A novel box-counting method for quantitative fractal analysis of threedimensional pore characteristics in sandstone

Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.

A Successive Shift Box-Counting Method for Calculating Fractal Dimensions and Its Application in Identification of Faults

Fractal dimensions of a terrain quantitatively describe the self-organizedstructure of the terrain geometry. However, the local topographic variation cannot be illustrated bythe conventional box-counting method. This paper proposes a successive shift box-counting method,in which the studied object is divided into small sub-objects that are composed of a series of gridsaccording to its characteristic scaling. The terrain fractal dimensions in the grids are calculatedwith the successive shift box-counting method and the scattered points with values of fractaldimensions are obtained. The present research shows that the planar variation of fractal dimensionsis well consistent with fault traces and geological boundaries.

Combining Fractals and Box-Counting Dimension

In this paper, the box-counting dimension is used to derive an explicit formula for the dimension of a fractal constructed using several contractions or by combining fractals. This dimension agrees with the Hausdorff dimension in the particular case when the scales factors considered are all the same. A more general sufficient condition for the box-counting dimension and the Hausdorff dimension to be the same is given. It is also shown that the dimension of the fractal obtained by combining two fractals is the weighted average of the dimensions of the two fractals.

DIMENSION AND DIFFERENTIABILIIY OF A CLASS OF FRACTAL INTERPOLATION FUNCTIONS

In this paper, a new iterated function system consisting of non-linear affinemaps is constructed. We investigate the fractal interpolation functions generated bysuch a system and get its differentiability, its box dimension, its packing dimension,and a lower bound of its Hansdorff dimension.

Fractal Dimension Based Shot Transition Detection in Sport Videos

Increase in application fields of video has boosted the demand to analyze and organize video libraries for efficient scene analysis and information retrieval. This paper addresses the detection of shot transitions, which plays a crucial role in scene analysis, using a novel method based on fractal dimension (FD) that carries information on roughness of image intensity surface and textural structure. The proposed method is tested on sport videos including soccer and tennis matches that contain considerable amount of abrupt and gradual shot transitions. Experimental results indicate that the FD based shot transition detection method offers promising performance with respect to pixel and histogram based methods available in the literature.

FINITE DIMENSION OF GLOBAL ATTRACTORS FOR DISSIPATIVE EQUATIONS GOVERNING MODULATED WAVE

The finite dimension of the global attractors for the systems of the perturbed and unperturbed dissipative Hamiltonian amplitude equations governing modulated wave are investigated.An interesting result is also obtained that the upper bound of the dimension of the global attractor for the perturbed equation is independent of ε.

Realizing the Box-counting Method for Calculating Fractal Dimension of Urban Form Based on Remote Sensing Image

In the research of fractal cities, the fractal dimension is very important. It is used to describe the fractal character of the city. The authors have designed two approaches to calculate the fractal dimension by the box-counting method through an example of Beijing, which are called the vector method and the grid method, respectively. The former calculates the fractal dimension through an intersecting analysis in ArcView; and the latter is carried out by programming in Matlab. They are compared from three aspects： the calculating process, the limits in use, and the results. As a result, the conclusion is made that there are merits and faults on both methods, and they should be chosen to use properly in practical situation.

Fractal characterization of sediment particle-size distribution in the water-level fluctuation zone of the Three Gorges Reservoir, China

The combined effect of periodic water impoundment and seasonal natural flood events has created a 30 m high water-level fluctuation zone(WLFZ) around the Three Gorges Reservoir(TGR), China, forming a unique eco-landscape. Siltation, eutrophication, enrichment of heavy metals, and methane emissions in the WLFZ have been widely associated with sediment and soil particles generated from the upstream catchment or upland slopes. However, little attention has been paid to the complexity of sediment particle-size distributions in the WLFZ. In the present study, core samples(from a 345 cm thick sediment core from the base of the WLFZ), slope transect surface samples(across/up a WLFZ slope), and along-river/longitudinal surface samples(from the reservoir reaches) were collected. Laser granulometry and a volume-based fractal model were used to reveal the characteristics of sediment particle-size distributions. Results indicate that the alternation of coarse and fine particles in the sedimentary core profile is represented as a fluctuation of low and high values of fractal dimension(D), ranging from 2.59 to 2.77. On the WLFZ slope transect, surface sediment particles coarsen with increasing elevation, sand content increases from 3.3% to 78.5%, and D decreases from 2.76 to 2.53. Longitudinally, surface sediments demonstrate a downstream-fining trend, and D increases gradually downstream. D is significantly positively correlated with the fine particle content. We conclude that D is a useful measure for evaluating sediment particle-size distribution.

