Novel Path Counting-Based Method for Fractal Dimension Estimation of the Ultra-Dense Networks

Next-generation networks,including the Internet of Things(IoT),fifth-generation cellular systems(5G),and sixth-generation cellular systems(6G),suf-fer from the dramatic increase of the number of deployed devices.This puts high constraints and challenges on the design of such networks.Structural changing of the network is one of such challenges that affect the network performance,includ-ing the required quality of service(QoS).The fractal dimension(FD)is consid-ered one of the main indicators used to represent the structure of the communication network.To this end,this work analyzes the FD of the network and its use for telecommunication networks investigation and planning.The clus-ter growing method for assessing the FD is introduced and analyzed.The article proposes a novel method for estimating the FD of a communication network,based on assessing the network’s connectivity,by searching for the shortest routes.Unlike the cluster growing method,the proposed method does not require multiple iterations,which reduces the number of calculations,and increases the stability of the results obtained.Thus,the proposed method requires less compu-tational cost than the cluster growing method and achieves higher stability.The method is quite simple to implement and can be used in the tasks of research and planning of modern and promising communication networks.The developed method is evaluated for two different network structures and compared with the cluster growing method.Results validate the developed method.

Estimation of Data Transfer Routes Fractal Dimension in Large Scale Networks

The article is devoted to the evaluation of fractal properties of routing data in computer large scale networks. Implemented the study of percolation network topological structures of large dimension and made their transformation into fractal macrostructure. An example of calculating the fractal dimension of the data path for the boundary of the phase transition between the states of network connectivity. The dependence of the fractal dimension of the percolation cluster on the size of the square δ-cover and conductivity value network of large dimension. It is shown that for the value of the fractal dimension of the route dc ≈ 1.5, network has a stable dynamics of development and size of clusters are optimized with respect to the current load on the network.

Studying Relationships between the Fractal Dimension of the Drainage Basins and Some of Their Geomorphological Characteristics

Complex nonlinear dynamic systems are ubiquitous in the landscapes and phenomena studied by earth sciences in general and by geomorphology in particular. Many natural landscape features have an aspect such as fractals. In the many geomorphologic phenomena such as river networks and coast lines this is visible. In recent years fractal geometry offers as an option for modeling river geometry and physical processes of rivers. The fractal dimension is a statistical quantity that indicates how a fractal scales with the shrink, the space occupied. This theory has the mathematical basis but also applied in geomorphology and also shown great success. Physical behavior of many natural processes as well as using fractal geometry is predictable relations. Behavior of complex natural phenomena as rivers has always been of interest to researchers. In this study using data basic maps, drainage networks map and Digital Elevation Model of the ground was prepared. Then applying the rules Horton-Strahler river network, fractal dimensions were calculated to examine the relationship between fractal dimension and some rivers geomorphic features were investigated. Results showed fractal dimension of watersheds have meaningful relations with factors such as shape form, area, bifurcation ratio and length ratio in the watersheds.

Dimensional Measurement of Complete-connective Network under the Condition of Particle’s Fission and Growth at a Constant Rate

We construct a complete-connective regular network based on Self-replication Space and the structural principles of cantor set and Koch curve. A new definition of dimension is proposed in the paper, and we also investigate a simplified method to calculate the dimension of two regular networks. By the study results, we can get a extension: the formation of Euclidean space may be built by the process of the Big Bang's continuously growing at a constant rate of three times.

RESEARCH ON FRACTAL CHARACTERISTICS OF URBAN TRAFFIC NETWORK STRUCTURE BASED ON GIS

Traffic network is an importance asp ect of researching controllable parameters of an urban spatial morpholo-gy.Based on GIS,traffic network str ucture complexity can be understood by using fractal geometry in which th e length-radius dimension describes change of network density,and ramification-radius dimension describes complexity and accessibility of urban network.It i s propitious to analyze urban traffic network and to understand dynamic c hange process of traffic network using expanding f ractal-dimension quantification.Meanwhile the length-radius dimension and ramifica-tion-radius dimension could be rega rd as reference factor of quantitative describing urban traffic network.

