Relevant bibliographies by topics / Dynamic Mode Decomposition (DMD)

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Academic literature on the topic 'Dynamic Mode Decomposition (DMD)'

Author: Grafiati
Published: 4 June 2021
Last updated: 29 January 2023

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Journal articles on the topic "Dynamic Mode Decomposition (DMD)"

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Kawashima, Takahiro, Hayaru Shouno, and Hideitsu Hino. "Bayesian Dynamic Mode Decomposition with Variational Matrix Factorization." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 9 (May 18, 2021): 8083–91. http://dx.doi.org/10.1609/aaai.v35i9.16985.

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Dynamic mode decomposition (DMD) and its extensions are data-driven methods that have substantially contributed to our understanding of dynamical systems. However, because DMD and most of its extensions are deterministic, it is difficult to treat probabilistic representations of parameters and predictions. In this work, we propose a novel formulation of a Bayesian DMD model. Our Bayesian DMD model is consistent with the procedure of standard DMD, which is to first determine the subspace of observations, and then compute the modes on that subspace. Variational matrix factorization makes it possible to realize a fully-Bayesian scheme of DMD. Moreover, we derive a Bayesian DMD model for incomplete data, which demonstrates the advantage of probabilistic modeling. Finally, both of nonlinear simulated and real-world datasets are used to illustrate the potential of the proposed method.
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Schmid, Peter J. "Dynamic Mode Decomposition and Its Variants." Annual Review of Fluid Mechanics 54, no. 1 (January 5, 2022): 225–54. http://dx.doi.org/10.1146/annurev-fluid-030121-015835.

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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.
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Schmid, Peter J. "Dynamic Mode Decomposition and Its Variants." Annual Review of Fluid Mechanics 54, no. 1 (January 5, 2022): 225–54. http://dx.doi.org/10.1146/annurev-fluid-030121-015835.

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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.
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Heiland, Jan, and Benjamin Unger. "Identification of Linear Time-Invariant Systems with Dynamic Mode Decomposition." Mathematics 10, no. 3 (January 28, 2022): 418. http://dx.doi.org/10.3390/math10030418.

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Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant under linear transformations in the image of the data matrix. If, in addition, the data are constructed from a linear time-invariant system, then we prove that DMD can recover the original dynamics under mild conditions. If the linear dynamics are discretized with the Runge–Kutta method, then we further classify the error of the DMD approximation and detail that for one-stage Runge–Kutta methods; even the continuous dynamics can be recovered with DMD. A numerical example illustrates the theoretical findings.
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Page, Jacob, and Rich R. Kerswell. "Koopman mode expansions between simple invariant solutions." Journal of Fluid Mechanics 879 (September 19, 2019): 1–27. http://dx.doi.org/10.1017/jfm.2019.686.

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A Koopman decomposition is a powerful method of analysis for fluid flows leading to an apparently linear description of nonlinear dynamics in which the flow is expressed as a superposition of fixed spatial structures with exponential time dependence. Attempting a Koopman decomposition is simple in practice due to a connection with dynamic mode decomposition (DMD). However, there are non-trivial requirements for the Koopman decomposition and DMD to overlap, which mean it is often difficult to establish whether the latter is truly approximating the former. Here, we focus on nonlinear systems containing multiple simple invariant solutions where it is unclear how to construct a consistent Koopman decomposition, or how DMD might be applied to locate these solutions. First, we derive a Koopman decomposition for a heteroclinic connection in a Stuart–Landau equation revealing two possible expansions. The expansions are centred about the two fixed points of the equation and extend beyond their linear subspaces before breaking down at a cross-over point in state space. Well-designed DMD can extract the two expansions provided that the time window does not contain this cross-over point. We then apply DMD to the Navier–Stokes equations near to a heteroclinic connection in low Reynolds number ($Re=O(100)$) plane Couette flow where there are multiple simple invariant solutions beyond the constant shear basic state. This reveals as many different Koopman decompositions as simple invariant solutions present and once more indicates the existence of cross-over points between the expansions in state space. Again, DMD can extract these expansions only if it does not include a cross-over point. Our results suggest that in a dynamical system possessing multiple simple invariant solutions, there are generically places in phase space – plausibly hypersurfaces delineating the boundary of a local Koopman expansion – across which the dynamics cannot be represented by a convergent Koopman expansion.
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Albidah, A. B., W. Brevis, V. Fedun, I. Ballai, D. B. Jess, M. Stangalini, J. Higham, and G. Verth. "Proper orthogonal and dynamic mode decomposition of sunspot data." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2190 (December 21, 2020): 20200181. http://dx.doi.org/10.1098/rsta.2020.0181.

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High-resolution solar observations show the complex structure of the magnetohydrodynamic (MHD) wave motion. We apply the techniques of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) to identify the dominant MHD wave modes in a sunspot using the intensity time series. The POD technique was used to find modes that are spatially orthogonal, whereas the DMD technique identifies temporal orthogonality. Here, we show that the combined POD and DMD approaches can successfully identify both sausage and kink modes in a sunspot umbra with an approximately circular cross-sectional shape. This article is part of the Theo Murphy meeting issue ‘High-resolution wave dynamics in the lower solar atmosphere’.
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Surasinghe, Sudam, and Erik M. Bollt. "Randomized Projection Learning Method for Dynamic Mode Decomposition." Mathematics 9, no. 21 (November 4, 2021): 2803. http://dx.doi.org/10.3390/math9212803.

