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.

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.

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).

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.

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.

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.

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.