elements of stochastic dynamics

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Elements Of Stochastic Dynamics

Author : Guo-Qiang Cai
ISBN : 9789814723343
Genre : Technology & Engineering
File Size : 39. 47 MB
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Stochastic dynamics has been a subject of interest since the early 20th Century. Since then, much progress has been made in this field of study, and many modern applications for it have been found in fields such as physics, chemistry, biology, ecology, economy, finance, and many branches of engineering including Mechanical, Ocean, Civil, Bio, and Earthquake Engineering. Elements of Stochastic Dynamics aims to meet the growing need to understand and master the subject by introducing fundamentals to researchers who want to explore stochastic dynamics in their fields and serving as a textbook for graduate students in various areas involving stochastic uncertainties. All topics within are presented from an application approach, and may thus be more appealing to users without a background in pure Mathematics. The book describes the basic concepts and theories of random variables and stochastic processes in detail; provides various solution procedures for systems subjected to stochastic excitations; introduces stochastic stability and bifurcation; and explores failures of stochastic systems. The book also incorporates some latest research results in modeling stochastic processes; in reducing the system degrees of freedom; and in solving nonlinear problems. The book also provides numerical simulation procedures of widely-used random variables and stochastic processes. A large number of exercise problems are included in the book to aid the understanding of the concepts and theories, and may be used for as course homework.

Stochastic Dynamics And Control

Author : Jian-Qiao Sun
ISBN : 0080463983
Genre : Mathematics
File Size : 46. 17 MB
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This book is a result of many years of author’s research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress processes are also presented. Classical feedback control, active damping, covariance control, optimal control, sliding control of stochastic systems, feedback control of stochastic time-delayed systems, and probability density tracking control are studied. Many control results are new in the literature and included in this book for the first time. The book serves as a reference to the engineers who design and maintain structures subject to harsh random excitations including earthquakes, sea waves, wind gusts, and aerodynamic forces, and would like to reduce the damages of structural systems due to random excitations. · Comprehensive review of probability theory, and stochastic processes · Random vibrations · Structural reliability and fatigue, Non-Gaussian fatigue · Monte Carlo methods · Stochastic calculus and engineering applications · Stochastic feedback controls and optimal controls · Stochastic sliding mode controls · Feedback control of stochastic time-delayed systems · Probability density tracking control

An Introduction To Stochastic Dynamics

Author : Jinqiao Duan
ISBN : 9781107075399
Genre : Mathematics
File Size : 86. 62 MB
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An accessible introduction for applied mathematicians to concepts and techniques for describing, quantifying, and understanding dynamics under uncertainty.

Stochastic Dynamics Filtering And Optimization

Author : Debasish Roy
ISBN : 9781107182646
Genre : Technology & Engineering
File Size : 55. 4 MB
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Targeted at graduate students, researchers and practitioners in the field of science and engineering, this book gives a self-contained introduction to a measure-theoretic framework in laying out the definitions and basic concepts of random variables and stochastic diffusion processes. It then continues to weave into a framework of several practical tools and applications involving stochastic dynamical systems. These include tools for the numerical integration of such dynamical systems, nonlinear stochastic filtering and generalized Bayesian update theories for solving inverse problems and a new stochastic search technique for treating a broad class of non-convex optimization problems. MATLAB codes for all the applications are uploaded on the companion website.

Stochastic Dynamics Of Structures

Author : Jie Li
ISBN : 0470824255
Genre : Technology & Engineering
File Size : 75. 78 MB
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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

Computational Methods In Stochastic Dynamics

Author : Manolis Papadrakakis
ISBN : 9789400751347
Genre : Technology & Engineering
File Size : 90. 17 MB
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The considerable influence of inherent uncertainties on structural behavior has led the engineering community to recognize the importance of a stochastic approach to structural problems. Issues related to uncertainty quantification and its influence on the reliability of the computational models are continuously gaining in significance. In particular, the problems of dynamic response analysis and reliability assessment of structures with uncertain system and excitation parameters have been the subject of continuous research over the last two decades as a result of the increasing availability of powerful computing resources and technology. This book is a follow up of a previous book with the same subject (ISBN 978-90-481-9986-0) and focuses on advanced computational methods and software tools which can highly assist in tackling complex problems in stochastic dynamic/seismic analysis and design of structures. The selected chapters are authored by some of the most active scholars in their respective areas and represent some of the most recent developments in this field. The book consists of 21 chapters which can be grouped into several thematic topics including dynamic analysis of stochastic systems, reliability-based design, structural control and health monitoring, model updating, system identification, wave propagation in random media, seismic fragility analysis and damage assessment. This edited book is primarily intended for researchers and post-graduate students who are familiar with the fundamentals and wish to study or to advance the state of the art on a particular topic in the field of computational stochastic structural dynamics. Nevertheless, practicing engineers could benefit as well from it as most code provisions tend to incorporate probabilistic concepts in the analysis and design of structures.

