Hysteresis Model Research Articles

Intelligent Hysteresis Modeling for Capturing Structural Features via Multi-Physics Guided Neural Network and Its Earthquake Resistant Test

ABSTRACT The hysteresis model simplifies the relationship between resilience and deformation in seismic performance analysis of structural components. However, accurately capturing structural performance poses a challenge due to the intricate nature of hysteresis data. To enhance precision, this study introduces a multi-physics-guided neural network model. This innovative approach integrates explicit hysteresis models with an implicit network to create a robust hybrid model. The network architecture is grounded in physical principles, with the loss function incorporating physical parameter relationships for effective training. Through quasi-static testing, this approach demonstrates its robust adaptability and precision to the unique hysteretic curves of diverse components.

Revisiting the dry friction-like magnetic vector hysteresis model

Physically correct simulations of magnetic devices require precise and energy-consistent hysteresis models. Electrical steel sheets of, e.g., power transformers or rotating machines represent one crucial element in such a simulation since the hysteresis is revealed uni- and multi-axial, and the steel sheets may have anisotropy. A dedicated vector hysteresis model based on dry friction-like pinning is revisited and derived in terms of thermodynamic state equations in a theoretical manner. The model is then linked to an incremental energy minimization procedure used in elasto-plasticity theory. A numerically efficient two-dimensional solution scheme of the hysteresis model is extended to the three-dimensional case. Rotational losses are also in the scope of this paper since the model cannot describe this loss type by nature. Therefore, numerical adaptations are discussed to account for vanishing rotational losses in saturation.

An improved dynamic Prandtl–Ishlinskii hysteresis model and a PID-type adaptive sliding mode controller for piezoelectric micro-motion platform

Piezoelectric actuators are widely used in the field of micro-nano driving due to their advantages of fast frequency response, high displacement resolution, large stiffness, small size, and low heat generation. However, the hysteresis non-linearity of piezoelectric actuators severely affects their positioning accuracy during operation. Therefore, the study of hysteresis model and compensation control for piezoelectric actuators has always been a hot topic in the field of micro-nano driving. However, existing hysteresis models and control methods cannot well describe the dynamic hysteresis curve of piezoelectric actuators and track the desired trajectory. To address this issue, this paper proposes an improved dynamic Prandtl–Ishlinskii (IDPI) model and a finite-time trajectory tracking adaptive sliding mode control method based on PID-type. Firstly, this paper introduces the construction and parameter identification method of the IDPI model. Secondly, the accuracy of the IDPI model in describing hysteresis curves under different input signals is verified through experiments, and the effectiveness of the feedforward controller based on the IDPI model is validated experimentally. Then, considering the modeling uncertainty, unmodeled internal dynamics, and external environmental disturbances of the piezoelectric micro-motion platform, a finite-time trajectory tracking adaptive sliding mode controller based on PID-type is designed to suppress the non-linear characteristics of the piezoelectric micro-motion platform. Finally, the performance of the compensator is verified through simulation experiments.

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.

THE MODELLING OF A HYSTERESIS GRAPH OF PIEZOELECTRIC ELEMENTS USING DEEP LEARNING BIDIRECTIONAL LSTM

The phenomenon of hysteresis is an integral part of dynamic systems in many fields of science such as physics, chemistry, biology and many more. It describes an inherent dependence of a system state based on the history of varying number of its previous states. Hysteresis can manifest as a dynamic lag between an input signal and an output system behaviour, which depends on the degree of that system dy-namics. Modelling systems containing hysteresis is a challenging mathematical task given their highly non-linear behaviour. This paper discusses and develop a deep learning model using bidirectional LSTM (long short-term memory) for predicting voltages necessary to stimulate a piezoelectric element to produce displacements in order to cancel or minimize vibrations. The predicted voltages rely on given displacements and time domain of the initial noise input. This noise input can then be amplified to match the resonance frequency of another piezoelectric element to generate the maximum voltage capable by this later piezoelectric element. This sinusoidal voltage then travels to a piezoelectric actuator to generate displacement that can cancel the initial noise. The model resulted a coefficient of determination score of 0.99983, a loss score of 0.0092 and MSE (mean squared error) of 8.5568e-05. Created model has proven that machine learning is a viable method for hysteresis modelling and can be further improved with increased input data availability and further investigation into different deep learning algorithms.

