scholarly journals Early Warning Signals for Bearing Failure Using Detrended Fluctuation Analysis

2020 ◽  
Vol 10 (23) ◽  
pp. 8489
Author(s):  
Laith Shalalfeh ◽  
Ashraf AlShalalfeh
Keyword(s):  
Long Range ◽  
Early Warning ◽  
Detrended Fluctuation Analysis ◽  
Short Range ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Bearing Failure ◽  
Kendall’S Tau ◽  
Vibration Data ◽  
Detrended Fluctuation

Prognostic techniques play a critical role in predicting upcoming faults and failures in machinery or a system by monitoring any deviation in the operation. This paper presents a novel method to analyze multidimensional sensory data and use its characteristics in bearing health prognostics. Firstly, detrended fluctuation analysis (DFA) is exploited to evaluate the long-range correlations in ball bearing vibration data. The results reveal the existence of the crossover phenomenon in vibration data with two scaling exponents at the short-range and long-range scales. Among several data sets, applying the DFA method to vibration signals shows a consistent increase in the short-range scaling exponent toward bearing failure. Finally, Kendall’s tau is used as a ranking coefficient to quantify the trend in the scaling exponent. It was found that the Kendall’s tau coefficient of the vibration scaling exponent could provide an early warning signal (EWS) for bearing failure.

scholarly journals DETRENDED FLUCTUATION ANALYSIS OF AUTOREGRESSIVE PROCESSES

2007 ◽  
Vol 07 (03) ◽  
pp. L249-L255 ◽  
Author(s):  
VASILE V. MORARIU ◽  
LUIZA BUIMAGA-IARINCA ◽  
CĂLIN VAMOŞ ◽  
ŞTEFAN M. ŞOLTUZ
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Short Range ◽  
Interaction Constant ◽  
Fluctuation Analysis ◽  
Autoregressive Processes ◽  
Long Range Correlations ◽  
Correlation Exponent ◽  
The Relationship ◽  
Detrended Fluctuation

Autoregressive processes (AR) have typical short-range memory. Detrended Fluctuation Analysis (DFA) was basically designed to reveal long-range correlations in non stationary processes. However DFA can also be regarded as a suitable method to investigate both long-range and short-range correlations in non stationary and stationary systems. Applying DFA to AR processes can help understanding the non-uniform correlation structure of such processes. We systematically investigated a first order autoregressive model AR(1) by DFA and established the relationship between the interaction constant of AR(1) and the DFA correlation exponent. The higher the interaction constant the higher is the short-range correlation exponent. They are exponentially related. The investigation was extended to AR(2) processes. The presence of an interaction between distant terms with characteristic time constant in the series, in addition to a near by interaction will increase the correlation exponent and the range of correlation while the effect of a distant negative interaction will significantly decrease the range of interaction, only. This analysis demonstrate the possibility to identify an AR(1) model in an unknown DFA plot or to distinguish between AR(1) and AR(2) models.

scholarly journals IMPACT OF TANDEM REPEATS ON THE SCALING OF NUCLEOTIDE SEQUENCES

2006 ◽  
Vol 16 (10) ◽  
pp. 3103-3108
Author(s):  
RADHAKRISHNAN NAGARAJAN ◽  
MEENAKSHI UPRETI
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Tandem Repeats ◽  
Nucleotide Sequences ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Long Range Correlations ◽  
Reliable Estimation ◽  
Detrended Fluctuation

Techniques such as detrended fluctuation analysis (DFA) and its extensions have been widely used to determine the nature of scaling in nucleotide sequences. In this brief communication we show that tandem repeats which are ubiquitous in nucleotide sequences can prevent reliable estimation of possible long-range correlations. Therefore, it is important to investigate the presence of tandem repeats prior to scaling exponent estimation.

