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.

arXiv comment22 pages, 12 figures

References in corpus (3)

• Direct observation of coherent energy transfer in nonlinear micro-mechanical oscillators
• Systematic experimental exploration of bifurcations with non-invasive control
• Application of control-based continuation to a nonlinear structure with harmonically coupled modes

Cited by in corpus (5)

• Methods of Continuation and their Implementation in the COCO Software Platform with Application to Delay Differential Equations
• Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach
• Experimental continuation in nonlinear dynamics: recent advances and future challenges
• Model-free Continuation of Periodic Orbits in Certain Nonlinear Systems Using Continuous-Time Adaptive Control
• Fold Bifurcation Identification through Scientific Machine Learning