Applications of Neural Networks in Electromagnetics

by Christodoulou, Christos; Georgiopoulos, Michael

• ISBN13: 9780890068809
• ISBN10: 0890068801
• Format: Hardcover
• Copyright: 2000-12-01
• Publisher: Artech House

Summary

The high-speed capabilities and learning abilities of neural networks can be applied to quickly solving numerous complex optimization problems in electromagnetics, and this book shows you how. Even if you have no background in neural networks, this book helps you understand the basics of each main network architecture in use today, including its strengths and limitations. Moreover, it gives you the knowledge you need to identify situations when the use of neural networks is the best problem-solving option.

Author Biography

Christos Christodoulou received a B.Sc. degree in physics and math from the American University of Cairo in 1979, and M.S. and Ph.D. degrees in electrical engineering from North Carolina State University, Raleigh, North Carolina, in 1981 and 1985, respectively. He served as a faculty member in the University of Central Florida, Orlando, from 1985 to 1998, where he received numerous teaching and research awards. In 1999, he joined the faculty of the Electrical and Computer Engineering Department of the University of New Mexico, Albuquerque as a Chair. In 1991 he was selected as the AP/MTT Engineer of the Year (Orlando Section). He is a senior member of IEEE and a member of URSI (Commission B). He served as the general Chair of the IEEE Antennas and Propagation Society/URSI 1999 Symposium in Orlando, Florida. He is the co-chair of the IEEE 2000 Symposium on Antennas and Propagation for wireless communications, in Waltham, Massachusetts. He has published over 150 papers in journals and conferences. He also has two patents. He is currently the co-editor for a column on "Wireless Communications" for the IEEE AP Magazine. His research interests are in the areas of wireless communications, modeling of electromagnetic systems, smart antennas, neural network applications in electromagnetics, and MEMS antennas Michael Georgiopoulos received a diploma in electrical engineering from the National Technical University of Athens in 1981. He also received his M.S. and Ph.D. degrees in electrical engineering from the University of Connecticut, Storrs, Connecticut, in 1983 and 1986, respectively. In 1987, he joined the University of Central Florida, where he is currently an associate professor in the School of Electrical Engineering and Computer Science. Dr. Georgiopoulos has served as the Technical Program Chair of the 1996 Southcon conference, and he has also served as the program committee member and session chair of several international neural network conferences. He has been conducting research in neural networks and applications of neural networks for over 10 years, and he has published over 140 papers in journals, conferences, and books. Dr. Georgiopoulos has worked on a variety of research topics throughout his career, including communication networks, spread spectrum communications, neural networks and applications of neural networks in computer-generated forces modeling, smart antennas, pattern recognition and image processing, electromagnetics, computer vision, manufacturing, and remote sensing. Currently, Dr. Georgiopoulos's research emphasis is on neural network algorithms (with special emphasis on ART neural network architectures), design of smart antennas using neural networks, and modeling of computer generated forces using neural network and symbolic techniques. Dr. Georgiopoulos is a member of the IEEE, a member of the International Neural Network Society, and a member of the Technical Chamber of Greece

