higher order dynamic mode decomposition and its applications

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Higher Order Dynamic Mode Decomposition and Its Applications
Author : Jose Manuel Vega,Soledad Le Clainche
Publisher : Academic Press
Release Date : 2020-09-30
ISBN 10 : 0128227664
Pages : 320 pages

Higher Order Dynamic Mode Decomposition and Its Applications provides detailed background theory, as well as several fully explained applications from a range of industrial contexts to help readers understand and use this innovative algorithm. Data-driven modelling of complex systems is a rapidly evolving field, which has applications in domains including engineering, medical, biological, and physical sciences, where it is providing ground-breaking insights into complex systems that exhibit rich multi-scale phenomena in both time and space. Starting with an introductory summary of established order reduction techniques like POD, DEIM, Koopman, and DMD, this book proceeds to provide a detailed explanation of higher order DMD, and to explain its advantages over other methods. Technical details of how the HODMD can be applied to a range of industrial problems will help the reader decide how to use the method in the most appropriate way, along with example MATLAB codes and advice on how to analyse and present results. Includes instructions for the implementation of the HODMD, MATLAB codes, and extended discussions of the algorithm Includes descriptions of other order reduction techniques, and compares their strengths and weaknesses Provides examples of applications involving complex flow fields, in contexts including aerospace engineering, geophysical flows, and wind turbine design

14th International Conference on Soft Computing Models in Industrial and Environmental Applications (SOCO 2019)
Author : Francisco Martínez Álvarez,Alicia Troncoso Lora,José António Sáez Muñoz,Héctor Quintián,Emilio Corchado
Publisher : Springer
Release Date : 2019-04-30
ISBN 10 : 3030200558
Pages : 609 pages

This book includes 57 papers presented at the SOCO 2019 conference held in the historic city of Seville (Spain), in May 2019. Soft computing represents a set of computational techniques in machine learning, computer science and various engineering disciplines, which investigate, simulate, and analyze very complex issues and phenomena. The selection of papers was extremely rigorous in order to maintain the high quality of the conference, which featured a number of special sessions, including sessions on: Soft Computing Methods in Manufacturing and Management Systems; Soft Computing Applications in the Field of Industrial and Environmental Enterprises; Optimization, Modeling and Control by Soft Computing Techniques; and Soft Computing in Aerospace, Mechanical and Civil Engineering: New methods and Industrial Applications.

Dynamic Mode Decomposition
Author : J. Nathan Kutz,Steven L. Brunton,Bingni W. Brunton,Joshua L. Proctor
Publisher : SIAM
Release Date : 2016-11-23
ISBN 10 : 1611974496
Pages : 234 pages

Data-driven dynamical systems is a burgeoning field?it connects how measurements of nonlinear dynamical systems and/or complex systems can be used with well-established methods in dynamical systems theory. This is a critically important new direction because the governing equations of many problems under consideration by practitioners in various scientific fields are not typically known. Thus, using data alone to help derive, in an optimal sense, the best dynamical system representation of a given application allows for important new insights. The recently developed dynamic mode decomposition (DMD) is an innovative tool for integrating data with dynamical systems theory. The DMD has deep connections with traditional dynamical systems theory and many recent innovations in compressed sensing and machine learning. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, the first book to address the DMD algorithm, presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development; blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses; highlights the numerous innovations around the DMD algorithm and demonstrates its efficacy using example problems from engineering and the physical and biological sciences; and provides extensive MATLAB code, data for intuitive examples of key methods, and graphical presentations.

IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018
Author : Jörg Fehr,Bernard Haasdonk
Publisher : Springer
Release Date : 2019-07-19
ISBN 10 : 3030210138
Pages : 222 pages

This volume contains the proceedings of the IUTAM Symposium on Model Order Reduction of Coupled System, held in Stuttgart, Germany, May 22–25, 2018. For the understanding and development of complex technical systems, such as the human body or mechatronic systems, an integrated, multiphysics and multidisciplinary view is essential. Many problems can be solved within one physical domain. For the simulation and optimization of the combined system, the different domains are connected with each other. Very often, the combination is only possible by using reduced order models such that the large-scale dynamical system is approximated with a system of much smaller dimension where the most dominant features of the large-scale system are retained as much as possible. The field of model order reduction (MOR) is interdisciplinary. Researchers from Engineering, Mathematics and Computer Science identify, explore and compare the potentials, challenges and limitations of recent and new advances.

