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Journal articles on the topic 'Wavelet-multifractal'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Barral, Julien, and Stéphane Seuret. "From Multifractal Measures to Multifractal Wavelet Series." Journal of Fourier Analysis and Applications 11, no. 5 (2005): 589–614. http://dx.doi.org/10.1007/s00041-005-5006-9.

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2

JIANG, ZHI-QIANG, XING-LU GAO, WEI-XING ZHOU, and H. EUGENE STANLEY. "MULTIFRACTAL CROSS WAVELET ANALYSIS." Fractals 25, no. 06 (2017): 1750054. http://dx.doi.org/10.1142/s0218348x17500542.

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Complex systems are composed of mutually interacting components and the output values of these components usually exhibit long-range cross-correlations. Using wavelet analysis, we propose a method of characterizing the joint multifractal nature of these long-range cross correlations, a method we call multifractal cross wavelet analysis (MFXWT). We assess the performance of the MFXWT method by performing extensive numerical experiments on the dual binomial measures with multifractal cross correlations and the bivariate fractional Brownian motions (bFBMs) with monofractal cross correlations. For

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3

Arneodo, Alain, Benjamin Audit, Pierre Kestener, and Stephane Roux. "Wavelet-based multifractal analysis." Scholarpedia 3, no. 3 (2008): 4103. http://dx.doi.org/10.4249/scholarpedia.4103.

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4

FIGLIOLA, ALEJANDRA, EDUARDO SERRANO, GUSTAVO PACCOSI, and MARIEL ROSENBLATT. "ABOUT THE EFFECTIVENESS OF DIFFERENT METHODS FOR THE ESTIMATION OF THE MULTIFRACTAL SPECTRUM OF NATURAL SERIES." International Journal of Bifurcation and Chaos 20, no. 02 (2010): 331–39. http://dx.doi.org/10.1142/s0218127410025788.

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Complex natural systems present characteristics of scalar invariance. This behavior has been experimentally verified and a large related bibliography has been reported. Multifractal Formalism is a way to evaluate this kind of behavior. In the past years, different numerical methods to estimate the multifractal spectrum have been proposed. These methods could be classified into those that originated from the wavelet analysis and others from numerical approximations like the Multifractal Detrended Fluctuation Analysis (MFDFA), proposed by Kantelhardt and Stanley. Recently, S. Jaffard and co-work

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5

MURGUÍA, J. S., M. MEJÍA CARLOS, C. VARGAS-OLMOS, M. T. RAMÍREZ-TORRES, and H. C. ROSU. "WAVELET MULTIFRACTAL DETRENDED FLUCTUATION ANALYSIS OF ENCRYPTION AND DECRYPTION MATRICES." International Journal of Modern Physics C 24, no. 09 (2013): 1350069. http://dx.doi.org/10.1142/s0129183113500691.

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In this paper, we study in detail the multifractal features of the main matrices of an encryption system based on a rule-90 cellular automaton. For this purpose, we consider the scaling method known as the wavelet transform multifractal detrended fluctuation analysis (WT-MFDFA). In addition, we analyze the multifractal structure of the matrices of different dimensions, and find that there are minimal differences in all the examined multifractal quantities such as the multifractal support, the most frequent singularity exponent, and the generalized Hurst exponent.

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6

Zhao, Tongzhou, Liang Wu, Dehua Li, and Yiming Ding. "Multifractal Analysis of Hydrologic Data Using Wavelet Methods and Fluctuation Analysis." Discrete Dynamics in Nature and Society 2017 (2017): 1–18. http://dx.doi.org/10.1155/2017/3148257.

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We study the multifractal properties of water level with a high-frequency 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 (MF-DFA). The dataset contains more than two million records from 10 observation sites at a northern China river. The multiscale behaviour is observed in this time series, which indicates the multifractality. This multifractality is detected via multiscale diagram. Then we focus on the multifractal analysis using MF-DFA and

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7

Oral, Emrah, and Gazanfer Unal. "Modeling and forecasting multifractal wavelet scale: Western market versus eastern market." International Journal of Modern Physics C 29, no. 11 (2018): 1850109. http://dx.doi.org/10.1142/s0129183118501097.

