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1

Unveiling the multifractal signatures of rainfall temporal organization: new insights into the complexity assessment of precipitation patterns over northeast Algeria

Taouti Mohamed Bachir, Chettih Mohamed

Acta Geophysica

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2026

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vol. 74, no. 3

art. no. 188, s. 1--23

EN

In recent years, the analysis of rainfall temporal structure becomes a fundamental area of research for hydrologists seeking to understand hydro-climatic variability, particularly in regions affected by climate change. In this context, the present study provides a comprehensive analysis of multifractal properties of temporal fluctuations in daily rainfall series measured in northeast Algeria, using the multifractal detrended fluctuation analysis (MF-DFA) method. The analysis of rainfall time series (1981-2019) across a wide range of time scales from 80 to 800 days shows the presence of a multiple scaling property that characterizes a significant multifractal behavior. The estimation of multifractal parameters leads to an average value of a0 = 0.642 ± 0.041 for the central Holder exponent, showing a persistence process reflecting long-term correlation dynamics. Furthermore, the distribution of multifractal spectrum width (Aa) values over a wide range (0.457 < Aa < 1.324) exhibits a significant heterogeneity in the multifractality degree between the studied stations. This research develops a rigorous integrated methodological analysis that explicitly links multifractal signatures to the geo-climatic factors controlling the complexity of precipitation patterns in the northeastern part of Algeria. The correlation analysis between these parameters reveals that sub-humid coastal areas exhibit greater structural complexity in rainfall variability than semiarid inland regions. These relationships suggest a new complexity-based framework as a robust physical approach for precipitation regionalization in Mediterranean environments. The results of this study demonstrate that multifractal analysis provides a solid framework for unveiling the complexity of rainfall dynamics, which provides useful information for better water resource management.

2

The mutual singularity of multifractal measures for some non-regular Moran fractals

Selmi Bilel

Bulletin of the Polish Academy of Sciences. Mathematics

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2021

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Vol. 69, no. 1

21--35

EN

We study the multifractal dimension functions of the Moran measure associated with a homogeneous (non-regular) Moran fractal and show that the multifractal measures are mutually singular when the multifractal Hausdorff and packing functions differ. As an application, we give concrete examples related to these concepts.

3

Multifractal analysis vehicle’s in-use speed profile for application in driving cycles

Puchalski A., Komorska I., Ślęzak M., Wiśniowski P.

Eksploatacja i Niezawodność

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2018

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Vol. 20, no. 2

177--181

EN

Time signals recorded by the on-board diagnostic system (OBD), describing the manner of vehicle’s movement in actual road conditions show non-stationarity and non-linearity, as well as statistical multiscalarity. In practice, it means that the analysis of registered time series requires modelling of non-linear phenomena. The aim of this study was to examine the nature of the vehicle speed profile in actual road conditions with the method of multifractal analysis. A number of studies indicates that the driving tests applied for many years have not been representative for the actual operating conditions of vehicles. For both the new Worldwide Harmonised Light duty Test Cycle (WLTC), a worldwide harmonised procedure of light vehicle testing, as well as in actual urban driving conditions along the measuring route, being subject to empirical research, confirmation of strong multifractal properties of the recorded vehicle speed time series have been obtained.

PL

Sygnały czasowe rejestrowane przez system diagnostyki pokładowej OBD i opisujące sposób ruchu pojazdu w rzeczywistych warunkach drogowych, wykazują niestacjonarność i nieliniowość oraz statystyczną wieloskalowość. W praktyce oznacza to, że analiza zarejestrowanych szeregów czasowych wymaga modelowania zjawisk nieliniowych. Celem niniejszej pracy było zbadanie charakteru profilu prędkości pojazdów w rzeczywistych warunkach drogowych metodą analizy multifraktalnej. Szereg badań wskazuje, że stosowane przez wiele lat testy jezdne nie były reprezentatywne dla rzeczywistych warunków eksploatacyjnych pojazdów. Zarówno dla nowego cyklu jezdnego WLTC, światowej zharmonizowanej procedury badań pojazdów lekkich jak i w rzeczywistych warunkach drogowych jazdy miejskiej na trasie pomiarowej, będącej przedmiotem badań doświadczalnych uzyskano potwierdzenie silnych własności multifraktalnych rejestrowanych szeregów czasowych prędkości pojazdu.

