Éditeur(s) : HAL CCSD Oxford University Press (OUP): Policy P - Oxford Open Option A Oxford University Press (OUP)
Résumé : International audience
It is well known that sedimentary rocks having same porosity can have very different pore size distribution. The pore distribution determines many characteristics of the rock, among which its transport properties are often the most useful. Multifractal analysis is a powerful tool that is increasingly used to characterize the pore space. In this study, we performed multifractal analysis of pore distribution on simulated sedimentary rocks using the relaxed bidisperse ballistic deposition model (RBBDM). The RBBDM can generate a 3-D structure of sedimentary rocks of variable porosity by tuning the fraction p of particles of two different sizes. We also performed multifractal analysis on two samples of real sedimentary rock to compare with the simulation studies. One sample, an oolitic limestone is of high porosity (40 per cent) while the other is a reefal carbonate of low porosity, around 7 per cent. 2-D sections of X-ray microtomographs of the real rocks were stacked sequentially to reconstruct the real rock specimens. Both samples show multifractal character. The results from analysis of real rock agree quite well with the simulated structure of low porosity. The simulated rock of high porosity showed a weak multifractal nature though the real rock sample of similar porosity was found to be strongly multifractal. We propose a ‘structure parameter’ ξ which is a function of porosity and the generalized dimensions, and controls the transport properties of the rock.
ISSN: 0956-540X

hal-01174142
https://hal.archives-ouvertes.fr/hal-01174142
DOI : 10.1093/gji/ggu417

Éditeur(s) : HAL CCSD
Résumé : 20 pp
We first analyze some atmospheric parameters measured in 2004 at the top of La Soufrière volcano: wind speed, pressure and temperature. Next, we study the stochastic process of the wind speed modulus which is of interest for prediction of pollution induced by the plume. We fit to the data various models : FARIMA, periodic trend plus multifractional Brownian noise, multifractal continuous cascades. The estimations show that they evoluate during some transition phases in response to environment changes. Thus, we finally suggest, for future works, some settings that should be more appropriate: time series with regime changes and stochastic processes in random environment.
https://hal.archives-ouvertes.fr/hal-00165572

hal-00165572
https://hal.archives-ouvertes.fr/hal-00165572
https://hal.archives-ouvertes.fr/hal-00165572/document
https://hal.archives-ouvertes.fr/hal-00165572/file/Windsouf_v11.pdf

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The objectives are to study and model the aggregate wind power fluctuations dynamics in the multifractal framework. We present here the analysis of aggregate power output sampled at 1 Hz during three years. We decompose the data into several Intrinsic Mode Functions (IMF) using Empirical Mode Decomposition (EMD). We use a new approach, arbitrary order Hilbert spectral analysis, a combination of EMD approach with Hilbert spectral analysis (or Hilbert Huang Transform) and the classical structure function analysis to extract the scaling exponents or multifractal spectrum $zeta(q)$: this function provides a full characterization of a process at all intensities and all scales. The application of both methods, i.e. structure function and arbitrary-order Hilbert spectral analyses, give similar results indicating that the aggregate power output from a wind farm, possesses intermittent and multifractal properties. In order to check this result, we generate stochastic simulations of a Multifractal Random Walk (MRW) using a log-normal stochastic equation. We show that the simulation results are fully compatible with the experimental results.
Physica A

hal-01527887
https://hal.archives-ouvertes.fr/hal-01527887
DOI : 10.1016/j.physa.2013.04.038

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
In this paper, we have presented a spectral and a multifractal analysis performed on 412 time series of wind speed data each of duration of 350 s and sampled at 20 Hz. The average spectrum for the wind speed displays a scaling behavior, in the inertial range, over two decades, with b ¼ 1:68 close to the Kolmogorov value À 5/3. A multifractal analysis has been motivated by the presence of scaling invariance in data set. Then we have considered their scaling properties in the framework of fully developed turbulence and multifractal cascades. The results obtained for wind speed confirm that the exponent scaling function z V ðqÞ is nonlinear and concave. This exponent characterizes the scaling functions in the inertial range indicating that the wind speed is intermittent and multifractal. Moreover the theoretical quadratic relation for lognormal multifractals is well fitted. We investigate the consequence for wind energy production: we generate stochastic simulations of a multifractal random walk, and using a power curve derived from experimental data, we generate the associated power time series. We show that, due to the saturation of the power curve for large speed values, when the input time series (turbulent wind speed) is multifractal, the output can be almost monofractal.
ISSN: 0167-6105

hal-01527886
https://hal.archives-ouvertes.fr/hal-01527886
DOI : 10.1016/j.jweia.2012.06.002

