EMD端点效应的改进型混沌延拓方法及其在机械故障诊断中的应用

针对经验模态分解(Empirical Mode Decomposition，EMD)的端点效应问题，分析了三次样条插值产生端点效应的机理，指出了现有延拓方法的不足，提出采用Lyapunov指数预测模型进行边界延拓，以此减小端点效应在经验模态分解过程中产生的影响。在采用最大Lyapunov指数法进行边界延拓时，针对Lyapunov指数预测模型所表示的平均发散度仅是轨道演化规律的一个近似模型，提出采用局域发散度代替最大Lyapunov指数进行改进，以改进预测模型的预测精度。基于改进型Lyapunov指数边界延拓方法，由于引入时间序列预测模型使端点处的延拓更加合理，所延拓数据更加趋于真实，在希尔伯特-黄变换（Hilbert-Huang Transform，HHT）实现过程中仅需一次延拓，实现了准确的EMD分解。仿真计算和转子系统故障试验分析结果表明，所用方法可以有效解决EMD的端点效应问题。

Processing method for end effects of EMD based on improved chaos forecasting model and its application in machinery fault diagnosis

The boundary effect of empirical mode decomposition(EMD),that appears when using spline interpolation to get two envelops of the data,was discussed.The shortage of ordinary boundary extending methods was pointed out.An extending method based on Lyapunov exponent forecasting model was proposed.After analysing the disadvantages of Lyapunov exponent forecasting model,a new modified forecasting model based on local radiation degree was put forward.By using the improved model,the data sequence was extended by ad...