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Xie, Xuping. "Large Eddy Simulation Reduced Order Models." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/77626.
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This dissertation uses spatial filtering to develop a large eddy simulation reduced order model (LES-ROM) framework for fluid flows. Proper orthogonal decomposition is utilized to extract the dominant spatial structures of the system. Within the general LES-ROM framework, two approaches are proposed to address the celebrated ROM closure problem. No phenomenological arguments (e.g., of eddy viscosity type) are used to develop these new ROM closure models.
The first novel model is the approximate deconvolution ROM (AD-ROM), which uses methods from image processing and inverse problems to solve the ROM closure problem. The AD-ROM is investigated in the numerical simulation of a 3D flow past a circular cylinder at a Reynolds number $Re=1000$. The AD-ROM generates accurate results without any numerical dissipation mechanism. It also decreases the CPU time of the standard ROM by orders of magnitude.
The second new model is the calibrated-filtered ROM (CF-ROM), which is a data-driven ROM. The available full order model results are used offline in an optimization problem to calibrate the ROM subfilter-scale stress tensor. The resulting CF-ROM is tested numerically in the simulation of the 1D Burgers equation with a small diffusion parameter. The numerical results show that the CF-ROM is more efficient than and as accurate as state-of-the-art ROM closure models.Ph. D.
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Chabot, John Alva. "VALIDATING STEADY TURBULENT FLOW SIMULATIONS USING STOCHASTIC MODELS." Miami University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=miami1443188391.
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Yuan, Mengfei. "Machine Learning-Based Reduced-Order Modeling and Uncertainty Quantification for "Structure-Property" Relations for ICME Applications." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1555580083945861.
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Zavar, Moosavi Azam Sadat. "Probabilistic and Statistical Learning Models for Error Modeling and Uncertainty Quantification." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/82491.
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Simulations and modeling of large-scale systems are vital to understanding real world phenomena.
However, even advanced numerical models can only approximate the true physics.
The discrepancy between model results and nature can be attributed to different sources of uncertainty including the parameters of the model, input data, or some missing physics that is not included in the model due to a lack of knowledge or high computational costs.
Uncertainty reduction approaches seek to improve the model accuracy by decreasing the overall uncertainties in models.
Aiming to contribute to this area, this study explores uncertainty quantification and reduction approaches for complex physical problems. This study proposes several novel probabilistic and statistical approaches for identifying the sources of uncertainty, modeling the errors, and reducing uncertainty to improve the model predictions for large-scale simulations.
We explore different computational models. The first class of models studied herein are inherently stochastic, and numerical approximations suffer from stability and accuracy issues.
The second class of models are partial differential equations, which capture the laws of mathematical physics; however, they only approximate a more complex reality, and have uncertainties
due to missing dynamics which is not captured by the models.
The third class are low-fidelity models, which are fast approximations of
very expensive high-fidelity models. The reduced-order models have uncertainty due
to loss of information in the dimension reduction process.
We also consider uncertainty analysis in the data assimilation framework, specifically for ensemble based methods where the effect of sampling errors is alleviated by localization.
Finally, we study the uncertainty in numerical weather prediction models coming from approximate descriptions of physical processes.Ph. D.
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Griffiths, Laurence. "Reduced order model updating." Thesis, University of Bristol, 2014. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.685041.
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Across all engineering disciplines, the differences found between experimental results and computational simulations gives rise to various degrees of uncertainty in the solutions. In fluid dynamics these differences can be broadly split into issues of boundary conditions and numerical accuracy. Within the computational fluid dynamics (CFD) community a great deal of effort has been invested in reducing numerical error, yet large discrepancies with experimental data persist. The nature of experimental and computational studies often dictates the application of different boundary conditions applied in each. Furthermore, for aerospace applications often both experimental and computational methods are attempting to model a free flying aircraft but doing so by applying fundamentally different conditions. Model updating provides the opportunity to modify the behaviour of the system to reduce these discrepancies. Initially this research concentrates on the update of reduced order models (ROMS). These models are a major area of research in CFD and promise the accuracy of CFD with much reduced computational cost. A novel framework is developed by which the steady state gradients of an unsteady eigenvalue based ROM may be updated. The new updating process is applied to remove tunnel wall interferences for Euler and RANS (Spalart-Allmaras) ROMS and to add the effects of viscosity to an inviscid Euler based ROM. Multistage updates are also demonstrated whereby a ROM is updated for both viscous and wind tunnel wall interference. A novel method is developed whereby the pulse input sizing for the production of ROMS from the nonlinear Euler and RANS equations equations may be automated. The method is proved accurate for a range of test cases. Finally a parameter study, investigating the suitability of a viscous-inviscid interactive model for updating, is performed. The study demonstrated that the equations in their original form are not sufficiently robust for an automated model updating process.
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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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Lappo, Vladislav. "Real-time aero-icing simulations using reduced order model." Thesis, McGill University, 2010. http://digitool.Library.McGill.CA:8881/R/?func=dbin-jump-full&object_id=92384.
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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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Ali, Naseem Kamil. "Thermally (Un-) Stratified Wind Plants: Stochastic and Data-Driven Reduced Order Descriptions/Modeling." PDXScholar, 2018. https://pdxscholar.library.pdx.edu/open_access_etds/4634.
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Wind energy is one of the significant sources of renewable energy, yet a number of challenges preclude optimal operation of wind plants. Research is warranted in order to minimize the power losses and improve the productivity of wind plants. Here, a framework combining turbulence theory and data mining techniques is built to elucidate physics and mechanisms driving the energy extraction of the wind plants under a number of atmospheric/operating conditions. The performance of wind turbines is subjected to adverse effects caused by wake interactions. Therefore, it is crucial to understand wake-to-wake interactions as well as wake-to-atmospheric boundary layer interactions. Experimental and numerical data sets are examined in order to provide descriptions of the wakes and extract relevant features. As wakes merge, it is of interest to observe characteristics within the turbulent velocity signal obtained via wind tunnel experiments. Higher order moments, structure functions, intermittency and multifractality analysis are investigated to distinguish the flow dynamics. In this manner, considered approaches highlight the flow deceleration induced by the wind turbines, which subsequently changes the energy transfer rate imposed by the coherent eddies, and adapt the equilibrium range in the energy cascade. Also, wind turbines induce scale interactions and cause the intermittency that lingers at large and small scales. When wind plants interact dynamically with small scales, the flow becomes highly intermittent and multifractality is increased, especially near the rotor. Multifractality parameters, including the Hurst exponent and the combination factor, show the ability to describe the flow state in terms of its development. Based on Markov theory, the time evolution of the probability density function of the velocity is described via the Fokker-Planck equation and its Kramers-Moyal coefficients. Stochastic analysis proves the non-universality of the turbulent cascade immediate to the rotor, and the impact of the generation mechanism on flow cascade. Classifying the wake flow based the velocity and intermittency signs emphasizes that a negative correlation is dominant downstream from the rotor. These results reflect large-scale organization of the velocity-intermittency events corresponding to a recirculation region near the hub height and bottom tip. A linear regression approach based on the Gram-Charlier series expansion of the joint probability density function successfully models the contribution of the second and fourth quadrants. Thus, the model is able to predict the imbalance in the velocity and intermittency contribution to momentum transfer. Via large eddy simulations, the structure of the turbulent flow within the array under stratified conditions is quantified through the use of the Reynolds stress anisotropy tensor, proper orthogonal decomposition and cluster-based modeling. Perturbations induced by the turbine wakes are absorbed by the background turbulence in the unstable and neutrally stratified cases. Contrary, the flow in the stable stratified case is fully dominated by the presence of turbines and extremely influenced by the Coriolis force. Also, during the unstable period the turbulent kinetic energy is maximum. Thus, leading to fast convergence of the cumulative energy with only few modes. Reynolds stress anisotropy tensor reveals that under unstable thermal stratification the turbulence state tends to be more isotropic. The turbulent mixing due to buoyancy determines the degree of anisotropy and the energy distribution between the flow layers. The wakes of the turbines display large degree of anisotropy due to the correlation with the turbulent kinetic energy production. A combinatorial technique merging image segmentation via K-Means clustering and colormap of the barycentric map is posed. Clustering aids in extracting identical features from the spatial distribution of anisotropy colormap images by minimizing the sum of squared error over all clusters. Clustering also enables to highlight the wake expansion and interaction as produced by the wind turbines as a function of thermal stratification. A cluster-based reduced-order dynamical model is proposed for flow field and passive scalars; the model relies on full-state measurements. The dynamical behavior is predicted through the cluster transition matrix and modeled as a Markov process. The geometric nature of the attractor shows the ability to assess the quality of the clustering and identify transition regions. Periodical trends in the cluster transition matrix characterize the intrinsic periodical behavior of the wake. The modeling strategy points out a feasible path for future design and control that can be used to maximize power output. In addition, characterization of intermittency with power integration model can allow for power fluctuation arrangement/prediction in wind plants.
