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The axial force will be altered as a result of the overturning influence exerted by both horizontal and vertical seismic events, as well as the secondary effects induced by gravitational loads. The variation of the axial force will greatly affect the seismic performance of reinforced concrete (RC) columns, thus warranting close attention. This paper proposes a hysteresis model of RC columns considering the cumulative damage effect under the action of variable axial force. First, three groups of cyclic loading tests were performed across three distinct groups. Subsequently, numerical analysis models were constructed, employing fiber-based finite element methods. Furthermore, according to the test and finite element simulation results, the existing damage value was modified to describe the degradation of the stiffness and load-bearing capacity. Next, through a regression analysis, the skeleton curve was established. Finally, the hysteresis behavior under the influence of variable axial load was ascertained. The results, when compared with the experimental data, show that the proposed hysteresis model can accurately describe the seismic performance of RC columns under the influence of variable axial force.

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.

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.

This paper develops a model for lithium-ion batteries under dynamic stress testing (DST) and federal urban driving schedule (FUDS) conditions that incorporates associated hysteresis characteristics of 18650-format lithium iron-phosphate batteries. Additionally, it introduces the adaptive sliding mode observer algorithm (ASMO) to achieve robust and swiftly accurate estimation of the state of charge (SOC) of lithium-iron-phosphate batteries during electric vehicle duty cycles. The established simplified hysteresis model in this paper significantly enhances the fitting accuracy during charging and discharging processes, compensating for voltage deviations induced by hysteresis characteristics. The SOC estimation, even in the face of model parameter changes under complex working conditions during electric vehicle duty cycles, maintains high robustness by capitalizing on the easy convergence and parameter insensitivity of ASMO. Lastly, experiments conducted under different temperatures and FUDS and DST conditions validate that the SOC estimation of lithium-iron-phosphate batteries, based on the adaptive sliding-mode observer and the simplified hysteresis model, exhibits enhanced robustness and faster convergence under complex working conditions and temperature variations during electric vehicle duty cycles.

The main purpose of this paper is to propose a practical approach for considering the soil – shallow foundation – superstructure interaction effect in nonlinear seismic analysis. Soil structure interaction is a complicated task dealing with various engineering problems. Taking into account the soil structure interaction extends beyond the numerical analysis, geotechnical investigation, or structural design fields. The artistry of considering the soil structure interaction effect lies in the balance between incorporating soil conditions and the superstructure into one collective model. Following this methodology alongside classical soil mechanics principles provides additional confidence to the structural engineering society in adopting a complete practical concept. The herein presented study introduces a fiber macroelement that represents the soil beneath shallow foundations. This allows for the direct utilization of the fiber macroelement in nonlinear pushover and dynamic analysis in commercial software, as well as its simple implementation in open software systems. The introduction of a procedure for forming the stiffness matrix of the element and a hysteresis soil model is also a key component. Special attention is devoted to obtaining the material backbone curve through experimental results and Eurocode 8’s procedures. Furthermore, this paper demonstrates the implementation of a macroelement for considering the soil-structure interaction effect in nonlinear seismic analysis within commercial software. The primary aim is to provide structural designers with a streamlined approach for incorporating soil conditions into superstructure analysis. Numerical analysis results from an example building with a reinforced concrete structure in commercial software highlight the significance of not underestimating soil conditions. This work emphasizes that relying solely on fixed models in everyday structural design could lead to dangerous and unexpected consequences.

Accurate modeling of the coupling between mechanical and magnetic behavior is a key challenge for designing many electromagnetic devices. The requirements for such modeling are notably the ability to consider multiaxial configurations, thermodynamic consistency to allow the calculation of losses, and the implementability into structural analysis tools. So far, the modeling approaches available in the literature do not usually combine these three features simultaneously. In this paper, for the first time, the influence of mechanical stress on the magnetic hysteretic behavior is modeled through the association of a reversible simplified multiscale approach and a macroscopic energy-based magnetic hysteresis model in a vector-play form. A phenomenological description of the dissipation parameters under mechanical stress is proposed. The non-monotonic effect of tensile stress on the magnetic permeability is modeled using a second-order development in the magneto-elastic energy. Material parameters for both reversible and irreversible behavior are identified from experimental characterization under mechanical stress performed on a DC04 electrical steel. The experimental tests include anhysteretic and hysteretic measurements. Modeling results of the anhysteretic magnetic permeability, the coercive field, and the remanent induction under several levels of peak magnetic field and uniaxial mechanical stress are satisfactorily compared with those obtained experimentally. The model is shown to reasonably predict the hysteresis losses under tensile and compressive stress, as well as the response of the material under a complex magnetic field waveform with harmonic content.

