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Le, Thai Hoa. "UNSTEADY BUFFETING FORCES AND GUST RESPONSE OF BRIDGES WITH PROPER ORTHOGONAL DECOMPOSITION APPLICATIONS". 京都大学 (Kyoto University), 2007. http://hdl.handle.net/2433/49126.
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学位授与大学：京都大学 ; 取得学位: 博士(工学) ; 学位授与年月日: 2007-09-25 ; 学位の種類: 新制・課程博士 ; 学位記番号: 工博第2843号 ; 請求記号: 新制/工/1418 ; 整理番号: 25528The unsteady buffeting forces and the gust response prediction of bridges in the atmospheric turbulent flows is recently attracted more attention due to uncertainties in both experiment and analytical theory. The correction functions such as the aerodynamic admittance function and the spatial coherence function have been supplemented to cope with limitations of the quasi-steady theory and strip one so far. Concretely, so-called single-variate quasi-steady aerodynamic admittance functions as the transfer functions between the wind turbulence and induced buffeting forces, as well as coherence of wind turbulence has been widely applied for the gust response prediction. Recent literatures, however, pointed out that the coherence of force exhibits higher than that of turbulence. These correction functions, in the other words, contain their uncertainties which are required to be more understanding. Proper orthogonal decomposition (POD), known as the Karhunen-Loeve decomposition has been applied popularly in many engineering fields. Main advantage of the POD is that the multi-variate correlated random fields/processes can be decomposed and described in such simplified way as a combination of limited number of orthogonally low-order dominant eigenvectors (or turbulent modes) which is convenient and applicable for order-reduced representation, simulation of the random fields/processes such as the turbulent fields, turbulent-induced force fields and stochastic response prediction as well. The POD and its proper transformations based on either zero-time-lag covariance matrix or cross spectral one of random fields/processes have been branched by either the covariance proper transformation (CPT) in the time domain or the spectral proper transformation (SPT) in the frequency domain. So far, the covariance matrix-based POD and its covariance proper transformation in the time domain has been used almost in the wind engineering topics due to its simplification in computation and interpretation. In this research, the unsteady buffeting forces and the gust response prediction of bridges with emphasis on the POD applications have been discussed. Investigations on the admittance function of turbulent-induced buffeting forces and the coherence one of the surface pressure as well as the spatial distribution and correlation of the unsteady pressure fields around some typically rectangular cylinders in the different unsteady flows have been carried out thanks to physical measurements in the wind tunnel. This research indicated effect of the bluff body flow and the wind-structure interaction on the higher coherence of buffeting forces than the coherence of turbulence, thus this effect should be accounted and undated for recent empirical formulae of the coherence function of the unsteady buffeting forces. Especially, the multi-variate nonlinear aerodynamic admittance function has been proposed in this research, as well as the temporo-spectral structure of the coherence functions of the wind turbulence and the buffeting forces has been firstly here using the wavelet transform-based coherence in order to detect intermittent characteristics and temporal correspondence of these coherence functions. In POD applications, three potential topics in the wind engineering field have been discussed in the research: (i) analysis and identification, modeling of unsteady pressure fields around model sections; (ii) representation and simulation of multi-variate correlated turbulent fields and (iii) stochastic response prediction of structures and bridges. Especially, both POD branches and their proper transformations in the time domain and the frequency one have been used in these applications. It found from these studies that only few low-order orthogonal dominant modes are enough accuracy for representing, modeling, simulating the correlated random fields (turbulence and unsteady surface pressure, unsteady buffeting forces), as well as predicting stochastic response of bridges in the time and frequency domains. The gust response prediction of bridges has been formulated in the time domain at the first time in this research using the covariance matrix-based POD and its covariance proper transformation which is very promising to solve the problems of the nonlinear and unsteady aerodynamics. Furthermore, the physical linkage between these low-order modes and physical causes occurring on physical models has been interpreted in some investigated cases.
Kyoto University (京都大学)
0048
新制・課程博士
博士(工学)
甲第13372号
工博第2843号
新制||工||1418(附属図書館)
25528
UT51-2007-Q773
京都大学大学院工学研究科社会基盤工学専攻
(主査)教授 松本 勝, 教授 河井 宏允, 准教授 白土 博通
学位規則第4条第1項該当
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Malm, Johan. "Spectral-element simulations of turbulent wall-bounded flows including transition and separation". Doctoral thesis, KTH, Stabilitet, Transition, Kontroll, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-50294.
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The spectral-element method (SEM) is used to study wall-bounded turbulent flowsin moderately complex geometries. The first part of the thesis is devoted to simulations of canonical flow cases, such as temporal K-type transitionand turbulent channel flow, to investigate general resolution requirements and computational efficiency of the numerical code nek5000. Large-eddy simulation (LES) is further performed of a plane asymmetric diffuser flow with an opening angle of 8.5 degrees, featuring turbulent flow separation. Good agreement with numerical studies of Herbst (2007) is obtained, and it is concluded that the use of a high-order method is advantageous for flows featuring pressure-induced separation. Moreover, it is shown, both a priori on simpler model problems and a posteriori using the full Navier--Stokes equations, that the numerical instability associated with SEM at high Reynolds numbers is cured either by employing over-integration (dealiasing) or a filter-based stabilisation, thus rendering simulations of moderate to high Reynolds number flows possible. The second part of the thesis is devoted to the first direct numerical simulation (DNS) of a truly three-dimensional, turbulent and separated diffuser flow at Re = 10 000 (based on bulk velocity and inflow-duct height), experimentally investigated by Cherry et al. (2008). The massively parallel capabilities of the spectral-element method are exploited by running the simulations on up to 32 768 processors. Very good agreement with experimental mean flow data is obtained and it is thus shown that well-resolved simulations of complex turbulent flows with high accuracy are possible at realistic Reynolds numberseven in complicated geometries. An explanation for the discovered asymmetry of the mean separated flow is provided and itis demonstrated that a large-scale quasi-periodic motion is present in the diffuser. In addition, a new diagnostic measure, based on the maximum vorticity stretching component in every spatial point, is designed and tested in a number of turbulent and transitional flows. Finally, Koopman mode decomposition is performed of a minimal channel flow and compared to classical proper orthogonal decomposition (POD).QC 20111206
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Spitz, Nicolas. "Prediction of Trailing Edge Noise from Two-Point Velocity Correlations". Thesis, Virginia Tech, 2005. http://hdl.handle.net/10919/32637.
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This thesis presents the implementation and validation of a new methodology developed by Glegg et al. (2004) for solving the trailing edge noise problem. This method is based on the premises that the noise produced by a surface can be computed by the integral of the cross product between the velocity and vorticity fields, of the boundary layer and shed vorticity (Howe (1978)). To extract the source terms, proper orthogonal decomposition is applied to the velocity cross spectrum to extract modes of the unsteady velocity and vorticity.
The new formulation of the trailing edge noise problem by Glegg et al. (2004) is attractive because it applies to the high frequencies of interest but does not require an excessive computational effort. Also, the nature of the formulation permits the identification of the modes producing the noise and their associated velocity fluctuations as well as the regions of the boundary layer responsible for the noise production.
The source terms were obtained using the direct numerical simulation of a turbulent channel flow by Moser et al. (1998). Two-point velocity and vorticity statistics of this data set were obtained by averaging 41 instantaneous fields. For comparisons purposes, experimental boundary layer data by Adrian et al. (2000) was chosen. Statistical reduction of 50 velocity fields obtained by particle image velocimetry was performed and analysis of the two-point correlation function showed features similar to the DNS data case. Also, proper orthogonal decomposition revealed identical dominant modes and eddy structures in the flow, therefore justifying considering the channel flow as an external boundary layer for noise calculations.
Comparison of noise predictions with experimental data from Brooks et al. (1989) showed realistic results with the largest discrepancies, on the order of 5 dB, occurring at the lowest frequencies. The DNS results are least applicable at these frequencies, since these correspond to the longest streamwise lengthscales, which are the most affected by the periodicity conditions used in the DNS and also are the least representative of the turbulence in an external boundary layer flow. Most of the noise was shown to be produced by low-frequency streamwise velocity modes in the bottom 10% of the boundary layer and locations closest to the wall. Only 6 modes were required to obtain noise levels within 1 dB of the total noise.
Finally, the method for predicting spatial velocity correlation from Reynolds stress data in wake flows, originally developed by Devenport et al. (1999, 2001) and Devenport and Glegg (2001), was adapted to boundary-layer type flows. This method, using Reynolds stresses and the prescription of a lengthscale to extrapolate the full two-point correlation, was shown to produce best results for a lengthscale prescribed as proportional to the turbulent macroscale.
Noise predictions using modeled two-point statistics showed good agreement with the DNS inferred data in all but frequency magnitude, a probable consequence of the modeling of the correlation function in the streamwise direction. Other quantities associated to noise were seen to be similar to the ones obtained using the DNS.Master of Science
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Di, Donfrancesco Fabrizio. "Reduced Order Models for the Navier-Stokes equations for aeroelasticity". Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS603.
