Dynamic Mode Decomposition and Its Variants

2021 ◽  
Vol 54 (1) ◽  
Author(s):  
Peter J. Schmid
Keyword(s):  
Dynamic Mode Decomposition ◽  
Annual Review ◽  
Dynamic Mode ◽  
Publication Date ◽  
Fluid Systems ◽  
Mode Decomposition ◽  
Dimensionality Reduction Technique ◽  
Essential Components ◽  
Complex Fluid ◽  
Sequential Measurements

Dynamic mode decomposition (DMD) is a factorization and dimensionality reduction technique for data sequences. In its most common form, it processes high-dimensional sequential measurements, extracts coherent structures, isolates dynamic behavior, and reduces complex evolution processes to their dominant features and essential components. The decomposition is intimately related to Koopman analysis and, since its introduction, has spawned various extensions, generalizations, and improvements. It has been applied to numerical and experimental data sequences taken from simple to complex fluid systems and has also had an impact beyond fluid dynamics in, for example, video surveillance, epidemiology, neurobiology, and financial engineering. This review focuses on the practical aspects of DMD and its variants, as well as on its usage and characteristics as a quantitative tool for the analysis of complex fluid processes. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 54 is January 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Experimental Measurement of In-Plane Rolling Nonpneumatic Tire Vibrations Using High-Speed Imaging

2019 ◽  
Vol 47 (3) ◽  
pp. 196-210
Author(s):  
Meghashyam Panyam ◽  
Beshah Ayalew ◽  
Timothy Rhyne ◽  
Steve Cron ◽  
John Adcox
Keyword(s):  
High Speed ◽  
Image Correlation ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
High Speed Imaging ◽  
Correlation Algorithm ◽  
Mode Decomposition ◽  
Series Of Experiments ◽  
Plane Deformations ◽  
Dominant Frequencies

ABSTRACT This article presents a novel experimental technique for measuring in-plane deformations and vibration modes of a rotating nonpneumatic tire subjected to obstacle impacts. The tire was mounted on a modified quarter-car test rig, which was built around one of the drums of a 500-horse power chassis dynamometer at Clemson University's International Center for Automotive Research. A series of experiments were conducted using a high-speed camera to capture the event of the rotating tire coming into contact with a cleat attached to the surface of the drum. The resulting video was processed using a two-dimensional digital image correlation algorithm to obtain in-plane radial and tangential deformation fields of the tire. The dynamic mode decomposition algorithm was implemented on the deformation fields to extract the dominant frequencies that were excited in the tire upon contact with the cleat. It was observed that the deformations and the modal frequencies estimated using this method were within a reasonable range of expected values. In general, the results indicate that the method used in this study can be a useful tool in measuring in-plane deformations of rolling tires without the need for additional sensors and wiring.

Oscillatory flow around a vertical wall-mounted cylinder: Dynamic mode decomposition

2021 ◽  
Vol 33 (2) ◽  
pp. 025113
Author(s):  
H. K. Jang ◽  
C. E. Ozdemir ◽  
J.-H. Liang ◽  
M. Tyagi
Keyword(s):  
Oscillatory Flow ◽  
Vertical Wall ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Mode Decomposition

Modeling the Turbulent Wake Behind a Wall-Mounted Square Cylinder

2020 ◽  
Author(s):  
Christian Amor ◽  
José M Pérez ◽  
Philipp Schlatter ◽  
Ricardo Vinuesa ◽  
Soledad Le Clainche
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Turbulent Wake ◽  
Orthogonal Decomposition ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Square Cylinder ◽  
Complex Flow ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Proper Orthogonal

Abstract This article introduces some soft computing methods generally used for data analysis and flow pattern detection in fluid dynamics. These techniques decompose the original flow field as an expansion of modes, which can be either orthogonal in time (variants of dynamic mode decomposition), or in space (variants of proper orthogonal decomposition) or in time and space (spectral proper orthogonal decomposition), or they can simply be selected using some sophisticated statistical techniques (empirical mode decomposition). The performance of these methods is tested in the turbulent wake of a wall-mounted square cylinder. This highly complex flow is suitable to show the ability of the aforementioned methods to reduce the degrees of freedom of the original data by only retaining the large scales in the flow. The main result is a reduced-order model of the original flow case, based on a low number of modes. A deep discussion is carried out about how to choose the most computationally efficient method to obtain suitable reduced-order models of the flow. The techniques introduced in this article are data-driven methods that could be applied to model any type of non-linear dynamical system, including numerical and experimental databases.