Fractal characterization and frequency properties of near-fault ground motions

This study explores the irregularity and complexity of strong earthquake ground motions from the perspective of fractal geometry, and constructs a relation with the frequency content of the ground motions. The box-counting fractal dimensions and five representative period parameters of near-fault ground motions from the Chi-Chi and Northridge earthquakes are calculated and compared. Numerical results indicate that the acceleration and velocity time histories of ground motions present the statistical fractal property, and the dominant pulses of near-fault ground motions have a significant influence on their box dimensions and periods. Further, the average box dimension of near-fault impulsive ground motions is smaller, and their irregular degree of wave forms is lower. Moreover, the box dimensions of ground motions reflect their frequency properties to a large extent, and can be regarded as an alternative indicator to represent their frequency content. Finally, the box dimension D of the acceleration histories shows a considerably negative correlation with the mean period T. Meanwhile, the box dimension of the velocity histories Dye is negatively correlated with the characteristic period T and improved characteristic period Tgi.

Fractal analysis of thermal conduction of loose coal

For deep mining engineering, heat transfer of coal mass is a vital factor in the thermal environment of coal mines. In order to study the thermal conduction mechanism, we obtained gray images of coal mass microstructure by scanning samples with a digital microscope. With the use of Matlab, these gray images were transformed into binary images, which were then transformed into a corresponding matrix consisting only of the values 0 and 1. According to the calculation method of box-counting dimension, we calculated the fractal dimension of the loose coal to be approximately 1.86. The thermal conductivity expressions of loose coal were derived based on the simulation method of thermal resistance. We calculated the thermal conductivity of loose coal by using a fractal model and compared the calculated values with our experimental data. The results show that the test data show an encourag-ing agreement with the calculated values. Hence fractal theory is a feasible method for studying thermal conductivity of loose coal.

基于3D-Hibert能量谱和多尺度分形特征的通信辐射源个体识别

针对通信辐射源的个体识别问题,提出一种基于希尔伯特—黄变换(HHT,Hilbert-Huang transform)和多尺度分形特征的新方法。首先,通过HHT得到时频能量谱,将其视为三维空间中的复杂曲面,即3D-Hilbert能量谱;然后,利用分形理论通过多尺度分块提取差分盒维数和多重分形维数二维特征组成特征向量;最后,采用支持向量机分类器结合二维特征向量实现通信辐射源的个体分类。分别利用仿真信号和调制方式相同的实际通信信号,验证并对比了所提方法与另外2种方法在2类及3类目标情况下的识别性能。实验结果表明,所提方法的识别率远高于其他2种方法,能够克服低信噪比和少训练样本数量对识别性能的负面影响,证明了所提特征的稳定性、充分性及可分性。

图像分形维数的差分盒方法的改进研究

分形可以提供大量关于自然景象复杂程度的信息,差分盒算法作为一种图像分形维数提取算法被广泛应用。针对差分盒算法计算精度不高和计算量大等问题,基于动态规划和残差分析的思想,提出了改进的差分盒分形维数计算方法。实验结果表明,该算法能够有效地区分不同类型的地貌,能够应用于遥感图像的地物分类。

中国矿业城市空间形态特征及其空间分异

矿业城市是以矿产资源开采和初加工为主的资源型城市,伴随矿业城市发展的各个阶段,城市空间会呈现相应的演变过程和格局,城市经济的转型也必将带来城市空间结构的响应。矿业城市空间结构受自然资源和产业发展的影响明显,是基于自然资源与产业转型的空间可持续发展的典型研究对象之一。选取中国33个公认的典型地级矿业城市作为研究样本,提取空间结构数据进行紧凑度和分形维数的计算与统计分析,力图总结我国矿业城市对比其他类型城市在空间形态上的基本特征和空间分异规律。结果表明,矿业城市空间形态的紧凑度较低,发展呈分散态;矿业城市空间的边界比较复杂,呈不规则状态;矿业城市紧凑度与边界维数呈负相关;矿业城市空间形态受城市发展阶段、有无依托、其他组织的人为规划等因素影响,呈现一定的空间分异规律;矿业城市空间形态与人口规模和经济发展水平存在相关。