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Le coût d’une simulation numérique aéroélastique peut devenir trop onéreuse lorsque une analyse paramétrique à haut fidélité est requise. Dans ce contexte, des Modèles d'Ordre Réduit (MOR) ont été développés en vue de réduire le coût de calcul des simulations numériques en préservant un haut niveau de précision. Ce travail de thèse porte sur la construction d'un MOR pour les équations de Navier-Stokes en tenant compte d'un maillage déformable dans le cas d'une application aéroélastique. Une base modale pour l'écoulement est obtenue via la Décomposition Orthogonale aux valeurs propres et une projection Galerkin est utilisée pour réduire le système d'équations de la mécanique des fluides. Pour pouvoir prendre en compte les non-linéarités des équation de Navier-Stokes une méthode de projection masquée est mise en œuvre et évaluée pour différent cas test avec maillage fixe. Le MOR est ensuite adapté pour prendre en compte des maillages déformables. Finalement, une méthode réduite spectrale en temps (ROTSM) a été formulée afin de répondre aux problèmes de stabilité qui concernent le MORs avec projection dans le domaine de la mécanique des fluides. Une évaluation du MOR obtenu est ensuite menée sur des études paramétriques pour des applications aéroélastiquesThe numerical prediction of aeroelastic systems responses becomes unaffordable when parametric analyses with high-fidelity CFD are required. Reduced order modeling (ROM) methods have therefore been developed in view of reducing the costs of the numerical simulations while preserving a high level of accuracy. The present thesis focuses on the family of projection based methods for the compressible Navier-Stokes equations involving deforming meshes in the case of aeroelastic applications. A vector basis obtained by Proper Orthogonal Decomposition (POD) combined to a Galerkin projection of the system equations is used in order to build a ROM for fluid mechanics. Masked projection approaches are therefore implemented and assessed for different test cases with fixed boundaries in order to provide a fully nonlinear formulation for the projection-based ROMs. Then, the ROM is adapted in the case of deforming boundaries and aeroelastic applications in a parametric context. Finally, a Reduced Order Time Spectral Method (ROTSM) is formulated in order to address the stability issues which involve the projection-based ROMs for fluid mechanics applications
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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.
8
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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Krenciszek, Joachim [Verfasser]. "Proper Orthogonal Decomposition for Contact and Free Boundary Problems / Joachim Krenciszek". München : Verlag Dr. Hut, 2014. http://d-nb.info/1055864148/34.
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Yuan, Tao. "Reduced order modeling for transport phenomena based on proper orthogonal decomposition". Texas A&M University, 2003. http://hdl.handle.net/1969.1/1470.
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In this thesis, a reduced order model (ROM) based on the proper orthogonal decomposition (POD) for the transport phenomena in fluidized beds has been developed. The reduced order model is tested first on a gas-only flow. Two different strategies and implementations are described for this case. Next, a ROM for a two-dimensional gas-solids fluidized bed is presented. A ROM is developed for a range of diameters of the solids particles. The reconstructed solution is calculated and compared against the full order solution. The differences between the ROM and the full order solution are
smaller than 3.2% if the diameters of the solids particles are in the range of diameters used for POD database generation. Otherwise, the errors
increase up to 10% for the cases presented herein. The computational time of the ROM varied between 25% and 33% of the computational time of the full order solution. The computational speed-up depended on the complexity of the transport phenomena, ROM methodology and reconstruction error. In this thesis, we also investigated the accuracy of the reduced order model based on the POD. When analyzing the accuracy, we used two simple sets of governing partial differential equations: a non-homogeneous Burgers' equation and a system of two coupled Burgers' equations.
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Lau, Tony 1978. "Application of the proper orthogonal decomposition to slat cove noise modeling". Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/82776.
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Jarvis, Christopher Hunter. "Reduced Order Model Study of Burgers' Equation using Proper Orthogonal Decomposition". Thesis, Virginia Tech, 2012. http://hdl.handle.net/10919/31580.
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In this thesis we conduct a numerical study of the 1D viscous Burgers' equation and several Reduced Order Models (ROMs) over a range of parameter values. This study is motivated by the need for robust reduced order models that can be used both for design and control. Thus the model should first, allow for selection of optimal parameter values in a trade space and second, identify impacts from changes of parameter values that occur during development, production and sustainment of the designs. To facilitate this study we apply a Finite Element Method (FEM) and where applicable, the Group Finite Element Method (GFE) due its demonstrated stability and reduced complexity over the standard FEM. We also utilize Proper Orthogonal Decomposition (POD) as a model reduction technique and modifications of POD that include Global POD, and the sensitivity based modifications Extrapolated POD and Expanded POD. We then use a single baseline parameter in the parameter range to develop a ROM basis for each method above and investigate the error of each ROM method against a full order "truth" solution for the full parameter range.Master of Science
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Atwell, Jeanne A. "Proper Orthogonal Decomposition for Reduced Order Control of Partial Differential Equations". Diss., Virginia Tech, 2000. http://hdl.handle.net/10919/26985.
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Numerical models of PDE systems can involve
very large matrix equations, but
feedback controllers for these systems must be computable
in real time to be implemented on physical systems.
Classical control design methods produce
controllers of the same order as the numerical models.
Therefore, emph{reduced} order control design is vital for practical
controllers. The main contribution of this research is a method
of control order reduction
that uses a newly developed low order basis. The low order basis
is obtained
by applying Proper Orthogonal Decomposition (POD) to a set of
functional gains, and is referred to as the functional gain
POD basis.
Low order controllers resulting from the
functional gain POD basis
are compared with low order controllers resulting from
more commonly used time snapshot POD bases, with the two dimensional
heat equation as a test problem. The functional gain
POD basis avoids subjective criteria associated
with the time snapshot POD basis and provides
an equally effective low order controller with larger stability
radii. An efficient and effective methodology is introduced for
using a low order basis in reduced order compensator design. This
method combines
"design-then-reduce" and "reduce-then-design" philosophies.
The desirable qualities of the resulting
reduced order compensator are verified by application
to Burgers' equation in numerical experiments.Ph. D.
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Beach, Benjamin Josiah. "An Implementation-Based Exploration of HAPOD: Hierarchical Approximate Proper Orthogonal Decomposition". Thesis, Virginia Tech, 2018. http://hdl.handle.net/10919/81938.
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Proper Orthogonal Decomposition (POD), combined with the Method of Snapshots and Galerkin projection, is a popular method for the model order reduction of nonlinear PDEs. The POD requires the left singular vectors from the singular value decomposition (SVD) of an n-by-m "snapshot matrix" S, each column of which represents the computed state of the system at a given time. However, the direct computation of this decomposition can be computationally expensive, particularly for snapshot matrices that are too large to fit in memory. Hierarchical Approximate POD (HAPOD) (Himpe 2016) is a recent method for the approximate truncated SVD that requires only a single pass over S, is easily parallelizable, and can be computationally cheaper than direct SVD, all while guaranteeing the requested accuracy for the resulting basis. This method processes the columns of S in blocks based on a predefined rooted tree of processors, concatenating the outputs from each stage to form the inputs for the next. However, depending on the selected parameter values and the properties of S, the performance of HAPOD may be no better than that of direct SVD. In this work, we numerically explore the parameter values and snapshot matrix properties for which HAPOD is computationally advantageous over the full SVD and compare its performance to that of a parallelized incremental SVD method (Brand 2002, Brand 2003, and Arrighi2015). In particular, in addition to the two major processor tree structures detailed in the initial publication of HAPOD (Himpe2016), we explore the viability of a new structure designed with an MPI implementation in mind.Master of Science
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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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Adnan, Farasatul. "Proper orthogonal decomposition (POD): application to finite element analysis of electromagnetic diffusion". Thesis, McGill University, 2011. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103769.
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Proper Orthogonal Decomposition (POD) is a technique which has been used successfully to reduce the computation time in various fields of engineering. Here POD is applied to electromagnetic field computations, specifically to the simulation of electromagnetic diffusion by the time-domain finite element method. The standard method requires a large matrix equation to be solved at every time step. POD is applied to greatly reduce the size of the matrices. Both 1-D and 2-D test cases are considered. Applying POD reduces the matrix dimension for a 2-D problem from 2,535 to just 5, with negligible loss of accuracy.La Décomposition Orthogonale Nécessaire (POD) est une technique qui a été utilisée avec succès pour réduire le temps de compte dans les champs différents d'ingénierie. Ici la POD est appliqué les comptes électromagnétiques de terrain, spécialement à la simulation de la diffusion électromagnétique par le domaine de temps la méthode d'élément finie. La norme la méthode exige à une grande équation matricielle d'être résolue au pas de chaque fois. La POD est appliquée beaucoup réduire la grandeur du matrices. De 1ème que 2ème cas tant d'essai sont considérés. L'application de la POD réduit la dimension matricielle pour un 2ème problème de 2,535 à juste 5, avec la perte négligeable d'exactitude.
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Caraballo, Edgar Javier. "An application of the proper orthogonal decomposition to an axisymmetric supersonic jet". The Ohio State University, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=osu1406646741.
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Rama, Ritesh Rao. "Proper orthogonal decomposition with interpolation-based real-time modelling of the heart". Doctoral thesis, University of Cape Town, 2017. http://hdl.handle.net/11427/26859.