scholarly journals DETRENDED FLUCTUATION ANALYSIS OF THE TCP-RED ALGORITHM

2009 ◽  
Vol 19 (12) ◽  
pp. 4237-4245 ◽  
Author(s):  
XI CHEN ◽  
SIU-CHUNG WONG ◽  
CHI K. TSE ◽  
LJILJANA TRAJKOVIĆ
Keyword(s):  
Time Series ◽  
Long Range ◽  
Power Law ◽  
Detrended Fluctuation Analysis ◽  
Time Series Data ◽  
Analytical Models ◽  
Series Data ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Detrended Fluctuation

It has been observed that Internet gateways employing Transport Control Protocol (TCP) and the Random Early Detection (RED) control algorithm may exhibit instability and oscillatory behavior. Most control methods proposed in the past have been based on analytical models that rely on statistical measurements of network parameters. In this paper, we apply the detrended fluctuation analysis (DFA) method to analyze stability of the TCP-RED system. The DFA is used to analyze time-series data and generate power-law scaling exponents, which indicate the long-range correlations of the time series. We quantify the stability of the TCP-RED system by examining the variation of the DFA power-law scaling exponent when the system parameters are varied. We also study the long-range power-law correlations of TCP window periods.

scholarly journals Investigating Long-Range Dependence of Emerging Asian Stock Markets Using Multifractal Detrended Fluctuation Analysis

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1157
Author(s):  
Faheem Aslam ◽  
Saima Latif ◽  
Paulo Ferreira
Keyword(s):  
Time Series ◽  
Long Range ◽  
Stock Markets ◽  
Detrended Fluctuation Analysis ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Financial Time ◽  
Detrended Fluctuation

The use of multifractal approaches has been growing because of the capacity of these tools to analyze complex properties and possible nonlinear structures such as those in financial time series. This paper analyzes the presence of long-range dependence and multifractal parameters in the stock indices of nine MSCI emerging Asian economies. Multifractal Detrended Fluctuation Analysis (MFDFA) is used, with prior application of the Seasonal and Trend Decomposition using the Loess (STL) method for more reliable results, as STL separates different components of the time series and removes seasonal oscillations. We find a varying degree of multifractality in all the markets considered, implying that they exhibit long-range correlations, which could be related to verification of the fractal market hypothesis. The evidence of multifractality reveals symmetry in the variation trends of the multifractal spectrum parameters of financial time series, which could be useful to develop portfolio management. Based on the degree of multifractality, the Chinese and South Korean markets exhibit the least long-range dependence, followed by Pakistan, Indonesia, and Thailand. On the contrary, the Indian and Malaysian stock markets are found to have the highest level of dependence. This evidence could be related to possible market inefficiencies, implying the possibility of institutional investors using active trading strategies in order to make their portfolios more profitable.

scholarly journals Comparative Multifractal Detrended Fluctuation Analysis of Heavy Ion Interactions at a Few GeV to a Few Hundred GeV

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Gopa Bhoumik ◽  
Argha Deb ◽  
Swarnapratim Bhattacharyya ◽  
Dipak Ghosh
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Heavy Ion ◽  
Projectile Energy ◽  
Fluctuation Analysis ◽  
Data Set ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Range Correlation ◽  
Multifractal Property ◽  
Detrended Fluctuation

We have studied the multifractality of pion emission process in16O-AgBr interactions at 2.1 AGeV  and  60 AGeV,12C-AgBr  and  24Mg-AgBr interactions at 4.5 AGeV, and32S-AgBr interactions at 200 AGeV using Multifractal Detrended Fluctuation Analysis (MFDFA) method which is capable of extracting the actual multifractal property filtering out the average trend of fluctuation. The analysis reveals that the pseudorapidity distribution of the shower particles is multifractal in nature for all the interactions; that is, pion production mechanism has inbuilt multiscale self-similarity property. We have employed MFDFA method for randomly generated events for32S-AgBr interactions at 200 AGeV. Comparison of expt. results with those obtained from randomly generated data set reveals that the source of multifractality in our data is the presence of long range correlation. Comparing the results obtained from different interactions, it may be concluded that strength of multifractality decreases with projectile mass for the same projectile energy and for a particular projectile it increases with energy. The values of ordinary Hurst exponent suggest that there is long range correlation present in our data for all the interactions.

