Inverse parameter-dependent Preisach operator in thermo-piezoelectricity modeling

TL;DR

This paper develops a Lipschitz continuous inverse for a parameter-dependent Preisach hysteresis operator, enabling more accurate modeling of thermo-piezoelectric systems with hysteresis effects and temperature dependence.

Contribution

It proves the invertibility of a general parameter-dependent Preisach operator and introduces a practical inversion algorithm considering temperature effects.

Findings

The Preisach operator admits a Lipschitz continuous inverse.

The inversion algorithm is time- and memory-discrete.

Higher input regularity yields higher output regularity.

Abstract

Hysteresis is an important issue in modeling piezoelectric materials, for example, in applications to energy harvesting, where hysteresis losses may influence the efficiency of the process. The main problem in numerical simulations is the inversion of the underlying hysteresis operator. Moreover, hysteresis dissipation is accompanied with heat production, which in turn increases the temperature of the device and may change its physical characteristics. More accurate models therefore have to take the temperature dependence into account for a correct energy balance. We prove here that the classical Preisach operator with a fairly general parameter-dependence admits a Lipschitz continuous inverse in the space of right-continuous regulated functions, propose a time-discrete and memory-discrete inversion algorithm, and show that higher regularity of the inputs leads to a higher regularity of the output of the inverse.