Download or read book Linearization Methods for Stochastic Dynamic Systems written by Leslaw Socha and published by Springer. This book was released on 2007-11-30 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. This book details the relatively simple and popular linearization techniques available, covering theory as well as application. It examines models with continuous external and parametric excitations, those that cover the majority of known approaches.
Download or read book Linearization Methods for Stochastic Dynamic Systems written by Lesław Socha and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. The aim of this book is to give a systematic introduction to and overview of the relatively simple and popular linearization methods available. The scope is limited to models with continous external and parametric excitations, yet these cover the majority of known approaches. The book contains an application chapter with emphasis on vibration analysis of stochastic mechanical structures as well as a chapter devoted to the assessment of the accuracy of the theoretical methods presented, both with respect to numerical and to experimental studies. The material derives partly from graduate course notes developed by the author for courses and seminars over the past 20 years.
Download or read book Linearization Methods for Stochastic Dynamic Systems written by Leslaw Socha and published by Springer Science & Business Media. This book was released on 2007-12-20 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. This book details the relatively simple and popular linearization techniques available, covering theory as well as application. It examines models with continuous external and parametric excitations, those that cover the majority of known approaches.
Download or read book Linear Systems Control written by Elbert Hendricks and published by Springer Science & Business Media. This book was released on 2008-10-13 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern control theory and in particular state space or state variable methods can be adapted to the description of many different systems because it depends strongly on physical modeling and physical intuition. The laws of physics are in the form of differential equations and for this reason, this book concentrates on system descriptions in this form. This means coupled systems of linear or nonlinear differential equations. The physical approach is emphasized in this book because it is most natural for complex systems. It also makes what would ordinarily be a difficult mathematical subject into one which can straightforwardly be understood intuitively and which deals with concepts which engineering and science students are already familiar. In this way it is easy to immediately apply the theory to the understanding and control of ordinary systems. Application engineers, working in industry, will also find this book interesting and useful for this reason. In line with the approach set forth above, the book first deals with the modeling of systems in state space form. Both transfer function and differential equation modeling methods are treated with many examples. Linearization is treated and explained first for very simple nonlinear systems and then more complex systems. Because computer control is so fundamental to modern applications, discrete time modeling of systems as difference equations is introduced immediately after the more intuitive differential equation models. The conversion of differential equation models to difference equations is also discussed at length, including transfer function formulations. A vital problem in modern control is how to treat noise in control systems. Nevertheless this question is rarely treated in many control system textbooks because it is considered to be too mathematical and too difficult in a second course on controls. In this textbook a simple physical approach is made to the description of noise and stochastic disturbances which is easy to understand and apply to common systems. This requires only a few fundamental statistical concepts which are given in a simple introduction which lead naturally to the fundamental noise propagation equation for dynamic systems, the Lyapunov equation. This equation is given and exemplified both in its continuous and discrete time versions. With the Lyapunov equation available to describe state noise propagation, it is a very small step to add the effect of measurements and measurement noise. This gives immediately the Riccati equation for optimal state estimators or Kalman filters. These important observers are derived and illustrated using simulations in terms which make them easy to understand and easy to apply to real systems. The use of LQR regulators with Kalman filters give LQG (Linear Quadratic Gaussian) regulators which are introduced at the end of the book. Another important subject which is introduced is the use of Kalman filters as parameter estimations for unknown parameters. The textbook is divided into 7 chapters, 5 appendices, a table of contents, a table of examples, extensive index and extensive list of references. Each chapter is provided with a summary of the main points covered and a set of problems relevant to the material in that chapter. Moreover each of the more advanced chapters (3 - 7) are provided with notes describing the history of the mathematical and technical problems which lead to the control theory presented in that chapter. Continuous time methods are the main focus in the book because these provide the most direct connection to physics. This physical foundation allows a logical presentation and gives a good intuitive feel for control system construction. Nevertheless strong attention is also given to discrete time systems. Very few proofs are included in the book but most of the important results are derived. This method of presentation makes the text very readable and gives a good foundation for reading more rigorous texts. A complete set of solutions is available for all of the problems in the text. In addition a set of longer exercises is available for use as Matlab/Simulink ‘laboratory exercises’ in connection with lectures. There is material of this kind for 12 such exercises and each exercise requires about 3 hours for its solution. Full written solutions of all these exercises are available.
