New seismic attribute: Fractal scaling exponent based on gray detrended fluctuation analysis

2015 ◽  
Vol 12 (3) ◽  
pp. 343-352 ◽  
Author(s):  
Ya-Ping Huang ◽  
Jian-Hua Geng ◽  
Tong-Lou Guo
Keyword(s):  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Seismic Attribute ◽  
Fractal Scaling ◽  
Detrended Fluctuation

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.

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.

The Application of Detrended Fluctuation Analysis in Rice Blast in the Early Warning

2014 ◽  
Vol 644-650 ◽  
pp. 6011-6014
Author(s):  
Xin Zhao ◽  
Yan Hong Huang Fu ◽  
Qian Sun ◽  
Lian Jun Yu
Keyword(s):  
Relative Humidity ◽  
Rice Blast ◽  
Detrended Fluctuation Analysis ◽  
Statistical Significance ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Temperature And Humidity ◽  
Detrended Fluctuation ◽  
Uniform Scaling ◽  
Scaling Index

In this paper, the 5-9 months of 2000-2011 temperature and humidity data, used the detrended fluctuation analysis, obtained how the two data series’ non-uniform scaling index changes with time. In order to comprehensive influence of temperature and relative humidity of the two meteorological factors, the temperature and humidity coefficient is introduced. We also proposed a new non-uniform scaling index taking into account the information of temperature and relative humidity, and discusses the possible correlation between temperature and humidity and rice blast. The preliminary results show, A long-range power-law correlation can be found in the time series of temperature and humidity. About 5-15 days before the occurrence of rice blast will appear anomalies of non-uniform scaling index. It reflects the rice blast made a difference of statistical significance to the characteristic of nonlinear system internal of temperature and humidity coefficient. It can predict the occurrence and prevalence of rice blast according to the abnormal changes of temperature and humidity coefficient scaling exponent.

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 Fractal scaling analysis of groundwater dynamics in confined aquifers

2017 ◽  
Vol 8 (4) ◽  
pp. 931-949 ◽  
Author(s):  
Tongbi Tu ◽  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Time Series ◽  
Groundwater Level ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Fractal Scaling ◽  
Groundwater Level Fluctuations ◽  
Groundwater Dynamics ◽  
Detrended Fluctuation ◽  
Infinite Moments

Abstract. Groundwater closely interacts with surface water and even climate systems in most hydroclimatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality, and multifractal detrended fluctuation analysis (MF-DFA) and multiscale multifractal analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation, is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes that can model both the long-memory behavior and the Brownian finite-memory behavior.

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 Модифицированный метод флуктуационного анализа нестационарных процессов

2020 ◽  
Vol 46 (6) ◽  
pp. 47
Author(s):  
А.Н. Павлов ◽  
О.Н. Павлова ◽  
А.А. Короновский (мл.)
Keyword(s):  
Experimental Data ◽  
Blood Flow ◽  
Detrended Fluctuation Analysis ◽  
Quantitative Description ◽  
Fluctuation Analysis ◽  
Stationary Processes ◽  
Scaling Exponent ◽  
Long Range Correlations ◽  
Proposed Modification ◽  
Detrended Fluctuation

A method of detrended fluctuation analysis (DFA) is considered, which enables studying long-range correlations in non-stationary processes. Its modification is proposed that includes estimation of an additional quantity, namely, a scaling exponent characterizing the effects of non-stationarity in the experimental data. Using the dynamics of blood flow velocity in cerebral vessels as an example, the possibilities of a quantitative description of changes in the signal structure using the proposed modification of DFA are shown.

scholarly journals Fractal Scaling Analysis of Groundwater Dynamics in Confined Aquifers

2017 ◽  
Author(s):  
Tongbi Tu ◽  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Time Series ◽  
Groundwater Level ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Fractal Scaling ◽  
Groundwater Level Fluctuations ◽  
Groundwater Dynamics ◽  
Detrended Fluctuation ◽  
Infinite Moments

Abstract. Groundwater closely interacts with surface water and even climate systems in most hydro-climatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations of confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality; and Multifractal detrended fluctuation analysis (MF-DFA) and Multiscale Multifractal Analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics which may be fitted by the Lévy stable distribution or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes, which can model both the long-memory behavior as well as the Brownian finite-memory behavior.

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