Preisach Model Research Articles

Neural Network Architectures and Magnetic Hysteresis: Overview and Comparisons

The development of innovative materials, based on the modern technologies and processes, is the key factor to improve the energetic sustainability and reduce the environmental impact of electrical equipment. In particular, the modeling of magnetic hysteresis is crucial for the design and construction of electrical and electronic devices. In recent years, additive manufacturing techniques are playing a decisive role in the project and production of magnetic elements and circuits for applications in various engineering fields. To this aim, the use of the deep learning paradigm, integrated with the most common models of the magnetic hysteresis process, has become increasingly present in recent years. The intent of this paper is to provide the features of a wide range of deep learning tools to be applied to magnetic hysteresis context and beyond. The possibilities of building neural networks in hybrid form are innumerable, so it is not plausible to illustrate them in a single paper, but in the present context, several neural networks used in the scientific literature, integrated with various hysteretic mathematical models, including the well-known Preisach model, are compared. It is shown that this hybrid approach not only improves the modeling of hysteresis by significantly reducing computational time and efforts, but also offers new perspectives for the analysis and prediction of the behavior of magnetic materials, with significant implications for the production of advanced devices.

A Preisach Model Defining Correlation between Monotonic and Cyclic Response of Structural Mild Steel

This article delivers a new Preisach model representing the correlation between the elastoplastic behavior of structural mild steel under axial monotonic and cyclic loading with damage. The newly formed model is based on the experimentally defined correlation between axial monotonic and cyclic behavior of structural mild steel. To examine the monotonic and cyclic behavior of structural mild steel and find fitting material properties for the model, monotonic and cyclic axial tensile tests are performed. Tests are executed on coupons of the commonly used European structural steel S275. The model represents a mathematical description of modified single-crystal material behavior under monotonic loading. Two different approaches were used to describe damage in the multilinear mechanical model. The excellent agreement with experimental results is achieved by infinitely linking many single-crystal elements in parallel, forming the polycrystalline model. This model provides a good solution for everyday engineering practice due to its geometric representation in the form of the Preisach triangle and the lower costs of monotonic tests used to define material properties compared to cyclic tests.

A novel scale-bridging method for MSMA linking continuum thermodynamics constitutive formulations to lumped system-level models

This work introduces a novel scale-bridging method between a continuum thermodynamics constitutive model and a lumped system-level model for magnetic shape memory alloys (MSMA). With this method, system models for real-time operations are generated based on virtual experiments using the constitutive model. The proposed method addresses the fact that, while constitutive models for MSMA typically only require small sets of parameters as input, their evaluation is still computationally expensive. System models for control engineering, however, require extensive experimental parameterization, while their evaluation is highly time-efficient. The proposed scale-bridging method has the potential to combine a small parameterization effort and a low computational cost of the real-time system model. Additionally, the constitutive model is utilized to investigate whether it can determine the individual behavior of MSMA samples. This is important since the inherent model parameters, while valid for ideal single crystals, deviate for non-ideal MSMA sample behavior. To this end, the MSMA constitutive model, based on a global variational principle originally proposed by Kiefer et al is supplemented by various extensions, including a more robust algorithmic treatment. A parameter identification procedure is introduced to optimize the constitutive model parameters based on an outer hysteresis curve for a particular load case. By conducting virtual experiments with the constitutive model, data sets are generated to parameterize Preisach hysteresis models as numerical approximations of the constitutive models. The resulting hysteresis models are compared with physical experiments using an MSMA test bench for different load cases. It is shown that the proposed scale-bridging method successfully generates hysteresis models derived from constitutive models. While maintaining accuracy comparable to strictly phenomenological models across various load cases (as validated through physical MSMA test bench experiments), these models require significantly less parameterization effort than classical system models. This translates to faster model creation and broader applicability.

Model of Shape Memory Alloy Actuator with the Usage of LSTM Neural Network.

