Thermodynamically-Consistent Modeling of Ferromagnetic Hysteresis.

Models of ferromagnetic hysteresis are established by following a thermodynamic approach. The class of constitutive properties is required to obey the second law, expressed by the Clausius-Duhem inequality, and the Euclidean invariance. While the second law states that the entropy production is non-negative for every admissible thermodynamic process, here the entropy production is viewed as a non-negative constitutive function. In a three-dimensional setting, the magnetic field and the magnetization are represented by invariant vectors. Next, hysteretic properties are shown to require that the entropy production is needed in an appropriate form merely to account for different behavior in the loading and the unloading portions of the loops. In the special case of a one-dimensional setting, a detailed model is determined for the magnetization function, in terms of a given susceptibility function. Starting from different initial magnetized states, hysteresis cycles are obtained by solving a nonlinear ordinary differential system. Cyclic processes with large and small amplitudes are established for materials such as soft iron.

The Effects of Sheet Thickness and Excitation Frequency on Hysteresis Loops of Non-Oriented Electrical Steel.

The paper focuses on modeling the rate dependence of hysteresis loops in conductive magnetic materials. The concept, which was advanced about fifty years ago by Chua, is discussed. It is shown that the viscous-type equation considered by Zirka and co-workers belongs to the class of Chua-type models. The dynamic effects are described with a simple fractional power law. The value of the exponent in the above-mentioned power law may be assessed on the basis of measurements of coercive field strength at different excitation frequencies. To verify the usefulness of the approach, the measurements of hysteresis loops were carried out at several excitation frequencies under standardized conditions for two grades of non-oriented electrical steel. The modeled curves are in a good correspondence with the measured ones. The considered model uses fewer parameters than approaches based on three-term loss separation schemes.

Hysteresis Modeling in Iron-Dominated Magnets Based on a Multi-Layered NARX Neural Network Approach.

A full-fledged neural network modeling, based on a Multi-layered Nonlinear Autoregressive Exogenous Neural Network (NARX) architecture, is proposed for quasi-static and dynamic hysteresis loops, one of the most challenging topics for computational magnetism. This modeling approach overcomes drawbacks in attaining better than percent-level accuracy of classical and recent approaches for accelerator magnets, that combine hybridization of standard hysteretic models and neural network architectures. By means of an incremental procedure, different Deep Neural Network Architectures are selected, fine-tuned and tested in order to predict magnetic hysteresis in the context of electromagnets. Tests and results show that the proposed NARX architecture best fits the measured magnetic field behavior of a reference quadrupole at CERN. In particular, the proposed modeling framework leads to a percent error below 0.02% for the magnetic field prediction, thus outperforming state of the art approaches and paving a very promising way for future real time applications.