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This leading primary study is about modeling multifractal wavelet scale time series data using multiple wavelet coherence (MWC), continuous wavelet transform (CWT) and multifractal detrended fluctuation analysis (MFDFA) and forecasting with vector autoregressive fractionally integrated moving average (VARFIMA) model. The data is acquired from Yahoo Finances!, which is composed of 1671 daily stock market of eastern (NIKKEI, TAIEX, KOPSI) and western (SP500, FTSE, DAX) markets. Once the co-movement dependencies on time-frequency space are determined with MWC, the coherent data is extracted out o

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8

Ibrahim Mahmoud, Masharif Mahmoud, Anouar Ben Mabrouk, and Mohsin Hassan Abdallah Hashim. "Wavelet multifractal modeling and prediction of transmembrane proteins series." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 06 (2016): 1650044. http://dx.doi.org/10.1142/s0219691316500442.

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We propose in this paper to study the multifractal properties of a special case of biological series, such as the transmembrane proteins. We prove that such series has a multifractal structure allowing their modeling by means of multifractal models issued from wavelet bases to be efficient. We apply the developed method to a numerical example in order to show its efficiency.

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9

Chen, Chang Zheng, Yu Zhang, Quan Gu, and Yan Ling Gu. "Wind Turbine Generator Fault Detection by Wavelet-Based Multifractal Analysis." Advanced Materials Research 644 (January 2013): 346–49. http://dx.doi.org/10.4028/www.scientific.net/amr.644.346.

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It is difficult to obtain the obvious fault features of wind turbine, because the vibration signal of them are non-linear and non-stationary. To solve the problem, a multifractal analysis based on wavelet is presented in this research. The real signals of 1.5 MW wind turbine are studied by multifractal theory. The incipient fault features are extracted from the original signal. Using the Wavelet Transform Modulo Maxima Method, the multifractal was obtained. The results show that fault features of high rotational frequency of wind turbine are different from low rotational frequency, and the com

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10

AOUIDI, JAMIL, and ANOUAR BEN MABROUK. "A WAVELET MULTIFRACTAL FORMALISM FOR SIMULTANEOUS SINGULARITIES OF FUNCTIONS." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 01 (2013): 1450009. http://dx.doi.org/10.1142/s021969131450009x.

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In this paper, a wavelet multifractal analysis is developed which permits to characterize simultaneous singularities for a vector of functions. An associated multifractal formalism is introduced and checked for the case of functions involving self similar aspects.

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11

Gamboa, Fabrice, and Jean-Michel Loubes. "Wavelet estimation of a multifractal function." Bernoulli 11, no. 2 (2005): 221–46. http://dx.doi.org/10.3150/bj/1116340292.

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12

Turiel, Antonio, and Néstor Parga. "Multifractal Wavelet Filter of Natural Images." Physical Review Letters 85, no. 15 (2000): 3325–28. http://dx.doi.org/10.1103/physrevlett.85.3325.

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13

Xiong, Gang, Shuning Zhang, Huichang Zhao, and Caiping Xi. "Wavelet leaders-based multifractal spectrum distribution." Nonlinear Dynamics 76, no. 2 (2014): 1225–35. http://dx.doi.org/10.1007/s11071-013-1206-z.

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14

Barral, Julien, and Stéphane Seuret. "Wavelet series built using multifractal measures." Comptes Rendus Mathematique 341, no. 6 (2005): 353–56. http://dx.doi.org/10.1016/j.crma.2005.06.029.

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15

YALAMOVA, ROSSITSA. "EMPIRICAL TESTING OF MULTIFRACTALITY OF FINANCIAL TIME SERIES BASED ON WTMM." Fractals 17, no. 03 (2009): 323–32. http://dx.doi.org/10.1142/s0218348x09004508.

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The multifractal spectrum calculated with wavelet transform modulus maxima (WTMM) provides information on the higher moments of market returns distribution and the multiplicative cascade of volatilities. This paper applies a wavelet based methodology for calculation of the multifractal spectrum of financial time series. WTMM methodology provides a better measure of risk changes compared to the structure function approach. It is well founded in applied mathematics and physics with little popularity among finance researchers.

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16

DOĞANGÜN, ITIR, and GAZANFER ÜNAL. "MULTIFRACTAL BEHAVIOR IN PRECIOUS METALS: WAVELET COHERENCY AND FORECASTING BY VARIMA AND V-FARIMA MODELS." Annals of Financial Economics 14, no. 02 (2019): 1950006. http://dx.doi.org/10.1142/s2010495219500064.