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Several studies have been carried out recently with the aim of achieving cardiac modelling of the whole heart for a full heartbeat. However, within the context of the Galerkin method, those simulations require high computational demand, ranging from 16 - 200 CPUs, and long calculation time, lasting from 1 h - 50 h. To solve this problem, this research proposes to make use of a Reduced Order Method (ROM) called the Proper Orthogonal Decomposition with Interpolation method (PODI) to achieve real-time modelling with an adequate level of solution accuracy. The idea behind this method is to first construct a database of pre-computed full-scale solutions using the Element-free Galerkin method (EFG) and then project a selected subset of these solutions to a low dimensional space. Using the Moving Least Square method (MLS), an interpolation is carried out for the problem-at-hand, before the resulting coefficients are projected back to the original high dimensional solution space. The aim of this project is to tackle real-time modelling of a patient-specific heart for a full heartbeat in different stages, namely: modelling (i) the diastolic filling with variations of material properties, (ii) the isovolumetric contraction (IVC), ejection and isovolumetric relation (IVR) with arbitrary time evolutions, and (iii) variations in heart anatomy. For the diastolic filling, computations are carried out on a bi-ventricle model (BV) to investigate the performance and accuracy for varying the material parameters. The PODI calculations of the LV are completed within 14 s on a normal desktop machine with a relative L₂-error norm of 6x10⁻³. These calculations are about 2050 times faster than EFG, with each displacement step generated at a calculation frequency of 1074 Hz. An error sensitivity analysis is consequently carried out to find the most sensitive parameter and optimum dataset to be selected for the PODI calculation. In the second phase of the research, a so-called "time standardisation scheme" is adopted to model a full heartbeat cycle. This is due to the simulation of the IVC, ejection, and IVR phases being carried out using a displacement-driven calculation method which does not use uniform simulation steps across datasets. Generated results are accurate, with the PODI calculations being 2200 faster than EFG. The PODI method is, in the third phase of this work, extended to deal with arbitrary heart meshes by developing a method called "Degrees of freedom standardisation" (DOFS). DOFS consists of using a template mesh over which all dataset result fields are projected. Once the result fields are standardised, they are consequently used for the PODI calculation, before the PODI solution is projected back to the mesh of the problem-at-hand. The first template mesh to be considered is a cube mesh. However, it is found to produce results with high errors and non-physical behaviour. The second template mesh used is a heart template. In this case, a preprocessing step is required where a non-rigid transformation based on the coherent point drift method is used to transform all dataset hearts onto the heart template. The heart template approach generated a PODI solution of higher accuracy at a relatively low computational time. Following these encouraging results, a final investigation is carried out where the PODI method is coupled with a computationally expensive gradient-based optimisation method called the Levenberg- Marquardt (PODI-LVM) method. It is then compared against the full-scale simulation one where the EFG is used with the Levenberg-Marquardt method (EFG-LVM). In this case, the PODI-LVM simulations are 1025 times faster than the EFG-LVM, while its error is less than 1%. It is also observed that since the PODI database is built using EFG simulations, the PODI-LVM behaves similarly to the EFG-LVM one.
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Sévénié, Benjamin. "Capsule deformation in a microfluidic channel : experiments, characterization and Proper Orthogonal Decomposition". Thesis, Compiègne, 2016. http://www.theses.fr/2016COMP2278/document.
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Nous étudions la déformation d'une capsule dans un canal microftuidique expérimentalement et numériquement. L'écoulement des rnicrocapsules est d'abord étudié numériquement dans un canal droit à section carrée. L'objectif est de développer une méthode de caractérisation des propriétés mécaniques de la membrane des capsules, à partir de leur déformation dans le canal. Nous avons mis en place une méthode d’identification afin de comparer la déformation des capsules observée expérimentalement et celle prédite par un modèle numérique tridimensionnel correspondant. La précision et la robustesse de l'algorithme d'analyse inverse ont été étudiées en faisant varier légèrement la géométrie des canaux. Finalement, la méthode a été utilisée afin de déterminer les propriétés mécaniques de rnicrocapsules dont la membrane est faite d’albumine réticulée. Nous avons ensuite appliqué une méthode de décomposition orthogonale aux valeurs propres (POD) aux formes prises par les capsules lors de leur passage dans un canal droit ou bifurqué. Des données numériques ont d 'abord été utilisées afin de déterminer la dimension de la variété des formes prises par une capsule dans un canal droit. La base POD ainsi construite a été utilisée pour interpoler les formes et obtenir la déformation d'une capsule à tous les temps, et pour tout paramètre d’écoulement. Nous avons également étudié expérimentalement les microcapsules lors de leur déformation dans un canal bifurqué. Nous avons ainsi obtenu les premiers résultats qualitatifs pour cette configuration. Nous avons développé un programme de détection de contour semi-automatique afin de faciliter le traitement d’image. Enfin, nous avons appliqué la méthode POD sur ces contours 2D réalistes et ainsi démontré la faisabilité d'utiliser une base réduite POD pour décrire la déformation de capsules clans un canal bifurquéThe motion and deformation of a liquid-filled classic microcapsule flowing in microchannels is investigated bath experimentally and numerically. The flow of capsules into a straight microfluidic channel with a square cross-section is firstly studied. The objective is to develop a method to determine the mechanical properties of the capsule membrane from its hydrodynamic deformation. A method of identification has been devised to compare the particle deformed shape measured experimentally in the microchannels to the ones predicted by a three-dimensional numerical model for the same configuration. The precision and robustness of the inverse analysis algorithm have been tested when the microfluidic channels slightly depart from pure squareness. We have finally applied the method on microcapsules with a membrane made of reticulated albumin and determined their rnechanical properties. A Proper Orthogonal Decomposition (POD) has then been applied to the shapes assumed by the capsules while flowing in either a straight or bi furcated channel. Using numerical data in a straight channel, we have determined the dimension of the capsule shape variety. We have then interpolated the coefficients resulting from the POD analysis to compute the capsule deformed shape at any time for any flow parameter. Capsules have finally been investigated flowing in a bifurcated microchannel. Qualitative results of the motion and deformation of capsules in such channel have been obtained. A semi-automatic contour detection program has been developed to improve the image analysis. The POD method has been applied to the experimental results, thus proving the feasibility of building a reduced-order model of the phenomenon by using a POD reduced basis
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Blanc, Trevor Jon. "Analysis and Compression of Large CFD Data Sets Using Proper Orthogonal Decomposition". BYU ScholarsArchive, 2014. https://scholarsarchive.byu.edu/etd/5303.
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Efficient analysis and storage of data is an integral but often challenging task when working with computation fluid dynamics mainly due to the amount of data it can output. Methods centered around the proper orthogonal decomposition were used to analyze, compress, and model various simulation cases. Two different high-fidelity, time-accurate turbomachinery simulations were investigated to show various applications of the analysis techniques. The first turbomachinery example was used to illustrate the extraction of turbulent coherent structures such as traversing shocks, vortex shedding, and wake variation from deswirler and rotor blade passages. Using only the most dominant modes, flow fields were reconstructed and analyzed for error. The reconstructions reproduced the general dynamics within the flow well, but failed to fully resolve shock fronts and smaller vortices. By decomposing the domain into smaller, independent pieces, reconstruction error was reduced by up to 63 percent. A new method of data compression that combined an image compression algorithm and the proper orthogonal decomposition was used to store the reconstructions of the flow field, increasing data compression ratios by a factor of 40.The second turbomachinery simulation studied was a three-stage fan with inlet total pressure distortion. Both the snapshot and repeating geometry methods were used to characterize structures of static pressure fluctuation within the blade passages of the third rotor blade row. Modal coefficients filtered by frequencies relating to the inlet distortion pattern were used to produce reconstructions of the pressure field solely dependent on the inlet boundary condition. A hybrid proper orthogonal decomposition method was proposed to limit burdens on computational resources while providing high temporal resolution analysis.Parametric reduced order models were created from large databases of transient and steady conjugate heat transfer and airfoil simulations. Performance of the models were found to depend heavily on the range of the parameters varied as well as the number of simulations used to traverse that range. The heat transfer models gave excellent predictions for temperature profiles in heated solids for ambitious parameter ranges. Model development for the airfoil case showed that accuracy was highly dependent on modal truncation. The flow fields were predicted very well, especially outside the boundary layer region of the flow.
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Wise, John Nathaniel. "Inverse modelling and optimisation in numerical groundwater flow models using proper orthogonal decomposition". Thesis, Saint-Etienne, EMSE, 2015. http://www.theses.fr/2015EMSE0773/document.