Éditeur(s) : HAL CCSD Intech
Résumé : International audience
The massive integration of sustainable energies into electrical grids (non-interconnectedor connected) is a major problem due to their stochastic character revealed by strongfluctuations at all scales. In this paper, the scaling behaviour or power law correlationsand the nature of scaling behaviour of sustainable resource data such as flow velocity,atmospheric wind speed, solar global solar radiation and sustainable energy such as,wind power output, are highlighted. For the first time, Fourier power spectral densitiesare estimated for each dataset. We show that the power spectrum densities obtained areclose to the 5/3 Kolmogorov spectrum. Furthermore, the multifractal and intermittentproperties of sustainable resource and energy data have been revealed by the concavityof the scaling exponent function. The proposed analysis frame allows a full descriptionof fluctuations of processes considered. A good knowledge of the dynamic of fluctua-tions is crucial to management of the integration of sustainable energies into a grid.
Sustainable Energy - Technological Issues, Applications and Case Studies

hal-01528087
https://hal.archives-ouvertes.fr/hal-01528087
DOI : 10.5772/106341

Éditeur(s) : HAL CCSD Oxford University Press (OUP)
Résumé : International audience
Several studies, both theoretical and experimental, show that sedimentary rocks have a fractal pore-grain interface. In this paper a computer simulated 3-D sedimentary rock structure generated by the Relaxed Ballistic Bidisperse Deposition Model (RBBDM), is investigated to characterize the micro structure of its pores. The pore volume and the rock-pore interface show the same fractal dimension indicating that the pore volume is a fractal. The two point density correlation is computed for the pore space and the results compare favourably with the range reported from experiments. An array of 2-D X-ray tomography micrograph sections of a real sedimentary rock, an oolitic limestone (pure calcite) from the Mondeville formation of Middle Jurassic age (Paris Basin, France), was used to generate a 3-D bitmap. The 3-D real rock sample generated in this manner, was analysed for similar studies as the simulated structure. The results were compared with those obtained from simulation. The simulation results agree qualitatively with the real rock sample. Diffusion through the connected pore space of the simulated structure was studied using a random walk algorithm and the results compared with the similar simulation study done on the 3-D oolitic limestone specimen. In both cases diffusion was found to be anomalous indicating that the sedimentary rock has a fractal geometry. The favourable comparability of results between the simulated and real rock supports the usefulness of the model of sedimentary rock generation which can be applicable to transport phenomena.
ISSN: 0956-540X

hal-00823061
https://hal.archives-ouvertes.fr/hal-00823061
DOI : 10.1093/gji/ggs084

Éditeur(s) : HAL CCSD American Geophysical Union
Résumé : International audience
This paper presents a multicontinuum approach to model fractal temporal scaling of catchment response in hydrological systems. The temporal scaling of discharge is quantified in frequency domain by the transfer function HðxÞ, which is defined as the ratio between the spectra of catchment response and recharge time series. The transfer function may scale with frequency x as HðxÞ x2b. While the classical linear and Dupuit models predict exponents of b52 and b51, observations indicate scalings with noninteger exponents b. Such behaviors have been described by multifractal models, which, however, often lack a relation to the medium characteristics. We revisit and extend the classical linear Dupuit aquifer models and discuss their physical meanings in the light of the resulting aquifer dynamics. On the basis of these classical models, we derive a multicontinuum approach that provides physical recharge models which are able to explain fractal behaviors with exponents 1=2 < b < 2. Furthermore, this approach allows to link the fractal dynamics of the discharge process to the physical aquifer characteristics as reflected in the distribution of storage time scales. We systematically analyze the catchment responses in the proposed multicontinuum models, and identify and quantify the time scales which characterize the dynamics of the catchment response to recharge.
ISSN: 0043-1397

insu-00952537
https://hal-insu.archives-ouvertes.fr/insu-00952537
https://hal-insu.archives-ouvertes.fr/insu-00952537/document
https://hal-insu.archives-ouvertes.fr/insu-00952537/file/russian.pdf
DOI : 10.1002/2013WR014255

