Title page for ETD etd-07092009-104222


Type of Document Dissertation
Author Childers, Adam Fletcher
Author's Email Address achldrs@vt.edu
URN etd-07092009-104222
Title Parameter Identification and the Design of Experiments for Continuous Non-Linear Dynamical Systems
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Burns, John A. Committee Chair
Ball, Joseph A. Committee Member
Cliff, Eugene M. Committee Member
Herdman, Terry L. Committee Member
Keywords
  • Sensitivity Functions
  • Bounded Error
  • Parameter Identification
  • D-Optimal
Date of Defense 2009-06-15
Availability unrestricted
Abstract
Mathematical models are useful for simulation, design, analysis, control, and optimization of complex systems. One important step necessary to create an effective model is designing an experiment from which the unknown model parameter can be accurately identified and then verified. The strategy which one approaches this problem is dependent on the amount of data that can be collected and the assumptions made about the behavior of the error in the statistical model. In this presentation we describe how to approach this problem using a combination of statistical and mathematical theory with reliable computation. More specifically, we present a new approach to bounded error parameter validation that approximates the membership set by solving an inverse problem rather than using the standard forward interval analysis methods. For our method we provide theoretical justification, apply this technique to several examples, and describe how it relates to designing experiments. We also address how to define infinite dimensional designs that can be used to create designs of any finite dimension. In general, finding a good design for an experiment requires a careful investigation of all available information and we provide an effective approach to dthe problem.
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