FRACTAL STUDIES IN A SELF-ASPIRATED REVERSED FLOW JET LOOP REACTOR

1 INTRODUCTIONSelf-aspirated reversed flow jet loop reactors,characterized by a well defined flow pat-tern,well better dispersing effects,relatively low power consumption and a high masstransfer coefficient,are widely used in chemical engineering,especially in biochemicalengineering.The characteristics of such reactors are highly random or stochastic due tothe influence of a variety of phenomena such as jetting and bubbling of the

LOCAL NONLINEAR CHARACTERISTICS OF GAS LIQUID SOLID THREE PHASE SELF ASPIRATED REVERSED FLOW JET LOOP REACTOR

Hursts rescaled range (R/S) analysis and Wolfs attractor reconstruction technique have been adopted to estimate the local fractal dimensions and the local largest Lyapunov exponents in terms of the time series pressure fluctuations obtained from a gas liquid solid three phase self aspirated reversed flow jet loop reactor,respectively.The results indicate that the local fractal dimensions and the local largest Lyapunov exponents in both the jet region and the tubular region inside the draft tube increase with the increase in the jet liquid flowrates and the solid loadings,the local fractal dimension profiles are similar to those of the largest Lyapunov exponent,the local largest lyapunov exponents are positive for all cases,and the flow behavior of such a reactor is chaotic.The local nonlinear characteristic parameters such as the local fractal dimension and the local largest Lyapunov exponent could be applied to further study the flow properties such as the flow regime transitions and flow structures of this three phase jet loop reactor.

Evolution of a mining induced fracture network in the overburden strata of an inclined coal seam

The geological conditions of the Pingdingshan coal mining group were used to construct a physical model used to study the distribution and evolution of mining induced cracks in the overburden strata.Digital graphics technology and fractal theory are introduced to characterize the distribution and growth of the mining induced fractures in the overburden strata of an inclined coal seam.A relationship between fractal dimension of the fracture network and the pressure in the overburden strata is suggested.Mining induced fractures spread dynamically to the mining face and up into the roof as the length of advance increases.Moreover,the fractal dimension of the fracture network increases with increased mining length,in general,but decreases during a period from overburden strata separation until the main roof collapses.It is a1so shown that overburden strata pressure plays an important role in the evolution of mining induced fractures and that the fractal dimension of the fractures increases with the pressure of the overburden.

Research on Evaluation of Degree of Complexity of Mining Fault Network Based on GIS

A large number of spatial and attribute data are involved in coal resource evaluation. Database is a relatively advanced data management technology, but its Major defects are the poor graphic and spatial data functions, from which it is difficult to realize scientific management of evaluation data with spatial characteristics and evaluation result maps. On account of these deficiencies, the evaluation of degree of complexity of mining fault network, based on GIS, is proposed, which integrates management of spatial and attribute data. Fractal is an index which can reflect the comprehensive information of faults' number, density, size, composition and dynamics mechanism. Fractal dimension is used as the quantitative evaluation index. Evaluation software has been developed based on a component GIS-MapX, with which the degree of complexity of fault network is evaluated quantitatively using the quantitative index of fractal dimensions in Liuqiao No.2 coal mine as an example. Results show that it is effective in acquiring model parameters and enhancing the definition of data and evaluation results with the application of GIS technology. The fault network is a system with fractal structure and its complexity can be described reasonably and accurately by fractal dimension, which provides an effective method for coal resource evaluation.

