An optimization based empirical mode decomposition scheme
An optimization based empirical mode decomposition scheme
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DOI：
10.1016/j.cam.2012.07.012
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发表时间：
2013-03-01
影响因子：
2.4
通讯作者：
Kunoth, Angela
中科院分区：
文献类型：
--
作者：
Huang, Boqiang;Kunoth, Angela
经验模态分解（Empirical Mode Decomposition，EMD）是由N. E. Huang等人于1998年提出的一种将非线性非平稳单变量函数叠加分解为多尺度分量的迭代方法。这些分量被称为本征模函数（IMF），它们被构造成相对于L-2内积彼此近似正交。此外，分量允许通过借助于希尔伯特变换的应用对每个分量进行复化来定义瞬时频率。然而，这种方法通过分析信号，并不能保证所得到的频率的组件总是非负的，因此，“物理意义”，并且振幅可以被解释为envelopes.In本文中，我们制定了一个优化问题，考虑到所需的重要功能，所得到的EMD。具体来说，我们提出了一个数据适应的迭代方法，最大限度地减少在每个迭代步骤的平滑功能受到不等式约束，涉及极值。通过这种方式，我们的方法为输入函数构造了一个稀疏的数据适应基础，以及函数的数学严格包络。此外，我们提出了一个基于优化的归一化提取瞬时频率的解析函数的方法。我们提出了相应的算法与几个例子。(c)2012爱思唯尔有限公司版权所有。
The empirical mode decomposition (EMD) has been developed by N.E. Huang et al. in 1998 as an iterative method to decompose a nonlinear and nonstationary univariate function additively into multiscale components. These components, called intrinsic mode functions (IMFs), are constructed such that they are approximately orthogonal to each other with respect to the L-2 inner product. Moreover, the components allow for a definition of instantaneous frequencies through complexifying each component by means of the application of the Hilbert transform. This approach via analytic signals, however, does not guarantee that the resulting frequencies of the components are always non-negative and, thus, 'physically meaningful', and that the amplitudes can be interpreted as envelopes.In this paper, we formulate an optimization problem which takes into account important features desired of the resulting EMD. Specifically, we propose a data-adapted iterative method which minimizes in each iteration step a smoothness functional subject to inequality constraints involving the extrema. In this way, our method constructs a sparse data-adapted basis for the input function as well as a mathematically stringent envelope for the function. Moreover, we present an optimization based normalization to extract instantaneous frequencies from the analytic function approach. We present corresponding algorithms together with several examples. (c) 2012 Elsevier B.V. All rights reserved.