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Des simulateurs numériques sont couramment utilisés pour la prédiction et l'optimisation de l'exploitation d'aquifères et pour la détermination de paramètres physiques (e.g perméabilité) par calcul inverse. L'équation de Richards, décrit l'écoulement d'un fluide dans un milieu poreux non saturé. C'est une équation aux dérivées partielles non linéaires, dont la résolution numérique en grande dimension 3D est très coûteuse et en particulier pour du calcul inverse.Dans ce travail, une méthode de réduction de modèle (ROM) est proposée par une décomposition orthogonale propre (POD) afin de réduire significativement le temps de calcul, tout maîtrisant la précision. Une stratégie de cette méthode est de remplacer localement dans l'algorithme d'optimisation, le modèle fin par un modèle réduit type POD. La méthode de Petroc-Galerkin POD est d'abord appliquée à l'équation de Richards et testée sur différents cas, puis adaptée en linéarisant les termes non linéaires. Cette adaptation ne fait pas appel à une technique d'interpolation et réduit le temps de calcul d'un facteur [10;100]. Bien qu'elle ajoute de la complexité du ROM, cette méthode évite d'avoir à ajuster les paramètres du noyau, comme c'est le cas dans les méthodes du POD par interpolation. Une exploration des propriétés d'interpolation et d'extrapolation inhérentes aux méthodes intrusives est ensuite faite. Des qualités d'extrapolation intéressantes permettent de développer une méthode d'optimisation nécessitant de petits plans d'expériences (DOE). La méthode d'optimisation recrée localement des modèles précis sur l'espace des paramètres, en utilisant une classification à vecteurs de support non linéaire pour délimiter la zone où le modèle est suffisamment précis, la région de confiance. Les méthodes sont appliquées sur un cas d'école en milieu non saturé régit par l'équation de Richards, ainsi que sur un aquifère situé dans le "Table Mountain Group" près de la ville du Cap en Afrique du SudThe Richards equation describes the movement of an unsaturated fluid through a porous media, and is characterised as a non-linear partial differential equation. The equation is subject to a number of parameters and is typically computationnaly expensive to solve. To determine the parameters in the Richards equation, inverse modelling studies often need to be undertaken. As a solution to overcome the computational expense incurred in inverse modelling, the use of Proper Orthogonal Decomposition (POD) as a Reduced Order Modelling (ROM) method is proposed in this thesis to speed-up individual simulations. The Petrov-Galerkin POD approach is initially applied to the Richards equation and tested on different case studies. However, due to the non-linear nature of the Richards equation the method does not result in significant speed up times. Subsquently, the Petrov-Galerkin method is adapted by linearising the nonlinear terms in the equation, resulting in speed-up times in the range of [10,100]., The adaptation, notably, does not use any interpolation techniques, favouring an intrusive, but physics-based, approach. While the use of intrusive POD approaches add to the complexity of the ROM, it avoids the problem of finding kernel parameters typically present in interpolative POD approaches. Furthermore, the interpolative and possible extrapolation properties inherent to intrusive PODROM's are explored. The good extrapolation propertie, within predetermined bounds, of intrusive POD's allows for the development of an optimisation approach requiring a very small Design of Experiments (DOE). The optimisation method creates locally accurate models within the parameters space usign Support Vector Classification. The limits of the locally accurate model are called the confidence region. The methods are demonstrated on a hypothetical unsaturated case study requiring the Richards equation, and on true case study in the Table Mountain Group near Cape Town, South Africa
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Sen, Mehmet Ali. "Proper Orthogonal Decomposition Methodology to Understand Underlying Physics of Rough-Wall Turbulent Boundary Layer". Fogler Library, University of Maine, 2007. http://www.library.umaine.edu/theses/pdf/SenMA2007.pdf.
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Gräßle, Carmen [Verfasser], i Michael [Akademischer Betreuer] Hinze. "Adaptivity in Model Order Reduction with Proper Orthogonal Decomposition / Carmen Gräßle ; Betreuer: Michael Hinze". Hamburg : Staats- und Universitätsbibliothek Hamburg, 2019. http://d-nb.info/1190819155/34.
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Gräßle, Carmen Verfasser], i Michael [Akademischer Betreuer] [Hinze. "Adaptivity in Model Order Reduction with Proper Orthogonal Decomposition / Carmen Gräßle ; Betreuer: Michael Hinze". Hamburg : Staats- und Universitätsbibliothek Hamburg, 2019. http://nbn-resolving.de/urn:nbn:de:gbv:18-98550.
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Wise, John Nathaniel. "Inverse modelling and optimisation in numerical groundwater flow models using proportional orthogonal decomposition". Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/97116.
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Thesis (PhD)--Stellenbosch University, 2015.ENGLISH ABSTRACT: Numerical simulations are widely used for predicting and optimising the exploitation of aquifers. They are also used to determine certain physical parameters, for example soil conductivity, by inverse calculations, where the model parameters are changed until the model results correspond optimally to measurements taken on site. The Richards’ equation describes the movement of an unsaturated fluid through porous media, and is characterised as a non-linear partial differential equation. The equation is subject to a number of parameters and is typically computationally expensive to solve. To determine the parameters in the Richards’ equation, inverse modelling studies often need to be undertaken. In these studies, the parameters of a numerical model are varied until the numerical response matches a measured response. Inverse modelling studies typically require 100’s of simulations, which implies that parameter optimisation in unsaturated case studies is common only in small or 1D problems in the literature. As a solution to overcome the computational expense incurred in inverse modelling, the use of Proper Orthogonal Decomposition (POD) as a Reduced Order Modelling (ROM) method is proposed in this thesis to speed-up individual simulations. An explanation of the Finite Element Method (FEM) is given using the Galerkin method, followed by a detailed explanation of the Galerkin POD approach. In the development of the Galerkin POD approach, the method of reducing matrices and vectors is shown, and the treatment of Neumann and Dirichlet boundary values is explained. The Galerkin POD method is applied to two case studies. The first case study is the Kogelberg site in the Table Mountain Group near Cape Town in South Africa. The response of the site is modelled at one well over the period of 2 years, and is assumed to be governed by saturated flow, making it a linear problem. The site is modelled as a 3D transient, homogeneous site, using 15 layers and ≈ 20000 nodes, using the FEM implemented on the open-source software FreeFem++. The model takes the evapotranspiration of the fynbos vegetation at the site into consideration, allowing the calculation of annual recharge into the aquifer. The ROM is created from high-fidelity responses taken over time at different parameter points, and speed-up times of ≈ 500 are achieved, corresponding to speed-up times found in the literature for linear problems. The purpose of the saturated groundwater model is to demonstrate that a POD-based ROM can approximate the full model response over the entire parameter domain, highlighting the excellent interpolation qualities and speed-up times of the Galerkin POD approach, when applied to linear problems. A second case study is undertaken on a synthetic unsaturated case study, using the Richards’ equation to describe the water movement. The model is a 2D transient model consisting of ≈ 5000 nodes, and is also created using FreeFem++. The Galerkin POD method is applied to the case study in order to replicate the high-fidelity response. This did not yield in any speed-up times, since the full matrices of non-linear problems need to be recreated at each time step in the transient simulation. Subsequently, a method is proposed in this thesis that adapts the Galerkin POD method by linearising the non-linear terms in the Richards’ equation, in a method named the Linearised Galerkin POD (LGP) method. This method is applied to the same 2D synthetic problem, and results in speed-up times in the range of 10 to 100. The adaptation, notably, does not use any interpolation techniques, favouring a code intrusive, but physics-based, approach. While the use of an intrusively linearised POD approach adds to the complexity of the ROM, it avoids the problem of finding kernel parameters typically present in interpolative POD approaches. Furthermore, the interpolation and possible extrapolation properties inherent to intrusive POD-based ROM’s are explored. The good extrapolation properties, within predetermined bounds, of intrusive POD’s allows for the development of an optimisation approach requiring a very small Design of Experiments (DOE) sets (e.g. with improved Latin Hypercube sampling). The optimisation method creates locally accurate models within the parameter space using Support Vector Classification (SVC). The region inside of the parameter space in which the optimiser is allowed to move is called the confidence region. This confidence region is chosen as the parameter region in which the ROM meets certain accuracy conditions. With the proposed optimisation technique, advantage is taken of the good extrapolation characteristics of the intrusive POD-based ROM’s. A further advantage of this optimisation approach is that the ROM is built on a set of high-fidelity responses obtained prior to the inverse modelling study, avoiding the need for full simulations during the inverse modelling study. In the methodologies and case studies presented in this thesis, initially infeasible inverse modelling problems are made possible by the use of the POD-based ROM’s. The speed up times and extrapolation properties of POD-based ROM’s are also shown to be favourable. In this research, the use of POD as a groundwater management tool for saturated and unsaturated sites is evident, and allows for the quick evaluation of different scenarios that would otherwise not be possible. It is proposed that a form of POD be implemented in conventional groundwater software to significantly reduce the time required for inverse modelling studies, thereby allowing for more effective groundwater management.