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We introduce a new approach to improve the forecasting performance by investigating the multifractal features and the dynamic correlations of return on spot prices of precious metals, namely, gold and platinum. The Hölder exponent of multifractal time series is employed to detect the critical fluctuations during the financial crises through measuring the multifractal behavior. We also consider co-movement of Hölder exponents and forecast the Hölder exponents of multifractal precious metal time series on coherent time periods. The results indicate that forecasting of multiple wavelet coherence

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17

Nicollet, M., A. Lemarchand, and G. M. L. Dumas. "Wavelets Transform of a Multifractal Measure in a Cool Flame Experiment." Fractals 05, no. 01 (1997): 35–46. http://dx.doi.org/10.1142/s0218348x9700005x.

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In order to characterize the chaotic variations of the cool flame temperature observed during the oxidation of a hydrocarbon at low temperature and under non-homogeneous conditions, we perform multifractal analyses of different measures. In the cool flame localization domain, the singularity spectrum obtained for the visited temperature histogram is comparable to the spectrum deduced from a wavelet transform. In the cool flame propagation domain where the temperature histogram is too narrow to be analyzed, the wavelet transform allows us to prove the multifractal character of the chaos observe

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18

Murguı́a, J. S., and Jesús Urı́as. "On the wavelet formalism for multifractal analysis." Chaos: An Interdisciplinary Journal of Nonlinear Science 11, no. 4 (2001): 858–63. http://dx.doi.org/10.1063/1.1423282.

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19

Morales, Carlos J., and Eric D. Kolaczyk. "Wavelet-Based Multifractal Analysis of Human Balance." Annals of Biomedical Engineering 30, no. 4 (2002): 588–97. http://dx.doi.org/10.1114/1.1478082.

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20

Ghez, J. M., and S. Vaienti. "On the wavelet analysis for multifractal sets." Journal of Statistical Physics 57, no. 1-2 (1989): 415–20. http://dx.doi.org/10.1007/bf01023655.

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21

Esser, Céline, and Stéphane Jaffard. "Divergence of wavelet series: A multifractal analysis." Advances in Mathematics 328 (April 2018): 928–58. http://dx.doi.org/10.1016/j.aim.2018.02.010.

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22

BEN SLIMANE, MOURAD, and BORHEN HALOUANI. "MULTIFRACTAL FORMALISM OF OSCILLATING SINGULARITIES FOR RANDOM WAVELET SERIES." Fractals 23, no. 02 (2015): 1550005. http://dx.doi.org/10.1142/s0218348x1550005x.

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The oscillating multifractal formalism is a formula conjectured by Jaffard expected to yield the spectrum d(h, β) of oscillating singularity exponents from a scaling function ζ(p, s'), for p > 0 and s' ∈ ℝ, based on wavelet leaders of fractional primitives f-s' of f. In this paper, using some results from Jaffard et al., we first show that ζ(p, s') can be extended on p ∈ ℝ to a function that is concave with respect to p ∈ ℝ and independent on orthonormal wavelet bases in the Schwartz class. We also establish its concavity with respect to s' when p > 0. Then, we prove that, under some ass

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23

Piñuela, J. A., D. Andina, K. J. McInnes, and A. M. Tarquis. "Wavelet analysis in a structured clay soil using 2-D images." Nonlinear Processes in Geophysics 14, no. 4 (2007): 425–34. http://dx.doi.org/10.5194/npg-14-425-2007.

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Abstract. The spatial variability of preferential pathways for water and chemical transport in a field soil, as visualized through dye infiltration experiments, was studied by applying multifractal and wavelet transform analysis (WTA). After dye infiltration into a 4 m² plot located on a Vertisol soil near College Station, Texas, horizontal planes in the subsoil were exposed at 5 cm intervals, and dye stain patterns were photographed. Box-counting methods and WTA were applied to all of the 16 digitalized high-resolution dye images and to the dye-mass image obtained merging all sections. The we

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24

ZHANG, ZHIBO, ENYUAN WANG, YINGHUA ZHANG, et al. "ANALYSIS ON THE TIME-FREQUENCY CHARACTERISTICS OF ULTRASONIC WAVEFORM OF COAL UNDER UNIAXIAL LOADING." Fractals 27, no. 06 (2019): 1950100. http://dx.doi.org/10.1142/s0218348x19501007.

