Academic literature on the topic 'Data-driven model order reduction'
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Journal articles on the topic "Data-driven model order reduction"
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Nagy, Peter, and Marco Fossati. "Adaptive Data-Driven Model Order Reduction for Unsteady Aerodynamics." Fluids 7, no. 4 (April 6, 2022): 130. http://dx.doi.org/10.3390/fluids7040130.
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A data-driven adaptive reduced order modelling approach is presented for the reconstruction of impulsively started and vortex-dominated flows. A residual-based error metric is presented for the first time in the framework of the adaptive approach. The residual-based adaptive Reduced Order Modelling selects locally in time the most accurate reduced model approach on the basis of the lowest residual produced by substituting the reconstructed flow field into a finite volume discretisation of the Navier–Stokes equations. A study of such an error metric was performed to assess the performance of the resulting residual-based adaptive framework with respect to a single-ROM approach based on the classical proper orthogonal decomposition, as the number of modes is varied. Two- and three-dimensional unsteady flows were considered to demonstrate the key features of the method and its performance.
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Gosea, Ion Victor, and Athanasios C. Antoulas. "Data-driven model order reduction of quadratic-bilinear systems." Numerical Linear Algebra with Applications 25, no. 6 (July 22, 2018): e2200. http://dx.doi.org/10.1002/nla.2200.
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Shah, Aarohi, and Julian J. Rimoli. "Smart parts: Data-driven model order reduction for nonlinear mechanical assemblies." Finite Elements in Analysis and Design 200 (March 2022): 103682. http://dx.doi.org/10.1016/j.finel.2021.103682.
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Sarna, Neeraj, and Peter Benner. "Data-Driven model order reduction for problems with parameter-dependent jump-discontinuities." Computer Methods in Applied Mechanics and Engineering 387 (December 2021): 114168. http://dx.doi.org/10.1016/j.cma.2021.114168.
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Pierquin, A., T. Henneron, and S. Clenet. "Data-Driven Model-Order Reduction for Magnetostatic Problem Coupled With Circuit Equations." IEEE Transactions on Magnetics 54, no. 3 (March 2018): 1–4. http://dx.doi.org/10.1109/tmag.2017.2771358.
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Peng, Haijun, Ningning Song, and Ziyun Kan. "Data-driven model order reduction with proper symplectic decomposition for flexible multibody system." Nonlinear Dynamics 107, no. 1 (November 6, 2021): 173–203. http://dx.doi.org/10.1007/s11071-021-06990-3.
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Kim, Hyejin, Haeseong Cho, Sihun Lee, SangJoon Shin, and Haedeong Kim. "Development of an Efficient Nonlinear Structural Analysis Using Data-driven Model Order Reduction." Transactions of the Korean Society for Noise and Vibration Engineering 31, no. 6 (December 20, 2021): 604–13. http://dx.doi.org/10.5050/ksnve.2021.31.6.604.
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Gosea, I. V., M. Petreczky, and A. C. Antoulas. "Data-Driven Model Order Reduction of Linear Switched Systems in the Loewner Framework." SIAM Journal on Scientific Computing 40, no. 2 (January 2018): B572—B610. http://dx.doi.org/10.1137/17m1120233.
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Spinosa, Angelo Giuseppe, Arturo Buscarino, Luigi Fortuna, Matteo Iafrati, and Giuseppe Mazzitelli. "Data-driven order reduction in Hammerstein–Wiener models of plasma dynamics." Engineering Applications of Artificial Intelligence 100 (April 2021): 104180. http://dx.doi.org/10.1016/j.engappai.2021.104180.
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Casciati, Fabio, and Lucia Faravelli. "Sensor placement driven by a model order reduction (MOR) reasoning." Smart Structures and Systems 13, no. 3 (March 25, 2014): 343–52. http://dx.doi.org/10.12989/sss.2014.13.3.343.
Full textDissertations / Theses on the topic "Data-driven model order reduction"
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Quaranta, Giacomo. "Efficient simulation tools for real-time monitoring and control using model order reduction and data-driven techniques." Doctoral thesis, Universitat Politècnica de Catalunya, 2019. http://hdl.handle.net/10803/667474.
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Numerical simulation, the use of computers to run a program which implements a mathematical model for a physical system, is an important part of today technological world. It is required in many scientific and engineering fields to study the behaviour of systems whose mathematical models are too complex to provide analytical solutions and it makes virtual evaluation of systems responses possible (virtual twins). This drastically reduces the number of experimental tests for accurate designs of the real system that the numerical model represents.
However these virtual twins, based on classical methods which make use of a rich representations of the system (ex. finite element method), rarely allows real-time feedback, even when considering high performance computing, operating on powerful platforms. In these circumstances, the real-time performance required in some applications are compromised. Indeed the virtual twins are static, that is, they
are used in the design of complex systems and their components, but they are not expected to accommodate or assimilate data so as to define dynamic data-driven application systems. Moreover significant deviations between the observed response and the one predicted by the model are usually noticed due to inaccuracy in the employed models, in the determination of the model parameters or in their time evolution.
In this thesis we propose different methods to solve these handicaps in order to perform real-time monitoring and control. In the first part Model Order Reduction (MOR) techniques are used to accommodate real-time constraints; they compute a good approximation of the solution by simplifying the solution procedure instead of the model. The accuracy of the predicted solution is not compromised and efficient simulations can be performed (digital twins). In the second part Data-Driven modelling are employed to fill the gap between the parametric solution computed by using non-intrusive MOR techniques and the measured fields, in order to make dynamic data-driven application systems, DDDAS, possible (Hybrid Twins).La simulación numérica, el uso de ordenadores para ejecutar un programa que implementa un modelo matemático de un sistema físico, es una parte importante del mundo tecnológico actual. En muchos campos de la ciencia y la ingeniería es necesario estudiar el comportamiento de sistemas cuyos modelos matemáticos son demasiado complejos para proporcionar soluciones analíticas, haciendo posible la evaluación virtual de las respuestas de los sistemas (gemelos virtuales). Esto reduce drásticamente el número de pruebas experimentales para los diseños precisos del sistema real que el modelo numérico representa. Sin embargo, estos gemelos virtuales, basados en métodos clásicos que hacen uso de una rica representación del sistema (por ejemplo, el método de elementos finitos), rara vez permiten la retroalimentación en tiempo real, incluso cuando se considera la computación en plataformas de alto rendimiento. En estas circunstancias, el rendimiento en tiempo real requerido en algunas aplicaciones se ve comprometido. En efecto, los gemelos virtuales son estáticos, es decir, se utilizan en el diseño de sistemas complejos y sus componentes, pero no se espera que acomoden o asimilen los datos para definir sistemas de aplicación dinámicos basados en datos. Además, se suelen apreciar desviaciones significativas entre la respuesta observada y la predicha por el modelo, debido a inexactitudes en los modelos empleados, en la determinación de los parámetros del modelo o en su evolución temporal. En esta tesis se proponen diferentes métodos para resolver estas limitaciones con el fin de realizar un seguimiento y un control en tiempo real. En la primera parte se utilizan técnicas de Reducción de Modelos para satisfacer las restricciones en tiempo real; estas técnicas calculan una buena aproximación de la solución simplificando el procedimiento de resolución en lugar del modelo. La precisión de la solución no se ve comprometida y se pueden realizar simulaciones efficientes (gemelos digitales). En la segunda parte se emplea la modelización basada en datos para llenar el vacío entre la solución paramétrica, calculada utilizando técnicas de reducción de modelos no intrusivas, y los campos medidos, con el fin de hacer posibles los sistemas de aplicación dinámicos basados en datos (gemelos híbridos).
