Data Driven Modeling Of Dynamical Systems
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Author | : Steven L. Brunton |
Publisher | : Cambridge University Press |
Total Pages | : 615 |
Release | : 2022-05-05 |
Genre | : Computers |
ISBN | : 1009098489 |
A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.
Author | : J. Nathan Kutz |
Publisher | : SIAM |
Total Pages | : 241 |
Release | : 2016-11-23 |
Genre | : Science |
ISBN | : 1611974496 |
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.
Author | : Jose Nathan Kutz |
Publisher | : |
Total Pages | : 657 |
Release | : 2013-08-08 |
Genre | : Computers |
ISBN | : 0199660336 |
Combining scientific computing methods and algorithms with modern data analysis techniques, including basic applications of compressive sensing and machine learning, this book develops techniques that allow for the integration of the dynamics of complex systems and big data. MATLAB is used throughout for mathematical solution strategies.
Author | : J. Nathan Kutz |
Publisher | : SIAM |
Total Pages | : 241 |
Release | : 2016-11-23 |
Genre | : Science |
ISBN | : 161197450X |
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.
Author | : Pritthi Chattopadhyay |
Publisher | : |
Total Pages | : |
Release | : 2018 |
Genre | : |
ISBN | : |
Human-engineered complex systems need to be monitored consistently to ensuretheir safety and efficiency, which might be affected due to degradation over timeor unanticipated disturbances. For systems that change at a fast time scale, insteadof active health monitoring, preventative system design is more feasible andeffective. Both active health monitoring and preventative system design can bedone using physics-based or data-driven models. In comparison to physics-basedmodels, data-driven models do not require knowledge of the underlying systemdynamics; they determine the relation between the relevant input and output variablesfrom a training data set. This is useful when there is lack of understandingof the system dynamics or the developed models are inadequate. One such scenariois combustion, where the difficulties include nonlinear dynamics involvingseveral input parameters; existence of bifurcations in the dynamic behavior andextremely high sensitivity of the combustor behavior to even small changes insome of the design parameters. Similarly, for batteries, sufficient knowledge of theelectrochemical characteristics is necessary to develop models for parameter identification at different operating points of the nonlinear battery dynamics. Thisdissertation develops dynamic data-driven models for combustor design and batteryhealth monitoring, using concepts of machine learning and statistics, whichdo not require much knowledge of the underlying system dynamics.But the performance of a data-driven algorithm depends on many factors namely:1. Availability of training data which covers all events of interest. For applicationsinvolving time series data, each individual time series must also besufficiently long, to encompass the dynamics of the underlying system foreach event.2. The quality of extracted features, i.e. whether they capture all the informationabout the system.3. The relation between the relevant input and output variables remaining constantduring the time the algorithm is being trained.Hence, the second part of the dissertation develops an unsupervised algorithm forscenarios where condition (iii) might not hold; quanties the eect of the nonconformityof condition (i) on the performance of an algorithm and proposes afeature extraction algorithm to ensure conformity of condition (ii).
Author | : Dhruv Khandelwal |
Publisher | : Springer Nature |
Total Pages | : 250 |
Release | : 2022-02-03 |
Genre | : Technology & Engineering |
ISBN | : 3030903435 |
This book describes a user-friendly, evolutionary algorithms-based framework for estimating data-driven models for a wide class of dynamical systems, including linear and nonlinear ones. The methodology addresses the problem of automating the process of estimating data-driven models from a user’s perspective. By combining elementary building blocks, it learns the dynamic relations governing the system from data, giving model estimates with various trade-offs, e.g. between complexity and accuracy. The evaluation of the method on a set of academic, benchmark and real-word problems is reported in detail. Overall, the book offers a state-of-the-art review on the problem of nonlinear model estimation and automated model selection for dynamical systems, reporting on a significant scientific advance that will pave the way to increasing automation in system identification.
Author | : M. Reza Rahimi Tabar |
Publisher | : Springer |
Total Pages | : 280 |
Release | : 2019-07-04 |
Genre | : Science |
ISBN | : 3030184722 |
This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation? Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data. The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results. The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations. The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements.
Author | : Carlo Novara |
Publisher | : Control, Robotics and Sensors |
Total Pages | : 300 |
Release | : 2019-09 |
Genre | : Technology & Engineering |
ISBN | : 1785617125 |
Using important examples, this book showcases the potential of the latest data-based and data-driven methodologies for filter and control design. It discusses the most important classes of dynamic systems, along with the statistical and set membership analysis and design frameworks.
