ME470 | Uncertainty Quantification

Introduction and Motivation

We introduce the material under the umbrella of uncertainty quantification. We examine its context from topics such as verification & validation, aleatory vs. epistemic uncertainty, and methods for characterizing uncertainties.

We also review some basic concepts in probability and approximation theory.

Assignments

Homework 0

Due April 12 at the beginning of class.

Documents

demo.tgz	This is the MATLAB demo we did in the first lecture.
Lecture1.pptx	Slides from the first lecture.
classnotesplato.rtf	Brandon's notes from our class brainstorming exercise during the second lecture.
Probability Notes	Notes we used for the 3rd lecture.
approxtheory.tgz	MATLAB demo for the approximation theory from the fourth lecture. You'll need the PMPack suite of MATLAB tools.

Links

Probability Text	An online version of the text used in a former STAT116 course. Chapters 2, 5, and 6 are the most relevant for our class.
STAT116	Old course website for STAT116: Introductory Probabilty.
AA222	Course website for Intro to Multidisciplinary Design Optimization -- a good reference for reviewing optimization.
Convex Optimization Book	Stephen Boyd's book on optimization -- another good reference.
Chebyshev and Fourier Spectral Methods	John P. Boyd's (no relation to Stephen as far as I know) book on spectral methods. The second chapter gives an excellent intuitive introduction to the convergence of Fourier/Chebyshev series
Chebfun and Approximation Theory	Chebfun is a Matlab suite for computing with functions via their Chebyshev expansions. This guide uses Chebfun to explore some basic approximation theory.
Approximation Theory and Approximation Practice	Lloyd N. Trefethen's upcoming book on approximation theory using Chebfun.

References

Computer Predictions with Quantified Uncertainty, Part I. Tinsley Oden, Robert Moser, and Omar Ghattas
Computer Predictions with Quantified Uncertainty, Part II. Tinsley Oden, Robert Moser, and Omar Ghattas
Error and Uncertainty in Modeling and Simulation. William L. Oberkampf, Sharon M. DeLand, Brian M. Rutherford, Kathleen V. Diegert, Kenneth F. Alvin
Verification, Validation, and Predictive Capability in Computational Engineering and Physics. William L. Oberkampf, Timothy G. Trucano, Charles Hirsch
Conceptual and Computational Basis for the Quantification of Margins and Uncertainty. Jon C. Helton
An Exploration of Alternative Approaches to the Representation of Uncertainty in Model Predictions. J. C. Helton, J. D. Johnson, and W. L. Oberkampf.
A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing. Christopher J. Roy and William L. Oberkampf.