Relevant bibliographies by topics / Proper Orthogonal Decomposition

Academic literature on the topic 'Proper Orthogonal Decomposition'

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Published: 4 June 2021
Last updated: 7 September 2023

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Journal articles on the topic "Proper Orthogonal Decomposition"

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Sieber, Moritz, C. Oliver Paschereit, and Kilian Oberleithner. "Spectral proper orthogonal decomposition." Journal of Fluid Mechanics 792 (March 4, 2016): 798–828. http://dx.doi.org/10.1017/jfm.2016.103.

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The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures the dominant flow structures. The most prominent candidates are the energy-ranked proper orthogonal decomposition (POD) and the frequency-ranked Fourier decomposition and dynamic mode decomposition (DMD). However, these methods are not suitable when the relevant coherent structures occur at low energies or at multiple frequencies, which is often the case. To overcome the deficit of these ‘rigid’ approaches, we propose a new method termed spectral proper orthogonal decomposition (SPOD). It is based on classical POD and it can be applied to spatially and temporally resolved data. The new method involves an additional temporal constraint that enables a clear separation of phenomena that occur at multiple frequencies and energies. SPOD allows for a continuous shifting from the energetically optimal POD to the spectrally pure Fourier decomposition by changing a single parameter. In this article, SPOD is motivated from phenomenological considerations of the POD autocorrelation matrix and justified from dynamical systems theory. The new method is further applied to three sets of PIV measurements of flows from very different engineering problems. We consider the flow of a swirl-stabilized combustor, the wake of an airfoil with a Gurney flap and the flow field of the sweeping jet behind a fluidic oscillator. For these examples, the commonly used methods fail to assign the relevant coherent structures to single modes. The SPOD, however, achieves a proper separation of spatially and temporally coherent structures, which are either hidden in stochastic turbulent fluctuations or spread over a wide frequency range. The SPOD requires only one additional parameter, which can be estimated from the basic time scales of the flow. In spite of all these benefits, the algorithmic complexity and computational cost of the SPOD are only marginally greater than those of the snapshot POD.
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Himpe, Christian, Tobias Leibner, and Stephan Rave. "Hierarchical Approximate Proper Orthogonal Decomposition." SIAM Journal on Scientific Computing 40, no. 5 (January 2018): A3267—A3292. http://dx.doi.org/10.1137/16m1085413.

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Borggaard, Jeff, Traian Iliescu, and Zhu Wang. "Artificial viscosity proper orthogonal decomposition." Mathematical and Computer Modelling 53, no. 1-2 (January 2011): 269–79. http://dx.doi.org/10.1016/j.mcm.2010.08.015.

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Narasimha, Roddam. "Kosambi and proper orthogonal decomposition." Resonance 16, no. 6 (June 2011): 574–81. http://dx.doi.org/10.1007/s12045-011-0062-8.

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Mendez, M. A., M. Balabane, and J. M. Buchlin. "Multi-scale proper orthogonal decomposition of complex fluid flows." Journal of Fluid Mechanics 870 (May 15, 2019): 988–1036. http://dx.doi.org/10.1017/jfm.2019.212.

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Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low-order models of complex phenomena. In this work, we analyse the main limits of two popular decompositions, namely the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as multi-scale proper orthogonal decomposition (mPOD) and combines multi-resolution analysis (MRA) with a standard POD. Using MRA, the mPOD splits the correlation matrix into the contribution of different scales, retaining non-overlapping portions of the correlation spectra; using the standard POD, the mPOD extracts the optimal basis from each scale. After introducing a matrix factorization framework for data-driven decompositions, the MRA is formulated via one- and two-dimensional filter banks for the dataset and the correlation matrix respectively. The validation of the mPOD, and a comparison with the discrete Fourier transform (DFT), DMD and POD are provided in three test cases. These include a synthetic test case, a numerical simulation of a nonlinear advection–diffusion problem and an experimental dataset obtained by the time-resolved particle image velocimetry (TR-PIV) of an impinging gas jet. For each of these examples, the decompositions are compared in terms of convergence, feature detection capabilities and time–frequency localization.
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Schmidt, Oliver T., and Tim Colonius. "Guide to Spectral Proper Orthogonal Decomposition." AIAA Journal 58, no. 3 (March 2020): 1023–33. http://dx.doi.org/10.2514/1.j058809.

