Digital Processing Of Random Oscillations
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Digital Processing Of Random Oscillations
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Author : Viacheslav Karmalita
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-06-17
Digital Processing Of Random Oscillations written by Viacheslav Karmalita and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-17 with Technology & Engineering categories.
This book deals with the autoregressive method for digital processing of random oscillations. The method is based on a one-to-one transformation of the numeric factors of the Yule series model to linear elastic system characteristics. This parametric approach allowed to develop a formal processing procedure from the experimental data to obtain estimates of logarithmic decrement and natural frequency of random oscillations. A straightforward mathematical description of the procedure makes it possible to optimize a discretization of oscillation realizations providing efficient estimates. The derived analytical expressions for confidence intervals of estimates enable a priori evaluation of their accuracy. Experimental validation of the method is also provided. Statistical applications for the analysis of mechanical systems arise from the fact that the loads experienced by machineries and various structures often cannot be described by deterministic vibration theory. Therefore, a sufficient description of real oscillatory processes (vibrations) calls for the use of random functions. In engineering practice, the linear vibration theory (modeling phenomena by common linear differential equations) is generally used. This theory’s fundamental concepts such as natural frequency, oscillation decrement, resonance, etc. are credited for its wide use in different technical tasks. In technical applications two types of research tasks exist: direct and inverse. The former allows to determine stochastic characteristics of the system output X(t) resulting from a random process E(t) when the object model is considered known. The direct task enables to evaluate the effect of an operational environment on the designed object and to predict its operation under various loads. The inverse task is aimed at evaluating the object model on known processes E(t) and X(t), i.e. finding model (equations) factors. This task is usually met at the tests of prototypes to identify (or verify) its model experimentally. To characterize random processes a notion of "shaping dynamic system" is commonly used. This concept allows to consider the observing process as the output of a hypothetical system with the input being stationary Gauss-distributed ("white") noise. Therefore, the process may be exhaustively described in terms of parameters of that system. In the case of random oscillations, the "shaping system" is an elastic system described by the common differential equation of the second order: X ̈(t)+2hX ̇(t)+ ω_0^2 X(t)=E(t), where ω0 = 2π/Т0 is the natural frequency, T0 is the oscillation period, and h is a damping factor. As a result, the process X(t) can be characterized in terms of the system parameters – natural frequency and logarithmic oscillations decrement δ = hT0 as well as the process variance. Evaluation of these parameters is subjected to experimental data processing based on frequency or time-domain representations of oscillations. It must be noted that a concept of these parameters evaluation did not change much during the last century. For instance, in case of the spectral density utilization, evaluation of the decrement values is linked with bandwidth measurements at the points of half-power of the observed oscillations. For a time-domain presentation, evaluation of the decrement requires measuring covariance values delayed by a time interval divisible by T0. Both estimation procedures are derived from a continuous description of research phenomena, so the accuracy of estimates is linked directly to the adequacy of discrete representation of random oscillations. This approach is similar a concept of transforming differential equations to difference ones with derivative approximation by corresponding finite differences. The resulting discrete model, being an approximation, features a methodical error which can be decreased but never eliminated. To render such a presentation more accurate it is imperative to decrease the discretization interval and to increase realization size growing requirements for computing power. The spectral density and covariance function estimates comprise a non-parametric (non-formal) approach. In principle, any non-formal approach is a kind of art i.e. the results depend on the performer’s skills. Due to interference of subjective factors in spectral or covariance estimates of random signals, accuracy of results cannot be properly determined or justified. To avoid the abovementioned difficulties, the application of linear time-series models with well-developed procedures for parameter estimates is more advantageous. A method for the analysis of random oscillations using a parametric model corresponding discretely (no approximation error) with a linear elastic system is developed and presented in this book. As a result, a one-to-one transformation of the model’s numerical factors to logarithmic decrement and natural frequency of random oscillations is established. It allowed to develop a formal processing procedure from experimental data to obtain the estimates of δ and ω0. The proposed approach allows researchers to replace traditional subjective techniques by a formal processing procedure providing efficient estimates with analytically defined statistical uncertainties.
Digital Processing Of Random Signals
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Author : Boaz Porat
language : en
Publisher:
Release Date : 1994
Digital Processing Of Random Signals written by Boaz Porat and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
An Introduction To Random Vibrations Spectral Wavelet Analysis
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Author : D. E. Newland
language : en
Publisher: Courier Corporation
Release Date : 2012-04-03
An Introduction To Random Vibrations Spectral Wavelet Analysis written by D. E. Newland and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-03 with Science categories.
