Date of Award

Spring 1-1-2018

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Brandon A. Jones

Second Advisor

Alireza Doostan

Third Advisor

Gregory Beylkin

Fourth Advisor

Daniel Scheeres

Abstract

In light of recent collisions and an increasing population of objects in Earth orbit, the space situational awareness community has significant motivation to develop novel and effective methods of predicting the behavior of object states under the presence of uncertainty. Unfortunately, approaches to uncertainty quantification often make simplifying assumptions in order to reduce computation cost. This thesis proposes the method of separated representations (SR) as an efficient and accurate approach to uncertainty quantification. The properties of an orthogonal polynomial basis and a uni-directional least squares regression approach allow for the theoretical computation cost of SR to remain low when compared to Monte Carlo or other surrogate methods. Specifically, SR does not suffer from the curse of dimensionality, where computation cost increases exponentially with respect to input dimension. Benefits of this low computation cost are shown in a series of low Earth orbit test cases, where SR is used to accurately approximate non-Gaussian posterior distribution functions. Here, the dimension of the problem is increased from 6 to 20 without incurring significantly more computation time. Taking advantage of a large input dimension, this research presents a global sensitivity analysis computed via SR, which affords a more nuanced analysis of a previously examined case in the literature. By considering design variables, SR is formulated to perform optimization under uncertainty. A novel method that utilizes a Brent optimizer to create training data at unique times of closest approach is devised and implemented in order to detect low probability collision events. This methodology is leveraged to design an optimal avoidance maneuver, which would be intractable when using traditional Monte Carlo. Lastly, a multi-element algorithm is formulated and presented to estimate solutions that are challenging for unmodified SR. This multi-element SR leads to orders of magnitude in accuracy improvement when considering the ability of unmodified SR to approximate discontinuous, multimodal, or diffuse solutions.

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