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Hierarchical fractal structure of perfect single-layer graphene

T. Zhang, K. Ding

《机械工程前沿（英文）》 2013年 第8卷 第4期   页码 371-382 doi: 10.1007/s11465-013-0279-1

摘要：

The atomic lattice structure of perfect single-layer graphene that can actually be regarded as a kind of hierarchical fractal structure from the perspective of fractal geometry was studied for the first time. Three novel and special discoveries on hierarchical fractal structure and sets were unveiled upon examination of the regular crystal lattices of the single-layer graphene. The interior fractal-type structure was discovered to be the fifth space-filling curve from physical realm. Two efficient methods for calculating the fractal dimension of this fresh member was also provided. The outer boundary curve had a fractal dimension equal to one, and a multi-fractal structure from a naturally existing material was found for the first time. A series of strict self-similar hexagons comprised a rotating fractal set. These hexagons slewed at a constant counterclockwise angle of 19.1° when observed from one level to the next higher level. From the perspective of fractal geometry, these pioneering discoveries added three new members to the existing regular fractal structures and sets. A fundamental example of a multi-fractal structure was also presented.

关键词： hierarchical fractal structure     fractal dimension     the fifth space-filling curve     multi-fractal structure    

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PD pattern recognition based on multi-fractal dimension in GIS

ZHANG Xiaoxing, YAO Yao, TANG Ju, ZHOU Qian, XU Zhongrong

《机械工程前沿（英文）》 2008年 第3卷 第3期   页码 270-275 doi: 10.1007/s11465-008-0042-1

摘要： This paper designs four types of gas insulated substation (GIS) defect models based on partial discharge (PD) characteristics and its defections. The GIS gray intensity images are constructed based on the mass specimens gathered by the ultra-high frequency and high-speed sampling systems. The multi-fractal dimension is founded on the box-counting dimension and multi-fractal theories. The GIS gray intensity images distillation methods, based on multi-fractal characteristics, is put forward. The box-counting dimension, multi-fractal dimension, and discharge centrobaric characteristics of the PD images are also extracted. The characteristic variables are then classified by the radial basis function (RBF) network. Identified results show that the methods can effectively elevate the discrimination of the four types of defects in GIS.

关键词： substation     high-speed     discharge centrobaric     network     ultra-high frequency    

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A new proof of Honeycomb Conjecture by fractal geometry methods

Tong ZHANG, Kai DING

《机械工程前沿（英文）》 2013年 第8卷 第4期   页码 367-370 doi: 10.1007/s11465-013-0273-7

摘要：

Based on fractal geometry, we put forward a concise and straightforward method to prove Honeycomb Conjecture—a classical mathematic problem. Hexagon wins the most efficient covering unit in the two- dimensional space, compared with the other two covering units—triangle and square. From this point of view, honeycomb is treated as a hierarchical fractal structure that fully fills the plane. Therefore, the total side length and area are easily calculated and from the results, the covering efficiency of each possible unit is provided quantitatively.

关键词： Honeycomb Conjecture     fractal geometry     hierarchical fractal structure    

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Aggregating structure in coal water slurry studied by eDLVO theory and fractal dimension

Qiang LI, Qian WANG, Jian HOU, Jiansheng ZHANG, Yang ZHANG

《能源前沿（英文）》 2023年 第17卷 第2期   页码 306-316 doi: 10.1007/s11708-021-0736-1

摘要： Coal water slurry gasification is a main source of hydrogen in the developing hydrogen economy. Moreover, biomass and waste can be added, making gasification process greener. To expand the application of coal water slurry and gasification process, it is necessary to understand the micro-structure in this large particle suspension system. In this paper, the micro-structure in coal water slurry was studied by extended DLVO (eDLVO) theory and fractal dimension, which is used to explain the mechanism of stability in large particle suspension systems. The interaction between two coal particles was characterized from the interparticle potential and energy barrier based on the eDLVO theory. The rheology and stability between different types of coals are measured and explained by the aggregating structure and fractal dimension in coal water slurry. The results indicated that there would be an aggregating structure in high rank coals, due to the interparticle potential caused by the surface properties, but probably not in low rank coals. This aggregating structure can be described and characterized by fractal dimension. The aggregation of particles is the source of the stability for high rank coals, as the close-packed 3D network structure in large particle suspension can support coal particles from settling down. The results have demonstrated that the combination of the eDLVO theory and rheological measurement is an effective way to investigate the stability of large particle suspension systems.

