Data-driven Nonlinear Model Reduction to Spectral Submanifolds in Mechanical Systems
This provides a general approach for nonlinear model reduction in mechanical systems, addressing a gap for non-linearizable cases with multiple steady states.
The paper tackles the problem of reducing nonlinear mechanical systems with multiple steady states by introducing a data-driven model reduction method based on spectral submanifolds, which constructs low-dimensional normal forms from unforced oscillation data to accurately predict forced system responses, as demonstrated on structural vibration examples.
While data-driven model reduction techniques are well-established for linearizable mechanical systems, general approaches to reducing non-linearizable systems with multiple coexisting steady states have been unavailable. In this paper, we review such a data-driven nonlinear model reduction methodology based on spectral submanifolds (SSMs). As input, this approach takes observations of unforced nonlinear oscillations to construct normal forms of the dynamics reduced to very low dimensional invariant manifolds. These normal forms capture amplitude-dependent properties and are accurate enough to provide predictions for non-linearizable system response under the additions of external forcing. We illustrate these results on examples from structural vibrations, featuring both synthetic and experimental data.