4

Analiza ruchu w sieci komputerowej w oparciu o modele multifraktalne

Burdacki M., Dymora P., Mazurek M.

Zeszyty Naukowe Politechniki Rzeszowskiej. Elektrotechnika

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2017

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z. 36 [296], nr 3

43--52

PL

Celem badań była analiza ruchu w sieci komputerowej z wykorzystaniem wybranych modeli multifraktalnych. W części teoretycznej omówiono podstawowe zagadnienia związane z oprogramowaniem zbierającym dane w sieci komputerowej, klasyfikacją przebiegów czasowych przy użyciu wykładnika Hurst’a. Opisano metody wykorzystane do wyznaczenia widm multifraktalnych. W części badawczej dokonano analizy przepływu ruchu w sieci komputerowej na podstawie liczby pakietów oraz prędkości przesyłania danych. Wykonano analizę wykładnika Hurst’a wyznaczanego dla poszczególnych przebiegów czasowych. Dokonano analizy widm multifraktalnych utworzonych dla badanych rodzajów ruchu sieciowego.

EN

The aim of this work was computer network traffic analysis. Theoretical part describes issues referring to network traffic capture software, time-series classification using Hurst exponent and multifractal spectrum creating methods. In research part was made an analysis of network traffic based on a number of packets and data transfer speed. It was also made a Hurst exponent analysis and a multifractal spectrum analysis for each type of analyzed network traffic. After the research it was possible to draw conclusions about characteristic of analyzed network traffic.

5

Multifractal characterization of epitaxial silicon carbide on silicon

Ţălu Ş., Stach S., Ramazanov S., Sobola D., Ramazanov G.

Materials Science Poland

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2017

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Vol. 35, No. 3

539--547

EN

The purpose of this study was to investigate the topography of silicon carbide films at two steps of growth. The topography was measured by atomic force microscopy. The data were processed for extraction of information about surface condition and changes in topography during the films growth. Multifractal geometry was used to characterize three-dimensional micro- and nano-size features of the surface. X-ray measurements and Raman spectroscopy were performed for analysis of the films composition. Two steps of morphology evolution during the growth were analyzed by multifractal analysis. The results contribute to the fabrication of silicon carbide large area substrates for micro- and nanoelectronic applications.

6

Cylinder-to-cylinder and cycle-to-cycle variation in combustion process in radial aircraft engine

Gęca M.

Combustion Engines

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2017

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R. 56, nr 1

77--83

EN

Cycle-to-cycle variation in combustion in a single cylinder of a radial engine has an impact on that in others and the entire engine. Steady- and transient-state engine operation was investigated, and the transient states were generated by cyclic changes in the timing of fuel injection to a given cylinder, having others operated on the same mixture composition. The measurement of pressure in the combustion chamber allowed for specifying indicated mean effective pressure (IMEP) in all cycles. The time series of IMEP were studied with mathematical techniques of non-linear dynamics, i.e. a wavelet transform and a multifractal analysis. Controlled disturbances in mixture composition in a single cylinder can have an impact on certain cylinders only. Cylinders 3, 5, 7 and 9 are most responsive to such disturbances, which proves their least cycle-to-cycle variation in combustion.

7

Music Performers Classification by Using Multifractal Features : A Case Study

Reljin N., Pokrajac D.

