Dimension Reduction of Large-Scale Systems

Dimension Reduction of Large-Scale Systems PDF Author: Peter Benner
Publisher: Springer Science & Business Media
ISBN: 3540279091
Category : Technology & Engineering
Languages : en
Pages : 404

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Book Description
In the past decades, model reduction has become an ubiquitous tool in analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, and many other disciplines dealing with complex physical models. The aim of this book is to survey some of the most successful model reduction methods in tutorial style articles and to present benchmark problems from several application areas for testing and comparing existing and new algorithms. As the discussed methods have often been developed in parallel in disconnected application areas, the intention of the mini-workshop in Oberwolfach and its proceedings is to make these ideas available to researchers and practitioners from all these different disciplines.

Dimension Reduction of Large-Scale Systems

Dimension Reduction of Large-Scale Systems PDF Author: Peter Benner
Publisher: Springer Science & Business Media
ISBN: 3540279091
Category : Technology & Engineering
Languages : en
Pages : 404

Get Book

Book Description
In the past decades, model reduction has become an ubiquitous tool in analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, and many other disciplines dealing with complex physical models. The aim of this book is to survey some of the most successful model reduction methods in tutorial style articles and to present benchmark problems from several application areas for testing and comparing existing and new algorithms. As the discussed methods have often been developed in parallel in disconnected application areas, the intention of the mini-workshop in Oberwolfach and its proceedings is to make these ideas available to researchers and practitioners from all these different disciplines.

Efficient Modeling and Control of Large-Scale Systems

Efficient Modeling and Control of Large-Scale Systems PDF Author: Javad Mohammadpour
Publisher: Springer Science & Business Media
ISBN: 144195757X
Category : Technology & Engineering
Languages : en
Pages : 335

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Book Description
Complexity and dynamic order of controlled engineering systems is constantly increasing. Complex large scale systems (where "large" reflects the system’s order and not necessarily its physical size) appear in many engineering fields, such as micro-electromechanics, manufacturing, aerospace, civil engineering and power engineering. Modeling of these systems often result in very high-order models imposing great challenges to the analysis, design and control problems. "Efficient Modeling and Control of Large-Scale Systems" compiles state-of-the-art contributions on recent analytical and computational methods for addressing model reduction, performance analysis and feedback control design for such systems. Also addressed at length are new theoretical developments, novel computational approaches and illustrative applications to various fields, along with: - An interdisciplinary focus emphasizing methods and approaches that can be commonly applied in various engineering fields -Examinations of applications in various fields including micro-electromechanical systems (MEMS), manufacturing processes, power networks, traffic control "Efficient Modeling and Control of Large-Scale Systems" is an ideal volume for engineers and researchers working in the fields of control and dynamic systems.

Model Reduction of Complex Dynamical Systems

Model Reduction of Complex Dynamical Systems PDF Author: Peter Benner
Publisher: Springer Nature
ISBN: 3030729834
Category : Mathematics
Languages : en
Pages : 415

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Book Description
This contributed volume presents some of the latest research related to model order reduction of complex dynamical systems with a focus on time-dependent problems. Chapters are written by leading researchers and users of model order reduction techniques and are based on presentations given at the 2019 edition of the workshop series Model Reduction of Complex Dynamical Systems – MODRED, held at the University of Graz in Austria. The topics considered can be divided into five categories: system-theoretic methods, such as balanced truncation, Hankel norm approximation, and reduced-basis methods; data-driven methods, including Loewner matrix and pencil-based approaches, dynamic mode decomposition, and kernel-based methods; surrogate modeling for design and optimization, with special emphasis on control and data assimilation; model reduction methods in applications, such as control and network systems, computational electromagnetics, structural mechanics, and fluid dynamics; and model order reduction software packages and benchmarks. This volume will be an ideal resource for graduate students and researchers in all areas of model reduction, as well as those working in applied mathematics and theoretical informatics.

Calm, Smooth and Smart

Calm, Smooth and Smart PDF Author: Peter Eberhard
Publisher: Springer Nature
ISBN: 3031361431
Category : Technology & Engineering
Languages : en
Pages : 353

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Book Description
This book contains and summarizes research carried out within the DFG Priority Programme 1897: "Calm, Smooth and Smart - Novel Approaches for Influencing Vibrations by Means of Deliberately Introduced Dissipation". The contributions help reduce unwanted vibrations by developing novel approaches for influencing them and lead to a “calm, smooth and smart” behaviour of technical units. “Calm” represents the demand to avoid or at least to severely reduce unwanted noise generated by technical installations. “Smooth” ensures a still comfortable and jerk-free operation of them. Finally, “smart” means that the introduced damping devices not only help to achieve the desired vibrational behaviour of the overall technical systems, but also that they take over additional functional tasks. The results presented in this volume summarize the state-of-the-art and provide motivation for future research. The book is intended for experienced researchers as well as for doctoral and post-doctoral students in engineering, mathematics and physics, as well as industrial researchers interested in the field.

