In the paper we use detrended cross-correlation analysis (DCCA) to study the electroencephalograms of healthy young subjects and healthy old subjects. It is found that the cross-correlation between different leads o...In the paper we use detrended cross-correlation analysis (DCCA) to study the electroencephalograms of healthy young subjects and healthy old subjects. It is found that the cross-correlation between different leads of a healthy young subject is larger than that of a healthy old subject. It was shown that the cross-correlation relationship decreases with the aging process and the phenomenon can help to diagnose whether the subject's brain function is healthy or not.展开更多
Multifractal detrended fluctuation analysis (MF-DFA) is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis (DFA), which was developed for detecting the long-range ...Multifractal detrended fluctuation analysis (MF-DFA) is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis (DFA), which was developed for detecting the long-range correlation and the fractal properties in stationary and non-stationary time series. Although MF-DFA has become a widely used method, some relationships among the exponents established in the original paper seem to be incorrect under the general situation. In this paper, we theoretically and experimentally demonstrate the invalidity of the expression r(q) = qh(q) - 1 stipulating the relationship between the multifractal exponent T(q) and the generalized Hurst exponent h(q). As a replacement, a general relationship is established on the basis of the universal multifractal formalism for the stationary series as .t-(q) = qh(q) - qH - 1, where H is the nonconservation parameter in the universal multifractal formalism. The singular spectra, a and f(a), are also derived according to this new relationship.展开更多
Epilepsy is a medical condition that produces seizures affecting a variety of mental and physical functions. Seizures can last from a few seconds to a few minutes. They can have many symptoms, from convulsions and los...Epilepsy is a medical condition that produces seizures affecting a variety of mental and physical functions. Seizures can last from a few seconds to a few minutes. They can have many symptoms, from convulsions and loss of consciousness to blank staring, lip smacking, or jerking movements of arms and legs. If early warning signals of an upcoming seizure (diagnosis of preictal period) are detected, proper treatment can be applied to the patient to help prevent the seizure. In this research, an epileptic disorder has been divided into three subsets: Normal, Preictal (just before the seizure), and Ictal (during seizure). By using Detrended Fluctuation Analysis (DFA), Bispectral Analysis (BIS), and Standard Deviation (SD) three features from single-channel EEG signals have been derived in the foresaid groups. A fuzzy classifier is used to separate the three groups which can successfully separate them with a separation degree of 100% and further a fuzzy inference engine is used to extract a Seizure Intensity Index (SII) from the Electroencephalogram (EEG) signals of the three different states. One can apparently see the distinction of SII amounts between the three states. It is more important when one remembers that these results are just from single-channel EEG signal.展开更多
We study the correlation between detrended fluctuation analysis(DFA) and the Lempel-Ziv complexity(LZC) in nonlinear time series analysis in this paper.Typical dynamic systems including a logistic map and a Duffin...We study the correlation between detrended fluctuation analysis(DFA) and the Lempel-Ziv complexity(LZC) in nonlinear time series analysis in this paper.Typical dynamic systems including a logistic map and a Duffing model are investigated.Moreover,the influence of Gaussian random noise on both the DFA and LZC are analyzed.The results show a high correlation between the DFA and LZC,which can quantify the non-stationarity and the nonlinearity of the time series,respectively.With the enhancement of the random component,the exponent α and the normalized complexity index C show increasing trends.In addition,C is found to be more sensitive to the fluctuation in the nonlinear time series than α.Finally,the correlation between the DFA and LZC is applied to the extraction of vibration signals for a reciprocating compressor gas valve,and an effective fault diagnosis result is obtained.展开更多
We present a multifractal detrended fluctuation analysis (MFDFA) of the time series of return generated by our recently-proposed Ising financial market model with underlying small world topology. The result of the M...We present a multifractal detrended fluctuation analysis (MFDFA) of the time series of return generated by our recently-proposed Ising financial market model with underlying small world topology. The result of the MFDFA shows that there exists obvious multifractal scaling behavior in produced time series. We compare the MFDFA results for original time series with those for shuffled series, and find that its multifractal nature is due to two factors: broadness of probability density function of the series and different correlations in small- and large-scale fluctuations. This may provide new insight to the problem of the origin of multifractality in financial time series.展开更多
A nonlinear method named detrended fluctuation analysis (DFA) was utilized to investigate the scaling behavior of the human electroencephalogram (EEG) in three emotional music conditions (fear, happiness, sadness...A nonlinear method named detrended fluctuation analysis (DFA) was utilized to investigate the scaling behavior of the human electroencephalogram (EEG) in three emotional music conditions (fear, happiness, sadness) and a rest condition (eyes-closed). The results showed that the EEG exhibited scaling behavior in two regions with two scaling exponents β1 and β2 which represented the complexity of higher and lower frequency activity besides α band respectively. As the emotional intensity decreased the value of β1 increased and the value of β2 decreased. The change of β1 was weakly correlated with the 'approach-withdrawal' model of emotion and both of fear and sad music made certain differences compared with the eyes-closed rest condition. The study shows that music is a powerful elicitor of emotion and that using nonlinear method can potentially contribute to the investigation of emotion.展开更多
