CC9671ADd01 - IEEE Transactions on Dielectrics and...

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IEEE Transactions on Dielectrics and Electrical Insulation Vol. 9 No. 5, October 2002 845 Linear and Nonlinear Data Fitting for Dielectrics H. J. Wintle Department of Physics Queen's Umveriity Kmgston Canada K7 L 3 N6 ABSTRACT We discuss some of the problems associated with data fitting, particularly the case of uncer- tainties in all the variables, the possibly misleading results of algorithmic convergence, and also the limitations imposed by some commercial software. We suggest that the presence of local minima in the fitting function means that the parameters derived from the fitting may be subject to much larger uncertainty than often is suggested. We also address the difficulty of making accurate numerical Laplace transforms, even when regularization techniques are em- ployed. Our general conclusion is that the parameters derived by modeling dielectric data are liable to have considerable uncertainty. 1 INTRODUCTION Measurements of dielectric properties and of insulator response are frequently many-faceted. Several variables are observed, often over a wide range of experimental conditions, and with uncertainties that often themselves vary over the span of the variables. One typical ex- ample is the measurement of dielectric loss where the variables may include frequency, temperature and sample composition in addition to the loss itself. Another is the measurement of partial discharges, where pulse height, inter-pulse delay, charge, phase response, temperature, time and sample preparation may all play a role. Clearly it is important to reduce the welter of data into an easily understood form by fitting an appropriate multidimensional surface to the results. The purpose of the present paper is to provide an overview of the present status of cwve fitting, pointing out some of the pitfalls that still persist in ths very ~rell explored field. There are a number of standard procedures given in the literature [1,2], and we will not go into detail but simply refer the reader to this body of work when needed. We begin by introducing the problems which may be encountered in the case of least mean squares fitting in the context of dielectric measurements, where normally the aim is to fit well known theoretical forms to the data. Section 2 of the paper deals with the alternatives to least mean squares fitting, and Section 3 indicates briefly the possibility of making empirical fits without reference to specific models. We then go on to consider the more specialized difficulties associated with the inversion of integral transforms. We close with a short summary 2 FITTING MODEL FUNCTIONS 2.1 LEAST MEAN SQUARE CURVE FITTING The observation of dielectric loss specka, thermally stimulated cur- rent (TSC) cwves, optical and acoustic absorption spectra, and many other responses result in families of experimental curves which may have, for example, the dielectric loss as a function of frequency, with the temperature, composition and thermal treatment as parameters, which
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This note was uploaded on 06/08/2011 for the course ELECTRICAL 124 taught by Professor Ghjk during the Spring '11 term at Institute of Technology.

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CC9671ADd01 - IEEE Transactions on Dielectrics and...

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