关联维数的计算及其在大机组故障诊断中的应用

论述了关联维数在大型旋转机械故障诊断中的应用 ,并针对故障诊断的实际情况 ,对关联维数的 G- P算法作了一定的改进 .传统的 G- P算法使用欧几里德范式计算点间距 ,包含了较多的重复运算 ,使用改进的点间距计算公式不仅简单 ,而且可借助于递推公式以节省计算时间 ;引入最小动态关联时间以便消除流数据的动态关联特性 ;建议采用局部斜率曲线以判断标度区间的范围 .对数据长度和噪声干扰对于关联维数计算结果的影响进行了仿真分析 .研究结果表明 :由于不同故障的动力学产生机制不同 ,通常也具有不同的关联维数 ,故关联维数可用于故障的特征提取

Calculation of Correlation Dimension and Its Application to Large Rotating Machinery Fault Diagnosis

This paper reported on the application of correlation dimension in large rotating machinery fault diagnosis. The shortcomings of the traditional G P algorithm were pointed out and a modified version was recommended. The traditional G P algorithm used the Euclidean norm to compute the distance between two reconstructed vectors while this paper presented another norm to compute the inter distance between two points. This alternative norm is found to be more practical in on line diagnosis because the computational time can be remarkably reduced. A cutoff parameter t min >1 was introduced to avoid dynamic correlation, which can improve the convergence of the standard correlation algorithm and can remove the influence of the locally one dimensional behavior of the trajectory. Finally, it was suggested that one should plot the D 2( m )-ln( r ) function to determine the beginning and the end of the scaling region. The influence of data length and noise level on correlation dimension computational precision was discussed. Non linear time series analysis theory based on correlation dimension for practical application, especially for large rotating machinery fault diagnosis, was introduced. The results show that the correlation dimension can usefully reflect the different kinematics mechanisms.