AFRIKAANSE OPSOMMING: Die Richards vergelyking beskryf die beweging van ’n vloeistof deur ’n onversadigde poreuse media, en word gekenmerk as ’n nie-lineêre parsiële differensiaalvergelyking. Die vergelyking is onderhewig aan ’n aantal parameters en is tipies berekeningsintensief om op te los. Om die parameters in die Richards vergelyking te bepaal, moet parameter optimering studies dikwels onderneem word. In hierdie studies, word die parameters van ’n numeriese model verander totdat die numeriese resultate die gemete resultate pas. Parameter optimering studies vereis in die orde van honderde simulasies, wat beteken dat studies wat gebruik maak van die Richards vergelyking net algemeen is in 1D probleme in die literatuur. As ’n oplossing vir die berekingskoste wat vereis word in parameter optimering studies, is die gebruik van Eie Ortogonale Ontbinding (POD) as ’n Verminderde Orde Model (ROM) in hierdie tesis voorgestel om individuele simulasies te versnel in die optimering konteks. Die Galerkin POD benadering is aanvanklik ondersoek en toegepas op die Richards vergelyking, en daarna is die tegniek getoets op verskeie gevallestudies. Die Galerkin POD metode word gedemonstreer op ’n hipotetiese gevallestudie waarin water beweging deur die Richards-vergelyking beskryf word. As gevolg van die nie-lineêre aard van die Richards vergelyking, het die Galerkin POD metode nie gelei tot beduidende vermindering in die berekeningskoste per simulasie nie. ’n Verdere gevallestudie word gedoen op ’n ware grootskaalse terrein in die Tafelberg Groep naby Kaapstad, Suid-Afrika, waar die grondwater beweging as versadig beskou word. Weens die lineêre aard van die vergelyking wat die beweging van versadigde water beskryf, is merkwaardige versnellings van > 500 in die ROM waargeneem in hierdie gevallestudie. Daarna was die die Galerkin POD metode aangepas deur die nie-lineêre terme in die Richards vergelyking te lineariseer. Die tegniek word die geLineariserde Galerkin POD (LGP) tegniek genoem. Die aanpassing het goeie resultate getoon, met versnellings groter as 50 keer wanneer die ROM met die oorspronklike simulasie vergelyk word. Al maak die tegniek gebruik van verder lineariseering, is die metode nogsteeds ’n fisika-gebaseerde benadering, en maak nie gebruik van interpolasie tegnieke nie. Die gebruik van ’n fisika-gebaseerde POD benaderings dra by tot die kompleksiteit van ’n volledige numeriese model, maar die kompleksiteit is geregverdig deur die merkwaardige versnellings in parameter optimerings studies. Verder word die interpolasie eienskappe, en moontlike ekstrapolasie eienskappe, inherent aan fisika-gebaseerde POD ROM tegnieke ondersoek in die navorsing. In die navorsing word ’n tegniek voorgestel waarin hierdie inherente eienskappe gebruik word om plaaslik akkurate modelle binne die parameter ruimte te skep. Die voorgestelde tegniek maak gebruik van ondersteunende vektor klassifikasie. Die grense van die plaaslik akkurate model word ’n vertrouens gebeid genoem. Hierdie vertrouens gebied is gekies as die parameter ruimte waarin die ROM voldoen aan vooraf uitgekiesde akkuraatheidsvereistes. Die optimeeringsbenadering vermy ook die uitvoer van volledige simulasies tydens die parameter optimering, deur gebruik te maak van ’n ROM wat gebaseer is op die resultate van ’n stel volledige simulasies, voordat die parameter optimering studie gedoen word. Die volledige simulasies word tipies uitgevoer op parameter punte wat gekies word deur ’n proses wat genoem word die ontwerp van eksperimente. Verdere hipotetiese grondwater gevallestudies is onderneem om die LGP en die plaaslik akkurate tegnieke te toets. In hierdie gevallestudies is die grondwater beweging weereens beskryf deur die Richards vergelyking. In die gevalle studie word komplekse en tyd-rowende modellerings probleme vervang deur ’n POD gebaseerde ROM, waarin individuele simulasies merkwaardig vinniger is. Die spoed en interpolasie/ekstrapolasie eienskappe blyk baie gunstig te wees. In hierdie navorsing is die gebruik van verminderde orde modelle as ’n grondwaterbestuursinstrument duidelik getoon, waarin voorsiening geskep word vir die vinnige evaluering van verskillende modellering situasies, wat andersins nie moontlik is nie. Daar word voorgestel dat ’n vorm van POD in konvensionele grondwater sagteware geïmplementeer word om aansienlike versnellings in parameter studies moontlik te maak, wat na meer effektiewe bestuur van grondwater sal lei.
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Richardson, Brian Ross. "A reduced-order model based on proper orthogonal decomposition for non-isothermal two-phase flows". [College Station, Tex. : Texas A&M University, 2008. http://hdl.handle.net/1969.1/ETD-TAMU-2623.
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Blanchard, Ryan P. "Simulating Bluff-body Flameholders: On the Use of Proper Orthogonal Decomposition for Combustion Dynamics Validation". Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/48430.
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Contemporary tools for experimentation and computational modeling of unsteady reacting flow open new opportunities for engineering insight into dynamic phenomena. In the work presented here, a novel use of proper orthogonal decomposition (POD) is described to validate the structure of dominant heat release and flow features in the flame, shear-layer, and wake of a bluff-body-stabilized flame. A general validation process is presented which involves a comparison of experimental and computational results, beginning with single-point mean statistics and then extending to the dynamic modes of the data using POD to reduce the ensemble of instantaneous flow field snapshots. The results demonstrate the use of this technique by applying it to large eddy simulations of the bluff body stabilized premixed combustion experiment.
Large-eddy simulations (LES) using both Fluent and OpenFOAM were conducted to reproduce experiments conducted in an experimental test rig which was built as part of this work to study the behavior of turbulent premixed flames stabilized by bluff bodies. Planar Particle-Image Velocimetry (PIV) and filtered chemiluminescence were used to characterize the flow in the experiment's reacting and non-reacting regimes respectively. While PIV measurements could be compared directly to the velocity field in the simulations, the chemiluminescence measurements represented a line-of sight signal which was not directly comparable to the LES model. To account for this, the heat release in the LES models was integrated along simulated lines of sight by solving an additional discretized differential equation with heat release as the source term.
The results show generally good agreement between the dominant modes of the experiment with those of the numerical simulations. By isolating the dynamic modes from each other via the proper orthogonal decomposition, it was shown the models were able to accurately reproduce the size, shape, amplitude, and timescale of various dynamic modes which exist the experiment, some of which are dwarfed by the other flow features and are not apparent using time-averaging approaches or by inspection of instantaneous snapshots of the flow.Ph. D.
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VERFAILLIE, SWANN. "CORRELATIVE STUDIES AND COHERENT STRUCTURES EDUCTION BASED ON PROPER ORTHOGONAL DECOMPOSITION AND LINEAR STOCHASTIC ESTIMATION". University of Cincinnati / OhioLINK, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1099519886.
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Maddux, Michael Richard. "Using In-Situ Error Tracking For Mode Selection in Proper Orthogonal Decomposition Reduced Order Modelling". Wright State University / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=wright1167858889.
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Moodley, Kamlin. "A Proper Orthogonal Decomposition-based inverse material parameter optimization method with applications to cardiac mechanics". Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/22777.
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We are currently witnessing the advent of a revolutionary new tool for biomedical research. Complex mathematical models of "living cells" are being arranged into representative tissue assemblies and utilized to produce models of integrated tissue and organ function. This enables more sophisticated simulation tools that allows for greater insight into disease and guide the development of modern therapies. The development of realistic computer models of mechanical behaviour for soft biological tissues, such as cardiac tissue, is dependent on the formulation of appropriate constitutive laws and accurate identification of their material parameters. The main focus of this contribution is to investigate a Proper Orthogonal Decomposition with Interpolation (PODI) based method for inverse material parameter optimization in the field of cardiac mechanics. Material parameters are calibrated for a left ventricular and bi-ventricular human heart model during the diastolic filling phase. The calibration method combines a MATLAB-based Levenberg Marquardt algorithm with the in-house PODIbased software ORION. The calibration results are then compared against the full-order solution which is obtained using an in-house code based on the element-free Galerkin method, which is assumed to be the exact solution. The results obtained from this novel calibration method demonstrate that PODI provides the means to drastically reduce computation time but at the same time maintain a similar level of accuracy as provided by the conventional approach.
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Steward, Jeff. "The solution of a Burgers' equation inverse problem with reduced-order modeling proper orthogonal decomposition". Tallahassee, Florida : Florida State University, 2009. http://etd.lib.fsu.edu/theses/available/etd-07062009-230217.
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Thesis (M.S.)--Florida State University, 2009.Advisor: Ionel M. Navon, Florida State University, College of Arts and Sciences, Dept. of Scientific Computing. Title and description from dissertation home page (viewed on Nov. 17, 2009). Document formatted into pages; contains ix, 67 pages. Includes bibliographical references.
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Wickersham, Andrew Joseph. "Development of Multi-perspective Diagnostics and Analysis Algorithms with Applications to Subsonic and Supersonic Combustors". Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/51145.
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There are two critical research needs for the study of hydrocarbon combustion in high speed flows: 1) combustion diagnostics with adequate temporal and spatial resolution, and 2) mathematical techniques that can extract key information from large datasets. The goal of this work is to address these needs, respectively, by the use of high speed and multi-perspective chemiluminescence and advanced mathematical algorithms.
To obtain the measurements, this work explored the application of high speed chemiluminescence diagnostics and the use of fiber-based endoscopes (FBEs) for non-intrusive and multi-perspective chemiluminescence imaging up to 20 kHz. Non-intrusive and full-field imaging measurements provide a wealth of information for model validation and design optimization of propulsion systems. However, it is challenging to obtain such measurements due to various implementation difficulties such as optical access, thermal management, and equipment cost. This work therefore explores the application of FBEs for non-intrusive imaging to supersonic propulsion systems. The FBEs used in this work are demonstrated to overcome many of the aforementioned difficulties and provided datasets from multiple angular positions up to 20 kHz in a supersonic combustor. The combustor operated on ethylene fuel at Mach 2 with an inlet stagnation temperature and pressure of approximately 640 degrees Fahrenheit and 70 psia, respectively. The imaging measurements were obtained from eight perspectives simultaneously, providing full-field datasets under such flow conditions for the first time, allowing the possibility of inferring multi-dimensional measurements.
Due to the high speed and multi-perspective nature, such new diagnostic capability generates a large volume of data and calls for analysis algorithms that can process the data and extract key physics effectively. To extract the key combustion dynamics from the measurements, three mathematical methods were investigated in this work: Fourier analysis, proper orthogonal decomposition (POD), and wavelet analysis (WA). These algorithms were first demonstrated and tested on imaging measurements obtained from one perspective in a sub-sonic combustor (up to Mach 0.2). The results show that these algorithms are effective in extracting the key physics from large datasets, including the characteristic frequencies of flow—flame interactions especially during transient processes such as lean blow off and ignition. After these relatively simple tests and demonstrations, these algorithms were applied to process the measurements obtained from multi-perspective in the supersonic combustor. compared to past analyses (which have been limited to data obtained from one perspective only), the availability of data at multiple perspective provide further insights into the flame and flow structures in high speed flows.
