Nonlinear Hysteresis Modeling of Piezoelectric Actuators Using a Generalized Bouc–Wen Model

Hysteresis behaviors exist in piezoelectric ceramics actuators (PCAs), which degrade the positioning accuracy badly. The classical Bouc–Wen (CB–W) model is mainly used for describing rate-independent hysteresis behaviors. However, it cannot characterize the rate-dependent hysteresis precisely. In this paper, a generalized Bouc–Wen (GB–W) model with relaxation functions is developed for both rate-independent and rate-dependent hysteresis behaviors of piezoelectric actuators. Meanwhile, the nonlinear least squares method through MATLAB/Simulink is adopted to identify the parameters of hysteresis models. To demonstrate the validity of the developed model, a number of experiments based on a 1-DOF compliant mechanism were conducted to characterize hysteresis behaviors. Comparisons of experiments and simulations show that the developed model can describe rate-dependent and rate-independent hysteresis more accurately than the classical Bouc–Wen model. The results demonstrate that the developed model is effective and useful.

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Design and Modeling of a Novel Double-Piston Magnetorheological Damper

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.574.588 ◽

2014 ◽

Vol 574 ◽

pp. 588-595

Author(s):

Qiang Wang ◽

Zhao Bo Chen ◽

Mehdi Ahmadian ◽

Wen Tao Liu

Keyword(s):

Vibration Suppression ◽

Least Squares Method ◽

Nonlinear Least Squares ◽

Magnetorheological Damper ◽

Truss Structures ◽

Space Truss ◽

Nonlinear Hysteresis ◽

Working Principle ◽

Series Of Experiments ◽

Nonlinear Least Squares Method

In order to develop a compact and lightweight controllable damper for space truss structures vibration suppression, a novel double-piston magnetorheological (MR) damper is proposed. Working principle of this damper has been analyzed. One prototype damper have been designed and fabricated according to the analysis results. A series of experiments have been performed to get this prototype damper's dynamical properties. Hyperbolic tangent model have been used to describe damper's nonlinear hysteresis. After model optimization using the nonlinear least squares method, the relationship between damper force and drive currents have been acquired under different excitation conditions. Comparison between the reconstructed results and testing data indicates that the optimized model shows enough accuracy to not only present the experimental data, but also forecast the hysteretic properties of this damper.

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Hysteresis modeling of piezoelectric actuators with the frequency-dependent behavior using a hybrid model

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406219897089 ◽

2019 ◽

Vol 234 (9) ◽

pp. 1848-1858

Author(s):

Cheng Qian ◽

Qing Ouyang ◽

Yulai Song ◽

Wei Zhao

Keyword(s):

Support Vector Machine ◽

Least Squares ◽

Hybrid Model ◽

Piezoelectric Actuators ◽

Support Vector ◽

Rate Dependent ◽

Nonlinear Hysteresis ◽

Dependent Behavior ◽

Hysteresis Modeling ◽

Dependent Model

In order to overcome the problem of positioning inaccuracy caused by nonlinear hysteresis of piezoelectric actuators, a hybrid model based on least-squares support vector machine and Bouc–Wen model is proposed to model the rate-dependent hysteresis of piezoelectric actuators. A rate-independent Bouc–Wen model and its parameters identification method is established as the basis of least-squares Bouc–Wen model. Least-squares support vector machine, which is optimized by particle swarm optimization, is introduced to improve the Bouc–Wen model into a rate-dependent model by adjusting parameters of Bouc–Wen dynamically. Experiment is carried out to validate both Bouc–Wen model and the proposed least-squares Bouc–Wen model. The results show that the proposed least-squares Bouc–Wen method is a valid and a more precise method compared to the rate-independent Bouc–Wen model.

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A Modified Duhem Model for Rate-Dependent Hysteresis Behaviors

Micromachines ◽

10.3390/mi10100680 ◽

2019 ◽

Vol 10 (10) ◽

pp. 680 ◽

Cited By ~ 3

Author(s):

Gan ◽

Mei ◽

Chen ◽

Zhou ◽

Keyword(s):

Experimental Data ◽

High Frequency ◽

Piezoelectric Ceramic ◽

Least Squares Method ◽

Nonlinear Least Squares ◽

High Amplitude ◽

Trigonometric Functions ◽

Hysteresis Model ◽

Rate Dependent ◽

Nonlinear Least Squares Method

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.

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Error estimation in fitting X-ray spectrum by nonlinear least-squares method

Nuclear Instruments and Methods in Physics Research Section B Beam Interactions with Materials and Atoms ◽

10.1016/0168-583x(89)90685-x ◽

1989 ◽

Vol 44 (1) ◽

pp. 35-39 ◽

Cited By ~ 5

Author(s):

Y. Watanabe ◽

T. Kubozoe ◽

T. Mukoyama

Keyword(s):

Least Squares ◽

Error Estimation ◽

Least Squares Method ◽

Nonlinear Least Squares ◽

X Ray ◽

Nonlinear Least Squares Method

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Core Power Modelling of High-Temperature Engineering Test Reactor (HTTR) Using Nonlinear Least Squares Method for Parameter Estimation

2021 International Conference on Artificial Intelligence and Mechatronics Systems (AIMS) ◽

10.1109/aims52415.2021.9466041 ◽

2021 ◽

Author(s):

Aulia Istiqomah ◽

Aries Subiantoro

Keyword(s):

