A New Method for the Identification of Coulomb and Viscous Friction

In this paper, a new method for simultaneously estimating Coulomb and viscous friction parameters from the free vibration of a damped oscillator is put forward. In the method, the nonlinear vibration equation with Coulomb and viscous friction is transformed into a linear procedure with equivalent viscous damping which is a function of velocity. The proposed method works well with both the displacement and velocity response data, while the case of zero velocity is not considered. From the displacement decaying curve, the equivalent viscous damping ratios are obtained by means of the local exponential fitting method, and different velocities corresponding to the equivalent viscous damping ratios are also obtained from the velocity decaying curve. Then, according to the relationship between the equivalent viscous damping ratio and the velocity, the Coulomb friction and the viscous damping are achieved using the least square method. The validity and accuracy of the proposed method are demonstrated through good simulation results.

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Identifying Coulomb and Viscous Friction in Forced Oscillators by Using a Harmonic Energy Balance

Design Engineering ◽

10.1115/imece2002-32401 ◽

2002 ◽

Author(s):

Jin-Wei Liang ◽

Brian F. Feeny

Keyword(s):

Dry Friction ◽

Mechanical Vibration ◽

Viscous Friction ◽

Viscous Damping ◽

Equivalent Viscous Damping ◽

Experimental Systems ◽

Estimation Equations ◽

Forced Oscillators ◽

Friction Parameters ◽

Relationship Of

This study makes use of energy dissipation to identify damping from mechanical vibration systems. Both the viscous damping and dry friction are assumed to coexist in vibration systems. By balancing the energy loss as registered in the force-displacement relationship of the real system against that of a theoretical model, consisting of viscous damping and dry friction components, the identification algorithms are developed and the equivalent viscous-damping and dry-friction parameters are estimated. We apply the estimation equations to both numerical and experimental systems to show the effectiveness and reliability of the new identification method.

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The Parameter Estimation of Double Exponential Pulse Based on a Least Infinity Norm Fitting Method

Journal of Physics Conference Series ◽

10.1088/1742-6596/2083/4/042002 ◽

2021 ◽

Vol 2083 (4) ◽

pp. 042002

Author(s):

Yuewu Shi ◽

Wei Wang ◽

Zhizhen Zhu ◽

Xin Nie

Keyword(s):

Estimation Error ◽

Estimation Method ◽

Maximum Amplitude ◽

Least Square Method ◽

Least Square ◽

Physical Parameters ◽

Infinity Norm ◽

Fitting Method ◽

Double Exponential ◽

Exponential Pulse

Abstract This paper presents an estimation method of double exponential pulse (DEP) between the physical parameters rise time (t r), full width at half maximum amplitude (t FWHM) and the mathematical parameters α, β. A newly fitting method based on the least infinity norm criterion is proposed to deal with the estimation problem of DEP. The calculation process and equation of parameters of this method is proposed based on an m-th-order polynomial fitting model. This estimation method is compared with the least square method by the same data and fitting function. The results show that the maximum estimation error of parameters of double exponential pulse obtained by the least infinity norm method is 1.5 %.

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Study on the Aging Time Variation Law of Mechanical Properties of the Laminated Rubber Bearing in Coastal Bridges considering Frictional Slip

Shock and Vibration ◽

10.1155/2021/3937362 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Yue Li ◽

Chongming Gao ◽

Chong Li ◽

Qian Li

Keyword(s):

Mechanical Properties ◽

Aging Time ◽

Damping Ratio ◽

Viscous Damping ◽

Equivalent Viscous Damping ◽

Coastal Bridges ◽

Shape Coefficient ◽

Rubber Bearings ◽

Frictional Slip ◽

Equivalent Viscous Damping Ratio

As an important support member in the structural system of coastal bridges, the frictional slip and the rubber aging of laminated rubber bearings will affect the service safety of the overall structure in earthquakes. In order to investigate the mechanical properties aging law of the rubber bearings considering frictional slip in the coastal bridges, a frictional slip experiment was carried out on the laminated rubber bearings. Moreover, the influence of rubber aging on the mechanical properties of the bearings with various shape coefficients was analyzed by the finite element method during the 100 years of service life of bridges. The results indicate that (1) the horizontal and vertical stiffness of the bearing increase linearly with the aging time of the rubber. The amplification of the bearing stiffness also grows with the shape coefficient of the bearing. (2) The frictional slip initiation displacement of the bearing grows with the rubber aging time. Furthermore, the larger the shape coefficient of the bearing is, the more the frictional slip initiation displacement of the bearing increases. (3) With the increase of the aging time, the equivalent viscous damping ratio of the bearing continues to increase and more energy is consumed by frictional slip. For the bearing with the shape coefficient of 16.38, the equivalent viscous damping ratio at 100 years of rubber aging time is 1.17 times higher than that of the initial state of the bearing, and 33.21% more energy is consumed through frictional slip. Given that the marine environment accelerates rubber aging and changes the mechanical properties, the effects of the frictional slip and rubber aging properties of the laminated rubber bearings on the seismic dynamic response of bridges should be considered in the seismic design of coastal bridges.

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Calculation and realization of new method grey residual error correction model

PLoS ONE ◽

10.1371/journal.pone.0254154 ◽

2021 ◽

Vol 16 (7) ◽

pp. e0254154

Author(s):

Lifang Xiao ◽

Xiangyang Chen ◽

Hao Wang

Keyword(s):

Prediction Model ◽

Least Square Method ◽

Residual Error ◽

Least Square ◽

Grey Model ◽

Grey Prediction ◽

Grey Prediction Model ◽

True Value ◽

Prediction Function ◽

Fitting Method

Aiming at the problem of prediction accuracy of stochastic volatility series, this paper proposes a method to optimize the grey model(GM(1,1)) from the perspective of residual error. In this study, a new fitting method is firstly used, which combines the wavelet function basis and the least square method to fit the residual data of the true value and the predicted value of the grey model(GM(1,1)). The residual prediction function is constructed by using the fitting method. Then, the prediction function of the grey model(GM(1,1)) is modified by the residual prediction function. Finally, an example of the wavelet residual-corrected grey prediction model (WGM) is obtained. The test results show that the fitting accuracy of the wavelet residual-corrected grey prediction model has irreplaceable advantages.