scholarly journals Scaling behaviour of the global tropopause

2009 ◽  
Vol 9 (2) ◽  
pp. 677-683 ◽  
Author(s):  
C. Varotsos ◽  
M. Efstathiou ◽  
C. Tzanis
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Sea Surface ◽  
Fluctuation Analysis ◽  
Tropopause Height ◽  
Time Intervals ◽  
Long Range Correlations ◽  
Scaling Behaviour ◽  
Detrended Fluctuation ◽  
Global Mean

Abstract. Detrended fluctuation analysis is applied to the time series of the global tropopause height derived from the 1980–2004 daily radiosonde data, in order to detect long-range correlations in its time evolution. Global tropopause height fluctuations in small time-intervals are found to be positively correlated to those in larger time intervals in a power-law fashion. The exponent of this dependence is larger in the tropics than in the middle and high latitudes in both hemispheres. Greater persistence is observed in the tropopause of the Northern than in the Southern Hemisphere. A plausible physical explanation of the fact that long-range correlations in tropopause variability decreases with increasing latitude is that the column ozone fluctuations (that are closely related with the tropopause ones) exhibit long range correlations, which are larger in tropics than in the middle and high latitudes at long time scales. This finding for the tropopause height variability should reduce the existing uncertainties in assessing the climatic characteristics. More specifically the reliably modelled values of a climatic variable (i.e. past and future simulations) must exhibit the same scaling behaviour with that possibly existing in the real observations of the variable under consideration. An effort has been made to this end by applying the detrended fluctuation analysis to the global mean monthly land and sea surface temperature anomalies during the period January 1850–August 2008. The result obtained supports the findings presented above, notably: the correlations between the fluctuations in the global mean monthly land and sea surface temperature display scaling behaviour which must characterizes any projection.

DETRENDED FLUCTUATION ANALYSIS OF CHROMATIN TEXTURE FOR DIAGNOSIS IN BREAST CYTOLOGY

Fractals ◽  
2002 ◽  
Vol 10 (01) ◽  
pp. 19-25 ◽  
Author(s):  
ANDREW J. EINSTEIN ◽  
HAI-SHAN WU ◽  
JUAN GIL
Keyword(s):  
Logistic Regression ◽  
Epithelial Cell ◽  
Epithelial Cells ◽  
Detrended Fluctuation Analysis ◽  
Breast Epithelial Cell ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Breast Epithelial Cells ◽  
Breast Epithelial ◽  
Detrended Fluctuation

Chromatin appearance in breast epithelial cells has been shown to have fractal properties, and detrended fluctuation analysis (DFA) is an effective method for characterizing the scaling in non-stationary fractal signals in terms of a scaling exponent. This study examines the use of DFA for the characterization of chromatin appearance in breast epithelial cells. Images of nuclei representative of fine-needle aspiration biopsies of the breast are characterized in terms of the scaling exponent for 19 patients with benign lesions and 22 patients with invasive ductal carcinoma. Characterizing patients by the standard deviations of the values of the scaling exponent for their representative nuclei, a statistically significant difference is noted between benign and malignant cases. This reflects that malignancies exhibit less variability in chromatin roughness than do benign cases. Previous logistic regression models for the diagnosis of breast epithelial cell lesions are improved upon by incorporating the standard deviation of the scaling exponent. Using leave-one-out cross-validation, the best logistic regression classifiers demonstrate a sensitivity of 95% and a specificity of 100%. A combination of DFA and lacunarity analysis is seen to provide the best approach to characterizing chromatin in breast epithelial cell nuclei.

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