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Novel Uncertainty Quantification Methods For Stochastic Isogeometric Analysis
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Book Synopsis Novel Uncertainty Quantification Methods for Stochastic Isogeometric Analysis by : Ramin Jahanbin
Download or read book Novel Uncertainty Quantification Methods for Stochastic Isogeometric Analysis written by Ramin Jahanbin and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this study is to develop novel computational methods for general high-dimensional uncertainty quantification (UQ) with a focus on stochastic isogeometric analysis. The objective is pursued by: (1) development of an isogeometric collocation method for random field discretization, (2) generalization of isogeometric methods for random field discretization on arbitrary multipatch domains, (3) establishment of a spline dimensional decomposition for high-dimensional UQ, (4) stochastic isogeometric analysis in linear elasticity, (5) stochastic isogeometric analysis on arbitrary multipatch domains, and (6) UQ in linear dynamical systems.
Book Synopsis Proceedings of the 6th International Symposium on Uncertainty Quantification and Stochastic Modelling by : José Eduardo Souza De Cursi
Download or read book Proceedings of the 6th International Symposium on Uncertainty Quantification and Stochastic Modelling written by José Eduardo Souza De Cursi and published by Springer Nature. This book was released on 2023-10-21 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings book covers a wide range of topics related to uncertainty analysis and its application in various fields of engineering and science. It explores uncertainties in numerical simulations for soil liquefaction potential, the toughness properties of construction materials, experimental tests on cyclic liquefaction potential, and the estimation of geotechnical engineering properties for aerogenerator foundation design. Additionally, the book delves into uncertainties in concrete compressive strength, bio-inspired shape optimization using isogeometric analysis, stochastic damping in rotordynamics, and the hygro-thermal properties of raw earth building materials. It also addresses dynamic analysis with uncertainties in structural parameters, reliability-based design optimization of steel frames, and calibration methods for models with dependent parameters. The book further explores mechanical property characterization in 3D printing, stochastic analysis in computational simulations, probability distribution in branching processes, data assimilation in ocean circulation modeling, uncertainty quantification in climate prediction, and applications of uncertainty quantification in decision problems and disaster management. This comprehensive collection provides insights into the challenges and solutions related to uncertainty in various scientific and engineering contexts.
Book Synopsis Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling by : José Eduardo Souza De Cursi
Download or read book Proceedings of the 5th International Symposium on Uncertainty Quantification and Stochastic Modelling written by José Eduardo Souza De Cursi and published by Springer Nature. This book was released on 2020-08-19 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Book Synopsis Uncertainty Quantification by : Ralph C. Smith
Download or read book Uncertainty Quantification written by Ralph C. Smith and published by SIAM. This book was released on 2013-12-02 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Novel Uncertainty Quantification Techniques for Problems Described by Stochastic Partial Differential Equations by : Peng Chen
Download or read book Novel Uncertainty Quantification Techniques for Problems Described by Stochastic Partial Differential Equations written by Peng Chen and published by . This book was released on 2014 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty propagation (UP) in physical systems governed by PDEs is a challenging problem. This thesis addresses the development of a number of innovative techniques that emphasize the need for high-dimensionality modeling, resolving discontinuities in the stochastic space and considering the computational expense of forward solvers. Both Bayesian and non-Bayesian approaches are considered. Applications demonstrating the developed techniques are investigated in the context of flow in porous media and reservoir engineering applications. An adaptive locally weighted projection method (ALWPR) is firstly developed. It adaptively selects the needed runs of the forward solver (data collection) to maximize the predictive capability of the method. The methodology effectively learns the local features and accurately quantifies the uncertainty in the prediction of the statistics. It could provide predictions and confidence intervals at any query input and can deal with multi-output responses. A probabilistic graphical model framework for uncertainty quantification is next introduced. The high dimensionality issue of the input is addressed by a local model reduction framework. Then the conditional distribution of the multi-output responses on the low dimensional representation of the input field is factorized into a product of local potential functions that are represented non-parametrically. A nonparametric loopy belief propagation algorithm is developed for studying uncertainty quantification directly on the graph. The nonparametric nature of the model is able to efficiently capture non-Gaussian features of the response. Finally an infinite mixture of Multi-output Gaussian Process (MGP) models is presented to effectively deal with many of the difficulties of current UQ methods. This model involves an infinite mixture of MGP's using Dirichlet process priors and is trained using Variational Bayesian Inference. The Bayesian nature of the model allows for the quantification of the uncertainties due to the limited number of simulations. The automatic detection of the mixture components by the Variational Inference algorithm is able to capture discontinuities and localized features without adhering to ad hoc constructions. Finally, correlations between the components of multi-variate responses are captured by the underlying MGP model in a natural way. A summary of suggestions for future research in the area of uncertainty quantification field are given at the end of the thesis.
