Date of Award
Dissertation - Restricted
Doctor of Philosophy (PhD)
Electrical and Computer Engineering
This dissertation proposes a new methodology for modeling and identifying nonlinear systems called the Group Method of Cartesian Programming. This new methodology combines the ideas of nonlinear functional networks and statistical optimization via the Group Method of Data Handling and Particle Swarm Optimization, respectively. The utility of Particle Swarm Optimization is demonstrated by applying it to the System Identification problem. In particular, Particle Swarm Optimization is used to determine the constants for several autoregressive moving average (ARMA) models. The ARMA models discovered using Particle Swarm Optimization were found to be competitive with traditional gradient based optimization techniques. Particle Swarm Optimization was next integrated into the Group Method of Data Handling methodology. It was demonstrated that it is practical to use statistical optimization (Particle Swarm Optimization) within a complex adaptive functional network (The Group Method of Data Handling). A methodology of Gaussian Regularization was developed that has the potential to further improve the adaptive modeling capabilities of a Complex Adaptive Functional Network. Several applications were used to illustrate the use of Particle Swarm Optimization and the Group Method of Data Handling. In particular the new Group Method of Cartesian Programming was utilized for optimal sensor design. The positive results of the sensor study lend support for further research that would implement all of the ideas set forth in this dissertation.