One of the first engineering books to cover wavelet analysis, this classic text describes and illustrates basic theory, with a detailed explanation of the workings of discrete wavelet transforms. Computer algorithms are explained and supported by examples and a set of problems, and an appendix lists ten computer programs for calculating and displaying wavelet transforms. Starting with an introduction to probability distributions and averages, the text examines joint probability distributions, ensemble averages, and correlation; Fourier analysis; spectral density and excitation response relations for linear systems; transmission of random vibration; statistics of narrow band processes; and accuracy of measurements. Discussions of digital spectral analysis cover discrete Fourier transforms as well as windows and smoothing. Additional topics include the fast Fourier transform; pseudo-random processes; multidimensional spectral analysis; response of continuous linear systems to stationary random excitation; and discrete wavelet analysis. Numerous diagrams and graphs clarify the text, and complicated mathematics are simplified whenever possible. This volume is suitable for upper-level undergraduates and graduate students in engineering and the applied sciences; it is also an important resource for professionals.
Digital Picture Processing
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Author : Azriel Rosenfeld
language : en
Publisher: Elsevier
Release Date : 2014-01-09
Digital Picture Processing written by Azriel Rosenfeld and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-09 with Computers categories.
The rapid rate at which the field of digital picture processing has grown in the past five years had necessitated extensive revisions and the introduction of topics not found in the original edition.
Plant Intelligent Automation And Digital Transformation
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Author : Swapan Basu
language : en
Publisher: Academic Press
Release Date : 2022-10-28
Plant Intelligent Automation And Digital Transformation written by Swapan Basu and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-28 with Technology & Engineering categories.
Plant Intelligent Automation and Digital Transformation: Process and Factory Automation is an expansive four volume collection reviewing every major aspect of the intelligent automation and digital transformation of power, process and manufacturing plants, from the specific control and automation systems pertinent to various power process plants through manufacturing and factory automation systems. This volume introduces the foundations of automation control theory, networking practices and communication for power, process and manufacturing plants considered as integrated digital systems. In addition, it discusses Distributed control System (DCS) for Closed loop controls system (CLCS) and PLC based systems for Open loop control systems (OLCS) and factory automation. This book provides in-depth guidance on functional and design details pertinent to each of the control types referenced above, along with the installation and commissioning of control systems. Introduces the foundations of control systems, networking and industrial data communications for power, process and manufacturing plant automation Reviews core functions, design details and optimized configurations of plant digital control systems Addresses advanced process control for digital control systems (inclusive of software implementations) Provides guidance for installation commissioning of control systems in working plants
Cybernetics Abstracts
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Author :
language : en
Publisher:
Release Date : 1987
Cybernetics Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Cybernetics categories.
Chaotic Oscillators
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Author : Tomasz Kapitaniak
language : en
Publisher: World Scientific
Release Date : 1992
Chaotic Oscillators written by Tomasz Kapitaniak and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Science categories.
This volume brings together a comprehensive selection of over fifty reprints on the theory and applications of chaotic oscillators. Included are fundamental mathematical papers describing methods for the investigation of chaotic behavior in oscillatory systems as well as the most important applications in physics and engineering. There is currently no book similar to this collection.
Digital Signal Processing
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Author : Abdaheer
language : en
Publisher: Firewall Media
Release Date : 2007-01-01
Digital Signal Processing written by Abdaheer and has been published by Firewall Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with categories.
The Noisy Oscillator
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Author : Moshe Gitterman
language : en
Publisher: World Scientific Publishing Company
Release Date : 2012-12-18
The Noisy Oscillator written by Moshe Gitterman and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-18 with Science categories.
The properties of the harmonic oscillator with random frequency or/and random damping formed the content of the first edition. The second edition includes hundreds of publications on this subject since 2005. The noisy oscillator continues to be the subject of intensive studies in physics, chemistry, biology, and social sciences. The new and the latest type of a stochastic oscillator has also been considered, namely, an oscillator with random mass. Such model describes, among other phenomena, Brownian motion with adhesion, where the molecules of the surrounding medium not only randomly collide, but also stick to the Brownian particle for some (random) time, thereby changing its mass. This edition contains two new chapters, eight new sections and an expanded bibliography. A wide group of researchers, students and teachers will benefit from this book.
Stochastic Dynamics Of Economic Cycles
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Author : Viacheslav Karmalita
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-10-12
Stochastic Dynamics Of Economic Cycles written by Viacheslav Karmalita and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-12 with Mathematics categories.
This book exposes the theory under the phenomenon of economic cycles and provides mathematical tools for their quantitative description. The approach allows to provide the stochastic description of the investment function, to recover the income function from GDP estimates, and to propose the identification procedure for pseudo-stationary models of economic cycles. .