Relationship between the moving and the product Preisach models

It has been shown that output-dependent Preisach models are not limited by the congruency property of other Preisach models. The problem of the relationship between two such models is addressed: the moving model and the product model. A study of the minor hysteresis loops generated by the two models highlights the essential difference between them.<>     

Generalized Constructive Model of Hysteresis

We describe a generalized constructive model of rate independent scalar hysteresis. It consists of an algorithm that uses a set of experimental hysteresis minor loop vertical chords. The introduced model requires new, less constraining properties than the congruency and equal vertical chords properties required by the classical and the generalized Preisach models. Our model allows for fitting transition curves of order greater than two, despite its simple mathematical notation. Further, we describe interesting performance of the model in numerical evaluation and inversion     

A genetic approach to solve numerical problems in the Preisach model identification

This paper introduces an identification procedure of the classical and modified scalar Preisach models based on genetic algorithms. It can be used when a reduced set of experimental data is known. The main advantage of this approach is the numerical stability of the solution. The results show that the coupling between our genetic identification procedure and the modified scalar Preisach model is able to reproduce the experimental behavior of different magnetic soft steels.     

Inverted and Forward Preisach Models for Numerical Analysis of Electromagnetic Field Problems

This paper discusses the use of the inverted ($B$-based) Preisach model and its incorporation into the finite-element method (FEM). First, the$B$-based Preisach model is studied thoroughly along with the forward ($H$-based) Preisach model, highlighting the advantages and disadvantages of both models. The study confirms that, in addition to the main purpose of the$B$-based model—to compute the magnetic field$H$directly—the$B$-based model can overcome the congruency problem. Thus, the$B$-based model proves to be more accurate than the$H$-based model. Second, the paper suggests that incorporating the$B$-based Preisach model into FEM models results in relatively accurate, computationally efficient simulations. The method has been validated by simulating hysteresis torque in a high-speed induction motor, and a comparative investigation of the effectiveness, accuracy, and efficiency of the models has been conducted.     

The wiping-out property of the moving model (magnetic hysteresis)

Some properties of the moving Preisach model are examined. It is found that this model can introduce hysteresis in materials where it is not intrinsically present. It is shown that the moving model has the wiping-out property, even in the case where a reversible component of magnetization is present in addition to the irreversible component computed by the moving model. The implication of this model to the overwrite problem in magnetic recording is discussed.<>     

Hysteresis Modeling Based on Symmetric Minor Loops

This paper presents a method for modeling symmetric minor loops in hysteretic magnetic media. The method employs symmetric minor loops combined with certain segments of the initial magnetization curve to identify the classical Preisach model. The proposed method is simple and effective. It exploits the symmetric positions of the reversal points lying on the initial magnetization curve and, therefore, guarantees monotonic symmetric change of the Preisach model input used in the calculation of the Everett function. A further advantage of the method is that it permits the use of the numerical Preisach model and omits the need of higher-order reversal curves. The method is applied to the prediction of symmetric minor loops of semi-hard magnetic material by using the classical scalar Preisach model. The simulation and measurement results show the high accuracy of the method and validate the proposed approach.     

Differential equation model for accommodation magnetization

We use the differential equation method of computing the accommodation magnetization in a modified Preisach model. We present the properties of this model for a Gaussian medium, and show that the resulting model has neither the congruency property nor the deletion property.     

Identification of 1D and 2D Preisach models for ferromagnets and shape memory alloys

A least-squares parameter fitting procedure is used in conjunction with one-dimensional (1D) and two-dimensional (2D) formulations of the Preisach formalism. The model can use any operator from a selection of 1D and 2D hysteresis operators appropriate for the modeling of hysteresis in ferromagnets, and shape memory alloys. The performance of the hysteresis operators is evaluated, and their applicability is discussed. The model is applied to experimental data from ferromagnetic samples, and shape memory alloys. The results suggest that the proposed approach can be a useful and adjustable tool in the modeling of hysteresis in various systems regardless of the underlying physical mechanism.     