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The objectives are to study and model the aggregate wind power fluctuations dynamics in the multifractal framework. We present here the analysis of aggregate power output sampled at 1 Hz during three years. We decompose the data into several Intrinsic Mode Functions (IMFs) using Empirical Mode Decomposition (EMD). We use a new approach, arbitrary order Hilbert spectral analysis, a combination of the EMD approach with Hilbert spectral analysis (or Hilbert-Huang Transform) and the classical structure-function analysis to extract the scaling exponents or multifractal spectrum ζ(q)ζ(q): this function provides a full characterization of a process at all intensities and all scales. The application of both methods, i.e. structure-function and arbitrary-order Hilbert spectral analyses, gives similar results indicating that the aggregate power output from a wind farm, possesses intermittent and multifractal properties. In order to check this result, we generate stochastic simulations of a Multifractal Random Walk (MRW) using a log-normal stochastic equation. We show that the simulation results are fully compatible with the experimental results
Physica A

hal-00846643
https://hal.archives-ouvertes.fr/hal-00846643
DOI : 10.1016/j.physa.2013.04.038

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
In this paper, we have presented a spectral and a multifractal analysis performed on 412 time series of wind speed data each of duration of 350 s and sampled at 20 Hz. The average spectrum for the wind speed displays a scaling behavior, in the inertial range, over two decades, with β=1.68 close to the Kolmogorov value −5/3. A multifractal analysis has been motivated by the presence of scaling invariance in data set. Then we have considered their scaling properties in the framework of fully developed turbulence and multifractal cascades. The results obtained for wind speed confirm that the exponent scaling function ζV(q) is nonlinear and concave. This exponent characterizes the scaling functions in the inertial range indicating that the wind speed is intermittent and multifractal. Moreover the theoretical quadratic relation for lognormal multifractals is well fitted. We investigate the consequence for wind energy production: we generate stochastic simulations of a multifractal random walk, and using a power curve derived from experimental data, we generate the associated power time series. We show that, due to the saturation of the power curve for large speed values, when the input time series (turbulent wind speed) is multifractal, the output can be almost monofractal.
ISSN: 0167-6105

hal-00779049
https://hal.archives-ouvertes.fr/hal-00779049
DOI : 10.1016/j.jweia.2012.06.002

Éditeur(s) : HAL CCSD
Résumé : International audience
This paper deals with image processing. This study takes place in a segmentation process based on texture analysis. We use the multifractal ap-proach to characterize the textures. More precisely we study a particular multi-fractal spectrum called the large deviation spectrum. We consider two statistical methods to numerically compute this spectrum. The resulting spectrum, com-puted by both methods over an image, is a one dimension spectrum. In the scope of this article, we extend these methods in order to obtain a two dimen-sions spectrum which could be assimilated to an image. This 2D spectrum al-lows a local characterization of the image singularities while a 1D spectrum is a global characterization. Moreover, the computation of the spectrum requires the use of a measure. We introduce here a pre processing based on the gradient to improve the measure. We show results on both synthetic and real world images. Finally, we remark that the resulting 2D spectrum is close to the resulting im-age of an edge detection process while edge detection using one dimension spectrum requires post processing methods. This statement will be used for fu-ture works.
SITIS Proceedings
Hammamet, Tunisia

hal-00602273
https://hal.archives-ouvertes.fr/hal-00602273

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
A good knowledge of the intermittency of global solar radiation is crucial for selecting the location of a solar power plant and predicting the generation of electricity. This paper presents a multifractal analysis study of 367 daily global solar radiation sequences measured with a sampling rate of 1 Hz over one year at Guadeloupean Archipelago (French West Indies) located at 16 150N latitude and 60 300W longitude. The mean power spectrum computed follows a power law behavior close to the Kolmogorov spectrum. The intermittent and multifractal properties of global solar radiation data are investigated using several methods. Under this basis, a characterization for each day using three multifractal parameters is proposed.
ISSN: 0038-092X

hal-00903410
https://hal.archives-ouvertes.fr/hal-00903410
DOI : 10.1016/j.solener.2013.09.018

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
A good knowledge of the intermittency of global solar radiation is crucial for selecting the location of a solar power plant and predicting the generation of electricity. This paper presents a multifractal analysis study of 367 daily global solar radiation sequences measured with a sampling rate of 1 Hz over one year at Guadeloupean Archipelago (French West Indies) located at 16°15'N latitude and 60°30'W longitude. The mean power spectrum computed follows a power law behaviour close to the Kolmogorov spectrum. The intermittent and multifractal properties of global solar radiation data are investigated using several methods. Under this basis, a characterization for each day using three multifractal parameters is proposed
ISSN: 0038-092X

hal-01527892
https://hal.archives-ouvertes.fr/hal-01527892
DOI : 10.1016/j.solener.2013.09.018

