一种新的振动信号分形无标度区间识别方法  

A new identification method for fractal scaling region of a vibration signal

作　　者：杜必强[1] 贾子文[1] 唐贵基[1] 

机构地区：[1]华北电力大学机械工程系,河北保定071003

出　　处：《振动与冲击》2013年第14期40-45,共6页Journal of Vibration and Shock

基　　金：中央高校基本科研业务费项目(10DG12)

摘　　要：为了提高振动信号关联维数计算的准确程度,提出了一种识别分形无标度区间的新方法。该方法首先采用圆拟合、求切线斜率的方法求出相关积分双对数曲线上各点的斜率,得到斜率变化曲线;其次基于斜率变化曲线不同区间内的相关系数进行线性度判断及显著性检验,保留其中线性度较好、相关程度较高的区域;最后选择其中方差最小的区间作为该振动信号的分形无标度区间。整个识别过程中无需任何人工干预,可以交由计算机自动完成,从而避免了主观因素对分形无标度区间识别以及关联维数计算结果的影响。应用该方法对Lorenz吸引子及实测振动信号进行了关联维数值的计算,计算结果验证了该方法的准确性和有效性。In order to obtain more accurate correlation dimension of a vibration signal,a new identification method for fractal scaling region of a vibration signal was proposed.Firstly,the methods of circle fitting and getting tangent＇s slope were aclopted to find the slope of each point on a double-logarithm correlation integral curve.As a result,a slope variation curve was obtained.Secondly,based on the linearity judgment and significance test for correlation coefficients of different regions of the whole slope variation curve,the regions with better linearity and higher correlation were kept.Finally,the region with the least variance was taken as the fractal scaling region of the vibration signal.The whole identification process could be automatically implemented without manual intervention,avoiding the effect of subjectivity on the results of the fractal scaling region and the correlation dimension.The correlation dimensions of Lorenz attractor and various measured vibration signals were calculated using the proposed method.The correctness and effectiveness of the proposed method was verified with the computed results.

关 键 词：振动信号 关联维数 分形无标度区间 相关系数 方差 

分 类 号：O322[理学—一般力学与力学基础]