Date of Award
Spring 1-1-2013
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Electrical and Computer Engineering
First Advisor
Feng, Xin
Second Advisor
Yaz, Edwin E.
Third Advisor
Povinelli, Richard J.
Abstract
This dissertation presents novel methods for analyzing nonlinear time series in dynamic systems. The purpose of the newly developed methods is to address the event prediction problem through modeling of predictive patterns. Firstly, a novel categorization mechanism is introduced to characterize different underlying states in the system. A new hybrid method was developed utilizing both generative and discriminative models to address the event prediction problem through optimization in multivariate systems.
Secondly, in addition to modeling temporal dynamics, a Bayesian approach is employed to model the first-order Markov behavior in the multivariate data sequences. Experimental evaluations demonstrated superior performance over conventional methods, especially when the underlying system is chaotic and has heterogeneous patterns during state transitions.
Finally, the concept of adaptive parametric phase space is introduced. The equivalence between time-domain phase space and associated parametric space is theoretically analyzed.