Utilizing four-node tetrahedra-shaped Hopfield neural network configurations in the local magnetization assessment of 3d objects exhibiting hysteresis

There is no doubt that the accurate assessment of local magnetization in three-dimensional objects exhibiting hysteresis is crucial to accurate performance estimation of a variety of electromagnetic devices. Recently, it has been demonstrated that a Stoner-Wohlfarth-like elementary hysteresis operator may be constructed using two-node Hopfield neural network (HNN) having internal positive feedback. Based upon the previously mentioned approach, this paper presents a methodology using which local magnetization in 3D objects exhibiting hysteresis may be assessed. The approach utilizes a four-node tetrahedron-shaped HNN with activation functions constructed using a weighted superposition of a step and sigmoidal functions in accordance with the M − H curve of the material under consideration. In this approach, the internal feedback factors between the different nodes for any tetrahedron are dependent on its geometrical configuration. Hence, shape configuration effects on the magnetization patterns of any three-dimensional object approximated by an ensemble of tetrahedra are implicitly taken into consideration. To demonstrate the applicability of the proposed approach, computations were carried out for different three-dimensional magnetized bodies having different M − H curves. Theoretical and computational details of the approach are given in the paper.