Empirical modeling of hysteresis in a tendon–sheath mechanism on multi-segmented curves

Empirical modeling of hysteresis in a tendon–sheath mechanism on multi-segmented curves

Magnetic behavior of 3D interconnect nanoporous FeCo synthesized by liquid metal dealloying

Liquid Metal Dealloying (LMD) is tested to enhance the near-surface magnetic properties of ferromagnetic Iron-Cobalt alloys. With a lower surface electrical conductivity, treated specimens are expected to accommodate the frequency effect better and exhibit a lower level of magnetic loss. This work focuses on the magnetic viability of LMD-treated samples. The magnetic hysteresis cycles of virgin, fully-dealloyed, and partially-dealloyed specimens are measured from quasi-static to dynamic regimes. For each category of specimens, experimental results are compared with numerical predictions given by dedicated hysteresis models. The simulation parameters of the fully-dealloyed and the virgin specimens are leveraged to predict the partially-dealloyed specimen's behavior and estimate the thickness of the treated area accurately and non-destructively. Together with SEM observations and finite element simulations, these results show that the magnetic behavior of the metallic part in the dealloyed layer is barely affected by the specimen porosity, but the average variations observed experimentally are primarily due to the distortion of the magnetic lines and changes in the local geometry.

On the Second Law of Thermodynamics in Continuum Physics

The paper revisits the formulation of the second law in continuum physics and investigates new methods of exploitation. Both the entropy flux and the entropy production are taken to be expressed by constitutive equations. In three-dimensional settings, vectors and tensors are in order and they occur through inner products in the inequality representing the second law; a representation formula, which is quite uncommon in the literature, produces the general solution whenever the sought equations are considered in rate-type forms. Next, the occurrence of the entropy production as a constitutive function is shown to produce a wider set of physically admissible models. Furthermore the constitutive property of the entropy production results in an additional, essential term in the evolution equation of rate-type materials, as is the case for Duhem-like hysteretic models. This feature of thermodynamically consistent hysteretic materials is exemplified for elastic–plastic materials. The representation formula is shown to allow more general non-local properties while the constitutive entropy production proves essential for the modeling of hysteresis.

Investigation of Viscoelastic Guided Wave Properties in Anisotropic Laminated Composites Using a Legendre Orthogonal Polynomials Expansion-Assisted Viscoelastodynamic Model.

This study investigates viscoelastic guided wave properties (e.g., complex-wavenumber-, phase-velocity-, and attenuation-frequency relations) for multiple modes, including different orders of antisymmetric, symmetric, and shear horizontal modes in viscoelastic anisotropic laminated composites. To obtain those frequency-dependent relations, a guided wave characteristic equation is formulated based on a Legendre orthogonal polynomials expansion (LOPE)-assisted viscoelastodynamic model, which fuses the hysteretic viscoelastic model-based wave dynamics and the LOPE-based mode shape approximation. Then, the complex-wavenumber-frequency solutions are obtained by solving the characteristic equation using an improved root-finding algorithm, which leverages coefficient matrix determinant ratios and our proposed local tracking windows. To trace the solutions on the dispersion curves of different wave modes and avoid curve-tracing misalignment in regions with phase-velocity curve crossing, we presented a curve-tracing strategy considering wave attenuation. With the LOPE-assisted viscoelastodynamic model, the effects of material viscosity and fiber orientation on different guided wave modes are investigated for unidirectional carbon-fiber-reinforced composites. The results show that the viscosity in the hysteresis model mainly affects the frequency-dependent attenuation of viscoelastic guided waves, while the fiber orientation influences both the phase-velocity and attenuation curves. We expect the theoretical work in this study to facilitate the development of guided wave-based techniques for the NDT and SHM of viscoelastic anisotropic laminated composites.

State of charge estimation with hysteresis-prone open circuit voltage in lithium-ion batteries using the trajectory correction hysteresis (TCH) model

State-of-the-art lithium-ion cell chemistries with pronounced open-circuit voltage hysteresis (OCV), characterised by asymmetry and directional dependence, present a challenge for estimating the state of charge (SOC). Without understanding the hysteresis behaviour, OCV measurement points that lie within the hysteresis window cannot be used for SOC correction. After obtaining the data efficiency of the trajectory correction hysteresis (TCH) model with the introduction of the transfer fit (TF) method, this work applies the TF TCH for OCV-based SOC correction. The TF method plays a key role as it enables the cell-specific adaptation of an existing TCH model - ageing update is achieved with solely 12 (SOC/OCV) measurement points. With the precise hysteresis model, the developed framework successfully corrects the faulty SOC history, which could originate from a vehicle data logger. Given that two OCV measurement points are available that arbitrarily lie within the SOC history, the SOC correction is achieved by minimising the voltage deviation between the measurement points and the TCH model’s simulation. Identifying the two SOC parameters shift and scale enables subsequent SOC estimation until an additional OCV measurement is available for a further update. The functionality of the presented SOC correction framework is demonstrated using two validation profiles.