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A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on a projected space. In the spirit of Johnson–Lindenstrauss lemma, we will use a random projection to estimate the DMD modes in a reduced dimensional space. In practical applications, snapshots are in a high-dimensional observable space and the DMD operator matrix is massive. Hence, computing DMD with the full spectrum is expensive, so our main computational goal is to estimate the eigenvalue and eigenvectors of the DMD operator in a projected domain. We generalize the current algorithm to estimate a projected DMD operator. We focus on a powerful and simple random projection algorithm that will reduce the computational and storage costs. While, clearly, a random projection simplifies the algorithmic complexity of a detailed optimal projection, as we will show, the results can generally be excellent, nonetheless, and the quality could be understood through a well-developed theory of random projections. We will demonstrate that modes could be calculated for a low cost by the projected data with sufficient dimension.
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Habibi, Milad, Scott T. M. Dawson, and Amirhossein Arzani. "Data-Driven Pulsatile Blood Flow Physics with Dynamic Mode Decomposition." Fluids 5, no. 3 (July 14, 2020): 111. http://dx.doi.org/10.3390/fluids5030111.

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Dynamic mode decomposition (DMD) is a purely data-driven and equation-free technique for reduced-order modeling of dynamical systems and fluid flow. DMD finds a best fit linear reduced-order model that represents any given spatiotemporal data. In DMD, each mode evolves with a fixed frequency and therefore DMD modes represent physically meaningful structures that are ranked based on their dynamics. The application of DMD to patient-specific cardiovascular flow data is challenging. First, the input flow rate is unsteady and pulsatile. Second, the flow topology can change significantly in different phases of the cardiac cycle. Finally, blood flow in patient-specific diseased arteries is complex and often chaotic. The objective of this study was to overcome these challenges using our proposed multistage dynamic mode decomposition with control (mDMDc) method and use this technique to study patient-specific blood flow physics. The inlet flow rate was considered as the controller input to the systems. Blood flow data were divided into different stages based on the inlet flow waveform and DMD with control was applied to each stage. The system was augmented to consider both velocity and wall shear stress (WSS) vector data, and therefore study the interaction between the coherent structures in velocity and near-wall coherent structures in WSS. First, it was shown that DMD modes can exactly represent the analytical Womersley solution for incompressible pulsatile flow in tubes. Next, our method was applied to image-based coronary artery stenosis and cerebral aneurysm models where complex blood flow patterns are anticipated. The flow patterns were studied using the mDMDc modes and the reconstruction errors were reported. Our augmented mDMDc framework could capture coherent structures in velocity and WSS with a fewer number of modes compared to the traditional DMD approach and demonstrated a close connection between the velocity and WSS modes.
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Bronstein, Emil, Aviad Wiegner, Doron Shilo, and Ronen Talmon. "The spatiotemporal coupling in delay-coordinates dynamic mode decomposition." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 12 (December 2022): 123127. http://dx.doi.org/10.1063/5.0123101.

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Dynamic mode decomposition (DMD) is a leading tool for equation-free analysis of high-dimensional dynamical systems from observations. In this work, we focus on a combination of DMD and delay-coordinates embedding, which is termed delay-coordinates DMD and is based on augmenting observations from current and past time steps, accommodating the analysis of a broad family of observations. An important utility of DMD is the compact and reduced-order spectral representation of observations in terms of the DMD eigenvalues and modes, where the temporal information is separated from the spatial information. From a spatiotemporal viewpoint, we show that when DMD is applied to delay-coordinates embedding, temporal information is intertwined with spatial information, inducing a particular spectral structure on the DMD components. We formulate and analyze this structure, which we term the spatiotemporal coupling in delay-coordinates DMD. Based on this spatiotemporal coupling, we propose a new method for DMD components selection. When using delay-coordinates DMD that comprises redundant modes, this selection is an essential step for obtaining a compact and reduced-order representation of the observations. We demonstrate our method on noisy simulated signals and various dynamical systems and show superior component selection compared to a commonly used method that relies on the amplitudes of the modes.
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Wynn, A., D. S. Pearson, B. Ganapathisubramani, and P. J. Goulart. "Optimal mode decomposition for unsteady flows." Journal of Fluid Mechanics 733 (September 24, 2013): 473–503. http://dx.doi.org/10.1017/jfm.2013.426.

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AbstractA new method, herein referred to as optimal mode decomposition (OMD), of finding a linear model to describe the evolution of a fluid flow is presented. The method estimates the linear dynamics of a high-dimensional system which is first projected onto a subspace of a user-defined fixed rank. An iterative procedure is used to find the optimal combination of linear model and subspace that minimizes the system residual error. The OMD method is shown to be a generalization of dynamic mode decomposition (DMD), in which the subspace is not optimized but rather fixed to be the proper orthogonal decomposition (POD) modes. Furthermore, OMD is shown to provide an approximation to the Koopman modes and eigenvalues of the underlying system. A comparison between OMD and DMD is made using both a synthetic waveform and an experimental data set. The OMD technique is shown to have lower residual errors than DMD and is shown on a synthetic waveform to provide more accurate estimates of the system eigenvalues. This new method can be used with experimental and numerical data to calculate the ‘optimal’ low-order model with a user-defined rank that best captures the system dynamics of unsteady and turbulent flows.
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Dissertations / Theses on the topic "Dynamic Mode Decomposition (DMD)"

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Quinlan, John Mathew. "Investigation of driving mechanisms of combustion instabilities in liquid rocket engines via the dynamic mode decomposition." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/54343.

