A Parametric and Feasibility Study for Data Sampling of the Dynamic Mode Decomposition: Spectral Insights and Further Explorations

Abstract

This work continues the parametric investigation on the sampling nuances of the Dynamic Mode Decomposition (DMD) under the Koopman analysis. Through turbulent wakes, the investigation corroborated the generality of the universal convergence states for all DMD implementations. It discovered the implications of sampling range and resolution -- the determinants of the spectral discretisation by discrete frequency bins and the highest resolved frequency, respectively. The work reaffirmed the necessity of the Convergence state for sampling independence, too. Results also suggested that the observables derived from the same flow may contain dynamically distinct information, thus altering the DMD output. The static pressure and vortex identification criteria are optimal variables for characterising structural response and fluid excitation. The pressure, velocity magnitude, and turbulence kinetic energy fields also suffice for general applications, but the Reynolds stresses and velocity components shall be avoided. Mean-subtraction is recommended for best approximations of the Koopman eigen tuples. Furthermore, the parametric investigation on truncation discovered some low-energy states that dictate a system's temporal integrity. The best practice for order reduction is to avoid truncation and employ dominant mode selection on a full-state subspace, though large-degree truncation supports fair data reconstruction with low computational cost. Finally, this work demonstrated the synthetic noise resulting from pre-decomposition interpolation. In unavoidable interpolations to increase the spatial dimension n, high-order schemes are recommended for better retention of the original dynamics. Finally, the observations herein, derived from inhomogeneous anisotropic turbulence, offer constructive references for DMD on fluid systems, if not also others beyond fluid mechanics.

75 page, 21 figures, Under Review at Physics of Fluids

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• Applied Koopmanism
• Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows
• Letter: Modified normalized Rortex/vortex identification method
• A Parametric and Feasibility Study for Data Sampling of the Dynamic Mode Decomposition--Range, Resolution, and Universal Convergence States
• Establishing Direct Phenomenological Connections between Fluid and Structure by the Koopman-Linearly-Time-Invariant Analysis
• On Some Modal Implications of the Dynamic Mode Decomposition Through the Lens of a Subcritical Prism Wake

Cited by in corpus (3)

• The Linear-Time-Invariance Notion of the Koopman Analysis-Part 1: The Architecture, Practical Rendering on the Prism Wake, and Fluid-Structure Association
• The Linear-Time-Invariance Notion of the Koopman Analysis-Part 2: Physical Interpretations of Invariant Koopman Modes and Phenomenological Revelations
• Nonintrusive reduced order modeling of convective Boussinesq flows