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The classical Preisach model and its modifications are one of the most generally applied simulations to model the behavior of magnetic materials, to describe hysteresis phenomena and different properties, as noncongruent minor loops, frequency dependence, temperature dependence, accommodation, and so on. Artificial neural networks (NNs) are widely used in fields of research where the solution of problems with conventional methods on traditional computers is very difficult to work out, for example system identification, modeling and function approximation. NNs can be considered as universal approximation for functions based on the theorem of Kolmogorov‐Arnold. In this paper a new NN model of scalar hysteresis characteristics is introduced. The examined method is built on the function approximation and continuous interpolation capability of NNs. The anhysteretic magnetization curve and a set of the ascending and a set of the descending first order reversal branches can be stored in a system of three neural networks. Different properties of magnetic materials can be simulated by a simple knowledge‐based algorithm. Value of differential susceptibility can be expressed in analytical form. Finally hysteresis characteristics predicted by the introduced model are compared with the results of the Preisach simulation.

Piezoelectric actuators (PEAs) exhibit hysteresis nonlinearity in open-loop operation, which may lead to unwanted inaccuracy and limit system performance. Classical Preisach model is widely used for representing hysteresis but it requires a large number of first-order reversal curves to ensure the model accuracy. All the curves may not be obtained due to the limitations of experimental conditions, and the detachment between the major and minor loops is not taken into account. The purpose of this paper is to propose a modified Preisach model that requires relatively few measurements and that describes the detachment, and then to implement the inverse of the modified model for compensation in PEAs.

The classical Preisach model is modified by adding a derivative term in parallel. The derivative gain is adjusted to an appropriate value so that the measured and predicted hysteresis loops are in good agreement. Subsequently, the new inverse model is similarly implemented by adding another derivative term in parallel with the inverse classical Preisach model, and is then inserted in open-loop operation to compensate the hysteresis. Tracking control experiments are conducted to validate the compensation.

The hysteresis in PEAs can be accurately and conveniently described by using the modified Preisach model. The experimental results prove that the hysteresis effect can be nearly completely compensated.

The proposed modified Preisach model is an effective and convenient mean to characterize accurately the hysteresis. The compensation method by inserting the inverse modified Preisach model in open-loop operation is feasible in practice.

The purpose of this paper is the modelling and estimation of inrush currents while energising power devices under no load conditions. An analytical representation of the nonlinear B-H curve serves for considering the hysteresis behaviour in the numerical model.

The model is implemented into a standard finite element formulation to compute transient problems.

Inrush currents behave like faults in power distribution facilities. Its prior estimation helps to distinguish between operating conditions and faults.

The magnetic cores may become extremely magnetised. At such high material saturations, the material characteristics are not measurable accurately. Hence, the results depend on the extrapolation of the B-H curves.

The use of first-order reversal curves within the major hysteresis loops helps in a convenient way to estimate peak and shape of the inrush currents.

This paper starts with the description of a purely mathematical model of the saturation curve and the hysteresis loop based on the fundamental similarities between the Langevin function the specified T(x) function and the sigmoid shape. The T(x) function which is composed of tangent hyperbolic and linear functions with its free parameters can describe the regular anhysteretic magnetisation curve. Developed from this function the model describes not only the regular hysteresis loop but also the biased and other minor loops like the ones produced by the interrupted and reversed magnetisation process and the open “loops” created by a piecewise monotonic magnetising field input of diminishing amplitude. The remanent magnetism as the function of the interrupted field co‐ordinates is predicted by the model in this mathematical form for the first time. The model presented here is based on the principle that all processes follow the shape of the T(x) function describing the shape of the major hysteresis loop of the ferromagnetic specimen under investigation. The model is also applicable to hysteretic processes in other fields.

On the basis of the Kolmogorov‐Arnold theory, the feedforward type artificial neural networks (NNs) are able to approximate any kind of nonlinear, continuous functions represented by its discrete set of measurements. A NN‐based scalar hysteresis model has been constructed preliminarily on the function approximation ability of NNs. An if‐then type knowledge‐base represents the properties of the hysteresis characteristics. Vectorial generalization to describe isotropic and anisotropic magnetic materials in two and three dimensions with an original identification method has been introduced in this paper.

This paper aims to compare different static history-independent hysteresis models (mathematical-, behavioural- and physical-based ones) and a history-dependent hysteresis model in terms of parameter identification effort and accuracy.

The discussed models were tested for distorted-excitation waveforms to explore their predictions of complex magnetization curves. Static hysteresis models were evaluated by comparing the calculated and measured major and minor static hysteresis loops.

The analysis shows that the resulting accuracy of the different hysteresis models is strongly dependent on the excitation waveform, i.e. smooth excitations, distorted flux waveforms, transients or steady-state regimes. Obtained results show significant differences between predictions of discussed static hysteresis models.

The general aim was to identify the models on a very basic and limited set of measured data, i.e. if possible using only the measured major static loop of the material. The quasi-static major hysteresis loop was measured at B_max = 1.5 T.