With temperatures increasing as a result of global warming,extreme high temperatures are becoming more intense and more frequent on larger scale during summer in China.In recent years,a variety of researches have exam...With temperatures increasing as a result of global warming,extreme high temperatures are becoming more intense and more frequent on larger scale during summer in China.In recent years,a variety of researches have examined the high temperature distribution in China.However,it hardly considers the variation of temperature data and systems when defining the threshold of extreme high temperature.In order to discern the spatio-temporal distribution of extreme heat in China,we examined the daily maximum temperature data of 83 observation stations in China from 1950 to 2008.The objective of this study was to understand the distribution characteristics of extreme high temperature events defined by Detrended Fluctuation Analysis(DFA).The statistical methods of Permutation Entropy(PE)were also used in this study to analyze the temporal distribution.The results showed that the frequency of extreme high temperature events in China presented 3 periods of 7,10—13 and 16—20 years,respectively.The abrupt changes generally happened in the 1960s,the end of 1970s and early 1980s.It was also found that the maximum frequency occurred in the early 1950s,and the frequency decreased sharply until the late 1980s when an evidently increasing trend emerged.Furthermore,the annual averaged frequency of extreme high temperature events reveals a decreasing-increasing-decreasing trend from southwest to northeast China,but an increasing-decreasing trend from southeast to northwest China.And the frequency was higher in southern region than that in northern region.Besides,the maximum and minimum of frequencies were relatively concentrated spatially.Our results also shed light on the reasons for the periods and abrupt changes of the frequency of extreme high temperature events in China.展开更多
Detrended fluctuation analysis (DFA) is a method foro estimating the long-range power-law correlation exponent in noisy signals. It has been used successfully in many different fields, especially in the research of ...Detrended fluctuation analysis (DFA) is a method foro estimating the long-range power-law correlation exponent in noisy signals. It has been used successfully in many different fields, especially in the research of physiological signals. As an inherent part of these studies, quantization of continuous signals is inevitable. In addition, coarse-graining, to transfer original signals into symbol series in symbolic dynamic analysis, can also be considered as a quantization-like operation. Therefore, it is worth considering whether the quantization of signal has any effect on the result of DFA and if so, how large the effect will be. In this paper we study how the quantized degrees for three types of noise series (anti-correlated, uncorrelated and long-range power-law correlated signals) affect the results of DFA and find that their effects are completely different. The conclusion has an essential value in choosing the resolution of data acquisition instrument and in the processing of coarse-graining of signals.展开更多
Most of sleep disorders are diagnosed based on the sleep scoring and assessments. The purpose of this study is to combine detrended fluctuation analysis features and spectral features of single electroencephalograph (...Most of sleep disorders are diagnosed based on the sleep scoring and assessments. The purpose of this study is to combine detrended fluctuation analysis features and spectral features of single electroencephalograph (EEG) channel for the purpose of building an automated sleep staging system based on the hybrid prediction engine model. The testing results of the model were promising as the classification accuracies were 98.85%, 92.26%, 94.4%, 95.16% and 93.68% for the wake, non-rapid eye movement S1, non-rapid eye movement S2, non-rapid eye movement S3 and rapid eye movement sleep stages, respectively. The overall classification accuracy was 85.18%. We concluded that it might be possible to employ this approach to build an industrial sleep assessment system that reduced the number of channels that affected the sleep quality and the effort excreted by sleep specialists through the process of the sleep scoring.展开更多
Multi-scale properties of Reynolds stress in decaying turbulence in a wind tunnel with high Reynolds number are investi-gated. Two filtering techniques i.e., the zeroth-order and first-order detrending methods are app...Multi-scale properties of Reynolds stress in decaying turbulence in a wind tunnel with high Reynolds number are investi-gated. Two filtering techniques i.e., the zeroth-order and first-order detrending methods are applied to the two velocity components, where the local mean value (resp. local linear trend) is removed in the former (latter) technique. Some basic statistics for thirty mea-surements show that the variation is very large at first two locations and relatively small at last two locations. Moderately good power law is found for the mean value of local Reynolds stress at last three measurement locations with scaling exponents approxi-mately being 1.0 and a dual power law exists for the mean value of standard deviation of local Reynolds stress at all four measureme-nt locations with scaling exponents being 0.53 and 0.58 for zeroth-and first-order filtering respectively. Present results about local Reynolds stress are useful to build and evaluate the model of sub-grid Reynolds stress in large eddy simulations.展开更多
This paper presents fault detection,classification,and location for a PV-Wind-based DC ring microgrid in the MATLAB/SIMULINK platform.Initially,DC fault signals are collected from local measurements to examine the out...This paper presents fault detection,classification,and location for a PV-Wind-based DC ring microgrid in the MATLAB/SIMULINK platform.Initially,DC fault signals are collected from local measurements to examine the outcomes of the proposed system.Accurate detection is carried out for all faults,(i.e.,cable and arc faults)under two cases of fault resistance and distance variation,with the assistance of primary and secondary detection techniques,i.e.second-order differential current derivatived2I3 dt2and sliding mode window-based Pearson’s correlation coefficient.For fault classification a novel approach using modified multifractal detrended fluctuation analysis(M-MFDFA)is presented.The advantage of this method is its ability to estimate the local trends of any order polynomial function with the help of polynomial and trigonometric functions.It also doesn’t require any signal processing algorithm for decomposition resulting and this results in a reduction of computational burden.The detected fault signals are directly passed through the M-MFDFA classifier for fault type classification.To enhance the performance of the proposed classifier,statistical data is obtained from the M-MFDFA feature vectors,and the obtained data is plotted in 2-D and 3-D scatter plots for better visualization.Accurate fault distance estimation is carried out for all types of faults in the DC ring bus microgrid with the assistance of recursive least squares with a forgetting factor(FF-RLS).To verify the performance and superiority of the proposed classifier,it is compared with existing classifiers in terms of features,classification accuracy(CA),and relative computational time(RCT).展开更多
