广义经验模态分解性能分析与应用

针对经验模态分解（empirical mode decomposition，EMD）的均值曲线采用三次样条拟合而容易引起包络过冲和不足等缺陷，相关学者提出了许多改进均值曲线的变种EMD方法，取得了一定的效果。广义经验模态分解（generalized EMD，GEMD）方法综合了多种改进EMD方法，通过定义不同的均值曲线对信号进行逐阶筛分，从得到的每一阶分量中选取最优作为最终的广义内禀模态函数（generalized intrinsic mode function，GIMF），由于每一阶的GIMF分量都是最优的，因此相较于EMD等单一均值曲线筛分方法，GEMD分解结果也是最优的。论文对GIMF分量准则进行了改进以及对GEMD性能进行了分析，并将GEMD应用于仿真和实测信号的分析，结论表明GEMD分解是完备的和正交的，有比EMD更强的分解能力，而且适合机械振动信号的处理和故障诊断。

Performance analysis and application of generalized empirical mode decomposition

As the mean curve defined in empirical mode decomposition (EMD) is founded on the cubic spline, which may cause envelope overshoot and undershoot, many variants of EMD in improving the mean curve have been proposed and have achieved some results. Generalized empirical mode decomposition (GEMD) integrates several improved EMD methods and selects the best component from different components obtained by sifting with different mean cures in each rank as the final generalized IMF (GIMF). Since the GIMF is the best in each rank, the corresponding results of GEMD are also the best. In this paper the GEMD is introduced firstly and then an improved criterion of GIMF is developed. Furthermore, GEMD has been employed to analyze simulation and mechanical vibration signals and the results show that GEMD is complete, orthogonal and has a better capacity of decomposition than EMD, is suitable for mechanical fault diagnosis as well.