Archives of Acoustics

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2017

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Vol. 42, No. 2

223--233

EN

In this paper, we investigated the possibility to classify different performers playing the same melodies at the same manner being subjectively quite similar and very difficult to distinguish even for musically skilled persons. For resolving this problem we propose the use of multifractal (MF) analysis, which is proven as an efficient method for describing and quantifying complex natural structures, phenomena or signals. We found experimentally that parameters associated to some characteristic points within the MF spectrum can be used as music descriptors, thus permitting accurate discrimination of music performers. Our approach is tested on the dataset containing the same songs performed by music group ABBA and by actors in the movie Mamma Mia. As a classifier we used the support vector machines and the classification performance was evaluated by using the four-fold cross-validation. The results of proposed method were compared with those obtained using mel-frequency cepstral coefficients (MFCCs) as descriptors. For the considered two-class problem, the overall accuracy and F-measure higher than 98% are obtained with the MF descriptors, which was considerably better than by using the MFCC descriptors when the best results were less than 77%.

8

Techniki budowy nieliniowych modeli diagnostycznych z wykorzystaniem szeregów czasowych drgań mechanicznych

Puchalski A.

Przegląd Mechaniczny

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2016

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nr 10

33--36

PL

W artykule omówiono zastosowanie metod analizy nieliniowych szeregów czasowych drgań do oceny ich wartości informacyjnej do celów diagnostycznych układów mechanicznych na przykładzie zespołów napędowych w pojazdach. Trzy techniki detekcji oraz ekstrakcji sygnałów obejmowały analizę w zrekonstruowanej, zanurzonej przestrzeni fazowej szeregu czasowego, prowadzącą do segmentacji sygnału w zakresie dynamiki chaotycznej i losowej, analizę multifraktalną oraz analizę rozkładów stabilnych prawdopodobieństwa.

EN

The paper discusses the use of methods of nonlinear time series analysis of vibrations to assess their informational value for the diagnostic purposes of the mechanical systems on the example of vehicle powertrain. Three detection and extraction techniques of signals included an analysis of the reconstructed embedded phase space of time series which leads to the segmentation of the signal in terms of the chaotic and random dynamics, multifractal analysis and the analysis of alpha-stable probability distributions.

9

Multifractal characteristics of titanium nitride thin films

Talu S., Stach S., Valedbagi S., Bavadi R., Elahi S. M., Talu M.

Materials Science Poland

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2015

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Vol. 33, No. 3

541--548

EN

The study presents a multi-scale microstructural characterization of three-dimensional (3-D) micro-textured surface of titanium nitride (TiN) thin films prepared by reactive DC magnetron sputtering in correlation with substrate temperature variation. Topographical characterization of the surfaces, obtained by atomic force microscopy (AFM) analysis, was realized by an innovative multifractal method which may be applied for AFM data. The surface micromorphology demonstrates that the multifractal geometry of TiN thin films can be characterized at nanometer scale by the generalized dimensions Dq and the singularity spectrum f(α). Furthermore, to improve the 3-D surface characterization according with ISO 25178-2:2012, the most relevant 3-D surface roughness parameters were calculated. To quantify the 3 D nanostructure surface of TiN thin films a multifractal approach was developed and validated, which can be used for the characterization of topographical changes due to the substrate temperature variation.

10

Operating system efficiency evaluation on the base of measurements analysis with the use of non-extensive statistics elements

Dymora P., Mazurek M., Żelazny K.

Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica

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2014

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Vol. 14, no. 3

65--75

EN

The major goal of this article was to evaluate the efficiency of Linux operating system using statistical self-similarity and multifractal analysis. In order to collect the necessary data, thetools available in Linux such as vmstat, top and iostat were used. The measurement data collected witht hose tools had to be converted into a format acceptable by applications which analyze statistical selfsimilarity and multifractal spectra. Measurements collected while using the MySQL database systemin a host operating system were therefore analyzed with the use of statistical self-similarity and allowedto determine the occurrence of long-range dependencies. Those dependencies were analyzed with theuse of adequately graduated diagrams. Multifractal analysis was conducted with the help of FracLab application. Two methods were applied to determine the multifractal spectra. The obtained spectra were analyzed in order to establish the multifractal dependencies.