The shrinkage of the Aral Sea,which is closely related to the Amu Darya River,strongly affects the sustainability of the local natural ecosystem,agricultural production,and human well-being.In this study,we used the B...The shrinkage of the Aral Sea,which is closely related to the Amu Darya River,strongly affects the sustainability of the local natural ecosystem,agricultural production,and human well-being.In this study,we used the Bayesian Estimator of Abrupt change,Seasonal change,and Trend(BEAST)model to detect the historical change points in the variation of the Aral Sea and the Amu Darya River and analyse the causes of the Aral Sea shrinkage during the 1950–2016 period.Further,we applied multifractal detrend cross-correlation analysis(MF-DCCA)and quantitative analysis to investigate the responses of the Aral Sea to the runoff in the Amu Darya River,which is the main source of recharge to the Aral Sea.Our results showed that two significant trend change points in the water volume change of the Aral Sea occurred,in 1961 and 1974.Before 1961,the water volume in the Aral Sea was stable,after which it began to shrink,with a shrinkage rate fluctuating around 15.21 km3/a.After 1974,the water volume of the Aral Sea decreased substantially at a rate of up to 48.97 km3/a,which was the highest value recorded in this study.In addition,although the response of the Aral Sea's water volume to its recharge runoff demonstrated a complex non-linear relationship,the replenishment of the Aral Sea by the runoff in the lower reaches of the Amu Darya River was identified as the dominant factor affecting the Aral Sea shrinkage.Based on the scenario analyses,we concluded that it is possible to slow down the retreat of the Aral Sea and restore its ecosystem by increasing the efficiency of agricultural water use,decreasing agricultural water use in the middle and lower reaches,reducing ineffective evaporation from reservoirs and wetlands,and increasing the water coming from the lower reaches of the Amu Darya River to the 1961–1973 level.These measures would maintain and stabilise the water area and water volume of the Aral Sea in a state of ecological restoration.Therefore,this study focuses on how human consumption of recharge runoff affects the Aral Sea and provides scientific perspective on its ecological conservation and sustainable development.展开更多
Massive seamounts have been surveyed and documented in the last decades.However,the morphologies of seamounts are usually described in qualitative manners,yet few quantitative detections have been carried out.Here,bas...Massive seamounts have been surveyed and documented in the last decades.However,the morphologies of seamounts are usually described in qualitative manners,yet few quantitative detections have been carried out.Here,based on the high-re solution multi-beam bathymetric data,we report a recentlysurveyed guy ot on the Caroline Ridge in the West Pacific,and the large-scale volcanic structures and smallscale erosive-depositional landforms in the guyot area have been identified.The multifractal features of the guyot are characterized for the first time by applying multifractal detrended fluctuation analysis on the surveyed bathymetric data.The results indicate that the multifractal spectrum parameters of the seafloor have strong spatial dependency on the fluctuations of local landforms.Both small-and large-scale components contribute to the degree of asymmetry of the multifractal spectrum(B),while the fluctuations of B are mostly attributed to the changes in small-scale roughness.The maximum singularity strength(α0)correlates well with the roughness of large-scale landforms and likely reflects the large-scale topographic irregularity.Comparing to traditional roughness parameters or monofractal exponents,multifractal spectra are able to depict not only the multiscale characteristics of submarine landforms,but also the spatial variations of scaling behaviors.Although more comparative works are required for various seamounts,we hope this study,as a case of quantifying geomorphological characters and multiscale behaviors of seamounts,can encourage further studies on seamounts concerning geomorphological processes,ocean bottom circulations,and seamount ecosystems.展开更多
Types and structure of plant communities in the Yellow River Delta were investigated by using detrended canonical correspon-dence analyses(DCCAs) and a two-way indicator species analysis(TWINSPAN).The distribution pat...Types and structure of plant communities in the Yellow River Delta were investigated by using detrended canonical correspon-dence analyses(DCCAs) and a two-way indicator species analysis(TWINSPAN).The distribution pattern and influential factors of the plant communities were also analyzed by testing elevation, slope, soil characteristics, longitude and latitude of 134 vegetation samples collected by representative plot sampling methods.Results showed that all the 134 vegetation samples could be divided into seven vegetation groups, separately dominated by Robinia pseucdoacacia, Imperata cylindrical, Miscanthus saccharifleus, Suaeda salsa, Aeluropus sinensis, Phragmites australis and Tamarix chinensis.The vegetation distribution pattern was mainly related to elevation, ground water depth and soil characteristics such as salinity and soluble potassium.Among the factors affecting distribution pattern of the plant communities, the species matrix explained by non-spatial environmental variation accounts for 45.2% of total variation.Spatial variation and spatial-structured environmental variation explain 11.8%, and 2.2%, respectively.Remained 40.8% of undetermined variation is attributed to biological and stochastic factors.展开更多
We study the dynamical properties of heart rate variability (HRV) in sleep by analysing the scaling behaviour with the multifractal detrended fluctuation analysis method. It is well known that heart rate is regulate...We study the dynamical properties of heart rate variability (HRV) in sleep by analysing the scaling behaviour with the multifractal detrended fluctuation analysis method. It is well known that heart rate is regulated by the interaction of two branches of the autonomic nervous system: the parasympathetic and sympathetic nervous systems. By investigating the multifractal properties of light, deep, rapid-eye-movement (REM) sleep and wake stages, we firstly find an increasing multifractal behaviour during REM sleep which may be caused by augmented sympathetic activities relative to non-REM sleep. In addition, the investigation of long-range correlations of HRV in sleep with second order detrended fluctuation analysis presents irregular phenomena. These findings may be helpful to understand the underlying regulating mechanism of heart rate by autonomic nervous system during wake-sleep transitions.展开更多
Pollen analysis of 23 surface samples in the east of Qaidam Basin reveals the characteristics of pollen assemblages and their relationships with vegetation and climate. In pollen assemblages, Chenopodiaceae and Artemi...Pollen analysis of 23 surface samples in the east of Qaidam Basin reveals the characteristics of pollen assemblages and their relationships with vegetation and climate. In pollen assemblages, Chenopodiaceae and Artemisia are preponderant types in all the samples, and Ephedra, Gramineae and Compositae are common types. The results of DCA (Detrended Correspondance Analysis) and Correlation Analysis show different pollen assemblages indicate different vegetations, coincided with respective vegetation types. A/C (Artemisia/Chenopodiaceae) in the desert can indicate the aridity. Depending on the aridity, the vegetation communities are divided into four groups: severe drought group, moderate drought group, slight drought group and tropophilous group. A/C value is less 0.2 in the severe drought group, 0.2-0.5 in the moderate drought group, 1.63 in the slight drought group and 5.72 slight-wetness group.展开更多
