基于相空间重构改进算法的混沌奇异谱分析及应用

针对混沌奇异谱分析嵌入维数和延迟时间不确定性问题,提出相空间重构的改进算法。利用补充准则E2(m)进行联合判断,同时对Cao算法进行了改进,给出了一种改进的嵌入维数的稳定性准则。嵌入维数利用改进的Cao算法,能够快速准确地确定嵌入维数m的值,具有准确性和高效性;用基于符号分析的极大联合熵求取延迟时间的方法,减少计算量和误差。通过数值验证对比实验验证了该方法的优越性。将该方法在滚动轴承早期故障识别中应用,结果表明:混沌奇异谱可以清楚看出不同故障信号的图形分布,实现对机械故障信号的特征提取。为机械故障早期诊断提供一种新的有效途径。

Chaotic Singular Spectrum Analysis Based on Improved Phase Space Reconstruction Algorithm and Its Application

An improved algorithm for phase space reconstruction is proposed for the problem of embedding dimension and delay time uncertainty in chaotic singular spectrum analysis. The joint criterion is evaluated by the supplementary criterion, and the Cao algorithm is improved. An improved embedding dimension stability criterion embedding dimension using the improved Cao algorithm, can quickly and accurately determine the value of the embedding dimension, with accuracy and efficiency; The method of obtaining the delay time based on the maximum joint entropy based on symbol analysis can reduce the amount of calculation and reduce the error. The superiority of the proposed method is verified by numerical comparison experiments. The method is applied in the early fault identification of rolling bearings. The results show that the chaotic singular spectrum can clearly see the pattern distribution of different fault signals and realize the feature extraction of mechanical fault signals. Provide a new and effective way for early diagnosis of mechanical failure.