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Study on Ship Form Technical and Economic Evaluation DS Based on Interactive MCDM

Volume 2: Ocean Engineering and Polar and Arctic Sciences and Technology ◽

10.1115/omae2006-92634 ◽

2006 ◽

Cited By ~ 2

Author(s):

Sang Song ◽

Li-Hua Jun

Keyword(s):

Decision Making ◽

Analytical Hierarchy Process ◽

Accurate Result ◽

Multiple Criteria Decision Making ◽

Least Square Method ◽

Least Square ◽

New Method ◽

Decision Systems ◽

Complex Decision ◽

Hierarchy Process

A new method of interactive Multiple Criteria Decision Making (MCDM) is presented. In order to settle the problem that in the cases for the ship designers sometimes it is difficult to make a decision when facing so complex ship form schemes. The conventional AHP (Analytical Hierarchy Process) is adopted, but it mostly depends on the designer’s subjective and leads to the systematic error. The new method can obtain the accurate result with the rigid least square method as a tool, making full use of the AHP and the objective information entropy, which reflects the inherent attribute. When applied in the practice, it is proved to be effective, practical and dependable for future ships’ complex Decision Systems (DS).

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Reliability and Usefulness of the Fitting of a Modified Gamma Function to Time-Activity Curves by Means of a Non-Linear Iterative Least-Square Method

Nuklearmedizin ◽

10.1055/s-0037-1620740 ◽

1981 ◽

Vol 20 (04) ◽

pp. 195-197

Author(s):

J. M. Fránquiz

Keyword(s):

Gamma Function ◽

Least Square Method ◽

Least Square ◽

Base Line ◽

Time Activity ◽

Appearance Time ◽

Least Square Fitting ◽

Fitting Method ◽

Non Linear ◽

Least Square Fitting Method

A non-linear iterative least-square fitting method is presented for calculating the parameters of a modified gamma function. The method permits the correction of the appearance time (AT) and the curve parameters in those situations in which AT cannot be estimated with accuracy. The reliability and accuracy of the method is studied in experimental and simulated curves by means of a computer, comparing the results with those obtained by the method of Starmer and Clark for different initial selections of AT and noise at the base line. The usefulness of the method is shown in situations where the curves are distorted in their initial part.

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Determination of the Sediment Carrying Capacity Based on Perturbed Theory

The Scientific World JOURNAL ◽

10.1155/2014/240858 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Zhi-hui Ni ◽

Qiang Zeng ◽

Wu Li-chun

Keyword(s):

Carrying Capacity ◽

Influencing Factor ◽

Least Square Method ◽

Least Square ◽

New Method ◽

Linear Regression Method ◽

Average Flow Velocity ◽

New Formula ◽

Sediment Carrying Capacity

According to the previous studies of sediment carrying capacity, a new method of sediment carrying capacity on perturbed theory was proposed. By taking into account the average water depth, average flow velocity, settling velocity, and other influencing factors and introducing the median grain size as one main influencing factor in deriving the new formula, we established a new sediment carrying capacity formula. The coefficients were determined by the principle of dimensional analysis, multiple linear regression method, and the least square method. After that, the new formula was verified through measuring data of natural rivers and flume tests and comparing the verified results calculated by Cao Formula, Zhang Formula, Li Formula, Engelung-Hansen Formula, Ackers-White Formula, and Yang Formula. According to the compared results, it can be seen that the new method is of high accuracy. It could be a useful reference for the determination of sediment carrying capacity.

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A New Method for Automatically Measurement of Vickers Hardness Using Thick Line Hough Transform and Least Square Method

2009 2nd International Congress on Image and Signal Processing ◽

10.1109/cisp.2009.5305653 ◽

2009 ◽

Cited By ~ 8

Author(s):

Yu Ji ◽

Aiwei Xu

Keyword(s):

Vickers Hardness ◽

Hough Transform ◽

Least Square Method ◽

Least Square ◽

New Method ◽

Thick Line

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A New Method to Identify the Preisach Distribution Function of Hysteresis

Materials Science Forum ◽

10.4028/www.scientific.net/msf.475-479.2107 ◽

2005 ◽

Vol 475-479 ◽

pp. 2107-2110 ◽

Cited By ~ 3

Author(s):

Fan Li ◽

Jian Qin Mao ◽

Hai Shan Ding ◽

Wen Bo Zhang ◽

Hui Bin Xu ◽

...

Keyword(s):

Distribution Function ◽

Least Squares ◽

Fuzzy Inference System ◽

Fuzzy Inference ◽

Least Squares Method ◽

Input Sequence ◽

Least Square Method ◽

Least Square ◽

New Method ◽

Inference System

In this paper, a new method which combines the least square method with Tree-Structured fuzzy inference system is presented to approximate the Preisach distribution function. Firstly, by devising the input sequence and measure the output, discrete Preisach measure can be identified by the use of the least squares method. Then, the Preisach function can be obtained with Tree-Structured fuzzy inference system without any special smoothing means. So, this new method is not sensitive to noise, and is a universal approximator of the Preisach function. It collect the merit and overcome the deficiency of the existing methods.

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