Ma Wenping, Yin Shuxin, Jiang Chunlei, Zhang Yansheng
College of Electrical and Information Engineering, Northeast Petroleum University, Daqing 163318, China.
Rev Sci Instrum. 2017 Mar;88(3):035109. doi: 10.1063/1.4978029.
Variational mode decomposition (VMD) is a recently introduced adaptive signal decomposition algorithm with a solid theoretical foundation and good noise robustness compared with empirical mode decomposition (EMD). However, there is still a problem with this algorithm associated with the selection of relevant modes. To solve this problem, this paper proposes a novel signal-filtering method that combines VMD with Hausdorff distance (HD) in the VMD-HD method. A noisy signal is first decomposed into a given number K of band-limited intrinsic mode functions by VMD. The probability density function is then estimated for each mode. The aim of this method is to reconstruct the signal using the relevant modes, which are selected on the basis of noticeable similarities between the probability density function of the input signal and that of each mode. Various similarity measures are investigated and compared, and the HD is shown to offer the best performance. The results of filtering of simulation signals illustrate the validity of the proposed method when compared with EMD-based methods under comprehensive quantitative evaluation criteria. As a specific example, the proposed method is successfully used for filtering the pipeline leakage signal as evaluated by the de-trended fluctuation analysis algorithm.
变分模态分解（VMD）是一种最近提出的自适应信号分解算法，与经验模态分解（EMD）相比，它具有坚实的理论基础和良好的噪声鲁棒性。然而，该算法在相关模态的选择方面仍然存在问题。为了解决这个问题，本文提出了一种新颖的信号滤波方法，即在VMD-HD方法中将VMD与豪斯多夫距离（HD）相结合。首先，通过VMD将带噪信号分解为给定数量K的带宽有限的本征模态函数。然后估计每个模态的概率密度函数。该方法的目的是使用相关模态来重构信号，这些相关模态是根据输入信号的概率密度函数与每个模态的概率密度函数之间显著的相似性来选择的。研究并比较了各种相似性度量，结果表明HD具有最佳性能。在综合定量评估标准下，与基于EMD的方法相比，仿真信号的滤波结果说明了所提方法的有效性。作为一个具体实例，经去趋势波动分析算法评估，所提方法成功用于管道泄漏信号的滤波。
