Author : Chakraverty, S.
Publisher : IGI Global
Page : 442 pages
File Size : 48,97 MB
Release : 2014-01-31
Category : Mathematics
ISBN : 1466649925
"This book provides the reader with basic concepts for soft computing and other methods for various means of uncertainty in handling solutions, analysis, and applications"--Provided by publisher.
Author : Snehashish Chakraverty
Publisher :
Page : 0 pages
File Size : 31,88 MB
Release : 2014
Category : Civil engineering
ISBN : 9781466649941
"This book provides the reader with basic concepts for soft computing and other methods for various means of uncertainty in handling solutions, analysis, and applications"--
Author : Bilal Ayyub
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 32,77 MB
Release : 1997-10-31
Category : Computers
ISBN : 9780792380306
Uncertainty has been of concern to engineers, managers and . scientists for many centuries. In management sciences there have existed definitions of uncertainty in a rather narrow sense since the beginning of this century. In engineering and uncertainty has for a long time been considered as in sciences, however, synonymous with random, stochastic, statistic, or probabilistic. Only since the early sixties views on uncertainty have ~ecome more heterogeneous and more tools to model uncertainty than statistics have been proposed by several scientists. The problem of modeling uncertainty adequately has become more important the more complex systems have become, the faster the scientific and engineering world develops, and the more important, but also more difficult, forecasting of future states of systems have become. The first question one should probably ask is whether uncertainty is a phenomenon, a feature of real world systems, a state of mind or a label for a situation in which a human being wants to make statements about phenomena, i. e. , reality, models, and theories, respectively. One cart also ask whether uncertainty is an objective fact or just a subjective impression which is closely related to individual persons. Whether uncertainty is an objective feature of physical real systems seems to be a philosophical question. This shall not be answered in this volume.
Author : Subrat Kumar Jena
Publisher : CRC Press
Page : 162 pages
File Size : 31,35 MB
Release : 2024-12-09
Category : Technology & Engineering
ISBN : 1040154727
The uncertainties or randomness of the material properties of structural components are of serious concern to engineers. Structural analysis is usually done by taking into account only deterministic or crisp parameters; however, building materials can have the aspects of uncertainty. The causes of this uncertainty or randomness are defects in atomic configurations, measurement errors, environmental conditions, and other factors. The influence of uncertainties is more profound for nanoscale and microstructures due to their small-scale effects. Several nanoscale experiments and molecular dynamics studies also support the claim of possible attachment of randomness for various parameters. With regard to these concerns, it is necessary to propose new models that specifically integrate and effectively overcome imprecisely defined parameters of the system. Structural Dynamics in Uncertain Environments presents the uncertainty modeling of nanobeams, microbeams, and Funtionally Graded (FG) beams using non-probabilistic approaches which include interval and fuzzy concepts. Vibration and stability analyses of the beams are conducted using different analytical, semi-analytical, and numerical methods for finding exact and/or approximate solutions of governing equations arising in uncertain environments. In this context, this book addresses structural uncertainties and investigates the dynamic behavior of micro-, nano-, and FG beams. Examines the concepts of fuzzy uncertain environments in structural dynamics Presents comprehensive analysis of propagation of uncertainty in vibration and buckling analyses Explains efficient mathematical methods to handle uncertainties in the governing equations
Author : Snehashish Chakraverty
Publisher : John Wiley & Sons
Page : 324 pages
File Size : 19,2 MB
Release : 2016-08-09
Category : Mathematics
ISBN : 1119004179
Presents a systematic treatment of fuzzy fractional differential equations as well as newly developed computational methods to model uncertain physical problems Complete with comprehensive results and solutions, Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications details newly developed methods of fuzzy computational techniquesneeded to model solve uncertainty. Fuzzy differential equations are solved via various analytical andnumerical methodologies, and this book presents their importance for problem solving, prototypeengineering design, and systems testing in uncertain environments. In recent years, modeling of differential equations for arbitrary and fractional order systems has been increasing in its applicability, and as such, the authors feature examples from a variety of disciplines to illustrate the practicality and importance of the methods within physics, applied mathematics, engineering, and chemistry, to name a few. The fundamentals of fractional differential equations and the basic preliminaries of fuzzy fractional differential equations are first introduced, followed by numerical solutions, comparisons of various methods, and simulated results. In addition, fuzzy ordinary, partial, linear, and nonlinear fractional differential equations are addressed to solve uncertainty in physical systems. In addition, this book features: Basic preliminaries of fuzzy set theory, an introduction of fuzzy arbitrary order differential equations, and various analytical and numerical procedures for solving associated problems Coverage on a variety of fuzzy fractional differential equations including structural, diffusion, and chemical problems as well as heat equations and biomathematical applications Discussions on how to model physical problems in terms of nonprobabilistic methods and provides systematic coverage of fuzzy fractional differential equations and its applications Uncertainties in systems and processes with a fuzzy concept Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications is an ideal resource for practitioners, researchers, and academicians in applied mathematics, physics, biology, engineering, computer science, and chemistry who need to model uncertain physical phenomena and problems. The book is appropriate for graduate-level courses on fractional differential equations for students majoring in applied mathematics, engineering, physics, and computer science.
