Approximation of Hysteresis Functional

TL;DR

This paper introduces a practical discrete hysteresis model based on nonlinear and generalized play, suitable for conservation laws and adsorption-desorption applications, with proven stability and demonstrated effectiveness on experimental data.

Contribution

It presents a new, easy-to-calibrate hysteresis model that compares favorably with Preisach models and includes theoretical stability analysis.

Findings

Model is easy to calibrate from sparse data

Offers rich secondary hysteresis curves

Proven well-posedness and numerical stability

Abstract

We develop a practical discrete model of hysteresis based on nonlinear play and generalized play, for use in first-order conservation laws with applications to adsorption-desorption hysteresis models. The model is easy to calibrate from sparse data, and offers rich secondary curves. We compare it with discrete regularized Preisach models. We also prove well-posedness and numerical stability of the class of hysteresis operators involving all those types, describe implementation and present numerical examples using experimental data.