基于新的无标度区确定方法求取分形路面不平度的分形维数

The Fractal Dimension of Fractal Road Roughness based on the New Method of Determining Scale-free Area

用W-M函数生成了分形路面不平度,采用结构函数法求取了分形路面不平度具有的标度律.在确定无标度区间时,提出了一种新方法,该方法对双对数坐标内由测度和标度构成的数据点进行分段处理,计算出各分段的相关系数;通过各分段的外扩,筛选出满足相关系数阈值的区域,最终确定出无标度区.在无标度区内采用最小二乘法进行了直线拟合,基于结构函数法,求出了分形维数.同时,采用人工观测方法确定了无标度区,并求取了分形维数.通过对比发现,本文提出的方法求取的分形维数误差较小,且能实现计算机的快速自动处理.另外,验证了分形路面不平度具有分形特征.

This paper generates fractal pavement inequality by W-M function, and solves scale of fractal pavement inequality by structural function method. In looking for non-scale section, it puts forward a new method. This method solves relative each subsection coefficient, which is to sectionally deal with data based on measure and scale in both logarithm coordinate. Through external expansion of each subsection, it chooses region, which satisfies threshold value of relative coefficient, then finds non-scale region finally. It matches linearly by least square method in non-scale region, and solves fractal dimension based on structural function. At the same time, it defines non-scale region by observation way, and solves fractal dimension. Through comparison, this way that solves fractal dimension has less error and realizes automatic processing fast by computer. Moreover, it verifies that fractal pavement inequality has fractal feature.