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Combustion instability due to feedback coupling between unsteady heat release and natural acoustic modes can cause catastrophic failure in liquid rocket engines and to predict and prevent these instabilities the mechanisms that drive them must be further elucidated. With this goal in mind, the objective of this thesis was to develop techniques that improve the understanding of the specific underlying physical processes involved in these driving mechanisms. In particular, this work sought to develop a small-scale, optically accessible liquid rocket engine simulator and to apply modern, high-speed diagnostic techniques to characterize the reacting flow and acoustic field within the simulator. Specifically, high-speed (10 kHz), simultaneous data were acquired while the simulator was experiencing a 170 Hz combustion instability using particle image velocimetry, OH planar laser induced fluorescence, CH* chemiluminescence, and dynamic pressure measurements. In addition, this work sought to develop approaches to reduce the large quantities of data acquired, extracting key physical phenomena involved in the driving mechanisms. The initial data reduction approach was chosen based on the fact that the combustion instability problem is often simplified to the point that it can be characterized by an approximately linear constant coefficient system of equations. Consistent with this simplification, the experimental data were analyzed by the dynamic mode decomposition method. The developed approach to apply the dynamic mode decomposition to simultaneously acquired data located a coupled hydrodynamic/combustion/acoustic mode at 1017 Hz. On the other hand, the dynamic mode decomposition's assumed constant operator approach failed to locate any modes of interest near 170 Hz. This led to the development of two new data analysis techniques based on the dynamic mode decomposition and Floquet theory that assume that the experiment is governed by a linear, periodic system of equations. The new periodic-operator data analysis techniques, the Floquet decomposition and the ensemble Floquet decomposition, approximate, from experimental data, the largest moduli Floquet multipliers, which determine the stability of the periodic solution trajectory of the system. The unstable experiment dataset was analyzed with these techniques and the ensemble Floquet decomposition analysis found a large modulus Floquet multiplier and associated mode with a frequency of 169.6 Hz. Furthermore, the approximate Rayleigh criterion indicated that this mode was unstable with respect to combustion instability. Overall, based on the positive finding that the ensemble Floquet decomposition was able to locate an unstable combustion mode at 170 Hz when the operator's time period was set to 1 ms, suggests that the dynamic mode decomposition based 1017 Hz mode parametrically forces the 170 Hz mode, resulting in what could be characterized as a parametric combustion instability.
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Waindim, Mbu. "On Unsteadiness in 2-D and 3-D Shock Wave/Turbulent Boundary Layer Interactions." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1511734224701396.

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Renaud, Antoine. "Étude de la stabilisation des flammes et des comportements transitoires dans un brûleur étagé à combustible liquide à l'aide de diagnostics rapides." Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLC003/document.

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La combustion prévaporisée prémélangée pauvre est une piste de choix pour réduire les émissions polluantes des moteurs d'avions mais peut conduire à l'apparition d'instabilités thermo-acoustiques. Afin d'améliorer la stabilité de telles flammes, l'étagement du combustible consiste à contrôler la distribution spatiale du carburant. Une telle procédure s'accompagne cependant d'une complexité accrue du système pouvant déboucher sur des phénomènes inattendus.Un brûleur à l'échelle de laboratoire alimenté par du dodécane liquide est utilisé dans cette thèse. Le combustible est injecté dans deux étages séparés, permettant ainsi de contrôler sa distribution. Cette particularité permet l'observation de différentes formes de flammes et notamment de points bistables pour lesquels deux flammes différentes peuvent exister malgré des conditions opératoires identiques.L'utilisation de diagnostics optiques à haute cadence (diffusion de Mie des gouttes de combustible et émission spontanée de la flamme) est couplée à des méthodes de post-traitement avancées comme la Décomposition en Modes Dynamiques. Ainsi, des mécanismes pilotant la stabilisation des flammes ainsi que leurs changements de forme sont proposés. Ils mettent notamment en lumière les interactions entre l'écoulement gazeux, les gouttes de combustible et la flamme
A promising way to reduce jet engines pollutant emissions is the use of lean premixed prevaporized combustion but it tends to trigger thermo-acoustic instabilities. To improve the stability of these flames, a procedure called staging consists in splitting the fuel injection to control its spatial distribution. This however leads to an increased complexity and unexpected phenomena can occur.In the present work, a model gas turbine combustor fed with liquid dodecane is used. It is equipped with two fuel injection stages to control the fuel distribution in the burner. Different flame stabilizations can be observed and a bistable case where two flame shapes can exist for the same operating conditions is highlighted.High-speed optical diagnostics (fuel droplets Mie scatering and chemiluminescence measurements) are coupled with advanced post-processing methods like Dynamic Mode Decomposition. The results enable to propose mechanisms leading to flame stabilization and flame shape transitions. They show a strong interplay between the gaseous flow, the fuel droplets and the flame itself
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Guéniat, Florimond. "Détection de structures cohérentes dans des écoulements fluides et interfaces homme-machine pour l'exploration et la visualisation interactive de données scientifiques." Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00947413.

