Preisach Hysteresis Research Articles

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.

Homogenization of partial differential equations with Preisach operators

The current work deals with initial boundary value parabolic problems with Preisach hysteresis whose the density functions are allowed to depend on the variable of space. The model contains nonlinear monotone operators in the diffusion term, arising from an energy. Thanks to the properties of Preisach hysteresis operators and to the sigma-convergence method, we obtain the convergence of themicroscopic solutions to the solution of the homogenized problem. The effective operator is obtained in terms of a solution of a nonlinear corrector equation addressed in the usual sense of distributions, leading in an approximate scheme for the homogenizedcoefficient which is an important step towards the numerical implementation of the results from the homogenization theory beyond the periodic setting.

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.

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.

Tracking Control of Uncertain Neural Network Systems with Preisach Hysteresis Inputs: A New Iteration-Based Adaptive Inversion Approach

To describe the hysteresis nonlinearities in smart actuators, numerous models have been presented in the literature, among which the Preisach operator is the most effective due to its capability to capture multi-loop or sophisticated hysteresis curves. When such an operator is coupled with uncertain nonlinear dynamics, especially in noncanonical form, it is a challenging problem to develop techniques to cancel out the hysteresis effects and, at the same time, achieve asymptotic tracking performance. To address this problem, in this paper, we investigate the problem of iterative inverse-based adaptive control for uncertain noncanonical nonlinear systems with unknown input Preisach hysteresis, and a new adaptive version of the closest-match algorithm is proposed to compensate for the Preisach hysteresis. With our scheme, the stability and convergence of the closed-loop system can be established. The effectiveness of the proposed control scheme is illustrated through simulation and experimental results.

Adaptive Pseudoinverse Control for Constrained Hysteretic Nonlinear Systems and its Application on Dielectric Elastomer Actuator

Flexible smart material actuators, such as dielectric elastomer actuators (DEA) and ionic polymer metal composites, have shown greatly potential applications in the field of soft biomimetic robots and rehabilitation robots due to their human-like muscle softness, large stretch, and high energy density characteristics. In this article, a fuzzy logic system (FLS) and barrier Lyapunov function (BLF) based adaptive pseudoinverse control scheme is proposed for a class of state-constrained hysteretic nonlinear systems, where all the states are always strictly limited in each constrained set. The main features of this article are: 1) the hysteresis nonlinearity in the actuators is considered and mitigated by the proposed pseudoinverse control algorithms, which implies that the direct hysteresis inverse model is not required, instead a searching mechanism of the actual control signal from the temporary control signal; 2) the all-state-constrained control problem of the Preisach hysteresis model is overcome when the control signal is coupled in the double integral functions with the aid of an FLS, BLFs, and the proposed hysteresis pseudoinverse algorithms; and 3) the DEA-based motion control platform is constructed, and the experiments are conducted to validate the effectiveness of our proposed control scheme.

Harmonic and DC Bias Hysteresis Characteristics Simulation Based on an Improved Preisach Model.

Transformers, reactors and other electrical equipment often work under harmonics and DC-bias working conditions. It is necessary to quickly and accurately simulate the hysteresis characteristics of soft magnetic materials under various excitation conditions in order to achieve accurate calculations of core loss and the optimal design of electrical equipment. Based on Preisach hysteresis model, a parameter identification method for asymmetric hysteresis loop simulation is designed and applied to the simulation of hysteresis characteristics under bias conditions of oriented silicon steel sheets. In this paper, the limiting hysteresis loops of oriented silicon steel sheets are obtained through experiments under different working conditions. The first-order reversal curves(FORCs) with asymmetric characteristics is generated numerically, and then the Everett function is established under different DC bias conditions. The hysteresis characteristics of the oriented silicon steel sheets under harmonics and DC bias are simulated by improving FORCs identification method of the Preisach model. By comparing the results of simulation and experiment, the effectiveness of the proposed method is verified, so as to provide an important reference for material production and application.

