由面积-周长关系测量的分形维数与材料韧性的关系

本文分析与研究了 Slit Island Method(SIM)测量断口磨面“小岛”周长-面积关系,指出由这种方法所测得的分形维数 Dm 不是金属断裂表面的真正分形维数 D_o,D_m 取决于测量“小岛”时的码尺长度并与 D_o 有定量关系。只有当测量码尺足够小时,D_m 才接近真正的分形维数 D_o。同时指出,许多作者所得到的 D_m 与韧性之间相反变化的原因是由于测量码尺太大造成的,当测量码尺的绝对长度小于临界长度,即“小岛”周长 Koch 曲线始图的边长时,D_m 与韧性之间才会呈现正变化的关系。     

一种分形图像编码的新方法

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。     

基于提升小波变换和分形维数的声纳图像识别

分形理论在图像的纹理识别中得到了广泛应用,由于分形维数不能反映图像的空间信息,容易造成误识别。针对该问题并结合声纳图像的特点,通过提升结构构造了Haar小波,并将提升小波变换同分形理论相结合,利用小波分解的多分辨率特点和分形维数的多尺度特性,提高图像的识别率。采用Levenberg-Marquardt(L-M)算法优化的BP神经网络对不同信噪比的声纳图像进行分类识别。实验结果表明,文中方法不论在识别率还是识别时间上均优于传统纹理识别方法。     

基于图像特征的分形压缩方法

介绍了分形图像压缩的理论基础和基本编码思想。设计了一种基于图像特征的分形压缩编码方法,该方法在分析图像本身的结构特征的同时,充分利用了人眼对灰度的敏感程度随背景变化而变化的特点。在综合考虑图像的平均灰度与图像块的灰度阶差和图像块灰度方差的前提下,将图像块分为普通块和特征块,并对不同的图像块动态地改变搜索范围、匹配精度及压缩仿射变换因子,从而提高压缩效率。     

石墨中碳原子的扫描显微镜观察及分形研究

用扫描隧道显微镜观察了石墨表面碳原子形貌，并与其晶体结构理论模型进行了比较，获得了一致的结果。同时，计算了石墨原子ＳＴＭ图像的分形维数，得到了合理的结果，表明了计算是可行的，从而为扫描隧道显微图像的分形研究做出了初步的尝试。     

基于分形特征的图像边缘检测方法

运用分形理论描述图像纹理特征,通过分析不同纹理图像及图像边缘处的分形参数,得到一种新的边缘检测分形特征,从而提出一种基于分形特征的图像边缘检测方法。自适应阈值的引入,能够实现不同图像的边缘检测。该算法简单迅速,并具有良好的抗噪性能。     

IFS分形码的快速图像检索算法

图像经分形编码后产生IFS分形码,它可被用来进行图像检索操作。针对图像检索的特点,将分形码中的位置参数替换为相对距离与方向系数。定义了分形码间的距离以及图像间的分形码距离,并取出分形码距离最小的前门幅图像作为检索结果,由此提出了基于IFS分形码的快速图像检索算法。从时间复杂性上分析,利用本文算法所需的检索时间与值域块的个数有关。实验结果表明,相对缩放与旋转变化,算法对位移与亮度变化具有较强的稳定性,其分形码距离的均值仅为14.07和20．05;并可检索到具有一定相似性的图像,且类间与类内分形码距离约相差8,类内距离远小于类间距离。     

分形图像分析及其在纳米ZnO中的应用

研究了分形图像的分析过程,利用MATLAB软件完成了分形维数计算程序的设计.并提取了纳米ZnO透射电镜像的分形图像,利用分形维数计算程序计算其分形维数,证明这种图像数字化方法能对纳米ZnO的形态进行评判,从而实现了定量描述纳米ZnO的形态.     

钛酸钾晶须增韧尼龙66及其断面分形研究

钛酸钾晶须用弹性体表面改性后实现了对尼龙66的有效增韧,改性剂 氧树脂用量为晶须的1．5％（质量）时,复合体系的冲击强度比纯尼66提高132％,同时弯曲,拉伸强度分别提高55％和48％,采用显微图像灰度法,对晶须增韧尼龙进行了基于断面小岛周长－面积关系的分形研究,考察了小岛选取对断面分维数测量结果的影响,研究表明,测得的分维数随选取小岛的面积阈值增加而增大,面积阈值达500η^2(η为侧量码尺）后,分维数趋于稳定,晶须增韧尼龙的力学强度与材料断面分维数之间的变化规律一致,对于从材断断裂机制与断面形貌进行了解释。     

珠光体球化的分形研究

珠光体球化反映到金相上，是一种不规则图像的变化，并且具有分形的特征，可望用分形几何的方法来进行描述。以Cr-Mo钢的珠光体球化为例，用分形维数来描述珠光体球化程度；用小岛法对15CrMo钢的珠光体球化图谱进行了测量。实验表明，珠光体球化从1级到6级，其相应的分形维数范围为1.3156-1.9282。从电厂运行了10^5h的15CrMo钢管上取样，实测了该试样的珠光体球化等级，结果表明，以分形维数表示的球化程度与按图谱评定的球化等级完全吻合。     

