# Surrogate model approach for investigating the stability of a friction-induced oscillator of Duffing's type

## TL;DR

This paper introduces a surrogate modeling approach combining Gaussian process regression and adaptive classification to efficiently explore the stability of a Duffing-type oscillator with elasto-plastic friction, enabling rapid detection of instability regions.

## Contribution

It presents a novel surrogate strategy integrating kriging and MiVor classification for stability analysis of nonlinear oscillators with complex friction models.

## Key findings

- Efficient detection of instability domains in parametric space.
- Use of Lyapunov exponent as an indicator of non-regular behavior.
- High proficiency of the MiVor classification in complex response surfaces.

## Abstract

Parametric studies for dynamic systems are of high interest to detect instability domains. This prediction can be demanding as it requires a refined exploration of the parametric space due to the disrupted mechanical behavior. In this paper, an efficient surrogate strategy is proposed to investigate the behavior of an oscillator of Duffing's type in combination with an elasto-plastic friction force model. Relevant quantities of interest are discussed. Sticking time is considered using a machine learning technique based on Gaussian processes called kriging. The largest Lyapunov exponent is proposed as an efficient indicator of non-regular behavior. This indicator is estimated using a perturbation method. A dedicated adaptive kriging strategy for classification called MiVor is utilized and appears to be highly proficient in order to detect instabilities over the parametric space and can furthermore be used for complex response surfaces in multi-dimensional parametric domains.