A flattest constrained envelope approach for empirical mode decomposition.
A flattest constrained envelope approach for empirical mode decomposition.
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DOI：
10.1371/journal.pone.0061739
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发表时间：
2013
期刊：
影响因子：
3.7
通讯作者：
Chen X
中科院分区：
文献类型：
--
作者：
Zhu W;Zhao H;Xiang D;Chen X
经验模式分解(EMD)是一种自适应的非线性、非平稳信号分析方法。然而，用三次样条插值法(CSI)拟合的上、下包络往往会发生超调。提出了一种新的基于最平约束插值法的包络拟合方法。该方法有效地将极值差融入到代价函数中，并利用混沌粒子群算法对插值节点的导数进行优化。该方法在三种不同类型的数据上进行了测试：确定信号、随机信号和真实心电信号。实验结果表明：(1)提出的最平包络有效地解决了CSI法产生的超调和分段抛物线插值法(PPI)产生的人工弯曲问题。(2)对于确定信号、随机信号和心电信号，基于该方法的固有模式函数的正交性指数分别为0.04054、0.02222±0.01468和0.04013±0.03953，低于CSI方法和PPI方法，说明固有模式函数具有更大的正交性。(3)确定信号、随机信号和心电信号的能量守恒指数分别为0.96193、0.93501±0.03290和0.93041±0.00429，比其他两种方法更接近1，表明各分量之间的总能量偏差较小。(4)希尔伯特谱的比较表明，该方法很好地克服了模式混合问题，并使瞬时频率具有更大的物理意义。
Empirical mode decomposition (EMD) is an adaptive method for nonlinear, non-stationary signal analysis. However, the upper and lower envelopes fitted by cubic spline interpolation (CSI) may often occur overshoots. In this paper, a new envelope fitting method based on the flattest constrained interpolation is proposed. The proposed method effectively integrates the difference between extremes into the cost function, and applies a chaos particle swarm optimization method to optimize the derivatives of the interpolation nodes. The proposed method was tested on three different types of data: ascertain signal, random signals and real electrocardiogram signals. The experimental results show that: (1) The proposed flattest envelope effectively solves the overshoots caused by CSI method and the artificial bends caused by piecewise parabola interpolation (PPI) method. (2) The index of orthogonality of the intrinsic mode functions (IMFs) based on the proposed method is 0.04054, 0.02222±0.01468 and 0.04013±0.03953 for the ascertain signal, random signals and electrocardiogram signals, respectively, which is lower than the CSI method and the PPI method, and means the IMFs are more orthogonal. (3) The index of energy conversation of the IMFs based on the proposed method is 0.96193, 0.93501±0.03290 and 0.93041±0.00429 for the ascertain signal, random signals and electrocardiogram signals, respectively, which is closer to 1 than the other two methods and indicates the total energy deviation amongst the components is smaller. (4) The comparisons of the Hilbert spectrums show that the proposed method overcomes the mode mixing problems very well, and make the instantaneous frequency more physically meaningful.
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作者：
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