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Uncertainty Quantification And Stochastic Modeling With Matlab

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Uncertainty Quantification and Stochastic Modeling with Matlab

Uncertainty Quantification and Stochastic Modeling with Matlab Book
Author : Eduardo Souza de Cursi,Rubens Sampaio
Publisher : Elsevier
Release : 2015-04-09
ISBN : 0081004710
Language : En, Es, Fr & De

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Book Description :

Uncertainty Quantification (UQ) is a relatively new research area which describes the methods and approaches used to supply quantitative descriptions of the effects of uncertainty, variability and errors in simulation problems and models. It is rapidly becoming a field of increasing importance, with many real-world applications within statistics, mathematics, probability and engineering, but also within the natural sciences. Literature on the topic has up until now been largely based on polynomial chaos, which raises difficulties when considering different types of approximation and does not lead to a unified presentation of the methods. Moreover, this description does not consider either deterministic problems or infinite dimensional ones. This book gives a unified, practical and comprehensive presentation of the main techniques used for the characterization of the effect of uncertainty on numerical models and on their exploitation in numerical problems. In particular, applications to linear and nonlinear systems of equations, differential equations, optimization and reliability are presented. Applications of stochastic methods to deal with deterministic numerical problems are also discussed. Matlab® illustrates the implementation of these methods and makes the book suitable as a textbook and for self-study. Discusses the main ideas of Stochastic Modeling and Uncertainty Quantification using Functional Analysis Details listings of Matlab® programs implementing the main methods which complete the methodological presentation by a practical implementation Construct your own implementations from provided worked examples

Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling

Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling Book
Author : José Eduardo Souza De Cursi
Publisher : Springer Nature
Release : 2020-08-19
ISBN : 3030536696
Language : En, Es, Fr & De

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Book Description :

This proceedings book discusses state-of-the-art research on uncertainty quantification in mechanical engineering, including statistical data concerning the entries and parameters of a system to produce statistical data on the outputs of the system. It is based on papers presented at Uncertainties 2020, a workshop organized on behalf of the Scientific Committee on Uncertainty in Mechanics (Mécanique et Incertain) of the AFM (French Society of Mechanical Sciences), the Scientific Committee on Stochastic Modeling and Uncertainty Quantification of the ABCM (Brazilian Society of Mechanical Sciences) and the SBMAC (Brazilian Society of Applied Mathematics).

Optimization of Complex Systems Theory Models Algorithms and Applications

Optimization of Complex Systems  Theory  Models  Algorithms and Applications Book
Author : Hoai An Le Thi,Hoai Minh Le,Tao Pham Dinh
Publisher : Springer
Release : 2019-06-15
ISBN : 3030218031
Language : En, Es, Fr & De

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Book Description :

This book contains 112 papers selected from about 250 submissions to the 6th World Congress on Global Optimization (WCGO 2019) which takes place on July 8–10, 2019 at University of Lorraine, Metz, France. The book covers both theoretical and algorithmic aspects of Nonconvex Optimization, as well as its applications to modeling and solving decision problems in various domains. It is composed of 10 parts, each of them deals with either the theory and/or methods in a branch of optimization such as Continuous optimization, DC Programming and DCA, Discrete optimization & Network optimization, Multiobjective programming, Optimization under uncertainty, or models and optimization methods in a specific application area including Data science, Economics & Finance, Energy & Water management, Engineering systems, Transportation, Logistics, Resource allocation & Production management. The researchers and practitioners working in Nonconvex Optimization and several application areas can find here many inspiring ideas and useful tools & techniques for their works.

