Fractal-based Approach Research Articles

Fractal-Based Reliability Measure for Heterogeneous Manufacturing Networks

Nowadays, production-oriented manufacturing is transforming to service-oriented one, which leads to an increasing demand for high reliability of manufacturing systems. However, a popular approach to measuring terminal reliability of complex networked systems is based on graph theory, which has been shown to be an NP-hard problem. Though the NP-hard problem can be avoided by employing a statistical measure method for terminal reliability of random networks based on percolation theory, there is still lack of a general assessment approach to calculating terminal reliability of heterogeneous complex networks in intelligent manufacturing. In this paper, we propose a novel fractal-based approach to measuring the terminal reliability of heterogeneous networks. With help of the renormalization procedure that coarse grains a network into boxes containing nodes within given lateral size and inverse renormalization, which gives a fractal network growth model, a fractal network approximation of an arbitrary complex network is obtained. This fractal network topology can be described by a superposition of fractal elements based on fractal theory. Following this description, terminal reliability is the function of reliability of fractal elements. Then, a reliability assessment algorithm with computational complexity $O(N^2)$ based on fractal elements is developed. Numerical simulation is performed on a real network and a fractal network to validate the effectiveness of our method.

Mammogram Mass Segmentation Using Fractals

A new fractal-based technique for the segmentation of masses from digital mammograms is shown in this paper. This proposed fractal-based approach aims to detect and segment the masses from mammograms after successful suppression of pectoral muscle. This paper identifies and suppresses the pectoral muscle efficiently from the input mammogram and further segments the masses precisely with the help of fractal dimensions and fractal hurst based thresholding oriented computation. This approach is proved to be efficient in getting accurate segmentation results that guarantees the virtue of the projected technique.

Fractal-Based Computation of Heat Source Depths and Temperatures for the Soutpansberg Basin, South Africa

The fractal-based approach was used for computing magnetic depths and temperatures for the Soutpansberg Basin in South Africa. The average depth to the top Zt and basement depth Zo for the Soutpansberg Basin were 4.36 ± 0.28 km, 10.43 ± 0.65 km, respectively. The average temperature at depth Zt was 184.69 ± 7.66 ºC. Magnetic source depths and basal temperatures that were in the Curie point range were determined, to be within 20.35 km to 21.68 km and 549.34 ºC to 585.24 ºC, respectively. Increasing the value of the fractal parameter β from 0 to 4, had an effect of retaining deeper depths and higher temperatures. The fractal parameter values of β > 3 retained Curie point depths and temperatures that indicated basal rock types with an igneous predisposition. The fractal-based approach proved to be an improved technique as compared to the conventional centroid method.

A fractal-based approach for modeling stock price variations.

The recent global financial crisis has threatened the financial system with total collapse of many economic sectors with a particular penetration to world's stock markets. The large swings in the prices of international stocks or indexes have reinvigorated the debate on their mathematical modeling. The traditional approaches do not seem to be very exhaustive and satisfactory, especially when extreme events occur. We propose a fractal-based approach to model the actual prices by assuming that they follow a Multifractional Process with Random Exponent. An empirical evidence is offered that this stochastic process is able to provide an appropriate modeling of actual series in terms of goodness of fit by comparing three main stock indexes.

A Simple Fractal-Based Model for Soil-Water Characteristic Curves Incorporating Effects of Initial Void Ratios

In this paper, a simple and efficient fractal-based approach is presented for capturing the effects of initial void ratio on the soil-water characteristic curve (SWCC) in a deformable unsaturated soil. In terms of testing results, the SWCCs (expressed by gravimetric water content) of the unsaturated soils at different initial void ratios were found to be mainly controlled by the air-entry value (Ψa), while the fractal dimension (D) could be assumed to be constant. As a result, in contrast to the complexity of existing models, a simple and efficient model with only two parameters (i.e., D and Ψa) was established for predicting the SWCC considering the effects of initial void ratio. The procedure for determining the model parameters with clear physical meaning were then elaborated. The applicability and accuracy of the proposed model were well demonstrated by comparing its predictions with four sets of independent experimental data from the tests conducted in current work, as well as the literature on a wide range of soils, including Wuhan Clay, Hefei and Guangxi expansive soil, Saskatchewan silt, and loess. Good agreements were obtained between the experimental data and the model predictions in all of the cases considered.

