# Numerical Continuation in Nonlinear Experiments using Local Gaussian Process Regression

## TL;DR

This paper introduces a noise-robust continuation method combining control-based experiments with local Gaussian process regression to effectively track nonlinear response features like folds.

## Contribution

It presents a novel continuation algorithm that uses Gaussian process models for local response surface approximation, enabling robust tracking of nonlinear features in noisy experimental data.

## Key findings

- Successfully tracked fold points in a nonlinear structure experiment.
- Revealed the presence of an isola branch of responses.
- Demonstrated robustness to experimental noise.

## 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.