Multifractal detrended fluctuation analysis of temperature. The program performance was tested with many synthetical fractals and field data. Multifractal dynamics of activity data in bipolar disorder. In stochastic processes, chaos theory and time series analysis, detrended fluctuation analysis dfa is a method for determining the statistical selfaffinity of a signal by computing alpha or hurst exponent h. Using multifractal detrended fluctuation analysis to assess sacral. In this paper, methods were proposed to study in the powerlaw autocorrelation and crosscorrelation of power operating data based on multifractal detrended analysis mfdfa and multifractal detrended crosscorrelation analysis mfdxa. The first zipfile below contains matlab codes for step 3 and 4 in a methodological framework for multifractal analyses of time series. Multifractal analysis, pexponent, wavelet pleaders, negative regularity, multifractal detrendend uctuation analysis 1. Algorithm of the multifractal detrended fluctuation analysis mf dfa and some remarks concerning our case ryszard kutner 1 two basic sources of multifractality two basic sources of multifractality in time series can be distinguished. Multifractal detrended moving average analysis for texture. Detection of climate zones using multifractal detrended cross. Section 4 gives the survey of the methods, their principles and limitations. Section 7 discusses the main applications of fractalsmultifractals in the medical image analysis procedures and the methods.
We perform a comparative study of applicability of the multifractal detrended fluctuation analysis mfdfa and the wavelet transform modulus maxima wtmm method in proper detecting of mono and multifractal character of data. Multifractal detrended crosscorrelation analysis mfdxa the mfdxa method was proposed by zhou et al. Appendix c methods and programs used in multifractal analysis. We summarize the use of local holder exponents, generalized hurst exponents, and the multifractal spectrum in characterizing the way that the sample paths of a multifractal stochastic process exhibit light or heavytailed fluctuations as well as short or longrange dependence on different time scales. A smoothing technique for the multifractal analysis of a.
Physionet a good overview of dfa and c code to calculate it. Sections 5 and 6 are respectively reserved to multifractal analysis and the associated algorithms. Jun 04, 2012 the present tutorial is an introduction to multifractal detrended fluctuation analysis mfdfa that estimates the multifractal spectrum of biomedical time series. The multifractal spectrum identifies the deviations in fractal structure within time periods with large and small fluctuations. The results showed that the time series from all grid points exhibit the same behavior. Section multifractal detrended fluctuation analysis in matlab. Multifractal analysis consists of determining whether some type of powerlaw scaling exists for various statistical moments at different scales.
Multifractal detrended fluctuation analysis of streamflow in. The numerical results are in good agreement with eq. Fractals and multifractals a fractal is a rough or fragmented geometrical object that can be subdivided in parts, each of which is at least approximately a reducedsize copy of the whole. An index, i 0, that characterizes the relation of the intraspecies variances and interspecies variances is.
The construction of mfdfa is divided into eight steps. Wavelet versus detrended fluctuation analysis of multifractal. Detrending moving average algorithm for multifractals. It is useful for analysing time series that appear to be longrange dependent processes. In this paper, a novel method is proposed to identify plant species by using the two dimensional multifractal detrended fluctuation analysis 2d mfdfa. Jan 31, 2015 mma is a generalization of the standard multifractal detrended fluctuation analysis mfdfa method kantelhardt et al. Fractal structures are found in biomedical time series from a wide range of physiological phenomena. A fast matlab program to estimate the multifractal spectrum. In this study, multifractal spectra mfs analysis, which depends on empirical mode decomposition detrended fluctuation analysis emddfa, was used to measure the complexity of the monthly precipitation series from 1964 to 20 50 years of 11 districts in harbin, heilongjiang province, china.