3-D fracture network dynamic simulation based on error analysis in rock mass of dam foundation

Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network model and measured data,a 3-D fracture network dynamic modeling method based on error analysis was proposed.Firstly,errors of four fracture volume density estimation methods(proposed by ODA,KULATILAKE,MAULDON,and SONG)and that of four fracture size estimation methods(proposed by EINSTEIN,SONG and TONON)were respectively compared,and the optimal methods were determined.Additionally,error index representing the deviation between fracture network model and measured data was established with integrated use of fractal dimension and relative absolute error(RAE).On this basis,the downhill simplex method was used to build the dynamic modeling method,which takes the minimum of error index as objective function and dynamically adjusts the fracture density and size parameters to correct the error index.Finally,the 3-D fracture network model could be obtained which meets the requirements.The proposed method was applied for 3-D fractures simulation in Miao Wei hydropower project in China for feasibility verification and the error index reduced from 2.618 to 0.337.

A fractal-based model for the microstructure evolution of silicon bronze wires fabricated by dieless drawing

The back-propagation neural （BPN） network was proposed to model the relationship between the parameters of the dieless draw- ing process and the microstrecmres of the QSi3-1 silicon bronze alloy. Combined with image processing techniques, grain sizes and grain-boundary morphologies were respectively determined by the quantitative metallographic method and the flactal theory. The outcomes obtained show that the deformed microstructures exhibit typical fractal features, and the boundaries can be characterized quantitatively by ffactal dimensions. With the temperature of 600-800℃ and the drawing speed of 0.67-1.00 mm-s-1, either a lower temperature or a higher speed will cause a smaller grain size together with an elevated fractal dimension. The developed model can be capable for forecasting the microstructure evolution with a minimum error. The average relative errors between the predicted results and the experimental values of grain size and fractal dimension are 3.9% and 0.9%, respectively.

FPGA implementation of fractal patterns classifier for multiple cardiac arrhythmias detection

This paper proposes the fractal patterns classifier for multiple cardiac arrhythmias on field-programmable gate array (FPGA) device. Fractal dimension transformation (FDT) is employed to adjoin the fractal features of QRS-complex, including the supraventricular ectopic beat, bundle branch ectopic beat, and ventricular ectopic beat. FDT with fractal dimension (FD) is addressed for constructing various symptomatic patterns, which can produce family functions and enhance features, making clear differences between normal and unhealthy subjects. The probabilistic neural network (PNN) is proposed for recognizing multiple cardiac arrhythmias. Numerical experiments verify the efficiency and higher accuracy with the software simulation in order to formulate the mathematical model logical circuits. FDT results in data self-similarity for the same arrhythmia category, the number of dataset requirement and PNN architecture can be reduced. Its simplified model can be easily embedded in the FPGA chip. The prototype classifier is tested using the MIT-BIH arrhythmia database, and the tests reveal its practicality for monitoring ECG signals.

Two Network Structure Indicators for Conventional Public Transit

The significance of network structure indicators for the planning and management of conventional public transit is widely acknowledged.In order to improve and enrich the conventional public transit assessment system,two network structure indicators are proposed.Firstly,according to the obvious defects lying in the traditional no-linear coefficient,the realistic no-linear coefficient γRNL,a modified no-linear coefficient indicator,is put forward,which takes into account the effects of barriers in a city.Secondly,to cover the gap of an indicator which can reflect the coverage homogeneity of a transit network,the length dimension LDis proposed on the basis of Fractal Theory.Finally,a case study is applied to verify the validity and practicability of the two indicators in problem diagnosis using regression analysis.The results validate that γRNLcan evaluate the detour of bus lines more reasonably than the previous no-linear coefficient because it reflects the layout of bus lines,and LDcan represent the rate of change of the network density,adding a new member to the scheme of network structure indicators for public transit.

