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Uncertainty Quantification Of Stochastic Defects In Materials
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Book Synopsis Uncertainty Quantification of Stochastic Defects in Materials by : Liu Chu
Download or read book Uncertainty Quantification of Stochastic Defects in Materials written by Liu Chu and published by CRC Press. This book was released on 2021-12-16 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty Quantification of Stochastic Defects in Materials investigates the uncertainty quantification methods for stochastic defects in material microstructures. It provides effective supplementary approaches for conventional experimental observation with the consideration of stochastic factors and uncertainty propagation. Pursuing a comprehensive numerical analytical system, this book establishes a fundamental framework for this topic, while emphasizing the importance of stochastic and uncertainty quantification analysis and the significant influence of microstructure defects on the material macro properties. Key Features Consists of two parts: one exploring methods and theories and the other detailing related examples Defines stochastic defects in materials and presents the uncertainty quantification for defect location, size, geometrical configuration, and instability Introduces general Monte Carlo methods, polynomial chaos expansion, stochastic finite element methods, and machine learning methods Provides a variety of examples to support the introduced methods and theories Applicable to MATLAB® and ANSYS software This book is intended for advanced students interested in material defect quantification methods and material reliability assessment, researchers investigating artificial material microstructure optimization, and engineers working on defect influence analysis and nondestructive defect testing.
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 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 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 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 in Engineering by : Louis J. M. Aslett
Download or read book Uncertainty in Engineering written by Louis J. M. Aslett and published by Springer Nature. This book was released on 2022 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides an introduction to uncertainty quantification in engineering. Starting with preliminaries on Bayesian statistics and Monte Carlo methods, followed by material on imprecise probabilities, it then focuses on reliability theory and simulation methods for complex systems. The final two chapters discuss various aspects of aerospace engineering, considering stochastic model updating from an imprecise Bayesian perspective, and uncertainty quantification for aerospace flight modelling. Written by experts in the subject, and based on lectures given at the Second Training School of the European Research and Training Network UTOPIAE (Uncertainty Treatment and Optimization in Aerospace Engineering), which took place at Durham University (United Kingdom) from 2 to 6 July 2018, the book offers an essential resource for students as well as scientists and practitioners.
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 by : Luis Chase
Download or read book Uncertainty Quantification written by Luis Chase and published by Nova Science Publishers. This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent times, polynomial chaos expansion has emerged as a dominant technique to determine the response uncertainties of a system by propagating the uncertainties of the inputs. In this regard, the opening chapter of Uncertainty Quantification: Advances in Research and Applications, an intrusive approach called Galerkin Projection as well as non-intrusive approaches (such as pseudo-spectral projection and linear regression) are discussed.Next, the authors introduce a new methodology to determine the uncertainties of input parameters using CIRCÉ software to overcome the reliance on expert judgment. The goal is to determinate and evaluate the uncertainty bounds for physical models related to reflood model of MARS-KS code Vessel module (coupled with COBRA-TF) using both CIRCÉ and the experimental data of FEBA.Lastly, uncertainties related to rheological model parameters of skeletal muscles are modeled and analyzed, and available data are acquired and fused for hyperelastic constitutive model parameters with Neo-Hookean and Mooney-Rivlin formulations.