关键词： coal water slurry     extended DLVO (eDLVO)     fractal dimension     stability    

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Theoretical study on the confine-stiffening effect and fractal cracking of square concrete filled steel

《结构与土木工程前沿（英文）》 2021年 第15卷 第6期   页码 1317-1336 doi: 10.1007/s11709-021-0763-3

摘要： Tension stress in steel-concrete composite is widely observed in engineering design. Based on an experimental program on tension performance of three square concrete-filled tubes (SCFT), the tension theory of SCFT is proposed using a mechanics-based approach. The tension stiffening effect, the confining strengthening effect and the confining stiffening effect, observed in tests of SCFTs are included in the developed tension theory model. Subsequently, simplified constitutive models of steel and concrete are proposed for the axial tension performance of SCFT. Based on the MSC.MARC software, a special fiber beam-column element is proposed to include the confining effect of SCFTs under tension and verified. The proposed analytical theory, effective formulas, and equivalent constitutive laws are extensively verified against three available tests reported in the literature on both global level (e.g., load-displacement curves) and strain level. The experimental verification proves the accuracy of the proposed theory and formulations in simulating the performance of SCFT members under tension with the capability to accurately predict the tensile strength and stiffness enhancements and realistically simulate the fractal cracking phenomenon.

关键词： square concrete filled tubes     confine-stiffening     confine-strengthening     fractal cracking     fracture    

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Copper fractal growth during recycling from waste printed circuit boards by slurry electrolysis

《环境科学与工程前沿（英文）》 2021年 第15卷 第6期 doi: 10.1007/s11783-021-1405-7

摘要：

• Copper fractal growth was observed during WPCBs recycling by slurry electrolysis.

关键词： Dendritic copper     Fractal growth     WPCBs     Slurry electrolysis    

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Anisotropy of multi-layered structure with sliding and bonded interlayer conditions

Lingyun YOU, Kezhen YAN, Jianhong MAN, Nengyuan LIU

《结构与土木工程前沿（英文）》 2020年 第14卷 第3期   页码 632-645 doi: 10.1007/s11709-020-0617-4

摘要： A better understanding of the mechanical behavior of the multi-layered structure under external loading is the most important item for the structural design and the risk assessment. The objective of this study are to propose and develop an analytical solution for the mechanical behaviors of multi-layered structure generated by axisymmetric loading, and to investigate the impact of anisotropic layers and interlayer conditions on the multi-layered structure. To reach these objectives, first, according to the governing equations, the analytical solution for a single layer was formulated by adopting the spatial Hankel transform. Then the global matrix technique is applied to achieve the analytical solution of multi-layered structure in Hankel domain. The sliding and bonded interlayer conditions were considered in this process. Finally, the numerical inversion of integral transform was used to solve the components of displacement and stress in real domain. Gauss-Legendre quadrature is a key scheme in the numerical inversion process. Moreover, following by the verification of the proposed analytical solution, one typical three-layered flexible pavement was applied as the computing carrier of numerical analysis for the multi-layered structure. The results have shown that the anisotropic layers and the interlayer conditions significantly affect the mechanical behaviors of the proposed structure.

关键词： multi-layered structure     Hankel transformation     anisotropic     transversely isotropic     interlayer condition     Gauss-Legendre quadrature    

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Fractal characteristic evaluation and interpolation reconstruction for surface topography of drilled

《机械工程前沿（英文）》 2021年 第16卷 第4期   页码 840-854 doi: 10.1007/s11465-021-0643-5

摘要： In this paper, an improved fractal interpolation model is proposed to reconstruct the surface topography of composite hole wall. This model adopts the maximum positive deviations and maximum negative deviations between the measured values and trend values to determine the contraction factors. Hole profiles in 24 directions are measured. Fractal parameters are calculated to evaluate the measured surface profiles. The maximum and minimum fractal dimension of the hole wall are 1.36 and 1.07, whereas the maximum and minimum fractal roughness are 4.05 × 10 −5 and 4.36 × 10 −10 m, respectively. Based on the two-dimensional evaluation results, three-dimensional surface topographies in five typical angles (0°, 45°, 90°, 135°, and 165°) are reconstructed using the improved model. Fractal parameter D s and statistical parameters Sa, Sq, and Sz are used to evaluate the reconstructed surfaces. Average error of D s, Sa, Sq, and Sz between the measured surfaces and the reconstructed surfaces are 1.53%, 3.60%, 5.60%, and 9.47%, respectively. Compared with the model in published literature, the proposed model has equal reconstruction effect in relatively smooth surface and is more advanced in relatively rough surface. Comparative results prove that the proposed model for calculating contraction factors is more reasonable.