Shape Memory Alloys (SMAs) are used to design actuators, which are one of the most fascinating applications of SMA. Usually, they are on-off actuators because, in the case of continuous actuators, the nonlinearity of their characteristics is the problem. The main problem, especially in control systems in these actuators, is a hysteretic loop. There are many models of hysteresis, but from a control theory point of view, they are not helpful. This study used an artificial neural network (ANN) to model the SMA actuator hysteresis. The ANN structure and training method are presented in the paper. Data were generated from the Preisach model for training. This approach allowed for quick and controllable data generation, making experiments thoroughly planned and repeatable. The advantage and disadvantage of this approach is the lack of disturbances. The paper's main goal is to model an SMA actuator. Additionally, it explores whether and how an ANN can describe and model the hysteresis loop. A literature review shows that ANNs are used to model hysteresis, but to a limited extent; this means that the hysteresis loop was modelled with a hysteretic element.

Hysteresis Compensation of Tendon-Sheath Mechanism Using Nonlinear Programming Based on Preisach Model

Hysteresis Compensation of Tendon-Sheath Mechanism Using Nonlinear Programming Based on Preisach Model

A Calculation Method for Static Hysteresis Loop and its Applications

Background: Due to experimental equipment limitations, it is usually difficult to measure the quasi-static hysteresis loop at extremely low frequencies, which inevitably introduces errors in the static hysteresis model. Objective: This study aims to propose a method for calculating the static hysteresis loops of grainoriented silicon steel sheets so as to improve the accuracy of the static and dynamic hysteresis model. Methods: The parameters n0 and V0 in the magnetic field strength expression of the excess loss are determined by the measured losses within the range of 0-100Hz. Subsequently, the dynamic components in the quasi-static hysteresis loops are eliminated. Furthermore, a dynamic hysteresis model is established based on the loss and field separation theory, which incorporates the inverse Preisach model. Results: The dynamic hysteresis loops of the grain-oriented silicon steel sheets are measured in the range of 8-250Hz and compared with the results of both the improved model and the original model. Conclusion: Experimental results demonstrate the effectiveness and accuracy of the improved model. The proposed method for calculating static hysteresis loops has universal applicability and is meaningful for accurate simulation and prediction of magnetic properties in soft magnetic materials.

Acoustic Wave-Induced FeRh Magnetic Phase Transition and Its Application in Antiferromagnetic Pattern Writing and Erasing.

We explore the FeRh magnetic phase transition (MPT) and magnetic phase domain (MPD) with the introduction of surface acoustic waves (SAWs). The effects of the SAW pulses with different pulse widths and powers on resistance-temperature loops are investigated, revealing that the SAW can reduce the thermal hysteresis. Meanwhile, the SAW-induced comb-like antiferromagnetic (AFM) phase domains are observed. By changing the pulse width and SAW frequency, we further realize a writing-erasing process of the different comb-like AFM phase domains in the mixed-phase regime of the cooling transition branch. Resistance measurements also display the repeated SAW writing-erasing and the nonvolatile characteristic clearly. MPT paths are measured to demonstrate that short SAW pulses induce isothermal MPT and write magnetic phase patterns via the dynamic strain, whereas long SAW pulses erase patterns via the acoustothermal effect. The Preisach model is introduced to model the FeRh MPT under the SAW pulses, and the calculated results correspond well with our experiments, which reveals the SAW-induced energy modulation promotes FeRh MPT. COMSOL simulations of the SAW strain field also support our results. Our study not only can be used to reduce the thermal hysteresis but also extends the application of the SAW as a tool to write and erase AFM patterns for spintronics and magnonics.