Characterization of Terfenol-D and Comparison With Predictions of a Thermodynamically Consistent Two-Input, Two-Output Model of Hysteresis

Since its discovery more than forty years ago, Terfenol-D has promised much but has not yet been fully exploited in applications.The main reason for this is that it shows significant hysteresis and other nonlinearities, such as saturation, which need to be modeled correctly in order to maximize the application potential. In this article, we focus on the characterization of a Terfenol-D sample with the intention of developing a predictive two-input (magnetic field and stress) and two-output (magnetic flux density and strain) model of magnetostriction that exhibits hysteresis and saturation and is compatible with the laws of thermodynamics. Compatibility with thermodynamics is essential to ensure that numerical simulations do not exhibit unphysical behavior. The model is based on the Preisach hysteresis operator and its storage function and may be interpreted as a two-input, two-output neural net with elementary hysteresis operators as the neurons. In order to estimate the parameters, it is necessary to collect data over a wide range of magnetic fields (-300 kA/m to 300 kA/m) and compressive stresses (up to 60 MPa). Using the rate-independent memory evolution properties of the Preisach operator, we split the parameter estimation problem into three numerically well-conditioned, linear least squares problems with constraints. We show that the model is able to fit experimental data for strain and magnetization over a wide range of magnetic fields and stress.

Stationary random response evaluation of nonlinear oscillators with Preisach hysteresis discretized by RNN model

This manuscript is devoted to evaluating random stationary responses of nonlinear oscillators including Preisach hysteresis, which is modeled by a powerful tool, viz. Recurrent Neural Networks (RNN). First, a generalized harmonic transformation is introduced by adopting a geometric viewpoint of RNN-described hysteresis and intentionally separating the hysteretic force into conservative and dissipative components, to circumvent direct mathematical calculations of amounts of difference equations. The hysteretic force could be equivalently mimicked by a force that only depends on the present system states. Then, the system dimension is reduced by stochastic averaging, which is derived from the corresponding low-dimensional Fokker–Planck–Kolmogorov (FPK) equation associated with the probability density of slow-varying process. Additionally, solving the FPK equation yields the stationary probability density as well as various-order response statistics. Finally, two numerical examples, i.e., Duffing oscillator and van der Pol oscillator, are investigated to verify the efficacy of the proposed procedure.

Data based constitutive modelling of rate independent inelastic effects in composite cables using Preisach hysteresis operators

AbstractThis contribution aims at introducing first steps to develop hysteresis operator type inelastic constitutive laws for Cosserat rods for the simulation of cables composed of complex interior components. Motivated by the basic elements of Cosserat rod theory, we develop a specific approach to constitutive modelling adapted for this application. Afterwards, we describe the hysteretical behaviour arising from cyclic bending experiments on cables by means of the Preisach operator. As shown in pure bending experiments, slender structures such as electric cables behave inelastically, and open hysteresis loops arise with noticeable difference between the first load cycle and the following ones. The Preisach operator plays an important role in describing the input-output relation in hysteresis behaviours, and it can be expressed as a superposition of relay operators. Hence, a mathematical formulation of the problem is introduced, and a first attempt is made to determine the hysteresis behaviour that describes the relation between curvature and bending moment. Therefore, a suitable kernel function is identified in a way that its integration over the Preisach plane results in the bending moment of the specimen, and a comparison between different kernel functions is performed.

Parameter identification for a model for multi-functional materials with hysteresis and thermodynamic compatibility

Multifunctional materials have tremendous potential for engineering applications as they are able to convert mechanical to electromagnetic energy and vice-versa. One of the features of this class of materials is that they show significant hysteresis, which needs to be modeled correctly in order to maximize their application potential. A method of modeling multifunctional materials that exhibit the phenomenon of hysteresis and is compatible with the laws of thermodynamics was developed recently. The model is based on the Preisach hysteresis operator and its storage function and may be interpreted as a two-input, two-output neural net with elementary hysteresis operators as the neurons. The difficulty is that the parameters in the model appear in a non-linear fashion, and there are several constraints that must be satisfied by the parameters for thermodynamic compatibility. In this article, we present a novel methodology that uses the rate-independent memory evolution properties of the Preisach operator to split the parameter estimation problem into three numerically well-conditioned, linear least squares problems with constraints. The alternative direction method of multipliers (ADMM) algorithm and accelerated proximal gradient method are used to compute the Preisach weights. Numerical results are presented over data collected from experiments on a Galfenol sample. We show that the model is able to fit not only experimental data for strain and magnetization over a wide range of magnetic fields and stress but also able to predict the response for stress and magnetic fields not used in the parameter estimation.