关键词： surface topography     fractal evaluation     fractal interpolation     reconstruction     composite    

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Uncertain and multi-objective programming models for crop planting structure optimization

Mo LI,Ping GUO,Liudong ZHANG,Chenglong ZHANG

《农业科学与工程前沿（英文）》 2016年 第3卷 第1期   页码 34-45 doi: 10.15302/J-FASE-2016084

摘要： Crop planting structure optimization is a significant way to increase agricultural economic benefits and improve agricultural water management. The complexities of fluctuating stream conditions, varying economic profits, and uncertainties and errors in estimated modeling parameters, as well as the complexities among economic, social, natural resources and environmental aspects, have led to the necessity of developing optimization models for crop planting structure which consider uncertainty and multi-objectives elements. In this study, three single-objective programming models under uncertainty for crop planting structure optimization were developed, including an interval linear programming model, an inexact fuzzy chance-constrained programming (IFCCP) model and an inexact fuzzy linear programming (IFLP) model. Each of the three models takes grayness into account. Moreover, the IFCCP model considers fuzzy uncertainty of parameters/variables and stochastic characteristics of constraints, while the IFLP model takes into account the fuzzy uncertainty of both constraints and objective functions. To satisfy the sustainable development of crop planting structure planning, a fuzzy-optimization-theory-based fuzzy linear multi-objective programming model was developed, which is capable of reflecting both uncertainties and multi-objective. In addition, a multi-objective fractional programming model for crop structure optimization was also developed to quantitatively express the multi-objective in one optimization model with the numerator representing maximum economic benefits and the denominator representing minimum crop planting area allocation. These models better reflect actual situations, considering the uncertainties and multi-objectives of crop planting structure optimization systems. The five models developed were then applied to a real case study in Minqin County, north-west China. The advantages, the applicable conditions and the solution methods of each model are expounded. Detailed analysis of results of each model and their comparisons demonstrate the feasibility and applicability of the models developed, therefore decision makers can choose the appropriate model when making decisions.

关键词： crop planting structure     optimization model     uncertainty     multi-objective    

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Permeability analysis and seepage process study on crystal layer in melt crystallization with fractal

Xiaobin JIANG, Baohong HOU, Yongli WANG, Jingkang WANG

《化学科学与工程前沿（英文）》 2011年 第5卷 第4期   页码 435-441 doi: 10.1007/s11705-011-1139-3

摘要： In this paper a porous media seepage model was applied to analyze the permeability and study the seepage process of crystal pillar formed in the preparation of electronic grade phosphoric acid (EGPA). By inspecting the seeping process, the structure parameter of crystal pillar could be obtained. Two basic ideal models (perfectly separated model and perfectly connected model) were presented and a characterized factor was introduced to modify the model. A good simulation result was obtained which met the experiment result well. The relationship between and permeability were also discussed. The characterized factor showed potential application on optimizing process.

关键词： melt crystallization     porous media     fractal     permeability     hyperpure material     simulation    

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Application of fractal theory to unsaturated soil mechanics

XU Yongfu, TONG Lixin

《结构与土木工程前沿（英文）》 2007年 第1卷 第4期   页码 411-421 doi: 10.1007/s11709-007-0056-5

摘要： The mechanical properties of unsaturated soils are a function of the saturation degree or matric suction, and can be obtained based on currently available procedures. However, each procedure has its limitations and consequently, care should be taken in the selection of a proper procedure. The fractal approach seems to be a potentially useful tool to describe hierarchical systems and is suitable to model the structure and hydraulic properties of unsaturated soils. In this paper, the soil-water characteristics, unsaturated hydraulic conductivity function, unsaturated shear strength, swelling deformation and compression were derived from the fractal model for the pore-size distribution, and were expressed by only two independent physical parameters, the fractal dimension and the air entry value. The predictions of the proposed soil-water characteristics, unsaturated hydraulic conductivity, unsaturated shear strength, swelling deformation and compression were in good agreement with published experimental data. Comparisons between the experimental results of unsaturated hydraulic conductivity and the predictions of the both fractal model and the van Genuchten-Mualem model were also performed, and it was found that the predictions of the fractal model were better than that of the van Genuchten-Mualem model.

关键词： selection     soil-water     independent physical     unsaturated     strength    

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Finite element model updating of a large structure using multi-setup stochastic subspace identification

Reza KHADEMI-ZAHEDI, Pouyan ALIMOURI

《结构与土木工程前沿（英文）》 2019年 第13卷 第4期   页码 965-980 doi: 10.1007/s11709-019-0530-x

摘要： In the present contribution, operational modal analysis in conjunction with bees optimization algorithm are utilized to update the finite element model of a solar power plant structure. The physical parameters which required to be updated are uncertain parameters including geometry, material properties and boundary conditions of the aforementioned structure. To determine these uncertain parameters, local and global sensitivity analyses are performed to increase the solution accuracy. An objective function is determined using the sum of the squared errors between the natural frequencies calculated by finite element method and operational modal analysis, which is optimized using bees optimization algorithm. The natural frequencies of the solar power plant structure are estimated by multi-setup stochastic subspace identification method which is considered as a strong and efficient method in operational modal analysis. The proposed algorithm is efficiently implemented on the solar power plant structure located in Shahid Chamran university of Ahvaz, Iran, to update parameters of its finite element model. Moreover, computed natural frequencies by numerical method are compared with those of the operational modal analysis. The results indicate that, bees optimization algorithm leads accurate results with fast convergence.