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Moroz, Adam. "Reduced order modelling of bone resorption and formation." Thesis, De Montfort University, 2011. http://hdl.handle.net/2086/5409.
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The bone remodelling process, performed by the Bone Multicellular Unit (BMU) is a key multi-hierarchically regulated process, which provides and supports various functionality of bone tissue. It is also plays a critical role in bone disorders, as well as bone tissue healing following damage. Improved modelling of bone turnover processes could play a significant role in helping to understand the underlying cause of bone disorders and thus develop more effective treatment methods. Moreover, despite extensive research in the field of bone tissue engineering, bonescaffold development is still very empirical. The development of improved methods of modelling the bone remodelling process should help to develop new implant designs which encourage rapid osteointegration. There are a number of limitations with respect to previous research in the field of mathematical modelling of the bone remodelling process, including the absence of an osteocyte loop of regulation. It is within this context that this research presented in this thesis utilises a range of modelling methods to develop a framework for bone remodelling which can be used to improve treatment methods for bone disorders. The study concentrated on dynamic and steady state variables that in perspective can be used as constraints for optimisation problem considering bone remodelling or tissue remodelling with the help of the grafts/scaffolds.The cellular and combined allosteric-regulation approaches to modelling of bone turnover, based on the osteocyte loop of regulation, have been studied. Both approaches have been studied different within wide range of rate parameters. The approach to the model validation has been considered, including a statistical approach and parameter reduction approach. From a validation perspective the cellular class of modes is preferable since it has fewer parameters to validate. The optimal control framework for regulation of remodelling has been studied. Future work in to improve the models and their application to bone scaffold design applications have been considered. The study illustrates the complexity of formalisation of the metabolic processes and the relations between hierarchical subsystems in hard tissue where a relatively small number of cells are active. Different types/modes of behaviour have been found in the study: relaxational, periodical and chaotic modes. All of these types of behaviour can be found, in bone tissue. However, a chaotic or periodic modes are ones of the hardest to verify although a number of periodical phenomena have been observed empirically in bone and skeletal development. Implementation of the allosteric loop into cellular model damps other types of behaviour/modes. In this sense it improves the robustness, predictability and control of the system. The developed models represent a first step in a hierarchical model of bone tissue (system versus local effects). The limited autonomy of any organ or tissue implies differentiation on a regulatory level as well as physiological functions and metabolic differences. Implementation into the cellular phenomenological model of allosteric-like loop of regulation has been performed. The results show that the robustness of regulation can be inherited from the phenomenological model. An attempt to correlate the main bone disorders with different modes of behaviour has been undertaken using Paget’s disorder in bone, osteoporosis and some more general skeleton disorders which lead to periodical changes in bone mass, reported by some authors. However, additional studies are needed to make this hypothesis significant. The study has revealed a few interesting techniques. When studying a multidimensional phenomenon, as a bone tissue is, the visualisation and data reduction is important for analysis and interpretation of results. In the study two novel technical methods have been proposed. The first is the graphical matrix method to visualise/project the multidimensional phase space of variables into diagonal matrix of regular combination of two-dimensional graphs. This significantly simplifies the analysis and, in principle, makes it possible to visualise the phase space higher than three-dimensional. The second important technical development is the application of the Monte-Carlo method in combination with the regression method to study the character and stability of the equilibrium points of a dynamic system. The advantage of this method is that it enables the most influential parameters that affect the character and stability of the equilibrium point to be identified from a large number of the rate parameters/constants of the dynamic system. This makes the interpretation of parameters and conceptual verification of the model much easier.
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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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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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Haznedar, Baris. "Reduced order infinite horizon Model Predictive Control of sheet forming processes." Thesis, Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/11222.
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Salmanoff, Jason. "A Finite Element, Reduced Order, Frequency Dependent Model of Viscoelastic Damping." Thesis, Virginia Tech, 1997. http://hdl.handle.net/10919/36518.
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This thesis concerns itself with a finite element model of nonproportional viscoelastic damping and its subsequent reduction. The Golla-Hughes-McTavish viscoelastic finite element has been shown to be an effective tool in modeling viscoelastic damping. Unlike previous models, it incorporates physical data into the model in the form of a curve fit of the complex modulus. This curve fit is expressed by minioscillators. The frequency dependence of the complex modulus is accounted for by the addition of internal, or dissipation, coordinates. The dissipation coordinates make the viscoelastic model several times larger than the original. The trade off for more accurate modeling of viscoelasticity is increased model size.
Internally balanced model order reduction reduces the order of a state space model by considering the controllability/observability of each state. By definition, a model is internally balanced if its controllability and observability grammians are equal and diagonal. The grammians serve as a ranking of the controllability/observability of the states. The system can then be partitioned into most and least controllable/observable states; the latter can be statically reduced out of the system. The resulting model is smaller, but the transformed coordinates bear little resemblance to the original coordinates. A transformation matrix exists that transforms the reduced model back into original coordinates, and it is a subset of the transformation matrix leading to the balanced model. This whole procedure will be referred to as Yae's method within this thesis.
By combining GHM and Yae's method, a finite element code results that models nonproportional viscoelastic damping of a clamped-free, homogeneous, Euler-Bernoulli beam, and is of a size comparable to the original elastic finite element model. The modal data before reduction compares well with published GHM results, and the modal data from the reduced model compares well with both. The error between the impulse response before and after reduction is negligible. The limitation of the code is that it cannot model sandwich beam behavior because it is based on Euler-Bernoulli beam theory; it can, however, model a purely viscoelastic beam. The same method, though, can be applied to more sophisticated beam models. Inaccurate results occur when modes with frequencies beyond the range covered by the curve fit appear in the model, or when poor data are used. For good data, and within the range modeled by the curve fit, the code gives accurate modal data and good impulse response predictions.
Master of Science
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Jarvis, Christopher Hunter. "Reduced Order Model Study of Burgers' Equation using Proper Orthogonal Decomposition." Thesis, Virginia Tech, 2012. http://hdl.handle.net/10919/31580.
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In this thesis we conduct a numerical study of the 1D viscous Burgers' equation and several Reduced Order Models (ROMs) over a range of parameter values. This study is motivated by the need for robust reduced order models that can be used both for design and control. Thus the model should first, allow for selection of optimal parameter values in a trade space and second, identify impacts from changes of parameter values that occur during development, production and sustainment of the designs. To facilitate this study we apply a Finite Element Method (FEM) and where applicable, the Group Finite Element Method (GFE) due its demonstrated stability and reduced complexity over the standard FEM. We also utilize Proper Orthogonal Decomposition (POD) as a model reduction technique and modifications of POD that include Global POD, and the sensitivity based modifications Extrapolated POD and Expanded POD. We then use a single baseline parameter in the parameter range to develop a ROM basis for each method above and investigate the error of each ROM method against a full order "truth" solution for the full parameter range.Master of Science
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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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Hagerlind, Simon. "Empirical evaluation of a stochastic model for order book dynamics." Thesis, Uppsala universitet, Matematiska institutionen, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-181603.
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Abstract A stochastic model for orderbook dynamics is proposed in Cont et al.(2010) and empirically evaluated in thisthesis. Arrival rates of limit, marketand cancellation orders are described interms of a Markov chain where thearrival rates are exponentiallydistributed. The model not onlyconsiders the best bid and ask queuesbut also additional price levels of theorder book. Methods for computingseveral quantities important to highfrequency trading are proposed usingLaplace transforms and continuedfractions. These quantities includeconditional probabilities such as theprobability of a price increasedepending on the profile of the orderbook. Computing these probabilities aresupposed to be easy enough to computeanalytically. However this was not thecase. We failed in the inversion of theLaplace transform methods and the mainreason is that the instructions in Contet al. (2010) are not adequate when itcomes to perform the inversion. Hence wedraw the conclusion that the method isno good for predicting short termbehavior of limit order books. For longterm applications the model can be usedto simulate the order book with goodresults.
