Efficient modeling of vector hysteresis using a novel Hopfield neural network implementation of Stoner–Wohlfarth-like operators

Abstract

Incorporation of hysteresis models in electromagnetic analysis approaches is indispensable to accurate field computation in complex magnetic media. Throughout those computations, vector nature and computational efficiency of such models become especially crucial when sophisticated geometries requiring massive sub-region discretization are involved. Recently, an efficient vector Preisach-type hysteresis model constructed from only two scalar models having orthogonally coupled elementary operators has been proposed. This paper presents a novel Hopfield neural network approach for the implementation of Stoner–Wohlfarth-like operators that could lead to a significant enhancement in the computational efficiency of the aforementioned model. Advantages of this approach stem from the non-rectangular nature of these operators that substantially minimizes the number of operators needed to achieve an accurate vector hysteresis model. Details of the proposed approach, its identification and experimental testing are presented in the paper.

Utilizing neural networks in magnetic media modeling and field computation: A review

“…The non-smooth nature of this rectangular building block suggests that a realistic simulation of a typical magnetic material hysteretic property will require a superposition of a relatively large number of those blocks. In order to obtain a smoother operator, a new hybrid activation function has been introduced in [19] . More specifically, the new activation function is expressed as: where c and d are two positive constants such that c + d = 1 and fc and fd are given by (5) and (8) , respectively.…”

“…The operators shown in Fig. 2 b maintain a constant loop width of 0.48 because k is set to (0.48/2 d ) for all curves [19] .…”

“…7 (please refer to [14] ). The approach was further generalized by using HHNN as described in the overview section [19] . Based upon this generalization and referring to (10) and (11) , expression (25) is re-adjusted to the form: where …”

“…This generalization has resulted in an increase in the modeling computational efficiency (please refer to [19] ).…”

A neural approach for the numerical modeling of two-dimensional magnetic hysteresis

“…To face this problem, a possible alternative is to use "black box" approaches, fully numeric and away from any physical interpretation of the phenomena, but usually fast and reliable for a given numeric reconstruction of data. Among these approaches, we propose in this paper, [9][10][11][12][13][14][15][16][17][18][19][20] a suitably trained Neural System (NS) composed by more than one Feed-Forward Neural Networks (FFNNs) for the modeling of two-dimensional magnetic hysteresis. The NS can be coupled as constitutive functional of the magnetic materials to a FEM solver.…”