Table of Contents

Preface	xiii
Acknowledgments	xiv
Introduction to Neural Networks	1	(38)
Preliminaries	1	(1)
Benefits of Neural Networks	2	(3)
Models of a Neuron	5	(2)
Types of Activation Function	7	(4)
Neural Network Architectures	11	(7)
Single-Layer Feed-Forward Networks	11	(1)
Multilayer Feed-Forward Networks	11	(3)
Recurrent Networks	14	(4)
Learning Procedures	18	(4)
Supervised Learning	19	(1)
Unsupervised Learning	19	(1)
Hybrid Learning	19	(3)
Learning Tasks	22	(8)
Approximation	22	(1)
Association	23	(1)
Pattern Classification	23	(1)
Prediction	23	(4)
Clustering	27	(3)
Knowledge Representation	30	(3)
Brief History of Neural Networks	33	(2)
Why Neural Networks in Electromagnetics	35	(4)
References	37	(2)
Single-Layer and Multilayer Perceptron Networks	39	(80)
Introduction	39	(1)
The Single-Layer Perceptron	40	(2)
Perceptron Learning Algorithm	42	(10)
A Geometrical Interpretation of the Perceptron Learning Algorithm	43	(6)
A Single-Layer Perceptron Example	49	(3)
Adaline Network	52	(12)
An Adaline Example	62	(2)
Multilayer Perceptron	64	(2)
The Back-Propagation Algorithm	66	(25)
A Multilayer Perceptron Example	76	(15)
Issues With Back-Propagation Learning	91	(5)
Initialization	91	(1)
Modes of Training	92	(1)
Stopping Criteria	93	(1)
Number of Hidden Layers/Units	94	(2)
Learning Rates	96	(1)
Randomized Inputs	96	(1)
Variations of the Back-Propagation Algorithm	96	(7)
Back-Propagation With Momentum	98	(1)
Delta-Bar-Delta Algorithm	99	(2)
The Modified Error Function Algorithm	101	(2)
The Multilayer Perceptron Neural Network for an Automatic Target Recognition Application	103	(5)
Matlab Code	108	(11)
References	117	(2)
Radial Basis Function Networks---Kohonen Networks	119	(44)
Introduction	119	(2)
Preliminaries of Radial Basis Function Neural Networks	121	(5)
Learning Strategies With Radial Basis Function Neural Networks	126	(18)
Fixed Centers Selected at Random (Learning Strategy 1)	127	(2)
Self-Organized Selection of Centers (Learing Strategy 2)	129	(11)
Supervised Selection of Centers (Learning Strategy 3)	140	(3)
Supervised Selection of Centers and Variances (Learning Strategy 4)	143	(1)
A Radial Basis Function Neural Network Algorithm	144	(1)
A Radial Basis Function Neural Network Example	145	(2)
Comparison of Radial Basis Function Neural Network Learning Strategies	147	(1)
Issues With Radial Basis Function Neural Network Learning	148	(1)
The General Regression Neural Network (GRNN)	149	(6)
A Neural Network Implementation of the General Regression Neural Network	152	(1)
A General Regression Neural Network Example	153	(2)
Matlab Code	155	(8)
References	160	(3)
Adaptive Resonance Theory Neural Networks	163	(68)
Introduction	163	(4)
The Fuzzy ARTMAP Neural Network	167	(9)
The Fuzzy ARTMAP Architecture	167	(2)
Operating Phases of Fuzzy ARTMAP	169	(7)
Templates in Fuzzy ARTMAP: A Geometrical Interpretation	176	(6)
Example	182	(5)
Convergence Speed of Fuzzy ARTMAP	187	(12)
Result 1	189	(1)
Result 2	190	(1)
Result 3	190	(3)
Result 4	193	(4)
Result 1'	197	(1)
Result 2'	197	(1)
Result 3'	197	(1)
Result 4'	198	(1)
Order of Search in Fuzzy ARTMAP	199	(12)
The Definition of Distance in Fuzzy ART	199	(12)
Applications of Fuzzy ARTMAP	211	(2)
MATLAB Code	213	(18)
Appendix 4A	219	(1)
Training Phase of Fuzzy ARTMAP	219	(6)
Appendix 4B	225	(1)
Test Phase of Fuzzy ARTMAP	225	(2)
References	227	(4)
Recurrent Neural Networks	231	(84)
Introduction	231	(2)
Preliminaries of Associative Memories	233	(2)
The Hopfield Model	235	(3)
Node Transition Modes	236	(2)
Associative Memory Application of the Hopfield Neural Network	238	(4)
Example of an Associate Memory Application	239	(3)
Discussion	242	(4)
Optimization Problems Using the Hopfield Neural Network	246	(23)
Number Representation Schemes	246	(4)
The Hitchcock Problem	250	(15)
The Traveling Salesman Problem	265	(4)
