Width Of Multifractal Spectrum Research Articles

Fractal-Based Multi-Criteria Feature Selection to Enhance Predictive Capability of AI-Driven Mineral Prospectivity Mapping

AI-driven mineral prospectivity mapping (MPM) is a valid and increasingly accepted tool for delineating the targets of mineral exploration, but it suffers from noisy and unrepresentative input features. In this study, a set of fractal and multifractal methods, including box-counting calculation, concentration–area fractal modeling, and multifractal analyses, were employed to excavate the underlying nonlinear mineralization-related information from geological features. Based on these methods, multiple feature selection criteria, namely prediction–area plot, K-means clustering, information gain, chi-square, and the Pearson correlation coefficient, were jointly applied to rank the relative importance of ore-related features and their fractal representations, so as to choose the optimal input feature dataset readily used for training predictive AI models. The results indicate that fault density, the multifractal spectrum width (∆α) of the Yanshanian intrusions, information dimension (D1) of magnetic anomalies, correlation dimension (D2) of iron-oxide alteration, and the D2 of argillic alteration serve as the most effective predictor features representative of the corresponding ore-controlling elements. The comparative results of the model assessment suggest that all the AI models trained by the fractal datasets outperform their counterparts trained by raw datasets, demonstrating a significant improvement in the predictive capability of fractal-trained AI models in terms of both classification accuracy and predictive efficiency. A Shapley additive explanation was employed to trace the contributions of these features and to explain the modeling results, which imply that fractal representations provide more discriminative and definitive feature values that enhance the cognitive capability of AI models trained by these data, thereby improving their predictive performance, especially for those indirect predictor features that show subtle correlations with mineralization in the raw dataset. In addition, fractal-trained models can benefit practical mineral exploration by outputting low-risk exploration targets that achieve higher capturing efficiency and by providing new mineralization clues extracted from remote sensing data. This study demonstrates that the fractal representations of geological features filtered by multi-criteria feature selection can provide a feasible and promising means of improving the predictive capability of AI-driven MPM.

Promoting Sustainable Coal Mining: Investigating Multifractal Characteristics of Induced Charge Signals in Coal Damage and Failure Process

Monitoring and preventing coal–rock dynamic disasters are essential for ensuring sustainable and safe mining. Induced charge monitoring, as a geophysical method, enables sustainable monitoring of coal–rock deformation and failure. The induced charge signal contains crucial information regarding damage evolution, making it imperative and important to explore its temporal characteristics for effective monitoring and early warnings of dynamic disasters in deep mining. This paper conducted induced charge monitoring tests at different loading rates, investigating the multifractal characteristics of induced charge signals during the early and late stages of loading. It proposed the maximum generalized dimension D(q)max, multifractal spectrum width Δα, and height difference Δf as multifractal parameters for induced charge signals. Additionally, quantitative characterization of coal damage was performed, studying the variation patterns of signal multifractal characteristic parameters with coal damage evolution. This study revealed the induced charge signal of the coal body multifractal characteristics in the whole loading process. In the late loading stage, the double logarithmic curve demonstrated some nonlinearity compared to the previous period, indicating the higher non-uniformity of the induced charge time series. D(q)max and Δα in the late loading stage were higher than those in the early stage and increased with loading rates. As coal damage progressed, there were significant jumps of D(q)max in both the early and late stages of damage, with larger jumps indicating richer fracture events in the coal. The width Δα showed an overall trend of increase–decrease–increase with coal damage evolution, while the height difference Δf fluctuated around zero in the early stage of damage development but increased significantly during severe damage and destruction. By studying the multifractal characteristics of induced charge signals, this study provides insights for the early identification of coal–rock dynamic disasters.

Pallidal multifractal complexity is a new potential physiomarker of dystonia

ObjectiveLow-frequency 4–12 Hz pallidal oscillations are being considered as potential physiomarkers for dystonia. We suggest investigating the multifractal properties of pallidal activity as an additional marker. MethodsWe employed local field potentials (LFP) recordings from 23 patients with dystonia who were undergoing deep brain stimulation (DBS) surgery to explore the connection between disease severity and the multifractal characteristics of pallidal activity. Furthermore, we performed an analysis of LFP recordings from four patients, following the externalization of DBS lead electrodes, to investigate the impact of DBS and neck muscle vibration on multifractal parameters. ResultsGreater dystonia severity exhibited a correlation with a narrower multifractal spectrum width but higher multifractal spectral asymmetry. Both GPi DBS and muscle vibration in dystonia patients expanded the multifractal spectrum width while restoring multifractal spectral symmetry. Notably, the threshold peak intensities for an increase in multifractal spectrum width substantially overlapped with the optimal volume of tissue activated. A broader multifractal spectrum during DBS corresponded to more favorable clinical outcomes. ConclusionsMultifractal properties of pallidal neuronal activity serve as indicators of neural dysfunction in dystonia. SignificanceThese findings suggest the potential of utilizing multifractal characteristics as predictive factors for the DBS outcome in dystonia.

