Bouc-Wen Model Research Articles

A novel reliable parametric model for predicting the nonlinear hysteresis phenomenon of composite magnetorheological fluid

Abstract Magnetorheological fluid, as a novel intelligent composite material, possesses unique controllable properties in the presence of a magnetic field, thereby opening up new possibilities for its engineering applications. In this study, a novel parametric model is proposed to accurately describe the nonlinear hysteresis behavior of a magnetorheological fluid composed of micron-scale carbonyl iron particles. Experimental investigations involving large-amplitude shear tests, employing strain amplitudes of 10% and frequencies of 0.1 Hz and 1 Hz, were conducted at five different current levels (0A, 0.5A, 1A, 1.5A, and 2A) to determine the model parameters. The genetic optimization algorithm was employed to identify the optimal solution for the model parameters. Subsequently, the model parameters were generalized with respect to the applied current, and the relationship between these parameters and current variations was explored. Research findings demonstrate the superiority of the proposed model over existing models such as the Bouc-Wen model and the hyperbolic tangent model in accurately capturing the nonlinear hysteresis behavior of magnetorheological fluid. This study holds significant potential for predicting the nonlinear hysteresis behavior of automotive dampers and provides a solid theoretical foundation for semi-active suspension control.

Stiffness Compensation in Variable Displacement Mechanisms of Swash Plate Axial Piston Pumps Utilizing Piezoelectric Actuators.

Swash plate axial piston pumps play an important role in hydraulic systems due to their superior performance and compact design. As the controlled object of the valve-controlled hydraulic cylinder, the swash plate is affected by the complex fluid dynamics effect and the mechanical structure, which is prone to vibration, during the working process, thereby adversely affecting the dynamic performance of the system. In this paper, an electronically controlled ball screw type variable displacement mechanism with stiffness compensation is proposed. By introducing piezoelectric ceramic materials into the nut assembly, dynamic stiffness compensation of the system is achieved, which effectively changes the vibration characteristics of the swash plate and thus significantly improves the working stability of the system. Based on this, the stiffness model of a double nut ball screw is established to obtain the relationship between piezoelectric ceramics and the double nut. An asymmetric Bouc-Wen piezoelectric actuator model with nonlinear hysteresis characteristics is also established, and a particle swarm algorithm with improved inertia weights is utilized to identify the parameters of the asymmetric Bouc-Wen model. Finally, a piezoelectric actuator model based on the feedforward inverse model and a PID composite control algorithm is applied to the variable displacement mechanism system for stiffness compensation.

Optimization of a viscous-elastic damper coupling two simple oscillators based on nonlinear stochastic response

Abstract Among the techniques used to control or mitigate the structural vibrations induced by dynamic input, such as wind and earthquake, the dissipative coupling is one of the most applied, especially for its ease of implementation. Indeed, for example in large urban areas, it is common to find adjacent structures where the space between the buildings becomes smaller. To optimally select the visco-elastic features of the dissipative device to be used, the paper retraces the path followed by the previous scientific works proposing new design criteria. Such criteria are based on the nonlinear stochastic response of two simple oscillators linked by a damper whose hysteretic behavior is represented by a Bouc-Wen model. A state-space formulation of the equations of motion has been adopted to facilitate the analysis of the dynamic response. At the same time, the loading is hypothesized as a zero-mean Gaussian excitation. Consequently, the nonlinear response has been approximately evaluated by the equivalent linearized standard deviations for both displacements and accelerations. Subsequently, formulations of objective functions, based on the Minimax and Total Energy of the equivalent linearized stochastic response, have been applied to determine the optimal configurations of the coupled system. The influence of both noise power amplitude and soil typology on the designed systems has been also investigated. Suggestions related to the path to achieve pre-fixed targets (as balancing of displacements and accelerations) are provided.

Development of an Innovative Magnetorheological Gearbox for Positioning Control and Anti-Disturbance of a Robotic Arm

The robotic arm is a critical component of modern industrial manufacturing. However, its positioning performance can be hindered by overshooting and oscillation. External disturbances, including collisions or impacts with other objects, can also affect its accuracy and precision. To resolve this problem, this work integrates a compact magnetorheological (MR) bearing, which is capable of switching between locking and unlocking states utilizing the MR effect, into the gearbox of the actuation system of the robotic arm. This integration enables the gearbox (referred to as the MR gearbox) to exhibit variable damping characteristics. This controllable damping property will play an important role in improving the positioning accuracy by offering additional damping. In this study, the MR gearbox was first designed and prototyped. A characterization test was then conducted to verify its variable damping property. The classic Bouc–Wen model was used to describe the MR gearbox and then a mathematical model was established for the whole robotic arm. Additionally, a new variable damping control method was proposed for further improving the positioning precision and reducing energy consumption. As follows, the positioning and the anti-disturbance performances of the robotic arm system installed with the MR gearbox were assessed through numerical simulations and experimental tests. The result shows that the robotic arm under the new control method achieves reductions of 11.76% in overshoot, 14.73% in settling time, and 26.1% in energy consumption compared to the uncontrolled case under the step trajectory, indicating improved positioning performance.