11

Fractal Format for Bitmap Images

Siwocha A., Cader A., Kolibabka M., Krupski M.

Journal of Applied Computer Science Methods

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2012

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Vol. 4 No. 2

41--54

EN

The conception of proposed recording format is the example of the theoretical and practical application of the FBS method, which was precisely described in thesis [18,19,20]. The foundation of the presented recording format is the use of a new method of fractal basis splines (FB-splines), which allows the reconstruction of complex geometric structures with the properties of fractals. Fractral basis splines method is based on the use of non-local characteristics to describe the interpolation nodes. With that the one-parameter family of fractal curves is used as the basic approximating elements.

12

Multifractal analysis of laser Doppler flowmetry signals: partition function and generalized dimensions of data recorded before and after local heating

Humeau A., Buard B., Rousseau D., Chapeau-Blondeau F., Abraham P.

Biocybernetics and Biomedical Engineering

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2012

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Vol. 32, no. 1

17-26

EN

Laser Doppler flowmetry (LDF) signals - that reflect the peripheral cardiovascular system - are now widespread in blood microcirculation research. Over the last few years, the central cardiovascular system has been the subject of many fractal and multifractal works. However, only very few multifractal studies of LDF signals have been published. Such multifractal analyses have shown that LDF data can be weakly multifractal but the origin of such characteristics are still unknown. We therefore herein propose a multifractal analysis of LDF signals recorded on the forearm of twelve healthy subjects, before and after skin local heating. The results show that the partition functions for all the signals have power-law characteristics. Moreover, generalized dimensions present very few variations with q for the signals recorded before heating; these variations are larger 20 minutes after local heating. Physiological activities may therefore play a role in the weak multifractal properties of LDF data.

13

Predicting properties of PVD and CVD coatings based on fractal quantities describing their surface

Kwaśny W.

Journal of Achievements in Materials and Manufacturing Engineering

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2009

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Vol. 37, nr 2

125-192

EN

Purpose: The goal of the presented study was to develop a methodology giving a possibility to predict functional properties of coatings obtained in the PVD and CVD processes on tool materials, based on fractal- and multi-fractal quantities describing their surface. Design/methodology/approach: Effect of process type and deposition conditions on structure and shape of surface, as well as mechanical and service properties of the obtained coatings were determined. Methodology and detailed description of coatings topography obtained in PVD and CVD process on tool materials, including use of the fractal- and multi-fractal geometry based on images obtained on the atomic forces microscope were worked out. Relationships between fractal- and multi-fractal quantities and their mechanical and service properties were determined. Findings: The investigation results confirmed the feasibility to predict hardness and erosion resistance of coatings obtained in the magnetron PVD process, as well as the service properties defined in the cutting ability test for coatings obtained in the arc PVD process and in the high-temperature CVD process, based on the surface fractal dimension Ds value for their surface topography. Practical implications: Determining significant quantitative correlations between fractal quantities defining coatings’ surfaces, as well as their service and/or mechanical properties provides the opportunity to predict their end-user properties. Originality/value: Fractal analysis was applied for characterization of PVD and CVD coatings surfaces.

14

Koncepcja fraktalnej kompresji obrazu

Siwocha A., Krupski M., Cader A.

Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

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2006

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T. 10, z. 3

155-166

PL

Zaawansowane metody kompresji obrazu traktują naturalne obrazy jako obiekty multifraktalne. W publikacji zaproponowano odmienną koncepcję kompresji fraktalnej obrazów, wykorzystującą nową metodę interpolacji fraktalnej. Opiera się ona na koncepcji fraktalnych splajnów bazowych (FB-splines) i jest modyfikacją klasycznej metody splajnów bazowych.

EN

The advanced methods of picture compression treat the natural pictures as multifractal objects. In this paper there is proposed a distinct conception of fractal picture compression, which uses a new method of fractal interpolation. This method is based on a conception of fractal base splines and it is a modification of conventional method of base splines.