Effect of axial preloads on torsional behavior of superelastic shape memory alloy tubes – experimental investigation and simulation/predictions of intricate inner loops

Shape memory alloy (SMA) devices (utilizing wires/rods, springs or tubes) engage unique superelastic/pseudoelastic (SE) phenomenon for large stroke recovery, energy dissipation and damping applications. In particular, SMA components in torsion are also generally subjected to some pre-tension loads and hence understanding their combined effects on the torsional response is vital. In this work, some intricate internal loop and outer loop responses (large twists > 1500°) of SMA tubes under different twisting-untwisting scenarios are investigated to understand the effects of static pre-load on torsional responses. Key SMA hysteretic features like sink point memory (SPM) and return point memory (RPM) have not been well understood under torsion (with and without axial loads) have been investigated here. Further, a modified two variant thermodynamic Preisach modeling approach is proposed to simulate responses of twisted tubes with varying extents of twist and different axial loads. The central principle here is the use of a Gibbs Potential framework to separate the dissipative and thermoelastic parts of the SE responses using well established thermodynamic principles and then utilizing a non-ideal switching type disjunctive Preisach model to fit the nonlinear hysteretic dissipative section of the SE response. By using the outer loop response for model calibration, other complex loading unloading scenarios leading to intricate internal loops and effects of axial loads on these can be predicted. It is also shown that addition of a single interior loop detail for model calibration significantly enhances prediction of other more intricate internal loops. This approach dramatically simplifies the experimental data needed for the simulation of SMA components even under complex loading.

A comparative study of J–A and Preisach improved models for core loss calculation under DC bias

Power transformer is widely used in the power system with the rapid development of the power converters connected to the grid. When a transformer operates under DC bias conditions, its iron core loss increases significantly, causing local overheating and threatening the proper operation of the transformer. However, there are persistent difficulties in accurately assessing the core loss when the induction waveform is influenced by a DC bias. This paper first proposes improvements to the J–A and Preisach models to evaluate the core loss of the iron core under DC bias. Additionally, we incorporate the hysteresis models into the finite element method (FEM) by modifying the fundamental constitutive equations in the FEM model in order to perform a precise core loss/distribution calculation. To verify the accuracy of prediction, a transformer prototype with a laminated core is developed. The improved J–A-FEM and Preisach-FEM models were directly compared in terms of calculation accuracy, numerical implementation, and computational burden.

Modeling and simulation of magnetostrictive actuators based on ΔE effect Preisach model

Based on the classical Preisach model, combined with the magneto-mechanical coupling effect of Giant magnetostrictive materials (GMM), this paper introduces the Everett function to optimize the classical Preisach hysteresis model and improve its accuracy. By importing dynamic parameters, the dynamic Preisach hysteresis model is established. Combined with the constitutive model of GMM, a dynamic Preisach hysteretic nonlinear magnetostrictive actuator model based on the ΔE effect is established. Then, the finite element simulation is carried out by Comsol software and compared with the theoretical model simulation. The results show that the error between the magnetostrictive strain of the established hysteresis model and the finite element simulation results is less than 100 ppm, which verifies the accuracy of the proposed model. Finally, the curves of magnetic field intensity, magnetic induction intensity, magnetization, magnetostrictive strain and ΔE effect of GMA are obtained by using this model.

Prediction of Core Loss in Transformer Laminated Core Under DC Bias Based on Generalized Preisach Model

Prediction of Core Loss in Transformer Laminated Core Under DC Bias Based on Generalized Preisach Model

A novel approach for modelling voltage hysteresis in lithium-ion batteries demonstrated for silicon graphite anodes: Comparative evaluation against established Preisach and Plett model

Lithium-ion batteries with silicon-graphite composite anodes feature an asymmetric and direction-dependent voltage hysteresis. Upon comparing established hysteresis models from literature, it was found that a separate modelling of charge and discharge direction is required for both the operator-based Preisach model and the differential equation-based one-state model, often referred to as Plett model. This paper presents the first bidirectional implementation of the one-state hysteresis model based on extensive measurements of first-order reversal branches of a Si/C NMC cell. The approach accounts for directionality but cannot deal with the complexity of the hysteresis traverses, so an extension of the Preisach model is discussed and found to be infeasible. This justifies the development of a novel hysteresis model, the trajectory correction hysteresis (TCH) model, that fulfils the identified requirements for bidirectionality, closed-loop property and direct data fit and can be generally applied to any cell chemistry. The TCH model considers the traverse starting point, which allows for the unambiguous definition of hysteresis states and enables the simulation of complex trajectories due to two correction mechanisms. The static and dynamic current profiles in complex hysteresis scenarios demonstrate superior performance with 4.5 mV mae compared to Preisach (19.6 mV mae) and Plett (11.7 mV mae) models.

