分形理论中无标度区间的识别方法  

Fractal scaleless band automatic identification for fractal theory application

作　　者：贾子文[1] 王鹏[1] 方俊元[1] 

机构地区：[1]华北电力大学机械与动力工程学院,河北保定071003

出　　处：《机械》2012年第11期24-26,30,共4页Machinery

基　　金：中央高校基本科目业务费项目(10DG12)

摘　　要：针对不规则分形维数求解过程中线性无标度区间不易寻找,提高分形维数的计算精度和效率,减少无标度区间确定时的主观因素,基于关联积分算法计算分形维数,建立了故障诊断中分形无标度的一种自动识别的算法。该算法在保证计算精度的前提下,由于对于数据长度依赖性不强,大大提高了运算效率,并且在实验中证明了其可行性。计算结果表明,应用本方法能够很好地识别无标度区间,区间内曲线线性度很好。这样要说明的是,由于此方法比较保守,在无标度区边缘外的位置也有可能属于无标度区。For fractal scaleless band is hard to find when calculate fractal dimension,the need of a higher efficiency and accuracy,and reduce subjective factor.A new method for automatic identify fractal scaleless band,which based on integral calculus.The method is not relay on the length of data,and it is a fresh way to deal with fractal problems,like scaleless band,for its high efficiency and accuracy.According to the result,the fractal scaleless band can be identified accurately and linear in the band is obvious by this method.And what should be noticed that for its preservation,some points near the edge of fractal scaleless band may still belong to theory band.

关 键 词：关联维数 无标度区 相空间重构 关联积分 

分 类 号：O322[理学—一般力学与力学基础]