In summary, this work shows that high speed chemiluminescence is a simple yet powerful combustion diagnostic. Especially when combined with FBEs and the analyses algorithms described in this work, such diagnostics provide full-field imaging at high repetition rate in challenging flows. Based on such measurements, a wealth of information can be obtained from proper analysis algorithms, including characteristic frequency, dominating flame modes, and even multi-dimensional flame and flow structures.Ph. D.
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Durmaz, Oguz. "Dynamical Modeling Of The Flow Over Flapping Wing By Applying Proper Orthogonal Decomposition And System Identification". Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613549/index.pdf.
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In this study the dynamical modeling of the unsteady flow over a flapping wing is considered. The technique is based on collecting instantaneous velocity field data of the flow using Particle Image Velocimetry (PIV), applying image processing to these snapshots to locate the airfoil, filling the airfoil and its surface with proper velocity data, applying Proper Orthogonal Decomposition (POD) to these post-processed images to compute the POD modes and time coefficients, and finally fitting a discrete time state space dynamical model to the trajectories of the time coefficients using subspace system identification (N4SID). The procedure is applied using MATLAB for the data obtained from NACA 0012, SD 7003, elliptic airfoil and flat plate, and the results show that the dynamical model obtained can represent the flow dynamics with acceptable accuracy.
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Lee, Kyunghoon. "Investigation of probabilistic principal component analysis compared to proper orthogonal decomposition methods for basis extraction and missing data estimation". Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/34796.
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The identification of flow characteristics and the reduction of high-dimensional simulation data have capitalized on an orthogonal basis achieved by proper orthogonal decomposition (POD), also known as principal component analysis (PCA) or the Karhunen-Loeve transform (KLT). In the realm of aerospace engineering, an orthogonal basis is versatile for diverse applications, especially associated with reduced-order modeling (ROM) as follows: a low-dimensional turbulence model, an unsteady aerodynamic model for aeroelasticity and flow control, and a steady aerodynamic model for airfoil shape design. Provided that a given data set lacks parts of its data, POD is required to adopt a least-squares formulation, leading to gappy POD, using a gappy norm that is a variant of an L2 norm dealing with only known data. Although gappy POD is originally devised to restore marred images, its application has spread to aerospace engineering for the following reason: various engineering problems can be reformulated in forms of missing data estimation to exploit gappy POD. Similar to POD, gappy POD has a broad range of applications such as optimal flow sensor placement, experimental and numerical flow data assimilation, and impaired particle image velocimetry (PIV) data restoration.
Apart from POD and gappy POD, both of which are deterministic formulations, probabilistic principal component analysis (PPCA), a probabilistic generalization of PCA, has been used in the pattern recognition field for speech recognition and in the oceanography area for empirical orthogonal functions in the presence of missing data. In formulation, PPCA presumes a linear latent variable model relating an observed variable with a latent variable that is inferred only from an observed variable through a linear mapping called factor-loading. To evaluate the maximum likelihood estimates (MLEs) of PPCA parameters such as a factor-loading, PPCA can invoke an expectation-maximization (EM) algorithm, yielding an EM algorithm for PPCA (EM-PCA). By virtue of the EM algorithm, the EM-PCA is capable of not only extracting a basis but also restoring missing data through iterations whether the given data are intact or not. Therefore, the EM-PCA can potentially substitute for both POD and gappy POD inasmuch as its accuracy and efficiency are comparable to those of POD and gappy POD. In order to examine the benefits of the EM-PCA for aerospace engineering applications, this thesis attempts to qualitatively and quantitatively scrutinize the EM-PCA alongside both POD and gappy POD using high-dimensional simulation data.
In pursuing qualitative investigations, the theoretical relationship between POD and PPCA is transparent such that the factor-loading MLE of PPCA, evaluated by the EM-PCA, pertains to an orthogonal basis obtained by POD. By contrast, the analytical connection between gappy POD and the EM-PCA is nebulous because they distinctively approximate missing data due to their antithetical formulation perspectives: gappy POD solves a least-squares problem whereas the EM-PCA relies on the expectation of the observation probability model. To juxtapose both gappy POD and the EM-PCA, this research proposes a unifying least-squares perspective that embraces the two disparate algorithms within a generalized least-squares framework. As a result, the unifying perspective reveals that both methods address similar least-squares problems; however, their formulations contain dissimilar bases and norms. Furthermore, this research delves into the ramifications of the different bases and norms that will eventually characterize the traits of both methods. To this end, two hybrid algorithms of gappy POD and the EM-PCA are devised and compared to the original algorithms for a qualitative illustration of the different basis and norm effects. After all, a norm reflecting a curve-fitting method is found to more significantly affect estimation error reduction than a basis for two example test data sets: one is absent of data only at a single snapshot and the other misses data across all the snapshots.
From a numerical performance aspect, the EM-PCA is computationally less efficient than POD for intact data since it suffers from slow convergence inherited from the EM algorithm. For incomplete data, this thesis quantitatively found that the number of data-missing snapshots predetermines whether the EM-PCA or gappy POD outperforms the other because of the computational cost of a coefficient evaluation, resulting from a norm selection. For instance, gappy POD demands laborious computational effort in proportion to the number of data-missing snapshots as a consequence of the gappy norm. In contrast, the computational cost of the EM-PCA is invariant to the number of data-missing snapshots thanks to the L2 norm. In general, the higher the number of data-missing snapshots, the wider the gap between the computational cost of gappy POD and the EM-PCA. Based on the numerical experiments reported in this thesis, the following criterion is recommended regarding the selection between gappy POD and the EM-PCA for computational efficiency: gappy POD for an incomplete data set containing a few data-missing snapshots and the EM-PCA for an incomplete data set involving multiple data-missing snapshots.
Last, the EM-PCA is applied to two aerospace applications in comparison to gappy POD as a proof of concept: one with an emphasis on basis extraction and the other with a focus on missing data reconstruction for a given incomplete data set with scattered missing data.
The first application exploits the EM-PCA to efficiently construct reduced-order models of engine deck responses obtained by the numerical propulsion system simulation (NPSS), some of whose results are absent due to failed analyses caused by numerical instability.
Model-prediction tests validate that engine performance metrics estimated by the reduced-order NPSS model exhibit considerably good agreement with those directly obtained by NPSS. Similarly, the second application illustrates that the EM-PCA is significantly more cost effective than gappy POD at repairing spurious PIV measurements obtained from acoustically-excited, bluff-body jet flow experiments. The EM-PCA reduces computational cost on factors 8 ~ 19 compared to gappy POD while generating the same restoration results as those evaluated by gappy POD. All in all, through comprehensive theoretical and numerical investigation, this research establishes that the EM-PCA is an efficient alternative to gappy POD for an incomplete data set containing missing data over an entire data set.
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RULLI, FEDERICO. "UN’INDAGINE SULLA VARIABILITA’ CICLICA NEI MOTORI A COMBUSTIONE INTERNA UTILIZZANDO PROPER ORTHOGONAL DECOMPOSITION E LARGE-EDDY SIMULATIONS". Doctoral thesis, Università degli studi di Modena e Reggio Emilia, 2020. http://hdl.handle.net/11380/1200665.
