this solution never appears in a real-life system, one may still gain valuable information from tracing it as it gives an indication about the level of perturbation that would drive the system from one stable solution to the other. However, the complexity of the laws governing partial sticking and sliding in the tyre-ground contact makes the numerical bifurcation analysis with the traditional, collocation-based techniques infeasible. Instead, this study is based on numerical simulations and the technique of control-based continuation (CBC) to track the stable and unstable periodic solutions of the system allowing for the assessment of the accuracy of the non-smooth, delayed tyre model in replicating the dynamics observed in experiments. In the meantime, the physics-based model provides an insight into the relationship between the sticking and sliding regions appearing in the tyre-ground contact and the global dynamics of the system.

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Reduced-Order Modelling of Flutter Oscillations Using Normal Forms and Scientific Machine Learning

Cited by 6 publications

References 13 publications

Using scientific machine learning for experimental bifurcation analysis of dynamic systems

Using scientific machine learning for experimental bifurcation analysis of dynamic systems

Bayesian Local Surrogate Models for the Control-Based Continuation of Multiple-Timescale Systems

Nonlinear analysis of the delayed tyre model with control-based continuation

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