基于有理四次Hermite插值和PSO的EMD包络线拟合算法

An EMD Envelope Fitting Algorithm Based on Rational Quadratic Hermite Interpolation and PSO

针对经典三次样条插值在EMD分解中存在undershoot现象,模态混叠问题及分段三次Hermite插值不够灵活等问题,提出一种基于有理四次Hermite插值和PSO的EMD包络线算法.该算法利用有理四次Hermite中的形状参数调整曲线形状,并采用粒子群优化算法从曲线簇中找到最优平滑包络线.通过仿真信号实验和非平稳信号实验,表明该方法能够有效克服传统方法带来的undershoot问题,改善模态混叠效应,同时分解后的IMF分量正交性和能量保存度指标亦均优于经典CSI方法和PCHI方法.

In Empirical mode decomposition(EMD)method,the upper and lower envelopes fitted by cubic spline interpolation(CSI)may often occur undershoots phenomenon and mode mixing problem.The Piecewise Cubic Hermite interpolation(PCHI)is not flexible enough.A new quadratic Hermite interpolation algorithm for EMD envelope based on PSO is proposed.The algorithm can adjust the shape of the curve with the shape parameters,and find the optimal smooth envelope by PSO.The experimental result of simulation signal and nonstationary signals show that,the proposed algorithm can effectively overcome the undershoot problem caused by the traditional method,improve the modal aliasing effect,the IO and IEC of the decentralized IMF components are superior to the traditional method.