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Ultrasonic receiving wave can reflect physical properties and damage degree of coal samples. Therefore, it is of great significance to deeply study the parameters of ultrasonic. In this paper, time-domain characteristics of receiving wave are analyzed systematically, which present good correlation with stress. The frequency spectrum of receiving wave is obtained using Fast Fourier Transform (FFT), and peak frequency and centroid frequency are calculated. During the entire loading process, peak frequency fluctuates around 110[Formula: see text]kHz, but corresponding centroid frequency decreases

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25

Holdsworth, Amber M., Nicholas K. R. Kevlahan, and David J. D. Earn. "Multifractal signatures of infectious diseases." Journal of The Royal Society Interface 9, no. 74 (2012): 2167–80. http://dx.doi.org/10.1098/rsif.2011.0886.

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Incidence of infection time-series data for the childhood diseases measles, chicken pox, rubella and whooping cough are described in the language of multifractals. We explore the potential of using the wavelet transform maximum modulus (WTMM) method to characterize the multiscale structure of the observed time series and of simulated data generated by the stochastic susceptible-exposed-infectious-recovered (SEIR) epidemic model. The singularity spectra of the observed time series suggest that each disease is characterized by a unique multifractal signature, which distinguishes that particular

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26

Zhang, Qiaoyan, Lixian Wang, Shang Jin, Xiaozhen Hao, and Zhenlong Chen. "Asymmetric Multifractal Analysis of Rebar Futures and Spot Market in China." Journal of Advanced Computational Intelligence and Intelligent Informatics 24, no. 3 (2020): 282–92. http://dx.doi.org/10.20965/jaciii.2020.p0282.

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In this study, a wavelet denoising method is first used to eliminate the influence of noise. Then, an overlapping smooth window technique is introduced into the asymmetric multifractal detrended cross-correlation analysis method, which was combined with the multiscale multifractal analysis method, resulting in the proposed asymmetric multiscale multifractal detrended cross-correlation analysis method. This method not only remedies the pseudo-fluctuation defect of the traditional method, but also explores the asymmetric multifractal cross-correlation between China’s rebar futures and spot marke

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27

Puchalski, Andrzej, and Iwona Komorska. "Data-driven monitoring of the gearbox using multifractal analysis and machine learning methods." MATEC Web of Conferences 252 (2019): 06006. http://dx.doi.org/10.1051/matecconf/201925206006.

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Data-driven diagnostic methods allow to obtain a statistical model of time series and to identify deviations of recorded data from the pattern of the monitored system. Statistical analysis of time series of mechanical vibrations creates a new quality in the monitoring of rotating machines. Most real vibration signals exhibit nonlinear properties well described by scaling exponents. Multifractal analysis, which relies mainly on assessing local singularity exponents, has become a popular tool for statistical analysis of empirical data. There are many methods to study time series in terms of thei

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28

Pavlov, Alexyi Nikolaevich, and Vadim Semenovich Anishchenko. "Multifractal Analysis of Signals Based on Wavelet-Transform." Izvestiya of Saratov University. New series. Series: Physics 7, no. 1 (2007): 3–25. http://dx.doi.org/10.18500/1817-3020-2007-7-1-3-25.

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29

Peng, Zhike. "WAVELET MULTIFRACTAL SPECTRUM: APPLICATION TO ANALYSIS VIBRATION SIGNALS." Chinese Journal of Mechanical Engineering 38, no. 08 (2002): 59. http://dx.doi.org/10.3901/jme.2002.08.059.

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30

MARUYAMA, Fumio, Kenji KAI, and Hiroshi MORIMOTO. "Wavelet-Based Multifractal Analysis on Climatic Regime Shifts." Journal of the Meteorological Society of Japan. Ser. II 93, no. 3 (2015): 331–41. http://dx.doi.org/10.2151/jmsj.2015-018.

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31

Shimizu, Yu, Markus Barth, Christian Windischberger, Ewald Moser, and Stefan Thurner. "Wavelet-based multifractal analysis of fMRI time series." NeuroImage 22, no. 3 (2004): 1195–202. http://dx.doi.org/10.1016/j.neuroimage.2004.03.007.

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32

Maruyama, Fumio. "The solar activity by wavelet-based multifractal analysis." NRIAG Journal of Astronomy and Geophysics 5, no. 2 (2016): 301–5. http://dx.doi.org/10.1016/j.nrjag.2016.10.003.

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33

Bayart, Frédéric. "Convergence and divergence of wavelet series: multifractal aspects." Proceedings of the London Mathematical Society 119, no. 2 (2019): 547–78. http://dx.doi.org/10.1112/plms.12239.