scholarly journals Analysis of transonic buffet using dynamic mode decomposition

2021 ◽  
Vol 62 (4) ◽  
Author(s):  
Antje Feldhusen-Hoffmann ◽  
Christian Lagemann ◽  
Simon Loosen ◽  
Pascal Meysonnat ◽  
Michael Klaas ◽  
...  
Keyword(s):  
Shock Wave ◽  
Flow Field ◽  
Acoustic Waves ◽  
Feedback Loop ◽  
Measurement Data ◽  
Dynamic Mode Decomposition ◽  
Recirculation Region ◽  
Dynamic Mode ◽  
Mode Decomposition ◽  
Transonic Buffet

AbstractThe buffet flow field around supercritical airfoils is dominated by self-sustained shock wave oscillations on the suction side of the wing. Theories assume that this unsteadiness is driven by a feedback loop of disturbances in the flow field downstream of the shock wave whose upstream propagating part is generated by acoustic waves. High-speed particle-image velocimetry measurements are performed to investigate this feedback loop in transonic buffet flow over a supercritical DRA 2303 airfoil. The freestream Mach number is $$M_{\infty } = 0.73$$ M ∞ = 0.73 , the angle of attack is $$\alpha = 3.5^{\circ }$$ α = 3 . 5 ∘ , and the chord-based Reynolds number is $${\mathrm{Re}}_{c} = 1.9\times 10^6$$ Re c = 1.9 × 10 6 . The obtained velocity fields are processed by sparsity-promoting dynamic mode decomposition to identify the dominant dynamic features contributing strongest to the buffet flow field. Two pronounced dynamic modes are found which confirm the presence of two main features of the proposed feedback loop. One mode is related to the shock wave oscillation frequency and its shape includes the movement of the shock wave and the coupled pulsation of the recirculation region downstream of the shock wave. The other pronounced mode represents the disturbances which form the downstream propagating part of the proposed feedback loop. The frequency of this mode corresponds to the frequency of the acoustic waves which are generated by these downstream traveling disturbances and which form the upstream propagating part of the proposed feedback loop. In this study, the post-processing, i.e., the DMD, is highlighted to substantiate the existence of this vortex mode. It is this vortex mode that via the Lamb vector excites the shock oscillations. The measurement data based DMD results confirm numerical findings, i.e., the dominant buffet and vortex modes are in good agreement with the feedback loop suggested by Lee. Graphic abstract

scholarly journals Analysis of V-Gutter Reacting Flow Dynamics Using Proper Orthogonal and Dynamic Mode Decompositions

Energies ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 4886 ◽  
Author(s):  
Yang Yang ◽  
Xiao Liu ◽  
Zhihao Zhang
Keyword(s):  
Shear Layer ◽  
Large Scale ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Reacting Flow ◽  
Eddy Simulation ◽  
Mode Decomposition ◽  
Wake Instability ◽  
Shedding Frequency ◽  
Proper Orthogonal

The current work is focused on investigating the potential of data-driven post-processing techniques, including proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) for flame dynamics. Large-eddy simulation (LES) of a V-gutter premixed flame was performed with two Reynolds numbers. The flame transfer function (FTF) was calculated. The POD and DMD were used for the analysis of the flame structures, wake shedding frequency, etc. The results acquired by different methods were also compared. The FTF results indicate that the flames have proportional, inertial, and delay components. The POD method could capture the shedding wake motion and shear layer motion. The excited DMD modes corresponded to the shear layer flames’ swing and convect motions in certain directions. Both POD and DMD could help to identify the wake shedding frequency. However, this large-scale flame oscillation is not presented in the FTF results. The negative growth rates of the decomposed mode confirm that the shear layer stabilized flame was more stable than the flame possessing a wake instability. The corresponding combustor design could be guided by the above results.

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