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Depuis l'identification par Brown \& Roshko, en 1974, de structures jouant un rôle majeur dans le mélange d'un écoulement turbulent, la recherche de structures cohérentes a été un des principaux axes d'étude en mécanique des fluides.Les travaux présentés dans ce manuscrit s'inscrivent dans cette voie.La première partie du manuscrit traite ainsi de l'identification de structures cohérentes. Elle se compose de trois chapitres abordant deux techniques d'identification. La Décomposition en mode dynamique (DMD), ainsi que des variantes généralisant son champ applicatif est présenté dans le premier chapitre. Cette méthode propose une représentation par modes spatiaux et temporels d'un ensemble de données. Une méthode pour la sélection de composantes particulièrement représentatives de la dynamique, i.e. présentant de bonnes qualités d'observabilité, se basant sur cette décomposition est également décrite dans ce chapitre.Le deuxième chapitre traite de la détection de structures cohérentes lagrangienne, par suivi de particules. Ces structures permettent d'identifier les frontières matérielles et apportent des éclaircissements sur les mécanismes du mélange au sein de l'écoulement considéré.Ces méthodes sont appliquées, dans le chapitre trois, au cas d'un écoulement incompressible affleurant une cavité ouverte.La seconde partie du manuscrit traite des questions de représentation et discrimination de données scientifiques.Une réponse à la question de la représentation de structures cohérentes a été la mise en place d'outils permettant la visualisation interactive de jeux de données scientifiques, qui dont la présentation fait l'objet du chapitre quatre. En particulier, l'utilisation d'objets tangibles, représentant les données dans le monde réel, permet une exploration plus efficace des ensembles de volumétriques de données scientifiques. La question d'une perception et discrimination efficace de données représentées, e.g. la différentiation entre deux valeurs proches, est abordée dans le cinquième chapitre.
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André, Thierry. "Contrôle actif de la transition laminaire-turbulent en écoulement hypersonique." Thesis, Orléans, 2016. http://www.theses.fr/2016ORLE2022/document.

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Lors d’un vol hypersonique (Mach 6, 20 km d’altitude) la couche limite se développant sur l’avant-corps d’un véhicule hypersonique est laminaire. Cet état cause un désamorçage du moteur (statoréacteur) assurant la propulsion du véhicule. Pour pallier ce problème, il faut forcer la transition de la couche limite á l’aide d’un dispositif de contrôle dont l’effet est permanent (passif) ou modulable (actif) pendant le vol. Dans ce travail, nous analysons l’efficacité d’un dispositif actif d’injection d’air á la paroi pour forcer la transition de la couche limite sur un avant-corps générique. L’interaction jet d’air/couche limite est simulée numériquement avec une approche aux grandes échelles (LES). Une étude paramétrique sur la pression d’injection permet de quantifier l’efficacité du jet á déstabiliser la couche limite. L’influence des conditions de vol (altitude, Mach) sur la transition est également étudiée. Une analyse des résultats de simulation par Décomposition en Modes Dynamiques (DMD) est menée pour comprendre quels sont les modes dynamiques responsables de la transition et les mécanismes sous-jacents. Des essais dans la soufflerie silencieuse de l’université de Purdue (BAM6QT) ont été effectués pour tester expérimentalement l’efficacité des dispositifs passifs (rugosité isolée en forme de losange) et actifs (mono-injection d’air) pour faire transitionner la couche limite. Une peinture thermo-sensible et des capteurs de pression (PCB, Kulite) ont été utilisés pour déterminer la nature de la couche limite. Les résultats de ce travail montrent qu’une injection sonique suffit pour forcer la couche limite. On observe des essais, que pour une même hauteur de pénétration, les rugosités isolées sont moins efficaces que les jets (mono injection) pour déstabiliser la couche limite
During a hypersonic flight (Mach 6, 20 km altitude), the boundary layer developing on the forebody of a vehicle is laminar. This state may destabilize the scramjet engine propelling the vehicle. To overcome this problem during the flight, the boundary layer transition has to be forced using a control device whose effect is fixed (passive) or adjustable (active). In this work, we analyze the efficiency of a jet in crossflow in forcing the boundary layer transition on a generic forebody. The flow is computed with a Large Eddy Simulations (LES) approach. A parametric study of the injection pressure allows the efficiency of the jet in tripping the boundary layer to be quantified. The influence of flight conditions (Mach, altitude) on the transition is also studied. Dynamic Mode Decomposition (DMD) is applied to the simulation results to determine the transition leading to dynamic modes and to understand underlying transition mechanisms. Experiments in the Purdue University quiet wind tunnel (BAM6QT) were performed to quantify the efficiency of a passive transition device (diamond roughnesses) and an active transition device (single air jet) in tripping the boundary layer. A thermo-sensitive paint and pressure transducers (Kulite, PCB) were used to determine the state of the boundary layer on the generic forebody. Experimental and numerical results show a sonic injection is sufficient to induce transition. We observe from the experiments that for the same penetration height, a single roughness is less efficient than a single air jet in destabilizing the boundary layer
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Tirunagari, Santosh. "Dynamic mode decomposition for computer vision and signal processing." Thesis, University of Surrey, 2017. http://epubs.surrey.ac.uk/813255/.