Uncertainty Modeling for Engineering Applications

Uncertainty Modeling for Engineering Applications Book
Author : Flavio Canavero
Publisher : Springer
Release : 2018-12-29
ISBN : 3030048705
Language : En, Es, Fr & De

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Book Description :

This book provides an overview of state-of-the-art uncertainty quantification (UQ) methodologies and applications, and covers a wide range of current research, future challenges and applications in various domains, such as aerospace and mechanical applications, structure health and seismic hazard, electromagnetic energy (its impact on systems and humans) and global environmental state change. Written by leading international experts from different fields, the book demonstrates the unifying property of UQ theme that can be profitably adopted to solve problems of different domains. The collection in one place of different methodologies for different applications has the great value of stimulating the cross-fertilization and alleviate the language barrier among areas sharing a common background of mathematical modeling for problem solution. The book is designed for researchers, professionals and graduate students interested in quantitatively assessing the effects of uncertainties in their fields of application. The contents build upon the workshop “Uncertainty Modeling for Engineering Applications” (UMEMA 2017), held in Torino, Italy in November 2017.

Computational Intelligence in Emerging Technologies for Engineering Applications

Computational Intelligence in Emerging Technologies for Engineering Applications Book
Author : Orestes Llanes Santiago,Carlos Cruz Corona,Antônio José Silva Neto,José Luis Verdegay
Publisher : Springer Nature
Release : 2020-02-14
ISBN : 3030344096
Language : En, Es, Fr & De

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Book Description :

This book explores applications of computational intelligence in key and emerging fields of engineering, especially with regard to condition monitoring and fault diagnosis, inverse problems, decision support systems and optimization. These applications can be beneficial in a broad range of contexts, including: water distribution networks, manufacturing systems, production and storage of electrical energy, heat transfer, acoustic levitation, uncertainty and robustness of infinite-dimensional objects, fatigue failure prediction, autonomous navigation, nanotechnology, and the analysis of technological development indexes. All applications, mathematical and computational tools, and original results are presented using rigorous mathematical procedures. Further, the book gathers contributions by respected experts from 22 different research centers and eight countries: Brazil, Cuba, France, Hungary, India, Japan, Romania and Spain. The book is intended for use in graduate courses on applied computation, applied mathematics, and engineering, where tools like computational intelligence and numerical methods are applied to the solution of real-world problems in emerging areas of engineering.

The Science and Management of Uncertainty

The Science and Management of Uncertainty Book
Author : Bruce G. Marcot
Publisher : CRC Press
Release : 2020-11-26
ISBN : 1000244512
Language : En, Es, Fr & De

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Book Description :

Uncertainty can take many forms, can be represented in many ways, and can have important implications in decision-making and policy development. This book provides a rigorous scientific framework for dealing with uncertainty in real-world situations, and provides a comprehensive study of concepts, measurements, and applications of uncertainty in ecological modeling and natural resource management. The focus of this book is on the kinds and implications of uncertainty in environmental modeling and management, with practical guidelines and examples for successful modeling and risk analysis in the face of uncertain conditions and incomplete information. Provided is a clear classification of uncertainty; methods for measuring, modeling, and communicating uncertainty; practical guidelines for capturing and representing expert knowledge and judgment; explanations of the role of uncertainty in decision-making; a guideline to avoiding logical fallacies when dealing with uncertainty; and several example cases of real-world ecological modeling and risk analysis to illustrate the concepts and approaches. Case topics provide examples of structured decision-making, statistical modeling, and related topics. A summary provides practical next steps that the reader can take in analyzing and interpreting uncertainty in real-world situations. Also provided is a glossary and a suite of references.

Philosophies of Structural Safety and Reliability

Philosophies of Structural Safety and Reliability Book
Author : Vladimir Raizer,Isaac Elishakoff
Publisher : CRC Press
Release : 2022-07-28
ISBN : 1000550745
Language : En, Es, Fr & De

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Book Description :

Uncertainty is certain to be found in structural engineering, making it crucial to structure design. This book covers three competing philosophies behind structural safety and reliability: probabilistic analysis, fuzzy set-based treatments, and the convex approach. Explaining the theory behind probabilistic analysis, fuzzy set-based treatments, and the convex approach in detail, alongside their implementation, use, and benefits, the book compares and contrasts these methods, enabling the reader to solve problems associated with uncertainty. These uncertainty issues can be seen in civil engineering structures, risk of earthquakes, impact of rough seas on ships, and turbulence affecting aerospace vehicles. Building on the authors’ many years of experience in the field, Philosophies of Structural Safety and Reliability is an essential guide to structural uncertainty. Topics covered in the book include properties of materials and their structural deterioration, safety factor and reliability, risk evaluation and loads, and their combinations. This book will be of interest to students and professionals in the fields of aerospace, civil, mechanical, marine, and ocean engineering.

