Long Range Dependence Prognostics for Bearing Vibration Intensity Chaotic Time Series

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.

Incipient Fault Feature Extraction for Rotating Machinery Based on Improved AR-Minimum Entropy Deconvolution Combined with Variational Mode Decomposition Approach

“…The detailed algorithm of EVI is given in our previous work [37]. Figure 8b reveals that the evolution of kurtosis can be divided into three stages, i.e., normal operation, incipient fault and severe fault stage.…”

Incipient Fault Diagnosis of Rolling Bearings Based on Impulse-Step Impact Dictionary and Re-Weighted Minimizing Nonconvex Penalty Lq Regular Technique

“…Therefore, the incipient fault diagnosis (IFD) and health management of rolling bearings are becoming more and more crucial in engineering applications [1][2][3].…”

Intelligent Prognostics of Degradation Trajectories for Rotating Machinery Based on Asymmetric Penalty Sparse Decomposition Model

“…From the view of application, roughly, the existing prediction approaches can be divided into two categories: (a) parametric-based methods and (b) nonparametric-based methods. In the literature, parametric-based methods mainly include time-series methods such as autoregressive moving average (ARMA) [7,8], fractional autoregressive integrated moving average (FARIMA) [9,10], fractional Brownian motion (FBM) [11,12], hidden Markov model (HMM) [13,14] and grey theoretical model (GTM) [15,16], etc. Generally, the parametric-based methods overcome the hurdle of predictive availability during long-term prediction (according to needs) which assumes the model's parameters to be constants in the predicted region.…”

“…Figure 8 shows the peak-to-peak values of the whole lifetime of bearing 1. Accordingly, the health indicators, i.e., equivalent vibration intensity (EVI) [9,11], Kurtosis and EVI of bearing 2, bearing 3 and bearing 4 are illustrated in Figure 9a-c, respectively. It is seen that the amplitudes of bearings 1, 3 and 4 have gradual increasing trends, in addition, the whole test life of bearing 3 is the shortest due to harsh operating conditions, which indicates that the extremely failures are occurred before the experiment stops, thus, representing abrupt degradation processes, whereas the EVI amplitudes of bearings 2 show gradual increases; it might be concluded that the design/manufacturing quality and fatigue resistance strength are much higher than others under the same operating conditions.…”