DATA FITTING AND LEAST-SQUARE ESTIMATION OF NONLINEAR PARAMETERS FOR MODELS OF DIELECTRIC RELAXATION DATA

Abstract

<p> The work in this thesis is to develop a tool for calculating the parameters corresponding to certain theoretical model of dielectric relaxation phenomena and then doing the curve fitting using the result after fetching the data from the user. To our best knowledge, this the first such tool to calculate the parameters corresponding to certain theoretical model of dielectric relaxation phenomena while the user only need to provide the experimental data. The parameters are calculated by using a nonlinear least square algorithm implemented in Matlab and a nonlinear function minimizer available in Matlab. The way to do the curve fitting is not by the traditional way such as cubic spline but by calculating the simulated data using the chosen model and the calculated result for the parameters. </p> <p> The available mathematical models include all of popular theoretical models, the Cole-Davidson (DC), the Kohlrausch-Williams-Watts (KWW), the Havriliak-Negami (HN) and the model proposed by R. Hilfer (FD). </p> <p> There are two ways to calculate the parameters for each model as mentioned before. The result returned by this system may not be unique. Especially if the frequency range of data is not wide enough, the result would most likely be non-unique. Since the iterative method is used in the system, it is suggested that the user provides the initial values for the system with his best knowledge or background for the data and the tested sample related to dielectric relaxation process. </p> <p> It is normal if there is a part having worse fitting than the other parts. One of reasons could be the mathematical model's defect, which the model does not work for that part. For the further information, please contact me by email at zouhaijun at yahoo.com. </p>