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Monti, Francesca. "Combining structural and reduced-form models for macroeconomic forecasting and policy analysis." Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209970.
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Can we fruitfully use the same macroeconomic model to forecast and to perform policy analysis? There is a tension between a model’s ability to forecast accurately and its ability to tell a theoretically consistent story. The aim of this dissertation is to propose ways to soothe this tension, combining structural and reduced-form models in order to have models that can effectively do both.Doctorat en Sciences économiques et de gestion
info:eu-repo/semantics/nonPublished
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Shen, Yichang. "Reduced-order models for geometrically nonlinear vibrations of thin structures." Thesis, Institut polytechnique de Paris, 2021. http://www.theses.fr/2021IPPAE012.
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Lorsqu'elles vibrent avec de grandes amplitudes, les structures minces montrent un comportement non linéaire géométrique, provenant de la relation non linéaire entre les déformations et les déplacements. Les analyses des systèmes complets font appel à des calculs extrêmement couteux de telle sorte que l'établissement de modèles d'ordre réduit efficaces est un sujet d'intérêt majeur pour le calcul prédictif de vibrations de structures minces.Dans cette thèse, des méthodes non linéaires de réduction de modèle pour les structures discrétisées par la méthode des éléments finis et comportant une non-linéarité géométrique, sont étudiées. Trois méthodes non intrusives sont plus particulièrement examinées et systématiquement comparées: la méthode de condensation implicite, la méthode des dérivées modales, et la réduction sur variétés invariantes du système. Les analyses théoriques montrent que les deux premières méthodes ne peuvent donner de résultats fiables que sous hypothèse d'une séparation spectrale entre les fréquences propres des modes maitres et celles des modes esclaves. La méthode de réduction sur variétés invariantes permet quant à elle d'avoir une méthode directe, ne nécessitant pas de pré-calculs, ni d'hypothèses préalables sur les fréquences propres des modes esclaves, afin de fournir des résultats corrects.De nombreuses applications et de comparaisons numériques sont montrées sur diverses structures discrétisées avec la méthode des éléments finis. Pour appliquer la méthode des variétés invariantes, une méthode récemment développée, permet de proposer un calcul direct de la forme normale du problème, à partir de la base physique et donc des degrés de liberté du maillage éléments finis. Les exemples montrent clairement les avantage et inconvénients de chaque méthode, validant aussi les résultats théoriques montrés précédemment.Dans la dernière partie de la thèse, la dynamique non linéaire d'un système présentant une relation de résonance interne 1:2 est analysée, en tenant compte des termes cubiques. La forme normale réelle du problème est d'abord établie. Ensuite les branches de solution du problème sont analysées et comparées avec celles du modèle plus simple négligeant la non-linéarité cubique. Le comportement divergent observé lorsqu'on réduit le problème à un seul mode et que l'on cherche à prédire le comportement raidissant ou assouplissant, est ensuite étudié avec ce modèle plus completWhen vibrating with large amplitudes, thin structures experience geometric nonlinearity due to the nonlinear relationship between strains and displacements. Because full-order nonlinear analysis on geometrically nonlinear models are computationally very expensive, the derivation of efficient reduced-order models (ROMs) has always been a topic of interest.In this thesis, nonlinear reduction methods for building ROMs with geometric nonlinearity in the framework of the Finite Element (FE) procedure, are investigated. Three non-intrusive nonlinear reduction methods are specifically investigated and systematically compared. They are: implicit condensation and expansion (ICE), modal derivatives (MD), and the reduction to invariant manifold. Theoretical analysis shows that the first two methods can give reliable results only if a slow/fast assumption between slave and master coordinates holds. On the other hand, reduction to invariant manifolds allows proposing a simulation-free reduction method that can be applied without restricting assumptions on the frequencies of the slave modes.Numerical comparisons and numerous applications to continuous structures discretized with the FE procedure, are given subsequently. For application of the invariant manifold-based method, the computation is based on a direct application of the normal form to the physical space and hence to the nodes of the FE mesh, a method recently developed. The examples show the advantages and drawbacks of each reduction method when deriving ROM, and the results of the theoretical comparison are validated.Finally, the analysis of the dynamics of a system with 1:2 internal resonance and cubic nonlinearity is given in the last part of the thesis. The real normal form of the problem is first derived. Then the solution branches of the problem are investigated and compared to simpler solutions with the dynamics truncated at order two. The divergent behaviour of the hardening/softening characteristics for single-mode reduction is investigated with this more complete model
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Scherling, Alexander I. "Reduced-Order Reference Models for Adaptive Control of Space Structures." DigitalCommons@CalPoly, 2014. https://digitalcommons.calpoly.edu/theses/1199.
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In addition to serving as a brief overview of aspects relevant to reduced-order modeling (in particular balanced-state and modal techniques) as applied to structural finite element models, this work produced tools for visualizing the relationship between the modes of a model and the states of its balanced representation.
Specifically, error contour and mean error plots were developed that provide a designer with frequency response information absent from a typical analysis of a balanced model via its Hankel singular values. The plots were then used to analyze the controllability and observability aspects of finite element models of an illustrative system from a modal perspective -- this aided in the identification of computational artifacts in the models and helped predict points at which to halt the truncation of balanced states.
Balanced reduced-order reference models of the illustrative system were implemented as part of a direct adaptive control algorithm to observe the effectiveness of the models. It was learned that the truncation point selected by observing the mean error plot produced the most satisfactory results overall -- the model closely approximated the dominant modes of the system and eliminated the computational artifacts.
The problem of improving the performance of the system was also considered. The truncated balanced model was recast in modal form so that its damping could be increased, and the settling time decreased by about eighty percent.
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Kolman, Marek. "Pricing and modeling credit risk." Doctoral thesis, Vysoká škola ekonomická v Praze, 2017. http://www.nusl.cz/ntk/nusl-264720.
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The thesis covers a wide range of topics from the credit risk modeling with the emphasis put on pricing of the claims subject to the default risk. Starting with a separate general contingent claim pricing framework the key topics are classified into three fundamental parts: firm-value models, reduced-form models, portfolio problems, with a possible finer sub-classification. Every part provides a theoretical discussion, proposal of self-developed methodologies and related applications that are designed so as to be close to the real-world problems. The text also reveals several new findings from various fields of credit risk modeling. In particular, it is shown (i) that the stock option market is a good source of credit information, (ii) how the reduced-form modeling framework can be extended to capture more complicated problems, (iii) that the double t copula together with a self-developed portfolio modeling framework outperforms the classical Gaussian copula approaches. Many other, partial findings are presented in the relevant chapters and some other results are also discussed in the Appendix.
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Zhang, Wenxian. "Direct sensitivity techniques in regional air quality models: development and application." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/52941.
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Sensitivity analysis based on a chemical transport model (CTM) serves as an important approach towards better understanding the relationship between trace contaminant levels in the atmosphere and emissions, chemical and physical processes. Previous studies on ozone control identified the high-order Decoupled Direct Method (HDDM) as an efficient tool to conduct sensitivity analysis. Given the growing recognition of the adverse health effects of fine particulate matter (i.e., particles with an aerodynamic diameter less than 2.5 micrometers (PM2.5)), this dissertation presents the development of a HDDM sensitivity technique for particulate matter and its implementation it in a widely used CTM, CMAQ. Compared to previous studies, two new features of the implementation are 1) including sensitivities of aerosol water content and activity coefficients, and 2) tracking the chemical regimes of the embedded thermodynamic model. The new features provide more accurate sensitivities especially for nitrate and ammonium. Results compare well with brute force sensitivities and are shown to be more stable and computationally efficient. Next, this dissertation explores the applications of HDDM. Source apportionment analysis for the Houston region in September 2006 indicates that nonlinear responses accounted for 3.5% to 33.7% of daily average PM2.5, and that PM2.5 formed rapidly during night especially in the presence of abundant ozone and under stagnant conditions. Uncertainty analysis based on the HDDM found that on average, uncertainties in the emissions rates led to 36% uncertainty in simulated daily average PM2.5 and could explain much, but not all, of the difference between simulated and observed PM2.5 concentrations at two observations sites. HDDM is then applied to assess the impact of flare VOC emissions with temporally variable combustion efficiency. Detailed study of flare emissions using the 2006 Texas special inventory indicates that daily maximum 8-hour ozone at a monitoring site can increase by 2.9 ppb when combustion is significantly decreased. The last application in this dissertation integrates the reduced form model into an electricity generation planning model, and enables representation of geospatial dependence of air quality-related health costs in the optimization process to seek the least cost planning for power generation. The integrated model can provide useful advice on selecting fuel types and locations for power plants.
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Oguz, Hatice Dilek. "Pricing Us Corporate Bonds By Jarrow/turnbull (1995) Model." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/2/12611174/index.pdf.
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In this study Jarrow Turnbull (1995) Model, which is a reduced form approach for credit risk models, is employed to estimate the default intensity of US corporate bonds conditionally based on a fixed recovery rate. The estimations are performed with respect to the ratings of the bonds and the results were consistent with the ratings. US Treasury Bills are also used to since zero coupon default free prices, modeled by Svensson (1994) are necessary for pricing the default risky coupon bonds.
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Reschreiter, Andreas. "Conventional and indexed UK bond returns and the macroeconomy : an empirical analysis based on asset pricing and reduced form VAR models." Thesis, Imperial College London, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.271099.