Research on coal crushing behavior under supercritical CO2 transient high-pressure fracturing

CO2 fracturing enhances gas permeability by creating a complex network of fractures in coal seams. Crushing serves as the foundation of fracture development, and studying the coal crushing behavior under supercritical CO2 transient high-pressure fracturing is of great significance to understand fracture evolution and guide precise fracturing. This study utilized a self-built experimental platform for supercritical CO2 transient high-pressure fracturing to obtain fractured coals at different energy levels. Based on multifractal theory, the relationship between fracturing energy and crushing behavior was studied by laser particle analysis and scanning electron microscopy. The results showed that the volume average particle size (D4,3), and the particle sizes at which the cumulative particle size distribution reached 50% (D50), and 90% (D90) decreased significantly with the increase of fracturing energy. The converted diameter and the crushing work ratio exhibited an exponential relationship with the fracturing energy. The larger the fracturing energy, the smaller the values of the multifractal generalized dimension spectrum parameters (D0, D1, and ΔD(q)), the larger the values of the multifractal singular spectrum width (Δα (q)), and the denser and more even the particle size distribution of fractured coal. The multifractal parameters and shape coefficients exhibited phased change during the fracturing process. The coal particles progressed from an initial stage with numerous microcracks and fissures to a honeycomb structures with small pores. After the disintegration of the honeycomb structures, agglomerated ultrafine particles were formed. The findings provide a theoretical reference for optimizing the selection of fracturing parameters.

Multifractality in stride-to-stride variations reveals that walking involves more movement tuning and adjusting than running

Introduction: The seemingly periodic human gait exhibits stride-to-stride variations as it adapts to the changing task constraints. The optimal movement variability hypothesis (OMVH) states that healthy stride-to-stride variations exhibit “fractality”—a specific temporal structure in consecutive strides that are ordered, stable but also variable, and adaptable. Previous research has primarily focused on a single fractality measure, “monofractality.” However, this measure can vary across time; strideto-stride variations can show “multifractality.” Greater multifractality in stride-tostride variations would highlight the ability to tune and adjust movements more.Methods: We investigated monofractality and multifractality in a cohort of eight healthy adults during self-paced walking and running trials, both on a treadmill and overground. Footfall data were collected through force-sensitive sensors positioned on their heels and feet. We examined the effects of self-paced walking vs. running and treadmill vs. overground locomotion on the measure of monofractality, α-DFA, in addition to the multifractal spectrum width, W, and the asymmetry in the multifractal spectrum, WAsym, of stride interval time series.Results: While the α-DFA was larger than 0.50 for almost all conditions, α-DFA was higher in running and locomoting overground than walking and locomoting on a treadmill. Similarly, W was greater while locomoting overground than on a treadmill, but an opposite trend indicated that W was greater in walking than running. Larger WAsym values in the negative direction suggest that walking exhibits more variation in the persistence of shorter stride intervals than running. However, the ability to tune and adjust movements does not differ between treadmill and overground, although both exhibit more variation in the persistence of shorter stride intervals.Discussion: Hence, greater heterogeneity in shorter than longer stride intervals contributed to greater multifractality in walking compared to running, indicated by larger negative WAsym values. Our results highlight the need to incorporate multifractal methods to test the predictions of the OMVH.

Quantitative study on particle shaping of recycled aggregate by multifractal spectrum

In this study, the feasibility of quantifying the shaping effect of aggregate particles through multifractal spectrum analysis was explored, and the relationships between the amount, particle size, and shape of aggregates and the multifractal spectrum eigenvalues of aggregate images were experimentally investigated. Finally, the multifractal spectrum before and after the shaping of real aggregate particles was compared, and the following conclusions were obtained: the aggregate distribution image satisfies the multifractal characteristics; the greater the number of aggregates in the image, the greater the multifractal spectrum width; the larger the aggregate particle size, the smaller the multifractal spectrum width; the smoother the aggregate surface, the greater the multifractal spectrum width; the unit-pixel multifractal spectrum of the real aggregate is found with an increase of 47.1% in width after the shaping, suggesting that the multifractal spectrum eigenvalues can effectively quantify the aggregate shaping effect.