Dynamic Characteristics of M-Shape Metal Rubber-Coated Pipeline System: Numerical Modeling and Experimental Analysis

As a high-temperature resistant damping material, reducing vibration by coating with M-shape metal rubber (MMR) in a pipeline system is a promising solution due to its energy dissipation induced by micro dry friction between metallic wires. The main challenge for dynamic calculation and performance evaluation of elastic-porous metal rubber (MR) is derived from the intricate spatial network structure. In this work, the dynamic properties including acceleration admittance and insertion loss of the MMR-coated pipeline system were conducted by numerical simulation and experimental analysis. The constitutive models used to characterize hysteresis phenomena, including Yeoh and Bergström–Boyce models, were identified with different density parameters and adopted for steady-state dynamic numerical analysis. The sine sweep frequency test was conducted to verify the accuracy of the developed numerical model. The results indicate that the maximum error of stress–strain curve between numerical prediction and experimental measurement is 10.7%. In the frequency range of 0–1 500[Formula: see text]Hz, the insertion loss of the MMR-coated pipeline system is positively correlated with the density of MMR, as opposed to the coating distance of pipeline clamps and the influence of excitation force is minimal. Furthermore, the error of dynamic response of the pipeline system in low frequency between the experiment and simulation is 4.7%, indicating that the accuracy of the hysteresis model in predicting the dynamic characteristic of MR materials is effective.

Trajectory compensation based adaptive control (TCAC) for high-precision piezoelectric actuators

Piezoelectric actuator (PEA) has been widely used in micro-systems, due to the advantages of nano-scale precision, rapid response speed, high stiffness, etc. Nevertheless, the intrinsic nonlinearities of PEA, particularly hysteresis, severely deteriorate its positioning and tracking control accuracy. In most existing control algorithms of PEA, the approximate inverse model of hysteresis is developed to compensate for motion error, which requires high modeling accuracy. To avoid the influence of complex modeling procedures and modeling errors on tracking precision, a trajectory compensation-based adaptive control method has been proposed in this paper. Firstly, a simple linear controller is used to establish the closed-loop feedback system and to guarantee the basic tracking performance of the PEA system. And then, the trajectory compensation is designed according to the frequency analysis of the closed-loop control system. Finally, nonlinear adaptive compensation is used to eliminate the residual errors of the above linear frequency domain model. Different from conventional controllers, the proposed method can achieve excellent tracking control performance without any hysteresis model of PEA. The stability and convergence of the proposed method have been theoretically proved. In addition to theoretical guarantees, the proposed method is validated experimentally and demonstrated to achieve the root-mean-square and maximum value of tracking errors to less than 8 nm and 25 nm, respectively, which has a clear accuracy advantage over other methods.

Incorporation of a 3-D Energy-Based Vector Hysteresis Model Into the Finite Element Method Using a Reduced Scalar Potential Formulation

Incorporation of a 3-D Energy-Based Vector Hysteresis Model Into the Finite Element Method Using a Reduced Scalar Potential Formulation

Cross-Medium Time-Delay active vibration isolation method based on Voltage-Force hysteresis model

Micro-vibration significantly impacts spacecraft precision equipment operations, which can be resolved by using a piezoelectric actuator. The voltage-displacement relationship is the primary focus of current research on the hysteresis nonlinearity of piezoelectric actuators. Nevertheless, when tracking and controlling the acceleration/force signals of micro-vibration, control method based on the voltage-displacement introduces needless errors. In this paper, a cross-medium active vibration isolation control method based on voltage-force hysteresis model that can be utilised to track micro-vibration acceleration signals with high accuracy is proposed. The method exploits the slow transmission speed of vibration waves in a rubber medium to design a hybrid actuator mechanism containing a slow buffer medium and a piezoelectric actuator, and adopts a sliding mode control method to achieve accurate force control. Experiments demonstrated that compared with the vibration isolation control method based on voltage-displacement hysteresis model, the vibration isolation accuracy of the proposed method can be improved by 23.4%

Comprehensive compensation of dynamic hysteresis and creep for piezoelectric actuator

This paper addresses the modeling of dynamic hysteresis and creep in piezoelectric actuators, and employs feedforward open-loop control based on inverse models to compensate for hysteresis and creep phenomena. The comprehensive model consists of quasi-dynamic and dynamic components. The quasi-dynamic model combines the quasi-dynamic Prandtl–Ishlinskii (PI) model with an PI-based linear time-invariant model, while the dynamic part utilizes the auto-regressive exogenous model. The model accurately describes creep and dynamic hysteresis with modeling errors of less than 0.01 μm and 0.14 μm, respectively. The inversion of the comprehensive model has been proven to exhibit unique convergence. Under inverse feedforward control, the improvement in dynamic hysteresis and hysteresis with creep can be achieved at 94% and 83%, respectively. The comprehensive model proposed in this paper accurately describes the dynamic hysteresis and creep phenomena in piezoelectric actuators and realizes open-loop compensation control, achieving precise actuation of piezoelectric actuators.

