Automated two-dimensional field computation in nonlinear magnetic media using Hopfield neural networks

Abstract

It is well known that the computation of magnetic fields in nonlinear magnetic media may be carried out using different approaches. In the case of problems involving complex geometries and/or magnetic media, numerical techniques become especially more appealing. In this paper, we present an automated integral equation approach using which two-dimensional field computations may be carried out in nonlinear magnetic media. This approach is constructed in terms of a continuous Hopfield neural network (HNN) whose neuron activation functions are set to mimic the vectorial magnetic properties of the media. Using well-established HNN energy minimization algorithms, an automated solution of the problem is then obtained. The approach has been implemented and resulted in good agreement with finite-element (FE) computations. Details of the approach, computations, and FE results are given in this paper.Index Terms-Continuous Hopfield neural networks, nonlinear magnetic media, 2-D field computations.

Active electromagnetic suspension system design using hybrid neural-swarm optimization

“…2 -which includes an ensemble of the continuous HNNs representing the sub-region blocks instead of the usual neurons -may be used to carry out field computation in an active electromagnetic suspension system involving non-linear magnetic media. It should be mentioned that the evolution of this modular network follows the same reasoning previously described (and verified accuracy-wise) in [3]. Finally, output values of the blocks (i.e., local vectorial magnetization values) as a whole converge based upon energy minimization criterion.…”

“…As demonstrated in [3], assuming constant magnetization within every sub-region and adopting n-th root approximate relation for non-linear M-H magnetic properties, Eq. (1) may be re-written in the form:…”

“…It should be pointed out that a G-node fully connected HNN having neuron activation functions given by f (x) may be used to mimic a vectorial M-H relation in a particular magnetic sub-region [3]. More specifically, the G-nodes are assumed to represent a collection of scalar relations oriented along all possible 2-D directions as follows:…”

“…1). Within this approach, 2D field computations are carried out using the integral equation approach in an automated mechanism through continuous Hopfield neural network (HNN) implementation in which neuron activation functions are set to mimic the vectorial magnetic properties of the media [2,3]. Optimal dimensions of the system are identified, on the other hand, through the minimization of an error function of some target performance using the particle swarm optimization (PSO) evolutionary approach (refer, for instance, to [4][5][6][7]).…”

Field computation in non-linear magnetic media using particle swarm optimization

“…In the case of problems involving complex geometries, both numerical and artificial intelligence techniques become especially more appealing (refer for instance to Ref. [1]). Irrespective of the adopted approach, geometrical domain subdivision is usually performed and local magnetic quantities are considered.…”