Mathematics Of Uncertainty Modeling In The Analysis Of Engineering And Science Problems
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Mathematics Of Uncertainty Modeling In The Analysis Of Engineering And Science Problems
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Author : Chakraverty, S.
language : en
Publisher: IGI Global
Release Date : 2014-01-31
Mathematics Of Uncertainty Modeling In The Analysis Of Engineering And Science Problems written by Chakraverty, S. and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-31 with Mathematics categories.
"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.
Mathematics Of Uncertainty Modeling In The Analysis Of Engineering And Science Problems
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Author : Snehashish Chakraverty
language : en
Publisher:
Release Date : 2014
Mathematics Of Uncertainty Modeling In The Analysis Of Engineering And Science Problems written by Snehashish Chakraverty and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Civil engineering categories.
"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"--
Formalized Probability Theory And Applications Using Theorem Proving
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Author : Hasan, Osman
language : en
Publisher: IGI Global
Release Date : 2015-03-31
Formalized Probability Theory And Applications Using Theorem Proving written by Hasan, Osman and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-31 with Mathematics categories.
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.
Uncertainty Analysis For Engineers And Scientists
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Author : Faith A. Morrison
language : en
Publisher: Cambridge University Press
Release Date : 2021-01-07
Uncertainty Analysis For Engineers And Scientists written by Faith A. Morrison and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-07 with Computers categories.
Build the skills for determining appropriate error limits for quantities that matter with this essential toolkit. Understand how to handle a complete project and how uncertainty enters into various steps. Provides a systematic, worksheet-based process to determine error limits on measured quantities, and all likely sources of uncertainty are explored, measured or estimated. Features instructions on how to carry out error analysis using Excel and MATLAB®, making previously tedious calculations easy. Whether you are new to the sciences or an experienced engineer, this useful resource provides a practical approach to performing error analysis. Suitable as a text for a junior or senior level laboratory course in aerospace, chemical and mechanical engineering, and for professionals.
Fuzzy Differential Equations And Applications For Engineers And Scientists
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Author : S. Chakraverty
language : en
Publisher: CRC Press
Release Date : 2016-11-25
Fuzzy Differential Equations And Applications For Engineers And Scientists written by S. Chakraverty and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-25 with Mathematics categories.
Differential equations play a vital role in the modeling of physical and engineering problems, such as those in solid and fluid mechanics, viscoelasticity, biology, physics, and many other areas. In general, the parameters, variables and initial conditions within a model are considered as being defined exactly. In reality there may be only vague, imprecise or incomplete information about the variables and parameters available. This can result from errors in measurement, observation, or experimental data; application of different operating conditions; or maintenance induced errors. To overcome uncertainties or lack of precision, one can use a fuzzy environment in parameters, variables and initial conditions in place of exact (fixed) ones, by turning general differential equations into Fuzzy Differential Equations ("FDEs"). In real applications it can be complicated to obtain exact solution of fuzzy differential equations due to complexities in fuzzy arithmetic, creating the need for use of reliable and efficient numerical techniques in the solution of fuzzy differential equations. These include fuzzy ordinary and partial, fuzzy linear and nonlinear, and fuzzy arbitrary order differential equations. This unique work?provides a new direction for the reader in the use of basic concepts of fuzzy differential equations, solutions and its applications. It can serve as an essential reference work for students, scholars, practitioners, researchers and academicians in engineering and science who need to model uncertain physical problems.
Uncertainty Modeling And Analysis In Engineering And The Sciences
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Author : Bilal M. Ayyub
language : en
Publisher: CRC Press
Release Date : 2006-05-25
Uncertainty Modeling And Analysis In Engineering And The Sciences written by Bilal M. Ayyub and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-25 with Business & Economics categories.
Engineers and scientists often need to solve complex problems with incomplete information resources, necessitating a proper treatment of uncertainty and a reliance on expert opinions. Uncertainty Modeling and Analysis in Engineering and the Sciences prepares current and future analysts and practitioners to understand the fundamentals of knowledge a
Multifaceted Uncertainty Quantification
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Author : Isaac Elishakoff
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-09-23
Multifaceted Uncertainty Quantification written by Isaac Elishakoff 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 2024-09-23 with Technology & Engineering categories.
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.
Advanced Numerical And Semi Analytical Methods For Differential Equations
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Author : Snehashish Chakraverty
language : en
Publisher: John Wiley & Sons
Release Date : 2019-04-16
Advanced Numerical And Semi Analytical Methods For Differential Equations written by Snehashish Chakraverty and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-16 with Mathematics categories.
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.
Fuzzy Arbitrary Order System
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Author : Snehashish Chakraverty
language : en
Publisher: John Wiley & Sons
Release Date : 2016-08-09
Fuzzy Arbitrary Order System written by Snehashish Chakraverty and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-09 with Mathematics categories.
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.
An Introduction To Data Analysis And Uncertainty Quantification For Inverse Problems
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Author : Luis Tenorio
language : en
Publisher: SIAM
Release Date : 2017-07-06
An Introduction To Data Analysis And Uncertainty Quantification For Inverse Problems written by Luis Tenorio and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-06 with Mathematics categories.
Inverse problems are found in many applications, such as medical imaging, engineering, astronomy, and geophysics, among others. To solve an inverse problem is to recover an object from noisy, usually indirect observations. Solutions to inverse problems are subject to many potential sources of error introduced by approximate mathematical models, regularization methods, numerical approximations for efficient computations, noisy data, and limitations in the number of observations; thus it is important to include an assessment of the uncertainties as part of the solution. Such assessment is interdisciplinary by nature, as it requires, in addition to knowledge of the particular application, methods from applied mathematics, probability, and statistics. This book bridges applied mathematics and statistics by providing a basic introduction to probability and statistics for uncertainty quantification in the context of inverse problems, as well as an introduction to statistical regularization of inverse problems. The author covers basic statistical inference, introduces the framework of ill-posed inverse problems, and explains statistical questions that arise in their applications. An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems?includes many examples that explain techniques which are useful to address general problems arising in uncertainty quantification, Bayesian and non-Bayesian statistical methods and discussions of their complementary roles, and analysis of a real data set to illustrate the methodology covered throughout the book.