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

TL;DR

This paper introduces a robust, analytic B-spline based method for constructing Everett maps in hysteresis modeling, effectively eliminating artifacts and accurately reproducing various benchmark signals.

Contribution

It presents a novel, fully analytic B-spline surface fitting approach for Everett maps that improves accuracy and artifact elimination in hysteresis modeling.

Findings

Successfully eliminated model artifacts in Everett maps.

Accurately reproduced multiple benchmark signals.

Validated robustness across different excitation types.

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.