Exploring localization in nonlinear oscillator systems through network-based predictions

TL;DR

This paper introduces a network-based method to predict localized vibrations in nonlinear oscillator systems, enhancing early detection and understanding of high-amplitude vibrations that could cause component failure.

Contribution

A novel approach using functional network analysis to detect and locate imminent localized vibrations in nonlinear oscillator systems, demonstrated on a model of coupled Duffing oscillators.

Findings

Method effectively predicts localization with small parameter uncertainties.

Robust against measurement noise and data sample length.

Applicable to complex nonlinear systems like bladed disks.

Abstract

Localized vibrations, arising from nonlinearities or symmetry breaking, pose a challenge in engineering, as the resulting high-amplitude vibrations may result in component failure due to fatigue. During operation, the emergence of localization is difficult to predict, partly because of changing parameters over the life cycle of a system. This work proposes a novel, network-based approach to detect an imminent localized vibration. Synthetic measurement data is used to generate a functional network, which captures the dynamic interplay of the machine parts, complementary to their geometric coupling. Analysis of these functional networks reveals an impending localized vibration and its location. The method is demonstrated using a model system for a bladed disk, a ring composed of coupled nonlinear Duffing oscillators. Results indicate that the proposed method is robust against small parameter uncertainties, added measurement noise, and the length of the measurement data samples. The source code for this work is available.