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Il principale obbiettivo della ricerca sui motori a combustione interna (internal combustion engines, ICEs) consiste nell’incremento della potenza erogata a fronte di una contemporanea riduzione di consumi ed emissioni inquinanti. La variabilità ciclica (Cycle-to-cycle variability, CCV) è fortemente legata alla natura intrinsecamente turbolenta della fluidodinamica dei motori a combustione interna, ed i suoi effetti sono nocivi sull’efficienza di combustione, sul consumo di carburante e sulle emissioni inquinanti. A causa delle fluttuazioni nella propagazione del fronte di fiamma, nel rilascio di calore e nella formazione dei prodotti di combustione, la CCV è individuata tra i fattori più limitanti per il raggiungimento di sempre più alte potenze specifiche a fronte di minori consumi. È dunque fondamentale capire e controllare la CCV per migliorare l’efficienza e le prestazioni dei motori. Tecniche sperimentali come la Particle Image Velocimetry (PIV) forniscono un consistente supporto tecnico per l’analisi dell’evoluzione spaziale e temporale dei flussi nei motori. La Proper Orthogonal Decomposition (POD) è stata largamente usata insieme alla PIV per analizzare le caratteristiche del campo di moto dei motori. Negli ultimi anni, diversi metodi basati sulla POD sono stati proposti per analizzare la CCV sui motori. In questo lavoro vengono illustrati la phase invariant POD, la media condizionale, e la decomposizione tripla e quadrupla della POD. Questi metodi sono applicati ad un vasto database di dati PIV sul motore di ricerca ad accesso ottico TCC-III. I risultati sono discussi dando particolare risalto alle capacità di ciascun metodo di dare una stima sia qualitativa che quantitativa della CCV. Un nuovo metodo di decomposizione quadrupla della POD viene proposto e comparato ai metodi presenti in letteratura. Oltre alle tecniche sperimentali, la fluidodinamica computazionale (Computational Fluid Dynamics, CFD) è ormai diventata uno strumento imprescindibile per la comprensione dei complessi fenomeni aero-termochimici che hanno luogo nel cilindro e per guidare lo sviluppo di nuove soluzioni tecniche. Le simulazioni LES (large-eddy simulations) sono lo strumento più indicato per simulare la CCV. In questo lavoro è stato valutato il potenziale della CFD nella simulazione della CCV. Diverse tecniche di analisi della CCV sono state valutate su un dataset di 50 cicli LES sul motore TCC-III in trascinato. L’accuratezza e l’affidabilità delle simulazioni CFD sono insite nei modelli usati per discretizzare il dominio fluidodinamico e per risolvere le equazioni che governano i fenomeni fisici. La strategia di discretizzazione (meshing) assume un ruolo centrale nell’efficienza computazionale, nella gestione dei componenti in movimento nel motore e nell’accuratezza dei risultati. L’approccio overset mesh, chiamato anche Chimera o Composite grid, è stato raramente applicato ai motori, soprattutto a causa delle difficoltà nell’adattamento di questa tecnica alle complessità specifiche della fluidodinamica dei motori. In questo lavoro viene dimostrata l’applicabilità della tecnica overset mesh ai motori a combustione interna, attraverso un approccio di discretizzazione sviluppato appositamente, e ne viene mostrata l’efficacia. 50 cicli LES sono stati calcolati sul motore TCC-III in trascinato. La tecnica di decomposizione quadrupla della POD sviluppata è stata ampiamente applicata per valutare sia l’accuratezza dei risultati simulati, sia l’efficacia del metodo stesso nella comprensione della CCV.The main goal of research on reciprocating internal combustion engines (ICEs) consists in increasing the power output while reducing pollutant emission and fuel consumption. Cycle-to-cycle variability (CCV) is closely coupled with the intrinsic turbulent nature of in-cylinder flow and is detrimental in terms of combustion efficiency, fuel consumption, and tailpipe emissions. Due to fluctuations in flame propagation, heat release, and burnt product formation, CCV is now seen as one of the major limiting factors for higher power output and lower fuel consumption in ICEs. Therefore, it is essential to understand and control CCV to improve the overall engine efficiency and performance. Experimental techniques like particle image velocimetry (PIV) provide a powerful technical support for the analysis of the spatial and temporal evolution of the flow field in ICEs. Proper orthogonal decomposition (POD) has been largely used in conjunction with PIV to analyze flow field characteristics. Several methods involving POD have been proposed in the recent years to analyze engine CCV. In this work, phase invariant POD analysis, conditional averaging, and triple and quadruple POD decomposition methods are introduced and applied to a large database of PIV data from the optically accessible TCC-III research engine. Results are discussed with particular emphasis on the capability of the methods to perform both quantitative and qualitative evaluations on CCV. A new quadruple POD decomposition methodology is proposed and compared to those available in the literature. Besides experimental techniques, Computational Fluid Dynamics (CFD) has become a fundamental tool for understanding the complex aero-thermochemical processes that take place in the cylinder and for driving the development of new technological solutions. Large-eddy simulation (LES) is the most practical simulation tool to understand the nature of CCV. This work investigates the CFD capabilities to simulate CCV. Several methods of analysis were assessed on a 50 LES cycles dataset on the TCC-III engine under motored conditions. The accuracy and the reliability of CFD simulations stands in the models used for the discretization of the fluid domain and for the numerical computation of the governing equations. The meshing strategy plays a central role in the computational efficiency, in the management of the moving components of the engine and in the accuracy of results. The overset mesh approach, usually referred to as Chimera grid or Composite grid, was rarely applied to the simulation of ICEs, mainly because of the difficulty in adapting the technique to the specific complexities of ICE flows. This work demonstrates the feasibility and the effectiveness of the overset mesh technique application to ICEs thanks to a purposely designed meshing approach. 50 LES cycles were performed on the TCC-III engine under motored conditions. The proposed POD quadruple decomposition methodology was extensively applied to assess both the accuracy of the simulated results and the potential of the method itself for understanding CCV.
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Dinckal, Cigdem. "Decomposition Of Elastic Constant Tensor Into Orthogonal Parts". Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612226/index.pdf.
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All procedures in the literature for decomposing symmetric second rank (stress) tensor and symmetric fourth rank (elastic constant) tensor are elaborated and compared which have many engineering and scientific applications
for anisotropic materials. The decomposition methods for symmetric second rank tensors are orthonormal tensor basis method, complex variable representation and spectral method. For symmetric fourth rank (elastic constant)
tensor, there are four mainly decomposition methods namely as, orthonormal tensor basis, irreducible, harmonic decomposition and spectral. Those are
applied to anisotropic materials possessing various symmetry classes which are isotropic, cubic, transversely isotropic, tetragonal, trigonal and orthorhombic.
For isotropic materials, an expression for the elastic constant tensor different than the traditionally known form is given. Some misprints found in the literature are corrected.
For comparison purposes, numerical examples of each decomposition process are presented for the materials possessing different symmetry classes. Some
applications of these decomposition methods are given. Besides, norm and norm ratio concepts are introduced to measure and compare the anisotropy degree for
various materials with the same or di¤erent symmetries. For these materials,norm and norm ratios are calculated. It is suggested that the norm of a tensor may be used as a criterion for comparing the overall e¤
ect of the properties of anisotropic materials and the norm ratios may be used as a criterion to represent the anisotropy degree of the properties of materials. Finally, comparison of all methods are done in order to determine similarities and differences between them. As a result of this comparison process, it is proposed that the spectral method is a non-linear decomposition method which yields non-linear orthogonal decomposed parts. For symmetric second rank and fourth rank tensors, this case is a significant innovation in decomposition procedures in the literature.
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Viggiano, Bianca Fontanin. "Reduced Order Description of Experimental Two-Phase Pipe Flows: Characterization of Flow Structures and Dynamics via Proper Orthogonal Decomposition". PDXScholar, 2017. https://pdxscholar.library.pdx.edu/open_access_etds/3829.
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Multiphase pipe flow is investigated using proper orthogonal decomposition for tomographic X-ray data, where holdup, cross-sectional phase distributions and phase interface characteristics within the pipe are obtained. Six cases of stratified and mixed flow with water content of 10%, 30% and 80% are investigated to gain insight into effects of velocity and proportion of water on the flow fields. Dispersed and slug flows are separately analyzed to consider the added interface complexity of the flow fields. These regimes are also highly applicable to industry operational flows. Instantaneous and fluctuating phase fractions of the four flow regime are analyzed and reduced order dynamical descriptions are generated. Stratified flow cases display coherent structures that highlight the liquid-liquid interface location while the mixed flow cases show minimal coherence of the eigenmodes. The dispersed flow displays coherent structures for the first few modes near the horizontal center of the pipe, representing the liquid-liquid interface location while the slug flow case shows coherent structures that correspond to the cyclical formation and break up of the slug in the first 5 modes. The low order descriptions of the high water content, stratified flow field indicates that main characteristics can be captured with minimal degrees of freedom. Reconstructions of the dispersed flow and slug flow cases indicate that dominant features are observed in the low order dynamical description utilizing less than 1% of the full order model. POD temporal coefficients a1, a2 and a3 show a high level of interdependence for the slug flow case. The coefficients also describe the phase fraction holdup as a function of time for both dispersed and slug flow. The second coefficient, a2, and the centerline holdup profile show a mean percent difference below 9% between the two curves. The mathematical description obtained from the decomposition will deepen the understanding of multiphase flow characteristics and is applicable to long distance multiphase transport pipelines, fluidized beds, hydroelectric power and nuclear processes to name a few.
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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 ouvertureIn 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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Ceccato, Chiara. "THE LATTICE DISCRETE PARTICLE MODEL (LDPM) FOR FRP CONFINED CONCRETE COLUMNS, EXPLORING THE PROPER ORTHOGONAL DECOMPOSITION (POD) TECHNIQUE". Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3424817.
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Fiber Reinforced Polymers (FRP) have been widely exploited in different civil engineering applications to enhance the performance of concrete structures through flexural, shear or compression strengthening. One of the most common and successful use of FRP sheets can be found in confinement of existing concrete vertical elements which need rehabilitation or increased capacity in terms of strength and ductility. The efficient design of FRP retrofitting requires full understanding of the concrete behavior under the complex triaxial stress state due to the passive confinement mechanisms and, for this reasons, realistic numerical models are commonly sought by the research community. In this study, experimental data gathered from the literature and relevant to the problem of FRP-confined columns subjected to uniaxial compression are simulated by the so called Lattice Discrete Particle Model (LDPM) which was recently developed to simulate concrete materials by modeling the meso-scale interaction of coarse aggregate particles. LDPM has been extensively calibrated and validated with comparison to a large variety to experimental data under both quasi-static and dynamic loading conditions but it has not been fully validated with reference to low confinement compressive stress states, relevant to the targeted application. This task is pursued in the present research. The results show that, with the improvement of the existing LDPM constitutive equations to account for low confinement effects, LDPM is able to predict the concrete material response under FRP-confinement and the developed model can capture the realistic behavior of FRP confined columns with different cross sections.
