Fundamentals Of Uncertainty Quantification For Engineers
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Fundamentals Of Uncertainty Quantification For Engineers
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Author : Yan Wang
language : en
Publisher: Elsevier
Release Date : 2025-05-30
Fundamentals Of Uncertainty Quantification For Engineers written by Yan Wang and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-30 with Technology & Engineering categories.
Fundamentals of Uncertainty Quantification for Engineers: Methods and Models provides a comprehensive introduction to uncertainty quantification (UQ) accompanied by a wide variety of applied examples and implementation details to reinforce the concepts outlined in the book. Sections start with an introduction to the history of probability theory and an overview of recent developments of UQ methods in the domains of applied mathematics and data science. Major concepts of copula, Monte Carlo sampling, Markov chain Monte Carlo, polynomial regression, Gaussian process regression, polynomial chaos expansion, stochastic collocation, Bayesian inference, modelform uncertainty, multi-fidelity modeling, model validation, local and global sensitivity analyses, linear and nonlinear dimensionality reduction are included. Advanced UQ methods are also introduced, including stochastic processes, stochastic differential equations, random fields, fractional stochastic differential equations, hidden Markov model, linear Gaussian state space model, as well as non-probabilistic methods such as robust Bayesian analysis, Dempster-Shafer theory, imprecise probability, and interval probability. The book also includes example applications in multiscale modeling, reliability, fatigue, materials design, machine learning, and decision making. • Introduces all major topics of uncertainty quantification with engineering examples and implementation details• Features examples from a wide variety of science and engineering disciplines (e.g., fluids, structural dynamics, materials, manufacturing, multiscale simulation)• Discusses sampling methods, surrogate modeling, stochastic expansion, sensitivity analysis, dimensionality reduction and more
Uncertainty Quantification And Predictive Computational Science
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Author : Ryan G. McClarren
language : en
Publisher: Springer
Release Date : 2018-11-23
Uncertainty Quantification And Predictive Computational Science written by Ryan G. McClarren and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-23 with Science categories.
This textbook teaches the essential background and skills for understanding and quantifying uncertainties in a computational simulation, and for predicting the behavior of a system under those uncertainties. It addresses a critical knowledge gap in the widespread adoption of simulation in high-consequence decision-making throughout the engineering and physical sciences. Constructing sophisticated techniques for prediction from basic building blocks, the book first reviews the fundamentals that underpin later topics of the book including probability, sampling, and Bayesian statistics. Part II focuses on applying Local Sensitivity Analysis to apportion uncertainty in the model outputs to sources of uncertainty in its inputs. Part III demonstrates techniques for quantifying the impact of parametric uncertainties on a problem, specifically how input uncertainties affect outputs. The final section covers techniques for applying uncertainty quantification to make predictions under uncertainty, including treatment of epistemic uncertainties. It presents the theory and practice of predicting the behavior of a system based on the aggregation of data from simulation, theory, and experiment. The text focuses on simulations based on the solution of systems of partial differential equations and includes in-depth coverage of Monte Carlo methods, basic design of computer experiments, as well as regularized statistical techniques. Code references, in python, appear throughout the text and online as executable code, enabling readers to perform the analysis under discussion. Worked examples from realistic, model problems help readers understand the mechanics of applying the methods. Each chapter ends with several assignable problems. Uncertainty Quantification and Predictive Computational Science fills the growing need for a classroom text for senior undergraduate and early-career graduate students in the engineering and physical sciences and supports independent study by researchers and professionals who must include uncertainty quantification and predictive science in the simulations they develop and/or perform.
Uncertainty Quantification
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Author : Ralph C. Smith
language : en
Publisher: SIAM
Release Date : 2013-12-02
Uncertainty Quantification written by Ralph C. Smith and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-02 with Science categories.