Author | : Damien Gueho |
Publisher | : |
Total Pages | : 0 |
Release | : 2022 |
Genre | : |
ISBN | : |
This dissertation advances the understanding of data-driven modeling and delivers tools to pursue the ambition of complete unsupervised identification of dynamical systems. From measured data only, the proposed framework consists of a series of modules to derive accurate mathematical models for the state prediction of a wide range of linear and nonlinear dynamical systems. Identified models are constructed to be of low complexity and amenable for analysis and control. This developed framework provides a unified mathematical structure for the identification of nonlinear systems based on the Koopman operator. A main contribution of this dissertation is to introduce the concept of time-varying Koopman operator for accurate modeling of dynamical systems in a given domain around a reference trajectory. Subspace identification methods coupled with sparse approximation techniques deliver accurate models both in the continuous and discrete time domains. This allows for perfect reconstruction of several classes of nonlinear dynamical systems, from the chaotic behavior of the Lorenz oscillator to identifying the Newton's law of gravitation. The connection between the Koopman operator and higher-order state transition matrices (STMs) is explicitly discussed. It is shown that subspace methods based on the Koopman operator are able to accurately identify the linear time varying model for the propagation of higher order STMs when polynomial basis are used as lifting functions. Such algorithms are validated on a wide range of nonlinear dynamical systems of varying complexity and are proven to be very effective on nonlinear systems of higher dimension where traditional methods either fail or perform poorly. Applications include model-order reduction in hypersonic aerothermoelasticity and reduced-order dynamics in a high-dimensional finite-element model of the Von Kàrmàn Beam. Numerical simulation results confirm better prediction accuracy by several orders of magnitude using this framework. Additionally, a major objective of this research is to enhance the field of data-driven uncertainty quantification for nonlinear dynamical systems. Uncertainty propagation through nonlinear dynamics is computationally expensive. Conventional approaches focus on finding a reduced order model to alleviate the computational complexity associated with the uncertainty propagation algorithms. This dissertation exploits the fact that the moment propagation equations form a linear time-varying (LTV) system and use system theory to identify this LTV system from data only. By estimating and propagating higher-order moments of an initial probability density function, two new approaches are presented and compared to analytical and quadrature-based methods for estimating the uncertainty associated with a system's states. In all test cases considered in this dissertation, a newly-introduced indirect method using a time-varying subspace identification technique jointly with a quadrature method achieved the best results. This dissertation also extends the Koopman operator theoretic framework for controlled dynamical systems and offers a global overview of bilinear system identification techniques as well as perspectives and advances for bilinear system identification. Nonlinear dynamics with a control action are approximated as a bilinear system in a higher-dimensional space, leading to increased accuracy in the prediction of the system's response. In the same context, a data-driven parameter sensitivity method is developed using bilinear system identification algorithms. Finally, this dissertation investigates new ways to alleviate the effect of noise in the data, leading to new algorithms with data-correlations and rank optimization for optimal subspace identification.
Author | : Marian Bubak |
Publisher | : Springer Science & Business Media |
Total Pages | : 1376 |
Release | : 2004-05-26 |
Genre | : Computers |
ISBN | : 3540221166 |
The International Conference on Computational Science (ICCS 2004) held in Krak ́ ow, Poland, June 6–9, 2004, was a follow-up to the highly successful ICCS 2003 held at two locations, in Melbourne, Australia and St. Petersburg, Russia; ICCS 2002 in Amsterdam, The Netherlands; and ICCS 2001 in San Francisco, USA. As computational science is still evolving in its quest for subjects of inves- gation and e?cient methods, ICCS 2004 was devised as a forum for scientists from mathematics and computer science, as the basic computing disciplines and application areas, interested in advanced computational methods for physics, chemistry, life sciences, engineering, arts and humanities, as well as computer system vendors and software developers. The main objective of this conference was to discuss problems and solutions in all areas, to identify new issues, to shape future directions of research, and to help users apply various advanced computational techniques. The event harvested recent developments in com- tationalgridsandnextgenerationcomputingsystems,tools,advancednumerical methods, data-driven systems, and novel application ?elds, such as complex - stems, ?nance, econo-physics and population evolution.