Book Synopsis Introduction to Uncertainty Quantification by : T.J. Sullivan
Download or read book Introduction to Uncertainty Quantification written by T.J. Sullivan and published by Springer. This book was released on 2015-12-14 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a framework in which the main objectives of the field of uncertainty quantification (UQ) are defined and an overview of the range of mathematical methods by which they can be achieved. Complete with exercises throughout, the book will equip readers with both theoretical understanding and practical experience of the key mathematical and algorithmic tools underlying the treatment of uncertainty in modern applied mathematics. Students and readers alike are encouraged to apply the mathematical methods discussed in this book to their own favorite problems to understand their strengths and weaknesses, also making the text suitable for a self-study. Uncertainty quantification is a topic of increasing practical importance at the intersection of applied mathematics, statistics, computation and numerous application areas in science and engineering. This text is designed as an introduction to UQ for senior undergraduate and graduate students with a mathematical or statistical background and also for researchers from the mathematical sciences or from applications areas who are interested in the field. T. J. Sullivan was Warwick Zeeman Lecturer at the Mathematics Institute of the University of Warwick, United Kingdom, from 2012 to 2015. Since 2015, he is Junior Professor of Applied Mathematics at the Free University of Berlin, Germany, with specialism in Uncertainty and Risk Quantification.
Book Synopsis Stochastic Systems by : Mircea Grigoriu
Download or read book Stochastic Systems written by Mircea Grigoriu and published by Springer Science & Business Media. This book was released on 2012-05-15 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty is an inherent feature of both properties of physical systems and the inputs to these systems that needs to be quantified for cost effective and reliable designs. The states of these systems satisfy equations with random entries, referred to as stochastic equations, so that they are random functions of time and/or space. The solution of stochastic equations poses notable technical difficulties that are frequently circumvented by heuristic assumptions at the expense of accuracy and rigor. The main objective of Stochastic Systems is to promoting the development of accurate and efficient methods for solving stochastic equations and to foster interactions between engineers, scientists, and mathematicians. To achieve these objectives Stochastic Systems presents: A clear and brief review of essential concepts on probability theory, random functions, stochastic calculus, Monte Carlo simulation, and functional analysis Probabilistic models for random variables and functions needed to formulate stochastic equations describing realistic problems in engineering and applied sciences Practical methods for quantifying the uncertain parameters in the definition of stochastic equations, solving approximately these equations, and assessing the accuracy of approximate solutions Stochastic Systems provides key information for researchers, graduate students, and engineers who are interested in the formulation and solution of stochastic problems encountered in a broad range of disciplines. Numerous examples are used to clarify and illustrate theoretical concepts and methods for solving stochastic equations. The extensive bibliography and index at the end of the book constitute an ideal resource for both theoreticians and practitioners.