La simulation numérique, c'est-à-dire l'utilisation des ordinateurs pour exécuter un programme qui met en oeuvre un modèle mathématique d'un système physique, est une partie importante du monde technologique actuel. Elle est nécessaire dans de nombreux domaines scientifiques et techniques pour étudier le comportement de systèmes dont les modèles mathématiques sont trop complexes pour fournir des solutions analytiques et elle rend possible l'évaluation virtuelle des réponses des systèmes (jumeaux virtuels). Cela réduit considérablement le nombre de tests expérimentaux nécessaires à la conception précise du système réel que le modèle numérique représente. Cependant, ces jumeaux virtuels, basés sur des méthodes classiques qui utilisent une représentation fine du système (ex. méthode des éléments finis), permettent rarement une rétroaction en temps réel, même dans un contexte de calcul haute performance, fonctionnant sur des plates-formes puissantes. Dans ces circonstances, les performances en temps réel requises dans certaines applications sont compromises. En effet, les jumeaux virtuels sont statiques, c'est-à-dire qu'ils sont utilisés dans la conception de systèmes complexes et de leurs composants, mais on ne s'attend pas à ce qu'ils prennent en compte ou assimilent des données afin de définir des systèmes d'application dynamiques pilotés par les données. De plus, des écarts significatifs entre la réponse observée et celle prévue par le modèle sont généralement constatés en raison de l'imprécision des modèles employés, de la détermination des paramètres du modèle ou de leur évolution dans le temps. Dans cette thèse, nous proposons di érentes méthodes pour résoudre ces handicaps afin d'effectuer une surveillance et un contrôle en temps réel. Dans la première partie, les techniques de Réduction de Modèles sont utilisées pour tenir compte des contraintes en temps réel ; elles calculent une bonne approximation de la solution en simplifiant la procédure de résolution plutôt que le modèle. La précision de la solution n'est pas compromise et des simulations e caces peuvent être réalisées (jumeaux numériquex). Dans la deuxième partie, la modélisation pilotée par les données est utilisée pour combler l'écart entre la solution paramétrique calculée, en utilisant des techniques de réduction de modèles non intrusives, et les champs mesurés, afin de rendre possibles des systèmes d'application dynamiques basés sur les données (jumeaux hybrides).
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Ibañez, Pinillo Ruben. "Advanced physics-based and data-driven strategies." Thesis, Ecole centrale de Nantes, 2019. http://www.theses.fr/2019ECDN0021.
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Les sciences de l'ingénieur basées sur la simulation (Simulation Based Engineering Science, SBES) ont apporté des améliorations majeures dans l'optimisation, le contrôle et l'analyse inverse, menant toutes à une meilleure compréhension de nombreux processus se produisant dans le monde réel. Ces percées notables sont présentes dans une grande variété de secteurs tels que l'aéronautique ou l'automobile, les télécommunications mobiles ou la santé, entre autres. Néanmoins, les SBES sont actuellement confrontées à plusieurs difficultés pour fournir des résultats précis dans des problèmes industriels complexes. Outre les coûts de calcul élevés associés aux applications industrielles, les erreurs introduites par la modélisation constitutive deviennent de plus en plus importantes lorsqu'il s'agit de nouveaux matériaux. Parallèlement, un intérêt sans cesse croissant pour des concepts tels que les données massives (big data), l'apprentissage machine ou l'analyse de données a été constaté. En effet, cet intérêt est intrinsèquement motivé par un développement exhaustif des systèmes d'acquisition et de stockage de données. Par exemple, un avion peut produire plus de 500 Go de données au cours d'un seul vol. Ce panorama apporte une opportunité parfaite aux systèmes d'application dynamiques pilotés par les données (Dynamic Data Driven Application Systems, DDDAS), dont l'objectif principal est de fusionner de manière dynamique des algorithmes de simulation classiques avec des données provenant de mesures expérimentales. Dans ce scénario, les données et les simulations ne seraient plus découplées, mais une symbiose à exploiter permettrait d'envisager des situations jusqu'alors inconcevables. En effet, les données ne seront plus comprises comme un étalonnage statique d'un modèle constitutif donné mais plutôt comme une correction dynamique du modèle dès que les données expérimentales et les simulations auront tendance à diverger. Plusieurs algorithmes numériques seront présentés tout au long de ce manuscrit dont l'objectif principal est de renforcer le lien entre les données et la mécanique computationnelle. La première partie de la thèse est principalement axée sur l'identification des paramètres, les techniques d'analyse des données et les techniques de complétion de données. La deuxième partie est axée sur les techniques de réduction de modèle (MOR), car elles constituent un allié fondamental pour satisfaire les contraintes temps réel découlant du cadre DDDASSimulation Based Engineering Science (SBES) has brought major improvements in optimization, control and inverse analysis, all leading to a deeper understanding in many processes occurring in the real world. These noticeable breakthroughs are present in a vast variety of sectors such as aeronautic or automotive industries, mobile telecommunications or healthcare among many other fields. Nevertheless, SBES is currently confronting several difficulties to provide accurate results in complex industrial problems. Apart from the high computational costs associated with industrial applications, the errors introduced by constitutive modeling become more and more important when dealing with new materials. Concurrently, an unceasingly growing interest in concepts such as Big-Data, Machine Learning or Data-Analytics has been experienced. Indeed, this interest is intrinsically motivated by an exhaustive development in both dataacquisition and data-storage systems. For instance, an aircraft may produce over 500 GB of data during a single flight. This panorama brings a perfect opportunity to the socalled Dynamic Data Driven Application Systems (DDDAS), whose main objective is to merge classical simulation algorithms with data coming from experimental measures in a dynamic way. Within this scenario, data and simulations would no longer be uncoupled but rather a symbiosis that is to be exploited would achieve milestones which were inconceivable until these days. Indeed, data will no longer be understood as a static calibration of a given constitutive model but rather the model will be corrected dynamically as soon as experimental data and simulations tend to diverge. Several numerical algorithms will be presented throughout this manuscript whose main objective is to strengthen the link between data and computational mechanics. The first part of the thesis is mainly focused on parameter identification, data-driven and data completion techniques. The second part is focused on Model Order Reduction (MOR) techniques, since they constitute a fundamental ally to achieve real time constraints arising from DDDAS framework
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Waseem, Abdullah. "Numerical Homogenization and Model Reduction for Transient Heat, Diffusion and coupled Mechanics Problems." Thesis, Ecole centrale de Nantes, 2020. http://www.theses.fr/2020ECDN0028.