Seismic Behaviors of Shuttle-Shaped Double-Restrained Buckling-Restrained Braces: Experimental, Numerical, and Restoring Force Model Parameter Identification

The research aims to explore seismic behaviors of a novel shuttle-shaped double-restrained buckling-restrained brace (SDR-BRB). To this end, three SDR-BRB specimens showing various restraining ratios were first prepared to conduct low-cycle cyclic loading tests to investigate their failure modes, hysteretic performance, and fatigue performance. Afterwards, the ABAQUS finite element (FE) model verified by experiments was established, and effects of multiple critical factors upon seismic behaviors of SDR-BRBs were discussed through parametric analysis. Finally, an improved dung beetle optimization (DBO) algorithm considering global optimization and local exploration was proposed by combining Tent chaotic mapping, adaptive T-distribution perturbation strategy, and Osprey optimization algorithm. Based on this algorithm, the parameter identification method was developed for the improved Bouc–Wen model of SDR-BRB. Results indicate that hysteretic curves of SDR-BRBs are plump and symmetrical, showing excellent energy-dissipation capacity and fatigue performance, and obvious strain-strengthening characteristics. The restraining ratio, core yield length, initial imperfection, and core diameter-thickness ratio have significant effects upon seismic behavior of SDR-BRBs, while the gap of the core and the external tube merely exerts a slight effect. As recommended, the restraining ratio should exceed 2.0, the diameter-thickness ratio need to be less than 15, and the gap should not be less than 2[Formula: see text]mm. The proposed parameter identification method for the restoring force model of SDR-BRB has high accuracy and agrees well with experimental and numerical results. It provides reference for applying SDR-BRBs to analyze elastoplastic seismic responses of a structural system.

Effect of Nonlinear Hysteresis Details of Isolation System on In-Structure Response Spectra

To evaluate the seismic safety of components in a structure, an in-structure response spectrum (ISRS) must be obtained, and this also applies to seismically isolated structures. The main variables for designing seismic isolators are effective stiffness and effective damping, which can be given as the characteristic strength and secondary stiffness in seismic isolators for nonlinear behaviors. Many studies on the ISRS of isolated structures have been conducted to evaluate the effects of these two variables of isolators, but the effect of other variables related to the hysteresis curve of isolators also needs to be studied. This study focused on the effect of the initial stiffness of isolators on an ISRS because there were no clear criteria for determining the initial stiffness in isolator design standards, which has an effect on the ISRS that cannot be ignored. As a result, the initial stiffness contributed significantly to the ISRS not only at the natural frequency of the structure but also at low frequencies. An analysis was also performed in terms of the uncertainty of each variable. The sharpness of the yield point in the hysteresis curve was implemented using the Bouc–Wen model, and its impact was analyzed. In addition, the frequency content of the ISRS depending on the seismic intensity, which can considerably change the nonlinear hysteresis behavior, was examined. Through this study, although secondary stiffness and characteristic strength are the most important characteristics of seismic isolation design, it was confirmed that other variables also have a significant impact on the frequency content of an ISRS. Based on this study, the considerations when developing the ISRS of an isolated structure can be established.

Study on the dual-segment arctangent model of magnetorheological damper (MRD)

Abstract Magnetorheological fluid damper (MRD) is a damping device that utilizes the instantaneous variable characteristics of magnetorheological fluid (MRF) in magnetic field to control damping force. At present, there are some problems with the existing mechanical parametric models of MRD, such as the complexity of parameters in the Bouc-Wen model, low model accuracy, and the inability of the Bingham model to accurately capture the hysteresis characteristics of damping force with velocity variation. In response to these issues, on the base of MRD performance testing, a dual-segment arctangent model based on arctangent function is proposed. This model uses the arctangent function to describe the nonlinearity of the damping force output curve. And using piecewise fitting method to accurately capture the hysteresis characteristics of the output curve. Compared with existing parametric models such as the Bingham model, Sigmoid model, Bouc-wen improved model, et.al., the dual-segment arctangent model shows simpler parameters and higher model fitting accuracy. The comparative analysis of the fitting results based on experimental data confirms the effectiveness and accuracy of the proposed model, providing valuable reference for the development of high-precision MRD mechanical models.