基于卷积神经网络的页岩CT分形维数预测及其抗干扰能力应用

【目的】为了深入探究页岩储层内部的孔裂隙分布规律以优化页岩油气的开发方案和提高产能。【方法】提出一种基于卷积神经网络的页岩CT图片分形维数预测方法,自主搭建适用于油页岩CT图片的卷积神经网络模型,分别将不同温度热解下的油页岩样品CT切片和其对应的分形维数作为数据集和标签,对搭建好的卷积神经网络进行训练并预测,实现对页岩CT图片分形维数的提取。【结果】结果证明,通过卷积神经网络预测的页岩CT图片分形维数与盒子计数法计算得到的分形维数十分接近,大约差0.01,且在计算速度更快的情况下还可以很大程度地忽略CT图片的噪声和伪影。新方法有效地捕捉到了图像的结构特征,能够对图片的分形维数进行可靠的预估并具有较好的抗干扰能力。

致密砂岩裂缝网络复杂性及其影响因素研究

裂缝网络分析在油气藏勘探开发过程中发挥着着重要作用,致密砂岩裂缝网络复杂性分析对水力压裂优化、裂缝网络预测、裂缝建模等具有重要意义。文章结合致密砂岩复杂的裂缝网络动态演化的实验研究,明确了裂缝网络的分形和多重分形谱特征,深入分析了裂缝网络的复杂性及其主控因素。通过岩石力学和X射线CT扫描实验确定了岩石力学和裂缝网络特征;通过扫描电镜实验、裂缝网络的分形分析定量化表征了致密砂岩微观组构和裂缝网络的分形特征。研究结果表明:致密砂岩的石英含量为28.08~52.88%,黏土含量为11.54~25.45%,粒度为61.18~184.55μm,孔隙度为8.125%~10.296%;单轴抗压强度介于69.09~188.33 MPa,弹性模量介于31.69~92.76 GPa;分形维数(DB)为1.28~2.35,谱宽(Δα)平均值为1.0851~1.3638。裂缝的萌生、扩展贯穿于应力–应变的全过程,裂缝网络的复杂性主要受控于致密砂岩的微观组构特征,并且具有明显的围压和尺度效应。三维裂缝网络的分形维数、多重分形谱的谱宽平均值可分别表征裂缝空间分布的复杂性和非均质性,两者之间具有相对的独立性。砂岩中石英、长石等脆性矿物含量越高、储层孔隙度越大、砂岩组成粒度越小裂缝网络分形维数越大,谱宽平均值越小;无围压情况下,样品裂缝网络的复杂性主要受控于微观组构特征,且随着轴向压力的增加而增加;存在围压的情况下,围压起主导作用,围压越大分形维数越小,谱宽平均值越大。而黏土矿物不利于复杂裂缝的形成;小尺度样品的分形维数和谱宽平均值大于尺度大样品的分形维数和谱宽平均值。砂岩的弹性模量和抗压强度与分形维数和谱宽平均值具有一定的正相关性。

不同破断距下开采覆岩裂隙网络分形特征研究

为研究神东矿区不同破断距下开采覆岩裂隙网络分形特征,分析了基本顶周期破断距影响因素,选取大柳塔煤矿52505和上湾煤矿12401工作面进行物理相似模拟实验,探究了不同破断距影响下覆岩裂隙网络分布特征,借助Matlab软件获取不同覆岩裂隙网络分布分形维数,定量描述了覆岩裂隙发育特征,进一步探讨了覆岩裂隙传播影响下不同岩层沉降规律。研究结果表明:影响基本顶周期破断距主要因素包括基本顶厚度、抗拉强度以及承载载荷;大柳塔52505工作面、上湾12401工作面模拟开采平均破断距分别为20和30.4 m;不同破断距下覆岩裂隙网络的分形维数随煤层工作面推进呈现阶梯形增长态势,分形维数可较好地表征覆岩裂隙分布。两工作面最高离层裂隙发育高度与分形维数变化趋势均近似呈非线性正相关;不同破断距对覆岩整体裂隙发育扩展趋势影响显著,工作面回采前期大柳塔52505工作面分形维数相对较低,回采中后期则相反,破断距小,覆岩整体裂隙发育程度相对较高;两工作面覆岩沉降曲线呈“凸”型,近似以采空区中部对称。