Parameter Estimation ◽

High Temperature ◽

Least Squares ◽

Least Squares Method ◽

Nonlinear Least Squares ◽

Test Reactor ◽

Nonlinear Least Squares Method

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MIM and nonlinear least‐squares inversions of AEM data in Barataria basin, Louisiana

Geophysics ◽

10.1190/1.1598104 ◽

2003 ◽

Vol 68 (4) ◽

pp. 1126-1131 ◽

Cited By ~ 2

Author(s):

Melissa Whitten Bryan ◽

Kenneth W. Holladay ◽

Clyde J. Bergeron ◽

Juliette W. Ioup ◽

George E. Ioup

Keyword(s):

Least Squares ◽

Water Depth ◽

Least Squares Method ◽

Nonlinear Least Squares ◽

Image Method ◽

Water Conductivity ◽

Near Surface ◽

Barataria Basin ◽

Airborne Electromagnetic Survey ◽

Nonlinear Least Squares Method

An airborne electromagnetic survey was performed over the marsh and estuarine waters of the Barataria basin of Louisiana. Two inversion methods were applied to the measured data to calculate layer thicknesses and conductivities: the modified image method (MIM) and a nonlinear least‐squares method of inversion using two two‐layer forward models and one three‐layer forward model, with results generally in good agreement. Uniform horizontal water layers in the near‐shore Gulf of Mexico with the fresher (less saline, less conductive) water above the saltier (more saline, more conductive) water can be seen clearly. More complex near‐surface layering showing decreasing salinity/conductivity with depth can be seen in the marshes and inland areas. The first‐layer water depth is calculated to be 1–2 m, with the second‐layer water depth around 4 m. The first‐layer marsh and beach depths are computed to be 0–3 m, and the second‐layer marsh and beach depths vary from 2 to 9 m. The first‐layer water conductivity is calculated to be 2–3 S/m, with the second‐layer water conductivity around 3 to 4 S/m and the third‐layer water conductivity 4–5 S/m. The first‐layer marsh conductivity is computed to be mainly 1–2 S/m, and the second‐ and third‐layer marsh conductivities vary from 0.5 to 1.5 S/m, with the conductivities decreasing as depth increases except on the beach, where layer three has a much higher conductivity, ranging up to 3 S/m.

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The Strength Evaluation and Reliability Analysis of Periodic Symmetric Struts Support

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.462-463.1164 ◽

2011 ◽

Vol 462-463 ◽

pp. 1164-1169

Author(s):

Jing Xiang Yang ◽

Ya Xin Zhang ◽

Mamtimin Gheni ◽

Ping Ping Chang ◽

Kai Yin Chen ◽

...

Keyword(s):

Distribution Function ◽

Probability Distribution ◽

Stress Distribution ◽

Least Squares ◽

Reliability Analysis ◽

Least Squares Method ◽

Nonlinear Least Squares ◽

Distribution Model ◽

Different Types ◽

Nonlinear Least Squares Method

In this paper, strength evaluations and reliability analysis are conducted for different types of PSSS(Periodically Symmetric Struts Supports) based on the FEA(Finite Element Analysis). The numerical models are established at first, and the PMA(Prestressed Modal Analysis) is conducted. The nodal stress value of all of the gauss points in elements are extracted out and the stress distributions are evaluated for each type of PSSS. Then using nonlinear least squares method, curve fitting is carried out, and the stress probability distribution function is obtained. The results show that although using different number of struts, the stress distribution function obeys the exponential distribution. By using nonlinear least squares method again for the distribution parameters a and b of different exponential functions, the relationship between number of struts and distribution function is obtained, and the mathematical models of the stress probability distribution functions for different supports are established. Finally, the new stress distribution model is introduced by considering the DSSI(Damaged Stress-Strength Interference), and the reliability evaluation for different types of periodically symmetric struts supports is carried out.

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A NONLINEAR LEAST‐SQUARES METHOD FOR SEISMIC REFRACTION MAPPING—PART I: ALGORITHM AND PROCEDURE

Geophysics ◽

10.1190/1.1440257 ◽

1972 ◽

Vol 37 (2) ◽

pp. 260-272 ◽

Cited By ~ 6

Author(s):

Leonidas C. Ocola

Keyword(s):

Least Squares ◽

Least Squares Method ◽

Seismic Refraction ◽

Vertical Plane ◽

Nonlinear Least Squares ◽

Inversion Method ◽

Almost Everywhere ◽

Isotropic Media ◽

Time Term ◽

Nonlinear Least Squares Method

An iterative inversion method (Reframap) based on the kinematic properties of critically refracted waves is developed. The method is based on ray tracing and assumes homogeneous and isotropic media and ray paths confined to a vertical plane through each source‐detector pair. Unlike the earlier Profile or Time‐Term Methods, no restrictions are imposed on interface topography except that it be continuous almost everywhere (in the mathematical sense). As in the preexisting methods, more observations than unknowns are assumed. The algorithm and procedure, on which the Reframap Method is based, generate apparent dips for each source detector pair at the noncritical interfaces from the slope of a least‐squares line approximation to the interface functional in the neighborhood of each refraction point. In turn, the dip and path along the critical refractor is, at every iteration, pairwise approximated by a line through the critical refracting points. The incidence angles are computed recursively by Snell’s law. The solution of the overdetermined, nonlinear multiple refractor time‐distance system of simultaneous equations is sought by Marquardt’s algorithm for least‐squares estimation of critical refractor velocity and vertical thickness under each element.

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