The target on the sea surface is complex and difficult to detect due to the interference of backscattered returns from the sea surface illuminated by the radar pulse. Detrended fluctuation analysis (DFA) has been us...The target on the sea surface is complex and difficult to detect due to the interference of backscattered returns from the sea surface illuminated by the radar pulse. Detrended fluctuation analysis (DFA) has been used successfully to extract the time-domain Hurst exponent of sea-clutter series. Since the frequency of the sea clutter mainly concentrates around Doppler center so that we consider to extract frequency-do- main fractal characterization and then detect a weak target within sea clutter by using the difference of frequency-domain fractal characterization. The generalized detrended fluctuation analysis (GDFA) is more flexible than traditional DFA owing to its smoothing action for the clutters. In this paper, we apply the GDFA to evaluate the generalized Hurst exponent of sea-clutter series in the frequency domain. The difference of generalized Hurst exponents between different sea-clutter range bins would be used to determine whether the target exists. Moreover, some simulations with the real IPIX radar data have also been demonstrated in order to suooort this conclusion.展开更多
A method for gearbox fault diagnosis consists of feature extraction andfault identification. Many methods for feature extraction have beendevised for exposing nature of vibration data of a defective gearbox. Inadditio...A method for gearbox fault diagnosis consists of feature extraction andfault identification. Many methods for feature extraction have beendevised for exposing nature of vibration data of a defective gearbox. Inaddition, features extracted from gearbox vibration data are identifiedby various classifiers. However, existing literatures leave much to bedesired in assessing performance of different combinatorial methods forgearbox fault diagnosis. To this end, this paper evaluated performance ofseveral typical combinatorial methods for gearbox fault diagnosis byassociating each of multifractal detrended fluctuation analysis (MFDFA),empirical mode decomposition (EMD) and wavelet transform (WT) witheach of neural network (NN), Mahalanobis distance decision rules(MDDR) and support vector machine (SVM). Following this,performance of different combinatorial methods was compared using agroup of gearbox vibration data containing slightly different faultpatterns. The results indicate that MFDFA performs better in featureextraction of gearbox vibration data and SVM does the same in faultidentification. Naturally, the method associating MFDFA with SVMshows huge potential for fault diagnosis of gearboxes. As a result, thispaper can provide some useful information on construction of a methodfor gearbox fault diagnosis.展开更多
When exploring the temporal and spatial change law of ocean environment, the most common method used is using smaller-scale observed data to derive the change law for a larger-scale system. For instance, using 30-year...When exploring the temporal and spatial change law of ocean environment, the most common method used is using smaller-scale observed data to derive the change law for a larger-scale system. For instance, using 30-year observation data to derive 100-year return period design wave height. Therefore, the study of inherent self-similarity in ocean hydrological elements becomes increasingly important to the study of multi-year return period design wave height derivation. In this paper, we introduced multifractal to analyze the statistical characteristics of wave height series data observed from oceanic hydrological station. An improvement is made to address the existing problems of the multifractal detrended fluctuation analysis (MF-DFA) method, where trend function showed a discontinuity between intervals. The improved MFDFA method is based on signal mode decomposition, replacing piecewise polynomial fitting used in the original method. We applied the proposed method to the wave height data collected at Chaolian Island, Shandong, China, from 1963 to 1989 and was able to conclude the wave height sequence presented weak multi-fractality. This result provided strong support to the past research on the derivation of multi-year return period design wave height with observed data. Moreover, the new method proposed in this paper also provides a new perspective to explore the intrinsic characteristic of data.展开更多
Topography and soil factors are known to play crucial roles in the species composition of plant communities in subtropical evergreen-deciduous broadleaved mixed forests.In this study,we used a systematic quantitative ...Topography and soil factors are known to play crucial roles in the species composition of plant communities in subtropical evergreen-deciduous broadleaved mixed forests.In this study,we used a systematic quantitative approach to classify plant community types in the subtropical forests of Hubei Province(central China),and then quantified the relative contribution of drivers responsible for variation in species composition and diversity.We classified the subtropical forests in the study area into 12 community types.Of these,species diversity indices of three communities were significantly higher than those of others.In each community type,species richness,abundance,basal area and importance values of evergreen and deciduous species were different.In most community types,deciduous species richness was higher than that of evergreen species.Linear regression analysis showed that the dominant factors that affect species composition in each community type are elevation,slope,aspect,soil nitrogen content,and soil phosphorus content.Furthermore,structural equation modeling analysis showed that the majority of variance in species composition of plant communities can be explained by elevation,aspect,soil water content,litterfall,total nitrogen,and total phosphorus.Thus,the major factors that affect evergreen and deciduous species distribution across the 12 community types in subtropical evergreendeciduous broadleaved mixed forests include elevation,slope and aspect,soil total nitrogen content,soil total phosphorus content,soil available nitrogen content and soil available phosphorus content.展开更多
基金supported by the Science Foundation of Jiangsu Province of China (Grant No.BK2011759)
文摘In the paper we use detrended cross-correlation analysis (DCCA) to study the electroencephalograms of healthy young subjects and healthy old subjects. It is found that the cross-correlation between different leads of a healthy young subject is larger than that of a healthy old subject. It was shown that the cross-correlation relationship decreases with the aging process and the phenomenon can help to diagnose whether the subject's brain function is healthy or not.