An imaging and fractal approach towards understanding reservoir scale changes in coal due to bioconversion

Microbially enhanced coalbed methane (MECBM) aims to replicate the natural process of microbial methane generation in coal under in situ conditions. Considerable work has been reported over the years to optimize the associated microbial geo-chemistry. However, there is very little insight with regards to changes in the physical structure of coal due to bioconversion, and its impact on fluid flow properties. This paper presents the result of an image and fractal-based approach used to evaluate the changes in physical properties of coal. Samples of coal treated over 30, 60 and 120 days respectively were imaged before and after bioconversion. The results revealed that coal bioconversion resulted in swelling of the coal matrix. Cleats narrower than 5 µm reduced in its width post-bioconversion. A 77% drop in the permeability of coal is expected from the obtained results. Bioconversion also resulted in separation of thin layers of coal flakes from the coal surface, serving as a potential source of fines. Fractal analysis of the images revealed a decrease in the fractal dimension post bioconversion, which is in agreement with the previously reported studies, thus corroborating the variations in sorption-trends observed due to bioconversion. Additionally, the methodology to determine the fractal dimension via two-dimensional image processing was modified to improve its accuracy, and remove the dependency of the dimension to the scale of the obtained images. Bioconversion also resulted in formation of new pores/fractures. Shorter treatment duration resulted in nanometer-scale discontinuous pores, which do not contribute to Darcian flow. Longer treatment periods resulted in sub-micron wide continuous pores. Also, few larger fractures (>5 µm wide) saw an increase in its aperture post-treatment. This opens up new avenues, such as, utilizing artificially induced fracturing techniques to enhance biogenic methane production in future.

AN INTRODUCTION TO FRACTAL-BASED APPROACHES IN UNCONVENTIONAL RESERVOIRS — PART I

In recent years, unconventional reservoirs have drawn tremendous attention worldwide. This special issue collects a series of recent works on various fractal-based approaches in unconventional reservoirs. The topics covered in this introduction include fractal characterization of pore (throat) structure and its influences on the physical properties of unconventional rocks, fractal characteristics of crack propagation in coal and fluid flow in rock fracture network under shearing, porous flow phenomena and gas adsorption mechanism, fractal geophysical method in reservoirs.

Assessment of distribution networks performance considering residential photovoltaic systems with demand response applications

The large penetration of solar photovoltaic (PV) systems at low voltage (LV) networks has started to introduce new challenges to distribution network operators. With the emergence of smart grid technology, the demand response (DR) has been identified as one of the promising approaches for network operators to increase operational flexibility, particularly in the presence of renewable energy resources. Therefore, it is important to investigate how DR applications at a LV consumer level can help to improve network performance. However, so far, only a limited number of works have addressed the implications of DR at LV networks with a PV system. The parametric analysis of the benefits of DR has not been adequately addressed for LV networks with multiple DR-PV interaction scenarios. In this regard, three case studies have been considered in this work, namely, consumers who respond to their own demand profile, consumers who respond to the PV generation profile, and the optimized demand response from consumers. The fractal-based approach has been utilized to model a large number of urban LV networks. Subsequently, the particle swarm optimization technique is utilized to model individual consumers' optimized DR profiles. Comprehensive network case studies are performed considering 100 urban LV network samples under the influence of different DR-PV scenarios. The results suggest that with 100% PV penetration, DR applications at a residential consumer level can achieve 32% peak reduction, reduce network losses by 42%, and achieve 12% load factor increment for the optimized demand response case.

