Uncertainty Quantification

1. Front Matter

   Pages i-xxii

   PDF

2. Fundamental Notions in Stochastic Modeling of Uncertainties and Their Propagation in Computational Models

   • Christian Soize

   Pages 1-15

3. Elements of Probability Theory

   • Christian Soize

   Pages 17-40

4. Markov Process and Stochastic Differential Equation

   • Christian Soize

   Pages 41-59

5. MCMC Methods for Generating Realizations and for Estimating the Mathematical Expectation of Nonlinear Mappings of Random Vectors

   • Christian Soize

   Pages 61-76

6. Fundamental Probabilistic Tools for Stochastic Modeling of Uncertainties

   • Christian Soize

   Pages 77-132

7. Brief Overview of Stochastic Solvers for the Propagation of Uncertainties

   • Christian Soize

   Pages 133-139

8. Fundamental Tools for Statistical Inverse Problems

   • Christian Soize

   Pages 141-153

9. Uncertainty Quantification in Computational Structural Dynamics and Vibroacoustics

   • Christian Soize

   Pages 155-216

10. Robust Analysis with Respect to the Uncertainties for Analysis, Updating, Optimization, and Design

    • Christian Soize

    Pages 217-243

11. Random Fields and Uncertainty Quantification in Solid Mechanics of Continuum Media

    • Christian Soize

    Pages 245-300

12. Back Matter

    Pages 301-329

    PDF

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.

• High Stochastic Dimension
• Maximum Entropy Principle
• MCMC Methods
• Model Uncertainties
• Model-parameter Uncertainties
• Non-Gaussian Random Fields
• Nonparametric Uncertainties
• Polynomial Chaos Expansion
• Random Matrices
• Robust Design
• Statistical Inverse Problems
• Stochastic Reduced-order Computational Models

“The book under review serves as an excellent reference for the uncertainty analysis community. … the author has included an extensive bibliography in the end of the book that will be very useful to the interested reader. … the book is an excellent reference for advanced users and practitioners of UQ and is strongly recommended.” (Tujin Sahai, Mathematical Reviews, September, 2018)​

• Laboratoire Modélisation et Simulation Multi-Echelle (MSME), Université Paris-Est Marne-la-Vallée (UPEM), Marne-la-Vallée, France

  Christian Soize

Christian Soize is professor at Universite Paris-Est Marne-la-Valee.  His research interests include stochastic modeling of uncertainties in computational mechanics, their propagation and their quantification.

Policies and ethics