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34

MUZY, J. F., E. BACRY, and A. ARNEODO. "THE MULTIFRACTAL FORMALISM REVISITED WITH WAVELETS." International Journal of Bifurcation and Chaos 04, no. 02 (1994): 245–302. http://dx.doi.org/10.1142/s0218127494000204.

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The multifractal formalism originally introduced for singular measures is revisited using the wavelet transform. This new approach is based on the definition of partition functions from the wavelet transform modulus maxima. We demonstrate that the f(α) singularity spectrum can be readily determined from the scaling behavior of these partition functions. We show that this method provides a natural generalization of the classical box-counting techniques to fractal functions (the wavelets actually play the role of “generalized boxes”). We report on a systematic comparison between this alternative

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35

STRUZIK, ZBIGNIEW R. "DETERMINING LOCAL SINGULARITY STRENGTHS AND THEIR SPECTRA WITH THE WAVELET TRANSFORM." Fractals 08, no. 02 (2000): 163–79. http://dx.doi.org/10.1142/s0218348x00000184.

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We present a robust method of estimating the effective strength of singularities (the effective Hölder exponent) locally at an arbitrary resolution. The method is motivated by the multiplicative cascade paradigm, and implemented on the hierarchy of singularities revealed with the wavelet transform modulus maxima (WTMM) tree. In addition, we illustrate the direct estimation of the scaling spectrum of the effective singularity strength, and we link it to the established partition function-based multifractal formalism. We motivate both the local and the global multifractal analysis by showing exa

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36

Li, Jiming, Xinyan Ma, Meng Zhao, and Xuezhen Cheng. "A Novel MFDFA Algorithm and Its Application to Analysis of Harmonic Multifractal Features." Electronics 8, no. 2 (2019): 209. http://dx.doi.org/10.3390/electronics8020209.

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A power grid harmonic signal is characterized as having both nonlinear and nonstationary features. A novel multifractal detrended fluctuation analysis (MFDFA) algorithm combined with the empirical mode decomposition (EMD) theory and template movement is proposed to overcome some shortcomings in the traditional MFDFA algorithm. The novel algorithm is used to study the multifractal feature of harmonic signals at different frequencies. Firstly, the signal is decomposed and the characteristics of wavelet transform multiresolution analysis are employed to obtain the components at different frequenc

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37

CARDO, ROMINA, and ALVARO CORVALÁN. "NON-CONCAVE MULTIFRACTAL SPECTRA WITH WAVELET LEADERS PROJECTION OF SIGNALS WITH AND WITHOUT CHIRPS." Fractals 17, no. 03 (2009): 311–22. http://dx.doi.org/10.1142/s0218348x09004338.

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The multifractal spectrum has been revealed recently as a very useful tool for the analysis of signals, especially in those coming from the measurement of physical variables in chaotic or critical systems with multifractal structure, and in which many phenomena interact in multiple scales. In addition, in this context, the presence of singularities of rapid oscillation, chirps, is frequently difficult to handle. In this work we propose a way for using "wavelet leaders", avoiding the Legendre transform, for developing a new method capable of recognizing if a non-concave multifractal spectrum ar

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38

Pavlov, Alexey N., Arkady S. Abdurashitov, Olga N. Pavlova, et al. "Hidden stage of intracranial hemorrhage in newborn rats studied with laser speckle contrast imaging and wavelets." Journal of Innovative Optical Health Sciences 08, no. 05 (2015): 1550041. http://dx.doi.org/10.1142/s1793545815500418.

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Using the laser speckle contrast imaging and wavelet-based analyses, we investigate a latent (a "hidden") stage of the development of intracranial hemorrhages (ICHs) in newborn rats. We apply two measures based on the continuous wavelet-transform of blood flow velocity in the sagittal sinus, namely, the spectral energy in distinct frequency ranges and a multiscality degree characterizing complexity of experimental data. We show that the wavelet-based multifractal formalism reveals changes in the cerebrovascular blood flow at the development of ICH.

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39

Decoster, N., S. G. Roux, and A. Arnéodo. "A wavelet-based method for multifractal image analysis. II. Applications to synthetic multifractal rough surfaces." European Physical Journal B 15, no. 4 (2000): 739–64. http://dx.doi.org/10.1007/s100510051179.

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40

Peng, Z., Ying He, Dan Guo, and Fu Lei Chu. "Wavelet Multifractal Approaches for Singularity Analysis of Vibration Signals." Key Engineering Materials 245-246 (July 2003): 565–70. http://dx.doi.org/10.4028/www.scientific.net/kem.245-246.565.

