A hybrid magnetic field model for axisymmetric magnets

A hybrid model, synergistically fusing the accuracy of artificial neutral networks (ANNs) and the efficiency of the single magnetic dipole (MD) model, is presented to characterize the magnetic field of axisymmetric cylindrical permanent magnets. While the MD model is widely used due to its simplicity, its efficacy reduces dramatically near the source as it is unable to compensate for geometry and physical imperfections. The approach undertaken here retains the parametric nature of the MD to model fields far from the source and simultaneously capitalizes on the non-parametric nature of ANNs to precisely model the magnetic field close to the source. To do so, the space around the magnet is segregated into two regions, where the one closer to the magnet is assigned to the ANN model and the one further to the MD model. Two methods are used to determine the optimum transition point between the two regions: dividing the space along magnetic equipotential lines via the Levenberg-Marquardt algorithm (LMA) and calculating the parameters of a straight line boundary with genetic algorithms (GAs). This hybrid ANN-MD (HAM) model was evaluated with experimental field data, and it was on average 15 times more accurate than that of the dipole based model and twice as accurate as an ANN-only model.