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Dans cette thèse, des techniques d'homogénéisation numérique efficaces en termes de calcul sont présentées pour les phénomènes de diffusion dans des matériaux hétérogènes. Comme étape préliminaire, une réduction de modèle pour l'équation de diffusion de chaleur transitoire est effectuée à la microéchelle en utilisant la synthèse en mode composants, qui fournit une description émergente enrichie-continuum à l’échelle macroscopique. Sur la base de la localisation des variables d'enrichissement, soit sur les nœuds d'éléments finis, soit sur les points de quadrature, deux schémas de discrétisation spatiale sont analysés pour le diplacement milieu continu. La formulation du potentiel chimique et des champs de déformation est utilisée, ce qui permet l'utilisation d'éléments finis continus en C0 standard. Le problème de la micro-échelle, qui implique généralement une solution coûteuse du problème de la mécanique de diffusion de masse couplée est maintenant remplacée par un ensemble d'équations différentielles ordinaires grâce à la réduction du modèle. Enfin, une approche alternative de réduction de modèle utilisant la mécanique basée sur les données est explorée. Il repose sur une recherche directe et une interpolation à partir d'une base de données au lieu de la solution d'un problème microscopique. La base de données est construite et stockée en utilisant les calculs microscopiques dans une étape hors ligne. Il fournit également une voie pour étendre la méthode de réduction du modèle proposée au régime non linéaireIn this thesis computationally efficient numerical homogenization techniques are presented for diffusion phenomena in heterogeneous materials. As a preliminary step, a model reduction for the transient heat diffusion equation is performed at the micro-scale using component mode synthesis, which provides an emergent enriched-continuum description at the macro-scale. Based on the location of the enrichmentvariables, either on the finite element nodes or the quadrature points, two spatial discretization schemes are analyzed for the enrichedcontinuum. The proposed model reduction is also extended to the transient mass diffusion coupled to the mechanics with application to lithium-ion batteries. Chemical potential and strain fields formulation is used which allows the use of standard C0-continuous finite elements. The micro-scale problem, which usually involves an expensive solution of the coupled mass diffusionmechanics problem is now replaced by a set of ordinary differential equations through model reduction. Finally, an alternative model reduction approach using data-driven mechanics is explored. It relies on a direct search and interpolation from a database instead of the solution of a microscopic problem. The database is constructed and stored using the microscopic calculations in an offline stage. It also provides a route to extend the proposed model reduction method to the nonlinear regime
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Taddei, Tommaso. "Model order reduction methods for data assimilation : state estimation and structural health monitoring." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/108942.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2017.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 243-258).
The objective of this thesis is to develop and analyze model order reduction approaches for the efficient integration of parametrized mathematical models and experimental measurements. Model Order Reduction (MOR) techniques for parameterized Partial Differential Equations (PDEs) offer new opportunities for the integration of models and experimental data. First, MOR techniques speed up computations allowing better explorations of the parameter space. Second, MOR provides actionable tools to compress our prior knowledge about the system coming from the parameterized best-knowledge model into low-dimensional and more manageable forms. In this thesis, we demonstrate how to take advantage of MOR to design computational methods for two classes of problems in data assimilation. In the first part of the thesis, we discuss and extend the Parametrized-Background Data-Weak (PBDW) approach for state estimation. PBDW combines a parameterized best knowledge mathematical model and experimental data to rapidly estimate the system state over the domain of interest using a small number of local measurements. The approach relies on projection-by-data, and exploits model reduction techniques to encode the knowledge of the parametrized model into a linear space appropriate for real-time evaluation. In this work, we extend the PBDW formulation in three ways. First, we develop an experimental a posteriori estimator for the error in the state. Second, we develop computational procedures to construct local approximation spaces in subregions of the computational domain in which the best-knowledge model is defined. Third, we present an adaptive strategy to handle experimental noise in the observations. We apply our approach to a companioni heat transfer experiment to prove the effectiveness of our technique. In the second part of the thesis, we present a model-order reduction approach to simulation based classification, with particular application to Structural Health Monitoring (SHM). The approach exploits (i) synthetic results obtained by repeated solution of a parametrized PDE for different values of the parameters, (ii) machine-learning algorithms to generate a classifier that monitors the state of damage of the system, and (iii) a reduced basis method to reduce the computational burden associated with the model evaluations. The approach is based on an offline/online computational decomposition. In the offline stage, the fields associated with many different system configurations, corresponding to different states of damage, are computed and then employed to teach a classifier. Model reduction techniques, ideal for this many-query context, are employed to reduce the computational burden associated with the parameter exploration. In the online stage, the classifier is used to associate measured data to the relevant diagnostic class. In developing our approach for SHM, we focus on two specific aspects. First, we develop a mathematical formulation which properly integrates the parameterized PDE model within the classification problem. Second, we present a sensitivity analysis to take into account the error in the model. We illustrate our method and we demonstrate its effectiveness through the vehicle of a particular companion experiment, a harmonically excited microtruss.
by Tommaso Taddei.
Ph. D.
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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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Akhtar, Sabina. "Vérification Formelle d'Algorithmes Distribués en PlusCal-2." Phd thesis, Université de Lorraine, 2012. http://tel.archives-ouvertes.fr/tel-00815570.
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La conception d'algorithmes pour les systèmes concurrents et répartis est subtile et difficile. Ces systèmes sont enclins à des blocages et à des conditions de course qui peuvent se produire dans des entrelacements particuliers d'actions de processus et sont par conséquent difficiles à reproduire. Il est souvent non-trivial d'énoncer précisément les propriétés attendues d'un algorithme et les hypothèses que l'environnement est supposé de satisfaire pour que l'algorithme se comporte correctement. La vérification formelle est une technique essentielle pour modéliser le système et ses propriétés et s'assurer de sa correction au moyen du model checking. Des langages formels tels TLA+ permettent de décrire des algorithmes compliqués de manière assez concise, mais les concepteurs d'algorithmes trouvent souvent difficile de modéliser un algorithme par un ensemble de formules. Dans ce mémoire nous présentons le langage PlusCal-2 qui vise à allier la simplicité de pseudo-code à la capacité d'être vérifié formellement. PlusCal-2 améliore le langage algorithmique PlusCal conçu par Lamport en levant certaines restrictions de ce langage et en y ajoutant de nouvelles constructions. Notre langage est destiné à la description d'algorithmes à un niveau élevé d'abstraction. Sa syntaxe ressemble à du pseudo-code mais il est tout à fait expressif et doté d'une sémantique formelle. Des instances finies d'algorithmes écrits en PlusCal-2 peuvent être vérifiées à l'aide du model checker tlc. La deuxième contribution de cette thèse porte sur l'étude de méthodes de réduction par ordre partiel à l'aide de relations de dépendance conditionnelle et constante. Pour calculer la dépendance conditionnelle pour les algorithmes en PlusCal-2 nous exploitons des informations sur la localité des actions et nous générons des prédicats d'indépendance. Nous proposons également une adaptation d'un algorithme de réduction par ordre partiel dynamique pour une variante du model checker tlc. Enfin, nous proposons une variante d'un algorithme de réduction par ordre partiel statique (comme alternative à l'algorithme dynamique), s'appuyant sur une relation de dépendance constante, et son implantation au sein de tlc. Nous présentons nos résultats expérimentaux et une preuve de correction.
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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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Hammond, Janelle K. "Méthodes des bases réduites pour la modélisation de la qualité de l'air urbaine." Thesis, Paris Est, 2017. http://www.theses.fr/2017PESC1230/document.
