Frequency-domain system identification of nonlinear structures using experimental continuation data

This work introduces a nonlinear system identification method that uses frequency response data to estimate a compact and interpretable nonlinear state-space model of structural systems. A key novelty is the ability to directly exploit data from experimental continuation, including unstable branches, by minimizing the discrepancy between measured and predicted outputs across multiple harmonics. This enables accurate characterization of nonlinear dynamics from a limited dataset, while keeping computational costs low and ensuring robustness to noise and initialization. The method, called NFR-ID, is validated through two experimental cases: an electronic Duffing oscillator and a thin-walled plate, the latter exhibiting rich nonlinear behavior due to large-amplitude vibrations. Results demonstrate the accuracy and broad applicability of NFR-ID as an efficient and general framework for analyzing nonlinear structural dynamics.