Data Driven Uncertainty Quantification For High Dimensional Engineering Problems

Data-driven Uncertainty Quantification for High-dimensional Engineering Problems

Fundamentals of Uncertainty Quantification for Engineers

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

Computational Fluid Flow and Heat Transfer

The text provides insight into the different mathematical tools and techniques that can be applied to the analysis and numerical computations of flow models. It further discusses important topics such as the heat transfer effect on boundary layer flow, modeling of flows through porous media, anisotropic polytrophic gas model, and thermal instability in viscoelastic fluids. This book: Discusses modeling of Rayleigh-Taylor instability in nanofluid layer and thermal instability in viscoelastic fluids Covers open FOAM simulation of free surface problems, and anisotropic polytrophic gas model Highlights the Sensitivity Analysis in Aerospace Engineering, MHD Flow of a Micropolar Hybrid Nanofluid, and IoT-Enabled Monitoring for Natural Convection Presents thermal behavior of nanofluid in complex geometries and heat transfer effect on Boundary layer flow Explains natural convection heat transfer in non-Newtonian fluids and homotropy series solution of the boundary layer flow Illustrates modeling of flows through porous media and investigates Shock-driven Richtmyer-Meshkov instability It is primarily written for senior undergraduate, graduate students, and academic researchers in the fields of Applied Sciences, Mechanical Engineering, Manufacturing Engineering, Production Engineering, Industrial engineering, Automotive engineering, and Aerospace engineering.