Data Analysis for Direct Numerical Simulations of Turbulent Combustion
Author : Heinz Pitsch,Antonio Attili
Publisher : Springer Nature
Release Date : 2020-05-28
ISBN 10 : 3030447189
Pages : 292 pages

This book presents methodologies for analysing large data sets produced by the direct numerical simulation (DNS) of turbulence and combustion. It describes the development of models that can be used to analyse large eddy simulations, and highlights both the most common techniques and newly emerging ones. The chapters, written by internationally respected experts, invite readers to consider DNS of turbulence and combustion from a formal, data-driven standpoint, rather than one led by experience and intuition. This perspective allows readers to recognise the shortcomings of existing models, with the ultimate goal of quantifying and reducing model-based uncertainty. In addition, recent advances in machine learning and statistical inferences offer new insights on the interpretation of DNS data. The book will especially benefit graduate-level students and researchers in mechanical and aerospace engineering, e.g. those with an interest in general fluid mechanics, applied mathematics, and the environmental and atmospheric sciences.

15th International Conference on Soft Computing Models in Industrial and Environmental Applications (SOCO 2020)
Author : Álvaro Herrero,Carlos Cambra,Daniel Urda,Javier Sedano,Héctor Quintián,Emilio Corchado
Publisher : Springer Nature
Release Date : 2020-08-28
ISBN 10 : 303057802X
Pages : 876 pages

This book contains accepted papers presented at SOCO 2020 conference held in the beautiful and historic city of Burgos (Spain), in September 2020. Soft computing represents a collection or set of computational techniques in machine learning, computer science and some engineering disciplines, which investigate, simulate, and analyze very complex issues and phenomena. After a through peer-review process, the SOCO 2020 International Program Committee selected 83 papers which are published in these conference proceedings and represents an acceptance rate of 35%. Due to the COVID-19 outbreak, the SOCO 2020 edition was blended, combining on-site and on-line participation. In this relevant edition a special emphasis was put on the organization of special sessions. Eleven special session were organized related to relevant topics such as: Soft Computing Applications in Precision Agriculture, Manufacturing and Management Systems, Management of Industrial and Environmental Enterprises, Logistics and Transportation Systems, Robotics and Autonomous Vehicles, Computer Vision, Laser-Based Sensing and Measurement and other topics such as Forecasting Industrial Time Series, IoT, Big Data and Cyber Physical Systems, Non-linear Dynamical Systems and Fluid Dynamics, Modeling and Control systems The selection of papers was extremely rigorous in order to maintain the high quality of SOCO conference editions and we would like to thank the members of the Program Committees for their hard work in the reviewing process. This is a crucial process to the creation of a high standard conference and the SOCO conference would not exist without their help.

Data-Driven Science and Engineering
Author : Steven L. Brunton,J. Nathan Kutz
Publisher : Cambridge University Press
Release Date : 2019-02-28
ISBN 10 : 1108422098
Pages : 500 pages

This beginning graduate textbook teaches data science and machine learning methods for modeling, prediction, and control of complex systems.

Handbook of Robust Low-Rank and Sparse Matrix Decomposition
Author : Thierry Bouwmans,Necdet Serhat Aybat,El-hadi Zahzah
Publisher : CRC Press
Release Date : 2016-09-20
ISBN 10 : 1315353539
Pages : 520 pages

Handbook of Robust Low-Rank and Sparse Matrix Decomposition: Applications in Image and Video Processing shows you how robust subspace learning and tracking by decomposition into low-rank and sparse matrices provide a suitable framework for computer vision applications. Incorporating both existing and new ideas, the book conveniently gives you one-stop access to a number of different decompositions, algorithms, implementations, and benchmarking techniques. Divided into five parts, the book begins with an overall introduction to robust principal component analysis (PCA) via decomposition into low-rank and sparse matrices. The second part addresses robust matrix factorization/completion problems while the third part focuses on robust online subspace estimation, learning, and tracking. Covering applications in image and video processing, the fourth part discusses image analysis, image denoising, motion saliency detection, video coding, key frame extraction, and hyperspectral video processing. The final part presents resources and applications in background/foreground separation for video surveillance. With contributions from leading teams around the world, this handbook provides a complete overview of the concepts, theories, algorithms, and applications related to robust low-rank and sparse matrix decompositions. It is designed for researchers, developers, and graduate students in computer vision, image and video processing, real-time architecture, machine learning, and data mining.