基金Project supported by the National Natural Science Foundation of China (Grant No.11071282)the Chinese Program for New Century Excellent Talents in University (Grant No.NCET-08-06867)
文摘Multifractal detrended fluctuation analysis (MF-DFA) is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis (DFA), which was developed for detecting the long-range correlation and the fractal properties in stationary and non-stationary time series. Although MF-DFA has become a widely used method, some relationships among the exponents established in the original paper seem to be incorrect under the general situation. In this paper, we theoretically and experimentally demonstrate the invalidity of the expression r(q) = qh(q) - 1 stipulating the relationship between the multifractal exponent T(q) and the generalized Hurst exponent h(q). As a replacement, a general relationship is established on the basis of the universal multifractal formalism for the stationary series as .t-(q) = qh(q) - qH - 1, where H is the nonconservation parameter in the universal multifractal formalism. The singular spectra, a and f(a), are also derived according to this new relationship.
文摘Epilepsy is a medical condition that produces seizures affecting a variety of mental and physical functions. Seizures can last from a few seconds to a few minutes. They can have many symptoms, from convulsions and loss of consciousness to blank staring, lip smacking, or jerking movements of arms and legs. If early warning signals of an upcoming seizure (diagnosis of preictal period) are detected, proper treatment can be applied to the patient to help prevent the seizure. In this research, an epileptic disorder has been divided into three subsets: Normal, Preictal (just before the seizure), and Ictal (during seizure). By using Detrended Fluctuation Analysis (DFA), Bispectral Analysis (BIS), and Standard Deviation (SD) three features from single-channel EEG signals have been derived in the foresaid groups. A fuzzy classifier is used to separate the three groups which can successfully separate them with a separation degree of 100% and further a fuzzy inference engine is used to extract a Seizure Intensity Index (SII) from the Electroencephalogram (EEG) signals of the three different states. One can apparently see the distinction of SII amounts between the three states. It is more important when one remembers that these results are just from single-channel EEG signal.
基金Project supported by the National Natural Science Foundation of China (Grant No. 51175316)the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20103108110006)
文摘We study the correlation between detrended fluctuation analysis(DFA) and the Lempel-Ziv complexity(LZC) in nonlinear time series analysis in this paper.Typical dynamic systems including a logistic map and a Duffing model are investigated.Moreover,the influence of Gaussian random noise on both the DFA and LZC are analyzed.The results show a high correlation between the DFA and LZC,which can quantify the non-stationarity and the nonlinearity of the time series,respectively.With the enhancement of the random component,the exponent α and the normalized complexity index C show increasing trends.In addition,C is found to be more sensitive to the fluctuation in the nonlinear time series than α.Finally,the correlation between the DFA and LZC is applied to the extraction of vibration signals for a reciprocating compressor gas valve,and an effective fault diagnosis result is obtained.
基金Supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars of State Education Ministry
文摘We present a multifractal detrended fluctuation analysis (MFDFA) of the time series of return generated by our recently-proposed Ising financial market model with underlying small world topology. The result of the MFDFA shows that there exists obvious multifractal scaling behavior in produced time series. We compare the MFDFA results for original time series with those for shuffled series, and find that its multifractal nature is due to two factors: broadness of probability density function of the series and different correlations in small- and large-scale fluctuations. This may provide new insight to the problem of the origin of multifractality in financial time series.
基金This work was supported by the National Nature Science Foundation of China under Grant No. 60571019 and No. 30525030.
文摘A nonlinear method named detrended fluctuation analysis (DFA) was utilized to investigate the scaling behavior of the human electroencephalogram (EEG) in three emotional music conditions (fear, happiness, sadness) and a rest condition (eyes-closed). The results showed that the EEG exhibited scaling behavior in two regions with two scaling exponents β1 and β2 which represented the complexity of higher and lower frequency activity besides α band respectively. As the emotional intensity decreased the value of β1 increased and the value of β2 decreased. The change of β1 was weakly correlated with the 'approach-withdrawal' model of emotion and both of fear and sad music made certain differences compared with the eyes-closed rest condition. The study shows that music is a powerful elicitor of emotion and that using nonlinear method can potentially contribute to the investigation of emotion.
基金Key Projects in the National Science & Technology Pillar Program during the Eleventh Five-Year Plan Period(2007BAC29B05)Jiangsu Key Laboratory of Meteorological Disaster(KLME05005)
文摘With temperatures increasing as a result of global warming,extreme high temperatures are becoming more intense and more frequent on larger scale during summer in China.In recent years,a variety of researches have examined the high temperature distribution in China.However,it hardly considers the variation of temperature data and systems when defining the threshold of extreme high temperature.In order to discern the spatio-temporal distribution of extreme heat in China,we examined the daily maximum temperature data of 83 observation stations in China from 1950 to 2008.The objective of this study was to understand the distribution characteristics of extreme high temperature events defined by Detrended Fluctuation Analysis(DFA).The statistical methods of Permutation Entropy(PE)were also used in this study to analyze the temporal distribution.The results showed that the frequency of extreme high temperature events in China presented 3 periods of 7,10—13 and 16—20 years,respectively.The abrupt changes generally happened in the 1960s,the end of 1970s and early 1980s.It was also found that the maximum frequency occurred in the early 1950s,and the frequency decreased sharply until the late 1980s when an evidently increasing trend emerged.Furthermore,the annual averaged frequency of extreme high temperature events reveals a decreasing-increasing-decreasing trend from southwest to northeast China,but an increasing-decreasing trend from southeast to northwest China.And the frequency was higher in southern region than that in northern region.Besides,the maximum and minimum of frequencies were relatively concentrated spatially.Our results also shed light on the reasons for the periods and abrupt changes of the frequency of extreme high temperature events in China.