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Vogt, Jonas [Verfasser], Dominik [Akademischer Betreuer] Wied, and Walter [Gutachter] Krämer. "Reduced Form Credit Risk Models and the Second Dimension Risk Premium : Technical Foundations, Estimation and Applications / Jonas Vogt. Betreuer: Dominik Wied. Gutachter: Walter Krämer." Dortmund : Universitätsbibliothek Dortmund, 2013. http://d-nb.info/1107778700/34.
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Gaspar, Raquel M. "Credit risk & forward price models." Doctoral thesis, Stockholm : Economic Research Institute, Stockholm School of Economics [Ekonomiska forskningsinstitutet vid Handelshögskolan i Stockholm] (EFI), 2006. http://www.hhs.se/efi/summary/686.htm.
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Slinko, Irina. "Essays in option pricing and interest rate models." Doctoral thesis, Stockholm : Economic Research Institute, Stockholm School of Economics [Ekonomiska forskningsinstitutet vid Handelshögskolan i Stockholm] (EFI), 2006. http://www2.hhs.se/EFI/summary/706.htm.
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Winkler, Niklas. "Reduced models for flows in IC-engines." Doctoral thesis, KTH, Förbränningsmotorteknik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-41496.
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The finite response time of the turbocharger is the most notable effect of transient operation on a turbocharged diesel engine. To fulfill future emission requirements, high amounts of transient EGR will be required even though after-treatment devices are being used. This implies that advanced turbocharger systems have to be introduced to enable high boost pressure with improved or at least maintained response time. The increased amount of tuneable parameters from the more advanced turbocharging system will make it difficult and expensive to optimise the engine experimentally. Therefore, the wish is to optimise the engine design using numerical tools. This requires predictive models for the gas exchange system and its components, i.e. the turbocharger, the manifolds and the cylinder with its valves. The results have shown that engine simulation tools based on tabulated data from measurements can qualitatively predict the engine's performance and be used as a first step in engine design. However, these models have to be calibrated extensively in order to reflect the engine performance quantitatively. The objective of this research is therefore to find a modelling approach for the gas exchange system and its components that are more predictive than the tools used, but still computationally effective enough to be suited for engine simulations. The thesis contains a summary of on-engine experimental results as well as some One-Dimensional (1D) simulations. Since the 1D modelling approach has limited range of validity and applicability, we have considered two approaches for reducing the full Three-Dimensional (3D) governing equations, which are a set of Partial Differential Equations (PDE), in a systematic manner. The first approach is based on a numerical length scale analysis of the different terms in the governing equations after changing the coordinate system with one coordinate aligned with the flow path. By retaining the most important terms or neglecting the (significantly) smallest terms, different reductions may be attained, which in their simplest form may look like the boundary layer equations. The results for a double bent pipe, used to illustrate the approach, show that the most significant component of the viscous terms is the radial component, which is in the order of two magnitudes larger than the axial and azimuthal components. The convective terms are all in the same order of magnitude, whereas the radial component is of significant importance in the bends of the pipe due to centrifugal forces, and the azimuthal component after the second bend due to a swirling motion. For the flow in a straight pipe, the approach would give the same model as the common 1D simulation tool. However, for pipes with a more general shape, the approach is superior as it allows for a rational reduction of the governing equations. The main limitation of the approach is for flow situations that do not have a dominating flow direction. Under such conditions the a priori and/or the a posteriori analysis would reveal that the reduction is inconsistent. Thus, the approach implies maintained efficiency, but with improved (and assessable) accuracy as compared to the common 1D simulation tool. The second approach is based on the Galerkin projection of the governing equations projected onto Proper Orthogonal Decomposition (POD) modes. These POD modes are computed for the flow in a given geometry obtained through Large Eddy Simulations (LES). The Galerkin projection results in a system of Ordinary Differential Equations (ODE) for the time-dependent coefficients of the 3D POD modes. The results show that the method is best suited for flows with strong coherent structures. However, the system of ODEs may be inherently unstable (depending on the number of modes used in the simulation) and modelling errors grow with each time-step. This limitation may be remedied by numerically preventing any exponential growth. The approach can also be extended into a combined Galerkin (ODE) - LES (PDE) approach by replacing several steps of the LES by the same amount of time steps with the reduced model. It should be pointed out that this approach can provide the full 3D flow field in contrast to space reduced models (e.g. the common 1D tool) and thereby handle more complex flows with high degree of computational efficiency. To summarize, the thesis demonstrates new possibilities of obtaining reduced models suited for engine simulations based on 3D CFD. With this application in mind, these tools are novel and their evaluation and assessment should be extended to other components of the gas exchange system.QC 20110928
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Bryson, James R. "Reduced models for batch and continuous distillation." Thesis, University of Cambridge, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319468.
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Hopkins, Asa Sies Mabuchi Hideo Mabuchi Hideo. "Reduced order models for open quantum systems /." Diss., Pasadena, Calif. : California Institute of Technology, 2009. http://resolver.caltech.edu/CaltechETD:etd-11182008-113904.
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Zhou, Junjie 1979. "Reduced model for particle laden flow." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/17955.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2004.Includes bibliographical references (p. 133-138).
The flow of thin liquid films on solid surfaces is a significant phenomenon in nature and in industrial processes where uniformity and completeness of wetting are paramount in importance. It is well known that when a clear viscous fluid flows down an inclined surface under gravity, after some time, the initially straight contact line becomes unstable with respect to transverse perturbations. Clear fluid is easier to use in experiments, but industrial processes usually involve particulates in the form of either suspensions or dry granular flows. In this work, we study the flow of a thin film down an inclined plane. The particle-fluid mixture is modeled as a single fluid with effective density and viscosity, depending on the concentration of the particles. Since the flow is slow and the fluid layer is very thin, inertial effects are ignored and a lubrication approximation is applied to simplify the analysis. It is assumed that there is no variation in the transverse direction before the onset of instability, and the fluid properties and velocity are depth averaged to remove the height-dependence. The settling velocity of the particles is hindered by the presence of neighboring particles; this phenomenon is captured by the hindered velocity function that decreases with increasing concentration. The normal component of the settling velocity is neglected in this work and the resulting model is a system of two equations accounting for the film thickness and particle concentration changes as the mixture flows down the plane. Numerical simulations are performed and it is found that the mixtures with higher concentration flow more slowly. Compared to the clear viscous fluid, particle laden flow results in a bump that is much bigger and the size of the bump
(cont.) bump increases with concentration. We also observe that the front edge of the bump travels faster than the trailing edge and the bump width increases. Numerical simulations reveal that an intermediate plateau structure due to the presence of particles is formed behind the smaller bump due to surface tension. This intermediate state depends on the inclination angle and the initial concentration. When the higher order terms in our derived model are dropped, we discover that the resulting reduced model is still able to capture the bulk characteristics of the flow. The reduced model is a 2X2 system of conservation laws, in which the solutions can be obtained through classical shock theory analysis. It is found that our system involves a 1-shock at the trailing edge connected by an intermediate state to a 2-shock at the leading edge. The intermediate state as well as the shock speeds can be solved by shock theory analysis, and their values are found to agree very well with the simulations.
by Junjie Zhou.
S.M.
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Reyes, Sotomayor Ricardo. "Stabilized reduced order models for low speed flows." Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/669102.
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This thesis presents the a stabilized projection-based Reduced Order Model (ROM) formulation in low speed fluid flows using a Variational Multi-Scale (VMS) approach. To develop this formulation we use a Finite Element (FE) method for the Full Order Model (FOM) and a Proper Orthogonal Decomposition (POD) to construct the basis.
Additional to the ROM formulation, we introduce two techniques that became possible using this approach: a mesh-based hyper-reduction that uses an Adaptive Mesh Refinement (AMR) approach, and a domain decomposition scheme for ROMs.
To illustrate and test the proposed formulation we use five different models: a convection–diffusion–reaction, the incompressible Navier–Stokes, a Boussinesq approximation, a low Mach number model, and a three-field incompressible Navier–Stokes.Esta tesis presenta un modelo de orden reducido estabilizado paran fluidos a baja velocidad utilizando un enfoque de multiescala variacional. Para desarrollar esta formulación utilizamos el método de elementos finitos para el modelo no reducido y una descomposición en autovalores del mismo para construir la base. Adicional a la formulación del modelo reducido, presentamos dos técnicas que podemos formular al utilizar este enfoque: una reducción adicional del dominio, basada en la reducción de la malla, donde usamos una técnica de refinamiento adaptativa y un esquema de descomposición de dominio para el modelo reducido. Para ilustrar y probar la formulación propuesta, utilizamos cuatro diferentes modelos fisicos: una ecuación de convección-difusión-reacción, la ecuación de Navier-Stokes para fluidos incompresibles, una aproximación de Boussinesq para la ecuación de Navier-Stokes, y una aproximación para números de Mach bajos de la ecuación de Navier-Stokes.
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Xu, Shaokang. "Study of reduced kinetic models for plasma turbulence." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLX057/document.
