一种新的振动信号分形无标度区间识别方法

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。

A novel method to identify the fractal scaling region for vibration signal

In order to obtain more accurate correlation dimension for vibration signal, a novel fractal scaling region identification method is proposed. First, the method processes the circle fitting and treats the tangent’s slope as the slope of each point on the double logarithm correlation integral curve. As a result, a slope variation curve is got. Second, based on the linearity judgment and significance test associated with the whole slope variation curve, regions with high linearity and correlation are kept. Final, region with the least variance is regarded as the fractal scaling region for vibration signal. The whole identification process can be automatically implemented without manual intervention, preventing the effect of subjectivity on the results of the fractal scaling region and the correlation dimension. The correlation dimension of the Lorenz attractor and various measured vibration signals were calculated using the proposed method. Results verify the effectiveness and accuracy of our proposed method for vibration signal.