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The method of Dynamic Mode Decomposition (DMD) was introduced originally in the area of Computatational Fluid Dynamics (CFD) for extracting coherent structures from spatio-temporal complex fluid flow data. DMD takes in time series data and computes a set of modes, each of which is associated with a complex eigenvalue. DMD analysis is closely associated with spectral analysis of the Koopman operator, which provides linear but infinite-dimensional representation of nonlinear dynamical systems. Therefore, by using DMD a nonlinear system could be described by a superposition of modes whose dynamics are governed by the eigenvalues. The key advantage of DMD is its data-driven nature which does not rely on any prior assumptions except the inherent dynamics which are observed over time. Its capability for extracting relevant modes from complex fluid flows has seen significant application across multiple fields, including computer vision, robotics and neuroscience. This thesis, in order to expand DMD to other applications, advances the original formulation so that it can be used to solve novel problems in the fields of signal processing and computer vision. In signal processing this thesis introduces the method of using DMD for decomposing a univariate time series into a number of interpretable elements with different subspaces, such as noise, trends and harmonics. In addition, univariate time series forecasting is shown using DMD. The computer vision part of this thesis focuses on innovative applications pertaining to the areas of medical imaging, biometrics and background modelling. In the area of medical imaging a novel DMD framework is proposed that introduces windowed and reconstruction variants of DMD for quantifying kidney function in Dynamic Contrast Enhanced Magnetic Resonance imaging (DCE-MRI) sequences, through movement correction and functional segmentation of the kidneys. The biometrics portion of this thesis introduces a DMD based classification pipeline for counter spoofing 2D facial videos and static finger vein images. The finger vein counter spoofing makes use of a novel atemporal variant of DMD that captures micro-level artefacts that can differentiate the quality and light reflection properties between a live and a spoofed finger vein image, while the DMD on 2D facial image sequences distinguishes attack specific cues from a live face by capturing complex dynamics of head movements, eye-blinking and lip-movements in a data driven manner. Finally, this thesis proposes a new technique using DMD to obtain a background model of a visual scene in the colour domain. These aspects form the major contributions of this thesis. The results from this thesis present DMD as a promising approach for applications requiring feature extraction including: (i) trends and noise from signals, (ii) micro-level texture descriptor from images, and (iii) coherent structures from image sequences/videos, as well as applications that require suppression of movements from dynamical spatio-temporal image sequences.
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McLean, Jayse Clifton. "Modal Analysis of the Human Brain Using Dynamic Mode Decomposition." Thesis, North Dakota State University, 2020. https://hdl.handle.net/10365/31804.

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The human brain is the most important organ of the human body. It controls our thoughts, movements and emotions. For that reason, protecting the brain from harm is of the utmost importance but to protect the brain, one must first understand brain injuries. Currently, observations and criteria involving brain injury are focused around acceleration and forces. However, the brain is poorly understood in the frequency domain. This study uses finite element analysis to simulate impact for 5 different impact angles. Then a numerical technique called dynamic mode decomposition is used to extract modal properties for brain tissue in regions near the corpus callosum and brain stem. Three modal frequencies were identified with frequency ranges of (44-68) Hz, (68-155) Hz, and (114-299) Hz. Additionally, it was observed that impact angle, displacement direction, and region of the brain have a significant impact on the modal response of brain tissue during impact.
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Zigic, Jovan. "Optimization Methods for Dynamic Mode Decomposition of Nonlinear Partial Differential Equations." Thesis, Virginia Tech, 2021. http://hdl.handle.net/10919/103862.

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Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations. Naturally, reduced-order modeling techniques come at the price of either computational accuracy or computation time. Optimization techniques are studied to improve either or both of these objectives and decrease the total computational cost of the problem. This thesis focuses on the dynamic mode decomposition (DMD) applied to nonlinear PDEs with periodic boundary conditions. It provides one study of an existing optimization framework for the DMD method known as the Optimized DMD and provides another study of a newly proposed optimization framework for the DMD method called the Split DMD.
Master of Science
The Navier-Stokes (NS) equations are the primary mathematical model for understanding the behavior of fluids. The existence and smoothness of the NS equations is considered to be one of the most important open problems in mathematics, and challenges in their numerical simulation is a barrier to understanding the physical phenomenon of turbulence. Due to the difficulty of studying this problem directly, simpler problems in the form of nonlinear partial differential equations (PDEs) that exhibit similar properties to the NS equations are studied as preliminary steps towards building a wider understanding of the field. Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations. Naturally, reduced-order modeling techniques come at the price of either computational accuracy or computation time. Optimization techniques are studied to improve either or both of these objectives and decrease the total computational cost of the problem. This thesis focuses on the dynamic mode decomposition (DMD) applied to nonlinear PDEs with periodic boundary conditions. It provides one study of an existing optimization framework for the DMD method known as the Optimized DMD and provides another study of a newly proposed optimization framework for the DMD method called the Split DMD.
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Fahlaoui, Tarik. "Réduction de modèles et apprentissage de solutions spatio-temporelles paramétrées à partir de données : application à des couplages EDP-EDO." Thesis, Compiègne, 2020. http://www.theses.fr/2020COMP2535.

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On s’intéresse dans cette thèse à l’apprentissage d’un modèle réduit précis et stable, à partir de données correspondant à la solution d’une équation aux dérivées partielles (EDP), et générées par un solveur haute fidélité (HF). Pour ce faire, on utilise la méthode Dynamic Mode Decomposition (DMD) ainsi que la méthode de réduction Proper Orthogonal Decomposition (POD). Le modèle réduit appris est facilement interprétable, et par une analyse spectrale a posteriori de ce modèle on peut détecter les anomalies lors de la phase d’apprentissage. Les extensions au cas de couplage EDP-EDO, ainsi qu’au cas d’EDP d’ordre deux en temps sont présentées. L’apprentissage d’un modèle réduit dans le cas d’un système dynamique contrôlé par commutation, où la règle de contrôle est apprise à l’aide d’un réseau de neurones artificiel (ANN), est également traité. Un inconvénient de la réduction POD, est la difficile interprétation de la représentation basse dimension. On proposera alors l’utilisation de la méthode Empirical Interpolation Method (EIM). La représentation basse dimension est alors intelligible, et consiste en une restriction de la solution en des points sélectionnés. Cette approche sera ensuite étendue au cas d’EDP dépendant d’un paramètre, et où l’algorithme Kernel Ridge Regression (KRR) nous permettra d’apprendre la variété solution. Ainsi, on présentera l’apprentissage d’un modèle réduit paramétré. L’extension au cas de données bruitées ou bien au cas d’EDP d’évolution non linéaire est présentée en ouverture
In this thesis, an algorithm for learning an accurate reduced order model from data generated by a high fidelity solver (HF solver) is proposed. To achieve this goal, we use both Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD). Anomaly detection, during the learning process, can be easily done by performing an a posteriori spectral analysis on the reduced order model learnt. Several extensions are presented to make the method as general as possible. Thus, we handle the case of coupled ODE/PDE systems or the case of second order hyperbolic equations. The method is also extended to the case of switched control systems, where the switching rule is learnt by using an Artificial Neural Network (ANN). The reduced order model learnt allows to predict time evolution of the POD coefficients. However, the POD coefficients have no interpretable meaning. To tackle this issue, we propose an interpretable reduction method using the Empirical Interpolation Method (EIM). This reduction method is then adapted to the case of third-order tensors, and combining with the Kernel Ridge Regression (KRR) we can learn the solution manifold in the case of parametrized PDEs. In this way, we can learn a parametrized reduced order model. The case of non-linear PDEs or disturbed data is finally presented in the opening
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Hall, Brenton Taylor. "Using the Non-Uniform Dynamic Mode Decomposition to Reduce the Storage Required for PDE Simulations." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1492711382801134.

