Improving autocorrelation regression for the Hurst parameter estimation of long-range dependent time series based on golden section search

Abstract:In this paper, we propose a novel framework for the diagnosis of incipient bearing faults and trend prediction of weak faults which result in gradual aggravation with the bearing vibration intensity as the characteristic parameter. For the weak fault diagnosis, the proposed framework adopts the improved minimum entropy deconvolution (MED) theory to identify the weak fault characteristics of mechanical equipment. From a large number of actual data analysis, once a bearing shows a weak fault, the bearing vibration intensity not only has random non-stationary, but also long-range dependent (LRD) characteristics. Therefore, the stochastic model with LRD−fractional Brown motion (FBM) is proposed to evaluate and predict the condition of slowly varying bearing faults which is a gradual process from weak fault occurrence to severity. For the FBM stochastic model, we mainly implement the derivation and the parameter identification of the FBM model. This is the first study to slowly fault prediction with stochastic model FBM. Experimental results show that the proposed methods can obtain the best performance in incipient fault diagnosis and bearing condition trend prediction.

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“…There are many methods to estimate the Hurst value in the time domain and frequency domain way [25].…”

Section: Calculate the Hurst Index Of Vibration Intensity By R/s Methodsmentioning

confidence: 99%

Prediction of Bearing Fault Using Fractional Brownian Motion and Minimum Entropy Deconvolution

Song

Liang

2016

Entropy

Self Cite

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“…Several methods can be used to calculate the self-similarly parameter H such as the absolute value method, the periodogram estimation method, the wavelet estimation method, rescaled range method etc. [42][43][44]. Since the best accuracy is achieved by the rescaled range method [36], we use this method for the estimation of the self-similar parameters in LRD random processes.…”

Section: Long-range Dependence and Self-similarity Of Fractional Gene...mentioning

confidence: 99%

Finite Iterative Forecasting Model Based on Fractional Generalized Pareto Motion

et al. 2022

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In this paper, an efficient prediction model based on the fractional generalized Pareto motion (fGPm) with Long-Range Dependent (LRD) and infinite variance characteristics is proposed. Firstly, we discuss the meaning of each parameter of the generalized Pareto distribution (GPD), and the LRD characteristics of the generalized Pareto motion are analyzed by taking into account the heavy-tailed characteristics of its distribution. Then, the mathematical relationship H = 1 / α between the self-similar parameter H and the tail parameter α is obtained. Also, the generalized Pareto increment distribution is obtained using statistical methods, which offers the subsequent derivation of the iterative forecasting model based on the increment form. Secondly, the tail parameter α is introduced to generalize the integral expression of the fractional Brownian motion, and the integral expression of fGPm is obtained. Then, by discretizing the integral expression of fGPm, the statistical characteristics of infinite variance is shown. In addition, in order to study the LRD prediction characteristic of fGPm, LRD and self-similarity analysis are performed on fGPm, and the LRD prediction conditions H > 1 / α is obtained. Compared to the fractional Brownian motion describing LRD by a self-similar parameter H, fGPm introduces the tail parameter α, which increases the flexibility of the LRD description. However, the two parameters are not independent, because of the LRD condition H > 1 / α. An iterative prediction model is obtained from the Langevin-type stochastic differential equation driven by fGPm. The prediction model inherits the LRD condition H > 1 / α of fGPm and the time series, simulated by the Monte Carlo method, shows the superiority of the prediction model to predict data with high jumps. Finally, this paper uses power load data in two different situations (weekdays and weekends), used to verify the validity and general applicability of the forecasting model, which is compared with the fractional Brown prediction model, highlighting the “high jump data prediction advantage” of the fGPm prediction model.

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“…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.…”

Section: Of 27mentioning

confidence: 99%

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

Liang

2018

Symmetry

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The ability to accurately track the degradation trajectories of rotating machinery components is arguably one of the challenging problems in prognostics and health management (PHM). In this paper, an intelligent prediction approach based on asymmetric penalty sparse decomposition (APSD) algorithm combined with wavelet neural network (WNN) and autoregressive moving average-recursive least squares algorithm (ARMA-RLS) is proposed for degradation prognostics of rotating machinery, taking the accelerated life test of rolling bearings as an example. Specifically, the health indicators time series (e.g., peak-to-peak value and Kurtosis) is firstly decomposed into low frequency component (LFC) and high frequency component (HFC) using the APSD algorithm; meanwhile, the resulting non-convex regularization problem can be efficiently solved using the majorization-minimization (MM) method. In particular, the HFC part corresponds to the stable change around the zero line of health indicators which most extensively occurs; in contrast, the LFC part is essentially related to the evolutionary trend of health indicators. Furthermore, the nonparametric-based method, i.e., WNN, and parametric-based method, i.e., ARMA-RLS, are respectively introduced to predict the LFC and HFC that focus on abrupt degradation regions (e.g., last 100 points). Lastly, the final predicted data could be correspondingly obtained by integrating the predicted LFC and predicted HFC. The proposed methodology is tested using degradation health indicator time series from four rolling bearings. The proposed approach performed favorably when compared to some state-of-the-art benchmarks such as WNN and largest Lyapunov (LLyap) methods.

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Improving autocorrelation regression for the Hurst parameter estimation of long-range dependent time series based on golden section search

Cited by 10 publications

References 84 publications

Prediction of Bearing Fault Using Fractional Brownian Motion and Minimum Entropy Deconvolution

Prediction of Bearing Fault Using Fractional Brownian Motion and Minimum Entropy Deconvolution

Finite Iterative Forecasting Model Based on Fractional Generalized Pareto Motion

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

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