Abstract :
[en] Understanding and predicting the dynamic vibrational response of mechanical systems remains a core challenge in structural dynamics. Real-world structures frequently exhibit nonlinear behaviour, resulting in complex phenomena such as primary and secondary resonances, multistability, and the emergence of unstable response branches. These features lie beyond the reach of standard experimental modal analysis (EMA), which, based on linear assumptions and typically relying on swept-sine excitation, can only capture the stable portions of the frequency response. As a result, crucial information about bifurcations and unstable dynamics remains experimentally inaccessible. Although control-based continuation methods have been developed to overcome this limitation, their practical application is hindered by the need for precise controller tuning and complex feedback architectures.
This thesis proposes a novel data-driven methodology that bridges this gap by combining standard EMA techniques with deep learning. Specifically, it investigates whether unstable branches of nonlinear frequency response curves (FRCs) can be predicted solely from experimental swept-sine measurements, which contain only the stable portions of the response. To the best of the author's knowledge, this is the first approach that enables the prediction of unstable branches of nonlinear frequency response curves from experimental swept-sine data alone.
To this end, a supervised learning framework is developed and applied to the Duffing oscillator, a one-degree-of-freedom nonlinear system with cubic stiffness. A convolutional neural network is trained on synthetic datasets, with input data generated from binary image representations of swept-sine envelopes. The model successfully predicts not only the fundamental resonance but also subharmonic and superharmonic resonances, effectively reconstructing the full FRC.
Crucially, the methodology is validated on an experimental electronic Duffing oscillator, confirming that unstable branches can indeed be predicted from swept-sine tests alone. The approach is then extended to other oscillator types and nonlinearity forms, demonstrating promising generalization capabilities.
Overall, this work presents a practical and effective alternative to control-based methods for the analysis of nonlinear experimental data. It demonstrates the feasibility of integrating standard EMA techniques with machine learning to predict otherwise inaccessible dynamic features.