Author : Management Association, Information Resources
Publisher : IGI Global
Page : 2107 pages
File Size : 33,81 MB
Release : 2015-01-31
Category : Science
ISBN : 1466674571
Across a variety of disciplines, data and statistics form the backbone of knowledge. To ensure the reliability and validity of data, appropriate measures must be taken in conducting studies and reporting findings. Research Methods: Concepts, Methodologies, Tools, and Applications compiles chapters on key considerations in the management, development, and distribution of data. With its focus on both fundamental concepts and advanced topics, this multi-volume reference work will be a valuable addition to researchers, scholars, and students of science, mathematics, and engineering.
Author : Snehashish Chakraverty
Publisher : John Wiley & Sons
Page : 276 pages
File Size : 49,10 MB
Release : 2019-04-10
Category : Mathematics
ISBN : 1119423430
Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along. Featuring both traditional and recent methods, Advanced Numerical and Semi Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced next. The book then discusses Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM). Following that, analytical/semi analytic methods like Akbari Ganji's Method (AGM) and Exp-function are used to solve nonlinear differential equations. Nonlinear differential equations using semi-analytical methods are also addressed, namely Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM). Other topics covered include: emerging areas of research related to the solution of differential equations based on differential quadrature and wavelet approach; combined and hybrid methods for solving differential equations; as well as an overview of fractal differential equations. Further, uncertainty in term of intervals and fuzzy numbers have also been included, along with the interval finite element method. This book: Discusses various methods for solving linear and nonlinear ODEs and PDEs Covers basic numerical techniques for solving differential equations along with various discretization methods Investigates nonlinear differential equations using semi-analytical methods Examines differential equations in an uncertain environment Includes a new scenario in which uncertainty (in term of intervals and fuzzy numbers) has been included in differential equations Contains solved example problems, as well as some unsolved problems for self-validation of the topics covered Advanced Numerical and Semi Analytical Methods for Differential Equations is an excellent text for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically.
Author : Isaac Elishakoff
Publisher : Walter de Gruyter GmbH & Co KG
Page : 384 pages
File Size : 40,90 MB
Release : 2024-09-23
Category : Technology & Engineering
ISBN : 3111354237
The book exposes three alternative and competing approaches to uncertainty analysis in engineering. It is composed of some essays on various sub-topics like random vibrations, probabilistic reliability, fuzzy-sets-based analysis, unknown-but-bounded variables, stochastic linearization, possible difficulties with stochastic analysis of structures.
Author : Hasan, Osman
Publisher : IGI Global
Page : 310 pages
File Size : 21,47 MB
Release : 2015-03-31
Category : Mathematics
ISBN : 1466683163
Scientists and engineers often have to deal with systems that exhibit random or unpredictable elements and must effectively evaluate probabilities in each situation. Computer simulations, while the traditional tool used to solve such problems, are limited in the scale and complexity of the problems they can solve. Formalized Probability Theory and Applications Using Theorem Proving discusses some of the limitations inherent in computer systems when applied to problems of probabilistic analysis, and presents a novel solution to these limitations, combining higher-order logic with computer-based theorem proving. Combining practical application with theoretical discussion, this book is an important reference tool for mathematicians, scientists, engineers, and researchers in all STEM fields.
Author : Sergio E. Serrano
Publisher : Hydroscience Incorporated
Page : 461 pages
File Size : 49,29 MB
Release : 2011
Category : Technology & Engineering
ISBN : 9780965564311
Engineering Uncertainty and Risk Analysis offers an integrated coverage of the subjects of probability, statistics, Monte Carlo simulation, descriptive and inferential statistics, design of experiments, systems reliability, fitting random data to models, analysis of variance (ANOVA), stochastic processes, and stochastic differential equations. The author for first time presents an introduction to the broad field of engineering uncertainty analysis in one comprehensive, friendly, coverage. The focus is on engineering applications, rather than theoretical or mathematical considerations. Each concept is illustrated with several examples (177 solved examples) of relevance in engineering applications (no cards, colored balls, or dice). This second edition includes many new research advances in nonlinear stochastic equations; new simple methods to solve and graph boundary-value problems in several dimensions without the need of perturbation, or complex traditional analytical or numerical techniques; 478 pages; 177 solved examples; 147 proposed problems; 174 illustrations, 69 short computer programs; and 51 data and statistical tables