Multifractal detrended fluctuation analysis of insole pressure sensor data to diagnose vestibular system disorders.

The vestibular system (VS) is a sensory system that has a vital function in human life by serving to maintain balance. In this study, multifractal detrended fluctuation analysis (MFDFA) is applied to insole pressure sensor data collected from subjects in order to extract features to identify diseases related to VS dysfunction. We use the multifractal spectrum width as the feature to distinguish between healthy and diseased people. It is observed that multifractal behavior is more dominant and thus the spectrum is wider for healthy subjects, where we explain the reason as the long-range correlations of the small and large fluctuations of the time series for this group. We directly process the instantaneous pressure values to extract features in contrast to studies in the literature where gait analysis is based on investigation of gait dynamics (stride time, stance time, etc.) requiring long walking time. Thus, as the main innovation of this work, we detrend the data to give meaningful information even for a relatively short walk. Extracted feature set was input to fundamental classification algorithms where the Support-Vector-Machine (SVM) performed best with an average accuracy of 98.2% for the binary classification as healthy or suffering. This study is a substantial part of a big project where we finally aim to identify the specific VS disease that causes balance disorder and also determine the stage of the disease, if any. Within this scope, the achieved performance gives high motivation to work more deeply on the issue.

Multifractal analysis of malaria cases in India in a global warming scenario

Abstract An effort is made to evaluate the multifractal properties of malaria cases in India from 1980 to 2014. The possible changes in these properties in a global warming scenario (during 2015–2049) are also quantified. The malaria cases for this purpose are derived from the VECTRI dynamical malaria model, which uses rainfall and temperature data of Coupled Model Intercomparison Project Phase 6 models for the historical and SSP5–8.5 projection scenario, respectively. It is found that the generalized Hurst exponent h (q) and multifractal spectrum width Δα are strongly nonlinear decreasing functions of order q, thus confirming the multifractal nature (and heterogeneous distribution) of the malaria cases in India. The multifractal spectrum of the malaria cases exhibits right-tailed nature along with high inter-model variability, suggesting that the time series under consideration are fine scale and highly complex in nature. The multifractal spectrum width and change in singularity dimension are used to quantify the strength of multifractality for the historical and future projection scenario. It is demonstrated that the strength of multifractality of malaria cases is likely to decrease with an increase in greenhouse gas concentration, which may be happening due to a persistent increase in malaria cases in India as a result of global warming.

Multifractal descriptors ergodically characterize non-ergodic multiplicative cascade processes

Biological and psychological processes routinely break ergodicity, meaning they fail to have stable means (Mean) and independent variation over time that we might find in additive white Gaussian noise (awGn). One possible reason for this failure of ergodicity is the failure of biological and psychological processes to exhibit independence across time. Multifractal evidence has long suggested that biological and psychological processes show strong signatures of nonlinear interactions across scales. These cross-scale interactions sooner befit a cascade-dynamical process than awGn. The present work thus compares awGn to simulations of multiplicative binomial cascades, submitting both types of series and shuffled versions of each to the Thirumalai-Mountain method for estimating ergodicity breaking. Estimating ergodicity breaking for original awGn and cascade series allows us to examine the sources of ergodicity breaking across the sequence, e.g., in temporal correlations specifying nonlinear interactions across scales, and examining ergodicity breaking of the shuffled series allows us to assess the raw, sequence-independent contribution of distributional properties (e.g., the heavy tails of a cascade) without the original temporal sequence. Raw cascade fluctuations and the standard deviation (SD) and root mean square (RMS) series describing those raw fluctuations break ergodicity, but nonlinear, cascade-dynamical descriptors: multifractal spectrum width (Δα) and multifractal nonlinearity (tMF), maintain ergodicity. Interestingly, the fundamentally linear descriptor, fractal Hurst exponent (HfGn) shows moderate ergodicity breaking when describing the fundamentally nonlinear cascade processes, but the linear descriptor coefficient of variation (CV) controls for multiplicative relationships between SD and Mean and maintains ergodicity. We conclude that the ergodicity of statistical descriptors depends on how well they can portray nonlinearity (Δα and tMF) or at least multiplicativity (CV) of the underlying cascade processes.