基金Project supported by the Natural Science Foundation for the Returned Overseas Chinese Scholars of the Ministry of Human Resources of China (Grant No. 2008102SB90203)Nanjing Normal University,China (Grant No. 2008102XLH0044)
文摘Detrended fluctuation analysis (DFA) is a method foro estimating the long-range power-law correlation exponent in noisy signals. It has been used successfully in many different fields, especially in the research of physiological signals. As an inherent part of these studies, quantization of continuous signals is inevitable. In addition, coarse-graining, to transfer original signals into symbol series in symbolic dynamic analysis, can also be considered as a quantization-like operation. Therefore, it is worth considering whether the quantization of signal has any effect on the result of DFA and if so, how large the effect will be. In this paper we study how the quantized degrees for three types of noise series (anti-correlated, uncorrelated and long-range power-law correlated signals) affect the results of DFA and find that their effects are completely different. The conclusion has an essential value in choosing the resolution of data acquisition instrument and in the processing of coarse-graining of signals.
文摘Most of sleep disorders are diagnosed based on the sleep scoring and assessments. The purpose of this study is to combine detrended fluctuation analysis features and spectral features of single electroencephalograph (EEG) channel for the purpose of building an automated sleep staging system based on the hybrid prediction engine model. The testing results of the model were promising as the classification accuracies were 98.85%, 92.26%, 94.4%, 95.16% and 93.68% for the wake, non-rapid eye movement S1, non-rapid eye movement S2, non-rapid eye movement S3 and rapid eye movement sleep stages, respectively. The overall classification accuracy was 85.18%. We concluded that it might be possible to employ this approach to build an industrial sleep assessment system that reduced the number of channels that affected the sleep quality and the effort excreted by sleep specialists through the process of the sleep scoring.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11272196,11202122)the Key Project of Shanghai Municipal Education Commission(Grant No.11ZZ87)the Shanghai Pujiang Project(Grant No.12PJ1403500)
文摘Multi-scale properties of Reynolds stress in decaying turbulence in a wind tunnel with high Reynolds number are investi-gated. Two filtering techniques i.e., the zeroth-order and first-order detrending methods are applied to the two velocity components, where the local mean value (resp. local linear trend) is removed in the former (latter) technique. Some basic statistics for thirty mea-surements show that the variation is very large at first two locations and relatively small at last two locations. Moderately good power law is found for the mean value of local Reynolds stress at last three measurement locations with scaling exponents approxi-mately being 1.0 and a dual power law exists for the mean value of standard deviation of local Reynolds stress at all four measureme-nt locations with scaling exponents being 0.53 and 0.58 for zeroth-and first-order filtering respectively. Present results about local Reynolds stress are useful to build and evaluate the model of sub-grid Reynolds stress in large eddy simulations.
文摘This paper presents fault detection,classification,and location for a PV-Wind-based DC ring microgrid in the MATLAB/SIMULINK platform.Initially,DC fault signals are collected from local measurements to examine the outcomes of the proposed system.Accurate detection is carried out for all faults,(i.e.,cable and arc faults)under two cases of fault resistance and distance variation,with the assistance of primary and secondary detection techniques,i.e.second-order differential current derivatived2I3 dt2and sliding mode window-based Pearson’s correlation coefficient.For fault classification a novel approach using modified multifractal detrended fluctuation analysis(M-MFDFA)is presented.The advantage of this method is its ability to estimate the local trends of any order polynomial function with the help of polynomial and trigonometric functions.It also doesn’t require any signal processing algorithm for decomposition resulting and this results in a reduction of computational burden.The detected fault signals are directly passed through the M-MFDFA classifier for fault type classification.To enhance the performance of the proposed classifier,statistical data is obtained from the M-MFDFA feature vectors,and the obtained data is plotted in 2-D and 3-D scatter plots for better visualization.Accurate fault distance estimation is carried out for all types of faults in the DC ring bus microgrid with the assistance of recursive least squares with a forgetting factor(FF-RLS).To verify the performance and superiority of the proposed classifier,it is compared with existing classifiers in terms of features,classification accuracy(CA),and relative computational time(RCT).
基金supported by the National Natural Science Foundation of China (42230708)the Joint CAS (Chinese Academy of Sciences) & MPG (Max-Planck-Gesellschaft) Research Project (HZXM20225001MI)the Tianshan Talent Project of Xinjiang Uygur Autonomous Region, China (2022TSYCLJ0056)。
文摘The shrinkage of the Aral Sea,which is closely related to the Amu Darya River,strongly affects the sustainability of the local natural ecosystem,agricultural production,and human well-being.In this study,we used the Bayesian Estimator of Abrupt change,Seasonal change,and Trend(BEAST)model to detect the historical change points in the variation of the Aral Sea and the Amu Darya River and analyse the causes of the Aral Sea shrinkage during the 1950–2016 period.Further,we applied multifractal detrend cross-correlation analysis(MF-DCCA)and quantitative analysis to investigate the responses of the Aral Sea to the runoff in the Amu Darya River,which is the main source of recharge to the Aral Sea.Our results showed that two significant trend change points in the water volume change of the Aral Sea occurred,in 1961 and 1974.Before 1961,the water volume in the Aral Sea was stable,after which it began to shrink,with a shrinkage rate fluctuating around 15.21 km3/a.After 1974,the water volume of the Aral Sea decreased substantially at a rate of up to 48.97 km3/a,which was the highest value recorded in this study.In addition,although the response of the Aral Sea's water volume to its recharge runoff demonstrated a complex non-linear relationship,the replenishment of the Aral Sea by the runoff in the lower reaches of the Amu Darya River was identified as the dominant factor affecting the Aral Sea shrinkage.Based on the scenario analyses,we concluded that it is possible to slow down the retreat of the Aral Sea and restore its ecosystem by increasing the efficiency of agricultural water use,decreasing agricultural water use in the middle and lower reaches,reducing ineffective evaporation from reservoirs and wetlands,and increasing the water coming from the lower reaches of the Amu Darya River to the 1961–1973 level.These measures would maintain and stabilise the water area and water volume of the Aral Sea in a state of ecological restoration.Therefore,this study focuses on how human consumption of recharge runoff affects the Aral Sea and provides scientific perspective on its ecological conservation and sustainable development.