The presented analysis allows selection of the most-suited hysteresis model for the sought-for application and appraisal of the individual limitations.

The presented analysis shows differences in intrinsic mechanisms to predict magnetization curves of the majority of the well-known static hysteresis models. The results are essential when selecting the most-suited hysteresis model for a specific application.

The purpose of this paper is to examine the effect of varying compaction pressure on magnetic properties of self-developed soft magnetic composite (SMC) cores. The change in shape of ferromagnetic hysteresis curves has – in turn – the impact on the values of hysteresis model parameters. The phenomenological GRUCAD model is chosen for description of hysteresis curves.

Several cylinder-shaped cores have been made from a mixture of iron powder and suspense polyvinyl chloride using a hydraulic press with a form and a band with a thermocouple for controlling heat treatment conditions. The only varying parameter in the study is the compaction pressure. The magnetic properties of developed cores have been measured using a computer-acquisition card and LabView software. The obtained hysteresis curves are fitted to the equations of the phenomenological GRUCAD model. This description is compliant with the laws of irreversible thermodynamics. The variations of model parameters are presented as functions of compacting pressure.

The compaction pressure has a significant impact on magnetic properties of self-developed SMC cores. The paper provides a number of charts useful for checking how the parameters of the hysteresis model are affected.

The present paper is limited to modelling symmetrical loops only. Description of more complex magnetization cycles is postponed to another, forthcoming paper.

The GRUCAD hysteresis model may be a useful tool for the designers of magnetic circuits. Its parameters depend on the processing conditions (in this study – the compaction pressure) of the SMC cores.

Modelling of magnetic properties of SMC cores has been carried so far using some well-known description like Preisach, Takács and Jiles–Atherton proposals. The GRUCAD model has a number of advantages, and it may be a useful alternative to the latter formalism. So far it has been used for description of hysteresis curves in conventional materials like non-oriented and grain-oriented electrical steels. In the present work, it is applied to novel SMC materials.

The aim of the paper is to provide a simple and reliable hysteresis model for prediction of magnetization curves of a resistance spot welding transformer (RSWT) core, operating in a wide range of flux densities and excitation frequencies.

The hysteresis model considered in the paper is the T(x) description advanced by J. Takács. Three options to extend the model to the dynamic magnetization conditions are considered. The excitation conditions differ from those prescribed by international standards.

The quasi‐static Takács model combined with a fractional viscosity equation similar to that proposed by S.E. Zirka outperforms other considered options. The effect of eddy currents may be considered as a disturbance factor to the frequency‐independent quasi‐static hysteresis loop.

The combined approach yields in most cases a satisfactory agreement between theory and experiment. For highest frequency considered in the paper (1 kHz) excessive “heels” were observed in the modelled loops. This artifact may be reduced by the introduction of a more complicated relationship for the viscous term. Future work shall be devoted to this issue.

The combined Takács‐Zirka model is a useful tool for prediction of magnetization curves of a RSWT core in a wide range of flux densities and excitation frequencies.

The usefulness of the Takács description has been verified in a practical application. The model is able to predict magnetization curves under non‐standard excitation conditions.

The thermally extended Tellinen model (Kühn et al., to appear) is here investigated and equipped with a hysteresis loss model, while preserving its simple structure.

As in the original model, these approaches are based upon phenomenal observations and measured saturation curves. The authors start with the original model and step-by-step add their extensions, such that in the end they can apply the extended model in a finite element method (FEM) simulation. During the process, care is taken to ensure that the applicability in a FEM simulation is not impaired, in terms of memory requirements and computing power.

In comparison to the original model, this extended model needs some further requirements and so is a little bit more limited in its application. It is in itself coherent and well defined. The authors provide an on-the-fly algorithm computation of hysteresis losses. First numerical results for a coupled field/thermal system show expected behavior.

The original model (Tellinen, 1998) does not take temperature into account. It includes a model for calculating hysteresis losses, but it differs largely from the approach presented here. The thermal extension is now also equipped with an on-the-fly method for hysteresis losses. Furthermore, the authors provide some analysis of simple, stable loops.

Widely used in micro‐position devices and vibration control, the piezoelectric actuator exhibits strong hysteresis effects, which can cause inaccuracy and oscillations, even lead to instability. If the hysteretic effects can be predicted, a controller can be designed to correct for these effects. This paper aims to present a neural network hysteresis model with an improved Preisach model to predict the output of piezoelectric actuator.

The improved Preisach model is given: A wiping‐out memory sequence is defined that is along a single axis only and at the same time the ascending and the descending extreme points are separated. The extended area variable is calculated according to wiping‐out memory sequence. The relationship between the two inputs (the extended area variable and variable rate of input signal) and the hysteresis output is implemented with a neural network to approximate the hysteresis model for the piezoelectric actuators.

Some experiments are carried out with a piezoelectric ceramic (PST150/7/40 VS12) and the results show the neural network hysteresis model can reliably predict the hysteretic behaviours in piezoelectric actuators.

The improved Preisach model is a simple model that is implemented by a neural network to reliably predict the hysteretic output in piezoelectric actuators.