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Rodríguez, Cruz Yolanda Rocío [Verfasser]. "Model Order Reduction for Stochastic Systems / Yolanda Rocío Rodríguez Cruz." München : Verlag Dr. Hut, 2018. http://d-nb.info/1162767596/34.
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Yuan, Tao. "Reduced order modeling for transport phenomena based on proper orthogonal decomposition." Texas A&M University, 2003. http://hdl.handle.net/1969.1/1470.
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In this thesis, a reduced order model (ROM) based on the proper orthogonal decomposition (POD) for the transport phenomena in fluidized beds has been developed. The reduced order model is tested first on a gas-only flow. Two different strategies and implementations are described for this case. Next, a ROM for a two-dimensional gas-solids fluidized bed is presented. A ROM is developed for a range of diameters of the solids particles. The reconstructed solution is calculated and compared against the full order solution. The differences between the ROM and the full order solution are
smaller than 3.2% if the diameters of the solids particles are in the range of diameters used for POD database generation. Otherwise, the errors
increase up to 10% for the cases presented herein. The computational time of the ROM varied between 25% and 33% of the computational time of the full order solution. The computational speed-up depended on the complexity of the transport phenomena, ROM methodology and reconstruction error. In this thesis, we also investigated the accuracy of the reduced order model based on the POD. When analyzing the accuracy, we used two simple sets of governing partial differential equations: a non-homogeneous Burgers' equation and a system of two coupled Burgers' equations.
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Zhou, Chao. "Model Uncertainty in Finance and Second Order Backward Stochastic Differential Equations." Palaiseau, Ecole polytechnique, 2012. https://pastel.hal.science/docs/00/77/14/37/PDF/Thesis_ZHOU_Chao_Pastel.pdfcc.
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L'objectif principal de cette thèse est d'étudier quelques problèmes de mathématiques financières dans un marché incomplet avec incertitude sur les modèles. Récemment, la théorie des équations différentielles stochastiques rétrogrades du second ordre (2EDSRs) a été développée par Soner, Touzi et Zhang sur ce sujet. Dans cette thèse, nous adoptons leur point de vue. Cette thèse contient quatre parties dans le domain des 2EDSRs. Nous commençons par généraliser la théorie des 2EDSRs initialement introduite dans le cas de générateurs lipschitziens continus à celui de générateurs à croissance quadratique. Cette nouvelle classe des 2EDSRs nous permettra ensuite d'étudier le problème de maximisation d'utilité robuste dans les modèles non-dominés. Dans la deuxième partie, nous étudions ce problème pour trois fonctions d'utilité. Dans chaque cas, nous donnons une caractérisation de la fonction valeur et d'une stratégie d'investissement optimale via la solution d'une 2EDSR. Dans la troisième partie, nous fournissons également une théorie d'existence et unicité pour des EDSRs réfléchies du second ordre avec obstacles inférieurs et générateurs lipschitziens, nous appliquons ensuite ce résultat à l'étude du problème de valorisation des options américaines dans un modèle financier à volatilité incertaine. Dans la quatrième partie, nous étudions des 2EDSRs avec sauts. En particulier, nous prouvons l'existence d'une unique solution dans un espace approprié. Comme application de ces résultats, nous étudions un problème de maximisation d'utilité exponentielle robuste avec incertitude sur les modèles. L'incertitude affecte à la fois le processus de volatilité, mais également la mesure des sautsThe main objective of this PhD thesis is to study some financial mathematics problems in an incomplete market with model uncertainty. In recent years, the theory of second order backward stochastic differential equations (2BSDEs for short) has been developed by Soner, Touzi and Zhang on this topic. In this thesis, we adopt their point of view. This thesis contains of four key parts related to 2BSDEs. In the first part, we generalize the 2BSDEs theory initially introduced in the case of Lipschitz continuous generators to quadratic growth generators. This new class of 2BSDEs will then allow us to consider the robust utility maximization problem in non-dominated models. In the second part, we study this problem for exponential utility, power utility and logarithmic utility. In each case, we give a characterization of the value function and an optimal investment strategy via the solution to a 2BSDE. In the third part, we provide an existence and uniqueness result for second order reflected BSDEs with lower obstacles and Lipschitz generators, and then we apply this result to study the problem of American contingent claims pricing with uncertain volatility. In the fourth part, we define a notion of 2BSDEs with jumps, for which we prove the existence and uniqueness of solutions in appropriate spaces. We can interpret these equations as standard BSDEs with jumps, under both volatility and jump measure uncertainty. As an application of these results, we shall study a robust exponential utility maximization problem under model uncertainty, where the uncertainty affects both the volatility process and the jump measure
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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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Rai, Manish 1968. "Design and implementation of a reduced base model construction technique for stochastic activity networks." Thesis, The University of Arizona, 1990. http://hdl.handle.net/10150/277849.
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Performance/dependability evaluation via modeling results in fast and economic system development. Traditionally, simulations have been used to evaluate realistic systems but do not yield exact results. Analytic solution methods can yield exact results, but can suffer from the state-space explosion problem. A reduced base model construction technique for stochastic activity networks, which exploits the net structure to generate a considerably reduced state-space for systems with high degree of replication, has been developed. An implementation of this technique shows that it can be successfully used for efficiently evaluating realistic systems, previously considered unsolvable by traditional stochastic Petri net methods.
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Antonelli, Jacopo. "Reduced order modeling of wind turbines in MatLab for grid integration and control studies." Thesis, Högskolan på Gotland, Institutionen för kultur, energi och miljö, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:hgo:diva-1865.
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The current trend in the wind power industry is to develop wind turbines of constantly increasing size and rated power, as well as wind farms of growing size and installed wind power. A careful study of the behaviour of the wind turbines during their operation is of crucial importance in the planning phase and in the design stage of a wind farm, in order to minimize the risks deriving from a non accurate prediction of their impact in the electric grid causing sensible faults of the system. To analyze the impact of the wind turbines in the system, motivates the development of accurate yet simple models. To be able to practically deal with this topics, a simple model of a wind turbine system is investigated and developed; it has the aim to describe the behaviour of a wind turbine in operation on a mechanical standpoint. The same reduced order simple model can also be employed for control system studies; the control system model that can’t be used in generation, can use the reduced model. Together with the analytical description of such model, is realized a MatLab code to numerically analyse the response of the system, and the results of the simulation through such code are presented. The objective of this thesis has been to provide a simple benchmark tool in MatLab for grid integration and control studies for interested researchers.
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Ghosh, Rajat. "Transient reduced-order convective heat transfer modeling for a data center." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/50380.
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A measurement-based reduced-order heat transfer modeling framework is developed to optimize cooling costs of dynamic and virtualized data centers. The reduced-order model is based on a proper orthogonal decomposition-based model order reduction technique. For data center heat transfer modeling, the framework simulates air temperatures and CPU temperatures as a parametric response surface with different cooling infrastructure design variables as the input parameters. The parametric framework enables an efficient design optimization tool and is used to solve several important problems related to energy-efficient thermal design of data centers.
The first of these problems is about determining optimal response time during emergencies such as power outages in data centers. To solve this problem, transient air temperatures are modeled with time as a parameter. This parametric prediction framework is useful as a near-real-time thermal prognostic tool.
The second problem pertains to reducing temperature monitoring cost in data centers. To solve this problem, transient air temperatures are modeled with spatial location as the parameter. This parametric model improves spatial resolution of measured temperature data and thereby reduces sensor requisition for transient temperature monitoring in data centers.
The third problem is related to determining optimal cooling set points in response to dynamically-evolving heat loads in a data center. To solve this problem, transient air temperatures are modeled with heat load and time as the parameters. This modeling framework is particularly suitable for life-cycle design of data center cooling infrastructure.