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Books on the topic "Dynamic Mode Decomposition (DMD)"

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Vega, Jose Manuel, and Soledad Le Clainche. Higher Order Dynamic Mode Decomposition and Its Applications. Elsevier Science & Technology Books, 2020.

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Vega, Jose Manuel, and Soledad Le Clainche. Higher Order Dynamic Mode Decomposition and Its Applications. Elsevier Science & Technology, 2020.

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Higher Order Dynamic Mode Decomposition and Its Applications. Elsevier, 2021. http://dx.doi.org/10.1016/c2019-0-00038-6.

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Kutz, J. Nathan, Steven L. Brunton, Bingni W. Brunton, and Joshua L. Proctor. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems. SIAM-Society for Industrial and Applied Mathematics, 2016.

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Book chapters on the topic "Dynamic Mode Decomposition (DMD)"

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Li, Long, Etienne Mémin, and Gilles Tissot. "Stochastic Parameterization with Dynamic Mode Decomposition." In Mathematics of Planet Earth, 179–93. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-18988-3_11.

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AbstractA physical stochastic parameterization is adopted in this work to account for the effects of the unresolved small-scale on the large-scale flow dynamics. This random model is based on a stochastic transport principle, which ensures a strong energy conservation. The dynamic mode decomposition (DMD) is performed on high-resolution data to learn a basis of the unresolved velocity field, on which the stochastic transport velocity is expressed. Time-harmonic property of DMD modes allows us to perform a clean separation between time-differentiable and time-decorrelated components. Such random scheme is assessed on a quasi-geostrophic (QG) model.
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Kern, Moritz, Christian Uhl, and Monika Warmuth. "A Comparative Study of Dynamic Mode Decomposition (DMD) and Dynamical Component Analysis (DyCA)." In Lecture Notes in Electrical Engineering, 93–103. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-58653-9_9.

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Loosen, Simon, Matthias Meinke, and Wolfgang Schröder. "Numerical Analysis of the Turbulent Wake for a Generic Space Launcher with a Dual-Bell Nozzle." In Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 163–77. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53847-7_10.

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Abstract The turbulent wake of an axisymmetric generic space launcher equipped with a dual-bell nozzle is simulated at transonic ($$Ma_\infty = 0.8$$ and $$Re_D = 4.3\cdot 10^5$$) and supersonic ($$Ma_\infty = 3$$ and $$Re_D = 1.2\cdot 10^6$$) freestream conditions, to investigate the influence of the dual-bell nozzle jet onto the wake flow and vice versa. In addition, flow control by means of four in circumferential direction equally distributed jets injecting air encountering the backflow in the recirculation region is utilized to determine if the coherence of the wake and consequently, the buffet loads can be reduced by flow control. The simulations are performed using a zonal RANS/LES approach. The time-resolved flow field data are analyzed by classical spectral analysis, two-point correlation analysis, and dynamic mode decomposition (DMD). At supersonic freestream conditions, the nozzle counter pressure is reduced by the expansion of the outer flow around the nozzle lip leading to a decreased transition nozzle pressure ratio. In the transonic configuration a spatio-temporal mode with an eigenvalue matching the characteristic buffet frequency of $$Sr_D=0.2$$ is extracted by the spectral and DMD analysis. The spatial shape of the detected mode describes an antisymmetric wave-like undulating motion of the shear layer inducing the low frequency dynamic buffet loads. By flow control this antisymmetric coherent motion is weakened leading to a reduction of the buffet loads on the nozzle fairing.
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Drmač, Zlatko. "Dynamic Mode Decomposition—A Numerical Linear Algebra Perspective." In Lecture Notes in Control and Information Sciences, 161–94. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-35713-9_7.

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Tan, Weiwei, Junqiang Bai, Zengdong Tian, and Li Li. "Parallel Dynamic Mode Decomposition for Rayleigh–Taylor Instability Flows." In Lecture Notes in Electrical Engineering, 800–815. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-3305-7_63.

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Baldia, Antonio, Sébastien Equis, and Pierre Jacquot. "Phase Extraction in Dynamic Speckle Interferometry by Empirical Mode Decomposition." In Experimental Analysis of Nano and Engineering Materials and Structures, 719–20. Dordrecht: Springer Netherlands, 2007. http://dx.doi.org/10.1007/978-1-4020-6239-1_357.