Fractal Structure Characteristics and Prospecting Direction of Dispersed Metals in the Eastern Guizhou Pb–Zn Metallogenic Belt, SW China

The eastern Guizhou Pb–Zn metallogenic belt (EGMB) is an important source of Pb–Zn resources and other critical minerals (including dispersed metals, such as Ge, Cd and Ga) in China. In order to ensure the continuous resource supply of Pb–Zn and associated dispersed metals, it is urgent to explore the direction of further prospecting for them. Fractal theory can realize the fractal structure characterization of fault structures and the spatial distribution of mineral deposits, which is helpful for mineral exploration. However, the fault fractal research and prospecting application are still seldom covered in the EGMB. We used fractal theory to determine fine-scale fractal structure characteristics of fault structures and ore deposits in the EGMB, and Fry analysis to delineate favorable metallogenic areas. The results show that within a scale range of 3.670–58.716 km, the integrated faults capacity dimension (CPD) is 1.5095, the information dimension (IND) is 1.5391, and the correlation dimension (CRD) is 1.5436, indicating fault structures with high maturity, which are conducive to the migration and accumulation of ore-forming fluids. The multi-fractal spectrum width and height are 0.3203 and 1.5355, respectively, implying a significant metallogenic potential. The spatial distribution fractal dimensions (SDD) of Pb–Zn specifically and metal deposits in general are 1.0193 and 1.0709, respectively; the quantity distribution fractal dimensions (QDD) are 1.4225 and 1.4716, respectively, and the density distribution fractal dimensions (DDD) are 1.422 and 1.472, respectively, indicating strong clustering. Hence, the favorable metallogenic regions can be divided into four grades, among which grade I region is continuously distributed in space and has the greatest prospecting potential.

Multifractal Correlation between Terrain and River Network Structure in the Yellow River Basin, China

As the most basic physical geographic elements, basin terrain and river networks have high spatial complexity and are closely related. However, there is little research on the correlation between terrain and river networks. In this paper, the Yellow River Basin was selected as the study area. Topographic factors of multiple dimensions were calculated. The influence of different topographic factors on the river network structure at different scales and their correlation from a multifractal perspective based on geographical detectors and a geographically weighted regression model were determined. The explanatory power of topography on the river network structure at different scales was: multifractal spectrum width > multifractal spectrum difference > slope > average elevation > elevation maximum > elevation minimum, which generally indicated that the topographic factor that has the greatest influence on the river network structure is the complexity and singularity of the terrain. The second-order clustering of regression coefficients from the results of the geographically weighted regression model revealed that the Yellow River basin was divided into three types of high-aggregation areas, which are dominated by the Qinghai-Tibet Plateau, the Loess Plateau, and the Huang-Huaihai Plain, respectively. The clustering results also revealed that the river network structure was affected by different key topographic factors in the different types of areas. This research studies and quantifies the relationship between basin topography and river network structure from a new perspective and provides a theoretical basis for unraveling the development of topography and river networks.

Study on the Effect of Judgment Excitation Mode to Relieve Driving Fatigue Based on MF-DFA.

Driving fatigue refers to a phenomenon in which a driver’s physiological and psychological functions become unbalanced after a long period of continuous driving, and their driving skills decline objectively. The hidden dangers of driving fatigue to traffic safety should not be underestimated. In this work, we propose a judgment excitation mode (JEM), which adds secondary cognitive tasks to driving behavior through dual-channel human–computer interaction, so as to delay the occurrence of driving fatigue. We used multifractal detrended fluctuation analysis (MF-DFA) to study the dynamic properties of subjects’ EEG, and analyzed the effect of JEM on fatigue retardation by Hurst exponent value and multifractal spectrum width value. The results show that the multifractal properties of the two driving modes (normal driving mode and JEM) are significantly different. The JEM we propose can effectively delay the occurrence of driving fatigue, and has good prospects for future practical applications.