Non-singular fast terminal sliding mode trajectory tracking control of cantilever piezo-electric stack actuator based on asymmetric hysteresis compensation

Abstract Piezoelectric actuators are widely employed in micro-precision applications due to their fast response and high resolution. This paper investigates the trajectory tracking control of a cantilever piezoelectric stack actuator (CPSA) under external perturbations and hysteresis. A control scheme is proposed that effectively compensates for hysteresis by employing an asymmetric Bouc–Wen model, integrated with a non-singular fast terminal sliding mode control (NFTSMC) featuring a variable convergence law. This methodology guarantees finite-time convergence and robustness, thereby enhancing the overall control performance of the CPSA. Experimental results reveal that the proposed control algorithm significantly improves control accuracy and speed, achieving stable closed-loop system performance and maintaining bounded closed-loop signals within a finite time frame. The effectiveness and superiority of the NFTSMC method are validated through comprehensive experimental studies.

On the hysteretic bending behavior of slack metallic cables

On the hysteretic bending behavior of slack metallic cables

Active micro-vibration isolation system for adaptive vibration suppression tests using piezoelectric stack actuator

An active micro-vibration isolation system for adaptive vibration suppression using piezoelectric stack actuators is presented, along with the discrete time modelling method, real-time adaptive controller design, and hardware implementation. The system comprises piezoelectric stack actuators, capacitive displacement sensors, power amplifiers, signal conditioners, and a real-time computer. A discrete asymmetric Bouc-Wen model is developed to characterize the nonlinear behavior of the piezoelectric stack actuators. System identification is conducted using an improved particle swarm optimization method, specifically the Hybrid PSO-Jaya algorithm, which sequentially integrates the PSO algorithm with the Jaya algorithm. Additionally, an improved adaptive filtering algorithm employing affine projection, referred to as the FXAPA algorithm, is introduced to facilitate real-time control. The efficacy of the proposed active micro-vibration isolation technology is validated through micro-vibration suppression tests.

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.

Improved active vibration control of a cantilever beam using MFC actuators with Hammerstein model-based hysteresis modeling and VSS-FxLMS control algorithm

This study aims to enhance active vibration control in a cantilever beam using macro fiber composite (MFC) actuators. To address the challenge of accurately modeling the complex hysteresis behavior of MFC actuators, an advanced hysteresis modeling technique is employed, integrating a non-symmetric Bouc–Wen model with an Auto-Regressive model with eXogenous inputs (ARX). The parameter estimation of this model is optimized using an adaptive mutation factor, and multiple mutation strategy differential evolution (AmFMMDE) algorithm. Additionally, a Variable Step Size Filtered-x Least Mean Square (VSS-FxLMS) algorithm with step size adaptation based on normalized error change is utilized for effective vibration control. This approach shows promising potential for practical engineering applications requiring precise and efficient active vibration control.

Rotor dynamic response prediction using physics-informed multi-LSTM networks

Rotor dynamic response prediction using physics-informed multi-LSTM networks

Magnetorheological damper parameter identification and its application in semi-active control of power equipment

In recent years, magnetorheological dampers (MRD) have played a significant role in vibration control in various fields such as vehicles, military, building structures, etc. However, the mechanical model of MRD is very complex due to its hysteresis, which makes it difficult to identify the model’s parameters. In addition to experimental data, under the condition of no other prior knowledge, eight unknown parameters of the Bouc-Wen model are identified in this study based on the particle swarm optimization (PSO) algorithm. According to the trend of parameter variation with current, fitting research is conducted, and the variation law of parameters with current is summarized. Based on the identified parameters, the MRD’s output force is predicted under any current other than the experimental current. Subsequently, the application of MRD in semi-active control of power equipment is performed out, and proposed Simulink calculation programs for single-stage and two-stage vibration control systems are built. Then, a comparative study with passive and active control is conducted. In this paper, linear quadratic regulator (LQR) control is adopted for the active control, and the controller’s parameters are optimized based on the PSO algorithm. The results show that the adopted semi-active control can significantly reduce the transmitted force from power equipment to the foundation and can effectively mitigate the disturbance of power equipment to the environment. This study offers important guidance for the vibration control of MRD in industrial engineering.

