Methods for Rigorous Uncertainty Quantification with Application to a Mars Atmosphere Model

The purpose of this dissertation is to develop and demonstrate methods appropriate for the quantification and propagation of uncertainty in large, high-consequence engineering projects. The term "rigorous uncertainty quantification" refers to methods equal to the proposed task. The motivating practical example is uncertainty in a Mars atmosphere model due to the incompletely characterized presence of dust. The contributions made in this dissertation, though primarily mathematical and philosophical, are driven by the immediate needs of engineers applying uncertainty quantification in the field. Arguments are provided to explain how the practical needs of engineering projects like Mars lander missions motivate the use of the objective probability bounds approach, as opposed to the subjectivist theories which dominate uncertainty quantification in many research communities. An expanded formalism for Dempster-Shafer structures is introduced, allowing for the representation of continuous random variables and fuzzy variables as Dempster-Shafer structures. Then, the correctness and incorrectness of probability bounds analysis and the Cartesian product propagation method for Dempster-Shafer structures under certain dependency conditions are proven. It is also conclusively demonstrated that there exist some probability bounds problems in which the best-possible bounds on probability can not be represented using Dempster-Shafer structures. Nevertheless, Dempster-Shafer theory is shown to provide a useful mathematical framework for a wide range of probability bounds problems. The dissertation concludes with the application of these new methods to the problem of propagating uncertainty from the dust parameters in a Mars atmosphere model to uncertainty in that model's prediction of atmospheric density. A thirty-day simulation of the weather at Holden Crater on Mars is conducted using a meso-scale atmosphere model, MRAMS. Although this analysis only addresses one component of Mars atmosphere uncertainty, it demonstrates the applicability of probability bounds methods in practical engineering work. More importantly, the Mars atmosphere uncertainty analysis provides a framework in which to conclusively establish the practical importance of epistemology in rigorous uncertainty quantification.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Aerospace and Ocean Engineering

Department dc:contributor.department

Aerospace and Ocean Engineering

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2010

Author dc:creator

• Balch, Michael Scott

Chair dc:contributor.committeechair

• Walters, Robert W.

Committee members dc:contributor.committeemember

• Tolson, Robert H.
• Hosder, Serhat
• Oberkampf, William L.
• McCue-Weil, Leigh S.
• Roy, Christopher J.

• Probability
• Dempster-Shafer theory
• imprecise probability
• probability bounds
• epistemology

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-12152010-164128

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/30115