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Le contrôle du transport turbulent est l'une des clés pour l'amélioration du temps de confinement nécessaire à la réalisation de la fusion thermonucléaire contrôlée. La description de la turbulence cinétique du plasma est un problème à 3 coordonnées spatiales et 3 coordonnées en vitesse. La théorie comme la simulation pour un problème de si haute dimensionnalité sont très difficiles, et des modèles réduits sont nécessaires pour comprendre la turbulence dans les Tokamaks. La technique largement utilisée est de faire moyenner le mouvement cyclotron, qui est beaucoup plus rapide que le phénomène de turbulence. Une telle réduction permet de simplifier le problème à trois coordonnées spatiales des centres-guides des particules, une vitesse parallèle ou énergie et une vitesse perpendiculaire apparaissant comme l'invariant adiabatique. La description gyrocinétique non linéaire requiert des simulations numériques de haute performance massivement parallèles. Toute la difficulté est due aux termes non linéaires (crochets de Poisson) qui décrivent les interactions multi-échelles, ce qui constitue un défi tant pour la théorie que pour la simulation. Toute approche réduite, basée sur des hypothèses bien contrôlées, est donc intéressante à développer.Sur la base de cette ambition, cette thèse concerne la turbulence des particules piégées dans le plasma magnétisé. C'est un système 4D, obtenu après avoir fait la moyenne de la fonction de distribution des particules sur les mouvements cyclotron et de rebond, ce qui peut être considéré comme une forme réduite de la théorie gyrocinétique standard. Nous l'avons appelé "bounce averaged gyrokinetics" pendant ce travail. Même si cette description est grandement réduite par rapport à la théorie gyrocinétique, la simulation directe non-linéaire reste un challenge.Une description des termes non linéaires en coordonnées polaires est choisie, avec une grille logarithmique en norme du vecteur d'onde, tandis que les angles sont discrétisés sur une grille régulière. L'utilisation d'une grille logarithmique permet de prendre en compte une large gamme de vecteurs d'ondes, donc la physique à très petite échelle. De manière analogue aux modèles en couches en turbulence fluide et afin de simplifier le système, seules les interactions entre couches voisines sont considérées.Dans un premier temps, l'étude du système linéaire est présentée, en particulier les seuils des paramètres et l'instabilité linéaire permettant de retrouver la forte anisotropie des taux de croissance des modes d'ions piégés (ou TIM) et des modes d'électrons piégés (ou TEM). Ces études permettent également de valider les codes numériques non-linéaires vis-à-vis d'un solveur aux valeurs propres développé indépendamment.Dans un second temps, l'hypothèse isotrope pour les termes non linéaires est utilisée. Ainsi il n'y a pas d'information de phase exacte pour de tels modèles en couches 1D, ce qui laisse un paramètre libre dans les coefficients d'interaction. Une loi de puissance originale est mise en évidence, qui n'est pas affectée par la valeur du paramètre libre, mesurant l'intensité des effets non-linéaires relativement aux termes linéaires.À partir de la simulation du modèle isotrope, l'information de phase apparaît très importante. Puisque l'instabilité linéaire est anisotrope pour la fusion, la simulation du modèle anisotrope est donc réalisée dans un troisième temps. Le système résolu numériquement est réduit à une espèce cinétique, en supposant que les autres espèces sont adiabatiques. Deux systèmes différents peuvent ainsi être étudiés: ions cinétiques + électrons adiabatiques et électrons cinétiques + ions adiabatiques. Des spectres différents sont observés dans chacun de ces deux cas, et la validité de l'hypothèse adiabatique est discutée pour chaque espèce, avec pour base de comparaison une simulation cinétique à deux espècesTurbulent transport is one of the keys to improve the energy confinement time required for thermonuclear fusion reactors. The description of the kinetic turbulence of the plasma is a problem with 3 spatial coordinates and 3 velocity coordinates. Both theory and simulation of a problem of such high dimensionality are very difficult, and reduced models are helpfull to understand turbulence in Tokamaks. A widely used technique consists into averaging the cyclotron motion, which is much faster than the turbulence time scale. Such a reduction makes it possible to simplify the problem to three spatial coordinates of the particle guide centers, a parallel velocity or energy, and a perpendicular velocity appearing as the adiabatic invariant. Nonlinear gyrokinetic description requires massively parallel high performance numerical simulations. The difficulty lies in the non-linear terms (Poisson hooks) that describe multi-scale interactions, which is a challenge for both theory and simulation. Any reduced approach, based on well-controlled hypotheses, is therefore interesting to develop.On the basis of this ambition, this thesis concerns the turbulence of particles trapped in magnetized plasma. It is a 4D system, obtained after averaging the particle distribution function on cyclotron and bounce motions, which can be considered as a reduced form of standard gyrokinetic theory. We called it "bounce averaged gyrokinetics" during this work. Even if this description is greatly reduced compared to the gyrokinetic theory, nonlinear direct simulation remains a challenge.A description of the nonlinear polar coordinate terms is chosen, with a logarithmic grid along the norm of the wave vector, while the angles are discretized on a regular grid. The use of a logarithmic grid makes it possible to take into account a wide range of wave vectors, so physics on a very small scale. In a similar way to shell models for fluid turbulence, and in order to simplify the system, only the interactions between neighboring shells are considered.In a first step, the study of the linear system is presented, in particular the paraetric dependence of the instability thresholds and the linear growth rate, allowing to recover the strong anisotropy of the growth rates of the trapped ion modes (or TIM) and the modes of trapped electrons (or TEM). These studies also make it possible to validate the non-linear numerical codes with respect to an independently developer eigenvalue solver.In a second step, the isotropic hypothesis for nonlinear terms is used. Thus, there is no exact phase information for such 1D layer models, which leaves with a free parameter in the interaction coefficients. An original power law is evidenced, which is unaffected by the value of the free parameter, measuring the intensity of the nonlinear effects relative to the linear terms.From the simulation of the isotropic model, the phase information appears very important. Since the linear instability is anisotropic for the fusion, the simulation of the anisotropic model is thus carried out in a third time. The numerically resolved system is reduced to a kinetic species, assuming that the other species are adiabatic. Two different systems can thus be studied: kinetic ions + adiabatic electrons and kinetic electrons + adiabatic ions. Different spectra are observed in each of these two cases, and the validity of the adiabatic hypothesis is discussed for each species, based on a kinetic simulation with two species
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DESHMUKH, DINAR V. "PHYSICS BASED REDUCED ORDER MODELS FOR FRICTIONAL CONTACTS." University of Cincinnati / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1115997302.
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Malik, Mohammad Rafi. "Reduced-orderCombustion Models for Innovative Energy Conversion Technologies." Doctoral thesis, Universite Libre de Bruxelles, 2021. https://dipot.ulb.ac.be/dspace/bitstream/2013/318799/4/TOC.pdf.
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The present research seeks to advance the understanding and application of Principal Component Analysis (PCA)-based combustion modelling for practical systems application. This work is a consistent extension to the standard PC-transport model, and integrates the use of Gaussian Process Regression (GPR) in order to increase the accuracy and the potential of size reduction offered by PCA. This new model, labelled PC-GPR, is successively applied and validated in a priori and a posteriori studies.In the first part of this dissertation, the PC-GPR model is validated in an a priori study based on steady and unsteady perfectly stirred reactor (PSR) calculations. The model showed its great accuracy in the predictions for methane and propane, using large kinetic mechanisms. In particular, for methane, the use of GPR allowed to model accurately the system with only 2 principal components (PCs) instead of the 34 variables in the original GRI-3.0 kinetic mechanism. For propane, the model was applied to two different mechanisms consisting of 50 species and 162 species respectively. The PC-GPR model was able to achieve a very significant reduction, and the thermo-chemical state-space was accurately predicted using only 2 PCs for both mechanisms.The second part of this work is dedicated to the application of the PC-GPR model in the framework of non-premixed turbulent combustion in a fully three-dimensional Large Eddy Simulation (LES). To this end, an a posteriori validation is performed on the Sandia flames D, E and F. The PC-GPR model showed very good accuracy in the predictions of the three flames when compared with experimental data using only 2 PCs, instead of the 35 species originally present in the GRI 3.0 mechanism. Moreover, the PC-GPR model was also able to handle the extinction and re-ignition phenomena in flames E and F, thanks to the unsteady data in the training manifold. A comparison with the FPV model showed that the combination of the unsteady data set and the best controlling variables for the system defined by PCA provide an alternative to the use of steady flamelets parameterized by user-defined variables and combined with a PDF approach.The last part of this research focuses on the application of the PC-GPR model in a more challenging case, a lifted methane/air flame. Several key features of the model are investigated: the sensitivty to the training data set, the influence of the scaling methods, the issue of data sampling and the potential of a subgrid scale (SGS) closure. In particular, it is shown that the training data set must contain the effects of diffusion in order to accurately predict the different properties of the lifted flame. Moreover, the kernel density weighting method, used to address the issue of non-homogenous data density usually found in numerical data sets, allowed to improve the predictions of the PC-GPR model. Finally, the integration of subgrid scale closure to the PC-GPR model allowed to significantly improve the simulations results using a presumed PDF closure. A qualitative comparison with the FPV model showed that the results provided by the PC-GPR model are overall very comparable to the FPV results, with a reduced numerical cost as PC-GPR requires a 4D lookup table, instead of a 5D in the case of FPV.Le double défi de l'énergie et du changement climatique mettent en avant lanécessité de développer des nouvelles technologies de combustion, étantdonné que les projections les plus réalistes montrent que la plus grandeaugmentation de l'offre d'énergie pour les décennies à venir se fera à partirde combustibles fossiles. Ceci représente donc une forte motivation pour larecherche sur l'efficacité énergétique et les technologies propres. Parmicelles-ci, la combustion sans flamme est un concept nouvellementdéveloppé qui permet d'obtenir des rendements thermiques élevés avecdes économies de carburant tout en maintenant les émissions polluantes àun niveau très bas. L'intérêt croissant pour cette technologie est égalementmotivé par sa grande flexibilité de carburant, ce qui représente uneprécieuse opportunité pour les carburants à faible valeur calorifique, lesdéchets industriels à haute valeur calorifique et les combustibles à based'hydrogène. Etant donné que cette technologie est plutôt récente, elle estde ce fait encore mal comprise. Les solutions d'une application industriellesont très difficiles à transposer à d'autres. Pour améliorer les connaissancesdans le domaine de la combustion sans flamme, il est nécessaire de menerdes études fondamentales sur ce nouveau procédé de combustion afin defavoriser son développement. En particulier, il y a deux différencesmajeures par rapport aux flammes classiques :d’une part, les niveaux deturbulence rencontrés dans la combustion sans flamme sont rehaussés, enraison des gaz de recirculation, réduisant ainsi les échelles de mélange.D'autre part, les échelles chimiques sont augmentées, en raison de ladilution des réactifs. Par conséquent, les échelles turbulentes et chimiquessont du même ordre de grandeur, ce qui conduit à un couplage très fort.Après un examen approfondi de l'état de l'art sur la modélisation de lacombustion sans flamme, le coeur du projet représentera le développementd'une nouvelle approche pour le traitement de l'interaction turbulence /chimie pour les systèmes sans flamme dans le contexte des simulationsaux grandes échelles (Large Eddy Simulations, LES). Cette approche serafondée sur la méthode PCA (Principal Component Analysis) afin d'identifierles échelles chimiques de premier plan du processus d'oxydation. Cetteprocédure permettra de ne suivre sur la grille LES qu'un nombre réduit descalaires non conservés, ceux contrôlant l'évolution du système. Destechniques de régression non-linéaires seront couplées avec PCA afind’augmenter la précision et la réductibilité du modèle. Après avoir été validégrâce à des données expérimentales de problèmes simplifiés, le modèlesera mis à l'échelle afin de gérer des applications plus grandes, pertinentespour la combustion sans flamme. Les données expérimentales etnumériques seront validées en utilisant des indicateurs de validationappropriés pour évaluer les incertitudes expérimentales et numériques.
Doctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished
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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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Torres, Leonardo de Gil. "On some reduced order models for packed separation processes." Thesis, University College London (University of London), 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338703.
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Anderson, Sharon Lee. "Reduced order power system models for transient stability studies." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-09052009-040743/.
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Kyriakou, S. "Reduced-bias estimation and inference for mixed-effects models." Thesis, University College London (University of London), 2018. http://discovery.ucl.ac.uk/10049958/.
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A popular method for reducing the mean and median bias of the maximum likelihood estimator in regular parametric models is through the additive adjustment of the score equation (Firth, 1993; Kenne Pagui et al., 2017). The current work focuses on mean and median bias-reducing adjusted score equations in models with latent variables. First, we give estimating equations based on a mean bias-reducing adjustment of the score function for mean bias reduction in linear mixed models. Second, we propose an extension of the adjusted score equation approach (Firth, 1993) to obtain bias-reduced estimates for models with either computationally infeasible adjusted score equations and/or intractable likelihood. The proposed bias-reduced estimator is obtained by solving an approximate adjusted score equation, which uses an approximation of the log-likelihood to obtain tractable derivatives, and Monte Carlo approximation of the bias function to get feasible expressions. Under certain general conditions, we prove that the feasible and tractable bias-reduced estimator is consistent and asymptotically normally distributed. The “iterated bootstrap with likelihood adjustment” algorithm is presented that can compute the solution of the new bias-reducing adjusted score equation. The effectiveness of the proposed method is demonstrated via simulation studies and real data examples in the case of generalised linear models and generalised linear mixed models. Finally, we derive the median bias-reducing adjusted scores for linear mixed models and random-effects meta-analysis and meta-regression models.
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Pau, George Shu Heng. "Reduced basis method for quantum models of crystalline solids." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/40376.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.Includes bibliographical references (p. 203-213).
Electronic structure problems in solids usually involve repetitive determination of quantities of interest, evaluation of which requires the solution of an underlying partial differential equation. We present in this thesis the application of the reduced basis method in accurate and rapid evaluations of outputs associated with some nonlinear eigenvalue problems related to electronic structure calculations. The reduced basis method provides a systematic procedure by which efficient basis sets and computational strategies can be constructed. The essential ingredients are (i) rapidly convergent global reduced basis approximation spaces; (ii) an offline-online computational procedure to decouple the generation and projection stages of the approximation process; and (iii) inexpensive a posteriori error estimation procedure for outputs of interest. We first propose two strategies by which we can construct efficient reduced basis approximations for vectorial eigensolutions - solutions consisting of several eigenvectors. The first strategy exploits the optimality of the Galerkin procedure to find a solution in the span of all eigenvectors at N judiciously chosen samples in the parameter space.
(cont.) The second strategy determines a solution in the span of N vectorial basis functions that are pre-processed to better represent the smoothness of the solution manifold induced by the parametric dependence of the solutions. We deduce from numerical results conditions in which these approximations are rapidly convergent. For linear eigenvalue problems, we construct a posteriori asymptotic error estimators for our reduced basis approximations - extensions on existing work in algebraic eigenvalue problems. We further construct efficient error estimation procedures that allow efficient construction of reduced basis spaces based on the "greedy" sampling procedure. We extend our methods to nonlinear eigenvalue problems, utilizing the empirical interpolation method. We also provide a more efficient construction procedure for the empirical interpolation method. Finally, we apply our methods to two problems in electronic structure calculations - band structure calculations and electronic ground state calculations. Band structure calculations involve approximations of linear eigenvalue problems; we demonstrate the applicability of our methods in the many query limit with several examples related to determination of spectral properties of crystalline solids.
(cont.) Electronic ground state energy calculations based on Density Functional Theory involve approximations of nonlinear eigenvalue problems; we demonstrate the potential of our methods within the context of geometry optimization.
by George Shu Heng Pau.
Ph.D.
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Willcox, Karen E. (Karen Elizabeth). "Reduced-order aerodynamic models for aeroelastic control of turbomachines." Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/9265.
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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2000.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 138-143).
Aeroelasticity is a critical consideration in the design of gas turbine engines, both for stability and forced response. Current aeroelastic models cannot provide high-fidelity aerodynamics in a form suitable for design or control applications. In this thesis low-order, high-fidelity aerodynamic models are developed using systematic model order reduction from computational fluid dynamic (CFD) methods. Reduction techniques are presented which use the proper orthogonal decomposition, and also a new approach for turbomachinery which is based on computing Arnoldi vectors. This method matches the input/output characteristic of the CFD model and includes the proper orthogonal decomposition as a special case. Here, reduction is applied to the linearized two-dimensional Euler equations, although the methodology applies to any linearized CFD model. Both methods make efficient use of linearity to compute the reduced-order basis on a single blade passage. The reduced-order models themselves are developed in the time domain for the full blade row and cast in state-space form. This makes the model appropriate for control applications and also facilitates coupling to other engine components. Moreover, because the full blade row is considered, the models can be applied to problems which lack cyclic symmetry. Although most aeroelastic analyses assume each blade to be identical, in practice variations in blade shape and structural properties exist due to manufacturing limitations and engine wear. These blade to blade variations, known as mistuning, have been shown to have a significant effect on compressor aeroelastic properties. A reduced-order aerodynamic model is developed for a twenty-blade transonic rotor operating in unsteady plunging motion, and coupled to a simple typical section structural model. Stability and forced response of the rotor to an inlet ow disturbance are computed and compared to results obtained using a constant coefficient model similar to those currently used in practice. Mistuning of this rotor and its effect on aeroelastic response is also considered. The simple models are found to inaccurately predict important aeroelastic results, while the relevant dynamics can be accurately captured by the reduced-order models with less than two hundred aerodynamic states. Models are also developed for a low-speed compressor stage in a stator/rotor configuration. The stator is shown to have a significant destabilizing effect on the aeroelastic system, and the results suggest that analysis of the rotor as an isolated blade row may provide inaccurate predictions.
by Karen Elizabeth Willcox.
Ph.D.
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Rabin, Gregory S. "A reduced-form statistical climate model suitable for coupling with economic emissions projections." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/41672.
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Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 36-37).
In this work, we use models based on past data and scientific analysis to determine possible future states of the environment. We attempt to improve the equations for temperature and greenhouse gas concentration used in conjunction with the MIT Emissions Prediction and Policy Analysis (EPPA) model or for independent climate analysis based on results from the more complex MIT Integrated Global Systems Model (IGSM). The functions we generate should allow a software system to approximate the environmental variables from the policy inputs in a matter of seconds. At the same time, the estimates should be close enough to the exact values given by the IGSM to be considered meaningful.
by Gregory S. Rabin.
M.Eng.
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Shrinivas, Srikrishna. "Reduced-order model identification for long-range prediction /." free to MU campus, to others for purchase, 2003. http://wwwlib.umi.com/cr/mo/fullcit?p1418064.