The last problem is related to determining optimal cooling set points in response to dynamically-evolving computing workload in a virtualized data center. To solve this problem, transient CPU temperatures under a given computing load profile are modeled with cooling resource set-points as the parameters.
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Qin, Lihai. "Development of Reduced-Order Models for Lift and Drag on Oscillating Cylinders with Higher-Order Spectral Moments." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/29542.
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An optimal solution of vortex-induced vibrations of structures would be a time-domain numerical simulation that simultaneously solves the fluid flow and structural response. Yet, the requirements in terms of computing power remains a major obstacle for implementing such a simulation. On the other hand, lower- or reduced-order models provide an alternative for determining structural response to forcing by fluid flow. The objective of this thesis is to provide a consistent approach for the development of reduced-order models for the lift and drag on oscillating cylinders and the identification of their parameters. Amplitudes and phases of higher-order spectral moments of the lift and drag coefficients data are combined with approximate solutions of the representative models to determine their parameters. The results show that the amplitude and phase of the trispectrum could be used to model the lift on the oscillating cylinder under different excitation conditions. Moreover, the amplitude and phase of the cross-bispectrum could be used to establish the lift-drag relation for oscillating cylinders. A forced van der Pol equation is used to represent the lift on a transversely oscillating cylinder, and a parametrically excited van der Pol equation is used to model the lift coefficient on an inline oscillating cylinder. All cases of excitations lead to close values for the damping and nonlinear parameters in the van der Pol equation. Consequently, and as shown in this thesis, different excitation cases could be used to identify the parameters in the governing equations. Moreover, the results show that the drag coefficient could be derived from the lift coefficient through a square relation that takes into account the effects of the forced motions.Ph. D.
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Fang, Chih. "A reduced-order meshless energy (ROME) model for the elastodynamics of mistuned bladed disks." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/12457.
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Zigic, Dragan. "Homotopy methods for solving the optimal projection equations for the reduced order model problem." Thesis, This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-11242009-020145/.
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Martin, Christopher Reed. "Reduced-Order Models for the Prediction of Unsteady Heat Release in Acoustically Forced Combustion." Diss., Virginia Tech, 2009. http://hdl.handle.net/10919/30238.
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This work presents novel formulations for models describing acoustically forced combustion in three disjoint regimes; highly turbulent, laminar, and the moderately turbulent flamelet regime. Particular emphasis is placed on simplification of the models to facilitate analytical solutions while still reflecting real phenomenology. Each derivation is treated by beginning with general reacting flow equations, identifying a small subset of physics thought to be dominant in the corresponding regime, and making appropriate simplifications. Each model is non-dimensionalized and both naturally occurring and popular dimensionless parameters are investigated.
The well-stirred reactor (WSR) is used to characterize the highly turbulent regime. It is confirmed that, consistent with the regime to which it is ascribed for static predictions, the WSR is most appropriate to predict the dynamics of chemical kinetics. Both convection time and chemical time dynamics are derived as explicit closed-form functions of dimensionless quantities such as the Damk\"ohler number and several newly defined parameters.
The plug-flow reactor (PFR) is applied to a laminar, burner stabilized flame, using a number of established approaches, but with new attention to developing simple albeit accurate expressions governing the flame's frequency response. The system is studied experimentally using a ceramic honeycomb burner, combusting a methane-air mixture, numerically using a nonlinear FEA solver, and analytically by exact solution of the simplified governing equations. Accurately capturing non-unity Lewis-number effects are essential to capturing both the static and the dynamic response of the flame. It is shown that the flame dynamics can be expressed solely in terms of static quantities.
Finally, a Reynolds-averaged flamelet model is applied to a hypothetical burner stabilized flame with homogeneous, isotropic turbulence. Exact solution with a simplified turbulent reaction model parallels that of the plug flow reactor closely, demonstrating a relation between static quantities and the flame frequency response. Comparison with published experiments using considerably more complex flame geometries yields unexpected similarities in frequency scale, and phase behavior. The observed differences are attributed to specific physical phenomena that were deliberately omitted to simplify the model's derivation.Ph. D.
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Balabanov, Oleg. "Randomized linear algebra for model order reduction." Doctoral thesis, Universitat Politècnica de Catalunya, 2019. http://hdl.handle.net/10803/668906.
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Solutions to high-dimensional parameter-dependent problems are in great demand in the contemporary applied science and engineering. The standard approximation methods for parametric equations can require computational resources that are exponential in the dimension of the parameter space, which is typically refereed to as the curse of dimensionality. To break the curse of dimensionality one has to appeal to nonlinear methods that exploit the structure of the solution map, such as projection-based model order reduction methods.
This thesis proposes novel methods based on randomized linear algebra to enhance the efficiency and stability of projection-based model order reduction methods for solving parameter-dependent equations. Our methodology relies on random projections (or random sketching). Instead of operating with high-dimensional vectors we first efficiently project them into a low-dimensional space. The reduced model is then efficiently and numerically stably constructed from the projections of the reduced approximation space and the spaces of associated residuals.
Our approach allows drastic computational savings in basically any modern computational architecture. For instance, it can reduce the number of flops and memory consumption and improve the efficiency of the data flow (characterized by scalability or communication costs). It can be employed for improving the efficiency and numerical stability of classical Galerkin and minimal residual methods. It can also be used for the efficient estimation of the error, and post-processing of the solution of the reduced order model. Furthermore, random sketching makes computationally feasible a dictionary-based approximation method, where for each parameter value the solution is approximated in a subspace with a basis selected from a dictionary of vectors.
We also address the efficient construction (using random sketching) of parameter-dependent preconditioners that can be used to improve the quality of Galerkin projections or for effective error certification for problems with ill-conditioned operators.
For all proposed methods we provide precise conditions on the random sketch to guarantee accurate and stable estimations with a user-specified probability of success. A priori estimates to determine the sizes of the random matrices are provided as well as a more effective adaptive procedure based on a posteriori estimates.Cette thèse introduit des nouvelles approches basées sur l’algèbre linéaire aléatoire pour améliorer l’efficacité et la stabilité des méthodes de réduction de modèles basées sur des projections pour la résolution d’équations dépendant de paramètres. Notre méthodologie repose sur des techniques de projections aléatoires ("random sketching") qui consistent à projeter des vecteurs de grande dimension dans un espace de faible dimension. Un modèle réduit est ainsi construit de manière efficace et numériquement stable à partir de projections aléatoires de l’espace d’approximation réduit et des espaces des résidus associés. Notre approche permet de réaliser des économies de calcul considérables dans pratiquement toutes les architectures de calcul modernes. Par exemple, elle peut réduire le nombre de flops et la consommation de mémoire et améliorer l’efficacité du flux de données (caractérisé par l’extensibilité ou le coût de communication). Elle peut être utilisée pour améliorer l’efficacité et la stabilité des méthodes de projection de Galerkin ou par minimisation de résidu. Elle peut également être utilisée pour estimer efficacement l’erreur et post-traiter la solution du modèle réduit. De plus, l’approche par projection aléatoire rend viable numériquement une méthode d’approximation basée sur un dictionnaire, où pour chaque valeur de paramètre, la solution est approchée dans un sous-espace avec une base sélectionnée dans le dictionnaire. Nous abordons également la construction efficace (par projections aléatoires) de préconditionneurs dépendant de paramètres, qui peuvent être utilisés pour améliorer la qualité des projections de Galerkin ou des estimateurs d’erreur pour des problèmes à opérateurs mal conditionnés. Pour toutes les méthodes proposées, nous fournissons des conditions précises sur les projections aléatoires pour garantir des estimations précises et stables avec une probabilité de succès spécifiée par l’utilisateur. Pour déterminer la taille des matrices aléatoires, nous fournissons des bornes a priori ainsi qu’une procédure adaptative plus efficace basée sur des estimations a posteriori
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Herath, Narmada Kumari. "Model order reduction for stochastic models of biomolecular systems with time-scale separation." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/118083.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 177-183).
