Machine learning for experimental bifurcation analysis

Nonlinear mechanical structures can exhibit multiple coexisting periodic solutions, including unstable responses that remain inaccessible to standard experimental testing. Conventional swept-sine measurements, rooted in linear assumptions, capture only the stable portions of the frequency response and thus overlook essential bifurcations and unstable dynamics. Beyond the fundamental resonance, nonlinear systems also resonate at integer multiples or fractions of the excitation frequency, giving rise to superharmonic and subharmonic responses, some of which may appear as isolated branches.

This work proposes a data-driven framework that leverages deep convolutional networks to complete the missing information from open-loop measurements. From open-loop experimental data alone, the method infers the full nonlinear frequency response. Experimental validation on an electronic Duffing oscillator confirms the accuracy of the predictions, while the framework can be readily extended by incorporating additional nonlinearities into the training dataset, paving the way toward a generic tool for nonlinear experimental analysis.