The present research also deals with the computational aspects of the simulations: the LDPM computational framework is implemented into a multi-purpose structural analysis program called MARS, which is based on an explicit dynamic algorithm scheme, advantageous in terms of convergence. However, decreasing the maximum stable time step with the highest natural frequency of the system, the computational time necessary to carry out simulations of quasi-static events, like the compression tests in the present study, might be highly demanding. In order to decrease the computational cost of the simulations, the Proper Orthogonal Decomposition (POD) as a model reduction technique has been explored for the application to the LDPM models of FRP confined columns and the relationship between efficiency gain and accuracy loss is discussed.I materiali fibrorinforzati a matrice polimerica (FRP) sono utilizzati in svariate applicazioni nel campo dell'ingegneria civile, per migliorare le prestazioni delle strutture in calcestruzzo, dal punto di vista della resistenza a flessione, a taglio, a compressione. Uno degli utilizzi più comuni e apprezzati di questi materiali è legato al confinamento di membrature verticali esistenti, che necessitano di recupero o di un'aumentata resistenza e/o duttilità. La progettazione efficace del rinforzo con FRP richiede piena comprensione del comportamento del calcestruzzo soggetto ai complessi stati tensionali dovuti al confinamento passivo e, per questa ragione, lo sviluppo di un modello numerico realistico è stato ed è tutt'ora uno degli obiettivi principali dei ricercatori. In questa sede, il cosiddetto Lattice Discrete Particle Model (LDPM), recentemente sviluppato per simulare il calcestruzzo attraverso l'interazione degli aggregati a livello di mesoscala, è stato applicato al problema della modellazione di colonne confinate con FRP e sottoposte a compressione, utilizzando come riferimento dati sperimentali di letteratura. LDPM era stato estesamente calibrato e validato sulla base di una larga varietà di condizioni di carico, sia quasi statiche che dinamiche, ma non in relazione a stati tensionali dovuti a compressione con bassi livelli di confinamento, che sono quelli rilevanti nella presente applicazione. Con il miglioramento proposto delle equazioni constitutive in compressione, LDPM è in grado di predire la risposta del calcestruzzo confinato con FRP e il modello sviluppato può simulare realisticamente il comportamento di colonne confinate con differenti sezioni. La presente ricerca affronta, parallelamente, gli aspetti più computazionali delle simulazioni con LDPM: questo modello è implementato in un software chiamato MARS, che si basa su un algoritmo esplicito, vantaggioso in termini di convergenza. Tuttavia, per ragioni di stabilità il costo computazionale richiesto per simulare eventi quasi statici, come i test di compressione di questo studio, può risultare molto sconveniente. Per ridurre i tempi di analisi, la tecnica della Proper Orthogonal Decomposition (POD) è stata esplorata in relazione all'applicazione di LDPM al caso delle colonne confinate con FRP sottoposte a compressione, valutando il rapporto tra guadagno computazionale e accuratezza dei risultati.
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Ghoman, Satyajit Sudhir. "A Hybrid Optimization Framework with POD-based Order Reduction and Design-Space Evolution Scheme". Diss., Virginia Tech, 2013. http://hdl.handle.net/10919/23113.
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The main objective of this research is to develop an innovative multi-fidelity multi-disciplinary design, analysis and optimization suite that integrates certain solution generation codes and newly developed innovative tools to improve the overall optimization process. The research performed herein is divided into two parts: (1) the development of an MDAO framework by integration of variable fidelity physics-based computational codes, and (2) enhancements to such a framework by incorporating innovative features extending its robustness.The first part of this dissertation describes the development of a conceptual Multi-Fidelity Multi-Strategy and Multi-Disciplinary Design Optimization Environment (M3 DOE), in context of aircraft wing optimization. M3 DOE provides the user a capability to optimize configurations with a choice of (i) the level of fidelity desired, (ii) the use of a single-step or multi-step optimization strategy, and (iii) combination of a series of structural and aerodynamic analyses. The modularity of M3 DOE allows it to be a part of other inclusive optimization frameworks. The M3 DOE is demonstrated within the context of shape and sizing optimization of the wing of a Generic Business Jet aircraft. Two different optimization objectives, viz. dry weight minimization, and cruise range maximization are studied by conducting one low-fidelity and two high-fidelity optimization runs to demonstrate the application scope of M3 DOE.
The second part of this dissertation describes the development of an innovative hybrid optimization framework that extends the robustness of M3 DOE by employing a proper orthogonal decomposition-based design-space order reduction scheme combined with the evolutionary algorithm technique. The POD method of extracting dominant modes from an ensemble of candidate configurations is used for the design-space order reduction. The snapshot of candidate population is updated iteratively using evolutionary algorithm technique of fitness-driven retention. This strategy capitalizes on the advantages of evolutionary algorithm as well as POD-based reduced order modeling, while overcoming the shortcomings inherent with these techniques. When linked with M3 DOE, this strategy offers a computationally efficient methodology for problems with high level of complexity and a challenging design-space. This newly developed framework is demonstrated for its robustness on a non-conventional supersonic tailless air vehicle wing shape optimization problem.
Ph. D.
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Sutton, Daniel. "Improved Reduced Order Modeling Strategies for Coupled and Parametric Systems". Thesis, Virginia Tech, 2005. http://hdl.handle.net/10919/34639.
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This thesis uses Proper Orthogonal Decomposition to model parametric and coupled systems. First, Proper Orthogonal Decomposition and its properties are introduced as well as how to numerically compute the decomposition. Next, a test case was used to show how well POD can be used to simulate and control a system. Finally, techniques for modeling a parametric system over a given range and a coupled system split into subdomains were explored, as well as numerical results.Master of Science
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Christ, Paul [Verfasser], Thomas [Akademischer Betreuer] Sattelmayer, Jürgen [Gutachter] Köhler i Thomas [Gutachter] Sattelmayer. "Modeling of Automotive HVAC Units Using Proper Orthogonal Decomposition / Paul Christ ; Gutachter: Jürgen Köhler, Thomas Sattelmayer ; Betreuer: Thomas Sattelmayer". München : Universitätsbibliothek der TU München, 2019. http://d-nb.info/118840878X/34.
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Lee, Jaehyung. "Study on aerodynamic interference and unsteady pressure field around B/D=4 rectangular cylinder based on proper orthogonal decomposition". 京都大学 (Kyoto University), 2006. http://hdl.handle.net/2433/136143.
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Kyoto University (京都大学)0048
新制・課程博士
博士(工学)
甲第12587号
工博第2700号
新制||工||1388(附属図書館)
UT51-2006-S595
京都大学大学院工学研究科社会基盤工学専攻
(主査)教授 松本 勝, 教授 河井 宏允, 助教授 白土 博通, 教授 田村 武
学位規則第4条第1項該当
49
Flores, Vera Rafael. "The Use of the Proper Orthogonal Decomposition for the Characterization of the Dynamic Response of Structures Due to Wind Loading". Thesis, Université d'Ottawa / University of Ottawa, 2011. http://hdl.handle.net/10393/19762.
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This thesis presents a study of the wind load forces and their influence on the response of structures. The study is based on the capacity of the Proper Orthogonal Decomposition method (POD) to identify and extract organized patterns that are hidden or embedded inside a complex field. Technically this complex field is defined as a multi-variate random process, which in wind engineering is represented by unsteady pressure signals recorded on multiple points of the surface of a structure. The POD method thus transforms the multi-variate random pressure field into a sequence of load shapes that are uncorrelated with each other. The effect of each uncorrelated load shape on the structural response is relatively easy to evaluate and the individual contributions can be added linearly afterwards. Additionally, since each uncorrelated load shape is associated with a percentage of the total energy involved in the loading process, it is possible to neglect those load shapes with low energy content. Furthermore, the load shapes obtained with the POD often reveal physical flow structures, like vortex shedding, oscillations of shear layers, etc. This later property can be used in conjunction with classical results in fluid mechanics to theorize about the physical nature of different flow mechanics and their interactions. The POD method is well suited to be used in conjunction with the classical modal analysis, not only to calculate the structural response for a given pressure field but to observe the details of the wind-structure interaction. A detailed and complete application is presented here but the methodology is very general since it can be applied to any recorded pressure field and for any type of structure.
50
Danby, Sean James. "Optimization of Proper Orthogonal Decomposition using Various Preconditioning Techniques to Analyze Autoignition Simulation Data of Non-Homogeneous Hydrogen-Air Mixtures". NCSU, 2004. http://www.lib.ncsu.edu/theses/available/etd-11042004-203408/.
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The proper orthogonal decomposition (POD) method is implemented on unsteady 2D data from direct numerical simulations (DNS) of auto-ignition in non-homogeneous hydrogen-air mixtures. The analysis is implemented to evaluate requirements for the reproduction of transient, multi-dimensional and multi-scalar processes in combustion. The resulting low-order models may be used to store and manage large data sets for post-processing and visualization, and for the implementation of POD reduced data as an integral element of model-based closure in turbulent combustion. Data reduction is implemented on a set of thirty snapshots of 2D fields of the passive scalar: the mixture fraction, and reactive scalars: the reaction progress variable, the reactants, hydrogen (H2) and oxygen (O2), mass fractions and intermediate species, H-radical and HO2 mass fractions. The snapshots cover the evolution of the hydrogen-air mixture from induction to high-temperature combustion stages. POD analysis shows that there are different requirements to reproduce passive and reactive scalars depending on the degree of their spatial and temporal variations during the autoignition process and the statistical distribution. The mixture fraction, which is affected by the mixing process only, requires the least number of eigenmodes, and yields a sufficient representation of the original data with only four eigenmodes. The success of the POD reduction of the reactive scalars depends upon the distribution of the statistics of the original scalar. On average, the reactive scalars require at least six modes to reproduce the original data. A number of pre-processing strategies of the scalar fields are explored to reduce the number of required eigenmodes. The strategies are designed to reduce the temporal and spatial spans of scalar values. The results show that different pre-processing strategies may yield different outcomes for the passive and reactive scalars reduction process depending on the statistical distributions of these scalars.