摘要
以普适模型FBM为工程背景,对Katz波形分形维计算方法的缺陷进行分析.以超立方体作为覆盖单元,从Hausdorff维和分配维理论出发,在拓扑映射技术下,提出了振动波形长度分形维的定义和计算公式.对其数学严密性及工程适用性进行分析,说明其具有物理概念明晰、简单易行、精确度高等优点.基于长度分形维的分形动力学分析能力,建立了工程缺陷分形检测系统,实例证明该系统对缺陷反应敏感、精度高,噪声免疫力强,有较好的实用价值.
Against the engineering background of the universal FBM model, the defects of Katz's method for calculating the length fractal dimension ( D L) of waveform are investigated. Then, by adoption of supercubes as covering cells and on the basis of the theoretical of the Hausdorff dimension and Divider dimension, the definition of the wavelength fractal dimension and its calculating formula are presented based on the technique of topologic mapping. By study of the strictness and applicability of the formula, some merits of the method are validated, including the clear concept, easy operation, and high precision. According to the dynamics analysis capacity of D L, a fractal defect detection system is developed. Practice shows that the system is of high sensitivity to defects, high precision of calculation, and high immunity to noise, so the method is of high value of application.
出处
《河海大学学报（自然科学版）》
CAS
CSCD
北大核心
2004年第1期51-54,共4页
Journal of Hohai University(Natural Sciences)
基金
水利部科技创新基金资助项目(SCX2000 56)
关键词
分形维
Katz法
长度分形维
地下连续墙
分数布朗运动
fractal dimension
Katz's method
length fractal dimension
underground continuous wall
defect detection
Fractional Brown Motion
