Chaos Prediction of Rolling Bearing Friction Torque

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.

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.443-444.87 ◽

2012 ◽

Vol 443-444 ◽

pp. 87-96 ◽

Cited By ~ 1

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.

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.382.167 ◽

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.

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Chaotic Characteristic and Nonlinear Dynamic Performance of Rolling Bearing Friction Torque

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.26-28.88 ◽

2010 ◽

Vol 26-28 ◽

pp. 88-92 ◽

Cited By ~ 7

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.

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Information Entropy of Rolling Bearing Friction Torque as Data Series

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.44-47.1115 ◽

2010 ◽

Vol 44-47 ◽

pp. 1115-1119 ◽

Cited By ~ 1

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.

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Dynamic Prediction of Rolling Bearing Friction Torque Using Lyapunov Exponent Method

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.44-47.1120 ◽

2010 ◽

Vol 44-47 ◽

pp. 1120-1124 ◽

Cited By ~ 1

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.

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Uncertainty of Rolling Bearing Friction Torque as Data Series Using Grey Bootstrap Method

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.44-47.1125 ◽

2010 ◽

Vol 44-47 ◽

pp. 1125-1129

Author(s):

Xin Tao Xia ◽

Long Chen ◽

Fan Nian Meng

Keyword(s):

System Theory ◽

Experimental Investigation ◽

Bootstrap Method ◽

Dynamic Performance ◽

Rolling Bearing ◽

Friction Torque ◽

Data Series ◽

Rolling Bearings ◽

The Mean ◽

Bearing Friction

Based on the information poor system theory, the grey bootstrap method is employed to estimate the uncertainty of the rolling bearing friction torque. The data series are obtained via the experimental investigation of the friction torque of the rolling bearings under the condition of different rotational speeds. And the results show that the mean of the dynamic fluctuant range (MDFR) 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.

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Evaluation of Dynamic Uncertainty of Rolling Bearing Vibration Performance

Mathematical Problems in Engineering ◽

10.1155/2019/2896046 ◽

2019 ◽

Vol 2019 ◽

pp. 1-17 ◽

Cited By ~ 2

Author(s):

Liang Ye ◽

Xintao Xia ◽

Zhen Chang

Keyword(s):

Time Series ◽

Chaos Theory ◽

Maximum Entropy Method ◽

Bootstrap Method ◽

Rolling Bearing ◽

Entropy Method ◽

Performance Time ◽

Dynamic Uncertainty ◽

Bearing Vibration ◽

Vibration Performance

The variation trend, failure trajectory, probability distribution, and other information vary with time and working conditions for rolling bearing vibration performance, which makes the evaluation and prediction of the evolution process difficult for the performance reliability. In view of this, the chaos theory, grey bootstrap method, and maximum entropy method were effectively fused to propose a mathematical model for the dynamic uncertainty evaluation of rolling bearing vibration performance. After reconstructing the phase space of the vibration performance time series, four local prediction methods were applied to predict the vibration values of bearings to verify the effectiveness and validity of chaos theory. The estimated true value and estimated interval were calculated using the grey bootstrap method (GBM) and maximum entropy method. Finally, the validity of the proposed model was verified by comparing the probability that the original data fall into the estimated interval with the given confidence level. The experimental results show that the proposed method can effectively predict the variation trend and failure trajectory of the vibration performance time series so as to realize the dynamic monitoring of the evolution process for rolling bearing vibration performance online.

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Spatio-temporal characteristics of friction torque of rolling bearing for space applications

2011 Second International Conference on Mechanic Automation and Control Engineering ◽

10.1109/mace.2011.5988426 ◽

2011 ◽

Author(s):

Xintao Xia ◽

Lili Fu

Keyword(s):

Rolling Bearing ◽

Friction Torque ◽

Space Applications ◽

Temporal Characteristics ◽

Spatio Temporal

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Local Piecewise-Linearity Prediction Method of Chaotic Time Series

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.712-715.2415 ◽

2013 ◽

Vol 712-715 ◽

pp. 2415-2418

Author(s):

Juan Liu ◽

Xue Wei Bai ◽

Dao Cai Chi

Keyword(s):

Time Series ◽

Lyapunov Exponent ◽

Prediction Method ◽

Chaotic Time Series ◽

Local Region ◽

Liaoning Province ◽

Largest Lyapunov Exponent ◽

Region Method ◽

Local Prediction ◽

Piecewise Linearity

A Local Piecewise-Linearity Prediction method is presented, Based on the advantages and limitations of local prediction of chaotic time series. Taking time series of rainfall as example for prediction the rainfall of one city in Liaoning province, which includes the application of the largest Lyapunov exponent, Local-region method and Local Piecewise-Linearity method. The method proposed is proved practical in comparison with the observed data.

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