Deep neural networks for the efficient simulation of macro-scale hysteresis processes with generic excitation waveforms

An effective and performing hysteresis model, based on a deep neural network, with the capability to reproduce the evolution of magnetization processes under arbitrary waveforms of excitation is here presented. The proposed model consists of a standalone multi-layer feed-forward neural network, with reserved input neurons for the past values of both the input (H) and output (M), aiming at the reproduction of the storage mechanism typical of hysteretic systems. The training set has been opportunely prepared starting from a set of simulations, performed by the Preisach hysteresis model. The optimized training procedure, based on multi-stage check of the model performance, will be comprehensively discussed. The comparative analysis between the neural network-based model, implemented at low level of abstraction, and the Preisach model covers additional hysteresis processes, different from those involved in the training. The mild/moderate memory requirement and the significant computational speed make the proposed approach suitable for a future coupling with finite-element analysis.

Phase transitions in porous media

The full quasistatic thermomechanical system of PDEs, describing water diffusion with the possibility of freezing and melting in a visco-elasto-plastic porous solid, is studied in detail under the hypothesis that the pressure-saturation hysteresis relation is given in terms of the Preisach hysteresis operator. The resulting system of balance equations for mass, momentum, and energy coupled with the phase dynamics equation is shown to admit a global solution under general assumptions on the data.

Application of Least-Squares Support-Vector Machine Based on Hysteresis Operators and Particle Swarm Optimization for Modeling and Control of Hysteresis in Piezoelectric Actuators

Nanopositioning systems driven by piezoelectric actuators are widely used in different fields. However, the hysteresis phenomenon is a major factor in reducing the positioning accuracy of piezoelectric actuators. This effect makes the task of accurate modeling and position control of piezoelectric actuators challenging. In this paper, the learning and generalization capabilities of the model are efficiently enhanced to describe and compensate for the rate-independent and rate-dependent hysteresis using a kernel-based learning method. The proposed model is inspired by the classical Preisach hysteresis model, in which a set of hysteresis operators is used to address the problem of mapping, and then least-squares support-vector machines (LSSVM) combined with a particle swarm optimization (PSO) algorithm are used for identification. Two control schemes are proposed for hysteresis compensation, and their performance is evaluated through real-time experiments on a nanopositioning platform. First, an inverse model-based feedforward controller is designed based on the LSSVM model, and then a combined feedback/feedforward control scheme is designed using a classical control strategy (PID) to further enhance the tracking performance. For performance evaluation, different datasets with a variety of hysteresis loops are used during the simulation and experimental procedures. The results show that the proposed method is successful in enhancing the generalization capabilities of LSSVM training and achieving the best tracking performance based on the combination of feedforward control and PID feedback control. The proposed control scheme outperformed the inverse Preisach model-based control scheme in terms of both positioning accuracy and execution time. The control scheme that uses the LSSVM based on nonlinear autoregressive exogenous (NARX) models has significantly less computational complexity compared to our control scheme but at the expense of accuracy.

Dynamics of SIR model with heterogeneous response to intervention policy

In classical epidemic theory, behavior is assumed to be stationary. In recent years, epidemic models have been extended to include behaviors that transition in response to the current state of the epidemic. However, it is widely known that human behavior can exhibit strong history-dependence as a consequence of learned experiences. This history-dependence is similar to hysteresis phenomena that have been well-studied in control theory. To illustrate the importance of history-dependence for epidemic theory, we study dynamics of a variant of the SIRS model where individuals exhibit lazy-switch responses to prevalence dynamics, based on the Preisach hysteresis operator. The resulting model can possess a continuum of endemic equilibrium states characterized by different proportions of susceptible, infected and recovered populations. We consider how the limit point of the epidemic trajectory and the infection peak along this trajectory depend on the degree of heterogeneity of the response. Our approach supports the argument that public health responses during the emergence of a new disease can have fundamental long-term consequences for subsequent management efforts.

Kalman filter and classical Preisach hysteresis model applied to the state of charge battery estimation

The goal of this work is first to include a hysteresis model in the classical equivalent circuit model (ECM) for a battery system and then to improve the estimation of the state of charge (SoC) by applying the Extended Kalman Filter (EKF). The hysteretic behavior of the open circuit voltage (OCV) is modelled with the classical Preisach model used for magnetic materials. The construction of the Preisach operator is made by means of the Everett function identified from experimental data which only involve the charging curves of the battery. Thus, a significant reduction in the time necessary to obtain the measurements is achieved. The model is assessed with some laboratory experiments performed on a lithium-ion battery and the results show that with this procedure hysteresis is very well reproduced, even when interior loops are present. In addition, the use of the EKF allows us to eliminate the measurements noise and ensure the accuracy of SoC estimation. The high computational efficiency and precision of the method, joined to the limited computational resources needed for the numerical implementation, make it particularly suitable for real-time embedded battery management system (BMS) applications. In addition, the proposed methodology is well-adapted to any battery type, independently of the SoC-OCV profile of the hysteresis cycle.