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Vithanage, Cheran Malsri. "Graphical models and approximate inference for reduced-complexity digital communications." Thesis, University of Bristol, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.440018.
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Dergham, Grégory. "Reduced-order models for linear dynamics and control in aerodynamics." Paris, ENSAM, 2011. http://www.theses.fr/2011ENAM0023.
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In aerodynamics, separated flows are often subject to strong instabilities which result in the shedding of large-scale vortices. Such low-frequency unsteadiness are commonly encountered in aeronautical applications and lead to detrimental effects such as severe structural vibrations or the generation of extensive noise pollution. This thesis aims at providing low-order models of such aerodynamic flows in order to design optimal control devices. The transitional backward-facing step flow is considered as a prototype of unstable separated flow. Firstly, the linear flow dynamics are examined using a global stability analysis. The flow is found to selectively amplify the upstream noise through the Kelvin-Helmholtz instability. Next, we use projection methods to construct low-order models of the linear two-dimensional dynamics of the flow. Three approaches are investigated: (i) the use of the least damped global modes, (ii) the Proper Orthogonal Decomposition (POD) and (iii) the balanced truncation. This thesis introduces a snapshot method in the frequency domain to compute the leading controllable, observable and balanced modes, as well as techniques to handle large fluid systems. Lastly, the question of the closed-loop control of the flow is addressed. An effective reduction of the perturbations is obtained by using a Linear Quadratic Gaussian compensator designed from a POD modelEn aérodynamique, les écoulements décollés sont souvent sujets à de fortes instabilités qui provoquent l'apparition de grosses structures tourbillonnaires. Ces écoulements caractérisés par des instationnarités à basses fréquences sont couramment observés dans les applications aéronautiques et entraînent des effets néfastes tels que d'importantes vibrations des structures ou la génération de bruit. Cette thèse a pour objectif de fournir des modèles d'ordre réduit de tels écoulements aérodynamiques dans le but de concevoir des dispositifs de contrôle optimaux. Un écoulement transitionnel de marche descendante est considéré comme prototype d'écoulement décollé instable. Dans un premier temps, la dynamique linéaire de l'écoulement est étudiée à l'aide d'une analyse de stabilité globale. Nous montrons que l'écoulement amplifie de manière sélective le bruit amont par l'instabilité de Kelvin-Helmholtz. Ensuite, nous utilisons des méthodes de projection pour construire des modèles d'ordre réduit de la dynamique linéaire bidimensionnelle de l'écoulement. Trois approches sont étudiées : (i) l'utilisation des modes globaux les moins stables, (ii) la Décomposition Orthogonale Propre (POD) et (iii) la troncature équilibrée. Cette thèse introduit une méthode des clichés dans le domaine fréquentiel pour calculer les modes contrôlables, observables et équilibrés dominants, ainsi que des techniques pour traiter les systèmes fluides de grande taille. Finalement, nous traitons la question du contrôle en boucle fermée de l'écoulement. Une réduction conséquente des perturbations est obtenue en utilisant une commande Linéaire Quadratique Gaussienne conçue à partir d'un modèle POD
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Koc, Birgul. "Numerical Analysis for Data-Driven Reduced Order Model Closures." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/103202.
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This dissertation contains work that addresses both theoretical and numerical aspects of reduced order models (ROMs). In an under-resolved regime, the classical Galerkin reduced order model (G-ROM) fails to yield accurate approximations. Thus, we propose a new ROM, the data-driven variational multiscale ROM (DD-VMS-ROM) built by adding a closure term to the G-ROM, aiming to increase the numerical accuracy of the ROM approximation without decreasing the computational efficiency.
The closure term is constructed based on the variational multiscale framework. To model the closure term, we use data-driven modeling. In other words, by using the available data, we find ROM operators that approximate the closure term. To present the closure term's effect on the ROMs, we numerically compare the DD-VMS-ROM with other standard ROMs. In numerical experiments, we show that the DD-VMS-ROM is significantly more accurate than the standard ROMs. Furthermore, to understand the closure term's physical role, we present a theoretical and numerical investigation of the closure term's role in long-time integration. We theoretically prove and numerically show that there is energy exchange from the most energetic modes to the least energetic modes in closure terms in a long time averaging.
One of the promising contributions of this dissertation is providing the numerical analysis of the data-driven closure model, which has not been studied before. At both the theoretical and the numerical levels, we investigate what conditions guarantee that the small difference between the data-driven closure model and the full order model (FOM) closure term implies that the approximated solution is close to the FOM solution. In other words, we perform theoretical and numerical investigations to show that the data-driven model is verifiable.
Apart from studying the ROM closure problem, we also investigate the setting in which the G-ROM converges optimality. We explore the ROM error bounds' optimality by considering the difference quotients (DQs). We theoretically prove and numerically illustrate that both the ROM projection error and the ROM error are suboptimal without the DQs, and optimal if the DQs are used.Doctor of Philosophy
In many realistic applications, obtaining an accurate approximation to a given problem can require a tremendous number of degrees of freedom. Solving these large systems of equations can take days or even weeks on standard computational platforms. Thus, lower-dimensional models, i.e., reduced order models (ROMs), are often used instead. The ROMs are computationally efficient and accurate when the underlying system has dominant and recurrent spatial structures. Our contribution to reduced order modeling is adding a data-driven correction term, which carries important information and yields better ROM approximations. This dissertation's theoretical and numerical results show that the new ROM equipped with a closure term yields more accurate approximations than the standard ROM.
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Zou, Xi. "Simulation tools for biomechanical applications with PGD-based reduced order models." Doctoral thesis, Universitat Politècnica de Catalunya, 2018. http://hdl.handle.net/10803/481988.
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Numerical simulation tools are generally used in all modern engineering fields, especially those having difficulties in performing large number of practical experiments, such as biomechanics. Among the computational methods, Finite Element (FE) is an essential tool. Nowadays, the fast-growing computational techniques, from the upgrading hardware to the emerging of novel algorithm, have already enabled extensive applications in biomechanics. For applications that require fast response and/or multiple queries, Reduced Order Modelling (ROM) methods have been developed based on existing methods such as FE, and have eventually enabled real-time numerical simulation for a large variety of engineering problems.
In this thesis, several novel computational techniques are developed to explore the capability of Proper Generalised Decomposition (PGD), which is an important approach of ROM. To assess the usability of the PGD-based ROM for biomechanical applications, a real human femur bone is chosen to study its mechanical behaviour as an example. Standard image-based modelling procedure in biomechanics is performed to create an FE model which is then validated with in vitro experimental results.
As a basis of this work, the medical image processing has to be performed, in order to generate an available FE model. This model is validated according to data collected from a previously performed \textit{in vitro} experimental test. The full procedure of image-based model generation and the validation of generated model is described in Chapter 2.
As a major objective of this thesis, a non-intrusive scheme for the PGD framework is developed in Chapter 3. It is implemented using in-house developed Matlab (Mathworks, USA) code to conduct the PGD work flow, and calling Abaqus as an external solver for devised fictitious mechanical problems.
The transformation of data from computed tomography (CT) image set to FE model including inhomogeneous material properties is subjected to some physical constraints, and when applying the load, there are also geometric constraints limiting the locations where load could be applied. These constraints will lead to a constrained parameter space, which possibly has difficulty to be separated in a Cartesian fashion. Therefore, a novel strategy to separate the parameters in a collective manner is proposed in Chapter 4.
Chapter 5 details a comprehensive application in biomechanics, the methodologies proposed in Chapter 3 and 4 are applied on the practical model generated in Chapter 2. As a typical application of the PGD vademecum, a material property identification problem is discussed. Further PGD vademecum is generated using the identified material properties with variable loading locations, and with this vademecum, real-time mechanical response of the femur is available.
In addition, for the purpose of extending the methodologies to orthotropic materials, which is commonly used in biomechanics, in Chapter 6 another linear elastic model is investigated with the non-intrusive PGD scheme. Nowadays, isogeometric analysis (IGA) is a very popular tool in computational mechanics. It is appealing to take advantage of non-uniform rational B-splines (NURBS) to discretise the model. For PGD, using B-splines for the discretisation of the parameter space could improve the quality of vademecum, especially for problems involving sensitivities with respect to the parameters during the online computations.
It is important and necessary to extend the PGD framework to nonlinear solid mechanics, because most biological soft tissues have been observed nonlinear mechanical behaviours. Consequently, in Chapter 7 we have developed a PGD framework for the St.Venant-Kirchhoff constitutive model using the Picard linearisation which is consistent with the fixed-point iteration algorithm commonly used in PGD.
In Chapter 8, conclusive remarks are addressed as well as forecasts of possible future works.
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Spottswood, Stephen Michael. "Identification of nonlinear parameters from experimental data for reduced rrder models." Cincinnati, Ohio : University of Cincinnati, 2006. http://www.ohiolink.edu/etd/view.cgi?ucin1163016945.
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Thesis (M.S.)--University of Cincinnati, 2006.Title from electronic thesis title page (viewed Jan. 26, 2007). Includes abstract. Keywords: sonic fatigue; nonlinear; identification; reduced order modeling. Includes bibliographical references.
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Gratton, David 1979. "Reduced-order, trajectory piecewise-linear models for nonlinear computational fluid dynamics." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/16658.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.Includes bibliographical references (p. 75-79).
