利用VMD的双标度分形维数特征提取方法

为从机械振动信号中提取出有效特征进行故障诊断,提出一种利用变分模态分解（VMD）求取振动信号双标度分形维数的特征提取方法. 变分模态分解通过迭代求解变分模型的方式将多分量的振动信号分解为若干个不同时间尺度的本征模态函数分量（IMF）. 在多维测度空间,某一时间段内多变量时间序列所占据的空间可以用多维超体体积进行度量. 由于VMD得到的IMF本质上为多变量的时间序列,因此,利用IMF定义和计算多维超体体积,得到振动信号的时间尺度和多维超体体积的双对数曲线. 根据分形理论和双对数曲线的突变点,对双对数曲线进行分段最小二乘线性拟合,定义并提取了振动信号的双标度分形维数特征. 仿真结果表明,利用VMD方法估计分形维数的平均相对误差为4.71%,提高了分形维数估计的精确度. 实测行星齿轮箱振动信号对比实验结果表明,利用VMD双标度分形维数特征能够更好地表征机械振动信号的分形特征,行星齿轮箱故障诊断准确率达到了100%.
To extract efficient feature from mechanical vibration signal for fault diagnosis, a feature extraction method of double-scale fractal dimension based on variational mode decomposition (VMD) for vibration signal was proposed. Variational mode decomposition decomposed multi-component vibration signal into several intrinsic mode functions (IMFs) in different time scale by solving variational model iteratively. In a multidimensional measure space, the space occupied by a multivariate time series within a certain period can be measured by a multidimensional super body volume. Due to IMFs produced by VMD were regarded as multivariate time series, the multidimensional super-body volume was defined and calculated utilizing IMFs in multidimensional measure space. Then the log-log curve with time scale and super-body volume for vibration signal was acquired. According to fractal theory and the abrupt point in log-log curve, the log-log curve was segmentally fitted by least-squares linear fitting. Then, the double-scale fractal dimension feature for vibration signal was defined and acquired. The simulated signal results showed that the average relative error of fractal dimension estimation using VMD method was 4.71%, which improved the accuracy of fractal dimension estimation. The experimental results of planetary gearbox vibration signal indicated that the double-scale fractal dimension feature based on VMD could describe the fractal feature of mechanical vibration signal efficiently, and the accuracy of planetary gearbox fault diagnosis had reached 100%.