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41

Leonarduzzi, Roberto F., María E. Torres, and Patrice Abry. "Scaling range automated selection for wavelet leader multifractal analysis." Signal Processing 105 (December 2014): 243–57. http://dx.doi.org/10.1016/j.sigpro.2014.06.002.

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42

Riedi, R. H., M. S. Crouse, V. J. Ribeiro, and R. G. Baraniuk. "A multifractal wavelet model with application to network traffic." IEEE Transactions on Information Theory 45, no. 3 (1999): 992–1018. http://dx.doi.org/10.1109/18.761337.

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43

Wendt, Herwig, Stéphane G. Roux, Stéphane Jaffard, and Patrice Abry. "Wavelet leaders and bootstrap for multifractal analysis of images." Signal Processing 89, no. 6 (2009): 1100–1114. http://dx.doi.org/10.1016/j.sigpro.2008.12.015.

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44

Ibarra-Junquera, V., J. S. Murguía, P. Escalante-Minakata, and H. C. Rosu. "Application of multifractal wavelet analysis to spontaneous fermentation processes." Physica A: Statistical Mechanics and its Applications 387, no. 12 (2008): 2802–8. http://dx.doi.org/10.1016/j.physa.2008.01.083.

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45

Pavlov, A. N., A. S. Abdurashitov, O. A. Sindeeva, et al. "Characterizing cerebrovascular dynamics with the wavelet-based multifractal formalism." Physica A: Statistical Mechanics and its Applications 442 (January 2016): 149–55. http://dx.doi.org/10.1016/j.physa.2015.09.007.

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46

Jaffard, Stéphane, and Clothilde Mélot. "Wavelet Analysis of Fractal Boundaries. Part 2: Multifractal Analysis." Communications in Mathematical Physics 258, no. 3 (2005): 541–65. http://dx.doi.org/10.1007/s00220-005-1353-2.

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47

Wirsing, Karlton, and Lamine Mili. "Multifractal analysis of geomagnetically induced currents using wavelet leaders." Journal of Applied Geophysics 173 (February 2020): 103920. http://dx.doi.org/10.1016/j.jappgeo.2019.103920.

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48

Ord, Alison, Bruce Hobbs, Greg Dering, and Klaus Gessner. "Nonlinear analysis of natural folds using wavelet transforms and recurrence plots." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2126 (2018): 20170257. http://dx.doi.org/10.1098/rsta.2017.0257.

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Three-dimensional models of natural geological fold systems established by photogrammetry are quantified in order to constrain the processes responsible for their formation. The folds are treated as nonlinear dynamical systems and the quantification is based on the two features that characterize such systems, namely their multifractal geometry and recurrence quantification. The multifractal spectrum is established using wavelet transforms and the wavelet transform modulus maxima method, the generalized fractal or Renyi dimensions and the Hurst exponents for longitudinal and orthogonal sections

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49

Serio, M., L. Bergamasco, M. Onorato, et al. "Multifractality of Air Transmittency at Small Time Scales." Fractals 06, no. 02 (1998): 159–70. http://dx.doi.org/10.1142/s0218348x98000201.

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The fluctuations of air transmittency over small time scales (20–500 s), in the presence and the absence of fog, are analyzed from different points of view: Fourier and wavelet transforms, multiscaling exponents, the multifractal spectrum and structure functions. All results indicate a multifractal structure associated with intermittency, and whose characteristics do not seem to change with the level of visibility. The origin of this multifractality, whether statistical or dynamical, cannot be established with certainty: there are however indications in favor of the presence of chaos.

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50

Chen, Chang Zheng, Ping Ping Pan, Qiang Meng, and Yan Ling Gu. "Wind Turbine Gearbox Fault Detection Based on Multifractal Analysis." Advanced Materials Research 644 (January 2013): 312–16. http://dx.doi.org/10.4028/www.scientific.net/amr.644.312.

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Abstract:

The presence of irregularity in periodical vibration signals usually indicates the occurrence of wind turbine gearbox faults. Unfortunately, detecting the incipient faults is a difficult job because they are rather weak and often interfered by heavy noise and higher level macro-structural vibrations. Therefore, a proper signal processing method is necessary. We used the wavelet-based multifractal method to extract the impulsive features buried in noisy vibration signals. We first calculated the wavelet transform modulo maxima lines from the real vibration signals, then, obtained the singularit

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