Open Access
Kim, Byounghee
Graduate Program:
Electrical Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
November 08, 2006
Committee Members:
  • Kwang Yun Lee, Committee Chair
  • Jeffrey Scott Mayer, Committee Member
  • Shizhuo Yin, Committee Member
  • Andre Louis Boehman, Committee Member
  • Semigroup Theory
  • neural networks
  • Extrapolation
Pure extrapolation of time series assumes that all we need to know is contained in the historical values of the series that is being forecasted. For extrapolations, it is assumed that evidence from one set of data can be generalized to another set. Because past behavior is a good predictor of future behavior, extrapolation is appealing. It is also appealing in that it is objective, replicable, and inexpensive. This makes it a useful approach when one needs many short-term forecasts. Using neural networks to make forecasts is controversial. One major limitation of neural nets is that one must rely on the data to lead him to the proper model. Also neural nets are more complex than many of the older time-series methods. The method is similar to stepwise regression, an earlier method in which the analyst depends on the data to produce a model. As it stands now, there is no universal method of solving a general extrapolation problem. As a matter of fact, there is no consensus of opinion concerning whether the general extrapolation problem is a mathematically well-posed problem. It is a central contention of this proposal that if the extrapolation problem carries with it a group-like property, extrapolation is possible. It is a second central contention of this proposal, that if extrapolation is possible, the mechanics involve developing a linkage between the extrapolating object and the extrapolating agent. In this thesis project we focus on an investigation of a mathematical approach to extrapolation, using a combination of a modified neural network architecture and semigroup theory. Semigroup theory provides a unified and powerful tool for the study of differential equations on abstract spaces, covering systems described by ordinary differential equations, partial differential equations, functional differential equations and combinations thereof. The target of this investigation will be the prediction (by way of extrapolation) of the temperatures within the boiler facility of a power plant. Given a set of empirical data with no analytic expression, we first develop an analytic model and then extend that model along a single axis. In this thesis, the empirical data set can be composed of experimental data or simulated data. For applications to control systems, estimation techniques are often required to compensate for an inadequate amount of data, arising from the unavailability of that data. Classical methods such as the Kalman filter have the major drawback of needing a model as their basis; the method being proposed requires no such model.