Biomolecular systems often involve reactions that take place on different time-scales, giving rise to 'slow' and 'fast' system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In deterministic systems, methods to obtain such reduced-order models are well defined by the singular perturbation or averaging techniques. However, model reduction of stochastic systems remains an ongoing area of research. In particular, existing model reduction methods for stochastic models of biomolecular systems lack rigorous error quantifications between the full and reduced dynamics. Furthermore, they only provide approximations for the slow variable dynamics, making the application of such methods to biomolecular systems difficult since the variables of interest are typically mixed (i.e., they encompass both fast and slow variables). In this thesis, we consider biomolecular systems modeled using the chemical Langevin equation (CLE) and the Linear Noise Approximation (LNA). Specifically, we consider biomolecular systems with linear propensity functions modeled by the CLE and systems with arbitrary propensity functions modeled by the LNA. For these systems, we obtain reduced-order models that approximate both the slow and fast variables under time-scale separation conditions. In particular, with suitable assumptions, we prove that the moments of the reduced-order models converge to those of the full systems as the time-scale separation becomes large. Our results further provide a rigorous justification for the accuracy of the stochastic total quasi-steady state approximation (tQSSA). We then consider two applications of these reduced-order models. In the first application, we analyze the trade-offs between modularity and signal noise in biomolecular networks. In the second application, we consider the application of the reduced-order LNA developed in this work to obtain reduced-order stochastic models for gene-regulatory networks.
by Narmada Kumari Herath.
Ph. D.
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Grogan, Terence M. "Active damping of vibration in large space structures using a Karhunen-Loeve reduced order model." Thesis, Monterey, California. Naval Postgraduate School, 1989. http://hdl.handle.net/10945/26845.
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Approved for public release; distribution is unlimited.Large space structures are difficult to control because of the high order of their mathematical models. The high order mathematical model makes the use of a reduced order model to control the structure desirable. The Karhunen-Loeve expansion along with Galerkin's method is used to generate a reduced order model. A control algorithm is achieved by applying linear quadratic regulator theory to the reduced order model. The Karhunen-Loeve basis functions or mode shapes must first be found to identify the reduced order model. Previous results have shown that in the limit as the structural damping approaches zero the Karhunen-Loeve mode shapes and natural mode shapes converge. Numerical techniques are applied to evaluate the structural damping required for convergence. Once the Karhunen-Loeve mode shapes are determined, the reduced order control model is applied to the full order system. The performance of various Karhunen-Loeve models is compared by measuring the modal energies in the controlled and uncontrolled modes. Keywords: Large space structure; Vibration damping. Theses. (JHD)
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Shih, Shih-Ming. "Reduced-order model-reference adaptive system identification of large scale systems with discrete adaptation laws." Thesis, Massachusetts Institute of Technology, 1985. http://hdl.handle.net/1721.1/15253.
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Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1985.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING.
Includes bibliographical references.
by Shih-Ming Shih.
Sc.D.
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Richardson, Brian Ross. "A reduced-order model based on proper orthogonal decomposition for non-isothermal two-phase flows." [College Station, Tex. : Texas A&M University, 2008. http://hdl.handle.net/1969.1/ETD-TAMU-2623.
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Deshmukh, Rohit. "Model Order Reduction of Incompressible Turbulent Flows." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1471618549.
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Malik, Muhammad Haris. "Reduced order modeling for smart grids' simulation and optimization." Doctoral thesis, Universitat Politècnica de Catalunya, 2017. http://hdl.handle.net/10803/405730.
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This thesis presents the study of the model order reduction for power grids and transmission networks. The specific focus has been the transient dynamics. A mathematical viewpoint has been adopted for model reduction. Power networks are huge and complex network, simulation for power grid analysis and design require large non-linear models to be solved. In the context of developing "Smart Grids" with the distributed generation of power, real time analysis of complex systems such as these needs fast, reliable and accurate models. In the current study we propose model order reduction methods both a-priori and a-posteriori suitable for dynamic models of power grids.
The model that describes the transient dynamics of the power grids is complex non-linear swing dynamics model. The non-linearity of the swing dynamics model necessitates special attention to achieve maximum benefit from the model order reduction techniques. In the current research, POD and LATIN methods were applied initially with varying degrees of success. The method of TPWL has been proved as the best-suited model reduction method for swing dynamics model; this method combines POD with multiple linear approximations. For the transmission lines, a distributed parameters model in frequency-domain is used. PGD based reduced-order models are proposed for the DP model of transmission lines. A fully parametric problem with electrical parameters of transmission lines included as coordinates of the separated representation. The method was extended to present the solution of frequency-dependent parameters model for transmission lines.Cette these présente l'étude de la réduction de modeles pour les réseaux électriques et les réseaux de transmission. Un point de vue mathématique a été adopté pour la réduction de modeles. Les réseaux électriques sont des réseaux immenses et complexes, dont l'analyse et la conception nécessite la simulation et la résolution de grands modeles non-linéaires. Dans le cadre du développement de réseaux électriques intelligents (smart grids) avec une génération distribuée de puissance, l'analyse en temps réel de systemes complexes tels que ceux-ci nécessite des modeles rapides, fiables et précis. Dans la présente étude, nous proposons des méthodes de réduction de de modeles a la fois a priori et a posteriori, adaptées aux modeles dynamiques des réseaux électriques. Un accent particulier a été mis sur la dynamique transitoire des réseaux électriques, décrite par un modele oscillant nonlinéaire et complexe. La non-linéarité de ce modele nécessite une attention particuliere pour bénéficier du maximum d'avantages des techniques de réduction de modeles. lnitialement, des méthodes comme POD et LATIN ont été adoptées avec des degrés de succes divers. La méthode de TPWL, qui combine la POD avec des approximations linéaires multiples, a été prouvée comme étant la méthode de réduction de modeles la mieux adaptée pour le modele dynamique oscillant. Pour les lignes de transmission, un modele de parametres distribués en domaine fréquentiel est utilisé. Des modeles réduits de type PGD sont proposés pour le modele DP des lignes de transmission. Un probleme multidimensionnel entierement paramétrique a été formulé, avec les parametres électriques des lignes de transmission inclus comme coordonnées additionnelles de la représentation séparée. La méthode a été étendue pour étudier la solution du modele des lignes de transmission pour laquelle les parametres dépendent de la fréquence.
Esta tesis presenta un estudio de la reducción de modelos (MOR) para redes de transmisión y distribución de electricidad. El enfoque principal utilizado ha sido la dinámica transitoria y para la reducción de modelos se ha adoptado un punto de vista matemático. Las redes eléctricas son complejas y tienen un tamaño importante. Por lo tanto, el análisis y diseño de este tipo de redes mediante la simulación numérica, requiere la resolución de modelos no-lineales complejos. En el contexto del desarrollo de redes inteligentes, el objetivo es un análisis en tiempo real de sistemas complejos, por lo que son necesarios modelos rápidos, fiables y precisos. En el presente estudio se proponen diferentes métodos de reducción de modelos, tanto a priori como a posteriori, adecuados para modelos dinámicos de redes eléctricas. La dinámica transitoria de redes eléctricas, se describe mediante modelos dinámicos oscilatorios no-lineales. Esta no-linearidad del modelo necesita ser bien tratada para obtener el máximo beneficio de las técnicas de reducción de modelos. Métodos como la POD y la LATIN han sido inicialmente utilizados en esta problemática con diferentes grados de éxito. El método de TPWL, que combina la POD con múltiples aproximaciones lineales, ha resultado ser el mas adecuado para sistemas dinámicos oscilatorios. En el caso de las redes de transmisión eléctrica, se utiliza un modelo de parámetros distribuidos en el dominio de la frecuencia. Se propone reducir este modelo basándose en la PGD, donde los parámetros eléctricos de la red de transmisión son incluidos como coordenadas de la representación separada del modelo paramétrico. Este método es ampliado para representar la solución de modelos con parámetros dependientes de la frecuencia para las redes de transmisión eléctrica
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Resseguier, Valentin. "Mixing and fluid dynamics under location uncertainty." Thesis, Rennes 1, 2017. http://www.theses.fr/2017REN1S004/document.
