scholarly journals Dynamic reconstruction and data reconstruction for subsampled or irregularly sampled data

2017 ◽  
Vol 825 ◽  
pp. 133-166
Author(s):  
Jakub Krol ◽  
Andrew Wynn
Keyword(s):  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Decomposition Algorithms ◽  
Cylinder Wake ◽  
Sampled Data ◽  
Mode Decomposition ◽  
Image Velocimetry ◽  
Flow Evolution ◽  
Irregularly Sampled Data ◽  
Low Order

The Nyquist–Shannon criterion indicates the sample rate necessary to identify information with particular frequency content from a dynamical system. However, in experimental applications such as the interrogation of a flow field using particle image velocimetry (PIV), it may be impracticable or expensive to obtain data at the desired temporal resolution. To address this problem, we propose a new approach to identify temporal information from undersampled data, using ideas from modal decomposition algorithms such as dynamic mode decomposition (DMD) and optimal mode decomposition (OMD). The novel method takes a vector-valued signal, such as an ensemble of PIV snapshots, sampled at random time instances (but at sub-Nyquist rate) and projects onto a low-order subspace. Subsequently, dynamical characteristics, such as frequencies and growth rates, are approximated by iteratively approximating the flow evolution by a low-order model and solving a certain convex optimisation problem. The methodology is demonstrated on three dynamical systems, a synthetic sinusoid, the cylinder wake at Reynolds number $Re=60$ and turbulent flow past the axisymmetric bullet-shaped body. In all cases the algorithm correctly identifies the characteristic frequencies and oscillatory structures present in the flow.

A new combination of Hankel and sparsity-promoting dynamic mode decompositions and its application to the prediction of plasma turbulence

2021 ◽  
Vol 61 (SA) ◽  
pp. SA1011
Author(s):  
Akira Kusaba ◽  
Tetsuji Kuboyama ◽  
Kilho Shin ◽  
Makoto Sasaki ◽  
Shigeru Inagaki
Keyword(s):  
Predictive Performance ◽  
Underlying Mechanism ◽  
Plasma Turbulence ◽  
Training Data ◽  
Dynamic Mode Decomposition ◽  
New Combination ◽  
Dynamic Mode ◽  
Decomposition Algorithms ◽  
Applied Physics ◽  
Mode Decomposition

Abstract A new combined use of dynamic mode decomposition algorithms is proposed, which is suitable for the analysis of spatiotemporal data from experiments with few observation points, unlike computational fluid dynamics with many observation points. The method was applied to our data from a plasma turbulence experiment. As a result, we succeeded in constructing a quite accurate model for our training data and it made progress in predictive performance as well. In addition, modal patterns from the longer-term analysis help to understand the underlying mechanism more clearly, which is demonstrated in the case of plasma streamer structure. This method is expected to be a powerful tool for the data-driven construction of a reduced-order model and a predictor in plasma turbulence research and also any nonlinear dynamics researches of other applied physics fields.

scholarly journals Recursive dynamic mode decomposition of transient and post-transient wake flows

2016 ◽  
Vol 809 ◽  
pp. 843-872 ◽  
Author(s):  
Bernd R. Noack ◽  
Witold Stankiewicz ◽  
Marek Morzyński ◽  
Peter J. Schmid
Keyword(s):  
Dynamic Mode Decomposition ◽  
Attractive Alternative ◽  
Dynamic Mode ◽  
Cylinder Wake ◽  
Frequency Content ◽  
Mode Decomposition ◽  
Nonlinear Transient ◽  
Galerkin Models ◽  
Nonlinear Transient Dynamics ◽  
Proper Orthogonal