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Akshay, S., K. P. Soman, Neethu Mohan, and S. Sachin Kumar. "Dynamic Mode Decomposition and Its Application in Various Domains: An Overview." In EAI/Springer Innovations in Communication and Computing, 121–32. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-35280-6_6.

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Gosea, Ion Victor, and Igor Pontes Duff. "Toward Fitting Structured Nonlinear Systems by Means of Dynamic Mode Decomposition." In Model Reduction of Complex Dynamical Systems, 53–74. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72983-7_3.

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Grenga, T., and M. E. Mueller. "Dynamic Mode Decomposition: A Tool to Extract Structures Hidden in Massive Datasets." In Data Analysis for Direct Numerical Simulations of Turbulent Combustion, 157–76. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44718-2_8.

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Yuan, Ye, Yongzhong Wang, and Zheng Wu. "Research on Dynamic Reaction of Gaseous Formaldehyde Detector Using Empirical Mode Decomposition." In Proceedings of the 2012 International Conference on Cybernetics and Informatics, 1737–44. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-3872-4_222.

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Conference papers on the topic "Dynamic Mode Decomposition (DMD)"

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Takeishi, Naoya, Yoshinobu Kawahara, Yasuo Tabei, and Takehisa Yairi. "Bayesian Dynamic Mode Decomposition." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/392.

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Dynamic mode decomposition (DMD) is a data-driven method for calculating a modal representation of a nonlinear dynamical system, and it has been utilized in various fields of science and engineering. In this paper, we propose Bayesian DMD, which provides a principled way to transfer the advantages of the Bayesian formulation into DMD. To this end, we first develop a probabilistic model corresponding to DMD, and then, provide the Gibbs sampler for the posterior inference in Bayesian DMD. Moreover, as a specific example, we discuss the case of using a sparsity-promoting prior for an automatic determination of the number of dynamic modes. We investigate the empirical performance of Bayesian DMD using synthetic and real-world datasets.
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Bohon, Myles, Richard Bluemner, Alessandro Orchini, Christian O. Paschereit, and Ephraim J. Gutmark. "Analysis of RDC operation by Dynamic Mode Decomposition (DMD)." In AIAA Propulsion and Energy 2019 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2019. http://dx.doi.org/10.2514/6.2019-4377.

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NEDZHIBOV, GYURHAN. "A NEW ALGORITHM FOR DYNAMIC MODE DECOMPOSITION." In INTERNATIONAL SCIENTIFIC CONFERENCE MATHTECH 2022. Konstantin Preslavsky University Press, 2022. http://dx.doi.org/10.46687/omem4329.

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Dynamic mode decomposition (DMD) is a data-driven mathematical technique to extract spectral information from complex data coming from numerical or experimental studies of various systems. It is an equation-free method in the sense that it does not require knowledge of the underlying governing equations. In this article we explore and demonstrate a new algorithm for calculating the DMD decomposition.
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Valášek, Jan, and Petr Sváček. "Dynamic Mode Decompositions of Phonation Onset – Comparison of Different Methods." In Topical Problems of Fluid Mechanics 2022. Institute of Thermomechanics of the Czech Academy of Sciences, 2022. http://dx.doi.org/10.14311/tpfm.2022.024.

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Four dynamic mode decomposition (DMD) methods are used to analyze a simulation of the phonation onset carried out by in-house solver based on the nite element method. The dataset consists of several last periods of the flow-induced vibrations of vocal folds (VFs). The DMD is a data-driven and model-free method typically used for finding a low-rank representation of a high-dimensional system. In general, the DMD decomposes a given dataset to modes with mono-frequency content and associated complex eigenvalues providing the growth/decay rate that allows a favourable physical interpretation and in some cases also a short-term prediction of system behaviour. The disadvantages of the standard DMD are non-orthogonal modes and sensitivity to an increased noise level which are addressed by following DMD variants. The recursive DMD (rDMD) is an iterative DMD decomposition producing orthogonal modes. The total least-square DMD and the higher order DMD (hoDMD) are methods substantially reducing a high DMD sensitivity to noise. All methods identi ed very similar DMD modes as well as frequency spectra. Substantial difference was found in the real part of the spectra. The nal dataset reconstruction is the most accurate in the case of the recursive variant. The higher order DMD method also outperforms the standard DMD. Thus the rDMD and the hoDMD decompositions are promising to be used further for the parametrization of a VF motion.
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Pavalavanni, Pradeep K., Jaehoon Ryu, and JeongYeol Choi. "Dynamic Mode Decomposition (DMD) Analysis of the Detonation Cell-Bifurcation Process." In AIAA Propulsion and Energy 2021 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2021. http://dx.doi.org/10.2514/6.2021-3680.

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Saito, Akira. "Model Order Reduction for a Piecewise Linear System Based on Dynamic Mode Decomposition." In ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/detc2021-70764.