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L'objectif principal de cette thèse est le développement d'outils numériques peu coûteux pour la cartographie de concentrations de polluants a partir de mesures et de modèles déterministes avancés. Le développement mondial et l'urbanisation des populations génèrent une hausse d’émissions et d'expositions. A n d'estimer les expositions individuelles et évaluer leur association à des pathologies diverses, les campagnes de mesure de qualité de l'air, et des études épidémiologiques sur les effets de santé de la pollution sont devenues plus courantes. Cependant, les concentrations de pollution de l'air sont très variables en temps et en espace. La sensibilité et la précision de ces études est souvent détériorée par de mauvais classements des expositions dus aux estimations grossières des expositions individuelles. Les méthodes d'assimilation de données intègrent des données de mesures et des modèles mathématiques a n de mieux approximer le champ de concentration. Quand ces méthodes sont basées sur un modèle de qualité de l'air (AQM) déterministe avancé, elles sont capables de fournir des approximations détaillées et de petite échelle. Ces informations précises permettront de meilleures estimations d'exposition. Néanmoins, ces méthodes sont souvent tr es coûteuses. Elles nécessitent la résolution a plusieurs reprises du modèle, qui peut être coûteux soi-même. Dans ce travail nous enquêtons sur la combinaison des méthodes des bases réduites (RB) et d'assimilation de données pour des AQM avancés a l'échelle urbaine. Nous souhaitons diminuer le coût de résolution en exploitant les RB, et incorporer des données de mesure a n d'améliorer la qualité de la solution. On étend la méthode de Parameterized-Background Data-Weak (PBDW) pour des AQMs basés sur la physique. Cette méthode est capable d'estimer de façon rapide et "online" des concentrations de polluants à l'échelle du quartier. Elle se sert des AQMs disponibles dans une procédure non intrusive et efficace par rapport aux temps de calculs pour réduire le coût de résolution par des centaines de fois. Les résultats de PBDW sont comparés à la méthode d'interpolation empirique généralisée (GEIM) et à une méthode inverse usuelle, la méthode adjointe, a n de mesurer l'efficacité de la PBDW. Cette comparaison montre la possibilité d'augmenter la précision de la solution, et d'une grande réduction en temps de calcul par rapport à des méthodes classiques. Dans nos applications sur un modèle imparfait, l'étude a fourni des estimations d'état avec erreur d'approximation de moins de 10% presque partout. Les résultats se montrent prometteurs pour la reconstruction en temps réel de champs de pollution sur de grands domaines par la PBDWThe principal objective of this thesis is the development of low-cost numerical tools for spatial mapping of pollutant concentrations from field observations and advanced deterministic models. With increased pollutant emissions and exposure due to mass urbanization and development worldwide, air quality measurement campaigns and epidemiology studies of the association between air pollution and adverse health effects have become increasingly common. However, as air pollution concentrations are highly variable spatially and temporally, the sensitivity and accuracy of these epidemiology studies is often deteriorated by exposure misclassi cation due to poor estimates of individual exposures. Data assimilation methods incorporate available measurement data and mathematical models to provide improved approximations of the concentration. These methods, when based on an advanced deterministic air quality models (AQMs), could provide spatially-rich small-scale approximations and can enable better estimates of effects and exposures. However, these methods can be computationally expensive. They require repeated solution of the model, which could itself be costly. In this work we investigate a combined reduced basis (RB) data assimilation method for use with advanced AQMs on urban scales. We want to diminish the cost of resolution, using RB arguments, and incorporate measurement data to improve the quality of the solution. We extend the Parameterized-Background Data-Weak (PBDW) method to physically-based AQMs. This method can rapidly estimate "online" pollutant concentrations at urban scale, using available AQMs in a non-intrusive and computationally effcient manner, reducing computation times by factors up to hundreds. We apply this method in case studies representing urban residential pollution of PM2.5, and we study the stability of the method depending on the placement or air quality sensors. Results from the PBDW are compared to the Generalized Empirical Interpolation Method (GEIM) and a standard inverse problem, the adjoint method, in order to measure effciency of the method. This comparison shows possible improvement in precision and great improvement in computation cost with respect to classical methods. We fi nd that the PBDW method shows promise for the real-time reconstruction of a pollution eld in large-scale problems, providing state estimation with approximation error generally under 10% when applied to an imperfect model
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Ulin, Samuel. "Digging deep : A data-driven approach to model reduction in a granular bulldozing scenario." Thesis, Umeå universitet, Institutionen för fysik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-152498.
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The current simulation method for granular dynamics used by the physics engine AGX Dynamics is a nonsmooth variant of the popular Discrete Element Method (DEM). While powerful, there is a need for close to real time simulations of a higher spatial resolution than currently possible. In this thesis a data-driven model reduction approach using machine learning was considered. A data-driven simulation pipeline was presented and partially implemented. The method consists of sampling the velocity and density field of the granular particles and teaching a machine learning algorithm to predict the particles' interaction with a bulldozer blade as well as predicting the time evolution of its velocity field. A procedure for producing training scenarios and training data for the machine learning algorithm was implemented as well as several machine learning algorithms; a linear regressor, a multilayer perceptron and a convolutional neural network. The results showed that the method is promising, however further work will need to show whether or not the pipeline is feasible to implement in a simulation.
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Savas, Berkant. "Algorithms in data mining using matrix and tensor methods." Doctoral thesis, Linköpings universitet, Beräkningsvetenskap, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-11597.
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In many fields of science, engineering, and economics large amounts of data are stored and there is a need to analyze these data in order to extract information for various purposes. Data mining is a general concept involving different tools for performing this kind of analysis. The development of mathematical models and efficient algorithms is of key importance. In this thesis we discuss algorithms for the reduced rank regression problem and algorithms for the computation of the best multilinear rank approximation of tensors. The first two papers deal with the reduced rank regression problem, which is encountered in the field of state-space subspace system identification. More specifically the problem is \[ \min_{\rank(X) = k} \det (B - X A)(B - X A)\tp, \] where $A$ and $B$ are given matrices and we want to find $X$ under a certain rank condition that minimizes the determinant. This problem is not properly stated since it involves implicit assumptions on $A$ and $B$ so that $(B - X A)(B - X A)\tp$ is never singular. This deficiency of the determinant criterion is fixed by generalizing the minimization criterion to rank reduction and volume minimization of the objective matrix. The volume of a matrix is defined as the product of its nonzero singular values. We give an algorithm that solves the generalized problem and identify properties of the input and output signals causing a singular objective matrix. Classification problems occur in many applications. The task is to determine the label or class of an unknown object. The third paper concerns with classification of handwritten digits in the context of tensors or multidimensional data arrays. Tensor and multilinear algebra is an area that attracts more and more attention because of the multidimensional structure of the collected data in various applications. Two classification algorithms are given based on the higher order singular value decomposition (HOSVD). The main algorithm makes a data reduction using HOSVD of 98--99 \% prior the construction of the class models. The models are computed as a set of orthonormal bases spanning the dominant subspaces for the different classes. An unknown digit is expressed as a linear combination of the basis vectors. The resulting algorithm achieves 5\% in classification error with fairly low amount of computations. The remaining two papers discuss computational methods for the best multilinear rank approximation problem \[ \min_{\cB} \| \cA - \cB\| \] where $\cA$ is a given tensor and we seek the best low multilinear rank approximation tensor $\cB$. This is a generalization of the best low rank matrix approximation problem. It is well known that for matrices the solution is given by truncating the singular values in the singular value decomposition (SVD) of the matrix. But for tensors in general the truncated HOSVD does not give an optimal approximation. For example, a third order tensor $\cB \in \RR^{I \x J \x K}$ with rank$(\cB) = (r_1,r_2,r_3)$ can be written as the product \[ \cB = \tml{X,Y,Z}{\cC}, \qquad b_{ijk}=\sum_{\lambda,\mu,\nu} x_{i\lambda} y_{j\mu} z_{k\nu} c_{\lambda\mu\nu}, \] where $\cC \in \RR^{r_1 \x r_2 \x r_3}$ and $X \in \RR^{I \times r_1}$, $Y \in \RR^{J \times r_2}$, and $Z \in \RR^{K \times r_3}$ are matrices of full column rank. Since it is no restriction to assume that $X$, $Y$, and $Z$ have orthonormal columns and due to these constraints, the approximation problem can be considered as a nonlinear optimization problem defined on a product of Grassmann manifolds. We introduce novel techniques for multilinear algebraic manipulations enabling means for theoretical analysis and algorithmic implementation. These techniques are used to solve the approximation problem using Newton and Quasi-Newton methods specifically adapted to operate on products of Grassmann manifolds. The presented algorithms are suited for small, large and sparse problems and, when applied on difficult problems, they clearly outperform alternating least squares methods, which are standard in the field.