Download or read book Nonlinear Dynamics and Stochastic Mechanics written by Wolfgang Kliemann and published by CRC Press. This book was released on 1995-04-18 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineering systems have played a crucial role in stimulating many of the modern developments in nonlinear and stochastic dynamics. After 20 years of rapid progress in these areas, this book provides an overview of the current state of nonlinear modeling and analysis for mechanical and structural systems. This volume is a coherent compendium written by leading experts from the United States, Canada, Western and Eastern Europe, and Australia. The 22 articles describe the background, recent developments, applications, and future directions in bifurcation theory, chaos, perturbation methods, stochastic stability, stochastic flows, random vibrations, reliability, disordered systems, earthquake engineering, and numerics. The book gives readers a sophisticated toolbox that will allow them to tackle modeling problems in mechanical systems that use stochastic and nonlinear dynamics ideas. An extensive bibliography and index ensure this volume will remain a reference standard for years to come.
Download or read book Numerical Methods for Reliability and Safety Assessment written by Seifedine Kadry and published by Springer. This book was released on 2014-09-30 with total page 807 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers unique insight on structural safety and reliability by combining computational methods that address multiphysics problems, involving multiple equations describing different physical phenomena and multiscale problems, involving discrete sub-problems that together describe important aspects of a system at multiple scales. The book examines a range of engineering domains and problems using dynamic analysis, nonlinear methods, error estimation, finite element analysis and other computational techniques. This book also: · Introduces novel numerical methods · Illustrates new practical applications · Examines recent engineering applications · Presents up-to-date theoretical results · Offers perspective relevant to a wide audience, including teaching faculty/graduate students, researchers and practicing engineers.
Download or read book Linearization Models for Complex Dynamical Systems written by Mark Elin and published by Springer Science & Business Media. This book was released on 2011-02-09 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linearization models for discrete and continuous time dynamical systems are the driving forces for modern geometric function theory and composition operator theory on function spaces. This book focuses on a systematic survey and detailed treatment of linearization models for one-parameter semigroups, Schröder’s and Abel’s functional equations, and various classes of univalent functions which serve as intertwining mappings for nonlinear and linear semigroups. These topics are applicable to the study of problems in complex analysis, stochastic and evolution processes and approximation theory.
Download or read book Quasilinear Control written by ShiNung Ching and published by Cambridge University Press. This book was released on 2010-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook and reference for readers interested in quasilinear control (QLC). QLC is a set of methods for performance analysis and design of linear plant or nonlinear instrumentation (LPNI) systems. The approach of QLC is based on the method of stochastic linearization, which reduces the nonlinearities of actuators and sensors to quasilinear gains. Unlike the usual - Jacobian linearization - stochastic linearization is global. Using this approximation, QLC extends most of the linear control theory techniques to LPNI systems. A bisection algorithm for solving these equations is provided. In addition, QLC includes new problems, specific for the LPNI scenario. Examples include Instrumented LQR/LQG, in which the controller is designed simultaneously with the actuator and sensor, and partial and complete performance recovery, in which the degradation of linear performance is either contained by selecting the right instrumentation or completely eliminated by the controller boosting.
Download or read book Control and Dynamic Systems V55 Digital and Numeric Techniques and Their Application in Control Systems written by C.T. Leonides and published by Academic Press. This book was released on 2012-12-02 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control and Dynamic Systems: Advances in Theory Applications, Volume 55: Digital and Numeric Techniques and their Applications in Control Systems, Part 1 of 2 covers advances in numerical and computational techniques for the design of modern complex control systems. This book presents a comprehensive treatment of the many issues that are dealt with in modern complex systems. It discusses the efficacy of significant techniques for robust control design; model reduction; adaptive estimation of discrete-time stochastic systems; parameter estimation; and loop transfer recovery. Students, research workers, and practising engineers will find this book invaluable.
Download or read book Mechanical Vibration Where Do We Stand written by Isaac Elishakoff and published by Springer Science & Business Media. This book was released on 2007-12-12 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by the world’s leading researchers on various topics of linear, nonlinear, and stochastic mechanical vibrations, this work gives an authoritative overview of the classic yet still very modern subject of mechanical vibrations. It examines the most important contributions to the field made in the past decade, offering a critical and comprehensive portrait of the subject from various complementary perspectives.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1988 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Dynamics and Stochastic Mechanics written by Wolfgang Kliemann and published by CRC Press. This book was released on 2018-05-04 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineering systems have played a crucial role in stimulating many of the modern developments in nonlinear and stochastic dynamics. After 20 years of rapid progress in these areas, this book provides an overview of the current state of nonlinear modeling and analysis for mechanical and structural systems. This volume is a coherent compendium written by leading experts from the United States, Canada, Western and Eastern Europe, and Australia. The 22 articles describe the background, recent developments, applications, and future directions in bifurcation theory, chaos, perturbation methods, stochastic stability, stochastic flows, random vibrations, reliability, disordered systems, earthquake engineering, and numerics. The book gives readers a sophisticated toolbox that will allow them to tackle modeling problems in mechanical systems that use stochastic and nonlinear dynamics ideas. An extensive bibliography and index ensure this volume will remain a reference standard for years to come.
