Exploring localization in nonlinear oscillator systems through

Localized vibrations, arising from nonlinearities or symmetry breaking, pose a challenge in engineering, as the resulting high-amplitude vibrations may lead to component failure due to fatigue. This work proposes a novel, network-based approach to detect an imminent localized vibration using synthetic measurement data to generate a functional network that captures the dynamic interplay of machine parts alongside their geometric coupling. By analyzing these functional networks, the emerging localized vibration and its location can be identified. The method is validated through a model system for a bladed disk, represented as a ring composed of coupled nonlinear Duffing oscillators. Results demonstrate that the proposed technique remains robust against small parameter uncertainties, measurement noise, and variations in data sample lengths. This study provides a data-driven methodology utilizing network-based techniques to anticipate high-amplitude localized vibrations by thoroughly analyzing system dynamics, potentially aiding in the development of early warning systems to prevent catastrophic system failures.