中文摘要：

经典经验模态分解（Empirical Mode Decomposition,EMD）采用三次样条插值方法进行包络拟和,存在较严重的＂过冲＂现象。在研究该问题已有方法基础上,提出了一种基于最小长度约束的包络拟合方法,以包络曲线长度最小为目标函数,采用Lagrange求极小值法优化极值点处的导数值,然后采用分段三次Hermite函数插值方法进行包络拟合,得到平滑包络线.实验表明该方法能有效地克服三次样条插值法的＂过冲＂现象和分段抛物线插值法的人为弯折现象,能拟合出更平滑的包络线,使得EMD分解更准确,有效改善模态混淆问题.

英文摘要：

In classic EMD,the envelopes fitted by cubic spline interpolation may often occur overshoots.In this paper,a new envelope fitting method based on the least-length constrained interpolation is proposed.Taking the length of the fitted envelope as the target function,Lagrange optimization method is used to optimize the derivatives of the interpolation nodes.With the optimized derivatives,piecewise Hermite interpolation method is used to fit the more smooth envelopes.The result of experiments proves that the new method can solve the overshoots caused by cubic spline interpolation and the artificial bends caused by piecewise parabola interpolation effectively and let the results of EMD more accurate.This method can overcome mode mixing well,which is one of the major drawbacks of the original EMD.