材料断裂形貌分维的测量及计算机模拟

材料断裂形貌如断口表面、断裂裂等均被认为具有分形结构而被称为实际分形体,论述了这类实际分形体维数的实验测量、计算方法和分维测量、计算中出现的分维不性问题,指出生分维不确定性的原因,并且通过计算机模拟演示了一些实际测量因素对测量和计算实际分形体维数的影响。     

断口分形研究与应用

采用经典的Ｍａｎｄｅｌｂｒｏｔ分形模型、Ｕｎｄｅｒｗｏｏｄ修正分形模型和分维谱模型对三种球墨铸铁断口的分形特性进行了研究，并应用于铸态铁拉伸断口的断 断裂机制分析。     

测量断口分维的周长-最大直径方法

本文提出了测量断口分维的周长—最大直径方法,并与周长—面积方法进行了对比。当测量码尺很小时,两种方法所测分维比较接近,当测量码尺增加时,周长—面积方法所测分维有下降趋势,而周长—最大直径方法所测分维比较稳定。     

数字图像单个像元分形维数的特征与计算方法

通过分形理论把空间结构信息引入遥感分类中,必须解决分形维数计算的问题,为此提出了一种通过相邻像元间灰度值大小的变化计算数字图像单个像元分形维数的算法。选定计算窗口值 L 后,运用所编程序对 TM 遥感数据进行运算,并得到所需分维值数据。发现所得分维值随窗口值 L 增大而减小;大窗口值的分维值图像较抽象,但建议窗口值不超过 61;小窗口值的分维值图像较清晰,但窗口值不能小于 5。     

Fractal dimension of metallic fracture surface

In this study, a complete method of determination of the fractal dimension for fracture surfaces of ferrous alloys has been proposed. This dimension is determined for the vertical profile obtained by the profile technique cross-section. The image of the profile, seen through the microscope coupled with a camera, is recorded in a computer, where numerical processing is performed. For calculation of the same fractal dimension, the fd3 program has been used, which is available through the Internet. The essential element of the method is optimisation concerning microscopic magnification (scale of a length), resolution of the recorded image and selection of the grey level threshold at binarization. The tests for the stability of discretization, which enable minimization of the error of the measurement, have also been carried out. These tests consist in checking the difference in fractal dimensions for the same profile obtained in two different methods of contouring as well as the difference between capacitive, informative and correlative dimensions. In both cases, too big difference suggests that the determined dimension is not reliable. This method allows determination of the fractal dimension with an absolute accuracy of 0.05 in non-dimensional units. The method has been employed in many studies. In this paper the following tests have been presented: a “fractal map” of the fracture surface was made, an influence of the mechanical notch radius in a compact specimen on the fractal dimension of the fracture surface, an influence of the distortion rate on the fractal dimension, an effect of fatigue crack propagation rate on the fractal dimension and influence of the stress-intensity factor on the fractal dimension of the fracture surface. The following materials were examined: Armco iron, P355N steel and 41Cr4 steel in different states after the heat treatment. The measurements have been made for the specimens of the compact type. There was considered an influence of location of the place of measurement on the fractal dimension being determined. The dimension was determined on the profiles lying longwise and crosswise the crack propagation direction. It has been found that the fractal dimension of the fracture surface does not depend on a place of measurement. This suggests, among other things, that a distinction between the places, which were created under conditions of the plane stress, and the places, which were created under conditions of the plane strain state, cannot be made with the help of the fractal dimension. When testing an influence of the radius of the mechanical tip notch on the fractal dimension of a fracture surface, this dimension was determined in the places located at different distances from the tip of the mechanical notch. With respect to the radii up to 1.0 mm, no significant differences in fractal dimensions have been found. The fractal dimensions of the fracture surface for all examined materials were practically the same and they ranged from 2.02 to 2.10. However in some ranges of da/dN rate the dimension was changing inversely proportional to da/dN. Obtained results confirm that fractal dimension do not depend on the investigated material.     

Perimeter-Area Relation and Fractal Dimension of Fracture Surfaces

We have theoretically analysed the perimeter-area relation and simulated its application to measuring the fractal dimension of fracture surfaces. It is proved that the fractal dimension Dobtained by slit island method (SIM) is related to the dependence of measured area A(δ) ofthe slit island on yardstick δ. So in some cases, the dimension D obtained by SIM is dependenton yardstick and in other cases independent on yardstick δ. But in all cases, when δ→0 thedimension D obtained by SIM approaches the real fractal dimension (similar dimension) of coastline' of the island. We analysed some experimental data and found some new and interestingcharacteristics of crack propagation in steels.     

分形维数与D6AC钢的韧性

本文研究了超高强度钢Ｄ６Ａｃ的断裂韧性、冲击韧性和拉伸面缩率与断口分形维数的关系。分别用二次电子线扫描和数字图象法测定断裂韧性试样的断口分形维数，得出试样的韧性与分形维数Ｄｓｅ、Ｄ_Ｈ和Ｄ_Ｌ成正比关系，即韧性随分形维数增大而增加。试样断口的粗糙度由夹杂物引起的差异小于金相组织不同引起的差异时，使用数字图象法测得的分形维数与韧性的线性关系优于二次电子线扫描的结果。     

粗糙表面轮廓的分形维数计算

本文介绍了粗糙表面轮廓盒维数的计算方法，并指出分形轮廓曲线的盒维数在１和２之间，而且其数值与取样长度、采样点数及测量仪器的分辨率均有关系．