Computational Methods for Approximation of Large-Scale Dynamical Systems

Computational Methods for Approximation of Large-Scale Dynamical Systems PDF Author: Mohammad Monir Uddin
Publisher: CRC Press
ISBN: 135102860X
Category : Mathematics
Languages : en
Pages : 279

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Book Description
These days, computer-based simulation is considered the quintessential approach to exploring new ideas in the different disciplines of science, engineering and technology (SET). To perform simulations, a physical system needs to be modeled using mathematics; these models are often represented by linear time-invariant (LTI) continuous-time (CT) systems. Oftentimes these systems are subject to additional algebraic constraints, leading to first- or second-order differential-algebraic equations (DAEs), otherwise known as descriptor systems. Such large-scale systems generally lead to massive memory requirements and enormous computational complexity, thus restricting frequent simulations, which are required by many applications. To resolve these complexities, the higher-dimensional system may be approximated by a substantially lower-dimensional one through model order reduction (MOR) techniques. Computational Methods for Approximation of Large-Scale Dynamical Systems discusses computational techniques for the MOR of large-scale sparse LTI CT systems. Although the book puts emphasis on the MOR of descriptor systems, it begins by showing and comparing the various MOR techniques for standard systems. The book also discusses the low-rank alternating direction implicit (LR-ADI) iteration and the issues related to solving the Lyapunov equation of large-scale sparse LTI systems to compute the low-rank Gramian factors, which are important components for implementing the Gramian-based MOR. Although this book is primarly aimed at post-graduate students and researchers of the various SET disciplines, the basic contents of this book can be supplemental to the advanced bachelor's-level students as well. It can also serve as an invaluable reference to researchers working in academics and industries alike. Features: Provides an up-to-date, step-by-step guide for its readers. Each chapter develops theories and provides necessary algorithms, worked examples, numerical experiments and related exercises. With the combination of this book and its supplementary materials, the reader gains a sound understanding of the topic. The MATLAB® codes for some selected algorithms are provided in the book. The solutions to the exercise problems, experiment data sets and a digital copy of the software are provided on the book's website; The numerical experiments use real-world data sets obtained from industries and research institutes.

Large Scale Inverse Problems

Large Scale Inverse Problems PDF Author: Mike Cullen
Publisher: Walter de Gruyter
ISBN: 3110282267
Category : Mathematics
Languages : en
Pages : 212

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Book Description
This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. Thiscollection of surveyarticlesfocusses onthe large inverse problems commonly arising in simulation and forecasting in the earth sciences. For example, operational weather forecasting models have between 107 and 108 degrees of freedom. Even so, these degrees of freedom represent grossly space-time averaged properties of the atmosphere. Accurate forecasts require accurate initial conditions. With recent developments in satellite data, there are between 106 and 107 observations each day. However, while these also represent space-time averaged properties, the averaging implicit in the measurements is quite different from that used in the models. In atmosphere and ocean applications, there is a physically-based model available which can be used to regularise the problem. We assume that there is a set of observations with known error characteristics available over a period of time. The basic deterministic technique is to fit a model trajectory to the observations over a period of time to within the observation error. Since the model is not perfect the model trajectory has to be corrected, which defines the data assimilation problem. The stochastic view can be expressed by using an ensemble of model trajectories, and calculating corrections to both the mean value and the spread which allow the observations to be fitted by each ensemble member. In other areas of earth science, only the structure of the model formulation itself is known and the aim is to use the past observation history to determine the unknown model parameters. The book records the achievements of Workshop2 "Large-Scale Inverse Problems and Applications in the Earth Sciences". Itinvolves experts in the theory of inverse problems together with experts working on both theoretical and practical aspects of the techniques by which large inverse problems arise in the earth sciences.

Large-Scale Inverse Problems and Quantification of Uncertainty

Large-Scale Inverse Problems and Quantification of Uncertainty PDF Author: Lorenz Biegler
Publisher: John Wiley & Sons
ISBN: 1119957583
Category : Mathematics
Languages : en
Pages : 388

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Book Description
This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications. The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods. Key Features: Brings together the perspectives of researchers in areas of inverse problems and data assimilation. Assesses the current state-of-the-art and identify needs and opportunities for future research. Focuses on the computational methods used to analyze and simulate inverse problems. Written by leading experts of inverse problems and uncertainty quantification. Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.

Principal Manifolds for Data Visualization and Dimension Reduction

Principal Manifolds for Data Visualization and Dimension Reduction PDF Author: Alexander N. Gorban
Publisher: Springer Science & Business Media
ISBN: 3540737502
Category : Technology & Engineering
Languages : en
Pages : 340

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Book Description
The book starts with the quote of the classical Pearson definition of PCA and includes reviews of various methods: NLPCA, ICA, MDS, embedding and clustering algorithms, principal manifolds and SOM. New approaches to NLPCA, principal manifolds, branching principal components and topology preserving mappings are described. Presentation of algorithms is supplemented by case studies. The volume ends with a tutorial PCA deciphers genome.

Index-aware Model Order Reduction Methods

Index-aware Model Order Reduction Methods PDF Author: N. Banagaaya
Publisher: Springer
ISBN: 9462391890
Category : Mathematics
Languages : en
Pages : 86

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Book Description
The main aim of this book is to discuss model order reduction (MOR) methods for differential-algebraic equations (DAEs) with linear coefficients that make use of splitting techniques before applying model order reduction. The splitting produces a system of ordinary differential equations (ODE) and a system of algebraic equations, which are then reduced separately. For the reduction of the ODE system, conventional MOR methods can be used, whereas for the reduction of the algebraic systems new methods are discussed. The discussion focuses on the index-aware model order reduction method (IMOR) and its variations, methods for which the so-called index of the original model is automatically preserved after reduction.

Model Order Reduction: Theory, Research Aspects and Applications

Model Order Reduction: Theory, Research Aspects and Applications PDF Author: Wilhelmus H. Schilders
Publisher: Springer Science & Business Media
ISBN: 3540788417
Category : Mathematics
Languages : en
Pages : 471

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Book Description
The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.