Publication Date

Spring 4-17-2017

Abstract

When modeling physical phenomena we want to solve the inverse problem by estimating the parameters that characterize the source model that we are interested in. In this thesis, we focus on the optimal placement of a finite number of individual sensors, called dosimeters, in two and three dimensions with a time dependent Gaussian wave source. Using a computational model along with experimental data, we design an iterative process to determine the optimal placement of an additional sensor such that the noise in the measurements has a minimal effect on the parameter estimation. First, we estimate the parameters that characterize the source model using a non-linear least squares optimization method. Then using the estimated parameters along with statistical analysis, we can determine an optimal location to place an additional sensor. Each time we iterate, we use new experimental data to determine a more accurate parameter estimation and optimal sensor placement. Upon reaching the maximum number of iterations, we can determine the optimal location to place an additional sensor such that we can most accurately characterize the wave source.

Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Matthew Pennybacker

Second Committee Member

Daniel Appelo

Third Committee Member

Olga Lavrova

Keywords

optimal experimental design

Document Type

Thesis

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