Experimental bifurcation analysis—Continuation for noise-contaminated zero problems

Schilder, Frank; Bureau, Emil; Santos, Ilmar; Thomsen, Jon Juel; Starke, Jens

doi:10.1016/j.jsv.2015.08.008

Cited by 41 publications

(42 citation statements)

References 15 publications

(53 reference statements)

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“…This resulted in a lack of robustness which was deemed not suitable for experiments. Similar conclusions about higherorder prediction methods were found by Schilder et al [2015].…”

Section: Algorithm IIsupporting

confidence: 85%

“…The NLFR of a bilinear oscillator and energy harvesters were traced out in the experiment using CBC in [Bureau et al, 2013;Schilder et al, 2015] and [Barton & Burrow, 2010;Barton & Sieber, 2013], respectively.…”

Section: Experimental Tracking Of Limit-point Bifurcations and Backbomentioning

confidence: 99%

“…A method of working out the original stability properties of the underlying uncontrolled system without turning off the controller was presented by Barton [2016]. The "full" CBC method combines Newtonlike algorithms with pseudo-arclength continuation techniques to track solutions of (3) and is presented in, for example, [Schilder et al, 2015]. For many forced systems, it is possible to exploit a unique amplitude parameterization of the response (at constant frequency) to derive a simplified CBC method dispensed with derivative calculations and pathfollowing techniques [Barton & Sieber, 2013].…”

Section: Control-based Continuationmentioning

confidence: 99%

See 2 more Smart Citations

Experimental Tracking of Limit-Point Bifurcations and Backbone Curves Using Control-Based Continuation

Renson

Barton

Neild

2017

Int. J. Bifurcation Chaos

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Control-based continuation (CBC) is a means of applying numerical continuation directly to a physical experiment for bifurcation analysis without the use of a mathematical model. CBC enables the detection and tracking of bifurcations directly, without the need for a post-processing stage as is often the case for more traditional experimental approaches. In this paper, we use CBC to directly locate limit-point bifurcations of a periodically forced oscillator and track them as forcing parameters are varied. Backbone curves, which capture the overall frequency-amplitude dependence of the system's forced response, are also traced out directly. The proposed method is demonstrated on a single-degree-of-freedom mechanical system with a nonlinear stiffness characteristic. Results are presented for two configurations of the nonlinearity -one where it exhibits a hardening stiffness characteristic and one where it exhibits softening-hardening.

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“…This resulted in a lack of robustness which was deemed not suitable for experiments. Similar conclusions about higherorder prediction methods were found by Schilder et al [2015].…”

Section: Algorithm IIsupporting

confidence: 85%

Section: Experimental Tracking Of Limit-point Bifurcations and Backbomentioning

confidence: 99%

Section: Control-based Continuationmentioning

confidence: 99%

See 1 more Smart Citation

Experimental Tracking of Limit-Point Bifurcations and Backbone Curves Using Control-Based Continuation

Renson

Barton

Neild

2017

Int. J. Bifurcation Chaos

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“…The process of adjusting the control inputs follows the same rules as one would use to solve any nonlinear system (for example, with a Newton iteration). Schilder et al [2015] give detailed instructions how one can modify standard numerical methods to cope with large disturbances as one might typically encounter in experiments. They also demonstrate feedback control-based bifurcation analysis in vibration experiments (other recent demonstrations and reviews on vibration experiments are listed by Barton [2017]).…”

Section: General Controllability Through Probingmentioning

confidence: 99%

Probing Shells Against Buckling: A Nondestructive Technique for Laboratory Testing

Thompson

Hutchinson

Sieber

2017

Int. J. Bifurcation Chaos

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Abstract. This paper addresses testing of compressed structures, such as shells, that exhibit catastrophic buckling and notorious imperfection sensitivity. The central concept is the probing of a loaded structural specimen by a controlled lateral displacement to gain quantitative insight into its buckling behaviour and to measure the energy barrier against buckling. This can provide design information about a structure's stiffness and robustness against buckling in terms of energy and force landscapes. Developments in this area are relatively new but have proceeded rapidly with encouraging progress.Recent experimental tests on uniformly compressed spherical shells, and axially loaded cylinders, show excellent agreement with theoretical solutions. The probing technique could be a valuable experimental procedure for testing prototype structures, but before it can be used a range of potential problems must be examined and solved. The probing response is highly nonlinear and a variety of complications can occur. Here, we make a careful assessment of unexpected limit points and bifurcations, that could accompany probing, causing complications and possibly even collapse of a test specimen. First, a limit point in the probe displacement (associated with a cusp instability and fold) can result in dynamic buckling as probing progresses, as demonstrated in the buckling of a spherical shell under volume control. Second, various types of bifurcations which can occur on the probing path which result in the probing response becoming unstable are also discussed. To overcome these problems, we outline the extra controls over the entire structure that may be needed to stabilize the response.

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“…This is not easily achievable in experiments where solutions and derivative estimates are corrupted by measurement noise. Schilder et al [25] discussed the effect of noise on continuation algorithms. In particular, the tangential prediction and orthogonal correction steps of the commonly-used pseudo-arclength continuation algorithm were shown to perform poorly in a noisy experimental context.…”

Section: Introductionmentioning

confidence: 99%

Numerical continuation in nonlinear experiments using local Gaussian process regression

et al. 2019

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Control-based continuation (CBC) is a general and systematic method to probe the dynamics of nonlinear experiments. In this paper, CBC is combined with a novel continuation algorithm that is robust to experimental noise and enables the tracking of geometric features of the response surface such as folds. The method uses Gaussian process regression to create a local model of the response surface on which standard numerical continuation algorithms can be applied. The local model evolves as continuation explores the experimental parameter space, exploiting previously captured data to actively select the next data points to collect such that they maximise the potential information gain about the feature of interest. The method is demonstrated experimentally on a nonlinear structure featuring harmonically-coupled modes. Fold points present in the response surface of the system are followed and reveal the presence of an isola, i.e. a branch of periodic responses detached from the main resonance peak.

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Experimental bifurcation analysis—Continuation for noise-contaminated zero problems

Cited by 41 publications

References 15 publications

Experimental Tracking of Limit-Point Bifurcations and Backbone Curves Using Control-Based Continuation

Experimental Tracking of Limit-Point Bifurcations and Backbone Curves Using Control-Based Continuation

Probing Shells Against Buckling: A Nondestructive Technique for Laboratory Testing

Numerical continuation in nonlinear experiments using local Gaussian process regression

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