A hysteresis motor produces output torque through the hysteresis effect of magnetic materials. It has the advantages of a simple structure, high-speed operation, high temperature resistance, low noise and self-starting capability. It can be applied to some special occasions requiring high speed and high stationarity. However, its disadvantage is low torque density, low efficiency and low power factor. The permanent magnet hysteresis motor is a compromise of the characteristics of permanent magnet motor and hysteresis motor, and it can be self-starting in the case of having a torque density comparable to that of a permanent magnet motor. In addition, there are some new structures of hysteresis motors, which open up the direction for innovative applications. Due to the complexity of magnetic properties, the calculation methods and dynamic models of hysteresis motors and permanent magnet hysteresis motors are special and also depend on the research of hysteresis materials and hysteresis models. This paper starts from the principle and classification of the hysteresis motor, and different structures and the corresponding analysis methods are reviewed. The motors with new structures and new methods are emphasized, the innovation and contribution of existing research are summarized, and the development trend of hysteresis motors is described.

The hysteresis model of the friction pendulum bearing (FPB) is very important for predicting its seismic performance. The previous hysteresis model is based on the horizontal force balance theory and cannot analyze the moment required when the FPB rotates. Because of this, this paper proposes a hysteresis model of the FPB based on the moment balance theory, which can be used to analyze the rotation performance of the FPB. In this paper, formulas of the hysteresis model of the FPB based on the moment balance theory are derived firstly. And it is found that the hysteresis loops calculated based on the moment balance theory is very close to those obtained from experiments. Then two main assumptions of the hysteresis model of the FPB based on the moment balance theory: Small rotation assumption and Normal stress assumption are introduced, and the expression of the hysteresis model of the FPB based on the moment balance theory without using the two assumptions is given. Finally, errors caused by the assumptions are analyzed in detail and the applicability of the simplified formula is verified.

Based on the Bouc-Wen model, a nonlinear hysteretic restoring force model is established with dynamic equations. The hardening and softening of the material after reaching the yield limit are described by the nonlinear restoring force-displacement hysteretic curve. The Gamultiobj algorithm and the group search optimization (GSO) algorithm are used to fit and identify the material softening and hardening hysteresis curves, respectively. The effectiveness of the optimization algorithm for identifying the parameters of the hysteretic model is verified, and the optimization effects of the two algorithms are compared. The results show that the Gamultiobj algorithm has better parameter identification ability and curve fitting ability for the hysteretic model. Then, the hysteresis curve describing the nonlinear characteristics of a clamp is obtained through the static stiffness experiment of the clamp. The experimental curve is fitted by the Gamultiobj algorithm. As a result, the nonlinear Bouc-Wen model parameters of the clamp are obtained, and the stiffness and damping of the clamp are recognized. The distribution statistics of the obtained parameters are performed, and it is found that each parameter satisfies a certain probability distribution, which indicates that the parameter identification result is reasonable.

Electromagnetic clutches are widely used devices in industrial applications when a torque must be transmitted between two components without mechanical contact avoiding friction and so reducing wear and maintenance time. Hysteresis clutches are a particular variant of electromagnetic couplers used when a constant torque from zero to the synchronous speed needs to be transmitted. This paper deals with the analysis, design and optimization of hysteresis clutches. After a brief introduction on the operating principle, a new method of analysis is then introduced. The latter allows a fast prediction of the performance of hysteresis couplers without sacrificing the accuracy of the performance evaluation even when adopting anisotropic magnetic materials. The introduced method, based on a static finite element simulation followed by a post-processing of the evaluated magnetic field, is then used within an automatic design procedure in order to identify the inevitable trade-offs encountered when optimizing the geometry of any hysteresis clutches with a given outer envelope. The obtained results are commented in-depth and allow to draw general design guidelines with special regards to the selection of the number of poles and the magnetic materials. The effect of the high level of anisotropy of the most common magnetic materials showing the highest energy density is carefully taken into account allowing to deduce the optimal preferred direction of magnetization.