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Pironneau, Olivier. "Proper orthogonal decomposition for pricing options." Journal of Computational Finance 16, no. 1 (September 2012): 33–46. http://dx.doi.org/10.21314/jcf.2012.246.

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Kunisch, Karl, and Stefan Volkwein. "Proper orthogonal decomposition for optimality systems." ESAIM: Mathematical Modelling and Numerical Analysis 42, no. 1 (January 2008): 1–23. http://dx.doi.org/10.1051/m2an:2007054.

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Bienkiewicz, B., H. J. Ham, and Y. Sun. "Proper orthogonal decomposition of roof pressure." Journal of Wind Engineering and Industrial Aerodynamics 50 (December 1993): 193–202. http://dx.doi.org/10.1016/0167-6105(93)90074-x.

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Carlson, Henry A., Rolf Verberg, and Charles A. Harris. "Aeroservoelastic modeling with proper orthogonal decomposition." Physics of Fluids 29, no. 2 (February 2017): 020711. http://dx.doi.org/10.1063/1.4975673.

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Dissertations / Theses on the topic "Proper Orthogonal Decomposition"

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Allison, Timothy Charles. "System Identification via the Proper Orthogonal Decomposition." Diss., Virginia Tech, 2007. http://hdl.handle.net/10919/29424.

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Although the finite element method is often applied to analyze the dynamics of structures, its application to large, complex structures can be time-consuming and errors in the modeling process may negatively affect the accuracy of analyses based on the model. System identification techniques attempt to circumvent these problems by using experimental response data to characterize or identify a system. However, identification of structures that are time-varying or nonlinear is problematic because the available methods generally require prior understanding about the equations of motion for the system. Nonlinear system identification techniques are generally only applicable to nonlinearities where the functional form of the nonlinearity is known and a general nonlinear system identification theory is not available as is the case with linear theory. Linear time-varying identification methods have been proposed for application to nonlinear systems, but methods for general time-varying systems where the form of the time variance is unknown have only been available for single-input single-output models. This dissertation presents several general linear time-varying methods for multiple-input multiple-output systems where the form of the time variance is entirely unknown. The methods use the proper orthogonal decomposition of measured response data combined with linear system theory to construct a model for predicting the response of an arbitrary linear or nonlinear system without any knowledge of the equations of motion. Separate methods are derived for predicting responses to initial displacements, initial velocities, and forcing functions. Some methods require only one data set but only promise accurate solutions for linear, time-invariant systems that are lightly damped and have a mass matrix proportional to the identity matrix. Other methods use multiple data sets and are valid for general time-varying systems. The proposed methods are applied to linear time-invariant, time-varying, and nonlinear systems via numerical examples and experiments and the factors affecting the accuracy of the methods are discussed.
Ph. D.
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Omar, Ahmed F. "Calibrating pressure sensitive paints using proper orthogonal decomposition." [Gainesville, Fla.] : University of Florida, 2006. http://purl.fcla.edu/fcla/etd/UFE0013431.

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Toal, David J. J. "Proper orthogonal decomposition & kriging strategies for design." Thesis, University of Southampton, 2009. https://eprints.soton.ac.uk/72023/.

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The proliferation of surrogate modelling techniques have facilitated the application of expensive, high fidelity simulations within design optimisation. Taking considerably fewer function evaluations than direct global optimisation techniques, such as genetic algorithms, surrogate models attempt to construct a surrogate of an objective function from an initial sampling of the design space. These surrogates can then be explored and updated in regions of interest. Kriging is a particularly popular method of constructing a surrogate model due to its ability to accurately represent complicated responses whilst providing an error estimate of the predictor. However, it can be prohibitively expensive to construct a kriging model at high dimensions with a large number of sample points due to the cost associated with the maximum likelihood optimisation. The following thesis aims to address this by reducing the total likelihood optimisation cost through the application of an adjoint of the likelihood function within a hybridised optimisation algorithm and the development of a novel optimisation strategy employing a reparameterisation of the original design problem through proper orthogonal decomposition.
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DOLCI, VALENTINA. "Proper Orthogonal Decomposition for Surrogate Models in Aerodynamics." Doctoral thesis, Politecnico di Torino, 2017. http://hdl.handle.net/11583/2678186.

