Theses

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Browsing Theses by Discipline "Applied Mathematics"

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    A Comparison of Threshold Parameters in Deterministic SIS and SI1I2S Models and Stochastic SIS and SI1I2S Models.
    (2013-11-04) Cuffney, Laurie Ann; John Franke, Chair; Ralph Smith, Member; James Selgrade, Member
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    Data Clustering via Dimension Reduction and Algorithm Aggregation
    (2008-11-07) Race, Shaina L; Ernest Stitzinger, Committee Member; Carl Meyer, Committee Chair; Ilse Ipsen, Committee Member
    We focus on the problem of clustering large textual data sets. We present 3 well-known clustering algorithms and suggest enhancements involving dimension reduction. We propose a novel method of algorithm aggregation that allows us to use many clustering algorithms at once to arrive on a single solution. This method helps stave off the inconsistency inherent in most clustering algorithms as they are applied to various data sets. We implement our algorithms on several large benchmark data sets.
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    Investigation of Active Failure Detection Algorithms
    (2006-02-28) Hannas, Benjamin L; Dr. Stephen L. Campbell, Committee Chair; Dr. Mette S. Olufsen, Committee Member; Dr. Hien T. Tran, Committee Member
    This study analyzes two robust failure detection algorithms and applies the algorithms to three power system models. An optimal test signal to distinguish between a failure model and a normal model is calculated using the two algorithms. Advantages and disadvantages of each algorithm, Direct Optimization (DO) and Constrained Control (CC), are discussed. DO uses complex software (Sparse Optimal Control Software by The Boeing Corporation) to solve the necessary and boundary conditions of the optimization problem directly. CC utilizes free software (SciLab by Inria, Enpc.) to solve a two-point boundary value problem based on the necessary and boundary conditions of the optimization problem. Both algorithms yield similar signals, but DO is faster and more accurate yet requires expensive software. CC is not as robust, but can be run on free software and does not need as much fine tuning as the DO algorithm. Examples presented are two DC motor models and a linearized gas turbine model.
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    Optimal Filtering of Complex Turbulent Systems with Memory Depth through Consistency Constraints.
    (2012-03-27) Bakunova, Eugenia Stanislavovna; John Harlim, Chair; Hien Tran, Member; Kazufumi Ito, Member
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    Sensitivity Analysis of the Applied Element Method for the Buckling of Uni-axially Compressed Plates.
    (2013-10-28) Mohamed, Ismail; Robert White, Chair; Ernest Stitzinger, Member; Zhilin Li, Member
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    Stochastics Volatility Corrections for Interest Rate Models
    (2002-07-26) Dai, Jin; Jean-Pierre Fouque, Committee Chair
    This paper is mainly focused on how to price the interest rate derivatives by stochastic volatility models. We will use CIR model and introduce a new Ito process to the model with fast mean-reverting stochastic volatility to compute the corrections of interest rate derivatives. There is a significant difference of the shape of yield curves between the corrected model and original CIR model. It can also be used to price interest rate derivatives such as bond options.