Discovery of sparse hysteresis models for piezoelectric materials

TL;DR

This paper introduces a sparse regression-based approach for modeling hysteresis in piezoelectric materials, achieving accurate predictions with concise models and demonstrating advantages over traditional methods.

Contribution

It pioneers the application of sparse regression techniques to nonlinear hysteresis modeling in piezoelectric materials, providing an efficient and robust alternative to existing methods.

Findings

Accurately models hysteresis in simulated and real data

Outperforms traditional regression and neural network methods

Produces concise, interpretable models

Abstract

This article presents an approach for modelling hysteresis in piezoelectric materials, that leverages recent advancements in machine learning, particularly in sparse-regression techniques. While sparse regression has previously been used to model various scientific and engineering phenomena, its application to nonlinear hysteresis modelling in piezoelectric materials has yet to be explored. The study employs the least-squares algorithm with a sequential threshold to model the dynamic system responsible for hysteresis, resulting in a concise model that accurately predicts hysteresis for both simulated and experimental piezoelectric material data. Several numerical experiments are performed, including learning butterfly-shaped hysteresis and modelling real-world hysteresis data for a piezoelectric actuator. The presented approach is compared to traditional regression-based and neural network methods, demonstrating its efficiency and robustness. Source code is available at https://github.com/chandratue/SmartHysteresis