摘要
介绍了分形及分形维数的基本概念 ,用分形方法对道路表面进行了分析 ,并提出了表观分形维数的概念。分析表明 ,道路表面具有不规则性和统计自相似性 ,即每一部分都可视为整体缩小尺度之后的相似形。以现有的道路表面功率谱数据为例 ,根据频谱方法对其分形进行计算 ,表明测度 (功率谱 )与尺度 (频率 )在双对数坐标上呈线性关系 ,即具有标度不变性 ,呈现明显的分形特征。道路表面越平坦 ,其分形维数值越高。表观分形维数结合分形维数的相似测量和尺度系数的绝对测量 ,其数值能够表达路表不平的程度 ,表观分形维数值越大 ,道路表面不平度越大。
The fundamental concept of fractals and the fractal curves were introduced and the fractal behavior of a rugged road surface was then discussed. The concept of superficial dimensions D * for a road surface was proposed in order to evaluate its rough level. The results showed that the road surface presents irregular performance and statistical self similarity, which means that each portion can be considered as a reduced scale image of the whole. In that case, the degree of complication can be described by a quantity D that contains many properties of a “dimension”. Based on the data of an available road surface power spectrum, the fractal was computed by means of the frequency spectrum method. The results showed that each power spectrum of these surfaces follows a power law with the frequencies and they present straight line in a log log plot with scale invariance. The more smooth the road surfaces, the larger the values of fractal dimension. However, it was also found that fractal dimension was not enough to characterize the roughness of road surface quantitatively owing to the relative measures in multiscales. The superficial dimensions D *, which consists of both the similarity of fractal dimension and the absolute representation of scale parameter, can be used as a parameter to evaluate roughness of road surface. The higher the value of D *, the rougher the road surface.
出处
《农业机械学报》
EI
CAS
CSCD
北大核心
2000年第6期22-24,共3页
Transactions of the Chinese Society for Agricultural Machinery
关键词
路面
分形
分析
Road surface
Fractal
Analysis