Preisach density is drawing increasing attention for interpreting material properties for memory and storage electronics. Preisach density can be linked to the observed hysteresis loops via the Preisach model that is based on the superposition of relay operators. Reconstructing Preisach density from hysteresis is an ill-posed problem with nonunique solutions. To alleviate ambiguities, we address Preisach density reconstruction as a constrained subset selection task utilizing structured sparsity regularizations. We validate our approach under various simulation settings and apply it on experimental band-excitation piezoresponse spectroscopy (BEPS) datasets to gain insights in microstructure-dependent properties of the tip-surface contact.

Currently, lithium-ion batteries are mainly used as central power components in electric vehicles. Usually, accurate battery cell modeling and state of charge estimation are required in order to effectively use the lithium-ion batteries in electrified vehicles. For an elaborate battery cell modeling on a wide temperature range, we select a temperature-dependent battery cell modeling approach, which relies on one resistance plus second-order resistance-capacitance equivalent circuit model. In order to corporate some temperature effects into the modeling, we derive the sixth-order polynomial functions using the curve fitting algorithm. The functions contribute to the accurate battery cell modeling on the wide temperature range. For a practical usage of the functions in real-time embedded systems, we propose an offset-based lookup table technique. In addition, we propose a novel hysteresis voltage unit model for more accurate parameter estimation of hysteresis voltages. This also leads to more accurate battery cell modeling. Based on the battery cell modeling, we propose a temperature-dependent estimation method for state of charge. This approach exploits the extended Kalman filter, which is suitable for nonlinear characteristics such as the hysteresis effect. Experimental evaluation exhibits that the proposed estimation method outperforms the conventional approaches in the wide temperature range.

Shape memory alloys (SMAs) are widely used in aerospace, automobile, and other fields because of their excellent properties, such as large driving force and large deformation. A training method with a bidirectional memory effect is proposed for SMA actuators. The trained SMA units can be heated and cooled to change their shape (shorten and extend). The trained SMA is used as an actuator to drive the deformation of a structure. Due to the obvious hysteresis characteristics of SMA, a temperature-displacement hysteresis model based on the Preisach model is proposed in order to reduce the influence of hysteresis in the process of structural deformation. The F function method (FFM) is used for Preisach numerical implementation, and a PID control method is used for the precise control of structural deformation. Compared with the PID control method without hysteresis model, this method is superior to the PID control method in response speed and control accuracy. The maximum relative error of three target points in the experiment is 5.45%, which is better than the PID control method without this model. The hysteresis model can be applied to the displacement control of a SMA-based actuator.

The fast tool servo (FTS) technology has unique advantages in the machining of complex surfaces such as special-shaped targets and free-form surfaces. In view of the shortcomings in the performance of the existing FTS device, this paper puts forward a novel FTS which uses two piezoelectric ceramics instead of flexure hinges to provide restoring force. Firstly, the feasibility of the double-drive principle is verified theoretically, and the corresponding mechanism is optimized accordingly. Then, the system control hysteresis model is established and identified, and the appropriate control strategy is designed. Finally, the performances of the proposed FTS device are tested, and a typical microstructure is machined based on the device and ultra-precision lathe. The results indicate that the proposed device effectively improves the performance of the FTS system, which is useful for the processing of microstructures and free-form surfaces.

An innovative symmetrical hysteresis model for reinforced concrete (RC) rectangular hollow columns is presented. The Bouc–Wen–Baber–Noori (BWBN) model was selected to depict the inelastic restoring forces and was improved by introducing a coefficient to describe the relationship between stiffness degradation and peak displacement. Sensitivity analysis was conducted at the local and global levels to clarify the importance of each parameter in the improved BWBN model. As such, a hybrid intelligence algorithm named PSOGSA was employed to identify the parameters of the BWBN model utilizing quasi-static tests of 16 hollow columns. The empirical formulas were regressed to bridge the connection between the BWBN model and design parameters of hollow columns. The results showed that the hysteresis curves of the improved BWBN model calibrated by the PSOGSA agreed well with the measured loops. In addition, the accuracy of the empirical prediction method of hysteretic parameters was checked through comparison with other hollow members. The calibrated improved BWBN model produced more precise hysteretic responses for RC hollow columns, since the peak and residual performance levels were simultaneously considered.

