IMMG Student Projects

2002-2003 Major Qualifying Project / Graduate Industrial Project:

Complex Permittivity Reconstruction with Neural Networks

Students: Gregory S. Pettigrew, '03 and Pawel Kopyt, Ph.D. Candidate at Warsaw University of Technology
Advisor: Vadim Yakovlev

Motivation

Interest in the dielectric properties of materials stems, at the fundamental level, from what they reveal about the mechanisms of interaction of electromagnetic fields and matter. Understanding of such interactions facilitate and help optimize their exploitation in numerous industrial, medical, and telecommunication applications. At the practical level, an interest in the dielectric properties has recently increased in view of the fact that appropriate modeling tools are now able to provide a designer with significant information about the characteristics of the constructed system prior to making its physical prototype. However, no trustworthy simulation is possible without an adequate presentation of dielectric properties (i.e., complex permittivity = ' - '') of materials involved. Getting reliable data on media parameters has thus become a crucial issue of engineering practice.

Approach

This project deals with an original method of complex permittivity reconstruction requiring a limited involvement of measurements, but heavily based on electromagnetic modeling and a special post-processing technique based on Artificial Neural Networks (NN). The frequency characteristic of the reflection coefficient of a cavity containing a sample of the studied material can be easily measured with the use of widely available equipment.

On the other hand, modeling software is able to accurately compute the reflection from the considered cavity containing the dielectric inclusion of the same configuration and known (randomly chosen) permittivity. A metal cavity is known to have a unique frequency characteristic of the reflection coefficient, so two dielectric samples of the same size and at the same position, but characterized by different permittivity, will produce different reflections in a particular frequency range. Treating the computed and measured characteristics as an initial guess and the goal function respectively, the method runs subsequent simulations of the model to get the computed curve in the form of the goal function.

Results

The basic aspects of the method have recently been developed in a joint project between The Ferrite Company, Inc. and WPI. This MQP was designed as the means to make further contributions in development and specifications of this method. The project has made the following contributions:

1. Analytical review of the relevant literature has shown that a standard Multilayer Perceptron (MLP) possesses enough capabilities to handle the problem's data and to solve the related optimization problem. No particular advantages of other suitable NN (particularly, Radial Basis Functions) have been found. This has proven the network's MLP-based structure implemented in the procedure.
2. The entire NN-based algorithm implementing the computational part of the method has been reviewed, revised and adjusted to the MATLAB 6 environment.
3. The experimental part of the method has been developed, built and thoroughly tested in conjunction with the computational part.
4. Verification of the method with materials of known properties has been made towards evaluation of accuracy of reconstruction of complex permittivity. The errors of determination of ' and '' were found to be 0.1 and 1.4 % (fresh water) and 0.1 and 4.6 % (saline water) respectively. In the following tables, the determined values are compared with the data generated by the polynomial model [1] characterized by less than 1% (for ') and 3% (for '') errors:
   
   
   
   
   
   
5. The method's sensitivity to the sample's geometry/position and quality of performance for different (small and large) values of complex permittivity have been studied both computationally and experimentally.
6. Specification of capabilities and limitations of the method have been generated: among them, the requirement for the imaginary part of permittivity to be larger than a certain value, the necessity to work with uniform materials, etc. Recommendations for the preferred experimental system have also been formulated.
7. Operation of the method has been demonstrated in determination of complex permittivity of unknown food materials (yams and potato).

Notes

1. The web page is based of the executive summary of the project presented at the WPI Project Day on Tuesday, April 15, 2003
2. The material of the project is included in the paper

   E. Eves, P. Kopyt, G. Pettigrew, and V.V. Yakovlev, Reconstruction of complex permittivity with neural networks, Proc. 9th AMPERE Conference on MW and High Frequency Heating, Loughborough, U.K., September 2003, pp. 141-144.

Part Two: Report (PDF, 3.3 MB)

vadim@wpi.edu

Last modified: Tue, Sept 30, 2003