A Dynamic Hysteresis Model for TMR-Current Sensors Based on Probability Estimation of Hysteresis Operator and Its Switching Time

Hysteresis is one of the main factors affecting the measurement accuracy of TMR sensors, especially in dynamic measurements. The commonly used Preisach hysteresis compensation model has some problems, such as complex modeling and difficulty in accurately measuring the step time, resulting in low accuracy in dynamic measurements. In this paper, considering the distribution characteristics of the conversion time of the hysteresis operator in dynamic measurements, a dynamic hysteresis model based on the probability estimation of the hysteresis operator and its conversion time is proposed. Compared with the existing methods, this method only needs to calculate the distribution of the sensor hysteresis operator to realize the calculation of hysteresis characteristics without a physical model or fitting algorithm. It has good generalization performance and a corresponding fast speed. In the test of two typical TMR sensors, compared with the transmission Preisach model, the maximum error of this method is reduced by 46.7%, the variance can be reduced by 90.2%, and the average value can be reduced by 65.1%.

Identification of Preisach Model Parameters Based on an Improved Particle Swarm Optimization Method for Piezoelectric Actuators in Micro-Manufacturing Stages.

The Preisach model is a typical scalar mathematical model used to describe the hysteresis phenomena, and it attracts considerable attention. However, parameter identification for the Preisach model remains a challenging issue. In this paper, an improved particle swarm optimization (IPSO) method is proposed to identify Preisach model parameters. Firstly, the Preisach model is established by introducing a Gaussian−Gaussian distribution function to replace density function. Secondly, the IPSO algorithm is adopted to Fimplement the parameter identification. Finally, the model parameter identification results are compared with the hysteresis loop of the piezoelectric actuator. Compared with the traditional Particle Swarm Optimization (PSO) algorithm, the IPSO algorithm demonstrates faster convergence, less calculation time and higher calculation accuracy. This proposed method provides an efficient approach to model and identify the Preisach hysteresis of piezoelectric actuators.

Recurrent Neural Network With Preisach Model for Configuration-Specific Hysteresis Modeling of Tendon-Sheath Mechanism

The tendon-sheath mechanism (TSM) is widely used for flexible surgical robots owing to its ability to transfer motion through complicated paths and small volumes. However, precise motion control of the robots is difficult owing to the nonlinear characteristics of the TSM due to hysteresis, friction, deformation, backlash, etc. The hysteretic behavior exhibits a certain tendency depending on the shape of the TSM. In this study, our goal is to derive a hysteresis model that applies to the arbitrary geometry of a single-curve TSM. A hysteresis model was formulated by combining the Preisach hysteresis model, which has the structure of a weighted sum, and a recurrent neural network (RNN). Hysteresis output data were experimentally gathered for several representative shapes of the TSM to train the model. During data preprocessing, the data in the section where the hysteresis characteristic was prominent was augmented. Hyperparameter tuning using the grid search method was conducted to improve the performance of the model. The results indicate that the proposed model successively learned the tendency of configuration-specific hysteresis and adapted to arbitrary shapes of a single-curve TSM, even with shapes that the model did not learn.

Accurate small major hysteresis loops calculation by the Preisach model with improved parametric distribution function

The inversed Preisach hysteresis model is widely used to realize the rapid coupling of hysteresis characteristics of core materials in finite element analysis. However, the small major hysteresis loop is difficult to be accurately simulated. In this paper, an improved inversed Preisach model based on an improved parametric distribution function is proposed. By analyzing the magnetic remanence, the waveform factor is coupled with the parametric distribution function, and the identification of the small major hysteresis loop is strengthened. The distribution function parameters can be found from the limit hysteresis loop through the optimization algorithm. In the numerical calculation process of the model, the amplitude correction coefficient in the discrete formula is extracted by the basic magnetization curve. Compared with the previous method, this method simulates the limit hysteresis loop well and has higher simulation accuracy for the small major hysteresis loops.