An effective neural network approach to reproduce magnetic hysteresis in electrical steel under arbitrary excitation waveforms

A computationally efficient and robust neural network-based model to reproduce the hysteresis phenomenon for soft ferromagnetic alloys is here presented, as well as a dedicated procedure to generate a suitable training set from a minimal set of experimental data. Firstly, an accurate experimental verification has been performed for a commercial NGO electrical steel, measuring a family of hysteresis loops under sinusoidal and non-sinusoidal magnetic induction waveforms. The Preisach model of hysteresis, identified with the sinusoidal loops, has been exploited to generate a wider data set, which consists of a family of first-order reversal curves (FORCs), suitable to train the neural network. Then, a neural network-based hysteresis model, with the capability to reproduce the eventual presence of sub-loops, has been developed. The two simulation approaches have been validated taking into account the other experimental data, which consist of a family of hysteresis loops measured under different types of magnetic induction waveforms. The comparison between the Preisach model and the neural network-based model also covers the simulation of the waveforms found in magnetic systems supplied by pulse-width modulated (PWM) signals. The substantial agreement found indicates that the neural network model can replicate the behaviour of the Preisach model with a considerable advantage in terms of computational cost and memory allocation. In addition, the possibility to be quickly inverted makes the proposed method suitable for matching with FEM solvers.