Geometrical, fractal and hydraulic properties of fractured reservoirs: A mini-review

Fractures and fracture networks play an important role in fluid flow and transport properties of oil and gas reservoirs. Accurate estimation of geometrical characteristics of fracture networks and their hydraulic properties are two key research directions in the fields of fluids flow in fractured porous media. Recent works focusing on the geometrical, fractal and hydraulic properties of fractured reservoirs are reviewed and summarized in this mini-review. The effects of several important parameters that significantly influences hydraulic properties are specifically discussed and analyzed, including fracture length distribution, aperture distribution, boundary stress and anisotropy. The methods for predicting fractal dimension of fractures and models for fracture networks and fractured porous media based on fractal-based approaches are addressed. Some comments and suggestions are also given on the future research directions and fractal fracture networks as well as fractured porous media. Cited as : Wei, W., Xia, Y. Geometrical, fractal and hydraulic properties of fractured reservoirs: A mini-review. Advances in Geo-Energy Research, 2017, 1(1): 31-38, doi: 10.26804/ager.2017.01.03

A fractal model for volume change dependency of the water retention curve

A fractal-based approach for volume change dependency of the water retention curve in a deformable unsaturated soil is presented. Conservation laws of solid mass and solid surface for uncrushable grains and Eshelby's classical theory for load–deformation of a single elastic ellipsoidal void embedded in an infinite isotropic elastic matrix are exploited to derive analytical expressions for the evolution of pore size distribution fractal dimension, air entry suction and hence water retention curve with void ratio. The applicability of the model to two experimental data sets from the literature is investigated.

An Approach for Finding Possible Presence of Water Ice Deposits on Lunar Craters Using MiniSAR Data

Investigating the feasibility of water-ice deposits on lunar surface has been a very challenging task, which requires meticulous effort. Conceptualization of MiniSAR was a breakthrough because it had capability to image the shadowed regions that may have higher possibility of water-ice. Earlier studies have found that circular polarization ratio (CPR) is greater than unity in regions having volume scattering due to dielectric mixing (or water-ice deposits). However, later experiments revealed that ${\rm CPR} >1$ might also occur due to surface roughness. Thus, instead of using single polarimetric parameter CPR, it is required to use textural (or roughness) behavior of lunar surface along with scattering mechanisms, for obtaining the regions having higher possibility of dielectric mixing. For this purpose, information of two different approaches namely, polarimetric approach (i.e., $m - \delta $ decomposition and $m - \chi $ decomposition) and fractal approach have been fused together. The polarimetric approaches, i.e., $m - \delta $ decomposition and $m - \chi $ decomposition, help in identifying scattering mechanisms associated with lunar surface, whereas fractal-based approach helps in characterizing lunar surface on the basis of surface roughness using a measure called fractal dimension “ $\bm{D}.$ ” Finally, a decision tree algorithm has been proposed, in which decision criteria are decided on the basis of CPR, $m - \delta $ decomposition, $m - \chi $ decomposition, and fractal dimension “ $\bm{D}.$ .” The proposed approach seems to resolve the vagueness caused by ${\rm CPR} >1$ assumption, and to segregate areas representing volume scattering in relatively smooth surfaces inside anomalous craters, where possibility of dielectric mixing (or water-ice) may be high.

A distinct and compact texture descriptor

In this paper, a statistical approach to static texture description is developed, which combines a local pattern coding strategy with a robust global descriptor to achieve highly discriminative power, invariance to photometric transformation and strong robustness against geometric changes. Built upon the local binary patterns that are encoded at multiple scales, a statistical descriptor, called pattern fractal spectrum, characterizes the self-similar behavior of the local pattern distributions by calculating fractal dimension on each type of pattern. Compared with other fractal-based approaches, the proposed descriptor is compact, highly distinctive and computationally efficient. We applied the descriptor to texture classification. Our method has demonstrated excellent performance in comparison with state-of-the-art approaches on four challenging benchmark datasets.

