#### Date of Award

3-2022

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Department of Systems Engineering and Management

#### First Advisor

Michael Grimaila, PhD

#### Abstract

System simulation models are often decomposed and abstracted as a collection of interconnected subsystem block models to facilitate system understanding, design, and analysis. Each subsystem block model contains mathematical functions that receive, process, and transmit signals that are modeled as real numbers, complex numbers, and/or logic values. This dissertation evaluates the use of a single two-layer complex-valued neural network model to approximate 4-input, 4-output subsystem reference block models in terms of accuracy, performance, and error. The research is novel in that it uses a neural network for continuous function approximation instead of data categorization; it uses a neural network designed to natively process complex numbers; and it uses a single neural network to approximate four independent outputs instead of using a separate neural network for each output. The major findings from this research include: (1) the accuracy of a complex-valued neural network approximation model is inversely proportional to the amount of nonlinearity present in the reference block model; (2) increasing the hidden layer neurons in a complex-valued neural network has limitations and leads to overfitting when this limit has been reached; (3) the number of hidden layer neurons when overfitting occurs is dependent upon the nonlinearity present in the reference block model; (4) the use of complex-valued neural network approximation models yields an 81.5% calculation time speed-up when approximating single subsystem reference block and an 87.94% speed-up when approximating three cascaded reference blocks; and (5) complex-valued multivariate regression polynomial approximation models yield a lower training error, lower training time, and reduced calculation time when compared to a complex-valued neural networks, but at the added expense of requiring four separate regression models to be developed to approximate a subsystem reference block.

#### AFIT Designator

AFIT-ENV-DS-22-M-01

#### DTIC Accession Number

AD1174059

#### Recommended Citation

Llewellyn, Larry C. II, "Characterizing Complex-Valued Neural Network Model Approximations of 4-Input 4-Output Complex-Valued Reference Block Models" (2022). *Theses and Dissertations*. 5408.

https://scholar.afit.edu/etd/5408