Books on the topic "Data-driven model order reduction"
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Kisanga, Elineema, Vincent Leyaro, Wahabi Matengo, Michael Noble, Helen Barnes, and Gemma Wright. Assessing the distributional impact of lowering the value-added tax rate for standard-rated items in Tanzania and options for recouping revenue losses. 38th ed. UNU-WIDER, 2021. http://dx.doi.org/10.35188/unu-wider/2021/976-1.
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This paper explores the distributional impact of lowering the value-added tax rate for standard-rated items in Tanzania Mainland. Using a static tax-benefit microsimulation model—TAZMOD—which is underpinned by data derived from the Household Budget Survey 2017/18, reductions in value-added taxes from 18 per cent to 17 per cent and 16 per cent are simulated. The revenue losses and impact on poverty are estimated. The rules for direct taxes are then modified in order to identify ways in which the revenue loss caused by the lowering of the standard rate of value-added taxes can be recouped.
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Bacior, Stanisław. Optymalizacja wiejskich układów gruntowych – badania eksperymentalne. Publishing House of the University of Agriculture in Krakow, 2019. http://dx.doi.org/10.15576/978-83-66602-37-3.
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Rural areas are subject to constant structural, spatial and economic transformations. The main purpose of this monograph was to present a new concept of shaping of rural land arrangement that takes into account the land value. The presented optimization methodology of shaping of the rural areas has a general range of application, not being limited by time or place. of the location of the consolidation object. The only condition for its use is the availability of a specific set of output data enabling the necessary calculations for the implementation of consolidation works. The described method has been successfully applied to the research object of the Mściowojów village, in a registry area located in the Dolnośląkie voivodeship, in the Jaworski district, providing with the assumed effects. In order to meet the research objectives, the shaping of rural land arrangement was conducted according to five models. The original arrangement of existing land division in a given village is considered as the 1st model. The 2nd model uses a rather accurate description of the locations of the lands in the village. To define this feature the location of farm parcels had to be determined. This model is the most accurate, but also the most labor-intensive of all. In the 3rd model, a fundamental simplification of the land arrangement was adopted, limiting the distance matrix to its measurement to the entry points from the settlements into the complexes. This simplification means that the location of parcels in the complex does not affect the average distance to the land in the whole village. On the basis of simplifications applied in the 3rd model allowing a significant reduction of the distance matrix the 4th model which uses a linear programming to minimize the distance to a parcel was developed. Introducing into the linear model an additional condition that eliminates distance growth in farms in relation to the initial state was important for the research. This was implemented in the 5th model and had a positive impact on the obtained results. The 6th model was developed by including the landowners' wants into the 5th model. These had to be taken into account so that the research/the new land arrangement did not cause complaints. The wants could not be fully included due to their inherently contradictory nature. The wants for having the parcel in a given arrangement was replaced with a guarantee of division, after which landowner receives no smaller share than the prior one. As demonstrated in the work, the solutions of the developed models allowed obtaining land arrangements close to the optimal in terms of distance to land and the shape of parcels and farms with regard to land specifics. The presented results allow to draw a conclusion that the methods and analyses applied in the research can have a wide range of application in shaping of rural land arrangement. Developing the most socially accepted optimization of parcel division in the process of land consolidation is important due to the actual needs for the implementation of the rural land arrangement research. This may also have influence on better use of the EU's financial resources for the consolidation of agricultural lands.
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Queloz, Matthieu. The Practical Origins of Ideas. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198868705.001.0001.
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Why did such highly abstract ideas as truth, knowledge, or justice become so important to us? What was the point of coming to think in these terms? In The Practical Origins of Ideas, Matthieu Queloz presents a philosophical method designed to answer such questions: the method of pragmatic genealogy. Pragmatic genealogies are partly fictional, partly historical narratives exploring what might have driven us to develop certain ideas in order to discover what these do for us. The book uncovers an under-appreciated tradition of pragmatic genealogy which cuts across the analytic–continental divide, running from the state-of-nature stories of David Hume and the early genealogies of Friedrich Nietzsche to recent work in analytic philosophy by Edward Craig, Bernard Williams, and Miranda Fricker. However, these genealogies combine fictionalizing and historicizing in ways that even philosophers sympathetic to the use of state-of-nature fictions or real history have found puzzling. To make sense of why both fictionalizing and historicizing are called for, the book offers a systematic account of pragmatic genealogies as dynamic models serving to reverse-engineer the points of ideas in relation not only to near-universal human needs, but also to socio-historically situated needs. This allows the method to offer us explanation without reduction and to help us understand what led our ideas to shed the traces of their practical origins. Far from being normatively inert, moreover, pragmatic genealogy can affect the space of reasons, guiding attempts to improve our conceptual repertoire by helping us determine whether and when our ideas are worth having.
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Li, Quan. Using R for Data Analysis in Social Sciences. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190656218.001.0001.
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This book seeks to teach undergraduate and graduate students in social sciences how to use R to manage, visualize, and analyze data in order to answer substantive questions and replicate published findings. This book distinguishes itself from other introductory R or statistics books in three ways. First, targeting an audience rarely exposed to statistical programming, it adopts a minimalist approach and covers only the most important functions and skills in R that one will need for conducting reproducible research projects. Second, it emphasizes meeting the practical needs of students using R in research projects. Specifically, it teaches students how to import, inspect, and manage data; understand the logic of statistical inference; visualize data and findings via histograms, boxplots, scatterplots, and diagnostic plots; and analyze data using one-sample t-test, difference-of-means test, covariance, correlation, ordinary least squares (OLS) regression, and model assumption diagnostics. Third, it teaches students how to replicate the findings in published journal articles and diagnose model assumption violations. The principle behind this book is to teach students to learn as little R as possible but to do as much reproducible, substance-driven data analysis at the beginner or intermediate level as possible. The minimalist approach dramatically reduces the learning cost but still proves adequate information for meeting the practical research needs of senior undergraduate and beginning graduate students. Having completed this book, students can use R and statistical analysis to answer questions regarding some substantively interesting continuous outcome variable in a cross-sectional design.
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Baumgaertner, Annette. Mixed Transcortical Aphasia: Repetition without Meaning. Edited by Anastasia M. Raymer and Leslie J. Gonzalez Rothi. Oxford University Press, 2015. http://dx.doi.org/10.1093/oxfordhb/9780199772391.013.10.
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Although mixed transcortical aphasia (MTA) is a rare syndrome, it constitutes an interesting case for modern neuroanatomically driven language models. This is because its existence may be seen as congruent with the assumption of an independently operating “dorsal stream” in language processing. Predicted by the earliest models of language processing in the brain, the syndrome also pushes the boundaries of neurolinguistic model building because its symptoms arise from an interplay between partially preserved linguistic functions and partially disrupted amodal higher-order cognitive control mechanisms. In summarizing 15 case reports of persons with MTA, this chapter provides details about neurobiological underpinnings, performance during standard language assessments, and speech characteristics of persons diagnosed as having MTA. The chapter raises critical issues, such as the question of how to operationalize “spared repetition,” and the difficulty of clearly differentiating between volitional repetition and nonvolitional echolalia. Data on the evolution of the syndrome are included, and assessment as well as treatment of MTA are discussed.
Book chapters on the topic "Data-driven model order reduction"
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Pontes Duff, Igor, Pawan Goyal, and Peter Benner. "Data-Driven Identification of Rayleigh-Damped Second-Order Systems." In Realization and Model Reduction of Dynamical Systems, 255–72. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95157-3_14.