Book Synopsis Uncertainty Quantification and Stochastic Modelling with EXCEL by : Eduardo Souza de Cursi
Download or read book Uncertainty Quantification and Stochastic Modelling with EXCEL written by Eduardo Souza de Cursi and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents techniques for determining uncertainties in numerical solutions with applications in the fields of business administration, civil engineering, and economics, using Excel as a computational tool. Also included are solutions to uncertainty problems involving stochastic methods. The list of topics specially covered in this volume includes linear and nonlinear programming, Lagrange multipliers (for sensitivity), multi objective optimization, and Game Theory, as well as linear algebraic equations, and probability and statistics. The book also provides a selection of numerical methods developed for Excel, in order to enhance readers' understanding. As such, it offers a valuable guide for all graduate and undergraduate students in the fields of economics, business administration, civil engineering, and others that rely on Excel as a research tool.
Book Synopsis Uncertainty Quantification by : Christian Soize
Download or read book Uncertainty Quantification written by Christian Soize and published by Springer. This book was released on 2017-04-24 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Uncertainty Quantification and Stochastic Modeling with Matlab by : Eduardo Souza de Cursi
Download or read book Uncertainty Quantification and Stochastic Modeling with Matlab written by Eduardo Souza de Cursi and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Handbook of Uncertainty Quantification by : Roger Ghanem
Download or read book Handbook of Uncertainty Quantification written by Roger Ghanem and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Uncertainty quantification for wave propagation and flow problems with random data by : Markus Wahlsten
Download or read book Uncertainty quantification for wave propagation and flow problems with random data written by Markus Wahlsten and published by Linköping University Electronic Press. This book was released on 2018-04-09 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we study partial differential equations with random inputs. The effects that different boundary conditions with random data and uncertain geometries have on the solution are analyzed. Further, comparisons and couplings between different uncertainty quantification methods are performed. The numerical simulations are based on provably strongly stable finite difference formulations based on summation-by-parts operators and a weak implementation of boundary and interface conditions. The first part of this thesis treats the construction of variance reducing boundary conditions. It is shown how the variance of the solution can be manipulated by the choice of boundary conditions, and a close relation between the variance of the solution and the energy estimate is established. The technique is studied on both a purely hyperbolic system as well as an incompletely parabolic system of equations. The applications considered are the Euler, Maxwell's, and Navier--Stokes equations. The second part focuses on the effect of uncertain geometry on the solution. We consider a two-dimensional advection-diffusion equation with a stochastically varying boundary. We transform the problem to a fixed domain where comparisons can be made. Numerical results are performed on a problem in heat transfer, where the frequency and amplitude of the prescribed uncertainty are varied. The final part of the thesis is devoted to the comparison and coupling of different uncertainty quantification methods. An efficiency analysis is performed using the intrusive polynomial chaos expansion with stochastic Galerkin projection, and nonintrusive numerical integration. The techniques are compared using the non-linear viscous Burgers' equation. A provably stable coupling procedure for the two methods is also constructed. The general coupling procedure is exemplified using a hyperbolic system of equations.
Book Synopsis Uncertainty Quantification for Stochastic Subspace Indentification Methods by : Xuan-Binh Lam
Download or read book Uncertainty Quantification for Stochastic Subspace Indentification Methods written by Xuan-Binh Lam and published by . This book was released on 2011 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Operational Modal Analysis, the modal parameters (natural frequencies, damping ratios, and mode shapes) obtained from Stochastic Subspace Identification (SSI) of a structure, are afflicted with statistical uncertainty. For evaluating the quality of the obtained results it is essential to know the appropriate uncertainty bounds of these terms. In this thesis, the algorithms, that automatically compute the uncertainty bounds of modal parameters obtained from SSI of a structure based on vibration measurements, are presented. With these new algorithms, the uncertainty bounds of the modal parameters of some relevant industrial examples are computed. To quantify the statistical uncertainty of the obtained modal parameters, the statistical uncertainty in the data can be evaluated and propagated to the system matrices and, thus, to the modal parameters. In the uncertainty quantification algorithm, which is a perturbation-based method, it has been shown how uncertainty bounds of modal parameters can be determined from the covariances of the system matrices, which are obtained from some covariance of the data and the covariances of subspace matrices. In this thesis, several results are derived. Firstly, a novel and more realistic scheme for the uncertainty calculation of the mode shape is presented, the mode shape is normalized by the phase angle of the component having the maximal absolute value instead of by one of its components. Secondly, the uncertainty quantification is derived and developed for several identification methods, first few of them are covariance- and data-driven SSI. The thesis also mentions about Eigensystem Realization Algorithm (ERA), a class of identification methods, and its uncertainty quantification scheme. This ERA approach is introduced in conjunction with the singular value decomposition to derive the basic formulation of minimum order realization. Besides, the thesis supposes efficient algorithms to estimate the system matrices at multiple model orders, the uncertainty quantification is also derived for this new multi-order SSI method. Two last interesting sections of the thesis are discovering the uncertainty of multi-setups SSI algorithm and recursive algorithms. In summary, subspace algorithms are efficient tools for vibration analysis, fitting a model to input/output or output-only measurements taken from a system. However, uncertainty quantification for SSI was missing for a long time. The uncertainty quantification is very important feature for credibility of modal analysis exploitation.
