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Title: Application of fractional-moments statistics to data for two-phase dielectric mixtures

Author
item NIGMATULLIN, R - KAZAN STATE UNIVERSITY
item OSOKIN, S - USDA
item Nelson, Stuart

Submitted to: IEEE Transactions on Dielectrics and electrical Insulation
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 5/12/2008
Publication Date: 10/15/2008
Citation: Nigmatullin, R.R., Osokin, S.I., Nelson, S.O. 2008. Application of fractional-moments statistics to data for two-phase dielectric mixtures. IEEE Transactions on Dielectrics and Electrical Insulation. 15(5):1385-1392.

Interpretive Summary: Dielectric properties of materials are those electrical properties that influence the interaction of the materials with electromagnetic fields. For example, the dielectric properties of foods determine how rapidly they will be heated in a microwave oven. These properties can also be utilized with appropriate electronic instruments for sensing moisture content in grain, oilseed, and other agricultural products, because the moisture content is highly correlated with the dielectric properties of the materials. Dielectric spectroscopy is a means for measuring the dielectric properties of materials over a broad range of radio and microwave frequencies. Dielectric spectroscopy data measured on ground hard red winter wheat at moisture contents of 12.5%, 17.9% and 21.2% over the frequency range from 10 to 1800 MHz at temperatures from 2 to 76 degrees Celsius were furnished to a Russian theoretician for advanced mathematical analysis of their dielectric relaxation characteristics, which determine the dielectric properties of these materials. These analyses identified several fitting parameters, which, when used with the mathematical relationships employed, provide excellent fitting of the curves for the dielectric properties. Further, the temperature dependence of the fitting parameters can be fitted by analytical functions that can be used as calibration curves. With further research, the dielectric properties fitting functions may be useful in the application of dielectric spectroscopy for sensing quality factors and other important characteristics, which could then be used in the development of new instruments for nondestructive testing of agricultural products. Such new tools would be of value to growers, packers and processors in providing products of improved quality for consumers.

Technical Abstract: A new method for quantitative “reading” of dielectric data of complex systems is suggested. This method is based on ideas (presented by one of the authors, R.R.N) related to the application of the generalized mean value (GMV) function to random data series (statistics of the fractional moments). The GMV function allows transformation of arbitrary random data series to smooth curves that in turn can be fitted by an analytical function with limited number of parameters. These fitting parameters are sensitive to the influence of an external factor, so the dependence of these parameters on the external factor can be used as calibration curves. In this instance we analyzed dielectric data measured for ground hard red winter wheat with 12.5%, 17.9% and 21.2% moisture contents in the temperature range from 2 'C to 76 'C. This system is a complex system from the viewpoint of the complexity of the dielectric data interpretation. The common treatment of these dielectric spectra does not give us any possibility to obtain a monotonic calibration curve. We treated these spectra as random data series by the use of the GMV function. As a result of this treatment, we obtained the monotonic temperature dependence of several fitting parameters for the given 12.5%, 17.9% and 21.2% moisture contents, and these relationships can be fitted by an analytical function and used as calibration curves. We hope that this new method will find wide application for analysis of other complex systems. Key words: dielectric properties, dielectric spectroscopy, hard red winter wheat, random series, statistics of fractional moments, generalized mean value, calibration curve.