Hilbert–Huang Transform and Its Applications
Author : Norden E Huang,Samuel S P Shen
Publisher : World Scientific
Release Date : 2014-04-22
ISBN 10 : 981450825X
Pages : 400 pages

This book is written for scientists and engineers who use HHT (Hilbert–Huang Transform) to analyze data from nonlinear and non-stationary processes. It can be treated as a HHT user manual and a source of reference for HHT applications. The book contains the basic principle and method of HHT and various application examples, ranging from the correction of satellite orbit drifting to detection of failure of highway bridges. The thirteen chapters of the first edition are based on the presentations made at a mini-symposium at the Society for Industrial and Applied Mathematics in 2003. Some outstanding mathematical research problems regarding HHT development are discussed in the first three chapters. The three new chapters of the second edition reflect the latest HHT development, including ensemble empirical mode decomposition (EEMD) and modified EMD. The book also provides a platform for researchers to develop the HHT method further and to identify more applications. Contents:Introduction to the Hilbert–Huang Transform and Its Related Mathematical ProblemsEnsemble Empirical Mode Decomposition and Its Multi-Dimensional ExtensionsMultivariate Extensions of Empirical Mode DecompositionB-Spline Based Empirical Mode DecompositionEMD Equivalent Filter Banks, From Interpretation to ApplicationsHHT Sifting and FilteringStatistical Significance Test of Intrinsic Mode FunctionsThe Time-Dependent Intrinsic CorrelationThe Application of Hilbert–Huang Transforms to Meteorological DatasetsEmpirical Mode Decomposition and Climate VariabilityEMD Correction of Orbital Drift Artifacts in Satellite Data StreamHHT Analysis of the Nonlinear and Non-Stationary Annual Cycle of Daily Surface Air Temperature DataHilbert Spectra of Nonlinear Ocean WavesEMD and Instantaneous Phase Detection of Structural DamageHTT-Based Bridge Structural Health-Monitoring MethodApplications of HHT in Image Analysis Readership: Applied mathematicians, climate scientists, highway engineers, medical scientists, geologists, civil engineers, mechanical engineers, electrical engineers, economics and graduate students in science or engineering. Keywords:Hilbert–Huang Transform;Empirical Mode Decomposition;Intrinsic Mode Function;Hilbert Spectral Analysis;Time-Frequency AnalysisKey Features:A tool book for analyzing nonlinear and non-stationary dataA source book for HHT development and applicationsThe most complete reference for HHT method and applications

Turbulence, Coherent Structures, Dynamical Systems and Symmetry
Author : Philip Holmes
Publisher : Cambridge University Press
Release Date : 2012-02-23
ISBN 10 : 1107008255
Pages : 386 pages

Describes methods revealing the structures and dynamics of turbulence for engineering, physical science and mathematics researchers working in fluid dynamics.

Numerical Linear Algebra
Author : Lloyd N. Trefethen,David Bau, III
Publisher : SIAM
Release Date : 1997-01-01
ISBN 10 : 9780898719574
Pages : 361 pages

A concise, insightful, and elegant introduction to the field of numerical linear algebra. Designed for use as a stand-alone textbook in a one-semester, graduate-level course in the topic, it has already been class-tested by MIT and Cornell graduate students from all fields of mathematics, engineering, and the physical sciences. The authors' clear, inviting style and evident love of the field, along with their eloquent presentation of the most fundamental ideas in numerical linear algebra, make it popular with teachers and students alike.