The results for mfdfa1 and mfdfa4 are compared in parts a and b. The dataset contains more than two million records from 10 observation sites at a northern china river. Learn more about multifractal analysis, multifractal analysis of image, image classification. Introduction to multifractal detrended fluctuation analysis. Using multifractal detrended fluctuation analysis to. The mfdfa are applied to detect longrange correlations and multifractal behavior of streamflow series at four hydrological stations toudaoguai, longmen, huangfu and ganguyi in the main. The paradigm of scalefree dynamics, scale invariance, or scaling, has been shown to be relevant to model empirical data from numerous realworld. Multifractal detrended fluctuation analyses matlab central.
Detrended fluctuation analysis wikimili, the best wikipedia. There are several approaches to the implementation of multifractal analysis and there numerous ways to present these olsen, 1995. Precipitation complexity measurement using multifractal. Fractals are generally selfsimilar and independent of scale fractal dimension. Feb 06, 2015 ihlens article, in the june 4th 2012 issue of frontiers of physiology, entitled introduction to multifractal detrended fluctuation analysis in matlab provides a guide to the application of the method hereafter mfdfa. The tutorial presents mfdfa stepbystep in an interactive matlab session.
Multifractal detrended fluctuation analysis version. Multifractal detrended fluctuation analysis of streamflow. Ihlens article, in the june 4th 2012 issue of frontiers of physiology, entitled introduction to multifractal detrended fluctuation. Introduction to multifractal detrended fluctuation analysis in matlab article pdf available in frontiers in physiology 3141. The paper is one of many about the implementation of multifractal analysis. To detect multifractal properties of the time series, kantelhardt et al. A multifractal system is a generalization of a fractal system in which a single exponent the fractal dimension is not enough to describe its dynamics. Ihlens article, in the june 4th 2012 issue of frontiers of physiology, entitled introduction to multifractal detrended fluctuation analysis in matlab provides a guide to the application of the method hereafter mfdfa. Multifractal detrended moving average analysis mfdma is recently employed to detect longrange correlation and multifractal nature in stationary and nonstationary time series. The present tutorial is an introduction to multifractal detrended. Mfdfa python implementation of multifractal detrended fluctuation analysis. Multifractal formalism and analysis have been described many times lopes and betrouni, 2009. Multifractal detrended crosscorrelation analysis for.
Fastdfa matlab code for rapidly calculating the dfa scaling exponent on very large datasets. The calculations used several data window sizes ranging from 2 3 8 to the power of two that is no greater than 20% of the number of observations in the time series. The vibration signals of rotating machinery in fault conditions are nonstationary and nonlinear. The tutorial presents mfdfa stepbystep in an interactive.
In this paper, we propose a method to calculate the generalized hurst exponent for each pixel of a surface based on mfdma, which we call the mfdmabased local. Twodimensional multifractal detrended fluctuation analysis. Sep 20, 2012 in stochastic processes, chaos theory and time series analysis, detrended fluctuation analysis dfa is a method for determining the statistical selfaffinity of a signal by computing alpha or hurst exponent h. For the nonstationary and nonlinear characteristics of fault vibration signals, a novel multifractal manifold mfm method based on detrended fluctuation analysis dfa is proposed. The current paper presents a datadriven detrending technique allowing to smooth complex sinusoidal trends from a realworld electric load time series before applying the detrended multifractal fluctuation analysis mfdfa. Frontiers multifractal analysis for all physiology. Interpolation and sampling effects on the fractal dimension and multifractal spectrum estimation were also studied. A multifractal signal, on the contrary, contains many subsets that have different scaling proper. Multifractal detrended fluctuation analysis mfdfa can provide information about inner regularity, randomness and longrange correlation of time series, promoting the knowledge of their evolution regularity.
A fast matlab program to estimate the multifractal. Multifractal detrended fluctuation analyses in matlab. Multifractal detrended fluctuation analysis in matlab. Multifractal data analyses were conducted using multifractal detrended fluctuation analysis mfdfa 15,16 programmed in r r 3. Multifractal analysis has been used in several scientific fields to characterize various types of datasets. How can i use multifractal analysis for classification of. The mfdfa are applied to detect longrange correlations and multifractal behavior of streamflow series at four hydrological stations toudaoguai, longmen, huangfu and ganguyi in the. Multifractal analysis for all connecting repositories. Multifractal detrended crosscorrelation analysis for power.