Bayesian Inference and Maximum Entropy Methods in Science and Engineering

Bayesian Inference and Maximum Entropy Methods in Science and Engineering Book
Author : Adriano Polpo,Julio Stern,Francisco Louzada,Rafael Izbicki,Hellinton Takada
Publisher : Springer
Release : 2018-07-12
ISBN : 3319911430
Language : En, Es, Fr & De

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Book Description :

These proceedings from the 37th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2017), held in São Carlos, Brazil, aim to expand the available research on Bayesian methods and promote their application in the scientific community. They gather research from scholars in many different fields who use inductive statistics methods and focus on the foundations of the Bayesian paradigm, their comparison to objectivistic or frequentist statistics counterparts, and their appropriate applications. Interest in the foundations of inductive statistics has been growing with the increasing availability of Bayesian methodological alternatives, and scientists now face much more difficult choices in finding the optimal methods to apply to their problems. By carefully examining and discussing the relevant foundations, the scientific community can avoid applying Bayesian methods on a merely ad hoc basis. For over 35 years, the MaxEnt workshops have explored the use of Bayesian and Maximum Entropy methods in scientific and engineering application contexts. The workshops welcome contributions on all aspects of probabilistic inference, including novel techniques and applications, and work that sheds new light on the foundations of inference. Areas of application in these workshops include astronomy and astrophysics, chemistry, communications theory, cosmology, climate studies, earth science, fluid mechanics, genetics, geophysics, machine learning, materials science, medical imaging, nanoscience, source separation, thermodynamics (equilibrium and non-equilibrium), particle physics, plasma physics, quantum mechanics, robotics, and the social sciences. Bayesian computational techniques such as Markov chain Monte Carlo sampling are also regular topics, as are approximate inferential methods. Foundational issues involving probability theory and information theory, as well as novel applications of inference to illuminate the foundations of physical theories, are also of keen interest.

Variational Methods for Engineers with Matlab

Variational Methods for Engineers with Matlab Book
Author : Eduardo Souza de Cursi
Publisher : John Wiley & Sons
Release : 2015-10-02
ISBN : 1119230152
Language : En, Es, Fr & De

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Book Description :

This book is issued from a 30 years’ experience on the presentation of variational methods to successive generations of students and researchers in Engineering. It gives a comprehensive, pedagogical and engineer-oriented presentation of the foundations of variational methods and of their use in numerical problems of Engineering. Particular applications to linear and nonlinear systems of equations, differential equations, optimization and control are presented. MATLAB programs illustrate the implementation and make the book suitable as a textbook and for self-study. The evolution of knowledge, of the engineering studies and of the society in general has led to a change of focus from students and researchers. New generations of students and researchers do not have the same relations to mathematics as the previous ones. In the particular case of variational methods, the presentations used in the past are not adapted to the previous knowledge, the language and the centers of interest of the new generations. Since these methods remain a core knowledge – thus essential - in many fields (Physics, Engineering, Applied Mathematics, Economics, Image analysis ...), a new presentation is necessary in order to address variational methods to the actual context.

