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
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
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
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
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.
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.
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.