A Problem in Communications Using the Hopfield Neural Netowork	269	(13)
The RTRL Neural Network	282	(5)
RTRL NN Examples	287	(3)
The Recurrent Time Recurrent Learning Neural Network for Channel Equalization	290	(6)
The Elman Neural Network	296	(2)
Elman Neural Network Examples	298	(4)
Angle of Arrival Estimation Using Elman Networks	302	(3)
Matlab Code	305	(10)
References	312	(3)
Applications in Antennas	315	(48)
Introduction	315	(1)
Design of Gratings and Frequency Selective Surfaces	316	(7)
Training	317	(2)
Results	319	(4)
Neural Network-Based Adaptive Array Antennas	323	(9)
Adaptive Beamforming With Circular Array Antennas	326	(3)
Neural Network Implementation	329	(1)
Generation of Training Data	329	(2)
Results	331	(1)
Beam Shaping With Antenna Arrays	332	(3)
Network Training	333	(1)
Results	334	(1)
Aperture Antenna Shape Prediction	335	(6)
Training	337	(2)
Results	339	(2)
Reflector Surface Error Compensation	341	(13)
Radiation Integral Decomposition	342	(3)
Neural Network Implementation	345	(2)
Scaling of Coefficients of Expansion Error Functions	347	(1)
Results	347	(7)
Resonance Frequency of Triangular Microstrip Antennas	354	(3)
Training of the Multilayer Perceptron Neural Network	355	(1)
Results	355	(2)
Design of Multilayer Phased Array Antennas	357	(6)
References	358	(5)
Applications in Radar and Remote Sensing	363	(28)
Introduction	363	(1)
Radar Target Classification	364	(8)
One-Dimensional Profile Classification	365	(3)
Classification of Two-Dimensional ISAR Images	368	(4)
Classification of Radar Clutter	372	(3)
Remote Sensing	375	(16)
Sea Ice Classification	375	(8)
An Improved Geophysical Neural Network-Based Model for High-Speed Winds	383	(5)
References	388	(3)
Applications in Mobile Communications	391	(38)
Introduction	391	(3)
Adaptive Antenna Array Processing	394	(2)
Neural Network-Based Direction Finding	396	(13)
Results	401	(8)
Direction of Arrival for Multiple Sources Using Multilayer Neural Networks	409	(8)
Detection Stage	411	(1)
Results	412	(5)
Adaptive Nulling and Steering	417	(3)
Adaptive Beamforming Using One-Dimensional Linear Arrays	417	(2)
Adaptive Beamforming Using Two-Dimensional Rectangular Arrays	419	(1)
Neural Network-Based Interference Cancellation	420	(9)
Results	422	(5)
References	427	(2)
Applications in Microwave Circuits and Devices	429	(32)
Introduction	429	(1)
Simulation and Optimization of Microwave Devices and Circuits	429	(5)
Simulation	431	(2)
Optimization	433	(1)
Modeling of Passive Devices for MMIC Design	434	(9)
Example 1: An X-Band Spiral Inductor	435	(1)
Example 2: Via Interconnects in Microstrip Circuits	436	(3)
Example 3: Multiconductor Lines	439	(4)
Speeding Up and Configuring the Optimum Size for a Neural Network	443	(9)
Combining the Infinite Impulse Response (IIR) Filters and Neural Networks for Time-Domain Problems	443	(5)
Determination of the NN Structure Using ``Pruning'' and Genetic Algorithms	448	(4)
A Modular, Knowledge-Based Development of Libraries of Neural Network Models	452	(9)
References	456	(5)
Applications in Computational Electromagnetics	461	(32)
Introduction	461	(1)
Finite Element Applications	461	(4)
Correlation Between FEM and NN	462	(1)
One-Dimensional Example	463	(1)
Two-Dimensional Examples	463	(2)
A General Neural Network Representation of FEM	465	(6)
The Forward Problem	467	(1)
The Inverse Problem	468	(3)
A Neural-Network Approach of the Method of Moments	471	(8)
Neural Network Implementation	472	(3)
The Inverse Problem	475	(4)
Combination of the Piecewise Harmonic Balance Technique and Neural Networks	479	(2)
A Simple Example	479	(2)
Combination of Finite Difference Time Domain and Neural Networks	481	(12)
Modeling of Microwave and Millimeter-Wave Circuits (MIMICs)	482	(3)
Modeling High-Q Structures	485	(3)
References	488	(5)
About the Authors	493	(2)
Index	495