Model Validation and Uncertainty Quantification Volume 3

Model Validation and Uncertainty Quantification  Volume 3 Book
Author : Robert Barthorpe,Roland Platz,Israel Lopez,Babak Moaveni,Costas Papadimitriou
Publisher : Springer
Release : 2017-06-07
ISBN : 3319548581
Language : En, Es, Fr & De

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Book Description :

Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics, 2017, the third volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on: Uncertainty Quantification in Material Models Uncertainty Propagation in Structural Dynamics Practical Applications of MVUQ Advances in Model Validation & Uncertainty Quantification: Model Updating Model Validation & Uncertainty Quantification: Industrial Applications Controlling Uncertainty Uncertainty in Early Stage Design Modeling of Musical Instruments Overview of Model Validation and Uncertainty

Uncertainty Quantification

Uncertainty Quantification Book
Author : Christian Soize
Publisher : Springer
Release : 2017-04-24
ISBN : 3319543393
Language : En, Es, Fr & De

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Book Description :

This book presents the fundamental notions and advanced mathematical tools in the stochastic modeling of uncertainties and their quantification for large-scale computational models in sciences and engineering. In particular, it focuses in parametric uncertainties, and non-parametric uncertainties with applications from the structural dynamics and vibroacoustics of complex mechanical systems, from micromechanics and multiscale mechanics of heterogeneous materials. Resulting from a course developed by the author, the book begins with a description of the fundamental mathematical tools of probability and statistics that are directly useful for uncertainty quantification. It proceeds with a well carried out description of some basic and advanced methods for constructing stochastic models of uncertainties, paying particular attention to the problem of calibrating and identifying a stochastic model of uncertainty when experimental data is available. This book is intended to be a graduate-level textbook for students as well as professionals interested in the theory, computation, and applications of risk and prediction in science and engineering fields.

Topics in Model Validation and Uncertainty Quantification Volume 5

Topics in Model Validation and Uncertainty Quantification  Volume 5 Book
Author : Todd Simmermacher,Scott Cogan,Babak Moaveni,Costas Papadimitriou
Publisher : Springer Science & Business Media
Release : 2013-05-30
ISBN : 1461465648
Language : En, Es, Fr & De

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Book Description :

Topics in Model Validation and Uncertainty Quantification, Volume : Proceedings of the 31st IMAC, A Conference and Exposition on Structural Dynamics, 2013, the fifth volume of seven from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Uncertainty Quantification & Propagation in Structural Dynamics Robustness to Lack of Knowledge in Design Model Validation

Topics in Model Validation and Uncertainty Quantification Volume 4

Topics in Model Validation and Uncertainty Quantification  Volume 4 Book
Author : T. Simmermacher,Scott Cogan,L.G. Horta,R. Barthorpe
Publisher : Springer Science & Business Media
Release : 2012-04-23
ISBN : 1461424313
Language : En, Es, Fr & De

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Book Description :

Topics in Model Validation and Uncertainty Quantification, Volume 4, Proceedings of the 30th IMAC, A Conference and Exposition on Structural Dynamics, 2012, the fourth volume of six from the Conference, brings together 19 contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Robustness to Lack of Knowledge in Design Bayesian and Markov Chain Monte Carlo Methods Uncertainty Quantification Model Calibration

Numerical Methods for Stochastic Partial Differential Equations with White Noise

Numerical Methods for Stochastic Partial Differential Equations with White Noise Book
Author : Zhongqiang Zhang,George Em Karniadakis
Publisher : Springer
Release : 2017-09-01
ISBN : 3319575112
Language : En, Es, Fr & De

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Book Description :

This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical comparison with other integration methods in random space is made. Part III covers spatial white noise. Here the authors discuss numerical methods for nonlinear elliptic equations as well as other equations with additive noise. Numerical methods for SPDEs with multiplicative noise are also discussed using the Wiener chaos expansion method. In addition, some SPDEs driven by non-Gaussian white noise are discussed and some model reduction methods (based on Wick-Malliavin calculus) are presented for generalized polynomial chaos expansion methods. Powerful techniques are provided for solving stochastic partial differential equations. This book can be considered as self-contained. Necessary background knowledge is presented in the appendices. Basic knowledge of probability theory and stochastic calculus is presented in Appendix A. In Appendix B some semi-analytical methods for SPDEs are presented. In Appendix C an introduction to Gauss quadrature is provided. In Appendix D, all the conclusions which are needed for proofs are presented, and in Appendix E a method to compute the convergence rate empirically is included. In addition, the authors provide a thorough review of the topics, both theoretical and computational exercises in the book with practical discussion of the effectiveness of the methods. Supporting Matlab files are made available to help illustrate some of the concepts further. Bibliographic notes are included at the end of each chapter. This book serves as a reference for graduate students and researchers in the mathematical sciences who would like to understand state-of-the-art numerical methods for stochastic partial differential equations with white noise.