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Computational fluid dynamics (CFD) is now widely used throughout the fluid dynamics community and yields accurate models for problems of interest. However, due to its high computational cost, CFD is limited for some applications. Therefore, model reduction has been used to derive low-order models that replicate CFD behavior over a restricted range of inputs, and various frameworks have been developed. Unfortunately, the majority of those methods are limited to linear cases and do not properly handle reduction of nonlinear systems. In order to overcome restrictions of weak nonlinearity and the costly representation of the system's nonlinearity found in other nonlinear reduction approaches, a trajectory piecewise-linear (TPWL) scheme is developed for a CFD model of the two-dimensional Euler equations. The approach uses a weighted combination of linearized models to represent the nonlinear CFD system. Using a set of training trajectories obtained via a simulation of the nonlinear CFD model, algorithms are presented for linearization point selection and weighting of the models. Using the same training trajectories to provide a snapshot ensemble, the proper orthogonal decomposition (POD) is used to create a reduced-space basis, onto which the TPWL model is projected. This projection yields an efficient reduced-order model of the nonlinear system, which does not require the evaluation of any full-order system residuals, while capturing a large portion of the nonlinear space. The method is applied to the case of flow through an actively controlled supersonic diffuser. Convergence of the TPWL approach is presented for both full-order and reduced-order cases.
(cont.) The TPWL approach and the POD combine naturally to form an efficient reduction procedure and the methodology is found to yield accurate results, including cases with significant shock motion. Reduced-order PWL models are shown to be three orders of magnitude more efficient than the nonlinear CFD for simulation of a representative test case.
by David Gratton.
S.M.
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Bradley, Andreas. "CFD Simulations for Film Cooling : Reduced Models at Engine Like Conditions." Licentiate thesis, Linköpings universitet, Mekanisk värmeteori och strömningslära, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-91716.
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In gas turbines some parts are exposed to combustion gases with temperatures well above the melting temperature of the material. Therefore, various cooling techniques are utilized in order to protect the parts exposed to these hot gases. One such technique, film cooling, is a common and well established way to protect the exposed parts. Film cooling involves the ejection of cold air on the surface of the parts that are to be protected, thus creating a film of colder air between the surface and the hot gases. Computational Fluid Dynamics (CFD) is a way of calculating fluid flow, and can be used to calculate the effectiveness of a cooling film in film cooling applications. CFD is demanding in terms of computer power, especially when advanced methods are to be used. Even the simpler methods, such as Reynolds Average Navier-Stokes (RANS), can be quite demanding, time and computer power-wise, and require resources not always available. Finding ways of limiting the needed computer power is therefore of large interest. The aim of this thesis is to reduce the computational time of film cooling CFD-simulations, by using reduced models. To achieve this, simulations has been conducted and compared to experiments. The investigated setup is of an enginelike equipment, where a guide vane is investigated for heat transfer coefficient and film effectiveness. The geometry in the experimental setup is constructed in such a way as to give the same pressure distribution around the guide vane as can be seen in a real gas turbine, although at lower temperatures than those in the real turbine. The CFD-simulations conducted on the test rig includes RANS-simulations using the realizable k- and the SST k-! turbulence models. The reduced model contains only the central part of the vane. The walls of the test rig is replaced with periodic boundary conditions. This narrow model gives good agreement with the full model for heat transfer coefficient. Due to the large computational cost required to conduct simulations with cooling on the full model no comparison were made between the cooled narrow and cooled full model. To further reduce the size of the computational domain, two additional models were investigated. The first one involves a reduction of the full domain to only include the section being studied, in this case the suction side of the guide vane. This infers a reduction of the mesh size to less than ten percent of the size of what a mesh of the cooled full domain would be. The next step to reduce the size of the model and mesh is to make a narrow version of the already shortened model. The results for these two models show that they perform adequately to each other and (in the cases where a comparison is possible), to the full domain.In the printed and electornic version is the ISBN incorrect: 978-97-7519-608-4. Correct ISBN is 978-91-7519-608-4.
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Aversano, Gianmarco. "Development of physics-based reduced-order models for reacting flow applications." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLC095/document.
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L’objectif final étant de développer des modèles d’ordre réduit pour les applications de combustion, des techniques d’apprentissage automatique non supervisées et supervisées ont été testées et combinées dans les travaux de la présente thèse pour l’extraction de caractéristiques et la construction de modèles d’ordre réduit. Ainsi, l’application de techniques pilotées par les données pour la détection des caractéristiques d’ensembles de données de combustion turbulente (simulation numérique directe) a été étudiée sur deux flammes H2 / CO: une évolution spatiale (DNS1) et une jet à évolution temporelle (DNS2). Des méthodes telles que l’analyse en composantes principales (ACP), l’analyse en composantes principales locales (LPCA), la factorisation matricielle non négative (NMF) et les autoencodeurs ont été explorées à cette fin. Il a été démontré que divers facteurs pouvaient affecter les performances de ces méthodes, tels que les critères utilisés pour le centrage et la mise à l’échelle des données d’origine ou le choix du nombre de dimensions dans les approximations de rang inférieur. Un ensemble de lignes directrices a été présenté qui peut aider le processus d’identification de caractéristiques physiques significatives à partir de données de flux réactifs turbulents. Des méthodes de compression de données telles que l’analyse en composantes principales (ACP) et les variations ont été combinées à des méthodes d’interpolation telles que le krigeage, pour la construction de modèles ordonnées à prix réduits et calculables pour la prédiction de l’état d’un système de combustion dans des conditions de fonctionnement inconnues ou des combinaisons de modèles valeurs de paramètre d’entrée. La méthodologie a d’abord été testée pour la prévision des flammes 1D avec un nombre croissant de paramètres d’entrée (rapport d’équivalence, composition du carburant et température d’entrée), avec des variantes de l’approche PCA classique, à savoir PCA contrainte et PCA locale, appliquée aux cas de combustion la première fois en combinaison avec une technique d’interpolation. Les résultats positifs de l’étude ont conduit à l’application de la méthodologie proposée aux flammes 2D avec deux paramètres d’entrée, à savoir la composition du combustible et la vitesse d’entrée, qui ont donné des résultats satisfaisants. Des alternatives aux méthodes non supervisées et supervisées choisies ont également été testées sur les mêmes données 2D. L’utilisation de la factorisation matricielle non négative (FNM) pour l’approximation de bas rang a été étudiée en raison de la capacité de la méthode à représenter des données à valeur positive, ce qui permet de ne pas enfreindre des lois physiques importantes telles que la positivité des fractions de masse d’espèces chimiques et comparée à la PCA. Comme méthodes supervisées alternatives, la combinaison de l’expansion du chaos polynomial (PCE) et du Kriging et l’utilisation de réseaux de neurones artificiels (RNA) ont été testées. Les résultats des travaux susmentionnés ont ouvert la voie au développement d’un jumeau numérique d’un four à combustion à partir d’un ensemble de simulations 3D. La combinaison de PCA et de Kriging a également été utilisée dans le contexte de la quantification de l’incertitude (UQ), en particulier dans le cadre de collaboration de données lié (B2B-DC), qui a conduit à l’introduction de la procédure B2B-DC à commande réduite. Comme pour la première fois, le centre de distribution B2B a été développé en termes de variables latentes et non en termes de variables physiques originalesWith the final objective being to developreduced-order models for combustion applications,unsupervised and supervised machine learningtechniques were tested and combined in the workof the present Thesis for feature extraction and theconstruction of reduced-order models. Thus, the applicationof data-driven techniques for the detection offeatures from turbulent combustion data sets (directnumerical simulation) was investigated on two H2/COflames: a spatially-evolving (DNS1) and a temporallyevolvingjet (DNS2). Methods such as Principal ComponentAnalysis (PCA), Local Principal ComponentAnalysis (LPCA), Non-negative Matrix Factorization(NMF) and Autoencoders were explored for this purpose.It was shown that various factors could affectthe performance of these methods, such as the criteriaemployed for the centering and the scaling of theoriginal data or the choice of the number of dimensionsin the low-rank approximations. A set of guidelineswas presented that can aid the process ofidentifying meaningful physical features from turbulentreactive flows data. Data compression methods suchas Principal Component Analysis (PCA) and variationswere combined with interpolation methods suchas Kriging, for the construction of computationally affordablereduced-order models for the prediction ofthe state of a combustion system for unseen operatingconditions or combinations of model input parametervalues. The methodology was first tested forthe prediction of 1D flames with an increasing numberof input parameters (equivalence ratio, fuel compositionand inlet temperature), with variations of the classicPCA approach, namely constrained PCA and localPCA, being applied to combustion cases for the firsttime in combination with an interpolation technique.The positive outcome of the study led to the applicationof the proposed methodology to 2D flames withtwo input parameters, namely fuel composition andinlet velocity, which produced satisfactory results. Alternativesto the chosen unsupervised and supervisedmethods were also tested on the same 2D data.The use of non-negative matrix factorization (NMF) forlow-rank approximation was investigated because ofthe ability of the method to represent positive-valueddata, which helps the non-violation of important physicallaws such as positivity of chemical species massfractions, and compared to PCA. As alternative supervisedmethods, the combination of polynomial chaosexpansion (PCE) and Kriging and the use of artificialneural networks (ANNs) were tested. Results from thementioned work paved the way for the developmentof a digital twin of a combustion furnace from a setof 3D simulations. The combination of PCA and Krigingwas also employed in the context of uncertaintyquantification (UQ), specifically in the bound-to-bounddata collaboration framework (B2B-DC), which led tothe introduction of the reduced-order B2B-DC procedureas for the first time the B2B-DC was developedin terms of latent variables and not in terms of originalphysical variables
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Huang, Xinming. "Development of Reduced-Order Flame Models for Prediction of Combustion Instability." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/29763.