基金the Senior User Project of R/V Kexue(No.KEXUE2018G11)the Science and Technology Basic Resources Investigation Program ofChina(No.2017FY100801)the Open Fund of the Key Laboratoryof Marine Geology and Environment,Chinese Academy of Sciences(No.MGE2018KG02)。
文摘Massive seamounts have been surveyed and documented in the last decades.However,the morphologies of seamounts are usually described in qualitative manners,yet few quantitative detections have been carried out.Here,based on the high-re solution multi-beam bathymetric data,we report a recentlysurveyed guy ot on the Caroline Ridge in the West Pacific,and the large-scale volcanic structures and smallscale erosive-depositional landforms in the guyot area have been identified.The multifractal features of the guyot are characterized for the first time by applying multifractal detrended fluctuation analysis on the surveyed bathymetric data.The results indicate that the multifractal spectrum parameters of the seafloor have strong spatial dependency on the fluctuations of local landforms.Both small-and large-scale components contribute to the degree of asymmetry of the multifractal spectrum(B),while the fluctuations of B are mostly attributed to the changes in small-scale roughness.The maximum singularity strength(α0)correlates well with the roughness of large-scale landforms and likely reflects the large-scale topographic irregularity.Comparing to traditional roughness parameters or monofractal exponents,multifractal spectra are able to depict not only the multiscale characteristics of submarine landforms,but also the spatial variations of scaling behaviors.Although more comparative works are required for various seamounts,we hope this study,as a case of quantifying geomorphological characters and multiscale behaviors of seamounts,can encourage further studies on seamounts concerning geomorphological processes,ocean bottom circulations,and seamount ecosystems.
基金supported by the Na-tional Natural Science Foundation of China (No. 40771172)the orientation project of the Chinese Academy of Sciences (No. kzcx2-yw-308)
文摘Types and structure of plant communities in the Yellow River Delta were investigated by using detrended canonical correspon-dence analyses(DCCAs) and a two-way indicator species analysis(TWINSPAN).The distribution pattern and influential factors of the plant communities were also analyzed by testing elevation, slope, soil characteristics, longitude and latitude of 134 vegetation samples collected by representative plot sampling methods.Results showed that all the 134 vegetation samples could be divided into seven vegetation groups, separately dominated by Robinia pseucdoacacia, Imperata cylindrical, Miscanthus saccharifleus, Suaeda salsa, Aeluropus sinensis, Phragmites australis and Tamarix chinensis.The vegetation distribution pattern was mainly related to elevation, ground water depth and soil characteristics such as salinity and soluble potassium.Among the factors affecting distribution pattern of the plant communities, the species matrix explained by non-spatial environmental variation accounts for 45.2% of total variation.Spatial variation and spatial-structured environmental variation explain 11.8%, and 2.2%, respectively.Remained 40.8% of undetermined variation is attributed to biological and stochastic factors.
基金Supported by the National Science Foundation of China under Grant Nos 60471057 and 70571075, and the Foundation for Graduate Student of USTC under Grant No KD2006046.
文摘We study the dynamical properties of heart rate variability (HRV) in sleep by analysing the scaling behaviour with the multifractal detrended fluctuation analysis method. It is well known that heart rate is regulated by the interaction of two branches of the autonomic nervous system: the parasympathetic and sympathetic nervous systems. By investigating the multifractal properties of light, deep, rapid-eye-movement (REM) sleep and wake stages, we firstly find an increasing multifractal behaviour during REM sleep which may be caused by augmented sympathetic activities relative to non-REM sleep. In addition, the investigation of long-range correlations of HRV in sleep with second order detrended fluctuation analysis presents irregular phenomena. These findings may be helpful to understand the underlying regulating mechanism of heart rate by autonomic nervous system during wake-sleep transitions.
基金Scientific research fund of Hebei Normal University, No.L2004B14 National Key Basic Research Program, No.2005CB422005+3 种基金 National Natural Science Foundation of China, No.90202012 No.40171095 Natural Science Foundation of Hebei Province, No.402615 Knowledge Innovation Project of CAS, No.KZCX3-SW-339
文摘Pollen analysis of 23 surface samples in the east of Qaidam Basin reveals the characteristics of pollen assemblages and their relationships with vegetation and climate. In pollen assemblages, Chenopodiaceae and Artemisia are preponderant types in all the samples, and Ephedra, Gramineae and Compositae are common types. The results of DCA (Detrended Correspondance Analysis) and Correlation Analysis show different pollen assemblages indicate different vegetations, coincided with respective vegetation types. A/C (Artemisia/Chenopodiaceae) in the desert can indicate the aridity. Depending on the aridity, the vegetation communities are divided into four groups: severe drought group, moderate drought group, slight drought group and tropophilous group. A/C value is less 0.2 in the severe drought group, 0.2-0.5 in the moderate drought group, 1.63 in the slight drought group and 5.72 slight-wetness group.