Stochastic Dynamics Of Marine Structures

Author : Arvid Naess
ISBN : 9780521881555
Genre : Mathematics
File Size : 67. 22 MB
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For students and professionals, this covers theory and methods for stochastic modelling and analysis of marine structures under environmental loads.

Stochastic Structural Dynamics

Author : Cho W. S. To
ISBN : 9781118402726
Genre : Mathematics
File Size : 43. 59 MB
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One of the first books to provide in-depth and systematic application of finite element methods to the field of stochastic structural dynamics The parallel developments of the Finite Element Methods in the 1950’s and the engineering applications of stochastic processes in the 1940’s provided a combined numerical analysis tool for the studies of dynamics of structures and structural systems under random loadings. In the open literature, there are books on statistical dynamics of structures and books on structural dynamics with chapters dealing with random response analysis. However, a systematic treatment of stochastic structural dynamics applying the finite element methods seems to be lacking. Aimed at advanced and specialist levels, the author presents and illustrates analytical and direct integration methods for analyzing the statistics of the response of structures to stochastic loads. The analysis methods are based on structural models represented via the Finite Element Method. In addition to linear problems the text also addresses nonlinear problems and non-stationary random excitation with systems having large spatially stochastic property variations. A systematic treatment of stochastic structural dynamics applying the finite element methods Highly illustrated throughout and aimed at advanced and specialist levels, it focuses on computational aspects instead of theory Emphasizes results mainly in the time domain with limited contents in the time-frequency domain Presents and illustrates direction integration methods for analyzing the statistics of the response of linear and nonlinear structures to stochastic loads Under Author Information - one change of word to existing text: He is a Fellow of the American Society of Mechanical Engineers (ASME)........

Stochastic Differential Equations

Author : Michael J. Panik
ISBN : 9781119377382
Genre : Mathematics
File Size : 79. 73 MB
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A beginner’s guide to stochastic growth modeling The chief advantage of stochastic growth models over deterministic models is that they combine both deterministic and stochastic elements of dynamic behaviors, such as weather, natural disasters, market fluctuations, and epidemics. This makes stochastic modeling a powerful tool in the hands of practitioners in fields for which population growth is a critical determinant of outcomes. However, the background requirements for studying SDEs can be daunting for those who lack the rigorous course of study received by math majors. Designed to be accessible to readers who have had only a few courses in calculus and statistics, this book offers a comprehensive review of the mathematical essentials needed to understand and apply stochastic growth models. In addition, the book describes deterministic and stochastic applications of population growth models including logistic, generalized logistic, Gompertz, negative exponential, and linear. Ideal for students and professionals in an array of fields including economics, population studies, environmental sciences, epidemiology, engineering, finance, and the biological sciences, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling: • Provides precise definitions of many important terms and concepts and provides many solved example problems • Highlights the interpretation of results and does not rely on a theorem-proof approach • Features comprehensive chapters addressing any background deficiencies readers may have and offers a comprehensive review for those who need a mathematics refresher • Emphasizes solution techniques for SDEs and their practical application to the development of stochastic population models An indispensable resource for students and practitioners with limited exposure to mathematics and statistics, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling is an excellent fit for advanced undergraduates and beginning graduate students, as well as practitioners who need a gentle introduction to SDEs. Michael J. Panik, PhD, is Professor in the Department of Economics, Barney School of Business and Public Administration at the University of Hartford in Connecticut. He received his PhD in Economics from Boston College and is a member of the American Mathematical Society, The American Statistical Association, and The Econometric Society.

Iutam Symposium On Nonlinear Stochastic Dynamics

Author : N. Sri Namachchivaya
ISBN : 1402014716
Genre : Mathematics
File Size : 64. 54 MB
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Non-linear stochastic systems are at the center of many engineering disciplines and progress in theoretical research had led to a better understanding of non-linear phenomena. This book provides information on new fundamental results and their applications which are beginning to appear across the entire spectrum of mechanics. The outstanding points of these proceedings are Coherent compendium of the current state of modelling and analysis of non-linear stochastic systems from engineering, applied mathematics and physics point of view. Subject areas include: Multiscale phenomena, stability and bifurcations, control and estimation, computational methods and modelling. For the Engineering and Physics communities, this book will provide first-hand information on recent mathematical developments. The applied mathematics community will benefit from the modelling and information on various possible applications.

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