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The correlation between the flow turbulence and the performances of a ma- rine current turbine is studied. First, the incoming flow encountered in the flume tank is characterized in the framework of fully developed turbulent cascades in the inertial range. The Reynolds number, the Kolmogorov dissipation scale and the integral scale, are estimated from flow measurements. The intermittency of the turbulence is characterized in the lognormal multifractal framework, and the influence of the turbulent flow on the turbine power is assessed. The rotor speed control unit characteristics used for the turbine regulation induces non-negligible effects on the turbine behavior under fluctuations loads. Even if the power spectrum does not reveal any scale invariance, a multiscale analysis allows us to show the correlations between the turbulence time se- ries and the power produced. The classical Mean Square Coherency function shows that for scales larger than 10 seconds, the upstream velocity and power have large correlations. In the framework of the Empirical Mode Decomposition method, such correlations are studied using the time-dependence intrinsic corre- lation analysis method. This method allows to zoom into time-frequency scales where the flow perturbations induced some modifications in power production
ISSN: 0960-1481

hal-01528296
https://hal.archives-ouvertes.fr/hal-01528296
DOI : 10.1016/j.renene.2017.05.024

Éditeur(s) : HAL CCSD
Résumé : International audience
In this paper, we use a multifractal approach based on the computation of two spectrums for image analysis and texture segmentation problems. The two spectrums are the Legendre Spectrum, determined by classical methods, and the Large Deviation Spectrum, determined by kernel density estimation. We propose a way for the fusion of these two spectrums to improve textured image segmentation results. An unsupervised k-means is used as clustering approach for the texture classification. The algorithm is applied on mosaic image built using IKONOS images and various natural textures from the Brodatz album. The segmentation obtained with our approach gives better results than the application of each spectrum separately.
CIARP Proceedings
Cancun, Mexico

hal-00602268
https://hal.archives-ouvertes.fr/hal-00602268

Éditeur(s) : HAL CCSD
Résumé : International audience
This paper deals with texture classification using a multifractal approach. More precisely we analyse the singularity/regularity exponent that compose the textures because they theoretically carry most of the information. The analysis is made using the Legendre spectrum. Then a parameter vector is computed to describe this spectrum in order to classify the textures with an unsupervised k-means classifier. The resulting algorithm is evaluated against a classification directly based on the textures.
CAS Proceedings
GOSIER, France

hal-00634750
https://hal.archives-ouvertes.fr/hal-00634750

Éditeur(s) : HAL CCSD Springer
Résumé : The analysis of gamma ray measurements provides valuable information about the basement's lithospherical model and the radioactive elements contained in the subsurface. To be exploited, the raw data need pre-processing operations which consist of corrections of the Compton effect, altimetry and the aircraft background, and 2D interpolations. These transformations may modify the data's stochastic component which reflects heterogeneities of the investigated medium. In this study, a fractal analysis is carried out on airborne gamma ray data measured in the Hoggar's area (Algeria). First, it is shown that the analyzed data exhibit fractal properties. Due to the dependence of the latter on the spatial location of the measures, the data can be considered as paths of multifractional Brownian motions. Another result worth noting is that the fractal nature of the raw data is not modified by the pre-processing operations. The fractal analysis can be then performed on the raw spectrometric measurements without submitting them to any pre-processing; thus, the stochastic component of the measurements is kept intact.
ISSN: 1866-7411

hal-00817494
https://hal.archives-ouvertes.fr/hal-00817494
DOI : 10.1007/s12517-011-0407-3

Éditeur(s) : HAL CCSD
Résumé : International audience
This paper deals with texture classification using a multifractal approach. More precisely we analyse the singularity/regularity exponent that compose the textures because they theoretically carry most of the information. The analysis is made using the Legendre spectrum. Then a parameter vector is computed to describe this spectrum in order to classify the textures with an unsupervised k-means classifier. The resulting algorithm is evaluated against a classification directly based on the textures.
ICSP Proceedings
Beijing, China

hal-00602270
https://hal.archives-ouvertes.fr/hal-00602270

Éditeur(s) : HAL CCSD American Geophysical Union
Résumé : International audience
An analytical solution in the Laplace domain is derived for modeling anomalous pressure diffusion during pumping tests in aquifer displaying hierarchical fractal fracture networks. The proposed solution generalizes all of the analytical models for fractal flow published previously by combining multifractal diffusion and nested multiporosity with transient exchanges, interface skin effects, and well storage effect. Solutions are derived for fracture-delimited blocks with planar, cylindrical, and spherical shapes, as well as with any fractional dimensional shapes. Any combinations of these shapes can be defined in order to model a large range of situations. Within each permeability level, the fractal properties of the fracture network can be specified and the fractal dimension can be distinct from the shape dimension of the block.
ISSN: 0043-1397

hal-00411549
https://hal.archives-ouvertes.fr/hal-00411549
DOI : 10.1029/2008WR007125