Poor Information Analysis of Rolling Bearing Friction Torque Characteristic Parameter Based on Phase Space

2011 ◽  
Vol 382 ◽  
pp. 167-171
Author(s):  
Lei Lei Gao ◽  
Xin Tao Xia
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Characteristic Parameter ◽  
Rolling Bearing ◽  
Friction Torque ◽  
Point Estimation ◽  
Experimental Result ◽  
Bayesian Probability ◽  
Characteristic Parameters ◽  
Bearing Friction

The friction torque of rolling bearings belongs to an information poor system with unknown probability distributions and trends. This counteracts dynamical assessment for the characteristics of the rolling bearing friction torque as a time series. For this reason, the chaos theory is employed to recover the original dynamic characteristics of a friction torque time series by means of the phase space reconstruction theory. The dynamical Bayesian probability density function of the characteristic parameters of the friction torque is constructed by the information poor theory based on the phase space. The method for point estimation, interval estimation, and trend estimation of the characteristic parameters is proposed in this paper. The investigation shows that the error between the calculated result and the experimental result is very small.

Chaotic Characteristic and Nonlinear Dynamic Performance of Rolling Bearing Friction Torque

2010 ◽  
Vol 26-28 ◽  
pp. 88-92 ◽  
Author(s):  
Xin Tao Xia ◽  
Tao Mei Lv ◽  
Fan Nian Meng
Keyword(s):  
Time Series ◽  
Nonlinear Dynamic ◽  
Dynamic Performance ◽  
Rolling Bearing ◽  
Friction Torque ◽  
Box Dimension ◽  
Rolling Bearings ◽  
Chaotic Characteristic ◽  
Chaotic Theory ◽  
Bearing Friction

Based on the chaotic theory, the methods of the Lyapunov exponent and the box dimension were applied to evaluate the chaotic characteristic and the nonlinear dynamic performance of the rolling bearing friction torque. The time series were obtained via the experimental investigation on the friction torque of the rolling bearings under the condition of different rotational speeds. It is found that the rolling bearing friction torque is of a chaotic system because the maximum of Lyapunov exponents of its time series is greater than zero according to the chaotic theory. And the result shows that the mean of the box dimension of the friction torque increases with the rotational speed of the rolling bearing, revealing the new dynamic performance of the rolling bearing friction torque as a time series.

Chaos Prediction of Rolling Bearing Friction Torque

2010 ◽  
Vol 26-28 ◽  
pp. 190-193 ◽  
Author(s):  
Xin Tao Xia ◽  
Tao Mei Lv
Keyword(s):  
Time Series ◽  
Experimental Investigation ◽  
Chaos Theory ◽  
Rolling Bearing ◽  
Friction Torque ◽  
Local Region ◽  
Space Applications ◽  
Region Method ◽  
Weight One ◽  
Bearing Friction

Based on the chaos theory, the adding-weight one-rank local-region method was applied to predict the time series of the rolling bearing friction torque. The experimental investigation on the rolling bearing for space applications shows that the method is able to predict effectively the rolling bearing friction torque, only with very small predicted error.

Dynamic Prediction of Rolling Bearing Friction Torque Using Lyapunov Exponent Method

2010 ◽  
Vol 44-47 ◽  
pp. 1120-1124 ◽  
Author(s):  
Xin Tao Xia ◽  
Tao Mei Lv
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Rolling Bearing ◽  
Friction Torque ◽  
Small Data ◽  
Data Sets ◽  
Dynamic Prediction ◽  
Information Method ◽  
Small Data Sets ◽  
Bearing Friction

Based on the chaos theory, the Lyapunov exponent method is employed to predict dynamically the time series of the rolling bearing friction torque. First, the embedding dimension and the delay time for the phase space reconstruction are estimated with the Cao method and the mutual information method, respectively. Second, the maximum of the Lyapunov exponents is calculated by small data sets. Lastly, the nearest neighboring point is sought via the Euclidean distance. The experimental investigation shows that the method proposed in this paper is able to forecast effectively the rolling bearing friction torque as a time series, only with very small predicted error.

scholarly journals Fault Dynamic Modeling and Characteristic Parameter Simulation of Rolling Bearing with Inner Ring Local Defects

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Zhang Fengling ◽  
Zhang Yuwei ◽  
Guan Jiaoyue ◽  
Tian Jing ◽  
Wang Yingjie
Keyword(s):  
Dynamic Model ◽  
Engineering Application ◽  
Characteristic Parameter ◽  
Rolling Bearing ◽  
Mean Value ◽  
Radial Clearance ◽  
Characteristic Parameters ◽  
Bearing Fault ◽  
Bearing Condition Monitoring ◽  
Local Defects

To further study the fault mechanism and fault features of rolling bearings, a two-DOF rolling bearing fault dynamic model with inner ring local defects considering the bearing radial clearance and time-varying displacement excitation is established based on Hertz contact theory. By comparing the simulated fault signal with bearing fault test data in the time domain and frequency domain, the accuracy of the established fault dynamic model is verified. Finally, the change rules of the characteristic parameters of the bearing inner ring fault signal, including effective value, absolute mean value, square root amplitude, peak value, kurtosis factor, pulse factor, peak factor, and shape factor, are simulated by the fault dynamic model. The results highlight that the proposed fault dynamic model is in good agreement with the experimental results. The model can simulate the fault signal characteristic parameters with the change of defect width, external load, and rotating speed effectively. The study in this paper is of engineering application value for bearing condition monitoring and fault diagnosis.