A novel data-driven modal decomposition of fluid flow is proposed, comprising key features of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). The first mode is the normalized real or imaginary part of the DMD mode that minimizes the time-averaged residual. The $N$th mode is defined recursively in an analogous manner based on the residual of an expansion using the first $N-1$ modes. The resulting recursive DMD (RDMD) modes are orthogonal by construction, retain pure frequency content and aim at low residual. Recursive DMD is applied to transient cylinder wake data and is benchmarked against POD and optimized DMD (Chen et al., J. Nonlinear Sci., vol. 22, 2012, pp. 887–915) for the same snapshot sequence. Unlike POD modes, RDMD structures are shown to have purer frequency content while retaining a residual of comparable order to POD. In contrast to DMD, with exponentially growing or decaying oscillatory amplitudes, RDMD clearly identifies initial, maximum and final fluctuation levels. Intriguingly, RDMD outperforms both POD and DMD in the limit-cycle resolution from the same snapshots. Robustness of these observations is demonstrated for other parameters of the cylinder wake and for a more complex wake behind three rotating cylinders. Recursive DMD is proposed as an attractive alternative to POD and DMD for empirical Galerkin models, in particular for nonlinear transient dynamics.

scholarly journals Dynamic mode decomposition of inertial particle caustics in Taylor–Green flow

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Omstavan Samant ◽  
Jaya Kumar Alageshan ◽  
Sarveshwar Sharma ◽  
Animesh Kuley
Keyword(s):  
Turbulent Flows ◽  
Particle Image ◽  
Experimental System ◽  
Stokes Number ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Complex Structures ◽  
Inertial Particles ◽  
Mode Decomposition ◽  
Image Velocimetry

AbstractInertial particles advected by a background flow can show complex structures. We consider inertial particles in a 2D Taylor–Green (TG) flow and characterize particle dynamics as a function of the particle’s Stokes number using dynamic mode decomposition (DMD) method from particle image velocimetry (PIV) like-data. We observe the formation of caustic structures and analyze them using DMD to (a) determine the Stokes number of the particles, and (b) estimate the particle Stokes number composition. Our analysis in this idealized flow will provide useful insight to analyze inertial particles in more complex or turbulent flows. We propose that the DMD technique can be used to perform similar analysis on an experimental system.

Experimental Investigation of Coherent Structure Dynamics in a Submerged Forced Jet

2013 ◽  
Vol 8 (1) ◽  
pp. 56-64
Author(s):  
Sergey Abdurakipov ◽  
Vladimir Dulin ◽  
Dmitriy Markovich
Keyword(s):  
Coherent Structures ◽  
Vortex Formation ◽  
Velocity Fields ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Analysis Tool ◽  
Modulation Amplitude ◽  
Mode Decomposition ◽  
Image Velocimetry ◽  
Statistical Analysis Tool

The present work investigates the dynamics of coherent structures, including their scales and intensity, in an initial region of a submerged round forced jet by a Particle Image Velocimetry (PIV) technique for measurements of instantaneous velocity fields and statistical analysis tool Dynamic Mode Decomposition (DMD). The PIV measurements were carried out with 1,1 kHz acquisition rate. Application of DMD to the measured set of the velocity fields provided information about dominant frequencies, contained in DMD spectrum, of velocity fluctuations in different flow regions and about scales of the corresponding spatial coherent structures, contained in DMD modes. Additional calculations of time-spectra from turbulent fluctuations showed good agreement between frequencies of the main harmonics and characteristic frequencies of the dominant dynamic modes. Superposition of relevant DMD modes approximately described nonlinear interaction of coherent structures: vortex formation, their quasi-periodic pairing with modulation amplitude of generated harmonics

Application of Dynamic Mode Decomposition to Study Temporal Flow Behavior in a Saccular Aneurysm

2021 ◽  
Author(s):  
Paulo Yu ◽  
Vibhav Durgesh
Keyword(s):  
Flow Behavior ◽  
Frame Rate ◽  
Dynamic Mode Decomposition ◽  
Mode Shapes ◽  
Dynamic Mode ◽  
Mode Decomposition ◽  
The Impact ◽  
Temporal Flow ◽  
Inflow Conditions ◽  
Low Order

