5/11/2023 0 Comments Loopman royale beat![]() To validate the results on a longer time trace, a statistical analysis of the dominant unstable eigenvalues captured by the two procedures is successively performed considering several temporal blocks for different inflow conditions. On a short time trace (10 KH periods), the Koopman analysis is shown to identify the proper KH vortex shedding frequency and wavelength for every condition tested, while DMD fails especially with low Tu and high Re. Successively, the robustness of DMD and Koopman modal decomposition has been examined for different Tu levels and Re numbers. The most effective definition of the observable matrix for Koopman analysis able to characterize these vortices is addressed first for a reference Tu and Re number condition. For every flow condition, instantaneous velocity fields clearly show the formation of Kelvin–Helmholtz (KH) vortices induced by the KH instability. The analysis accounts for two different Re numbers, two different Tu levels, and a fixed APG condition inducing flow separation, as it may occur in low pressure turbine-like conditions. Experiments concerning separated-flow transition process were carried out in a test section allowing the variation of the Reynolds number (Re), the adverse pressure gradient (APG) and the free-stream turbulence intensity (Tu). In the present work, dynamic mode decomposition (DMD) and Koopman spectral analysis are applied to flat plate particle image velocimetry experimental data. All of the systems analyzed in this work use an identical network architecture and results are more compact and interpretable compared to dynamic mode decomposition. Modal disaggregation is encouraged using a simple masking procedure. The learned models are able to successfully and robustly identify the underlying modes governing the system, even with a redundantly large embedding space. Practically, the CKN allows for flexibility in system data collection as the data can be easily obtainable observable variables. We demonstrate the ability of a deep convolutional Koopman network (CKN) in automatically identifying independent modes of simple simulated and atomization systems. While many related techniques have demonstrated their efficacy on low-dimensional systems and their associated state variables, in this work the system dynamics are observed optically (i.e., spatiotemporal data from video or simulation). These eigenfunctions can be linked to underlying system modes that govern the dynamical behavior of the system. Deep Koopman networks attempt to learn the Koopman eigenfunctions that capture the coordinate transformation to globally linearize system dynamics. Recent deep learning extensions in Koopman theory have enabled compact, interpretable representations of nonlinear dynamical systems that are amenable to linear analysis.
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