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  • © 2017

Uncertainty Quantification

An Accelerated Course with Advanced Applications in Computational Engineering

Authors:

  • Presents fundamental mathematical tools of probability and statistics that are directly useful for uncertainty quantification

  • Includes several topics not currently published in research monographs

  • Covers the basic models and advanced methodologies for constructing the stochastic modeling of uncertainties

Part of the book series: Interdisciplinary Applied Mathematics (IAM, volume 47)

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eBook USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-54339-0
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  • Readable on all devices
  • Own it forever
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Softcover Book USD 79.99
Price excludes VAT (USA)
Hardcover Book USD 109.99
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About this book

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.

Keywords

  • 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

Reviews

“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)​

Authors and Affiliations

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

    Christian Soize

About the author

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.

Bibliographic Information

Buying options

eBook USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-54339-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 79.99
Price excludes VAT (USA)
Hardcover Book USD 109.99
Price excludes VAT (USA)