Mathematical Modelling of a Single Magneto-Rheological for Car Suspension System Using Modified Bouc-Wen Model

Magneto-Rheological (MR) automotive suspension represents the most advanced technology currently available for enhancing passenger comfort through intelligent fluid behaviour. This work employed a Modified Bouc-Wen model to create a mathematical representation of a single MR vehicle suspension and compared its ride performance to that of passive suspension systems. The model was formulated and solved using second-order linear differential equations, with MATLAB software utilized to visualize the results. The maximum vertical displacement for the single MR mathematical model in this work was 0.031 m, while the minimum was -0.0124 m. At the minimum position, the vertical displacements for the passive model were 0.0532 m and -0.0133 m. The results demonstrated that the vertical displacement variation was similar for both the mathematical model and the passive system. All displacements obtained from the mathematical modeling of the single MR system were close to its mean of 0.000875 m (nearly zero). There was reduced vibration when zero displacement was achieved. It was concluded that MR damper significantly improved car suspension performance compared to passive solutions. This paper developed a single MR vehicle suspension system using the Modified Bouc-Wen model in a Proton Preve.

A generalized Bouc–Wen model for simulating the quasi-static and dynamic shear responses of helical wire rope isolators

This research investigates the mechanical behavior of a helical wire rope isolator deforming along its shear direction. In particular, we present the results of an extensive experimental campaign including both quasi-static and dynamic tests. The former provide hysteresis loops characterizing the device quasi-static behavior; the latter, performed by using an electro-mechanical shaker, furnish frequency response curves describing the dynamic behavior of a rigid block supported by the tested device. To simulate such a complex behavior, we adopt a generalized Bouc–Wen model and identify its parameters on the basis of the quasi-static test results. Subsequently, such a model is employed to reproduce the frequency response curves of the isolated rigid block. Since the results of the dynamic tests suggest the presence of rate-dependent hysteresis phenomena in the isolated system, the generalized Bouc–Wen model is enhanced by introducing a linear viscous component. Finally, to substantiate the model validation, the experimental results obtained by applying a series of white noise signals are compared with those obtained numerically to demonstrate the model capability of reproducing the device behavior in non-stationary response conditions.

Frequency-Dependent Bouc–Wen Modeling of Magnetorheological Damper Using Harmonic Balance Approach

Magnetorheological dampers (MRDs) are of great interest in engineering due to their continuously adjustable damping characteristics. Accurate models are essential for optimizing MRDs and analyzing system dynamics. However, conventional methods widely overlook the impact of excitation frequency and amplitude. To address this issue, this work proposes a modified Bouc–Wen model that can be adapted to various excitation conditions. The model’s parameters depend on the current, excitation frequency, and amplitude. The mechanical characteristics of the MRD were analyzed by the tests. The parameters in the Bouc–Wen model were identified by combining the harmonic balance method and the genetic algorithm. The modified Bouc–Wen model was established by analyzing the variation of each parameter with current, excitation frequency, and amplitude. Finally, the agreement between the modified prediction model and the test results was verified under sinusoidal excitation of 80 mm and 1 Hz. The average relative errors were 3.87%, 2.82%, 2.45%, 2.19%, and 3.27% for current excitations of 0 A, 0.5 A, 1 A, 1.5 A, and 2.0 A, respectively. Since the MRD in this paper operates from 0.5 Hz to 2 Hz, the modified model was validated in the same range. Experiments demonstrate that the modified Bouc–Wen model efficiently and accurately describes the mechanical properties of the MRD under various excitation conditions.

Piezoelectric-based smart structures for aero-engine blade: Piezoelectric layout optimization and vibration suppression tests

Piezoelectric-based smart structures for aero-engine blade: Piezoelectric layout optimization and vibration suppression tests

Effectiveness in protecting rigid-block-like objects through horizontal and vertical seismic isolation

In this paper, a double, horizontal and vertical base isolation, is considered for the protection of rigid-block-like objects against seismic excitation. The equations of motion, the uplift and impact conditions are obtained under the hypothesis that the block can undergo full-contact and rocking motions. It is assumed that the horizontal isolation device has a hysteretic behavior, described with the Bouc-Wen model, whereas the vertical isolation has a visco-elastic behavior, modeled through a Kelvin-Voight device. Three rigid-block-like objects, representing a caryatid, a server and hospital cabinets are considered. Moreover, as base excitation, three earthquake horizontal and vertical records are selected accounting for their spectral content and PGA. The results of the seismic analysis are arranged in rocking maps and a comparison among the systems with the horizontal and vertical isolation, with only the horizontal isolation, and with no isolation are performed to check the effectiveness of the proposed seismic protection. Results show that the coexistence of horizontal and vertical isolation in protection against seismic excitation is particularly effective under earthquakes with high vertical PGA and in objects with high slenderness and heaviness. Finally, an analysis that consists of exciting the system with horizontal and vertical one-sine, impulsive base accelerations is performed to build the overturning spectra. Also, in this case, the double, horizontal and vertical isolation has manifested better performances than the other analyzed systems.

Coupled wind-induced response of inter-story isolated eccentric tall buildings with friction-pendulum bearings

Coupled wind-induced response of inter-story isolated eccentric tall buildings with friction-pendulum bearings