Background Modeling and Foreground Detection for Video Surveillance
Author : Thierry Bouwmans,Fatih Porikli,Benjamin Höferlin,Antoine Vacavant
Publisher : CRC Press
Release Date : 2014-07-25
ISBN 10 : 1482205378
Pages : 631 pages

Background modeling and foreground detection are important steps in video processing used to detect robustly moving objects in challenging environments. This requires effective methods for dealing with dynamic backgrounds and illumination changes as well as algorithms that must meet real-time and low memory requirements. Incorporating both established and new ideas, Background Modeling and Foreground Detection for Video Surveillance provides a complete overview of the concepts, algorithms, and applications related to background modeling and foreground detection. Leaders in the field address a wide range of challenges, including camera jitter and background subtraction. The book presents the top methods and algorithms for detecting moving objects in video surveillance. It covers statistical models, clustering models, neural networks, and fuzzy models. It also addresses sensors, hardware, and implementation issues and discusses the resources and datasets required for evaluating and comparing background subtraction algorithms. The datasets and codes used in the text, along with links to software demonstrations, are available on the book’s website. A one-stop resource on up-to-date models, algorithms, implementations, and benchmarking techniques, this book helps researchers and industry developers understand how to apply background models and foreground detection methods to video surveillance and related areas, such as optical motion capture, multimedia applications, teleconferencing, video editing, and human–computer interfaces. It can also be used in graduate courses on computer vision, image processing, real-time architecture, machine learning, or data mining.

Subspace Methods for System Identification
Author : Tohru Katayama
Publisher : Springer Science & Business Media
Release Date : 2006-03-30
ISBN 10 : 184628158X
Pages : 392 pages

An in-depth introduction to subspace methods for system identification in discrete-time linear systems thoroughly augmented with advanced and novel results, this text is structured into three parts. Part I deals with the mathematical preliminaries: numerical linear algebra; system theory; stochastic processes; and Kalman filtering. Part II explains realization theory as applied to subspace identification. Stochastic realization results based on spectral factorization and Riccati equations, and on canonical correlation analysis for stationary processes are included. Part III demonstrates the closed-loop application of subspace identification methods. Subspace Methods for System Identification is an excellent reference for researchers and a useful text for tutors and graduate students involved in control and signal processing courses. It can be used for self-study and will be of interest to applied scientists or engineers wishing to use advanced methods in modeling and identification of complex systems.

The Koopman Operator in Systems and Control
Author : Alexandre Mauroy,Igor Mezić,Yoshihiko Susuki
Publisher : Springer Nature
Release Date : 2020-02-22
ISBN 10 : 3030357139
Pages : 556 pages

This book provides a broad overview of state-of-the-art research at the intersection of the Koopman operator theory and control theory. It also reviews novel theoretical results obtained and efficient numerical methods developed within the framework of Koopman operator theory. The contributions discuss the latest findings and techniques in several areas of control theory, including model predictive control, optimal control, observer design, systems identification and structural analysis of controlled systems, addressing both theoretical and numerical aspects and presenting open research directions, as well as detailed numerical schemes and data-driven methods. Each contribution addresses a specific problem. After a brief introduction of the Koopman operator framework, including basic notions and definitions, the book explores numerical methods, such as the dynamic mode decomposition (DMD) algorithm and Arnoldi-based methods, which are used to represent the operator in a finite-dimensional basis and to compute its spectral properties from data. The main body of the book is divided into three parts: theoretical results and numerical techniques for observer design, synthesis analysis, stability analysis, parameter estimation, and identification; data-driven techniques based on DMD, which extract the spectral properties of the Koopman operator from data for the structural analysis of controlled systems; and Koopman operator techniques with specific applications in systems and control, which range from heat transfer analysis to robot control. A useful reference resource on the Koopman operator theory for control theorists and practitioners, the book is also of interest to graduate students, researchers, and engineers looking for an introduction to a novel and comprehensive approach to systems and control, from pure theory to data-driven methods.