Nonlinear mechanical characteristics and damage constitutive model of coal under CO2 adsorption during geological sequestration

Geological sequestration of CO2 is an effective way to achieve the goal of reducing global warming and carbon neutralization. The complex CO2–coal interaction will lead to the change of mechanical properties of coal. Therefore, evaluating the mechanical characteristics of deep coal seam after CO2 adsorption is of great significance for analyzing the geological characteristics and structural stability of deep strata and storage site selection. In this study, the triaxial compression test and acoustic emission (AE) test were used to evaluate the effect of CO2 adsorption pressure on the mechanical properties of coal mass. On the basis of the evolution characteristics of AE ring down count (RDC), fractal theory was used to analyze the deformation and fracturing evolution of coal. Besides, an elastic damage constitutive model describing the nonlinear stress-strain relationship of coal under CO2 adsorption is established. Results show that the growth of adsorption pressure develops the risk of damage and fracturing of coal. With the increase in adsorption pressure, the value of singularity index width Δα presents a downward trend, indicating the development of internal cracks and the increase in the complexity of microunit fracturing process. When the adsorption pressure is low, the gas in large cracks and pores leads to the generation of small AE signal that occupies the dominant position. High adsorption pressure increases the complexity and nonlinearity of coal deformation, strengthens the proportion of large AE signal, and leads to the increase in the average value of multifractal spectrum width Δf. With the increase in adsorption pressure, the fracturing degree of coal is higher, a mass of large-size cracks appears, and more AE spectrum presents intensive distribution. In the plastic stage, the load level is close to the strength limit, the microcracks intersect with each other, and the average value of Δα in this stage is the smallest.

Vertical Growth Dynamics and Multifractality of the Surface of Electropolymerized Poly(o-ethoxyaniline) Thin Films

Electropolymerized poly(o-ethoxyaniline) (POEA) nanostructured thin films were successfully deposited on indium tin oxide (ITO) substrate. The surface dynamic of the films was extensively investigated using morphological and multifractal parameters extracted from the atomic force microscopy (AFM). AFM topographical maps reveal surfaces with different morphologies as a function of the deposition cycles. The height parameters show that there is greater spatial vertical growth for films deposited with higher cycles of deposition. After five cycles of deposition occurs the formation of a more isotropic surface, while for 15 cycles a less isotropic surface is observed. The Minkowski functionals confirm that morphological aspects of the two films change according to the amount of deposition cycles employed. The POEA surfaces also exhibit a strong multifractal nature with a decrease in the multifractal spectrum width as the number of deposition cycles increases. Our findings prove that deposition cycles can be useful in controlling the vertical growth and surface dynamics of electropolymerized POEA nanostructured samples, which can be useful for improving the fabrication of POEA-coated ITO-based devices.

The correlation between external magnetic field and multifractal characteristics of PLD deposited DLC films

The present study explores the application of the multifractal method in examining the surface characteristics of the diamond-like carbon (DLC) thin films deposited onto substrates of silicon through a magnetically-assisted pulsed laser deposition (MAPLD) method at room temperature (RT). Multifractal spectra f(α), obtained from atomic force microscopy (AFM) analysis, is adopted to investigate the surface morphology of the produced samples. The relationship between the applied magnetic field and multifractal characteristics of the obtained samples is examined as well. The findings attest to the apparent effect of the magnetic field on the quality of surface morphology and the multifractal spectrum width. Our results reveal that the root-mean-square (RMS) and average surface roughness are enhanced by applying and intensifying the magnetic field. Furthermore, the findings suggest that both the non-uniformity of the height distributions and the singularity spectrum width of the samples fabricated in this study increases with applying and intensifying the magnetic field. Further, Multifractal spectra f(α) demonstrate the multifractality nature of all the obtained samples, including conventionally and magnetically processed DLC thin films. Besides, the multifractality strength of thin films rises with increasing the magnetic field.

Microstructure Analysis on the Fracture Network in High‐Rank Coals

AbstractMicrofractures in the coal matrix have complex spatial structure because of the joint effects of coalification and tectonism. The accurate modeling and characterization of microfractures directly affect mechanism analysis of coal rock fracturing and mining. In this study, taking the high‐rank coal in the north of Qinshui Basin, structural characteristics of microfracture in intact and tectonic coals were analyzed systematically using 2D thin section, 3D micro‐CT modeling and mercury intrusion based on digital image analysis and fractal theory. The result indicates that the response sensitivity of fractal parameters obtained from different methods to microfractures from two types of coal structures is different greatly. Single fractal dimension (Df) in tectonic coal is higher than that of intact coal. Specially, for 2D thin sections, the indicative effect on the Df of manually corrected images is better than that of automatically extracted and linear ones. Df has a positive correlation with the pixel‐based microfracture porosity, as well as generalized fractal parameters. Moreover, microfracture permeability based on the Cubic‐Law increases with the increase of Df. For 3D micro‐CT modeling, the classical Watershed algorithm cannot segment the spatial microfracture network, which, however, can be segmented and characterized by the self‐developed FracSC3D program. Spatial microstructural parameters including volume, surface and length at three‐axis directions meet bifractal characteristics. Specially, for 2D micro‐CT slices, with the increase of porosity, the multifractal spectrum width Δα also increased. Besides, the fractal parameter based on Menger model from mercury intrusion experiment can act as a good indicator for identifying microfractures, flow pores and diffusion pores.