Pneumatic artificial muscle (PAM) is attractive in rehabilitation and biomimetic robots due to its flexibility. However, there exists a strong hysteretic nonlinearity in PAMs and strong coupling between the output displacement and the output force. At present, most commonly used hysteresis models can be treated as two-dimensional models, which only consider the nonlinearity between the input and the output displacement of the PAM without considering the coupling of the output force. As a result, high-precision modeling and estimation of the PAM’s behavior is difficult, especially when the external load of the system varies significantly. In this paper, the influence of the output force on the displacement is experimentally investigated. A three-dimensional model based on the modified Prandtl–Ishlinskii (MPI) model and the Nonlinear AutoRegressive Moving Average with eXogenous inputs (NARMAX) model is proposed to describe the relationship and couplings among the input, the output displacement, and the output force of the PAM. Experiments are conducted to verify the modeling accuracy of the proposed model when the external load of the PAM varies across a wide range. The experimental results show that the proposed model captures well the hysteresis and couplings of the PAM and can precisely predict the PAM’s behavior.

This paper presents the characterization and hysteresis modeling of magnetorheological (MR) damper with meandering type valve. The meandering type MR valve, which employs the combination of multiple annular and radial flow passages, has been introduced as the new type of high performance MR valve with higher achievable pressure drop and controllable performance range than similar counterparts in its class. Since the performance of a damper is highly determined by the valve performance, the utilization of the meandering type MR valve in an MR damper could potentially improve the damper performance. The damping force characterization of the MR damper is conducted by measuring the damping force as a response to the variety of harmonic excitations. The hysteresis behavior of the damper is identified by plotting the damping force relationship to the excitation displacement and velocity. For the hysteresis modeling purpose, some parts of the data are taken as the training data source for the optimization parameters in the neuro-fuzzy model. The performance of the trained neuro-fuzzy model is assessed by validating the model output with the remaining measurement data and benchmarking the results with the output of the parametric hysteresis model. The validation results show that the neuro-fuzzy model is demonstrating good agreement with the measurement results indicated by the average relative error of only around 7%. The model also shows robustness with no tendency of growing error when the input values are changed.

In the fast tool servo (FTS) system for microstructure surface cutting, the dynamic voltage hysteresis of piezoelectric actuators (PEAs) and the cutting force produced in the manufacturing affect the driving accuracy and the cutting performance. For a multi-input-single-output (MISO) cutting system, in this paper, a dynamic hysteresis model based on a rate-dependent Prandtl–Ishlinskii model is proposed. A backpropagation neural network (BPNN) is established to describe the cross-coupling effect between the applied voltage and external load. An inverse dynamic model is developed to compensate the nonlinearity of PEAs. The accuracy of the model and its inverse is discussed and the performance of the inverse feedforward compensator is validated through experiments.

Various seismic analysis methods are being used to predict the response of structures to earthquakes. Although nonlinear dynamic analysis (NDA) is considered an ideal method to represent the most realistic behavior of a structure among these various methods, correct results can be derived only when the analysis model is carefully developed by a knowledgeable person. It is particularly important to properly implement the behavior characteristics depending on the reversed cyclic load in the NDA of a building made of reinforced concrete (RC) moment frames. This study evaluated the hysteresis model suitable for NDA of existing RC moment frames, and 45 analysis models were reviewed, in which the pivot, concrete, and Takeda hysteresis models were applied differently to beams and columns. The pivot model was evaluated as the most reliable hysteresis model for each structural member by comparing and analyzing not only the responses of the entire frame but also the responses of column and beam members focusing on energy dissipation. However, this model can have practical limitations in that the parameters associated with the reinforcement detailing and applied loads need to be defined in detail. The analysis model applying Takeda to the beam, which predicted the average response at a reliable level compared to the reference model, was identified as a practical alternative when it is difficult to apply the pivot model to all frame members.

This paper proposes a new electrically controlled magnetic variable-speed gearing (EC-MVSG) machine, which is capable of providing controllable gear ratios for hybrid electric vehicle (HEV) applications. The key design feature involves the adoption of a magnetic gearing structure and acceptance of the memory machine flux-mnemonic concept. Hence, the proposed machine can not only offer a gear-shifting mechanism for torque and speed transmission, but also provide variable gear ratios for torque and speed variation. The electromagnetic design is studied and discussed. The finite-element method is developed with the hysteresis model to verify the validity of the machine design.