Data-Driven Modeling & Scientific Computation
Author : J. Nathan Kutz
Publisher : OUP Oxford
Release Date : 2013-08-08
ISBN 10 : 019163588X
Pages : 608 pages

The burgeoning field of data analysis is expanding at an incredible pace due to the proliferation of data collection in almost every area of science. The enormous data sets now routinely encountered in the sciences provide an incentive to develop mathematical techniques and computational algorithms that help synthesize, interpret and give meaning to the data in the context of its scientific setting. A specific aim of this book is to integrate standard scientific computing methods with data analysis. By doing so, it brings together, in a self-consistent fashion, the key ideas from: · statistics, · time-frequency analysis, and · low-dimensional reductions The blend of these ideas provides meaningful insight into the data sets one is faced with in every scientific subject today, including those generated from complex dynamical systems. This is a particularly exciting field and much of the final part of the book is driven by intuitive examples from it, showing how the three areas can be used in combination to give critical insight into the fundamental workings of various problems. Data-Driven Modeling and Scientific Computation is a survey of practical numerical solution techniques for ordinary and partial differential equations as well as algorithms for data manipulation and analysis. Emphasis is on the implementation of numerical schemes to practical problems in the engineering, biological and physical sciences. An accessible introductory-to-advanced text, this book fully integrates MATLAB and its versatile and high-level programming functionality, while bringing together computational and data skills for both undergraduate and graduate students in scientific computing.

Nonlinear and Adaptive Control with Applications
Author : Alessandro Astolfi,Dimitrios Karagiannis,Romeo Ortega
Publisher : Springer Science & Business Media
Release Date : 2007-12-06
ISBN 10 : 9781848000667
Pages : 290 pages

The authors here provide a detailed treatment of the design of robust adaptive controllers for nonlinear systems with uncertainties. They employ a new tool based on the ideas of system immersion and manifold invariance. New algorithms are delivered for the construction of robust asymptotically-stabilizing and adaptive control laws for nonlinear systems. The methods proposed lead to modular schemes that are easier to tune than their counterparts obtained from Lyapunov redesign.

Introduction to Applied Linear Algebra
Author : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Release Date : 2018-06-07
ISBN 10 : 1316518965
Pages : 500 pages

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Computer Vision
Author : Richard Szeliski
Publisher : Springer Science & Business Media
Release Date : 2010-09-30
ISBN 10 : 9781848829350
Pages : 812 pages

Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of “recipes,” this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques. Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

Feedback Systems
Author : Karl Johan Åström,Richard M. Murray
Publisher : Princeton University Press
Release Date : 2010-04-12
ISBN 10 : 1400828732
Pages : 408 pages

This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems. It is an ideal textbook for undergraduate and graduate students, and is indispensable for researchers seeking a self-contained reference on control theory. Unlike most books on the subject, Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. They provide exercises at the end of every chapter, and an accompanying electronic solutions manual is available. Feedback Systems is a complete one-volume resource for students and researchers in mathematics, engineering, and the sciences. Covers the mathematics needed to model, analyze, and design feedback systems Serves as an introductory textbook for students and a self-contained resource for researchers Includes exercises at the end of every chapter Features an electronic solutions manual Offers techniques applicable across a range of disciplines

Time-Frequency Signal Analysis and Processing
Author : Boualem Boashash
Publisher : Academic Press
Release Date : 2015-12-11
ISBN 10 : 0123985250
Pages : 1056 pages

Time-Frequency Signal Analysis and Processing (TFSAP) is a collection of theory, techniques and algorithms used for the analysis and processing of non-stationary signals, as found in a wide range of applications including telecommunications, radar, and biomedical engineering. This book gives the university researcher and R&D engineer insights into how to use TFSAP methods to develop and implement the engineering application systems they require. New to this edition: New sections on Efficient and Fast Algorithms; a "Getting Started" chapter enabling readers to start using the algorithms on simulated and real examples with the TFSAP toolbox, compare the results with the ones presented in the book and then insert the algorithms in their own applications and adapt them as needed. Two new chapters and twenty three new sections, including updated references. New topics including: efficient algorithms for optimal TFDs (with source code), the enhanced spectrogram, time-frequency modelling, more mathematical foundations, the relationships between QTFDs and Wavelet Transforms, new advanced applications such as cognitive radio, watermarking, noise reduction in the time-frequency domain, algorithms for Time-Frequency Image Processing, and Time-Frequency applications in neuroscience (new chapter). A comprehensive tutorial introduction to Time-Frequency Signal Analysis and Processing (TFSAP), accessible to anyone who has taken a first course in signals Key advances in theory, methodology and algorithms, are concisely presented by some of the leading authorities on the respective topics Applications written by leading researchers showing how to use TFSAP methods