利用分形维数和BP神经网络实现超声导波缺陷分类的实验研究

近年来,超声导波技术广泛应用于管道的无损检测中。然而,不同微小缺陷类型(如裂纹、孔洞、凹陷变形等)引起的缺陷回波微弱且无明显不同,使得微小缺陷的识别和分类始终是检测难点。为识别不同微小缺陷的类型,利用对微弱周期信号敏感的Duffing系统,提出了基于Duffing系统的动力学指标分形维数和反向传播(Back Propagation,BP)神经网络相结合的信号特征分类方法。利用BP神经网络对输入参数进行训练。其中,输入参数分为两组。第一组输入参数为由小波能量值、时域参数、分形维数特征等组成的21维k_(1)向量。第二组作为对照组,其输入参数为波能量值、时域参数组成的18维k_2向量。上述两组均输出3维向量,即输出缺陷类型。数值模拟及实验验证均表明,在加入混沌指标分形维数后识别准确率明显提升。其中,数值模拟的准确率由86.35%提升至91.85%,实验中的准确率由83.16%提升至86.06%。数值模拟和实验都验证了利用分形维数和BP神经网络结合能够更好地完成管道缺陷的识别和分类。创新性地将分形维数作为BP神经网络的特征输入,有效提高了分类的准确率,实现了因管道中小缺陷实验数据不足或检测难度大的有效识别和精确分类。研究对于实际工程中管道缺陷分类,预防管道事故具有重要意义。

基于概率穿越可视图的时间序列网络多重分形研究与应用

对有限穿越可视图进行改进,提出了概率穿越可视图.首先,将间接可视的节点之间的关联处理为穿越距离的函数,而且节点之间的关联随穿越距离的增加而减小,从而将无权图形式的时间序列网络推广到带权图;其次,采用复杂网络中的网络维数计算方法处理所得到的时间序列网络的分形维数,从而对其自相似特性进行分析;最后,通过划分不同的时间粒度得到多个不同的时间序列网络,对应有多个不同的分形维数,进而分析了所得到的时间序列网络的多重分形特性.在与经典的可视图法、水平可视图法及有限穿越可视图法的对比中论证了所提出的概率穿越可视图的优势.

基于卷积神经网络的三维表面分形维数识别

分形维数作为机械加工表面形貌的重要参数,可用于接触表面的摩擦特性分析。然而,现有的分形维数计算方法大多需要选择多组尺度计算相应的测度,这不仅影响分形维数的计算速度和精度,也增加了计算的复杂度。针对机加工表面的三维分形维数测量问题,提出一种基于卷积神经网络的分形维数的识别方法。采用Weierstrass-Mandelbrot分形函数构建一个包含不同分形维数的三维粗糙表面数据集,利用单因素实验法分析网络参数(网络深度、滤波器大小、滤波器数量)对三维分形维数识别精度的影响,以找到最优的神经网络参数组合。通过与差分盒维数法、三角棱镜表面积法和分形布朗运动法3种方法进行对比,验证卷积神经网络法识别三维分形维数的有效性。实验结果表明:基于卷积神经网络方法计算的分形维数平均绝对百分比误差可控制在1.5%以下;该方法在分形维数全动态范围内都表现出较小的误差,可用于计算三维表面轮廓分形维数。

基于GIS的重庆中心城区路网分形特征研究

基于GIS技术,引入分形理论,以重庆中心城区为研究区域,以城市路网为研究对象,测算重庆中心城区内部道路的盒覆盖维数、长度-半径维数、分枝数目-半径维数,总结分形特征。重庆中心城区的盒覆盖维数、长度-半径维数、分枝数目-半径维数分别为1.448、1.4867、1.3142,重庆中心城区作为山地城市,道路建设受山水影响较大,路网距离分形形态成熟度还有一定的差距,具有较大的发展潜力。