Section noise and random walk like variation in a time series introduces a method to convert a noise like time series into a random walk like time series that is a preliminary step for mfdfa. The stability of current methods of complexity measurement are generally inefficient. Multifractal analysis of hydrologic data using wavelet. We find that both the price and the load time series in california power market and pjm power. We study the multifractal properties of water level with a highfrequency and massive time series using wavelet methods estimation of hurst exponents, multiscale diagram, and wavelet leaders for multifractal analysis wlmf and multifractal detrended fluctuation analysis mfdfa. Pdf introduction to multifractal detrended fluctuation. Detection of climate zones using multifractal detrended crosscorrelation analysis. The dfa algorithm was extended to analyze the multifractal time series, which is termed as multifractal detrended fluctuation analysis mfdfa.
Multifractal detrended fluctuation analysis a monofractal signal is homogeneous, in the sense that it has the same scaling properties throughout the entire signal 17. The multifractal detrended fluctuation analysis mfdfa is used to examine the scaling behavior and the multifractal characteristics of the mean daily temperature time series of the erainterim reanalysis data for a domain centered over greece. May 02, 2019 contains the multifractal detrended fluctuation analysis mfdfa, multifractal detrended crosscorrelation analysis mfxdfa, and the multiscale multifractal analysis mma. By applying both methods to the same data sets coming from the german and the american stock markets and based on our earlier knowledge of how these methods detect multifractal.
All matlab tools needed are available in introduction to mfdfa. Our method involves calculating a set of multifractal parameters that characterize the texture features of each plant leaf image. If this scaling behavior is characterized by a single scaling exponent, or equivalently is a linear function of the moments, the process is monofractal. Detection of climate zones using multifractal detrended. Ihlen multifractal analysis in matlab of monofractal. A matlab toolbox implementing estimation procedures for performing pmultifractal. In this context, detection of climate zone is an important issue. A multifractal signal, on the contrary, contains many subsets that have different scaling properties. Introduction to multifractal detrended fluctuation. Multifractal manifold for rotating machinery fault.
The tutorial is intended to be a selfsustained guide to the. We first adopt the 2d mfdfa method proposed in to our setting as follows. Ihlen, introduction to multifractal detrended fluctuation analysis in matlab, frontiers in. A spatiotemporal data mining approach there has been a significant change in climate throughout the last few decades, resulting into the phenomenon of global warming with all its adverse effects on human life and activities. The following matlab project contains the source code and matlab examples used for multifractal detrended fluctuation analyses. Firstly, calculate the multifractal fluctuation functions of signal. We apply the multifractal detrended fluctuation analysis and the wavelet transform modulus maxima to investigate multifractal properties of stock price. The present tutorial is an introduction to multifractal detrended fluctuation analysis mfdfa that estimates the multifractal spectrum of biomedical time series. A matlab program based on the hou algorithm for estimation of fractal dimension and multifractal spectrum of fractures is presented. The second zipfile is an introduction to multifractal detrended fluctuation analysis mfdfa in matlab. We summarize the use of local holder exponents, generalized hurst exponents, and the multifractal spectrum in characterizing the way that the sample paths of a multifractal stochastic process exhibit light or heavytailed. They include the length of coastlines, fully developed turbulence, realworld scenes, the suns magnetic.
Algorithm of the multifractal detrended fluctuation analysis. Algorithm of the multifractal detrended fluctuation. In this paper, we propose a method to calculate the generalized hurst exponent for each pixel of a surface based on mfdma, which we call the mfdmabased local generalized hurst exponent. A modified multifractal detrended fluctuation analysis. Multifractal detrended fluctuation analysis of frictional. Section computing the rootmeansquare variation of a time series introduces root. All matlab tools needed are available in introduction to mfdfa folder at the website. Multifractal detrended fluctuation analysis version 1. Methods and programs used in multifractal analysis c.
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