分形维数的一种数值计算及统计检验方法

A DIGITAL APPROXIATION AND STATISTICAL TESTING METHOD FOR CALCULATION OF FRACTAL DIMENSION

基于分形维数的原始定义，本文给出一种维数的数值计算方法。若被测量对象在某一标度范围内确具有统计意义上的标度不变性，则该方法能够较好地得到所需精度的维数计算结果并进而反推“无标度区”范围。在假设维数集｛ｂｋ｝服从正态分布的前提下，引入柯氏检验方法对（ｂｋ｝样本分布的一致性进行检验，以此判断｛ｂｋ｝中是否具有“异常值”存在，并由标准化极差检验法对｛ｂｋ｝中“异常值”进行检测并剔除，其目的是在“直观判定”的基础上对维数作进一步的精确计算及对“无标在区”作进一步的精确界定．本文方法的一个显著特点是所有判断及统计检验皆针对最终结果（维数）。人造数据的应用检验亦表明了该方法的客观实用性．

According to the oraginal definition of fractal dimension,a digital approximation and statistical testing method for calculation of fractal dimension was given in this paper. If measured object is statistical independent of scale in some range of rule,this method can compute the fractal dimension in given computation accuracy and,go a step further,is helpful for discrimination of range of “scaling ruled”. On the premise that the {bk},set of dimension,corlespond to the normal distribution,the consistency of sample distribution of {bk} will be tested by коимоговtesting method. This process may help us to judge whether the (bk) contains“ abnormal value” or not. Here the “Normalization maximum difference testing method” can be used to find and reject the “abnormal value” from the {bk}.A obvious characteristic of the method given in this paper is :all the judging and statistical testing are direeted against the final datas (fractal dimension). The application of manmade datas also shows that the method is objective and practicable.