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Lean-premixed combustion has the advantage of low emissions for modern gas turbines, but it is susceptible to thermoacoustic instabilities, which can result in large amplitude pressure oscillations in the combustion chamber. The thermoacoustic limit cycle is generated by the unsteady heat release dynamics coupled to the combustor acoustics. In this dissertation, we focused on reduced-order modeling of the dynamics of a laminar premixed flame. From first principles of combustion dynamics, a physically-based, reduced-order, nonlinear model was developed based on the proper orthogonal decomposition technique and generalized Galerkin method. In addition, the describing function for the flame was measured experimentally and used to identify an empirical nonlinear flame model. Furthermore, a linear acoustic model was developed and identified for the Rijke tube experiment. Closed-loop thermoacoustic modeling using the first principles flame model coupled to the linear acoustics successfully reproduced the linear instability and predicted the thermoacoustic limit cycle amplitude. With the measured experimental flame data and the modeled linear acoustics, the describing function technique was applied for limit cycle analysis. The thermoacoustic limit cycle amplitude was predicted with reasonable accuracy, and the closed-loop model also predicted the performance for a phase shift controller. Some problems found in the predictions for high heat release cases were documented.Ph. D.
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Kang, Lei. "Reduced-Dimension Hierarchical Statistical Models for Spatial and Spatio-Temporal Data." The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1259168805.
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SPOTTSWOOD, STEPHEN MICHAEL. "IDENTIFICATION OF NONLINEAR PARAMETERS FROM EXPERIMENTAL DATA FOR REDUCED ORDER MODELS." University of Cincinnati / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1163016945.
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Vounou, Maria. "Sparse reduced-rank regression for imaging genetics studies : models and applications." Thesis, Imperial College London, 2012. http://hdl.handle.net/10044/1/9254.
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We present a novel statistical technique; the sparse reduced rank regression (sRRR) model which is a strategy for multivariate modelling of high-dimensional imaging responses and genetic predictors. By adopting penalisation techniques, the model is able to enforce sparsity in the regression coefficients, identifying subsets of genetic markers that best explain the variability observed in subsets of the phenotypes. To properly exploit the rich structure present in each of the imaging and genetics domains, we additionally propose the use of several structured penalties within the sRRR model. Using simulation procedures that accurately reflect realistic imaging genetics data, we present detailed evaluations of the sRRR method in comparison with the more traditional univariate linear modelling approach. In all settings considered, we show that sRRR possesses better power to detect the deleterious genetic variants. Moreover, using a simple genetic model, we demonstrate the potential benefits, in terms of statistical power, of carrying out voxel-wise searches as opposed to extracting averages over regions of interest in the brain. Since this entails the use of phenotypic vectors of enormous dimensionality, we suggest the use of a sparse classification model as a de-noising step, prior to the imaging genetics study. Finally, we present the application of a data re-sampling technique within the sRRR model for model selection. Using this approach we are able to rank the genetic markers in order of importance of association to the phenotypes, and similarly rank the phenotypes in order of importance to the genetic markers. In the very end, we illustrate the application perspective of the proposed statistical models in three real imaging genetics datasets and highlight some potential associations.
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Alqatari, Samar(Samar Ali A. ). "Reduced-dimension model for the Rayleigh-Taylor instability in a Hele-Shaw cell." Thesis, Massachusetts Institute of Technology, 2019. https://hdl.handle.net/1721.1/122316.
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Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2019Cataloged from PDF version of thesis.
Includes bibliographical references (pages 93-94).
In this thesis we present a reduced-dimension model for the density-driven hydrodynamic Rayleigh-Taylor instability. We motivate the project with experimental findings of a little-understood stabilizing effect of geometry and deviations of measured instability wavelength from theoretical predictions. We present novel methods of data analysis for the experimental data. We then present a reduced-dimension model for the governing equations of the system, Stoke's equations and Fick's law, using polynomial trial functions. We discuss the results and conduct a linear stability analysis of the reduced system. We compare the model to a finite element simulation of the full governing equations using COMSOL, and propose an optimization framework for the basis functions of the reduced model. The reduced model helps in developing physical intuition for the behavior of the instability in this confined geometry, and understanding the effects of certain parameters that are difficult to study experimentally or by simulating the full equations.
by Samar Alqatari.
S.M.
S.M. Massachusetts Institute of Technology, Computation for Design and Optimization Program
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Caraballo, Edgar J. "Reduced Order Model Development For Feedback Control Of Cavity Flows." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1225291592.
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Leroy, Thomas. "Reduced models and numerical methods for kinetic equations applied to photon transport." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066047/document.
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La modélisation d'expériences de fusion par confinement inertiel fait intervenir des équations cinétiques dont la discrétisation peut être très coûteuse. La recherche de modèles simplifiés permet de réduire la taille et donc la complexité de ces systèmes. La justification mathématique de ces modèles simplifiés devient alors un enjeu central. Dans ce travail nous étudions plusieurs modèles réduits pour l'équation du transfert radiatif dans différents contextes, tant du point de vue théorique que du point de vue numérique. En particulier nous étudions l'équation du transfert radiatif relativiste dans le régime de diffusion hors équilibre, et nous montrons la convergence de la solution de cette équation vers la solution d'une équation de drift diffusion, dans laquelle les effets Doppler sont modélisés par un terme de transport en fréquence. Cette équation de transport est discrétisée par une nouvelle classe de schémas "bien équilibrés" (well-balanced), pour lesquels nous montrons que ces nouveaux schémas sont consistants lorsque la vitesse d'onde tends vers zero, par opposition aux schémas de type Greenberg-Leroux. Nous étudions également de nouveaux modèles réduits pour le scattering Compton (collision inélastique photon-électron). Une hiérarchie d'équations cinétiques non linéaires généralisant l'équation de Kompaneets pour des distributions anisotropes sont dérivées et leurs propriétés étudiées. Les modèles aux moments de type P_1 et M_1 sont dérivés à partir de l'une de ces équations, et nous montrons que la prise en compte de l'anisotropie du rayonnement peut modifier le phénomène de condensation de Bose expliqué par Caflisch et Levermore. Ce manuscrit se termine avec les comptes rendus de deux projets. Le premier est une preuve technique de la convergence uniforme du schéma de Gosse-Toscani sur maillages non structurés. Ce schéma est "asymptotic preserving", au sens ou il préserve au niveau discret la limite de diffusion pour l'équation de la chaleur hyperbolique, et cette preuve de convergence uniforme sur maillage non structurés en 2D est originale. Le second concerne la dérivation d'un modèle cinétique pour le Bremsstrahlung électron-ion qui préserve la limite thermiqueThe modeling of inertial confinement experiments involves kinetic equations whose discretization can become very costly. The research of reduced models allows to decrease the size and the complexity of these systems. The mathematical justification of such reduced models becomes an important issue. In this work we study several reduced models for the transfer equation in several contexts, from the theoretical and numerical point of view. In particular we study the relativistic transfer equation in the non-equilibrium diffusion regime, and we prove the convergence of the solution of this equation to the solution of a drift diffusion equation, in which the Doppler effects are modeled by a frequency transport term. This transport equation is discretized by a new class of well-balanced schemes, and we show that these schemes are consistant as the wave velocity tends to zero, by opposition to the Greenberg-Leroux type schemes. We also study several original reduced models for the Compton scattering (inelastic electron-photon collision). A hierarchy of nonlinear kinetic equations generalizing the Kompaneets equation for anisotropic distributions are derived and their properties are studied. The M_1 and P_1 angular moments models are derived from one of these equations, and we show that the anisotropic part of a radiation beam can modify the Bose condensation phenomena observed by caflisch and Levermore. This work ends with the reports of two side projects. The first one is a technical proof of the uniform convergence of the Gosse-Toscani scheme on unstructured meshes. This scheme is asymptotic preserving, since it preserves at the discrete level the diffusion limit of the hyperbolic heat equation, and this proof on unstructured meshes in 2D is original. The second one is devoted to the derivation of a kinetic model for the electron-ion Bremsstrahlung that preserves the thermal limit
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Li, Zhengrong. "Model-based Tests for Standards Evaluation and Biological Assessments." Diss., Virginia Tech, 2006. http://hdl.handle.net/10919/29108.
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Implementation of the Clean Water Act requires agencies to monitor aquatic sites on a regular basis and evaluate the quality of these sites. Sites are evaluated individually even though there may be numerous sites within a watershed. In some cases, sampling frequency is inadequate and the evaluation of site quality may have low reliability.
This dissertation evaluates testing procedures for determination of site quality based on modelbased procedures that allow for other sites to contribute information to the data from the test site. Test procedures are described for situations that involve multiple measurements from sites within a region and single measurements when stressor information is available or when covariates are used to account for individual site differences.
