Applied Methods of the Theory of Random Functions


Book Description

International Series of Monographs in Pure and Applied Mathematics, Volume 89: Applied Methods of the Theory of Random Functions presents methods of random functions analysis with their applications in various branches of technology, such as in the theory of ships, automatic regulation and control, and radio engineering. This book discusses the general properties of random functions, spectral theory of stationary random functions, and determination of optimal dynamical systems. The experimental methods for the determination of characteristics of random functions, method of envelopes, and some supplementary problems of the theory of random functions are also deliberated. This publication is intended for engineers and scientists who use the methods of the theory of probability in various branches of technology.




Fundamentals of Applied Probability and Random Processes


Book Description

The long-awaited revision of Fundamentals of Applied Probability and Random Processes expands on the central components that made the first edition a classic. The title is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability to real-world problems, and introduce the basics of statistics. The book's clear writing style and homework problems make it ideal for the classroom or for self-study. - Demonstrates concepts with more than 100 illustrations, including 2 dozen new drawings - Expands readers' understanding of disruptive statistics in a new chapter (chapter 8) - Provides new chapter on Introduction to Random Processes with 14 new illustrations and tables explaining key concepts. - Includes two chapters devoted to the two branches of statistics, namely descriptive statistics (chapter 8) and inferential (or inductive) statistics (chapter 9).




Theory of Random Functions


Book Description

Theory of Random Functions and Its Application to Control Problems presents insights into a branch of probability theory, the theory of random functions, which studies and takes into account the effects of random factors on the functioning of control systems. The book does not require a high level of competency in the use of mathematical techniques and explains the basics of probability theory before focusing on the concepts of the theory of random functions. The selection also discusses in great detail the aspects of random functions and provides chapters that cover the determination and solution to problems of optimal systems. The text will be of value to telecommunications engineers, aeronautical engineers, meteorologists, seismologists, and other professionals engaged in applied sciences.




Traffic and Random Processes


Book Description

This book deals in a basic and systematic manner with the fundamentals of random function theory and looks at some aspects related to arrival, vehicle headway and operational speed processes at the same time. The work serves as a useful practical and educational tool and aims at providing stimulus and motivation to investigate issues of such a strong applicative interest. It has a clearly discursive and concise structure, in which numerical examples are given to clarify the applications of the suggested theoretical model. Some statistical characterizations are fully developed in order to illustrate the peculiarities of specific modeling approaches; finally, there is a useful bibliography for in-depth thematic analysis.




Correlation Theory of Stationary and Related Random Functions


Book Description

Correlation Theory of Stationary and Related Random Functions is an elementary introduction to the most important part of the theory dealing only with the first and second moments of these functions. This theory is a significant part of modern probability theory and offers both intrinsic mathematical interest and many concrete and practical applications. Stationary random functions arise in connection with stationary time series which are so important in many areas of engineering and other applications. This book presents the theory in such a way that it can be understood by readers without specialized mathematical backgrounds, requiring only the knowledge of elementary calculus. The first volume in this two-volume exposition contains the main theory; the supplementary notes and references of the second volume consist of detailed discussions of more specialized questions, some more additional material (which assumes a more thorough mathematical background than the rest of the book) and numerous references to the extensive literature.




Dramatic Effect of Cross-Correlations in Random Vibrations of Discrete Systems, Beams, Plates, and Shells


Book Description

This volume explains the dramatic effect of cross-correlations in forming the structural response of aircraft in turbulent excitation, ships in rough seas, cars on irregular roads, and other dynamic regimes. It brings into sharp focus the dramatic effect of cross correlations often neglected due to the analytical difficulty of their evaluation. Veteran author Professor Isaac Elishakoff illustrates how neglect of cross correlations could result in underestimation of the response by tens or hundreds of percentages the effect of the random vibrations of structures’ main elements, including beams, plates, and shells.




Numerical Modelling of Random Processes and Fields


Book Description

No detailed description available for "Numerical Modelling of Random Processes and Fields".




Parametric Random Vibration


Book Description

This systematic treatment examines linear and nonlinear dynamical systems subject to parametric random vibrations. It formulates stochastic stability theorems and analytical techniques for determining random response of nonlinear systems. 1985 edition.




Random Vibration and Spectral Analysis/Vibrations aléatoires et analyse spectral


Book Description

I became interested in Random Vibration during the preparation of my PhD dissertation, which was concerned with the seismic response of nuclear reactor cores. I was initiated into this field through the cla.ssical books by Y.K.Lin, S.H.Crandall and a few others. After the completion of my PhD, in 1981, my supervisor M.Gera.din encouraged me to prepare a course in Random Vibration for fourth and fifth year students in Aeronautics, at the University of Liege. There was at the time very little material available in French on that subject. A first draft was produced during 1983 and 1984 and revised in 1986. These notes were published by the Presses Poly techniques et Universitaires Romandes (Lausanne, Suisse) in 1990. When Kluwer decided to publish an English translation ofthe book in 1992, I had to choose between letting Kluwer translate the French text in-extenso or doing it myself, which would allow me to carry out a sustantial revision of the book. I took the second option and decided to rewrite or delete some of the original text and include new material, based on my personal experience, or reflecting recent technical advances. Chapter 6, devoted to the response of multi degree offreedom structures, has been completely rewritten, and Chapter 11 on random fatigue is entirely new. The computer programs which have been developed in parallel with these chapters have been incorporated in the general purpose finite element software SAMCEF, developed at the University of Liege.




Lectures on Probability and Second Order Random Fields


Book Description

This book of lecture notes contains theoretical background material required for computer generation of random fields, which is of interest in various fields of applied mathematics.The necessary probabilistic background suitable for applied work in engineering as well as signal and image processing is also covered.The book is a valuable guide for higher level engineering students.