Research on the linear driving characteristics of endoscopic continuous robot

Due to the way line drive, the continuous endoscope robot will have a certain lag in the process of movement, which will affect the accuracy and flexibility of the operation. In addition, the hysteresis and return difference caused by wire rope transmission will also increase the hysteresis effect of continuous robots. In this paper, the motion characteristics of the continuous endoscopic robot are analyzed, the hysteresis of the robot is modeled theoretically based on the Preisach model, and the effectiveness of the model is verified. Preisach hysteretic nonlinear hyperbola model predicts the bending changes under different positive and negative drives. The experimental results show that the maximum error between the model and the theoretical prediction is 3.18 degrees. The hysteresis model can predict the hysteresis characteristics of the continuous endoscope robot well.

A Data-Driven Bayesian Koopman Learning Method for Modeling Hysteresis Dynamics.

Exploring the mechanism of hysteresis dynamics may facilitate the analysis and controller design to alleviate detrimental effects. Conventional models, such as the Bouc-Wen and Preisach models consist of complicated nonlinear structures, limiting the applications of hysteresis systems for high-speed and high-precision positioning, detection, execution, and other operations. In this article, a Bayesian Koopman (B-Koopman) learning algorithm is therefore developed to characterize hysteresis dynamics. Essentially, the proposed scheme establishes a simplified linear representation with time delay for hysteresis dynamics, where the properties of the original nonlinear system are preserved. Furthermore, model parameters are optimized via sparse Bayesian learning together with an iterative strategy, which simplifies the identification procedure and reduces modeling errors. Extensive experimental results on piezoelectric positioning are elaborated to substantiate the effectiveness and superiority of the proposed B-Koopman algorithm for learning hysteresis dynamics.

An Improved Preisach Model for Magnetic Hysteresis of Grain-Oriented Silicon Steel under PWM Excitation

In this paper, the Preisach model for magnetic hysteresis of grain-oriented silicon steel under PWM excitation is improved. First, an improved Preisach model for the magnetic hysteresis of grain-oriented silicon steel under PWM excitation is proposed. Second, the experimental platform for grain-oriented silicon steel sheets under PWM excitation is established. Finally, by comparative analysis, it is concluded that the error of the improved model is far less than that of the classical model (the error here refers to the discrepancy between experimental results and theoretical model predictions). The improved model is 1.4% to 9% more accurate than the classical model. A more accurate model can provide more accurate material parameters for the calculation of the magnetic field in the transformer core, which is of great significance to the production and design of the transformer.

Review on the Nonlinear Modeling of Hysteresis in Piezoelectric Ceramic Actuators

Piezoelectric ceramic actuators have the advantages of fast response speed and high positioning accuracy and are widely used in micro-machinery, aerospace, precision machining machinery, and other precision positioning fields. However, hysteretic nonlinearity has a great influence on the positioning accuracy of piezoelectric ceramic actuators, so it is necessary to establish a hysteretic model to solve this problem. In this paper, the principles of the Preisach model, the Prandtl Ishilinskii (PI) model, the Maxwell model, the Duhem model, the Bouc–Wen model, and the Hammerstein model and their application and development in piezoelectric hysteresis modeling are described in detail. At the same time, the classical model, the asymmetric model and the rate-dependent model of these models are described in detail, and the application of the inverse model corresponding to these models in the feedforward compensation is explained in detail. At the end of the paper, the methods of inverse model acquisition and control frequency of these models are compared. In addition, the future research trend of the hysteresis model is also prospected. The ideas and suggestions highlighted in this paper will guide the development of piezoelectric hysteresis models.