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Wang, Jian, Wei Xing, Robert M. Kirby, and Miaomiao Zhang. "Data-Driven Model Order Reduction for Diffeomorphic Image Registration." In Lecture Notes in Computer Science, 694–705. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20351-1_54.
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Deschrijver, Dirk, and Tom Dhaene. "Data-Driven Model Order Reduction Using Orthonormal Vector Fitting." In Mathematics in Industry, 341–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78841-6_16.
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Grundel, Sara, Nils Hornung, and Sarah Roggendorf. "Numerical Aspects of Model Order Reduction for Gas Transportation Networks." In Simulation-Driven Modeling and Optimization, 1–28. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-27517-8_1.
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Liu, Wing Kam, Zhengtao Gan, and Mark Fleming. "Knowledge-Driven Dimension Reduction and Reduced Order Surrogate Models." In Mechanistic Data Science for STEM Education and Applications, 131–70. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-87832-0_5.
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Aguado, Jose Vicente, Domenico Borzacchiello, Elena Lopez, Emmanuelle Abisset-Chavanne, David Gonzalez, Elias Cueto, and Francisco Chinesta. "New Trends in Computational Mechanics: Model Order Reduction, Manifold Learning and Data-Driven." In From Microstructure Investigations to Multiscale Modeling, 239–66. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2017. http://dx.doi.org/10.1002/9781119476757.ch9.
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Zdybał, K., M. R. Malik, A. Coussement, J. C. Sutherland, and A. Parente. "Reduced-Order Modeling of Reacting Flows Using Data-Driven Approaches." In Lecture Notes in Energy, 245–78. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-16248-0_9.
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AbstractData-driven modeling of complex dynamical systems is becoming increasingly popular across various domains of science and engineering. This is thanks to advances in numerical computing, which provides high fidelity data, and to algorithm development in data science and machine learning. Simulations of multicomponent reacting flows can particularly profit from data-based reduced-order modeling (ROM). The original system of coupled partial differential equations that describes a reacting flow is often large due to high number of chemical species involved. While the datasets from reacting flow simulation have high state-space dimensionality, they also exhibit attracting low-dimensional manifolds (LDMs). Data-driven approaches can be used to obtain and parameterize these LDMs. Evolving the reacting system using a smaller number of parameters can yield substantial model reduction and savings in computational cost. In this chapter, we review recent advances in ROM of turbulent reacting flows. We demonstrate the entire ROM workflow with a particular focus on obtaining the training datasets and data science and machine learning techniques such as dimensionality reduction and nonlinear regression. We present recent results from ROM-based simulations of experimentally measured Sandia flames D and F. We also delineate a few remaining challenges and possible future directions to address them. This chapter is accompanied by illustrative examples using the recently developed Python software, PCAfold. The software can be used to obtain, analyze and improve low-dimensional data representations. The examples provided herein can be helpful to students and researchers learning to apply dimensionality reduction, manifold approaches and nonlinear regression to their problems. The Jupyter notebook with the examples shown in this chapter can be found on GitHub at https://github.com/kamilazdybal/ROM-of-reacting-flows-Springer.
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Ferranti, Francesco, Dirk Deschrijver, Luc Knockaert, and Tom Dhaene. "Data-Driven Parameterized Model Order Reduction Using z-Domain Multivariate Orthonormal Vector Fitting Technique." In Lecture Notes in Electrical Engineering, 141–48. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-94-007-0089-5_7.
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Tezzele, Marco, Nicola Demo, Andrea Mola, and Gianluigi Rozza. "An integrated data-driven computational pipeline with model order reduction for industrial and applied mathematics." In Mathematics in Industry, 179–200. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-96173-2_7.
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Rosafalco, Luca, Matteo Torzoni, Andrea Manzoni, Stefano Mariani, and Alberto Corigliano. "A Self-adaptive Hybrid Model/data-Driven Approach to SHM Based on Model Order Reduction and Deep Learning." In Structural Integrity, 165–84. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-81716-9_8.
Full textConference papers on the topic "Data-driven model order reduction"
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Fischer, P., K. Kaneko, and P. Tsai. "Model-Order Reduction of Buoyancy-Driven Heat-Transfer." In Tranactions - 2019 Winter Meeting. AMNS, 2019. http://dx.doi.org/10.13182/t31297.
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Saha, Sudipta, and M. Nabi. "Model Order Reduction of Axial Active Magnetic Bearing." In 2019 9th International Conference on Cloud Computing, Data Science & Engineering (Confluence). IEEE, 2019. http://dx.doi.org/10.1109/confluence.2019.8776931.
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Chelidze, David. "Smooth Robust Subspace Based Model Reduction." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13333.
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Long-time numerical simulations of large-scale mechanistic models of complex systems (e.g., molecular dynamics, computational fluid dynamics, structural finite element, or multi-body dynamics models) are still problematic, either due to numerical instabilities or the excessive necessary computational resources. Therefore, reduced models that can be simulated for long-time and provide truthful approximations to the actual long-time dynamics, are needed. A new framework — based on new concepts of dynamical consistency and subspace robustness — for identifying subspaces suitable for reduced-order model development is presented. Model reductions based on proper and smooth orthogonal decompositions (POD and SOD, respectively) are considered and tested using a nonlinear four-degree-of-freedom model. It is shown that the new framework identifies subspaces that provide accurate model reductions for a range of forcing parameters, and that only four and higher dimensional models could be dynamically consistent. In addition, for reduced-order models based on randomly driven data, a four-dimensional SOD-based model outperformed a five-dimensional POD-based model. Finally, randomly driven data-based models generally outperformed harmonically driven data-based models when tested for a wide range of forcing amplitudes.
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Abbasi, Mohammad Hossein, and Nathan Van de Wouw. "Model Order Reduction of Linear Sampled-Data Control Systems." In 2022 European Control Conference (ECC). IEEE, 2022. http://dx.doi.org/10.23919/ecc55457.2022.9837993.
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Anand, N. Vijay, M. Siva Kumar, and R. Srinivasa Rao. "Evolutionary Algorithm Based Model Order Reduction of MIMO Interval Systems." In Smart Technologies in Data Science and Communication 2017. Science & Engineering Research Support soCiety, 2017. http://dx.doi.org/10.14257/astl.2017.147.36.
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Saito, Akira. "Model Order Reduction for a Piecewise Linear System Based on Dynamic Mode Decomposition." In ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/detc2021-70764.
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Abstract This paper presents a data-driven model order reduction strategy for nonlinear systems based on dynamic mode decomposition (DMD). First, the theory of DMD is briefly reviewed and its extension to model order reduction of nonlinear systems based on Galerkin projection is introduced. The proposed method utilizes impulse response of the nonlinear system to obtain snapshots of the state variables, and extracts dynamic modes that are then used for the projection basis vectors. The equations of motion of the system can then be projected onto the subspace spanned by the basis vectors, which produces the projected governing equations with much smaller number of degrees of freedom (DOFs). The method is applied to the construction of the reduced order model (ROM) of a finite element model (FEM) of a cantilevered beam subjected to a piecewise-linear boundary condition. First, impulse response analysis of the beam is conducted to obtain the snapshot matrix of the nodal displacements. The DMD is then applied to extract the DMD modes and eigenvalues. The extracted DMD mode shapes can be used to form a reduction basis for the Galerkin projection of the equation of motion. The obtained ROM has been used to conduct the forced response calculation of the beam subjected to the piecewise linear boundary condition. The results obtained by the ROM agree well with that obtained by the full-order FEM model.