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This study describes the design and implementation of surrogate models for aerodynamic optimization or database generations. Two different methods are presented: the first one follows the classical methodology: a parametric POD is applied to a set of initial solutions or snapshots obtained with an high fidelity CFD model. With respect to approaches presented in literature, in this research work no truncation of the POD modes is performed and they are all used to construct the surrogate model. Several applications are presented: a backward facing step case, the analysis of the flow around a NACA 0012 airfoil and a RAE 2822 supercritical airfoil, the optimization of an automotive external shape and a database generation of a three-dimensional aircraft.
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Akkari, Nissrine. "Etude mathématique de la sensibilité POD (Proper orthogonal decomposition)." Phd thesis, Université de La Rochelle, 2012. http://tel.archives-ouvertes.fr/tel-01066073.

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Dans cette thèse, nous nous sommes intéressés à l'étude mathématique de la sensibilité paramétrique de la méthode de réduction de modèles par projection connue sous le nom de POD pour Proper Orthogonal Decomposition. Dans beaucoup d'applications de la mécanique des fluides,la base de projection (base POD) calculée à un paramètre caractéristique fixe du problème de Navier-Stokes, est utilisée à la suite pour construire des modèles d'ordre réduit ROM-POD pour d'autres valeurs du paramètre caractéristique. Alors, la prédiction du comportement de ce ROM-POD vis-à-vis du problème initial est devenue cruciale. Pour cela, nous avons discuté cette problématique d'un point de vue mathématique. Nous avons établi des résultats mathématiques de sensibilité paramétrique des erreurs induites par application de la méthode ROM-POD. Plus précisément, notre approche est basée sur l'établissement d'estimations a priori de ces erreurs paramétriques, en utilisant les méthodes énergétiques classiques. Nos résultats sont démontrés pour les deux problèmes de type Burgers et Navier-Stokes. Des validations numériques de ces résultats mathématiques ont été faites uniquement pour le problème de type Burgers.
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Behzad, Fariduddin. "Proper Orthogonal Decomposition Based Reduced Order Modeling for Fluid Flow." Thesis, Clarkson University, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3682451.

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Proper orthogonal decomposition-based reduced order modeling is a technique that can be used to develop low dimensional models of fluid flow. In this technique, the Navier-Stokes equations are projected onto a finite number of POD basis functions resulting in a system of ODEs that model the system. The overarching goal of this work is to determine the best methods of applying this technique to generate reliable models of fluid flow. The first chapter investigates some basic characteristics of the proper orthogonal decomposition using the Burgers equation as a surrogate model problem. In applying the POD to this problem, we found that the eigenvalue spectrum is affected by machine precision and this leads to non-phsical negative eigenvalues in the POD. To avoid this, we introduced a new method called deflation that gives positive eigenvalues, but has the disadvantage that the orthogonality of the POD modes is more affected by numerical precision errors. To reduce the size of eigenproblem of POD process, the well-known snapshot method was tested. It was found that the number of snapshots required to obtain an accurate eigenvalue spectrum was determined by the smallest time scale of the phenomenon. After resolving this time scale, the errors in the eigenvalues and modes drop rapidly then converge with second-order accuracy. After obtaing POD modes, the ROM error was assessed using two errors, the error of projection of the problem onto the POD modes (the out-plane error) and the error of the ROM in the space spanned by POD modes (the in-plane error). The numerical results showed not only is the in-plane error bounded by the out-plane error (in agreement with theory) but it actually converges faster than the out-of-plane error. The second chapter is dedicated to building a robust POD-ROM for long term simulation of Navier-Stokes equation. The ability of the POD method to decompose the simulation and the capability of POD-ROM to simulate a low and high Reynolds flow over a NACA0015 airfoil was studied. We observed that POD can be applied for low Reynolds flows successfully if a proper stabilization method is used. For the high Reynolds case, the convergence of the eigenvalues spectrum with respect to duration of time window from we observed that the number of modes needed to simulate a certain time window increases almost linearly with the length of the time window. So, generating a POD-ROM for high Reynolds flow that reproduced the correct long-term limit cycle behavior needs many more modes than has been usually used in the literature. In the last chapter, we address the problem that the standard method of generating POD modes may be inaccurate when used "off-design" (at parameter values not used to generate the POD). We tested some of the popular methods developed to remedy that problem. The accuracy of these methods was in direct relation with the amount of data provided for those methods. So, in order to generate appropriate POD modes, very large POD problems must be solved. To avoid this, a new multi-level method, called recursive POD, for enriching the POD modes is introduced that mathematically provides optimal POD modes while reducing the computational size of problem to a manageable degrees. A low Reynolds flow over NACA 0015, actuated with constant suction/blowing of a fluidic jet located on top surface of airfoil is used as benchmark to test the technique. The flow is shifted from one periodic state to another periodic state due to fluidic jet effect. It was found that the modes extracted with the recursive POD method are as accurate as the modes of the best known method, global POD, while the computational effort is lower.