基于Preisach理论的形状记忆合金温度-位移迟滞仿真研究

摘 要：智能材料如形状记忆合金(Shape Memory Alloy,SMA)已经广泛应用于驱动器和传感器的设计,实现定位和主动控制目的。然而,受迟滞影响,SMA驱动器的工作精度大大降低,限制了其应用。多数智能材料中,选择Preisach理论成为迟滞建模工具,近年来,也涉及到SMA材料系统。本文,讨论运用Preisach模型描述SMA驱动器系统的迟滞行为,尤其针对驱动器系统的模型建立过程,修正经典Preisach模型的几何解释和数值实现方法。最后,引入Gobert给出的Preisach平面的辨识函数执行仿真计算,数值结果表明该模型能够很好地描述SMA驱动器的迟滞行为。     

Frequency analysis of classical Preisach model

The paper contains an analysis of the classical Preisach model from a frequency point of view. A Fourier analysis retrieves the necessary and sufficient conditions on the Preisach weighting function to have an output with half-wave symmetry; i.e., only odd harmonics are present. For a wide class of weighting functions, it is shown that all odd frequencies are present. As a consequence, a filtering method is suggested that enhances time-series data from sinusoidal input, which can be used for Preisach model identification     

Hysteretic behavior of a magnetorheological fluid: experimental identification

Summary This paper presents the experimental identification of the field-dependent hysteretic behavior of a magnetorheological (MR) fluid. By adopting one of commercially available MR fluids, both the minor loop property and the wiping-out property are experimentally examined via the rotational rheometer. Subsequently, the Preisach model for the MR fluid is established in order to identify the field-dependent hysteretic behavior. The effectiveness of the identified hysteresis model is then verified in the time domain by comparing the predicted field-dependent shear stress with the measured one.     

气动肌肉的最小二乘支持向量机迟滞模型

针对传统迟滞模型存在的待辨识参数多、参数辨识过程复杂和辨识精度低等问题,采用最小二乘支持向量机对气动肌肉的位移/气压迟滞开展建模研究。通过非线性映射将原始数据空间映射到高维空间,将原系统的非线性问题变成高维空间中的线性问题,借助于最小二乘法求解该线性方程组,从而提高其求解速度及收敛精度。在气动肌肉迟滞特性实验的基础上,采用所建数学模型,与经典的PI模型进行对比。结果表明,采用最小二乘支持向量机建立的数学模型具有更高的建模精度,均方差和平均误差相比PI模型分别减小了99.21%和99.1%,该方法可为后续气动肌肉的迟滞补偿控制提供有效的手段。     

Subharmonic ferroresonance in an LCR circuit with hysteresis

We use the Preisach model of magnetic hysteresis to model the inductance in a series LCR circuit. By introducing a hysteresis parameter into the Preisach functions used, we are able to continuously vary the width of the hysteresis loop and thereby investigate the effects of magnetic hysteresis on the circuit's behavior. In particular, it is shown that the stability region of a period-3 subharmonic ferroresonant solution can increase significantly as the hysteresis losses are reduced. The bifurcations leading to the appearance and disappearance of this subharmonic solution are examined. Also, strong numerical evidence is provided for the unsuitability of single-valued M-H curves in the analysis of ferroresonant phenomena     

Hysteresis in a carbon nanotube based electroactive polymer microfiber actuator: numerical modeling

Hysteretic behavior is an important consideration for smart electroactive polymer actuators in a wide variety of nano/micro-scale applications. We prepared an electroactive polymer actuator in the form of a microfiber, based on single-wall carbon nanotubes and polyaniline, and investigated the hysteretic characteristics of the actuator under electrical potential switching in a basic electrolyte solution. For actuation experiments, we measured the variation of the length of the carbon-nanotube-based electroactive polymer actuator, using an Aurora Scientific Inc. 300B Series muscle lever arm system, while electrical potentials ranging from 0.2 V to 0.65 V were applied. Based on the classical Preisach hysteresis model, we presented and validated a numerical model that described the hysteretic behavior of the carbon-nanotube-based electroactive polymer actuator. Inverse hysteretic behavior was also simulated using the model to demonstrate its capability to predict an input from a desired output. This numerical model of hysteresis could be an effective approach to micro-scale control of carbon-nanotube-based electroactive polymer actuators in potential applications.     