Download or read book Random Vibration and Statistical Linearization written by John Brian Roberts and published by Courier Corporation. This book was released on 2003-12-09 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained volume explains the general method of statistical linearization and its use in solving random vibration problems. Numerous examples show advanced undergraduate and graduate students many practical applications. 1990 edition.
Download or read book Nonlinear Random Vibration Second Edition written by Cho W.S. To and published by CRC Press. This book was released on 2011-08-10 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition of the book, Nonlinear Random Vibration: Analytical Techniques and Applications, expands on the original edition with additional detailed steps in various places in the text. It is a first systematic presentation on the subject. Its features include: • a concise treatment of Markovian and non- Markovian solutions of nonlinear stochastic differential equations, • exact solutions of Fokker-Planck-Kolmogorov equations, • methods of statistical linearization, • statistical nonlinearization techniques, • methods of stochastic averaging, • truncated hierarchy techniques, and • an appendix on probability theory. A special feature is its incorporation of detailed steps in many examples of engineering applications. Targeted audience: Graduates, research scientists and engineers in mechanical, aerospace, civil and environmental (earthquake, wind and transportation), automobile, naval, architectural, and mining engineering.
Download or read book Nondeterministic Mechanics written by Isaac Elishakoff and published by Springer Science & Business Media. This book was released on 2013-07-30 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents: Stochastic methods in nonlinear structural dynamics.- Stochastic models of uncertainties in computational structural dynamics and structural acoustics.- The tale of stochastic linearization techniques: over half a century of progress.- Comprehensive modeling of uncertain systems using fuzzy set theory.- Bounding uncertainty in civil engineering: theoretical background and applications.- Combined methods in nondeterministic mechanics. In this book the current state of the art of nondeterministic mechanics in its various forms is presented. The topics range from stochastic problems to fuzzy sets; from linear to nonlinear problems; from specific methodologies to combinations of various techniques; from theoretical considerations to practical applications. It is specially designed to illuminate the various aspects of the three methodologies (probabilistic or stochastic modelling, fuzzy sets based analysis, antioptimization of structures) to deal with various uncertainties and deepen the discussion of their pros and cons.
Download or read book Stochastic Dynamics of Structures written by Jie Li and published by John Wiley & Sons. This book was released on 2009-07-23 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Stochastic Dynamics of Structures, Li and Chen present a unified view of the theory and techniques for stochastic dynamics analysis, prediction of reliability, and system control of structures within the innovative theoretical framework of physical stochastic systems. The authors outline the fundamental concepts of random variables, stochastic process and random field, and orthogonal expansion of random functions. Readers will gain insight into core concepts such as stochastic process models for typical dynamic excitations of structures, stochastic finite element, and random vibration analysis. Li and Chen also cover advanced topics, including the theory of and elaborate numerical methods for probability density evolution analysis of stochastic dynamical systems, reliability-based design, and performance control of structures. Stochastic Dynamics of Structures presents techniques for researchers and graduate students in a wide variety of engineering fields: civil engineering, mechanical engineering, aerospace and aeronautics, marine and offshore engineering, ship engineering, and applied mechanics. Practicing engineers will benefit from the concise review of random vibration theory and the new methods introduced in the later chapters. "The book is a valuable contribution to the continuing development of the field of stochastic structural dynamics, including the recent discoveries and developments by the authors of the probability density evolution method (PDEM) and its applications to the assessment of the dynamic reliability and control of complex structures through the equivalent extreme-value distribution." —A. H-S. Ang, NAE, Hon. Mem. ASCE, Research Professor, University of California, Irvine, USA "The authors have made a concerted effort to present a responsible and even holistic account of modern stochastic dynamics. Beyond the traditional concepts, they also discuss theoretical tools of recent currency such as the Karhunen-Loeve expansion, evolutionary power spectra, etc. The theoretical developments are properly supplemented by examples from earthquake, wind, and ocean engineering. The book is integrated by also comprising several useful appendices, and an exhaustive list of references; it will be an indispensable tool for students, researchers, and practitioners endeavoring in its thematic field." —Pol Spanos, NAE, Ryon Chair in Engineering, Rice University, Houston, USA
Download or read book Advanced Nonlinear Strategies for Vibration Mitigation and System Identification written by Alexander F. Vakakis and published by Springer Science & Business Media. This book was released on 2011-01-27 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume address advanced nonlinear topics in the general areas of vibration mitigation and system identification, such as, methods of analysis of strongly nonlinear dyanmical systems; techniques and methodologies for interpreting complex, multi-frequency transitions in damped nonlinear responses; new approaches for passive vibration mitigation based on nonlinear targeted energy transfer (TET) and the associated concept of nonlinear energy sink (NES); and an overview and assessment of current nonlinear system identification techniques.
