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Numerical Continuation in Nonlinear Experiments using Local Gaussian Process Regression

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Numerical Continuation in Nonlinear Experiments using Local Gaussian Process Regression. / Renson, Ludovic; Sieber, Jan; Barton, David; Shaw, Alexander; Neild, Simon.

In: Nonlinear Dynamics, 08.08.2019.

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Renson, Ludovic ; Sieber, Jan ; Barton, David ; Shaw, Alexander ; Neild, Simon. / Numerical Continuation in Nonlinear Experiments using Local Gaussian Process Regression. In: Nonlinear Dynamics. 2019.

Bibtex

@article{c83279f5e6a44982adb895ddb7850743,
title = "Numerical Continuation in Nonlinear Experiments using Local Gaussian Process Regression",
abstract = "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.",
keywords = "nonlinear experiment, regression-based, Control-based continuation, Gaussian Process Regression, Active data selection",
author = "Ludovic Renson and Jan Sieber and David Barton and Alexander Shaw and Simon Neild",
year = "2019",
month = "8",
day = "8",
doi = "10.1007{\%}2Fs11071-019-05118-y",
language = "English",
journal = "Nonlinear Dynamics",
issn = "0924-090X",
publisher = "Springer Netherlands",

}

RIS - suitable for import to EndNote

TY - JOUR

T1 - Numerical Continuation in Nonlinear Experiments using Local Gaussian Process Regression

AU - Renson, Ludovic

AU - Sieber, Jan

AU - Barton, David

AU - Shaw, Alexander

AU - Neild, Simon

PY - 2019/8/8

Y1 - 2019/8/8

N2 - 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.

AB - 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.

KW - nonlinear experiment

KW - regression-based

KW - Control-based continuation

KW - Gaussian Process Regression

KW - Active data selection

U2 - 10.1007%2Fs11071-019-05118-y

DO - 10.1007%2Fs11071-019-05118-y

M3 - Article

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

ER -