Gray Chaos Evaluation Model for Prediction of Rolling Bearing Friction Torque

2010 ◽  
Vol 38 (3) ◽  
pp. 102623 ◽  
Author(s):  
M. R. Mitchell ◽  
R. E. Link ◽  
Xia Xintao ◽  
Lv Taomei ◽  
Meng Fannian
Keyword(s):  
Evaluation Model ◽  
Rolling Bearing ◽  
Friction Torque ◽  
Bearing Friction

Dynamic Prediction Model for Rolling Bearing Friction Torque Using Grey Bootstrap Fusion Method and Chaos Theory

2012 ◽  
Vol 443-444 ◽  
pp. 87-96 ◽  
Author(s):  
Xin Tao Xia ◽  
Tao Mei Lv
Keyword(s):  
Probability Distributions ◽  
Rolling Bearing ◽  
Friction Torque ◽  
Local Region ◽  
Fusion Method ◽  
Dynamic Prediction ◽  
Region Method ◽  
True Value ◽  
Weight One ◽  
Bearing Friction

Synthesizing the grey bootstrap fusion method and the five chaos forecasting methods (viz., the adding-weight zero-rank local-region method, the one-rank local-region method, the adding-weight one-rank local-region method, the improved adding-weight one-rank local-region method, and the maximum Lyapunov exponent method), a dynamic prediction model is proposed to calculate the predicted true value and the predicted interval of a chaotic time series under the condition of unknown probability distributions and trends. At the same time, the five forecasting values are acquired with the help of the five chaos forecasting methods, respectively, and the five forecasting values are fused to deduce the predicted true value and the predicted interval by means of the grey bootstrap fusion method. As time goes on, a series of the predicted true value and the predicted interval is obtained dynamically. Experimental investigation of the rolling bearing friction torque shows that using the grey bootstrap fusion method, the predicted true value and the measured values have an identical trend only with a small error, the predicted interval is acquired along with a high reliability, and the dynamic prediction of the rolling bearing friction torque as a chaotic time series is made without any prior knowledge of probability distributions and trends.

Information Entropy of Rolling Bearing Friction Torque as Data Series

2010 ◽  
Vol 44-47 ◽  
pp. 1115-1119 ◽  
Author(s):  
Xin Tao Xia ◽  
Long Chen ◽  
Fan Nian Meng
Keyword(s):  
Experimental Investigation ◽  
Information Entropy ◽  
Rotational Speed ◽  
Dynamic Performance ◽  
Rolling Bearing ◽  
Friction Torque ◽  
Data Series ◽  
Entropy Theory ◽  
Rolling Bearings ◽  
Bearing Friction

The information entropy theory is applied to evaluate the uncertainty of the rolling bearing friction torque. The data series are obtained via the experimental investigation on the friction torque of the rolling bearings under the condition of different rotational speeds. And the result shows that the information entropy of the friction torque increases with the rotational speed of the rolling bearing, revealing the new dynamic performance of the rolling bearing friction torque as a data series.

scholarly journals Nonlinear analysis of gravitational wave signals based on recurrence quantification analysis

2018 ◽  
Vol 210 ◽  
pp. 05011
Author(s):  
Zhenyan Fan ◽  
Qianqian Chen ◽  
Guiqi Sun ◽  
Nikos Mastorakis ◽  
Xiaodong Zhuang
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Gravitational Wave ◽  
Recurrence Plot ◽  
Recurrence Quantification Analysis ◽  
Recurrence Plots ◽  
Characteristic Parameters ◽  
Recurrence Quantification ◽  
Movement Characteristic ◽  
Quantification Analysis

Recurrence plot and recurrence quantification analysis are used to analyze different features of gravitational wave signals. Firstly, the appropriate delay time and embedding dimension are respectively estimated by methods of the C_C method. One dimension time series of gravitational wave is extended to high dimension phase space by employing phase space reconstruction for studying the movement characteristic of neighboring points in time series. Then the recurrence plots of different gravitational wave signals are implemented intuitively and qualitatively analyzing different features of gravitational wave signals. Different nonlinear characteristic parameters are calculated by recurrence quantification analysis (RQA) methods, such as recurrence rate, recurrence entropy, determinism rate and stratification, based on which the features of different gravitational wave signals can be well analyzed quantitatively.

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