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Malla, Bhupatindra. "Study of High-speed Subsonic Jets using Proper Orthogonal Decomposition." University of Cincinnati / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1352397174.

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Mignee, Juliette L. "Proper Orthogonal Decomposition Applied to a Supersonic Single Flow Jet." University of Cincinnati / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1329935384.

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Spencer, Ronald Alex. "Analysis of High Fidelity Turbomachinery CFD Using Proper Orthogonal Decomposition." BYU ScholarsArchive, 2016. https://scholarsarchive.byu.edu/etd/5846.

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Assessing the impact of inlet flow distortion in turbomachinery is desired early in the design cycle. This thesis introduces and validates the use of methods based on the Proper Orthogonal Decomposition (POD) to analyze clean and 1/rev static pressure distortion simulation results at design and near stall operating condition. The value of POD comes in its ability to efficiently extract both quantitative and qualitative information about dominant spatial flow structures as well as information about temporal fluctuations in flow properties. Observation of the modes allowed qualitative identification of shock waves as well as quantification of their location and range of motion. Modal coefficients revealed the location of the passage shock at a given angular location. Distortion amplification and attenuation between rotors was also identified. A relationship was identified between how distortion manifests itself based on downstream conditions. POD provides an efficient means for extracting the most meaningful information from large CFD simulation data. Static pressure and axial velocity were analyzed to explore the flow physics of 3 rotors of a compressor with a distorted inlet. Based on the results of the analysis of static pressure using the POD modes, it was concluded that there was a decreased range of motion in passage shock oscillation. Analysis of axial velocity POD modes revealed the presence of a separated region on the low pressure surface of the blade which was most dynamic in rotor 1. The thickness of this structure decreased in the near stall operating condition. The general conclusion is made that as the fan approaches stall the apparent effects of distortion are lessened which leads to less variation in the operating condition. This is due to the change in operating condition placing the fan at a different position on the speedline such that distortion effects are less pronounced. POD modes of entropy flux were used to identify three distinct levels of entropy flux in the blade row passage. The separated region was the region with the highest entropy due to the irreversibilities associated with separation.
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Sze, Kin Wai. "Structural health monitoring and damage assessment based on proper orthogonal decomposition /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?CIVL%202004%20SZE.

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Books on the topic "Proper Orthogonal Decomposition"

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Center, Langley Research, ed. Proper orthogonal decomposition in optimal control of fluids. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1999.

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Arian, Eyal. Trust-region proper orthogonal decomposition for flow control. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 2000.

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Inverse analyses with model reduction: Proper orthogonal decomposition in structural mechanics. Berlin: Springer, 2012.

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Proper Orthogonal Decomposition Methods for Partial Differential Equations. Elsevier, 2019. http://dx.doi.org/10.1016/c2017-0-04826-7.

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Proper Orthogonal Decomposition Methods for Partial Differential Equations. Academic Press, 2018.