基金The National Natural Science Foundation of China Project under contract Nos 41276187 and 41076119the Scientific Research Foundation for Introducing Talents,Nanjing University of Information Science and Technology under contract No.20110310Jiangsu Natural Science Foundation under contract No.BK2011008
文摘The target on the sea surface is complex and difficult to detect due to the interference of backscattered returns from the sea surface illuminated by the radar pulse. Detrended fluctuation analysis (DFA) has been used successfully to extract the time-domain Hurst exponent of sea-clutter series. Since the frequency of the sea clutter mainly concentrates around Doppler center so that we consider to extract frequency-do- main fractal characterization and then detect a weak target within sea clutter by using the difference of frequency-domain fractal characterization. The generalized detrended fluctuation analysis (GDFA) is more flexible than traditional DFA owing to its smoothing action for the clutters. In this paper, we apply the GDFA to evaluate the generalized Hurst exponent of sea-clutter series in the frequency domain. The difference of generalized Hurst exponents between different sea-clutter range bins would be used to determine whether the target exists. Moreover, some simulations with the real IPIX radar data have also been demonstrated in order to suooort this conclusion.
基金supported by Shandong ProvincialNatural Science Foundation China (ZR2012EEL07).
文摘A method for gearbox fault diagnosis consists of feature extraction andfault identification. Many methods for feature extraction have beendevised for exposing nature of vibration data of a defective gearbox. Inaddition, features extracted from gearbox vibration data are identifiedby various classifiers. However, existing literatures leave much to bedesired in assessing performance of different combinatorial methods forgearbox fault diagnosis. To this end, this paper evaluated performance ofseveral typical combinatorial methods for gearbox fault diagnosis byassociating each of multifractal detrended fluctuation analysis (MFDFA),empirical mode decomposition (EMD) and wavelet transform (WT) witheach of neural network (NN), Mahalanobis distance decision rules(MDDR) and support vector machine (SVM). Following this,performance of different combinatorial methods was compared using agroup of gearbox vibration data containing slightly different faultpatterns. The results indicate that MFDFA performs better in featureextraction of gearbox vibration data and SVM does the same in faultidentification. Naturally, the method associating MFDFA with SVMshows huge potential for fault diagnosis of gearboxes. As a result, thispaper can provide some useful information on construction of a methodfor gearbox fault diagnosis.
基金Supported by the NSFC-Shandong Joint Fund “Study on the DisasterCausing Mechanism and Disaster Prevention Countermeasures of MultiSource Storm Surges”(No.U1706226)the National Natural Science Foundation of China “Coastal Engineering and Risk Assessment Based on a Four-Layer Nested Multi-Objective Probability Model”(No.51379195)+1 种基金the Natural Science Foundation of Shandong Province “Three-Layer Nested Multi-Objective Probability Prediction and Risk Assessment in Coastal Engineering”(No.ZR2013EEM034)the Program of Promotion Plan for Postgraduates’ Educational Quality “Paying More Attention to the Study on the Cultivation Mode of Mathematical Modeling for Engineering Postgraduates”(No.861801232417)
文摘When exploring the temporal and spatial change law of ocean environment, the most common method used is using smaller-scale observed data to derive the change law for a larger-scale system. For instance, using 30-year observation data to derive 100-year return period design wave height. Therefore, the study of inherent self-similarity in ocean hydrological elements becomes increasingly important to the study of multi-year return period design wave height derivation. In this paper, we introduced multifractal to analyze the statistical characteristics of wave height series data observed from oceanic hydrological station. An improvement is made to address the existing problems of the multifractal detrended fluctuation analysis (MF-DFA) method, where trend function showed a discontinuity between intervals. The improved MFDFA method is based on signal mode decomposition, replacing piecewise polynomial fitting used in the original method. We applied the proposed method to the wave height data collected at Chaolian Island, Shandong, China, from 1963 to 1989 and was able to conclude the wave height sequence presented weak multi-fractality. This result provided strong support to the past research on the derivation of multi-year return period design wave height with observed data. Moreover, the new method proposed in this paper also provides a new perspective to explore the intrinsic characteristic of data.
基金the National Natural Science Foundation of China(51809250)Hubei Provincial Natural Science Foundation for Innovation Groups(No.2019CFA019).
文摘Topography and soil factors are known to play crucial roles in the species composition of plant communities in subtropical evergreen-deciduous broadleaved mixed forests.In this study,we used a systematic quantitative approach to classify plant community types in the subtropical forests of Hubei Province(central China),and then quantified the relative contribution of drivers responsible for variation in species composition and diversity.We classified the subtropical forests in the study area into 12 community types.Of these,species diversity indices of three communities were significantly higher than those of others.In each community type,species richness,abundance,basal area and importance values of evergreen and deciduous species were different.In most community types,deciduous species richness was higher than that of evergreen species.Linear regression analysis showed that the dominant factors that affect species composition in each community type are elevation,slope,aspect,soil nitrogen content,and soil phosphorus content.Furthermore,structural equation modeling analysis showed that the majority of variance in species composition of plant communities can be explained by elevation,aspect,soil water content,litterfall,total nitrogen,and total phosphorus.Thus,the major factors that affect evergreen and deciduous species distribution across the 12 community types in subtropical evergreendeciduous broadleaved mixed forests include elevation,slope and aspect,soil total nitrogen content,soil total phosphorus content,soil available nitrogen content and soil available phosphorus content.