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 with Applications to Engineering Problems by : Daniele Bigoni
Download or read book Uncertainty Quantification with Applications to Engineering Problems written by Daniele Bigoni and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 . This book was released on 2015 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 Multifaceted Uncertainty Quantification by : Isaac Elishakoff
Download or read book Multifaceted Uncertainty Quantification written by Isaac Elishakoff and published by . This book was released on 2024-08-19 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Uncertainty Quantification in Stochastic Models for Extreme Loads by : Phong The Truong Nguyen
Download or read book Uncertainty Quantification in Stochastic Models for Extreme Loads written by Phong The Truong Nguyen and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many response parameters for offshore structures such as wave energy converters (WECs), wind turbines, oil and gas platforms, etc. can be modeled as stochastic processes. The extreme of such a response process over any selected interval of time is a random variable. Having accurate estimates of such extremes during a structure's life is crucial in structural design, but there are challenges in their estimation due to various sources of uncertainty. These include uncertainty from environmental conditions or the climate/weather as well as from short-term simulations of these stochastic processes at appropriate time and space resolution. Together, these uncertainty sources make up a high-dimension vector of random variables (that can be on the order of thousands). Many offshore structures must withstand many years of exposure and use return periods for design that are on order of 50 to 100 years. The focus of this study is on rare events or response levels that are associated with very low probabilities of exceedance (e.g., on the order of $10−6 over a typical 1-hour duration). Time-domain simulations of dynamic offshore structures can be computationally expensive even for a single simulation. Various approaches can be adopted in practice to account for uncertainties in extreme response prediction. Monte Carlo Simulation (MCS) is the most common for exhaustive prediction of the response for all conditions. Since MCS can be computationally very demanding, the development of efficient surrogate models is presented to more efficiently deal with these uncertainties. A proposed method, in this study, is based on the use of an ensemble of multiple polynomial chaos expansion (M-PCE) surrogate models to propagate the uncertainty from the environment through the stochastic input simulation to eventual design load prediction. In particular, each PCE model in the ensemble provides an approximate relationship between the structural response and the underlying environmental variables, while variability in the short-term simulations is accounted for by the multiple surrogates. M-PCE helps overcome the curse of dimensionality since, instead of dealing with development of a high-dimensional surrogate model, the M-PCE ensemble includes multiple low-dimensional PCE models, each defined in terms of only the long-term environmental variables, which are of low dimension. It is found that the M-PCE ensemble can efficiently predict long-term extreme loads associated at exceedance probability levels (in 1 hour) of $10−5 or higher. Next, by considering MCS and M-PCE as high-fidelity and low-fidelity models, respectively, this study proposes a bi-fidelity approach that combines M-PCE and MCS outputs so as to control, or even eliminate bias introduced by the use of the M-PCE ensemble alone. The approach takes advantage of the robustness of MCS on the one hand and the efficiency of M-PCE model on the other. The key idea is that many of the model simulations are carried out using the inexpensive M-PCE ensemble while a very small number of simulations use the costly high-fidelity model. In this way, the new method significantly enhances the efficiency of MCS and improves the accuracy of the M-PCE ensemble. Finally, this dissertation explores the use of a combination of sliced inverse regression (SIR) and polynomial chaos expansion in uncertainty quantification of response extremes. The SIR procedure is adopted to reduce the original high-dimensional problem to a low-dimensional one; then, the PCE model is employed as a surrogate in the reduced-dimension space in this SIR-PCE scheme. All the proposed approaches including the M-PCE ensemble, the bi-fidelity MPCE-MCS and the SIR-PCE scheme can help mitigate the curse of dimensionality issue; thus, they are all viable approaches for probabilistic assessment of high-dimensional stochastic models, especially when predicting very rare long-term extreme response levels for offshore structures. The proposed methods are validated using examples ranging from benchmarking analytical functions to offshore structures that include studies on a maximum wave elevation, a linear single-degree-of-freedom system response, and a nonlinear wave energy converter. All the proposed methods are found to be efficient and need significantly less effort to achieve unbiased estimations of extreme response levels compared with MCS
Book Synopsis Advances in Uncertainty Quantification and Inverse Problems in Computational Mechanics by : James Warner (E.)
Download or read book Advances in Uncertainty Quantification and Inverse Problems in Computational Mechanics written by James Warner (E.) and published by . This book was released on 2014 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is composed of three chapters, each of which addresses a specific topic and has been, or is in the process of being published in a research journal. Though relatively diverse, the topics in each chapter fall broadly under the theme of advancing research in uncertainty quantification and inverse problems within the field of computational mechanics. The first chapter is based on the stochastic reduced order model (SROM) concept for propagating uncertainty in engineering simulations. Here, the algorithm for constructing SROMs of random vectors is modified and significantly enhanced, yielding more accurate models in substantially less computational time. The second chapter focusses on inverse material identification in coupled acoustic-structure interaction (ASI) systems using either solid displacement or fluid pressure measurement data. This work represents the first time the modified error in constitutive equation (MECE) approach for inverse problems has been formulated and applied to elasticity imaging problems in ASI. Finally, the third chapter combines elements of the first two chapters and presents a novel approach to solve inverse problems under uncertainty using SROMs. The method provides a practical and efficient means of incorporating the effects of model and measurement uncertainties in inverse estimates of unknown system parameters. At the beginning of each chapter there is a separate abstract that has been prepared for the respective journal publication that introduces each project in detail.