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National Aeronautics and Space Administration (NASA) Staff. Proper Orthogonal Decomposition in Optimal Control of Fluids. Independently Published, 2018.

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Luo, Zhendong, and Goong Chen. Proper Orthogonal Decomposition Methods for Partial Differential Equations. Elsevier Science & Technology Books, 2018.

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Buljak, Vladimir. Inverse Analyses with Model Reduction: Proper Orthogonal Decomposition in Structural Mechanics. Springer, 2014.

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Buljak, Vladimir. Inverse Analyses with Model Reduction: Proper Orthogonal Decomposition in Structural Mechanics. Springer, 2011.

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Azam, Saeed Eftekhar. Online Damage Detection in Structural Systems: Applications of Proper Orthogonal Decomposition, and Kalman and Particle Filters. Springer London, Limited, 2014.

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Book chapters on the topic "Proper Orthogonal Decomposition"

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Gatski, T. B., and M. N. Glauser. "Proper Orthogonal Decomposition Based Turbulence Modeling." In Instability, Transition, and Turbulence, 498–510. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-2956-8_48.

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Silva, José P., E. Jan W. ter Maten, Michael Günther, and Matthias Ehrhardt. "Proper Orthogonal Decomposition in Option Pricing." In Novel Methods in Computational Finance, 441–52. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61282-9_24.

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Berkooz, Gal. "Observations on the Proper Orthogonal Decomposition." In Studies in Turbulence, 229–47. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-2792-2_16.

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Pinnau, René. "Model Reduction via Proper Orthogonal Decomposition." In Mathematics in Industry, 95–109. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78841-6_5.

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Alfonsi, Giancarlo, Leonardo Primavera, Giuseppe Passoni, and Carlo Restano. "Proper Orthogonal Decomposition of Turbulent Channel Flow." In Computational Fluid Dynamics 2000, 473–78. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56535-9_71.

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Keuzer, E., and O. Kust. "Controlling Torsional Vibrations Through Proper Orthogonal Decomposition." In Solid Mechanics and Its Applications, 207–14. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5778-0_26.

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Cueto, Elías, Francisco Chinesta, and Antonio Huerta. "Model Order Reduction based on Proper Orthogonal Decomposition." In Separated Representations and PGD-Based Model Reduction, 1–26. Vienna: Springer Vienna, 2014. http://dx.doi.org/10.1007/978-3-7091-1794-1_1.

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Awrejcewicz, Jan, Vadim A. Krys’ko, and Alexander F. Vakakis. "Order Reduction by Proper Orthogonal Decomposition (POD) Analysis." In Nonlinear Dynamics of Continuous Elastic Systems, 177–238. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-08992-7_3.

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Du, Qiang, and Max D. Gunzburger. "Centroidal Voronoi Tessellation Based Proper Orthogonal Decomposition Analysis." In Control and Estimation of Distributed Parameter Systems, 137–50. Basel: Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8001-5_9.

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Pham, Toan, and Damien Tromeur-Dervout. "Proper Orthogonal Decomposition In Decoupling Large Dynamical Systems." In Lecture Notes in Computational Science and Engineering, 193–202. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14438-7_20.

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Conference papers on the topic "Proper Orthogonal Decomposition"

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Astrid, Patricia, George Papaioannou, Jeroen C. Vink, and Mar Dirk Jansen. "Pressure Preconditioning Using Proper Orthogonal Decomposition." In SPE Reservoir Simulation Symposium. Society of Petroleum Engineers, 2011. http://dx.doi.org/10.2118/141922-ms.

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Mendez, Miguel Alfonso, Mikhael Balabane, and Jean Marie Buchlin. "Multi-scale proper orthogonal decomposition (mPOD)." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5043720.

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Yu, Dan, and Suman Chakravorty. "A randomized proper orthogonal decomposition technique." In 2015 American Control Conference (ACC). IEEE, 2015. http://dx.doi.org/10.1109/acc.2015.7170886.

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Marin, Oana, Elia Merzari, Phillipp Schlatter, and Andrew Siegel. "PROPER ORTHOGONAL DECOMPOSITION ON COMPRESSED DATA." In Tenth International Symposium on Turbulence and Shear Flow Phenomena. Connecticut: Begellhouse, 2017. http://dx.doi.org/10.1615/tsfp10.80.