Abstract Aneurysms are abnormal expansion of weakened blood vessels which can cause mortality or long-term disability upon rupture. Several studies have shown that inflow conditions spatially and temporally influence aneurysm flow behavior. The objective of this investigation is to identify impact of inflow conditions on spatio-temporal flow behavior in an aneurysm using Dynamic Mode Decomposition (DMD). For this purpose, low-frame rate velocity field measurements are performed in an idealized aneurysm model using Particle Image Velocimetry (PIV). The inflow conditions are precisely controlled using a ViVitro SuperPump system where non-dimensional fluid parameters such as peak Reynolds number (Rep) and Womersely number (α) are varied from 50-270 and 2-5, respectively. The results show the ability of DMD to identify the spatial flow structures and their frequency content. Furthermore, DMD captured the impact of inflow conditions, and change in mode shapes, amplitudes, frequency, and growth rate information is observed. The DMD low-order flow reconstruction also showed the complex interplay of flow features for each inflow scenario. Furthermore, the low-order reconstruction results provided a mathematical description of the flow behavior in the aneurysm which captured the vortex formation, evolution, and convection in detail. These results indicated that the vortical structure behavior varied with the change in α while its strength and presence of secondary structures is influenced by the change in Rep.

scholarly journals Coherent Gene Assemblies: Example, Yeast Cell Division Cycle, CDC

2021 ◽  
Author(s):  
Lawrence Sirovich
Keyword(s):  
Gene Expression ◽  
Cell Division ◽  
Yeast Cell ◽  
Dimensional Space ◽  
Cell Division Cycle ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Sampled Data ◽  
Mode Decomposition ◽  
Mother And Daughter

A fresh approach to the dynamics of gene assemblies is presented. Central to the exposition are the concepts of: high value genes; correlated activity; and the orderly unfolding of gene dynamics; and especially dynamic mode decomposition, DMD, a remarkable new tool for dissecting dynamics. This program is carried out, in detail, for the Orlando et al yeast database (Orlando et al. 2008). It is shown that the yeast cell division cycle, CDC, requires no more than a six dimensional space, formed by three complex temporal modal pairs, each associated with characteristic aspects of the cell cycle: (1) A mother cell cohort that follows a fast clock; (2) A daughter cell cohort that follows a slower clock; (3) inherent gene expression, unrelated to the CDC. A derived set of sixty high-value genes serves as a model for the correlated unfolding of gene activity. Confirmation of our results comes from an independent database, and other considerations. The present analysis, leads naturally, to a Fourier description, for the sparsely sampled data. From this, resolved peak times of gene expression are obtained. This in turn leads to prediction of precise times of expression in the unfolding of the CDC genes. The activation of each gene appears as uncoupled dynamics from the mother and daughter cohorts, of different durations. These deliberations lead to detailed estimates of the fraction of mother and daughter cells, specific estimates of their maturation periods, and specific estimates of the number of genes in these cells. An algorithmic framework for yeast modeling is proposed, and based on the new analyses, a range of theoretical ideas and new experiments are suggested.

Koopman-mode decomposition of the cylinder wake

2013 ◽  
Vol 726 ◽  
pp. 596-623 ◽  
Author(s):  
Shervin Bagheri
Keyword(s):  
Dynamic Mode Decomposition ◽  
Nonlinear Flow ◽  
Single Frequency ◽  
Dynamic Mode ◽  
Cylinder Wake ◽  
Koopman Operator ◽  
Mode Decomposition ◽  
Analytical Construction ◽  
Vortex Shedding Frequency ◽  
Global Modes

AbstractThe Koopman operator provides a powerful way of analysing nonlinear flow dynamics using linear techniques. The operator defines how observables evolve in time along a nonlinear flow trajectory. In this paper, we perform a Koopman analysis of the first Hopf bifurcation of the flow past a circular cylinder. First, we decompose the flow into a sequence of Koopman modes, where each mode evolves in time with one single frequency/growth rate and amplitude/phase, corresponding to the complex eigenvalues and eigenfunctions of the Koopman operator, respectively. The analytical construction of these modes shows how the amplitudes and phases of nonlinear global modes oscillating with the vortex shedding frequency or its harmonics evolve as the flow develops and later sustains self-excited oscillations. Second, we compute the dynamic modes using the dynamic mode decomposition (DMD) algorithm, which fits a linear combination of exponential terms to a sequence of snapshots spaced equally in time. It is shown that under certain conditions the DMD algorithm approximates Koopman modes, and hence provides a viable method to decompose the flow into saturated and transient oscillatory modes. Finally, the relevance of the analysis to frequency selection, global modes and shift modes is discussed.

Sign in / Sign up

Export Citation Format

Share Document