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Cette thèse concerne le développement, l'extension et l'application d'une formulation stochastique des équations de la mécanique des fluides introduite par Mémin (2014). La vitesse petite échelle, non-résolue, est modélisée au moyen d'un champ aléatoire décorrélé en temps. Cela modifie l'expression de la dérivée particulaire et donc les équations de la mécanique des fluides. Les modèles qui en découlent sont dénommés modèles sous incertitude de position. La thèse s'articulent autour de l'étude successive de modèles réduits, de versions stochastiques du transport et de l'advection à temps long d'un champ de traceur par une vitesse mal résolue. La POD est une méthode de réduction de dimension, pour EDP, rendue possible par l'utilisation d'observations. L'EDP régissant l'évolution de la vitesse du fluide est remplacée par un nombre fini d'EDOs couplées. Grâce à la modélisation sous incertitude de position et à de nouveaux estimateurs statistiques, nous avons dérivé et simulé des versions réduites, déterministe et aléatoire, de l'équation de Navier-Stokes. Après avoir obtenu des versions aléatoires de plusieurs modèles océaniques, nous avons montré numériquement que ces modèles permettaient de mieux prendre en compte les petites échelles des écoulements, tout en donnant accès à des estimés de bonne qualité des erreurs du modèle. Ils permettent par ailleurs de mieux rendre compte des évènements extrêmes, des bifurcations ainsi que des phénomènes physiques réalistes absents de certains modèles déterministes équivalents. Nous avons expliqué, démontré et quantifié mathématiquement l'apparition de petites échelles de traceur, lors de l'advection par une vitesse mal résolu. Cette quantification permet de fixer proprement des paramètres de la méthode d'advection Lagrangienne, de mieux le comprendre le phénomène de mélange et d'aider au paramétrage des simulations grande échelle en mécanique des fluidesThis thesis develops, analyzes and demonstrates several valuable applications of randomized fluid dynamics models referred to as under location uncertainty. The velocity is decomposed between large-scale components and random time-uncorrelated small-scale components. This assumption leads to a modification of the material derivative and hence of every fluid dynamics models. Through the thesis, the mixing induced by deterministic low-resolution flows is also investigated. We first applied that decomposition to reduced order models (ROM). The fluid velocity is expressed on a finite-dimensional basis and its evolution law is projected onto each of these modes. We derive two types of ROMs of Navier-Stokes equations. A deterministic LES-like model is able to stabilize ROMs and to better analyze the influence of the residual velocity on the resolved component. The random one additionally maintains the variability of stable modes and quantifies the model errors. We derive random versions of several geophysical models. We numerically study the transport under location uncertainty through a simplified one. A single realization of our model better retrieves the small-scale tracer structures than a deterministic simulation. Furthermore, a small ensemble of simulations accurately predicts and describes the extreme events, the bifurcations as well as the amplitude and the position of the ensemble errors. Another of our derived simplified model quantifies the frontolysis and the frontogenesis in the upper ocean. This thesis also studied the mixing of tracers generated by smooth fluid flows, after a finite time. We propose a simple model to describe the stretching as well as the spatial and spectral structures of advected tracers. With a toy flow but also with satellite images, we apply our model to locally and globally describe the mixing, specify the advection time and the filter width of the Lagrangian advection method, as well as the turbulent diffusivity in numerical simulations
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Al, Akhras Hassan. "Automatic isogeometric analysis suitable trivariate models generation : Application to reduced order modeling." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEI047/document.
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Cette thèse présente un algorithme automatique pour la construction d’un modèle NURBS volumique à partir d’un modèle représenté par ses bords (maillages ou splines). Ce type de modèle est indispensable dans le cadre de l’analyse isogéométrique utilisant les NURBS comme fonctions de forme. Le point d’entrée de l’algorithme est une triangulation du bord du modèle. Après deux étapes de décomposition, le modèle est approché par un polycube. Ensuite un paramétrage surfacique entre le bord du modèle et celui du polycube est établi en calculant un paramétrage global aligné à un champ de direction interpolant les directions de courbure principales du modèle. Finalement, le paramétrage volumique est obtenu en se basant sur ce paramétrage surfacique. Dans le contexte des études paramétriques basées sur des paramètres de formes géométriques, cette méthode peut être appliquée aux techniques de réduction de modèles pour obtenir la même représentation pour des objets ayant différentes géométries mais la même topologieThis thesis presents an effective method to automatically construct trivariate tensor-product spline models of complicated geometry and arbitrary topology. Our method takes as input a solid model defined by its triangulated boundary. Using cuboid decomposition, an initial polycube approximating the input boundary mesh is built. This polycube serves as the parametric domain of the tensor-product spline representation required for isogeometric analysis. The polycube's nodes and arcs decompose the input model locally into quadrangular patches, and globally into hexahedral domains. Using aligned global parameterization, the nodes are re-positioned and the arcs are re-routed across the surface in a way to achieve low overall patch distortion, and alignment to principal curvature directions and sharp features. The optimization process is based on one of the main contributions of this thesis: a novel way to design cross fields with topological (i.e., imposed singularities) and geometrical (i.e., imposed directions) constraints by solving only sparse linear systems. Based on the optimized polycube and parameterization, compatible B-spline boundary surfaces are reconstructed. Finally, the interior volumetric parameterization is computed using Coon's interpolation and the B-spline surfaces as boundary conditions. This method can be applied to reduced order modeling for parametric studies based on geometrical parameters. For models with the same topology but different geometries, this method allows to have the same representation: i.e., meshes (or parameterizations) with the same topology
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Raghupathy, Arun Prakash. "Boundary-Condition-Independent Reduced-Order Modeling for Thermal Analysis of Complex Electronics Packages." University of Cincinnati / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1240536463.
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Eftang, Jens Lohne. "Reduced basis methods for parametrized partial differential equations." Doctoral thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-12550.
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Xia, Liang. "Towards optimal design of multiscale nonlinear structures : reduced-order modeling approaches." Thesis, Compiègne, 2015. http://www.theses.fr/2015COMP2230/document.
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L'objectif principal est de faire premiers pas vers la conception topologique de structures hétérogènes à comportement non-linéaires. Le deuxième objectif est d’optimiser simultanément la topologie de la structure et du matériau. Il requiert la combinaison des méthodes de conception optimale et des approches de modélisation multi-échelle. En raison des lourdes exigences de calcul, nous avons introduit des techniques de réduction de modèle et de calcul parallèle. Nous avons développé tout d’abord un cadre de conception multi-échelle constitué de l’optimisation topologique et la modélisation multi-échelle. Ce cadre fournit un outil automatique pour des structures dont le modèle de matériau sous-jacent est directement régi par la géométrie de la microstructure réaliste et des lois de comportement microscopiques. Nous avons ensuite étendu le cadre en introduisant des variables supplémentaires à l’échelle microscopique pour effectuer la conception simultanée de la structure et de la microstructure. En ce qui concerne les exigences de calcul et de stockage de données en raison de multiples réalisations de calcul multi-échelle sur les configurations similaires, nous avons introduit: les approches de réduction de modèle. Nous avons développé un substitut d'apprentissage adaptatif pour le cas de l’élasticité non-linéaire. Pour viscoplasticité, nous avons collaboré avec le Professeur Felix Fritzen de l’Université de Stuttgart en utilisant son modèle de réduction avec la programmation parallèle sur GPU. Nous avons également adopté une autre approche basée sur le potentiel de réduction issue de la littérature pour améliorer l’efficacité de la conception simultanéeHigh-performance heterogeneous materials have been increasingly used nowadays for their advantageous overall characteristics resulting in superior structural mechanical performance. The pronounced heterogeneities of materials have significant impact on the structural behavior that one needs to account for both material microscopic heterogeneities and constituent behaviors to achieve reliable structural designs. Meanwhile, the fast progress of material science and the latest development of 3D printing techniques make it possible to generate more innovative, lightweight, and structurally efficient designs through controlling the composition and the microstructure of material at the microscopic scale. In this thesis, we have made first attempts towards topology optimization design of multiscale nonlinear structures, including design of highly heterogeneous structures, material microstructural design, and simultaneous design of structure and materials. We have primarily developed a multiscale design framework, constituted of two key ingredients : multiscale modeling for structural performance simulation and topology optimization forstructural design. With regard to the first ingredient, we employ the first-order computational homogenization method FE2 to bridge structural and material scales. With regard to the second ingredient, we apply the method Bi-directional Evolutionary Structural Optimization (BESO) to perform topology optimization. In contrast to the conventional nonlinear design of homogeneous structures, this design framework provides an automatic design tool for nonlinear highly heterogeneous structures of which the underlying material model is governed directly by the realistic microstructural geometry and the microscopic constitutive laws. Note that the FE2 method is extremely expensive in terms of computing time and storage requirement. The dilemma of heavy computational burden is even more pronounced when it comes to topology optimization : not only is it required to solve the time-consuming multiscale problem once, but for many different realizations of the structural topology. Meanwhile we note that the optimization process requires multiple design loops involving similar or even repeated computations at the microscopic scale. For these reasons, we introduce to the design framework a third ingredient : reduced-order modeling (ROM). We develop an adaptive surrogate model using snapshot Proper Orthogonal Decomposition (POD) and Diffuse Approximation to substitute the microscopic solutions. The surrogate model is initially built by the first design iteration and updated adaptively in the subsequent design iterations. This surrogate model has shown promising performance in terms of reducing computing cost and modeling accuracy when applied to the design framework for nonlinear elastic cases. As for more severe material nonlinearity, we employ directly an established method potential based Reduced Basis Model Order Reduction (pRBMOR). The key idea of pRBMOR is to approximate the internal variables of the dissipative material by a precomputed reduced basis computed from snapshot POD. To drastically accelerate the computing procedure, pRBMOR has been implemented by parallelization on modern Graphics Processing Units (GPUs). The implementation of pRBMOR with GPU acceleration enables us to realize the design of multiscale elastoviscoplastic structures using the previously developed design framework inrealistic computing time and with affordable memory requirement. We have so far assumed a fixed material microstructure at the microscopic scale. The remaining part of the thesis is dedicated to simultaneous design of both macroscopic structure and microscopic materials. By the previously established multiscale design framework, we have topology variables and volume constraints defined at both scales
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Braun, Mathias. "Reduced Order Modelling and Uncertainty Propagation Applied to Water Distribution Networks." Thesis, Bordeaux, 2019. http://www.theses.fr/2019BORD0050/document.