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Weiss, Julien. "A Tutorial on the Proper Orthogonal Decomposition." In AIAA Aviation 2019 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2019. http://dx.doi.org/10.2514/6.2019-3333.

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Robert, Arnaud, and Dirk Van Hertem. "Reduced Grid Representation through Proper Orthogonal Decomposition." In 2021 IEEE Madrid PowerTech. IEEE, 2021. http://dx.doi.org/10.1109/powertech46648.2021.9494759.

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Zheng, Yan, Shun Fujimoto, and Akira Rinoshika. "Comparing wavelet transform with proper orthogonal decomposition." In 2015 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR). IEEE, 2015. http://dx.doi.org/10.1109/icwapr.2015.7295936.

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Yao, Weigang. "Aerodynamic Data Reconstruction Using Proper Orthogonal Decomposition." In 39th AIAA Fluid Dynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2009. http://dx.doi.org/10.2514/6.2009-4203.

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Botha, N., S. Kok, and H. M. Inglis. "INTRAOCULAR PRESSURE ESTIMATION USING PROPER ORTHOGONAL DECOMPOSITION." In 10th World Congress on Computational Mechanics. São Paulo: Editora Edgard Blücher, 2014. http://dx.doi.org/10.5151/meceng-wccm2012-18292.

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Riaz, M. S., and B. F. Feeny. "Proper Orthogonal Decomposition of an Experimental Cantilever Beam." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8137.

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Abstract We apply proper orthogonal decomposition (POD) to an experimental cantilevered beam and obtain a set of proper orthogonal modes (POMs) and proper orthogonal values (POVs). The POMs form a bases that represents the optimal distribution of energy in the system. A set of experiments was performed excited by impulse inputs and sensed with strain gages. The strains were converted to displacements and POD was performed on the displacements. The POMs were compared with the theoretical normal modes. The results confirmed the validity of this method for acquiring lower modes of vibration. The identification of lower modes was robust with respect to the choice of data acquisition parameters and input locations. We also used different types of basis functions for converting strains to displacements.
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Reports on the topic "Proper Orthogonal Decomposition"

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Oxberry, Geoffrey M., Tanya Kostova-Vassilevska, Bill Arrighi, and Kyle Chand. Limited-memory adaptive snapshot selection for proper orthogonal decomposition. Office of Scientific and Technical Information (OSTI), April 2015. http://dx.doi.org/10.2172/1224940.

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Ly, Hung V., and Hien T. Tran. Modeling and Control of Physical Processes Using Proper Orthogonal Decomposition. Fort Belvoir, VA: Defense Technical Information Center, February 1999. http://dx.doi.org/10.21236/ada454477.

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Del Rosario, R. C., H. T. Tran, and H. T. Banks. Proper Orthogonal Decomposition Based Control of Transverse Beam Vibrations: Experimental Implementation. Fort Belvoir, VA: Defense Technical Information Center, January 1999. http://dx.doi.org/10.21236/ada454479.

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Narayanan, Vinod, and Benn Eilers. Identification of Coherent Structure Dynamics in Wall-Bounded Sprays using Proper Orthogonal Decomposition. Fort Belvoir, VA: Defense Technical Information Center, August 2010. http://dx.doi.org/10.21236/ada532067.

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Ly, Hung V., and Hien T. Tran. Proper Orthogonal Decomposition for Flow Calculations and Optimal Control in a Horizontal CVD Reactor. Fort Belvoir, VA: Defense Technical Information Center, March 1998. http://dx.doi.org/10.21236/ada451227.

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McDaniel, Dwayne, George Dulikravich, and Paul Cizmas. Development of a Reduced-Order Model for Reacting Gas-Solids Flow using Proper Orthogonal Decomposition. Office of Scientific and Technical Information (OSTI), November 2017. http://dx.doi.org/10.2172/1411716.

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Viggiano, Bianca. Reduced Order Description of Experimental Two-Phase Pipe Flows: Characterization of Flow Structures and Dynamics via Proper Orthogonal Decomposition. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.5723.

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