Parameter Estimation and Uncertainty Quantification in Water Resources Modeling

Parameter Estimation and Uncertainty Quantification in Water Resources Modeling Book
Author : Philippe Renard,Frederick Delay,Daniel M. Tartakovsky,Velimir V. Vesselinov
Publisher : Frontiers Media SA
Release : 2020-04-22
ISBN : 2889636747
Language : En, Es, Fr & De

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Book Description :

Numerical models of flow and transport processes are heavily employed in the fields of surface, soil, and groundwater hydrology. They are used to interpret field observations, analyze complex and coupled processes, or to support decision making related to large societal issues such as the water-energy nexus or sustainable water management and food production. Parameter estimation and uncertainty quantification are two key features of modern science-based predictions. When applied to water resources, these tasks must cope with many degrees of freedom and large datasets. Both are challenging and require novel theoretical and computational approaches to handle complex models with large number of unknown parameters.

An Introduction to Computational Stochastic PDEs

An Introduction to Computational Stochastic PDEs Book
Author : Gabriel J. Lord,Catherine E. Powell,Tony Shardlow
Publisher : Cambridge University Press
Release : 2014-08-11
ISBN : 0521899907
Language : En, Es, Fr & De

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Book Description :

This book offers a practical presentation of stochastic partial differential equations arising in physical applications and their numerical approximation.

Model Validation and Uncertainty Quantification Volume 3

Model Validation and Uncertainty Quantification  Volume 3 Book
Author : H. Sezer Atamturktur,Babak Moaveni,Costas Papadimitriou,Tyler Schoenherr
Publisher : Springer Science & Business Media
Release : 2014-04-11
ISBN : 3319045520
Language : En, Es, Fr & De

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Book Description :

This third volume of eight from the IMAC - XXXII Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Linear Systems Substructure Modelling Adaptive Structures Experimental Techniques Analytical Methods Damage Detection Damping of Materials & Members Modal Parameter Identification Modal Testing Methods System Identification Active Control Modal Parameter Estimation Processing Modal Data

Uncertainty Quantification

Uncertainty Quantification Book
Author : Ralph C. Smith
Publisher : SIAM
Release : 2013-12-02
ISBN : 161197321X
Language : En, Es, Fr & De

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Book Description :

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.

Uncertainty Quantification in Multiscale Materials Modeling

Uncertainty Quantification in Multiscale Materials Modeling Book
Author : Yan Wang,David L. McDowell
Publisher : Woodhead Publishing
Release : 2020-03-10
ISBN : 008102942X
Language : En, Es, Fr & De

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Book Description :

Uncertainty Quantification in Multiscale Materials Modeling provides a complete overview of uncertainty quantification (UQ) in computational materials science. It provides practical tools and methods along with examples of their application to problems in materials modeling. UQ methods are applied to various multiscale models ranging from the nanoscale to macroscale. This book presents a thorough synthesis of the state-of-the-art in UQ methods for materials modeling, including Bayesian inference, surrogate modeling, random fields, interval analysis, and sensitivity analysis, providing insight into the unique characteristics of models framed at each scale, as well as common issues in modeling across scales. Synthesizes available UQ methods for materials modeling Provides practical tools and examples for problem solving in modeling material behavior across various length scales Demonstrates UQ in density functional theory, molecular dynamics, kinetic Monte Carlo, phase field, finite element method, multiscale modeling, and to support decision making in materials design Covers quantum, atomistic, mesoscale, and engineering structure-level modeling and simulation

Uncertainty Quantification

Uncertainty Quantification Book
Author : Ralph C. Smith
Publisher : SIAM
Release : 2013-12-02
ISBN : 1611973228
Language : En, Es, Fr & De

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Book Description :

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.