Tests based on analysis of variance methods are described for fixed effects and random effects models. The proposed model-based tests compare limits (tolerance limits or prediction limits) for the data with the known standard. When the sample size for the test site is small, using model-based tests improves the detection of impaired sites. The effects of sample size, heterogeneity of variance, and similarity between sites are discussed. Reference-based standards and corresponding evaluation of site quality are also considered. Regression-based tests provide methods for incorporating information from other sites when there is information on stressors or covariates.
Extension of some of the methods to multivariate biological observations and stressors is also discussed. Redundancy analysis is used as a graphical method for describing the relationship between biological metrics and stressors. A clustering method for finding stressor-response relationships is presented and illustrated using data from the Mid-Atlantic Highlands. Multivariate elliptical and univariate regions for assessment of site quality are discussed.Ph. D.
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Nadalina, Jafabadi Hossein. "Investigation of Film Cooling Strategies CFD versus Experiments -Potential for Using Reduced Models." Thesis, Linköpings universitet, Mekanisk värmeteori och strömningslära, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-61263.
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The ability and efficiency of today’s gas turbine engines are highly dependent on development of cooling technologies, among which film cooling is one of the most important. Investigations have been conducted towards discovering different aspects of film cooling, utilizing both experiments and performing CFD simulations. Although, investigation by using CFD analysis is less expensive in general, the results obtained from CFD calculations should be validated by means of experimental results. In addition to validation, in cases like simulating a turbine vane, performing CFD simulations can be time consuming. Therefore, it is essential to find approaches that can reduce the computational cost while results are validated by experiments. This study has shown the potential for reduced models to be utilized for investigation of different aspects of film cooling by means of CFD at low turn-around time. This has been accomplished by first carrying out CFD simulations and experiments for an engine-like setting for a full vane. Then the computational domain is reduced in two steps where all results are compared with experiments including aerodynamic validation, heat transfer coefficient and film effectiveness. While the aerodynamic results are in close agreement with experiments, the heat transfer coefficient and film effectiveness results have also shown similarities within the expected range. Thus this study has shown that this approach can be very useful for e.g. early vane and film cooling design.
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Kingravi, Hassan. "Reduced-set models for improving the training and execution speed of kernel methods." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51799.
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This thesis aims to contribute to the area of kernel methods, which are a class of machine learning methods known for their wide applicability and state-of-the-art performance, but which suffer from high training and evaluation complexity. The work in this thesis utilizes the notion of reduced-set models to alleviate the
training and testing complexities of these methods in a unified manner. In the first part of the thesis, we use recent results in kernel smoothing and integral-operator learning to design a generic strategy to speed up various kernel methods. In Chapter 3, we present a method to speed up kernel PCA (KPCA), which is one of the fundamental kernel methods for manifold learning, by using reduced-set density estimates (RSDE) of the data. The proposed method induces an integral operator that is an approximation of the ideal integral operator associated to KPCA. It is shown that the error between the ideal and approximate integral operators is related to the error between the ideal and approximate kernel density estimates of the data. In Chapter 4, we derive similar approximation algorithms for Gaussian process regression, diffusion maps, and kernel embeddings of conditional distributions. In the second part of the thesis, we use reduced-set models for kernel methods to tackle online learning in model-reference adaptive control (MRAC). In Chapter 5, we relate the properties of the feature spaces induced by Mercer kernels to make a connection between persistency-of-excitation and the budgeted placement of kernels to minimize tracking and modeling error. In Chapter 6, we use a Gaussian process (GP) formulation of the modeling error to accommodate a larger class of errors, and design a reduced-set algorithm to learn a GP model of the modeling error. Proofs of stability for all the algorithms are presented, and simulation results on a challenging control problem validate the methods.
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Syrén, Ludvig. "A method for introducing flexibility in rigid multibodies from reduced order elastic models." Thesis, Umeå universitet, Institutionen för fysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-160417.
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In multibody dynamics simulation of robots and vehicles it is common to model the systems as being composed of mainly rigid bodies with articulation joints. With the trend to more lightweight robots, however, the structural flexibility of the robots link’s needs to be considered for realistic dynamic simulations. The link’s geometries are complex and finite element models (FEM) are required to compute the deformations. However, FEM includes too many degrees of freedom for time-efficient dynamics simulation. A popular method is to generate reduced order models from the FE models, but with much fewer degrees of freedom, for fast and precise simulations. In this thesis a method for introducing reduced order models in rigid multibody systems was developed. The method is to divide a rigid body into two rigid bodies. Their relative movement is described by a six degree of freedom restoration force, determined with a reduced order model from Guyan reduction (static condensation). The method was validated for quasistatic deformation of a homogenous beam, a robot link arm with a more complex geometry and in multibody dynamics simulations. Finally the method was tested in simulation of a complete ABB robot with joint actuators, and any significant differences in the motion of the robot tool centre point due to replacing a rigid link arm by a flexible one was demonstrated.The method show good results for computing deformations of the homogenous beam, of the link arm and in the multibody simulation. The differences observed in simulation of a complete robot was expected and demonstrated the method to be applicable in robotic simulations.
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Cooper, Rachel Gray. "Augmented Neural Network Surrogate Models for Polynomial Chaos Expansions and Reduced Order Modeling." Thesis, Virginia Tech, 2021. http://hdl.handle.net/10919/103423.
Full textAbstract:
Mathematical models describing real world processes are becoming increasingly complex to better match the dynamics of the true system. While this is a positive step towards more complete knowledge of our world, numerical evaluations of these models become increasingly computationally inefficient, requiring increased resources or time to evaluate. This has led to the need for simplified surrogates to these complex mathematical models.
A growing surrogate modeling solution is with the usage of neural networks. Neural networks (NN) are known to generalize an approximation across a diverse dataset and minimize the solution along complex nonlinear boundaries. Additionally, these surrogate models can be found using only incomplete knowledge of the true dynamics. However, NN surrogates often suffer from a lack of interpretability, where the decisions made in the training process are not fully understood, and the roles of individual neurons are not well defined.
We present two solutions towards this lack of interpretability. The first focuses on mimicking polynomial chaos (PC) modeling techniques, modifying the structure of a NN to produce polynomial approximations of the underlying dynamics. This methodology allows for an extractable meaning from the network and results in improvement in accuracy over traditional PC methods. Secondly, we examine the construction of a reduced order modeling scheme using NN autoencoders, guiding the decisions of the training process to better match the real dynamics. This guiding process is performed via a physics-informed (PI) penalty, resulting in a speed-up in training convergence, but still results in poor performance compared to traditional schemes.Master of Science
The world is an elaborate system of relationships between diverse processes. To accurately represent these relationships, increasingly complex models are defined to better match what is physically seen. These complex models can lead to issues when trying to use them to predict a realistic outcome, either requiring immensely powerful computers to run the simulations or long amounts of time to present a solution. To fix this, surrogates or approximations to these complex models are used. These surrogate models aim to reduce the resources needed to calculate a solution while remaining as accurate to the more complex model as possible. One way to make these surrogate models is through neural networks. Neural networks try to simulate a brain, making connections between some input and output given to the network. In the case of surrogate modeling, the input is some current state of the true process, and the output is what is seen later from the same system. But much like the human brain, the reasoning behind why choices are made when connecting the input and outputs is often largely unknown. Within this paper, we seek to add meaning to neural network surrogate models in two different ways. In the first, we change what each piece in a neural network represents to build large polynomials (e.g., $x^5 + 4x^2 + 2$) to approximate the larger complex system. We show that the building of these polynomials via neural networks performs much better than traditional ways to construct them. For the second, we guide the choices made by the neural network by enforcing restrictions in what connections it can make. We do this by using additional information from the larger system to ensure the connections made focus on the most important information first before trying to match the less important patterns. This guiding process leads to more information being captured when the surrogate model is compressed into only a few dimensions compared to traditional methods. Additionally, it allows for a faster learning time compared to similar surrogate models without the information.
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Taghipour, Ehsan. "Development of Reduced-Order Computational Models for Digital Manufacturing of Flexible Wire Harnesses." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1543404707742968.
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Faller, Kenneth John II. "Automated synthesis of a reduced-parameter model for 3D digital audio." FIU Digital Commons, 1996. http://digitalcommons.fiu.edu/etd/3245.
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Head-Related Impulse Responses (HRIRs) are used in signal processing to implement the synthesis of spatialized audio. They represent the modification that sound undergoes from its source to the listener's eardrums. HRIRs are somewhat different for each listener and require expensive specialized equipment for their individual measurement. Therefore, the development of a method to obtain customized HRIRs without specialized equipment is extremely desirable. A customizable representation of HRIRs can be created by modeling them in terms of an appropriate set of time delays and a resonant frequency. Previously, this was achieved manually, by trial and error. In this research an automated algorithm for the definition of the appropriate delays and resonant frequency needed to model an HRIR was developed, implemented and evaluated. This provides an objective, repeatable way to determine the parameters of the HRIR model. The automated process provided an average accuracy of 96.9% in the analysis of 2160 HRIRs.
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Brendlinger, Jack W. "Development of Guidance Laws for a Reduced Order Dynamic Aircraft Model." Wright State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=wright1516106170428761.
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Tracy, Jacob N. "Reduced-Dimension Groundwater Model Emulation for Scenario Analysis and Decision Support." University of Cincinnati / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1573574885505114.
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