Data-driven Nonlinear Model Reduction to Spectral Submanifolds in Mechanical Systems

Abstract

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.

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• Applied Koopmanism
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Cited by in corpus (5)

• Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifolds
• Nonlinear Model Reduction to Fractional and Mixed-Mode Spectral Submanifolds
• Data-Assisted Non-Intrusive Model Reduction for Forced Nonlinear Finite Elements Models
• Data-driven modeling of the regular and chaotic dynamics of an inverted flag from experiments
• Dynamics-based machine learning of transitions in Couette flow