Fitting magnetic hysteresis curves by using polynomials

For the identification of hysteresis models and characterization of magnetic materials, the derivatives of various curves are required. If the derivative of a curve is determined by means of numerical differentiation the noise in the experimental data is significantly amplified, therefore the smoothing method applied to the raw data is very important. For the determination of the saturating field and saturating induction the normal magnetization and the coercivity curves are used; the noise in these curves can lead to erroneous results. This paper presents an analytical method for fitting experimental data to polynomials such that the resulting curve and its derivative are smooth and can be obtained analytically. The input data are decomposed in a series of segments and for each segment is determined the coefficients of the cubic polynomials by means of linear regression. The coefficients of the polynomials are constrained by the condition of continuity of the fitted curve and its first and second derivatives, which will ensure the continuity and smoothness of the resulting curve and its derivative. Due to the imposed constraints the polynomial for each segment can be rewritten with the coefficients of the previous segment, and so on down to the first segment; thus with increasing number of segments, the complexity of the n^th polynomial will also increase. In this paper are presented the equations describing the polynomials, for any number of segments used for regression, and the method to determine the coefficients of the polynomials by means of linear regression. Finally, experimental results obtained using the described method are presented. By using the proposed method the derivative of a curve can be accurately estimated even if the measured data are characterized by noise.