A physically motivated voltage hysteresis model for lithium-ion batteries using a probability distributed equivalent circuit

The open circuit voltage hysteresis of lithium-ion batteries is a phenomenon that, despite intensive research, is still not fully understood. However, it must be taken into account for accurate state-of-charge estimation in battery management systems. Mechanistic models of the open circuit voltage hysteresis previously published are not suitable for deployment in a battery management system. Phenomenological models on the other hand can only superficially represent the processes taking place. To address this limitation, we propose a probability distributed equivalent circuit model motivated by the physical insights into hysteresis. The model incorporates hysteresis effects that are often disregarded for state estimation, while keeping the computational cost low. Although the parameterization is more demanding, the model has the advantage of providing insight into the internal state of the battery and intrinsically incorporating the effect of path-dependent rate capability.

State of the Art on Relative Permeability Hysteresis in Porous Media: Petroleum Engineering Application

This paper delivers an examination of relative permeability hysteresis in porous media in the field of petroleum engineering, encompassing mathematical modeling, experimental studies, and their practical implications. It explores two-phase and three-phase models, elucidating the generation of scanning curves and their applications in various porous materials. Building on the research of traditional relative permeability hysteresis models, we have incorporated literature on forward calculations of relative permeability based on digital rock core models. This offers a new perspective for studying the hysteresis effect in relative permeability. Additionally, it compiles insights from direct relative permeability and flow-through experiments, accentuating the methodologies and key findings. With a focus on enhanced oil recovery (EOR), carbon capture, utilization and sequestration (CCUS), and hydrogen storage applications, the paper identifies existing research voids and proposes avenues for future inquiry, laying the groundwork for advancing recovery techniques in oil and gas sectors.

Towards robust state estimation for LFP batteries: Model-in-the-loop analysis with hysteresis modelling and perspectives for other chemistries

The accurate estimation of a battery’s state of charge (SOC) is critical in battery management systems for various applications. Lithium Iron Phosphate (LFP) batteries, preferred for their long cycle life, cost efficiency, and enhanced safety, have emerged as favourable choices for stationary storage. Yet, they still face challenges in precise SOC estimation due to the flatness and hysteresis of their open circuit voltage. Addressing this, our study integrates a hysteresis model into a third-order battery model for BMS controlling a stationary storage system in frequency containment reserve (FCR) application. We analysed three advanced SOC estimation techniques — extended Kalman filter (EKF), dual unscented Kalman filter (DUKF), and particle filter (PF) — with the hysteresis model using a model-in-the-loop (MiL) toolchain. Performance testing under a 48-hour FCR load profile showed EKF with a 4% error, DUKF achieving the best result with a 1.1% error, and PF’s performance varying between 2.9% and 4% depending on particle count. Robustness tests against initialization and current sensor errors under an 8hr profile revealed DUKF maintained a 2% error boundary irrespective of the error introduced, highlighting the hysteresis model’s effectiveness. Broadening the scope, the study also explores extending the method to other lithium-ion chemistries.

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.

Seismic responses and loss evaluation of RC frame with slotted infill walls

Infill walls are a primary source of structural loss under service level and design basis earthquakes, so developing high-performance infill wall is an effective strategy to reduce seismic loss. While several high-performance infill walls have been proposed, most studies only reveal the damage characteristics of infill walls at the component level. However, the interaction between infill walls and structures can alter the seismic response of structures and consequently affect the loss of infill walls under earthquakes. Therefore, it is necessary to investigate the seismic responses and loss of high-performance infill wall at the structural level. In this paper, the working mechanism and damage characteristics of the slotted infill wall (SIW) are firstly introduced and verified through cyclic loading test. Then, an in-plane hysteresis model of SIW is developed, and the calculation method of key parameters is proposed. Finally, a numerical analysis model of a 10-story frame with slotted infill wall (SIW-F) is developed to study the seismic response and seismic losses. The results indicate that SIW-F’s displacement response is larger than that of the frame with ordinary infill wall (OIW-F) on most floors. However, the floor acceleration response is less. The seismic loss of SIW-F is less than that of OIW-F, particularly under design basis earthquakes. The repair cost ratio of infill wall decreases from 19% to 8%, the total repair cost of the SIW-F decreases by 41%, and the total repair time also reduces by 25%.