Data-driven nonlinear model reduction to spectral submanifolds via oblique projection.

Area of Science:

• Dynamical Systems Theory
• Nonlinear Dynamics
• Reduced-Order Modeling

Background:

• Spectral Submanifolds (SSMs) offer reduced-order models for nearby trajectories.
• Modeling dynamics far from SSMs is challenging due to system non-normality.
• Non-normality complicates direct projection methods for accurate reduced-order modeling.

Purpose of the Study:

• To develop an efficient projection technique for approximating nonlinear dynamics.
• To accurately model trajectories distant from primary spectral submanifolds.
• To overcome limitations of data requirements for constructing invariant foliations.

Main Methods:

• Developed an oblique projection technique.
• Applied the method to a significantly non-normal and nonlinear beam system.
• Utilized a single experimental trajectory for model construction.

Main Results:

• The oblique projection efficiently approximates the stable invariant foliation.
• Accurate modeling of trajectories distant from the primary SSM was achieved.
• The method demonstrated effectiveness even with limited experimental data.

Conclusions:

• Oblique projection is a viable method for reduced-order modeling of non-normal systems.
• This technique offers a practical approach for complex dynamical systems.
• Efficient modeling is possible even with sparse experimental data.