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Entropy 2016, 18(1), 23; doi:10.3390/e18010023

Long Range Dependence Prognostics for Bearing Vibration Intensity Chaotic Time Series

1
College of Mechanical Engineering, Donghua University, Shanghai 201620, China
2
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0560, USA
*
Author to whom correspondence should be addressed.
Academic Editor: J. A. Tenreiro Machado
Received: 26 September 2015 / Revised: 23 November 2015 / Accepted: 23 November 2015 / Published: 8 January 2016
(This article belongs to the Section Complexity)
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Abstract

According to the chaotic features and typical fractional order characteristics of the bearing vibration intensity time series, a forecasting approach based on long range dependence (LRD) is proposed. In order to reveal the internal chaotic properties, vibration intensity time series are reconstructed based on chaos theory in phase-space, the delay time is computed with C-C method and the optimal embedding dimension and saturated correlation dimension are calculated via the Grassberger–Procaccia (G-P) method, respectively, so that the chaotic characteristics of vibration intensity time series can be jointly determined by the largest Lyapunov exponent and phase plane trajectory of vibration intensity time series, meanwhile, the largest Lyapunov exponent is calculated by the Wolf method and phase plane trajectory is illustrated using Duffing-Holmes Oscillator (DHO). The Hurst exponent and long range dependence prediction method are proposed to verify the typical fractional order features and improve the prediction accuracy of bearing vibration intensity time series, respectively. Experience shows that the vibration intensity time series have chaotic properties and the LRD prediction method is better than the other prediction methods (largest Lyapunov, auto regressive moving average (ARMA) and BP neural network (BPNN) model) in prediction accuracy and prediction performance, which provides a new approach for running tendency predictions for rotating machinery and provide some guidance value to the engineering practice. View Full-Text
Keywords: long range dependence; chaotic time series; bearing vibration intensity; Hurst exponent long range dependence; chaotic time series; bearing vibration intensity; Hurst exponent
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Li, Q.; Liang, S.Y.; Yang, J.; Li, B. Long Range Dependence Prognostics for Bearing Vibration Intensity Chaotic Time Series. Entropy 2016, 18, 23.

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