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Les réseaux de distribution d’eau consistent en de grandes infrastructures réparties dans l’espace qui assurent la distribution d’eau potable en quantité et en qualité suffisantes. Les modèles mathématiques de ces systèmes sont caractérisés par un grand nombre de variables d’état et de paramètres dont la plupart sont incertains. Les temps de calcul peuvent s’avérer conséquents pour les réseaux de taille importante et la propagation d’incertitude par des méthodes de Monte Carlo. Par conséquent, les deux principaux objectifs de cette thèse sont l’étude des techniques de modélisation à ordre réduit par projection ainsi que la propagation spectrale des incertitudes des paramètres. La thèse donne tout d’abord un aperçu des méthodes mathématiques utilisées. Ensuite, les équations permanentes des réseaux hydrauliques sont présentées et une nouvelle méthode de calcul des sensibilités est dérivée sur la base de la méthode adjointe. Les objectifs spécifiques du développement de modèles d’ordre réduit sont l’application de méthodes basées sur la projection, le développement de stratégies d’échantillonnage adaptatives plus efficaces et l’utilisation de méthodes d’hyper-réduction pour l’évaluation rapide des termes résiduels non linéaires. Pour la propagation des incertitudes, des méthodes spectrales sont introduites dans le modèle hydraulique et un modèle hydraulique intrusif est formulé. Dans le but d’une analyse plus efficace des incertitudes des paramètres, la propagation spectrale est ensuite évaluée sur la base du modèle réduit. Les résultats montrent que les modèles d’ordre réduit basés sur des projections offrent un avantage considérable par rapport à l’effort de calcul. Bien que l’utilisation de l’échantillonnage adaptatif permette une utilisation plus efficace des états système pré-calculés, l’utilisation de méthodes d’hyper-réduction n’a pas permis d’améliorer la charge de calcul. La propagation des incertitudes des paramètres sur la base des méthodes spectrales est comparable aux simulations de Monte Carlo en termes de précision, tout en réduisant considérablement l’effort de calculWater distribution systems are large, spatially distributed infrastructures that ensure the distribution of potable water of sufficient quantity and quality. Mathematical models of these systems are characterized by a large number of state variables and parameter. Two major challenges are given by the time constraints for the solution and the uncertain character of the model parameters. The main objectives of this thesis are thus the investigation of projection based reduced order modelling techniques for the time efficient solution of the hydraulic system as well as the spectral propagation of parameter uncertainties for the improved quantification of uncertainties. The thesis gives an overview of the mathematical methods that are being used. This is followed by the definition and discussion of the hydraulic network model, for which a new method for the derivation of the sensitivities is presented based on the adjoint method. The specific objectives for the development of reduced order models are the application of projection based methods, the development of more efficient adaptive sampling strategies and the use of hyper-reduction methods for the fast evaluation of non-linear residual terms. For the propagation of uncertainties spectral methods are introduced to the hydraulic model and an intrusive hydraulic model is formulated. With the objective of a more efficient analysis of the parameter uncertainties, the spectral propagation is then evaluated on the basis of the reduced model. The results show that projection based reduced order models give a considerable benefit with respect to the computational effort. While the use of adaptive sampling resulted in a more efficient use of pre-calculated system states, the use of hyper-reduction methods could not improve the computational burden and has to be explored further. The propagation of the parameter uncertainties on the basis of the spectral methods is shown to be comparable to Monte Carlo simulations in accuracy, while significantly reducing the computational effort
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Wang, Zhu. "Reduced-Order Modeling of Complex Engineering and Geophysical Flows: Analysis and Computations." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/27504.
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Reduced-order models are frequently used in the simulation of complex flows to overcome the high computational cost of direct numerical simulations, especially for three-dimensional nonlinear problems.
Proper orthogonal decomposition, as one of the most commonly used tools to generate reduced-order models, has been utilized in many engineering and scientific applications.
Its original promise of computationally efficient, yet accurate approximation of coherent structures in high Reynolds number turbulent flows, however, still remains to be fulfilled. To balance the low computational cost required by reduced-order modeling and the complexity of the targeted flows, appropriate closure modeling strategies need to be employed.
In this dissertation, we put forth two new closure models for the proper orthogonal decomposition reduced-order modeling of structurally dominated turbulent flows: the dynamic subgrid-scale model and the variational multiscale model.
These models, which are considered state-of-the-art in large eddy simulation, are carefully derived and numerically investigated.
Since modern closure models for turbulent flows generally have non-polynomial nonlinearities, their efficient numerical discretization within a proper orthogonal decomposition framework is challenging. This dissertation proposes a two-level method for an efficient and accurate numerical discretization of general nonlinear proper orthogonal decomposition closure models. This method computes the nonlinear terms of the reduced-order model on a coarse mesh. Compared with a brute force computational approach in which the nonlinear terms are evaluated on the fine mesh at each time step, the two-level method attains the same level of accuracy while dramatically reducing the computational cost. We numerically illustrate these improvements in the two-level method by using it in three settings: the one-dimensional Burgers equation with a small diffusion parameter, a two-dimensional flow past a cylinder at Reynolds number Re = 200, and a three-dimensional flow past a cylinder at Reynolds number Re = 1000.
With the help of the two-level algorithm, the new nonlinear proper orthogonal decomposition closure models (i.e., the dynamic subgrid-scale model and the variational multiscale model), together with the mixing length and the Smagorinsky closure models, are tested in the numerical simulation of a three-dimensional turbulent flow past a cylinder at Re = 1000. Five criteria are used to judge the performance of the proper orthogonal decomposition reduced-order models: the kinetic energy spectrum, the mean velocity, the Reynolds stresses, the root mean square values of the velocity fluctuations, and the time evolution of the proper orthogonal decomposition basis coefficients. All the numerical results are benchmarked against a direct numerical simulation. Based on these numerical results, we conclude that the dynamic subgrid-scale and the variational multiscale models are the most accurate.
We present a rigorous numerical analysis for the discretization of the new models. As a first step, we derive an error estimate for the time discretization of the Smagorinsky proper orthogonal decomposition reduced-order model for the Burgers equation with a small diffusion parameter.
The theoretical analysis is numerically verified by two tests on problems displaying shock-like phenomena.
