Constrained B-Spline Based Everett Map Construction for Modeling Static Hysteresis Behavior

TL;DR

This work addresses static hysteresis modeling with the Preisach framework by constructing an Everett map as an analytic, constrained B-spline surface, enabling direct, artifact-free interpolation of measured data. The method embeds a correction scheme into a convex quadratic fitting problem to enforce non-negativity of the Preisach distribution, zero diagonal, and saturation peak, resulting in an analytic Everett map with improved robustness. Validation against degaussing, first-order reversal curves, arbitrary, and PWM-like excitations shows high fidelity and artifact elimination, though some discrepancies remain for reversal curves near the origin. Overall, the constrained B-spline Everett map provides a practical, interpolation-friendly, analytically defined hysteresis model suitable for integration with finite-element and other simulation frameworks.

Abstract

This work presents a simple and robust method to construct a B-spline based Everett map, for application in the Preisach model of hysteresis, to predict static hysteresis behavior. Its strength comes from the ability to directly capture the Everett map as a well-founded closed-form B-spline surface expression, while also eliminating model artifacts that plague Everett map based Preisach models. Contrary to other works, that applied numerical descriptions for the Everett map, the presented approach is of completely analytic nature. In this work the B-spline surface fitting procedure and the necessary set of constraints are explained. Furthermore, the B-spline based Everett map is validated by ensuring that model artifacts were properly eliminated. Additionally, the model was compared with four benchmark excitations. Namely, a degaussing signal, a set of first-order reversal curves, an arbitrary excitation with high-order reversal curves, and a PWM like signal. The model was able to reproduce all benchmarks with high accuracy.

Figures (3)

• Figure 1: (a) The normalized constrained B-spline based Everett map, and its control points ($\bullet$), with constraints applied in the Preisach plane, (b) the Preisach distribution, as determined from the unconstrained B-spline surface based Everett map, with heavy oscillations and problematic negative values, and (c) the Preisach distribution, as determined from the constrained B-spline surface based Everett map, with solely positive values.
• Figure 2: Model results and measurements of (a) a degaussing signal, and (b) a set of first-order reversal curves.
• Figure 3: Model results and measurements of (a) an arbitrary excitation, and (b) a PWM-like signal.