关键词： operational modal analysis     solar power plant structure     multi-setup stochastic subspace     bees optimization algorithm     sensitivity analysis    

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分形模型参数与粗糙度参数Ra关系的研究

潘玉良,吴立群,张云电

《中国工程科学》 2004年 第6卷 第5期   页码 49-51

摘要：

介绍了W－M分形模型参数（D,G,γ）的物理含义，研究了分形参数（D,G,γ）与粗糙度参数Ra之间的联系，导出了分形参数（D,G,γ）与粗糙度参数Ra关系式，用数值分析拟合方法验证了关系式的正确性。

关键词： W－M分形模型     分形参数     粗糙度Ra    

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一种分形图像编码的新方法

王秀妮,姜威,王利村

《中国工程科学》 2006年 第8卷 第1期   页码 54-57

摘要：

由于分形图像编码过程非常费时，因此在前人的基础上，通过分析影响分形图像编码速度的相关因素，提出了使用图像块的改进方差来提高分形压缩性能的思想。在证明迭代函数系统不会改变图像块的改进方差的基础上，给出了基于改进方差的分形图像压缩方法。实验结果说明该方法在保证快速性的同时，重建图像的质量又得到了进一步的提高。

关键词： 分形编码     图像压缩     方差    

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Deep convolutional neural network for multi-level non-invasive tunnel lining assessment

《结构与土木工程前沿（英文）》 2022年 第16卷 第2期   页码 214-223 doi: 10.1007/s11709-021-0800-2

摘要： In recent years, great attention has focused on the development of automated procedures for infrastructures control. Many efforts have aimed at greater speed and reliability compared to traditional methods of assessing structural conditions. The paper proposes a multi-level strategy, designed and implemented on the basis of periodic structural monitoring oriented to a cost- and time-efficient tunnel control plan. Such strategy leverages the high capacity of convolutional neural networks to identify and classify potential critical situations. In a supervised learning framework, Ground Penetrating Radar (GPR) profiles and the revealed structural phenomena have been used as input and output to train and test such networks. Image-based analysis and integrative investigations involving video-endoscopy, core drilling, jacking and pull-out testing have been exploited to define the structural conditions linked to GPR profiles and to create the database. The degree of detail and accuracy achieved in identifying a structural condition is high. As a result, this strategy appears of value to infrastructure managers who need to reduce the amount and invasiveness of testing, and thus also to reduce the time and costs associated with inspections made by highly specialized technicians.

关键词： concrete structure     GPR     damage classification     convolutional neural network     transfer learning    

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标题 作者 时间 类型 操作

Hierarchical fractal structure of perfect single-layer graphene

T. Zhang, K. Ding

期刊论文

PD pattern recognition based on multi-fractal dimension in GIS

ZHANG Xiaoxing, YAO Yao, TANG Ju, ZHOU Qian, XU Zhongrong

期刊论文

A new proof of Honeycomb Conjecture by fractal geometry methods

Tong ZHANG, Kai DING

期刊论文

Aggregating structure in coal water slurry studied by eDLVO theory and fractal dimension

Qiang LI, Qian WANG, Jian HOU, Jiansheng ZHANG, Yang ZHANG

期刊论文

Theoretical study on the confine-stiffening effect and fractal cracking of square concrete filled steel

期刊论文

Copper fractal growth during recycling from waste printed circuit boards by slurry electrolysis

期刊论文

Anisotropy of multi-layered structure with sliding and bonded interlayer conditions

Lingyun YOU, Kezhen YAN, Jianhong MAN, Nengyuan LIU

期刊论文

Fractal characteristic evaluation and interpolation reconstruction for surface topography of drilled

期刊论文

Uncertain and multi-objective programming models for crop planting structure optimization

Mo LI,Ping GUO,Liudong ZHANG,Chenglong ZHANG

期刊论文

Permeability analysis and seepage process study on crystal layer in melt crystallization with fractal

Xiaobin JIANG, Baohong HOU, Yongli WANG, Jingkang WANG

期刊论文

Application of fractal theory to unsaturated soil mechanics

XU Yongfu, TONG Lixin

期刊论文

Finite element model updating of a large structure using multi-setup stochastic subspace identification

Reza KHADEMI-ZAHEDI, Pouyan ALIMOURI

期刊论文

分形模型参数与粗糙度参数Ra关系的研究

潘玉良,吴立群,张云电

期刊论文

一种分形图像编码的新方法

王秀妮,姜威,王利村

期刊论文

Deep convolutional neural network for multi-level non-invasive tunnel lining assessment

期刊论文