空气-水两相流压差波动研究

两相流的压差波动过程包含了关于流动的大量信息 ,是实现流动监测与控制的重要研究内容。该文研究了U形管垂直上升段空气 水两相流压差波动过程的统计和分形特征 ,着重分析了压差波动过程的均值、均方根、分维数随折算气速和液速的变化规律。结果表明这些特征参数都与流型有密切的联系 ,但据此识别流型缺乏实用性。均方根在低液速下随气速的变化体现了流型的转变 ,高液速时则不明显。相关研究根据概率密度分布函数识别流型的方法不具有普适性。实验发现环状流区高气速时的压差波动分维数大于1.5 ,在其它流型内都小于 1.5。同时 ,折算液速的大小强烈影响压差波动的混沌特性。

基于Wigner分布和分形维数的柴油机故障诊断

针对柴油机配气机构故障诊断问题,提出了一种基于Wigner分布和差分分形盒维数的故障诊断方法。首先,利用改进局部均值分解算法对柴油机缸盖振动信号进行分解,并采用相关性分析剔除噪声和伪分量;然后,分别对各相关分量进行Wigner时频分析,将结果线性叠加得到振动时频图,再提取图像的差分分形盒维数作为故障特征;最后,利用k-最近邻(k-NN)实现故障诊断。仿真结果表明,改进局部均值分解算法可以抑制Wigner分布交叉项的干扰。实验结果显示,差分分形盒维数优于其他6种典型故障特征,利用本研究提出的方法对配气机构进行故障诊断的正确率为97.2%,该方法可以用于柴油机配气机构故障诊断。

基于分数维的图像检索新方法

在研究两种分数维———微分计盒维数和多分形维数的基础上提出了分数维直方图的概念 ,并把它用于基于内容的图像检索 ,提出了一种新的纹理特征检索算法———二维分数维直方图相交法 对Brodatz标准纹理库和真实图像库检索的结果表明其方法具有良好的性能 。

北喜马拉雅穹隆带然巴韧性剪切带石英动态重结晶颗粒的分维几何分析与主要流变参数的估算

位于北喜马拉雅穹隆带东段的然巴构造穹隆外围发育环形韧性剪切带,带内岩石经韧性剪切形成各类糜棱状岩石。石英为带内变形岩中最为常见的造岩矿物,在不同的温度、应变速率下产生不同的显微构造,其中动态重结晶最为常见。重结晶新晶颗粒边界普遍具有锯齿状或港湾状结构,是应变和变形环境的天然记录。新晶粒分维几何统计分析表明:带内动态重结晶石英颗粒边界形态具有自相似性(1≤D≤2),表现出分形特征,分维数值为1.14～1.19,变形温度大约500℃。同构造变质环境属中—高绿片岩相;初步估算古应变速率可能低于10-9.5S-1;根据重结晶粒径估算变形古应力6.2～58.8MPa。

苜蓿草粉对金属材料磨损表面的分形维数计算

基于分形理论和扫描电镜分析,采用差分计数盒法(DBC)计算了苜蓿草粉对金属材料磨损表面的三维分形维数。结果表明:基于DBC法和磨损表面SEM照片计算所得的分形维数,可以表征苜蓿草粉对金属材料磨损表面的形貌特征;相同加工条件下的金属加工表面具有相近的分形维数,但不能通过分形维数区分材料;苜蓿草粉磨损后的磨损表面分形维数与磨损体积损失有着密切的关系,体积磨损量越大,分形维数也越大。

基于纹理复杂度的自适应分数阶微分算法

图像分数阶微分算子具有较强的纹理细节信息增强能力,但最佳分数阶微分的阶数需要人为指定。为此,分析传统的分数盒维计算方法并对其进行改进,提出一种基于纹理复杂度的自适应分数阶微分算法。选择可以表示纹理细节复杂程度的分数维作为参数,自适应确定微分的阶数。实验结果表明,改进算法提取图像边缘的效果较好。

基于自适应分数阶微分的Harris角点检测算法

针对Harris算法在对纹理复杂程度高的图像进行角点检测时会出现大量伪角点,以及分数阶微分应用到图像处理中需要人为地指定阶数的缺点。分析了伪角点大量产生的原因,并提出以分数阶替换原算法中的整数阶对图像进行微分的改进方法,以及一种以图像的分形维数作为参数来自适应地选择微分所需要的阶数的方法。从而使图像做微分运算时能更好地保留图像中的边缘信息,使分数阶微分可以应用于视频目标追踪、视频稳像等实时性要求较高的场合。实验表明,改进算法在进行角点检测时具有更高的精确度。