The field of uncertainty quantification is evolving rapidly because of increasing emphasis on models that require quantified uncertainties for large-scale applications, novel algorithm development, and new computational architectures that facilitate implementation of these algorithms. Uncertainty Quantification: Theory, Implementation, and Applications provides readers with the basic concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models arising in a broad range of disciplines. The book begins with a detailed discussion of applications where uncertainty quantification is critical for both scientific understanding and policy. It then covers concepts from probability and statistics, parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, surrogate model construction, and local and global sensitivity analysis. The author maintains a complementary web page where readers can find data used in the exercises and other supplementary material.
Verification And Validation In Scientific Computing
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Author : William L. Oberkampf
language : en
Publisher: Cambridge University Press
Release Date : 2010-10-14
Verification And Validation In Scientific Computing written by William L. Oberkampf 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 2010-10-14 with Computers categories.
Advances in scientific computing have made modelling and simulation an important part of the decision-making process in engineering, science, and public policy. This book provides a comprehensive and systematic development of the basic concepts, principles, and procedures for verification and validation of models and simulations. The emphasis is placed on models that are described by partial differential and integral equations and the simulations that result from their numerical solution. The methods described can be applied to a wide range of technical fields, from the physical sciences, engineering and technology and industry, through to environmental regulations and safety, product and plant safety, financial investing, and governmental regulations. This book will be genuinely welcomed by researchers, practitioners, and decision makers in a broad range of fields, who seek to improve the credibility and reliability of simulation results. It will also be appropriate either for university courses or for independent study.
Fundamentals Of Ordinary Differential Equations
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Author : Mohit Chatterjee
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Fundamentals Of Ordinary Differential Equations written by Mohit Chatterjee and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Fundamentals of Ordinary Differential Equations" is a comprehensive guide designed for students, researchers, and professionals to master ODE theory and applications. We cover essential principles, advanced techniques, and practical applications, providing a well-rounded resource for understanding differential equations and their real-world impact. The book offers a multifaceted approach, from basic principles to advanced concepts, catering to fields like physics, engineering, biology, and economics. Mathematical ideas are broken down with step-by-step explanations, examples, and illustrations, making complex concepts accessible. Real-world examples throughout each chapter show how ODEs model and analyze systems in diverse disciplines. We also explain numerical methods such as Euler’s method, Runge-Kutta, and finite differences, equipping readers with computational tools for solving ODEs. Advanced topics include bifurcation, chaos theory, Hamiltonian systems, and singular perturbations, providing an in-depth grasp of ODE topics. With chapter summaries, exercises, glossaries, and additional resources, "Fundamentals of Ordinary Differential Equations" is an essential reference for students, professionals, and practitioners across science and engineering fields.
Engineering Design Reliability Handbook
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Author : Efstratios Nikolaidis
language : en
Publisher: CRC Press
Release Date : 2004-12-22
Engineering Design Reliability Handbook written by Efstratios Nikolaidis and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-22 with Mathematics categories.
Researchers in the engineering industry and academia are making important advances on reliability-based design and modeling of uncertainty when data is limited. Non deterministic approaches have enabled industries to save billions by reducing design and warranty costs and by improving quality. Considering the lack of comprehensive and defini
Structural Engineering
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Author : Adnan Ibrahimbegovic
language : en
Publisher: Springer Nature
Release Date : 2023-02-23
Structural Engineering written by Adnan Ibrahimbegovic and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-23 with Technology & Engineering categories.
This book presents a novel approach to the classical scientific discipline of Structural Engineering, which is inspired by numerous current applications from domains of Civil, Mechanical or Aerospace Engineering. The main goal of this book is to help with making the best choice between accuracy and efficiency, when it comes to building the most suitable structural models by practising engineers using modern computational tools available in commercial software products (SAP, FEAP, ANSYS ...) for which we have carried out many developments that have been become the main reference in the field. Any development of this kind is not a mere modification of discrete approximation, but a thorough treatment with a sound theoretical formulation based upon Hu-Washizu variational principle with independent rotation field, its corresponding regularization and finally the most appropriate finite element interpolation that can match those used for structural elements. Proposed approach allows us to provide a unified discrete approximation of complex structural assemblies and greatly simplify the modeling task for structural engineers. Thus, in conclusion, this book can also be perceived as the theoretical manual for using modern computer models successfully by practising engineers.
