Efficient Algorithms for the Inclusion of the Preisach Hysteresis Model in Nonlinear Finite-Element Methods

Abstract

This paper deals with key problems that have been commonly encountered in the implementation of the Preisach model into finite-element (FE) programs. Such problems include the inverse problem imposed by certain FE formulations, the abundance use of experimental data needed for identification, and the complex hysteretic nonlinearity inherited in electromagnetic problems. The aim is to alleviate these problems using new efficient algorithms to facilitate the inclusion of the Preisach model in FE equations. The inversion of the model is evaded by systematically creating an inverted Everett function identified from a few parameters usually provided by the makers of electrical steel. The Everett function and its derivatives are ensured to be smooth and continuous by using cubic spline interpolation, which is important for producing stable iterative solutions in the FE computations. Thorough investigations and FE simulations supported by experiments show that the proposed algorithms are capable of successfully accomplishing good accuracy, fast computation, and numerical convergence.Index Terms-Convergence, Everett function, finite-element analysis (FEA), fixed-point method, inverse problems, magnetic hysteresis, Preisach model, software simulation tools.

Study on Dynamic Hysteretic and Loss Properties of Silicon Steel Sheet Under Hybrid Harmonic and DC Bias Excitation

“…To investigate one and two dimensional (1&2-D) hysteretic and loss properties of ferromagnetic materials, researchers has proposed various hysteresis models such as Jile-Atherton (J-A), Energetic, E&S, and Preisach models [14]- [16], [25]- [29]. Concerning the physical mechanisms of magnetization, the Preisach model has been presented and developed from the perspective of a stringent mathematical definition to accurately model the hysteresis nonlinearity and predict the magnetic characteristics [30], [31].…”

“…The static or dynamic components of iron loss are assumed to be polynomial functions with respect to flux density to investigate the loss properties of iron core under sinusoidal or DC-biased excitations [11]- [13]. Another approach to estimate iron loss under harmonic or DC-biased magnetization is the field separation [14]- [16], which is equivalent to the loss separation. The static loss components is calculated by hysteresis model, and the modeling of dynamic loss requires the shape controlling factor g(B) of dynamic loop [17] or the statistical parameter V 0 associated with the distribution of local coercive field [18]- [20].…”

Anisotropic Generalization of Vector Preisach Hysteresis Models for Nonoriented Steels

“…The Preisach model is implemented using Everett functions constructed from the first-order reversal curves. Details on the inversion of the classical Preisach model as well as the employed identification and interpolation algorithms for the vector Everett functions can be found in [7]. The novelty of this paper lies in the extension of the generalized Mayergoyz model stated in [8], by defining the input projection of the flux density as…”

Modelling anisotropy in non-oriented electrical steel sheet using vector Jiles–Atherton model

“…Among diverse methods for predicting locally the isotropic hysteresis, the mathematical Preisach model and the phenomenological Jiles-Atherton (J-A) model received a growing attention these last decades. In order to account for the anisotropic behaviour of electrical steel sheets, the improvement of the Preisach model can be performed either with a phenomenological bistroide model (Vernescu-Spornic et al, 2000) or with a generalized Mayergoyz model (Mayergoyz, 2003;Dlala, 2011;Handgruber et al, 2015). Although the former presents some discrepencies at low amplitude of the flux density under rotational field, the diverse improvements of the latter can accuratly represent both alternating and rotating dissipative behaviour, including the excess field, of the ferromagnetic materials.…”