DYNAMICS OF AN ENERGY HARVESTER WITH HYSTERESIS FRICTION

A model of an energy harvester converter with hysteresis viscous friction is considered. The mechanical part of the energy harvester is made in the form of an inverted pendulum. The hysteresis is formalized within the framework of the Preisach model, which is a continuum analogue of a system of non-ideal relays connected in parallel. Within the framework of numerical experiments, the dependences of the dynamic parameters, in particular, the angle of deflection of the pendulum and the voltage on the load, as well as phase portraits, on the value of the coefficient characterizing the effect of hysteresis friction, were investigated. The role of nonlinear effects is demonstrated.

Analytical Inverse Preisach Model and Its Comparison With Inverse Jiles–Atherton Model in Terms of Accuracy and Computational Speed

Inverse hysteresis model with magnetic flux density and magnetic field intensity as input and output respectively is more preferred, compared with the forward one, for resolving the electromagnetic issues of electrical equipment in terms of magnetic vector potential or with voltage sources. And an inverse hysteresis model with high accuracy and high computation speed both has broader range of applications. However, the well known classical Preisach hysteresis model is formulated with the forward form, and has the double integration of its distribution function, making it inconvenient and unpractical in the electrical engineering. In this paper, an analytical inverse Preisach model is proposed for the first time. Firstly, the analytical expressions of permeability of initial magnetization curve, descending and ascending branches of the hysteresis loop are derived using one closed form of Everett integral function. Subsequently the analytical inverse Preisach model is derived by the difference method, considering the reversible magnetization component that classical Preisach model cannot simulate with an odd function analytically. The experiment of one grain oriented silicon steel sample and one non-oriented silicon steel sample, under different magnetic excitation levels is conducted, and the accuracy and efficiency of the proposed analytical inverse Preisach model are confirmed by comparing its simulated hysteresis loops with the experimental ones and that computed with the widely used inverse Jiles-Atherton hysteresis model.

The numerical simulation of a four-stage linear transformer driver module based on the Preisach magnetic core model.

The use of linear transformer drivers (LTDs) is widely considered the most promising technological approach for the development of future pulsed-power accelerators. In large-scale pulsed-power accelerators, abnormal conditions like switch prefire can occur frequently during tests and normal operations due to the presence of a large number of switches. The diagnosis of such faults based on signature waveforms requires further investigation. According to previous research, the characteristics of the magnetic cores greatly influence the fault waveforms. In this paper, a full-cycle mathematical model of the magnetic core is established utilizing a classical Preisach model based on experimental results. This model is coupled with the LTD circuit model in simulations, and simulation results are obtained under the condition of switch prefire. The simulation results are in good agreement with the experimental results from a four-stage LTD module with a sharing shell and de-ionized water insulated transmission line. The magnetization process of the cores is also determined under prefire conditions. Analyses of the magnetization process indicate that the completely demagnetized core shows high permeability under positive excitation and that the permeability abruptly decreases as the excitation is reversed. The hysteresis characteristics result in a phenomenon in which the output voltage in the prefired stage is almost unipolar. Finally, the features of the fault voltages captured in the experiments are also explained.

A dynamic hysteresis prediction model of grain-oriented silicon steel sheet under AC-DC hybrid magnetization

Firstly, a new method for parameter identification of inverted Preisach model is proposed to simulate static DC-biasing hysteresis behavior of the grain-oriented (GO) silicon steel sheet by using the measured quasi-static concentric hysteresis loops under DC-biasing magnetization. Then, the dynamic magnetic field intensity related to excess loss is improved by considering the nonlinear relationship between the statistical parameter V0 and the AC peaked magnetic flux density, DC magnetic field intensity as well as frequency. Finally, a dynamic hysteresis model in form of field separation is presented to predict asymmetric hysteresis curves under multi-harmonic and DC-biasing hybrid magnetization. The simulated hysteresis curves as well as losses under different AC-DC hybrid magnetizations are compared with the measured ones, which verifies the accuracy and effectiveness of the proposed method.