Hysteresis behaviors are inherent characteristics of piezoelectric ceramic actuators. The classical Duhem model (CDM) as a popular hysteresis model has been widely used, but cannot precisely describe rate-dependent hysteresis behaviors at high-frequency and high-amplitude excitations. To describe such behaviors more precisely, this paper presents a modified Duhem model (MDM) by introducing trigonometric functions based on the analysis of the existing experimental data. The MDM parameters are also identified by using the nonlinear least squares method. Six groups of experiments with different frequencies or amplitudes are conducted to evaluate the MDM performance. The research results demonstrate that the MDM can more precisely characterize the rate-dependent hysteresis behaviors comparing with the CDM at high-frequency and high-amplitude excitations.

Giant magnetostrictive actuators (GMA) driven by giant magnetostrictive material (GMM) has some advantages such as a large strain, high precision, large driving force, fast response, high reliability, and so on, and it has become the research hotspot in the field of microdrives. Research shows there is a nonlinear, intrinsic relationship between the output signal and the input signal of giant magnetostrictive actuators because of the strong coupling characteristics between the machine, electromagnetic field, and heat. It is very complicated to construct its nonlinear eigenmodel, and it is the basis of the practical process of giant magnetostrictive material to construct its nonlinear eigenmodel. Aiming at the design of giant magnetostrictive actuators, the magnetization model based on a free-energy hysteresis model has been deeply researched, constructed, and put forward by Smith, which combines Helmholtz−Gibbs free energy and statistical distribution theory, to simulate the hysteresis model at medium or high driving strengths. Its main input and output parameters include magnetic field strength, magnetization, and mechanical strain. Then, numerical realization and verification of the magnetization model are done by the Gauss−Legendre integral discretization method. The results show that the magnetization model and its numerical method are correct, and the research results provide a theoretical basis for the engineering application of giant magnetostrictive material and optimized structure of giant magnetostrictive material actuators, which have an important practical application value.

With the aim to model the seismic behavior of steel reinforced concrete (SRC) frame columns, in this research, hysteresis and skeleton curves were obtained based on the damage test results of SRC frame columns under low cyclic repeat loading and the hysteretic behavior of the frame columns was further analyzed. Then, the skeleton curve and hysteresis loops were further simplified. The simplified skeleton curve model was obtained through the corresponding feature points obtained by mechanical and regression analysis. The nonlinear combination seismic damage index, which was developed by the test results and can well reflect the effect of the loading path and the number of loading cycle of SRC frame columns, was used to establish the cyclic degradation index. The strength and stiffness degradation rule of the SRC frame columns was analyzed further by considering the effect of the accumulated damage caused by an earthquake. Finally, the hysteresis model of the SRC frame columns was established, and the specific hysteresis rules were given. The validity of the developed hysteresis model was verified by e comparison between the calculated results and the test results. The results showed that the model could describe the hysteresis characteristics of the SRC frame columns under cyclic loading and provide guidance for the elastoplastic time-history analysis of these structures.

Shape memory alloys (SMAs) offer a high power-to-weight ratio, large recovery strain, and low driving voltages, and have thus attracted considerable research attention. The difficulty of controlling SMA actuators arises from their highly nonlinear hysteresis and temperature dependence. This paper describes a combination of self-sensing and model-based control, where the model includes both the major and minor hysteresis loops as well as the thermodynamics effects. The self-sensing algorithm uses only the power width modulation (PWM) signal and requires no heavy equipment. The method can achieve high-accuracy servo control and is especially suitable for miniaturized applications.

This paper presents the Jiles and Atherton (J-A) hysteresis model parameter estimation for soft magnetic composite (SMC) material. The calculation of Jiles and Atherton hysteresis model parameters is based on experimental data and genetic algorithms (GA). Genetic algorithms operate in a given area of possible solutions. Finding the best solution of a problem in wide area of possible solutions is uncertain. A new approach in use of genetic algorithms is proposed to overcome this uncertainty. The basis of this approach is in genetic algorithm built in another genetic algorithm.