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Kovárnová, A., and M. Isoz. "Model Order Reduction for Particle-Laden Flows: Systems with Rotations and Discrete Transport Operators." In Topical Problems of Fluid Mechanics 2023. Institute of Thermomechanics of the Czech Academy of Sciences; CTU in Prague Faculty of Mech. Engineering Dept. Tech. Mathematics, 2023. http://dx.doi.org/10.14311/tpfm.2023.014.
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In the present work, we concentrate on particle-laden flows as an example of industry-relevant transport-dominated systems. Our previously-developed framework for data-driven model order reduction (MOR) of such systems, the shifted proper orthogonal decomposition with interpolation via artificial neural networks, is further extended by improving the handling of general transport operators. First, even with intrusive MOR approaches, the underlying numerical solvers can provide only discrete realizations of transports linked to the movement of individual particles in the system. On the other hand, our MOR methodology requires continuous transport operators. Thus, the original framework was extended by the possibility to reconstruct continuous approximations of known discrete transports via another artificial neural network. Second, the treatment of rotation-comprising transports was significantly improved.
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Ito, Hiroshi, Shoichiro Hosomi, Norikazu Tezuka, and Tomohiro Ishida. "On Virtual Clearance Monitoring of Steam Turbine by Using Model Order Reduction." In ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/gt2021-59003.
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Abstract With the increasing need for flexible operation (shorter startup time and higher load change rate etc.), clearance monitoring between the rotor and the stationary components in steam turbines is becoming more important. This is because as load change rate increases, minimum radial and axial clearances during operation tend to be smaller due to thermal deformation of steam turbines, and the risk of contact between the rotor and the stationary components becomes higher. This situation has accelerated development of clearance sensors. However, it is still difficult to monitor all possible points of contact only with physical sensors due to limited installation location and short lifetime in high temperature environment. From the above background, we have been developing a virtual clearance monitoring (VCM) technique based on a novel data fusion approach that utilizes both physical and data-driven models. Specifically, a reduced order model (ROM) is used as physical model in order to enable real-time prediction with an accuracy similar to that of finite element analysis (FEA). Then, the prediction error of the physical model is corrected by using a residual model built by machine learning from the past clearance sensor values and the corresponding physical model-based prediction results. As will be explained in this report, this technique has an advantage that the clearances can be predicted in real-time based only on operating data such as steam conditions at inlet and outlet, and some temperatures in the parts not modeled in the ROM. Therefore, the virtual sensor based on this technique can be used as a replacement for the physical sensor after it has failed. Furthermore, this technique can also be used to preliminarily study unsteady clearance behavior for inexperienced operating conditions. This paper describes how to build the ROM from a finite element model for thermal-structural analysis of an entire steam turbine by model order reduction (MOR), and the detail of the VCM technique, and a VCM system installed in a measurement room of a state-of-the-art GTCC power plant manufactured by Mitsubishi Power. In addition, the verification results of the VCM system are presented. In this research, the ROM and the residual model were built using the data obtained from four operations with different start-up modes each other. Then, VCM was performed for 12 operating cases. As a result, this survey revealed the followings: (1) This system is capable of real-time prediction with output intervals of roughly 2 seconds. (2) As for radial clearance prediction error during rotor rotating, the RMSEs and the absolute values of minimum value errors are less than or equal to 7.2 % and 7.0 % respectively relative to an initial radial clearance value during the steam turbine stopping. From the above results, we conclude that this VCM technique based on data fusion approach is effective in terms of computational speed and prediction accuracy. This means that if a physical clearance sensor fails, the radial clearance can be continuously monitored by a virtual clearance sensor with a residual model built using the data when the sensor was working normally. In the future, we plan to further improve the accuracy of this technique through improvement in physical modeling.
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Sullivan, Christopher C., Hiroki Yamashita, and Hiroyuki Sugiyama. "POD-Based Model Order Reduction for Tire-Soil Interaction Simulations." In ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/detc2021-69652.
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Abstract The objective of this study is to develop model order reduction capabilities for high-fidelity off-road mobility simulations. The model reduction technique using the proper orthogonal decomposition (POD) is implemented at the level of the numerical solver in order to decrease the number of equations that need to be solved at each iteration of the solution procedure. The POD is, however, limited in that the modes are dependent on snapshot data collected during the running of a full order model (FOM), limiting the modes to being accurate only for the specific scenario from which they were collected. Due to this limitation, a method of mode adaptation through interpolation on a tangent space of the Grassmann manifold is investigated to allow modes to be predicted for cases in which a full order model has not been run. Modes produced for known values of a simulation parameter are used to predict the modes for a value of the simulation parameter for which POD modes have not been directly produced. For a single tire soil bin mobility model, the POD modes are found to be effective at retaining accuracy with minimal errors while also reducing computational time.
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Fan, Guodong, and Marcello Canova. "Model Order Reduction of Electrochemical Batteries Using Galerkin Method." In ASME 2015 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/dscc2015-9788.
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This paper presents a model order reduction (MOR) method for modeling and estimation of a first-principles electrochemical Lithium-ion battery. The MOR approach combines the Galerkin method with coordinate transformation and is applied to solve the spherical diffusion problem with non-zero flux boundary conditions. The order of the reduced-order model (ROM) is carefully selected based on analysis in the frequency domain. With the reduced-order diffusion model, an enhanced single particle model which incorporates the electrolyte dynamics is developed and validated against the experimental data.
Reports on the topic "Data-driven model order reduction"
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Fytanidis, Dimitrios, Romit Maulik, Ramesh Balakrishnan, and Rao Kotamarthi. A physics-informed data-driven low order model for the wind velocity deficit at the wake of isolated buildings. Office of Scientific and Technical Information (OSTI), March 2021. http://dx.doi.org/10.2172/1782670.
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Meidani, Hadi, and Amir Kazemi. Data-Driven Computational Fluid Dynamics Model for Predicting Drag Forces on Truck Platoons. Illinois Center for Transportation, November 2021. http://dx.doi.org/10.36501/0197-9191/21-036.
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Fuel-consumption reduction in the truck industry is significantly beneficial to both energy economy and the environment. Although estimation of drag forces is required to quantify fuel consumption of trucks, computational fluid dynamics (CFD) to meet this need is expensive. Data-driven surrogate models are developed to mitigate this concern and are promising for capturing the dynamics of large systems such as truck platoons. In this work, we aim to develop a surrogate-based fluid dynamics model that can be used to optimize the configuration of trucks in a robust way, considering various uncertainties such as random truck geometries, variable truck speed, random wind direction, and wind magnitude. Once trained, such a surrogate-based model can be readily employed for platoon-routing problems or the study of pavement performance.
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Perera, Duminda, Ousmane Seidou, Jetal Agnihotri, Mohamed Rasmy, Vladimir Smakhtin, Paulin Coulibaly, and Hamid Mehmood. Flood Early Warning Systems: A Review Of Benefits, Challenges And Prospects. United Nations University Institute for Water, Environment and Health, August 2019. http://dx.doi.org/10.53328/mjfq3791.