Fractal-based estimation of hydraulic conductivity from soil–water characteristic curves considering hysteresis

A fractal-based approach is presented to estimate hydraulic conductivity from soil–water characteristic curves (SWCCs) exhibiting hydraulic hysteresis. By treating the pore geometry as a fractal it is possible to derive the hydraulic conductivity functions and water retention properties from the same set of parameters. A direct link exists between microstructural properties of the soil and the parameters. It is demonstrated, for a range of soils, that the hydraulic conductivity can be reasonably well estimated from known SWCCs. Analysis of flow in large unsaturated soil samples produced simulations of moisture content distribution in good agreement with measured data.

Simple Process-Based Simulators for Generating Spatial Patterns of Habitat Loss and Fragmentation: A Review and Introduction to the G-RaFFe Model

Landscape simulators are widely applied in landscape ecology for generating landscape patterns. These models can be divided into two categories: pattern-based models that generate spatial patterns irrespective of the processes that shape them, and process-based models that attempt to generate patterns based on the processes that shape them. The latter often tend toward complexity in an attempt to obtain high predictive precision, but are rarely used for generic or theoretical purposes. Here we show that a simple process-based simulator can generate a variety of spatial patterns including realistic ones, typifying landscapes fragmented by anthropogenic activities. The model “G-RaFFe” generates roads and fields to reproduce the processes in which forests are converted into arable lands. For a selected level of habitat cover, three factors dominate its outcomes: the number of roads (accessibility), maximum field size (accounting for land ownership patterns), and maximum field disconnection (which enables field to be detached from roads). We compared the performance of G-RaFFe to three other models: Simmap (neutral model), Qrule (fractal-based) and Dinamica EGO (with 4 model versions differing in complexity). A PCA-based analysis indicated G-RaFFe and Dinamica version 4 (most complex) to perform best in matching realistic spatial patterns, but an alternative analysis which considers model variability identified G-RaFFe and Qrule as performing best. We also found model performance to be affected by habitat cover and the actual land-uses, the latter reflecting on land ownership patterns. We suggest that simple process-based generators such as G-RaFFe can be used to generate spatial patterns as templates for theoretical analyses, as well as for gaining better understanding of the relation between spatial processes and patterns. We suggest caution in applying neutral or fractal-based approaches, since spatial patterns that typify anthropogenic landscapes are often non-fractal in nature.

A fractal-based approach for the determination of concrete surfaces using laser scanning techniques: a comparison of two different measuring systems

The aim of this study is to determine and compare surface parameters at the meso level of concrete fractured surfaces using two different laser scanning systems. One of the laser scanning systems is the cost-efficient system DAVID 3D; the other one is the high-end system LEICA T-Scan. By means of these two systems the following surface parameters were determined: the minimum distance between two points, the number of points, the roughness and the fractal dimension. A calculation routine in Matlab© was developed to estimate numerically the fractal dimension with a modified method. A major finding of this study is the suitability of the DAVID 3D system for scanning fractured concrete surfaces at the meso-level (1–100 mm). If a higher resolution is needed the LEICA system is preferable due to its ability to measure a higher number of points within a given area.

A Management Framework for Autonomous and Intelligent Resources in Distributed Manufacturing Systems: A Fractal-based Approach

A Management Framework for Autonomous and Intelligent Resources in Distributed Manufacturing Systems: A Fractal-based Approach

A fractal echelon approach for inventory management in supply chain networks

Abstract A major issue in supply chain inventory management is the coordination of inventory policies adopted by different members in a supply chain including suppliers, manufacturers, distributors, etc. This paper presents a fractal-based approach for inventory management in order to minimize inventory costs and smooth material flows between supply chain members while responsively meeting customer demand. Within this framework, each member in the supply chain is defined as a self-similar structure, referred to as a fractal. A fractal-based echelon does not indicate a functional level or composition of supply chain members but indicates a group of multi- or hetero-functional fractals. The basic fractal unit (BFU) consists of five functional modules including an observer, an analyzer, a resolver, an organizer, and a reporter. The application of the fractal concept into inventory management makes it easy to intuitively understand and manage supply chain inventories because similar functional modules can be iteratively applied to an inventory management system. More specifically, we apply the fractal concept to a vendor managed inventory (VMI) model, referred to as fractal-based VMI (fVMI), where a vendor assumes responsibility for maintaining inventory levels and determining order quantities for his buyers. In this paper, we develop mathematical models for the analyzer and resolver to effectively manage supply chain inventories. For validating the proposed approach, a comprehensive simulation model, representing two VMI initiatives including traditional VMI and fVMI, is constructed and used for comparative analyses of case studies.

