Robust identification of backbone curves using control-based continuation

Renson, Ludovic; Gonzalez-Buelga, Alicia; Barton, David A. W.; Neild, Simon A

doi:10.1016/j.jsv.2015.12.035

Cited by 115 publications

(108 citation statements)

References 33 publications

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“…Moreover, the new direct limit-point bifurcation tracking method avoids the artificial distortions that are observed in the limitpoint curves calculated from the Gaussian process regression. Finally, the backbone curves of the system were accurately tracked for both configurations of the nonlinearity, which further demonstrates the broad applicability of the method originally developed in [Renson et al, 2016b].…”

Section: Discussionmentioning

confidence: 67%

“…The second contribution is to exploit CBC to measure the backbone curve of the system, that is the response of the unforced, undamped system, further demonstrating the broad applicability of the method presented in [Renson et al, 2016b]. Backbone curves trace out the evolution in frequency of the peak response of the NLFR curves (not represented in Fig.…”

Section: Experimental Tracking Of Limit-point Bifurcations and Backbomentioning

confidence: 95%

“…It is possible to exploit this surface to extract relevant dynamic features such as the curve of limit-point (LP) bifurcations (solid orange curve in Fig. 1) [Barton & Sieber, 2013;Renson et al, 2016b]. LP bifurcation curves contain valuable information about the system's dynamics.…”

Section: Experimental Tracking Of Limit-point Bifurcations and Backbomentioning

confidence: 99%

“…In practice, this means it would be very difficult to measure the backbone curve without controlling the experiment. In this regard, the CBC method appears to be more robust than other existing methods such as resonant decay [Renson et al, 2016b]. bifurcation curve in the softening region (−) was followed with frequency steps of 0.05 Hz.…”

Section: Small-gap Configurationmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 67%

Section: Experimental Tracking Of Limit-point Bifurcations and Backbomentioning

confidence: 95%

Section: Experimental Tracking Of Limit-point Bifurcations and Backbomentioning

confidence: 99%

Section: Small-gap Configurationmentioning

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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“…This result will also be exploited in the study of the pluripotency GRN in Section 2.3. Similar principles were also used to capture the periodic orbits and fold bifurcations of several mechanical systems [12][13][14]21].…”

Section: Principles Of Control-based Continuationmentioning

confidence: 99%

Exploring the Dynamics of Nonlinear Biochemical Systems using Control-Based Continuation

Gomes

Cesare

Guarino

et al. 2019

Preprint

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Mathematical modelling is routinely used in Systems Biology to understand the mechanisms causing nonlinear phenomena in gene expression, such as switch-like behaviours and temporal oscillations. The reliability of model predictions and bifurcation analysis depend on modelling assumptions and specific choices of model parameters; however, the identification of models is highly challenging due to the complexity of biochemical interactions and noise in experimental data. This paper numerically investigates the use of control-based continuation (CBC) for tracking dynamical features of biochemical systems and, in particular, the bistable dynamics of a gene regulating pluripotency in embryonic stem cells. CBC is a method that exploits feedback control and path following algorithms to explore the dynamic features of a nonlinear physical system directly during experimental tests. CBC applications have so far been limited to non-living (i.e. electro-mechanical) systems. Our numerical simulations show that, in principle, CBC could also be applied to biological experiments to characterise the switch-like dynamics of genes that are important for cell decision making.

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Continuation methods for lab experiments of nonlinear vibrations

2023

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In this work, we will give an overview of our recent progress in experimental continuation. First, three different approaches are explained and compared which can be found in scientific papers on the topic. We then show S‐Curve measurements of a Duffing oscillator experiment for which we derived optimal controller gains analytically. The derived formula for stabilizing PD‐controller gains makes trial and error search for suitable values unnecessary. Since feedback control introduces higher harmonics in the driving signal, we consider a harmonization of the forcing signal. This harmonization is important to reduce shaker‐structure interaction in the treatment of nonlinear frequency responses. Finally, the controlled nonlinear testing and harmonization is enhanced by a continuation algorithm adapted from numerical analysis and applied to a geometrically nonlinear beam test rig for which we measure the nonlinear forced response directly in the displacement‐frequency plane.

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Robust identification of backbone curves using control-based continuation

Cited by 115 publications

References 33 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

Exploring the Dynamics of Nonlinear Biochemical Systems using Control-Based Continuation

Continuation methods for lab experiments of nonlinear vibrations

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