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Floods are major water-related disasters that affect millions of people resulting in thousands of mortalities and billiondollar losses globally every year. Flood Early Warning Systems (FEWS) - one of the floods risk management measures - are currently operational in many countries. The UN Office for Disaster Risk Reduction recognises their importance and strongly advocates for an increase in their availability under the targets of the Sendai Framework for Disaster Risk Reduction, and Sustainable Development Goals (SDGs). However, despite widespread recognition of the importance of FEWS for disaster risk reduction (DRR), there’s a lack of information on their availability and status around the world, their benefits and costs, challenges and trends associated with their development. This report contributes to bridging these gaps by analyzing the responses to a comprehensive online survey with over 80 questions on various components of FEWS (risk knowledge, monitoring and forecasting, warning dissemination and communication, and response capabilities), investments into FEWS, their operational effectiveness, benefits, and challenges. FEWS were classified as technologically “basic”, “intermediate” and “advanced” depending on the existence and sophistication of FEWS` components such as hydrological data = collection systems, data transfer systems, flood forecasting methods, and early warning communication methods. The survey questionnaire was distributed to flood forecasting and warning centers around the globe; the primary focus was developing and least-developed countries (LDCs). The questionnaire is available here: https://inweh.unu.edu/questionnaireevaluation-of-flood-early-warning-systems/ and can be useful in its own right for similar studies at national or regional scales, in its current form or with case-specific modifications. Survey responses were received from 47 developing (including LDCs) and six developed countries. Additional information for some countries was extracted from available literature. Analysis of these data suggests the existence of an equal number of “intermediate” and “advanced” FEWS in surveyed river basins. While developing countries overall appear to progress well in FEWS implementation, LDCs are still lagging behind since most of them have “basic” FEWS. The difference between types of operational systems in developing and developed countries appear to be insignificant; presence of basic, intermediate or advanced FEWS depends on available investments for system developments and continuous financing for their operations, and there is evidence of more financial support — on the order of USD 100 million — to FEWS in developing countries thanks to international aid. However, training the staff and maintaining the FEWS for long-term operations are challenging. About 75% of responses indicate that river basins have inadequate hydrological network coverage and back-up equipment. Almost half of the responders indicated that their models are not advanced and accurate enough to produce reliable forecasts. Lack of technical expertise and limited skilled manpower to perform forecasts was cited by 50% of respondents. The primary reason for establishing FEWS, based on the survey, is to avoid property damage; minimizing causalities and agricultural losses appear to be secondary reasons. The range of the community benefited by FEWS varies, but 55% of FEWS operate in the range between 100,000 to 1 million of population. The number of flood disasters and their causalities has declined since the year 2000, while 50% of currently operating FEWS were established over the same period. This decline may be attributed to the combined DRR efforts, of which FEWS are an integral part. In lower-middle-income and low-income countries, economic losses due to flood disasters may be smaller in absolute terms, but they represent a higher percentage of such countries’ GDP. In high-income countries, higher flood-related losses accounted for a small percentage of their GDP. To improve global knowledge on FEWS status and implementation in the context of Sendai Framework and SDGs, the report’s recommendations include: i) coordinate global investments in FEWS development and standardise investment reporting; ii) establish an international hub to monitor the status of FEWS in collaboration with the national responsible agencies. This will support the sharing of FEWS-related information for accelerated global progress in DRR; iii) develop a comprehensive, index-based ranking system for FEWS according to their effectiveness in flood disaster mitigation. This will provide clear standards and a roadmap for improving FEWS’ effectiveness, and iv) improve coordination between institutions responsible for flood forecasting and those responsible for communicating warnings and community preparedness and awareness.
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Kim, Changmo, Ghazan Khan, Brent Nguyen, and Emily L. Hoang. Development of a Statistical Model to Predict Materials’ Unit Prices for Future Maintenance and Rehabilitation in Highway Life Cycle Cost Analysis. Mineta Transportation Institute, December 2020. http://dx.doi.org/10.31979/mti.2020.1806.
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The main objectives of this study are to investigate the trends in primary pavement materials’ unit price over time and to develop statistical models and guidelines for using predictive unit prices of pavement materials instead of uniform unit prices in life cycle cost analysis (LCCA) for future maintenance and rehabilitation (M&R) projects. Various socio-economic data were collected for the past 20 years (1997–2018) in California, including oil price, population, government expenditure in transportation, vehicle registration, and other key variables, in order to identify factors affecting pavement materials’ unit price. Additionally, the unit price records of the popular pavement materials were categorized by project size (small, medium, large, and extra-large). The critical variables were chosen after identifying their correlations, and the future values of each variable were predicted through time-series analysis. Multiple regression models using selected socio-economic variables were developed to predict the future values of pavement materials’ unit price. A case study was used to compare the results between the uniform unit prices in the current LCCA procedures and the unit prices predicted in this study. In LCCA, long-term prediction involves uncertainties due to unexpected economic trends and industrial demand and supply conditions. Economic recessions and a global pandemic are examples of unexpected events which can have a significant influence on variations in material unit prices and project costs. Nevertheless, the data-driven scientific approach as described in this research reduces risk caused by such uncertainties and enables reasonable predictions for the future. The statistical models developed to predict the future unit prices of the pavement materials through this research can be implemented to enhance the current LCCA procedure and predict more realistic unit prices and project costs for the future M&R activities, thus promoting the most cost-effective alternative in LCCA.
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Zhang, Renduo, and David Russo. Scale-dependency and spatial variability of soil hydraulic properties. United States Department of Agriculture, November 2004. http://dx.doi.org/10.32747/2004.7587220.bard.
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Water resources assessment and protection requires quantitative descriptions of field-scale water flow and contaminant transport through the subsurface, which, in turn, require reliable information about soil hydraulic properties. However, much is still unknown concerning hydraulic properties and flow behavior in heterogeneous soils. Especially, relationships of hydraulic properties changing with measured scales are poorly understood. Soil hydraulic properties are usually measured at a small scale and used for quantifying flow and transport in large scales, which causes misleading results. Therefore, determination of scale-dependent and spatial variability of soil hydraulic properties provides the essential information for quantifying water flow and chemical transport through the subsurface, which are the key processes for detection of potential agricultural/industrial contaminants, reduction of agricultural chemical movement, improvement of soil and water quality, and increase of agricultural productivity. The original research objectives of this project were: 1. to measure soil hydraulic properties at different locations and different scales at large fields; 2. to develop scale-dependent relationships of soil hydraulic properties; and 3. to determine spatial variability and heterogeneity of soil hydraulic properties as a function of measurement scales. The US investigators conducted field and lab experiments to measure soil hydraulic properties at different locations and different scales. Based on the field and lab experiments, a well-structured database of soil physical and hydraulic properties was developed. The database was used to study scale-dependency, spatial variability, and heterogeneity of soil hydraulic properties. An improved method was developed for calculating hydraulic properties based on infiltration data from the disc infiltrometer. Compared with the other methods, the proposed method provided more accurate and stable estimations of the hydraulic conductivity and macroscopic capillary length, using infiltration data collected atshort experiment periods. We also developed scale-dependent relationships of soil hydraulic properties using the fractal and geostatistical characterization. The research effort of the Israeli research team concentrates on tasks along the second objective. The main accomplishment of this effort is that we succeed to derive first-order, upscaled (block effective) conductivity tensor, K'ᵢⱼ, and time-dependent dispersion tensor, D'ᵢⱼ, i,j=1,2,3, for steady-state flow in three-dimensional, partially saturated, heterogeneous formations, for length-scales comparable with those of the formation heterogeneity. Numerical simulations designed to test the applicability of the upscaling methodology to more general situations involving complex, transient flow regimes originating from periodic rain/irrigation events and water uptake by plant roots suggested that even in this complicated case, the upscaling methodology essentially compensated for the loss of sub-grid-scale variations of the velocity field caused by coarse discretization of the flow domain. These results have significant implications with respect to the development of field-scale solute transport models capable of simulating complex real-world scenarios in the subsurface, and, in turn, are essential for the assessment of the threat posed by contamination from agricultural and/or industrial sources.