Multiscale Segmentation of Elevation Images Using a Mixture-of-Experts Framework

Estimating and segmenting topography by fusing data acquired over multiple resolutions has been extensively studied over the years. The standard multiscale Kalman smoother estimator embedded with a single stochastic model parameterized using power-spectral matching methods has been found to give suboptimal performance in estimating nonstationary topographic variations. The modeling is based on the fact that topography and other geophysical phenomena exhibit a 1/f property. Although acceptable for data sets over large areas, this approximation is found to be poor for data sets over small areas. This letter employs multiple models regulated by a mixture-of-experts network to adaptively fuse the estimates. Alternate to power spectral methods, a fractal-based approach is used to segment data and parameterize the multiple models for better performance. Sensitivity and performance analyses are also performed on the parameters of the estimators, and ideal selection criteria are proposed.

Multiple-instance content-based image retrieval employing isometric embedded similarity measure

In image-based retrieval, global or local features sufficiently discriminative to summarize the image content are commonly extracted first. Traditional features, such as color, texture, shape or corner, characterizing image content are not reliable in terms of similarity measure. A good match in the feature domain does not necessarily map to image pairs with similar relationship. Applying these features as search keys may retrieve dissimilar false-positive images, or leave similar false-negative ones behind. Moreover, images are inherently ambiguous since they contain a great amount of information that justifies many different facets of interpretation. Using a single image to query a database might employ features that do not match user's expectation and retrieve results with low precision/recall ratios. How to automatically extract reliable image features as a query key that matches user's expectation in a content-based image retrieval (CBIR) system is an important topic. The objective of the present work is to propose a multiple-instance learning image retrieval system by incorporating an isometric embedded similarity measure. Multiple-instance learning is a way of modeling ambiguity in supervised learning given multiple examples. From a small collection of positive and negative example images, semantically relevant concepts can be derived automatically and employed to retrieve images from an image database. Each positive and negative example images are represented by a linear combination of fractal orthonormal basis vectors. The mapping coefficients of an image projected onto each orthonormal basis constitute a feature vector. The Euclidean-distance similarity measure is proved to remain consistent, i.e., isometric embedded, between any image pairs before and after the projection onto orthonormal axes. Not only similar images generate points close to each other in the feature space, but also dissimilar ones produce feature points far apart. The utilization of an isometric-embedded fractal-based technique to extract reliable image features, combined with a multiple-instance learning paradigm to derive relevant concepts, can produce desirable retrieval results that better match user's expectation. In order to demonstrate the feasibility of the proposed approach, two sets of test for querying an image database are performed, namely, the fractal-based feature extraction algorithm vs. three other feature extractors, and single-instance vs. multiple-instance learning. Both the retrieval results, execution time and precision/recall curves show favorably for the proposed multiple-instance fractal-based approach.

Video texture modelling and synthesis using fractal processes

The authors propose a new approach for the synthesis of natural video textures using a fractal-based approach. Specifically, a video texture is modelled according to the three-dimensional (3D) extended self-similar (ESS) model introduced, which generalises the fractional Brownian motion process. The analysis of original video textures is based on the estimation of the autocorrelation functions (ACFs) of the textures' increments. The 3D-ESS model is then used to synthesise a process whose increments have the same ACFs of the given prototype. The synthesis is accomplished by generalising to the 3D case the incremental Fourier synthesis algorithm. Experimental results for the analysis and synthesis of natural video textures are eventually provided.