PROBLEMS OF PREISACH MODEL APPLYING IN FINITE ELEMENT METHOD

The paper deals with determination of magnetic field, calculated by finite element method with regard to magnetic nonlinearity. The hysteresis loop of the material is modelled by the scalar Preisach model. A hysteresis motor problem was selected for the demonstration of the hysteresis effect

From model-driven to data-driven : a review of hysteresis modeling in structural and mechanical systems

Hysteresis is a natural phenomenon that widely exists in structural and mechanical systems. The characteristics of structural hysteretic behaviors are complicated. Therefore, numerous methods have been developed to describe hysteresis. In this paper, a review of the available hysteretic modeling methods is carried out. Such methods are divided into: a) model-driven and b) datadriven methods. The model-driven method uses parameter identification to determine parameters. Three types of parametric models are introduced including polynomial models, differential based models, and operator based models. Four algorithms as least mean square error algorithm, Kalman filter algorithm, metaheuristic algorithms, and Bayesian estimation are presented to realize parameter identification. The data-driven method utilizes universal mathematical models to describe hysteretic behavior. Regression model, artificial neural network, least square support vector machine, and deep learning are introduced in turn as the classical data-driven methods. Model-data driven hybrid methods are also discussed to make up for the shortcomings of the two methods. Based on a multi-dimensional evaluation, the existing problems and open challenges of different hysteresis modeling methods are discussed. Some possible research directions about hysteresis description are given in the final section

MODELLING OF ELECTROMAGNETIC FIELD IN FERROMAGNETIC MATERIALS

The paper presents some results and ideas in the field of electromagnetic field calculation in the case of ferromagnetic materials and eddy currents. The hysteresis phenomenon is modelled by the classical Preisach model and the field is calculated with finite element method in time domain. A convergent and physically good scheme is given also for the solution

Some Key Developments in Computational Electromagnetics and their Attribution

Key developments in computational electromagnetics are proposed. Historical highlights are summarized concentrating on the two main approaches of differential and integral methods. This is seen as timely as a retrospective analysis is needed to minimize duplication and to help settle questions of attribution

Hybrid dynamical model for reluctance actuators including saturation, hysteresis and eddy currents

A novel hybrid dynamical model for single-coil, short-stroke reluctance actuators is presented in this paper. The model, which is partially based on the principles of magnetic equivalent circuits, includes the magnetic phenomena of hysteresis and saturation by means of the generalized Preisach model. In addition, the eddy currents induced in the iron core are also considered, and the flux fringing effect in the air is incorporated by using results from finite element simulations. An explicit solution of the dynamics without need of inverting the Preisach model is derived, and the hybrid automaton that results from combining the electromagnetic and motion equations is presented and discussed. Finally, an identification method to determine the model parameters is proposed and experimentally illustrated on a real actuator. The results are presented and the advantages of our modeling method are emphasized

Mechanical design of structures -Optimization of structures under fatigue life criterion

MasterThese lectures are devoted to the presentation of a new computational procedure for fatigue analysis of structures. This method, which is based on the theory of hys-teresis operators, consists to reduce computation of the damage D caused by a time varying stress t ∈ [0, T ] → Σ e (t) to the energy dissipated in the hysteresis loops of the image H µ (Σ e) of Σ e by an appropriately calibrated Preisach operator H µ. We then see that this formalism allows to reduce the structure optimization problem, which consists to seek design parameters u minimizing the damage in some given parts of a structure, to the minimization of the mapping u → D(u) = T 0 H µ (Σ e , t) d t where Σ e (x u) is a numerical mapping governed by a system of second order differential equations M uẍ + W uẋ + K u x = F (t) describing the dynamical behavior of the considered structure. Furthermore, we provide and validate a series of algorithms allowing to solve the optimization problem by a steepest descent method tailored to manage large dynamical problems derived from finite element models. At last, the theoretical results obtained in this course are illustrated with the help of numerous examples, intended for supporting the relevancy of the approach and providing implementation templates in design engineering software

MODELING AND CONTROL OF MAGNETOSTRICTIVE ACTUATORS

Most smart actuators exhibit rate-dependant hysteresis when the working frequency is higher than 5Hz. Although the Preisach model has been a very powerful tool to model the static hysteresis, it cannot be directly used to model the dynamic hysteresis. Some researchers have proposed various generalizations of the Preisach operator to model the rate-dependant hysteresis, however, most of them are application-dependant and only valid for low frequency range. In this thesis, a first-order dynamic relay operator is proposed. It is then used to build a novel dynamic Preisach model. It can be used to model general dynamic hysteresis and is valid for a large frequency range. Real experiment data of magnetostrictive actuator is used to test the proposed model. Experiments have shown that the proposed model can predict all the static major and minor loops very well and at the same time give an accurate prediction for the dynamic hysteresis loops. The controller design using the proposed model is also studied. An inversion algorithm is developed and a PID controller with inverse hysteresis compensation is proposed and tested through simulations. The results show that the PID controller with inverse compensation is good at regulating control; its tracking performance is really limited (average error is 10 micron), especially for high frequency signals. Hence, a simplified predictive control scheme is developed to improve the tracking performance. It is proved through experiments that the proposed predictive controller can reduce the average tracking error to 2 micron while preserve a good regulating performance

Dynamic Ferromagnetic Hysteresis Modelling Using a Preisach-Recurrent Neural Network Model

In this work, a Preisach-recurrent neural network model is proposed to predict the dynamic hysteresis in ARMCO pure iron, an important soft magnetic material in particle accelerator magnets. A recurrent neural network coupled with Preisach play operators is proposed, along with a novel validation method for the identification of the model's parameters. The proposed model is found to predict the magnetic flux density of ARMCO pure iron with a Normalised Root Mean Square Error (NRMSE) better than 0.7%, when trained with just six different hysteresis loops. The model is evaluated using ramp-rates not used in the training procedure, which shows the ability of the model to predict data which has not been measured. The results demonstrate that the Preisach model based on a recurrent neural network can accurately describe ferromagnetic dynamic hysteresis when trained with a limited amount of data, showing the model's potential in the field of materials science

Hysteresis and economics - taking the economic past into account

The goal of this article is to discuss the rationale underlying the application of hysteresis to economic models. In particular, we explain why many aspects of real economic systems are hysteretic is plausible. The aim is to be explicit about the difficulties encountered when trying to incorporate hysteretic effects into models that can be validated and then used as possible tools for macroeconomic control. The growing appreciation of the ways that memory effects influence the functioning of economic systems is a significant advance in economic thought and, by removing distortions that result from oversimplifying specifications of input-output relations in economics, has the potential to narrow the gap between economic modeling and economic reality

Hysteresis Modeling in Magnetostrictive Materials Via Preisach Operators

A phenomenological characterization of hysteresis in magnetostrictive materials is presented. Such hysteresis is due to both the driving magnetic fields and stress relations within the material and is significant throughout, most of the drive range of magnetostrictive transducers. An accurate characterization of the hysteresis and material nonlinearities is necessary, to fully utilize the actuator/sensor capabilities of the magnetostrictive materials. Such a characterization is made here in the context of generalized Preisach operators. This yields a framework amenable to proving the well-posedness of structural models that incorporate the magnetostrictive transducers. It also provides a natural setting in which to develop practical approximation techniques. An example illustrating this framework in the context of a Timoshenko beam model is presented