Assessing The Reliability Of Complex Models
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Author : National Research Council
language : en
Publisher: National Academies Press
Release Date : 2012-07-26
Assessing The Reliability Of Complex Models written by National Research Council and has been published by National Academies Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-26 with Mathematics categories.
Advances in computing hardware and algorithms have dramatically improved the ability to simulate complex processes computationally. Today's simulation capabilities offer the prospect of addressing questions that in the past could be addressed only by resource-intensive experimentation, if at all. Assessing the Reliability of Complex Models recognizes the ubiquity of uncertainty in computational estimates of reality and the necessity for its quantification. As computational science and engineering have matured, the process of quantifying or bounding uncertainties in a computational estimate of a physical quality of interest has evolved into a small set of interdependent tasks: verification, validation, and uncertainty of quantification (VVUQ). In recognition of the increasing importance of computational simulation and the increasing need to assess uncertainties in computational results, the National Research Council was asked to study the mathematical foundations of VVUQ and to recommend steps that will ultimately lead to improved processes. Assessing the Reliability of Complex Models discusses changes in education of professionals and dissemination of information that should enhance the ability of future VVUQ practitioners to improve and properly apply VVUQ methodologies to difficult problems, enhance the ability of VVUQ customers to understand VVUQ results and use them to make informed decisions, and enhance the ability of all VVUQ stakeholders to communicate with each other. This report is an essential resource for all decision and policy makers in the field, students, stakeholders, UQ experts, and VVUQ educators and practitioners.
Princeton Companion To Applied Mathematics
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Author : Nicholas J. Higham
language : en
Publisher: Princeton University Press
Release Date : 2015-09-09
Princeton Companion To Applied Mathematics written by Nicholas J. Higham and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-09 with Mathematics categories.
The must-have compendium on applied mathematics This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index
Engineering Emergence
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Author : Larry B. Rainey
language : en
Publisher: CRC Press
Release Date : 2018-09-03
Engineering Emergence written by Larry B. Rainey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Technology & Engineering categories.
This book examines the nature of emergence in context of man-made (i.e. engineered) systems, in general, and system of systems engineering applications, specifically. It investigates emergence to interrogate or explore the domain space from a modeling and simulation perspective to facilitate understanding, detection, classification, prediction, control, and visualization of the phenomenon. Written by leading international experts, the text is the first to address emergence from an engineering perspective. "System engineering has a long and proud tradition of establishing the integrative view of systems. The field, however, has not always embraced and assimilated well the lessons and implications from research on complex adaptive systems. As the editors’ note, there have been no texts on Engineering Emergence: Principles and Applications. It is therefore especially useful to have this new, edited book that pulls together so many of the key elements, ranging from the theoretical to the practical, and tapping into advances in methods, tools, and ways to study system complexity. Drs. Rainey and Jamshidi are to be congratulated both for their vision of the book and their success in recruiting contributors with so much to say. Most notable, however, is that this is a book with engineering at its core. It uses modeling and simulation as the language in which to express principles and insights in ways that include tight thinking and rigor despite dealing with notably untidy and often surprising phenomena." — Paul K. Davis, RAND and Frederick S. Pardee RAND Graduate School The first chapter is an introduction and overview to the text. The book provides 12 chapters that have a theoretical foundation for this subject. Includes 7 specific example chapters of how various modeling and simulation paradigms/techniques can be used to investigate emergence in an engineering context to facilitate understanding, detection, classification, prediction, control and visualization of emergent behavior. The final chapter offers lessons learned and the proposed way-ahead for this discipline.