Book Synopsis Uncertainty Quantification for Stochastic Dynamical Systems by : Michael Schick
Download or read book Uncertainty Quantification for Stochastic Dynamical Systems written by Michael Schick and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Approximation of the Magnetoquasistatic Model with Uncertainties by : Ulrich Römer
Download or read book Numerical Approximation of the Magnetoquasistatic Model with Uncertainties written by Ulrich Römer and published by Springer. This book was released on 2016-07-27 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive mathematical approach for solving stochastic magnetic field problems. It discusses variability in material properties and geometry, with an emphasis on the preservation of structural physical and mathematical properties. It especially addresses uncertainties in the computer simulation of magnetic fields originating from the manufacturing process. Uncertainties are quantified by approximating a stochastic reformulation of the governing partial differential equation, demonstrating how statistics of physical quantities of interest, such as Fourier harmonics in accelerator magnets, can be used to achieve robust designs. The book covers a number of key methods and results such as: a stochastic model of the geometry and material properties of magnetic devices based on measurement data; a detailed description of numerical algorithms based on sensitivities or on a higher-order collocation; an analysis of convergence and efficiency; and the application of the developed model and algorithms to uncertainty quantification in the complex magnet systems used in particle accelerators.
Book Synopsis Stochastic Methods for Uncertainty Quantification in Radiation Transport by :
Download or read book Stochastic Methods for Uncertainty Quantification in Radiation Transport written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of generalized polynomial chaos (gPC) expansions is investigated for uncertainty quantification in radiation transport. The gPC represents second-order random processes in terms of an expansion of orthogonal polynomials of random variables and is used to represent the uncertain input(s) and unknown(s). We assume a single uncertain input-the total macroscopic cross section-although this does not represent a limitation of the approaches considered here. Two solution methods are examined: The Stochastic Finite Element Method (SFEM) and the Stochastic Collocation Method (SCM). The SFEM entails taking Galerkin projections onto the orthogonal basis, which, for fixed source problems, yields a linear system of fully -coupled equations for the PC coefficients of the unknown. For k-eigenvalue calculations, the SFEM system is non-linear and a Newton-Krylov method is employed to solve it. The SCM utilizes a suitable quadrature rule to compute the moments or PC coefficients of the unknown(s), thus the SCM solution involves a series of independent deterministic transport solutions. The accuracy and efficiency of the two methods are compared and contrasted. The PC coefficients are used to compute the moments and probability density functions of the unknown(s), which are shown to be accurate by comparing with Monte Carlo results. Our work demonstrates that stochastic spectral expansions are a viable alternative to sampling-based uncertainty quantification techniques since both provide a complete characterization of the distribution of the flux and the k-eigenvalue. Furthermore, it is demonstrated that, unlike perturbation methods, SFEM and SCM can handle large parameter uncertainty.
Book Synopsis Stochastic Methods for Uncertainty Quantification in Subsurface Flow and Transport Problems by : Florian Müller
Download or read book Stochastic Methods for Uncertainty Quantification in Subsurface Flow and Transport Problems written by Florian Müller and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
