Stochastic model of hysteresis

TL;DR

This paper introduces a stochastic model of hysteresis using probability theory, where reversal points are Markov points, explaining the accommodation process and properties of minor loops, differing from traditional models.

Contribution

It presents a novel stochastic approach to hysteresis modeling that accounts for non-zero susceptibilities and explains the convergence to limit curves and memory properties.

Findings

Reversal points are Markov points influencing the process.

Minor loops converge to limit curves with many cycles.

Model approximates Rayleigh quadratic law for small parameter variations.

Abstract

The methods of the probability theory have been used in order to build up a new model of hysteresis. It turns out that the reversal points of the control parameter (e. g., the magnetic field) are Markov points which determine the stochastic evolution of the process. It has been shown that the branches of the hysteresis loop are converging to fixed limit curves when the number of cyclic back-and-forth variations of the control parameter between two consecutive reversal points is large enough. This convergence to limit curves gives a clear explanation of the accommodation process. The accommodated minor loops show the return-point memory property but this property is obviously absent in the case of non-accommodated minor loops which are not congruent and generally not closed. In contrast to the traditional Preisach model the reversal point susceptibilities are non-zero finite values. The stochastic model can provide a good approximation of the Raylaigh quadratic law when the external parameter varies between two sufficiently small values.