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Abstract This paper presents a data-driven model order reduction strategy for nonlinear systems based on dynamic mode decomposition (DMD). First, the theory of DMD is briefly reviewed and its extension to model order reduction of nonlinear systems based on Galerkin projection is introduced. The proposed method utilizes impulse response of the nonlinear system to obtain snapshots of the state variables, and extracts dynamic modes that are then used for the projection basis vectors. The equations of motion of the system can then be projected onto the subspace spanned by the basis vectors, which produces the projected governing equations with much smaller number of degrees of freedom (DOFs). The method is applied to the construction of the reduced order model (ROM) of a finite element model (FEM) of a cantilevered beam subjected to a piecewise-linear boundary condition. First, impulse response analysis of the beam is conducted to obtain the snapshot matrix of the nodal displacements. The DMD is then applied to extract the DMD modes and eigenvalues. The extracted DMD mode shapes can be used to form a reduction basis for the Galerkin projection of the equation of motion. The obtained ROM has been used to conduct the forced response calculation of the beam subjected to the piecewise linear boundary condition. The results obtained by the ROM agree well with that obtained by the full-order FEM model.
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Rajasegar, Rajavasanth, Jeongan Choi, Shruti Ghanekar, Constandinos M. Mitsingas, Eric Mayhew, Qili Liu, Jihyung Yoo, and Tonghun Lee. "Extended Proper Orthogonal Decomposition (EPOD) and Dynamic Mode Decomposition (DMD) for Analysis of Mesoscale Burner Array Flame Dynamics." In 2018 AIAA Aerospace Sciences Meeting. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2018. http://dx.doi.org/10.2514/6.2018-0147.

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Kiewat, Marco, Lukas Haag, Thomas Indinger, and Vincent Zander. "Low-Memory Reduced-Order Modelling With Dynamic Mode Decomposition Applied on Unsteady Wheel Aerodynamics." In ASME 2017 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/fedsm2017-69299.

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Wheel aerodynamics has a major impact on the overall aerodynamic performance of a vehicle. Different vortex excitation mechanisms are responsible for the induced forces on the geometry. Due to the high degree of complexity, it is difficult to gain further insight into the vortex structures at the rotating wheel. Therefore, wheel aerodynamics is usually investigated using temporally averaged flow fields. This work presents an approach to apply a recently introduced low-memory variant of Dynamic Mode Decomposition (DMD), namely Streaming Total DMD (STDMD), to investigate temporally resolved simulations in greater detail. The performance of STDMD is shown to be comparable to conventional DMD for a rotating generic closed wheel simulation test case. By creating a Reduced-Order Model (ROM) using a comparably small amount of DMD modes, the amount of complexity in the flow field can be drastically reduced. Orthonormal basis compression, amplitude ordering and a newly introduced amplitude weighting method are analyzed for creating a suitable ROM of DMD modes. A combination of compression and ordering by eigenvalue-weighted amplitude is concluded to be best suited and applied to the Delayed Detached Eddy Simulation (DDES) of the rotating generic closed wheel and a production vehicle rim wheel. The most dominant flow structures are captured at frequencies between 18Hz and 176Hz. Leading modes for both geometries are found close to the wheel rotation frequency and multiples of that frequency. The modes are identified as recirculation modes and vortex shedding.
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Ludewig, Alexander, Gunther Brenner, and Kathrin Skinder. "DMD Analysis of Radial Turbomachinery." In ASME Turbo Expo 2022: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/gt2022-82953.

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Abstract In the design of turbomachinery, the avoidance of flow-induced vibrations offers optimisation potential with regard to noise reduction and the extension of the service life of a machine. To achieve this, damage-relevant should be analyzed in the development phase using methods such as forced response or flutter calculations. A forced response analysis requires the specification of flow-induced excitations in the spectral range, which can be obtained from a temporal numerical simulation using FFT. Since the FFT depends on the time span and therefore only reproduces discrete frequencies, only rotational frequencies and their integer harmonics can be determined from a single rotational period. To work around this, a Dynamic Mode Decomposition (DMD) is applied to analyse the flow field in a high performance centrifugal fan obtained from simulation and measurement data. DMD is a model order reduction method based on singular value decomposition. It extracts modes and eigenvalues of a nonlinear, dynamic system. DMD is considered an ideal combination of proper orthogonal decomposition in space and Fourier transform in time. The numerical data were generated with a CFD calculation based on the unsteady Reynolds-averaged Navier-Stokes equations together with the k-ω SST turbulence model. As a result of this study, it can be shown that the DMD agrees exactly with the analysis of the FFT based on transient local pressure sensors. For the two-dimensional pressure field, however, the DMD deviates significantly from the FFT in the amplitudes for higher-frequency excitations, partly showing better agreement with the measurements of the pressure sensors.
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Dang, Fengying, and Feitian Zhang. "DMD-Based Distributed Flow Sensing for Bio-Inspired Autonomous Underwater Robots." In ASME 2018 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/dscc2018-9113.

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This paper presents a novel flow sensing method for autonomous underwater robots using distributed pressure measurements. The proposed flow sensing method harnesses a Bayesian filter and a dynamic mode decomposition (DMD)-based reduced-order flow model to estimate the dynamic flow environments. This data-driven estimation method does not rely on any analytical flow models and is applicable to many and various dynamic flow fields for arbitrarily shaped underwater robots. To demonstrate the effectiveness of the proposed distributed flow sensing approach, a simulation study with a Joukowski-foil-shaped underwater robot is presented.
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Reports on the topic "Dynamic Mode Decomposition (DMD)"

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Yarrington, Cole, and Jeremy B. Lechman. Dynamic Mode Decomposition of Solids. Office of Scientific and Technical Information (OSTI), September 2016. http://dx.doi.org/10.2172/1562636.

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Hardy, Zachary. Survey of Dynamic Mode Decomposition Methods. Office of Scientific and Technical Information (OSTI), August 2020. http://dx.doi.org/10.2172/1657110.

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Fonoberova, Maria, Igor Mezic, and Sophie Loire. Application of Koopman Mode Decomposition Methods in Dynamic Stall. Fort Belvoir, VA: Defense Technical Information Center, March 2014. http://dx.doi.org/10.21236/ada606543.

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