PREDICTION OF THE ANTARCTIC MARGINAL ICE ZONE EXTENT BASED UPON ITS MULTIFRACTAL PROPERTY

The marginal ice zone (MIZ) around Antarctica is an important air–ice–ocean–wave interaction area and a crucial habitat for marine life. Given its dynamic nature, it is essential to understand and quantify both the short- and long-term changes of its extent. In this study, we investigated the MIZ extent time series using multifractal spectrum and [Formula: see text]/[Formula: see text] analysis, examining Antarctica as a whole and per sub-region. The MIZ extent was predicted using a back-propagation (BP) algorithm. The results show that the wide multifractal spectrum width of the MIZ extent time series has strong multifractal features for the entire Antarctic and for the five sub-regions. By comparing the spectrum width of the original time series with those of a shuffled series, we found that multifractality is related to long-range correlations in the time series. The Hurst exponent obtained using the [Formula: see text] analysis indicates that the long-range correlation over six months is strongest for all time intervals. Compared to the autoregressive integrated moving average model, the mean absolute percentage error obtained using the BP algorithm was lower by 4–15%. We conclude that the BP algorithm combined with the multifractal property is well suited to predict the Antarctic MIZ extent.

THE MULTIFRACTAL PROPERTY OF HETEROGENEOUS MICROSTRUCTURE IN CEMENT PASTE

Highlights (1) Microstructure of cement paste is acquired through computed tomography. (2) Multifractal property of heterogeneous microstructure is examined. (3) Incorporation of blast furnace slag results in a decrease of singularity width. The microstructure of cement paste is highly heterogeneous in nature that plays a significant role in macroscopic performance. This paper is dedicated to examining the multifractal property of microstructure in cement paste, based on which the microstructural heterogeneity could be quantified meanwhile. In particular, the X-ray computed tomography is adopted to acquire the realistic three-dimensional (3D) microstructure. Then, a thorough examination is performed on the multifractal property with respect to the partition function, the generalized dimension and the multifractal spectrum. Results indicate that the multifractal property in terms of local porosity can be recognized for the heterogeneous microstructure in both ordinary and blast furnace slag blended Portland cement pastes. The multifractal spectrum or singularity width is available to account for the degree of heterogeneity.

Multifractal analysis of rainfall in coastal area in Pernambuco, Brazil

Global warming and climate change are the mayor concerns of scientists, engineers and policy makers because they affect every aspect of nature and human life. Rainfall and air temperature are the most important variables used to detect climate change, through the statistical analysis of set of indices that describe temperature and rainfall extremes. Over the last decades concepts and methods from complex system science were applied in analysis of hydrological data to describe variability of hydrological processes on multiple temporal and spatial scales. In this work we analyzed daily rainfall temporal series in Recife, Brazil (during the period from 1962 to 2019) using Multifractal Detrended Fluctuation analysis (MFDFA) in order to study long term correlations in subsets of small and large rainfall fluctuations. We calculated multifractal parameters (that quantify position of maximum, width and asymmetry of multifractal spectrum) which are related to different properties of rainfall fluctuations. By comparing the values of these parameters for two subperiods of 29 years, we found that after 1990, rainfall dynamics changed towards stronger persistency, weaker multifractality and decreased dominance of small fluctuations.

Traffic modeling for communications networks: A multifractal approach based on few parameters

In this work, in order to model network traffic processes, an efficient multifractal model is proposed based on fewer parameters than other models present in the literature, called 2PEMV. The 2PEMV model (2-Parameter Exponential Modeling for Multipliers’ Variance) is based on a multiplicative cascade in the wavelet domain capable of synthesizing communication network traffic traces which present characteristics such as self-similarity and wide Multifractal Spectrum Width (MSW). For such a purpose, in the 2PEMV model, the energy decay of the wavelet coefficients is captured by means of an exponential modeling for the multipliers’ variance along the cascade scales. The performance of the 2PEMV model to represent the network traffic characteristics is evaluated in comparison to other models present in the literature through simulations that are carried out using real communication network traffic traces.