We then present a thorough numerical analysis for the finite element discretization of the variational multiscale proper orthogonal decomposition reduced-order model for convection-dominated convection-diffusion-reaction equations. Numerical tests show the increased numerical accuracy over the standard reduced-order model and illustrate the theoretical convergence rates.
We also discuss the use of the new reduced-order models in realistic applications such as airflow simulation in energy efficient building design and control problems as well as numerical simulation of large-scale ocean motions in climate modeling. Several research directions that we plan to pursue in the future are outlined.Ph. D.
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Truster, Nicholas Leigh. "A REDUCED-ORDER COMPUTATIONAL MODEL OF A TWO-PASS, CROSS-FLOW CONFORMAL HEAT EXCHANGER FOR AEROSPACE APPLICATIONS." Miami University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=miami1480535587051259.
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Auffredic, Jérémy. "A second order Runge–Kutta method for the Gatheral model." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-49170.
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In this thesis, our research focus on a weak second order stochastic Runge–Kutta method applied to a system of stochastic differential equations known as the Gatheral Model. We approximate numerical solutions to this system and investigate the rate of convergence of our method. Both call and put options are priced using Monte-Carlo simulation to investigate the order of convergence. The numerical results show that our method is consistent with the theoretical order of convergence of the Monte-Carlo simulation. However, in terms of the Runge-Kutta method, we cannot accept the consistency of our method with the theoretical order of convergence without further research.
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Lauzeral, Nathan. "Reduced order and sparse representations for patient-specific modeling in computational surgery." Thesis, Ecole centrale de Nantes, 2019. http://www.theses.fr/2019ECDN0062.
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Cette thèse a pour but d’évaluer l'utilisation des méthodes de réduction de modèles fondées sur des approches parcimonieuses pour atteindre des performances en temps réel dans la cadre de la chirurgie computationnelle. Elle se concentre notamment sur l’intégration de la simulation biophysique dans des modèles personnalisés de tissus et d'organes afin d'augmenter les images médicales et ainsi éclairer le clinicien dans sa prise de décision. Dans ce contexte, trois enjeux fondamentaux sont mis en évidence. Le premier réside dans l'intégration de la paramétrisation de la forme au sein du modèle réduit afin de représenter fidèlement l'anatomie du patient. Une approche non intrusive reposant sur un échantillonnage parcimonieux de l'espace des caractéristiques anatomiques est introduite et validée. Ensuite, nous abordons le problème de la complétion des données et de la reconstruction des images à partir de données partielles ou incomplètes via des à priori physiques. Nous explorons le potentiel de la solution proposée dans le cadre du recalage d’images pour la réalité augmentée en laparoscopie. Des performances proches du temps réel sont obtenues grâce à une nouvelle approche d'hyper-réduction fondée sur une technique de représentation parcimonieuse. Enfin, le troisième défi concerne la propagation des incertitudes dans le cadre de systèmes biophysiques. Il est démontré que les approches de réduction de modèles traditionnelles ne réussissent pas toujours à produire une représentation de faible rang, et ce, en particulier dans le cas de la simulation électrochirurgicale. Une alternative est alors proposée via la métamodélisation. Pour ce faire, nous étendons avec succès l'utilisation de méthodes de régression parcimonieuses aux cas des systèmes à paramètres stochastiquesThis thesis investigates the use of model order reduction methods based on sparsity-related techniques for the development of real-time biophysical modeling. In particular, it focuses on the embedding of interactive biophysical simulation into patient-specific models of tissues and organs to enhance medical images and assist the clinician in the process of informed decision making. In this context, three fundamental bottlenecks arise. The first lies in the embedding of the shape parametrization into the parametric reduced order model to faithfully represent the patient’s anatomy. A non-intrusive approach relying on a sparse sampling of the space of anatomical features is introduced and validated. Then, we tackle the problem of data completion and image reconstruction from partial or incomplete datasets based on physical priors. The proposed solution has the potential to perform scene registration in the context of augmented reality for laparoscopy. Quasi-real-time computations are reached by using a new hyperreduction approach based on a sparsity promoting technique. Finally, the third challenge concerns the representation of biophysical systems under uncertainty of the underlying parameters. It is shown that traditional model order reduction approaches are not always successful in producing a low dimensional representation of a model, in particular in the case of electrosurgery simulation. An alternative is proposed using a metamodeling approach. To this end, we successfully extend the use of sparse regression methods to the case of systems with stochastic parameters
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Balmaseda, Aguirre Mikel. "Reduced order models for nonlinear dynamic analysis of rotating structures : Application to turbomachinery blades." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSEI067.
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In the present work reduced order models (ROM) that are independent from the full order finite element models (FOM) considering geometrical non linearities are developed and applied to the dynamic study of rotating structures. The structure is considered to present nonlinear vibrations around the pre-stressed equilibrium induced by rotation enhancing the classical linearised approach. The reduced nonlinear forces are represented by a polynomial expansion obtained by the Stiffness. Evaluation Procedure (STEP) and then corrected by means of an original procedure by means of a Proper Orthogonal Decomposition (POD) that filters the full order nonlinear forces before projection. The latter model is named STEP with Correction (StepC). Different types of reduced basis are presented and tested. Some of these bases are parametrised with respect to the rotating velocity reducing considerably the construction of the ROM. The results obtained with the StepC ROM are in good agreement with the solutions of the FOM and are capable of reproducing the coupled motion of the structure. Furthermore they are more accurate than the classsical Linearised ROM solutions and than the STEP ROM without correction. The proposed StepC ROM provides the best compromise between accuracy and time consumption of the ROMDans le présent travail, des modèles d’ordre réduits (ROM) indépendant des modèles ́eléments finis d’haute fidélité (FOM) ont ́eté d ́eveloppés pour l’etude de la dynamique non linéaire des structures en rotation. Les vibrations de la structure autour de l’équilibre précontraint induit par la rotation sont considérées comme non linéaires, améliorant l’approche linéarisée classique. Les forces généralisées non linéaires sont approximées par un polynôme d’ordre trois obtenu avec la procédure Stiffness Evaluation Procedure (STEP). Ici, une approche originale est proposée pour corriger les forces non linéaires à l’aide d’une base de forces non linéaires obtenue avec une décomposition orthogonale aux valeurs propres (POD). Ce modèle est nommé STEP avec Correction (StepC). Différents types de base réduite sont présentés et testés. Certaines de ces bases sont paramétrées en fonction de la vitesse de rotation, ce qui réduit considérablement le temps de construction du modèle réduit. Les résultats obtenus avec le modèle StepC ROM sont en bon accord avec le FOM et sont capables de reproduire le couplage en déplacement entre les dégrés de liberté de la structure. De plus, elles sont plus précises que les solutions ROM linéarisées classiques et que le modèle STEP ROM sans correction. Le modèle StepC ROM proposé offre le meilleur compromis entre précision et temps de construction du ROM
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Brüderlin, Manuel Pedro [Verfasser], Marek [Akademischer Betreuer] Behr, and Kai-Uwe [Akademischer Betreuer] Schröder. "A procedure for reduced-order model based robust aeroelastic control / Manuel Pedro Brüderlin ; Marek Behr, Kai-Uwe Schröder." Aachen : Universitätsbibliothek der RWTH Aachen, 2019. http://d-nb.info/1193656699/34.
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Smith, Joshua Gabriel. "Loosely Coupled Hypersonic Airflow Simulation over a Thermally Deforming Panel with Applications for a POD Reduced Order Model." Miami University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=miami1501161884638821.
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Sinha, Aniruddha. "Development of reduced-order models and strategies for feedback control of high-speed axisymmetric jets." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1312886098.
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Urban, Ondřej. "Redukovaný model vírového proudění." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2017. http://www.nusl.cz/ntk/nusl-316999.
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This thesis deals with the formulation and application of reduced order models based on extraction of dominant structures from a system utilizing the method of proper orthogonal decomposition. Time evolution of computed modes is described by a system of ordinary differential equations, which is gained by means of Galerkin projection of these modes onto the Navier-Stokes equations. This methodology was applied on two test cases Kármán vortex street and vortex rope. In both cases, a CFD simulation of one refference point was carried out and by utilizing gained modes, the corresponding reduced order models were formulated. Their results were assessed by comparing to the refference simulation.