Fast Preisach-based magnetization model and fast inverse hysteresismodel

Fast computational methods for Preisach-based models and their inverses are presented. The methods are based on a differential equation approach to computing a sequence of magnetization values due to a sequence of applied fields. The method used to speed up calculations can be applied to any Preisach model. The Della Torre, Oti, Kadar model was used here as an illustration. Sequential computations for the magnetization model are substantially faster than for standard Preisach models with comparable output error. Computations for the inverse hysteresis model are even faster than for the model. Using the inverse, open loop control of magnetic hysteresis is simulated, showing hysteretic material tracking a desired magnetization in a linear manner for both major loops and minor loops, with less than 2% error in inversion for the waveforms used. The effect of misidentification of material parameters on operation of the inverse is also investigated through simulations     

Measurement and Modeling of Thermal Effects on Magnetic Hysteresis of Soft Ferrites

We present experimental measurement of thermal effects on magnetic hysteresis of soft ferrite cores commonly used in high-frequency inductors and transformers and propose a method to model the thermal effects. We measured the major hysteresis loops of soft ferrite core samples from various vendors at different temperatures, and found that the saturation points of the limiting hysteresis loops vary with the temperature substantially in a nonlinear manner, but within the normal operating temperature range, typically 20degC-100degC, this variation can be approximately regarded as linear with an acceptable error. We propose a simple method based on this approximation for determining the limiting hysteresis loop of a soft ferrite for a given temperature. This method is validated by the substantial agreement between the experimental measurement and simulation by the scalar Preisach hysteresis model of major hysteresis loops of the test samples at different temperatures. Since most manufacturers provide the limiting loops of their soft ferrite cores at two typical temperatures, the proposed method is very convenient for engineering applications.     

A method for the determination of the parameters of the hysteresismodel of magnetic materials

Many methods have been proposed for the determination of the hysteresis loops of magnetic materials, and many mathematical approaches have been proposed to find a good model for the hysteresis phenomenon. However, very few attempts have been made to determine the parameters of the hysteresis model experimentally. This paper shows how, starting from a digital method for the experimental determination of the hysteresis loop under different maximum induction values, the parameters of a hysteresis model can be automatically estimated with good accuracy. Due to its good behavior in terms of accuracy and to the comparative ease in determining its parameters, the Preisach model for rate-independent hysteresis phenomena was chosen. Experimental determination of the model and consequent hysteresis loop computation were carried out. An accuracy below 1% was attained over the peak induction range from 0.49 T to 1.68 T and the frequency range from 50 Hz to 100 Hz     

Parameter determination of Chaboche kinematic hardening model using a multi objective Genetic Algorithm

Chaboche model is a powerful tool to evaluate the cyclic behavior under different loading conditions using kinematic hardening theory. It can also predict the ratcheting phenomenon. To predict the ratcheting, it is required to determine the material parameters under strain control conditions. Although, these parameters can model the hysteresis loop fairly accurately, their ratcheting prediction does not have the same quality. A set of material parameters that could accurately predict both ratcheting and hysteresis loop is of great importance. The available models, generally for low cycle fatigue, are mostly complex and nonlinear. Therefore, an optimization procedure can be used for parameter determination and consequently improving the prediction of these models.Genetic Algorithm is a numerical approach for optimization of nonlinear problems. Using a multi objective Genetic Algorithm for Chaboche model, a set of parameters was obtained which improved both ratcheting prediction and hysteresis loop model. Two fitness functions were used for this approach. The proposed model was verified using Hassan and Corona’s experimental data conducted on CS 1026 low carbon steel. The model indicated a very good agreement in the case of uniaxial loading with the experimental data. The results of proposed model for biaxial loading histories are similar to the model by Hassan and his co-workers.     

A new approach to Preisach diagrams

Magnetization processes are complex. A simple Preisach diagram can describe only the irreversible component of magnetization. An extended Preisach model is introduced, including a reversible magnetization component given by a Langevin function which describes low-field experimental hysteresis loops very well. A family of anhysteretic curves are shown that are dependent on the amplitude and form of the ac used to generate them and the turning points on theM-Hplane.     

Reliable modeling of piezoceramic materials utilized in sensors and actuators

Piezoceramic materials are widely utilized in actuator and sensor devices. In order to model the behavior of these devices and to reduce their development time, numerical simulation tools are frequently applied. However, the simulation results strongly rely on the material behavior assumed for piezoceramics. Here, we present approaches for reliable modeling of this material behavior which have been developed at the Chair of Sensor Technology (Friedrich-Alexander-University Erlangen-Nuremberg) in recent years. Both the small signal behavior and the large signal behavior of piezoceramic materials are discussed. For the identification of material parameters required within the small signal model, we apply a mathematical Inverse Method. The large signal behavior of piezoceramics is described by means of a phenomenological approach that is based on the so-called Preisach hysteresis operator. As the presented results for different piezoceramics clearly show, the utilized modeling approaches lead to reliable simulation results and can, therefore, be applied to predict the behavior of piezoceramic materials.