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研究生: 陳良榮
Liang-Jung Chen
論文名稱: 使用迭代式高斯法與傾斜極值篩選法解決經驗模態分解法中的混波現象
Solution of Mode Mixing Phenomenon of Empirical Mode Decomposition by Using Iterative Gaussian Filter and Oblique-Extrema Based Sifting Process
指導教授: 吳順德
學位類別: 碩士
Master
系所名稱: 機電工程學系
Department of Mechatronic Engineering
論文出版年: 2011
畢業學年度: 99
語文別: 中文
論文頁數: 61
中文關鍵詞: 經驗模態分解法混波現象迭代式高斯法傾斜極值篩選法
英文關鍵詞: Empirical Mode Decomposition, mode mixing, terative Gaussian diffusive filter, OEMD
論文種類: 學術論文
相關次數: 點閱:215下載:3
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  • 1998年黃鍔等人提出了一種可以用來處理非線性、非穩態訊號的時頻分析工具,經驗模態分解法(Empirical mode decomposition, EMD)。經驗模態分解法可以將訊號拆解成數個零均值、近似單成分的本質模態函數(Intrinsic Mode Function, IMF)。可以比傅立葉分析(Fourier analysis)多處理非線性及非穩態訊號的優點,使得經驗模態分解法已被應用在各個不同的領域。然而經驗模態分解法存在著一些缺點例如停止準則、邊界效應、混波現象(mode mixing)…等。本論文提出了一個結合迭代式高斯法(iterative Gaussian filter)與傾斜極值篩選法(oblique-extrema based sifting process, OEMD)流程,可以用來解決經驗模態分解法中的主要缺點:混波問題。不論迭代式高斯法或傾斜極值篩選法都不是解決混波現象的完美解答,其中一個方法太耗時而另一個只能處理混波現象的特定種類。由實驗結果可以發現,本論文的流程的確可以有效阻止混波現象的發生。

    An ideal algorithm for nonlinear and non-stationary data analysis was proposed by Huang et al. in 1998, as known as Empirical Mode Decomposition (EMD). Comparing to Fourier analysis assuming the time series data is linear and stationary, EMD is a method capable of analyzing not only linear and stationary but also nonlinear and non-stationary. With this useful feature, EMD has been applied to many fields. However, lacking theoretical foundation, there are some drawbacks in EMD, such as sifting stop criterion, boundary effect, mode mixing, etc. To fix the mode mixing problem, the main drawback of EMD, a process is presented in this paper, which combines iterative Gaussian diffusive filter (IGDF) with oblique-extrema based sifting process (OEMD) since either IGDF or OEMD is not the perfect solution for mode mixing problem, for the reasons that one of them is only able to solve specific problems and the other one is too time-consuming. The experiments presented in this paper indicating that the proposed process works as expected.

    致謝 I 中文摘要 II Abstract III 目錄 IV 圖目錄 V 表目錄 VII 第一章 序論 1 1.1 前言 1 1.2 研究動機與目的 1 1.3 論文架構 2 第二章 經驗模態分解法與相關問題 3 2.1 經驗模態分解法(EMD)簡介 3 2.2 停止準則Stop criterion 6 2.3 邊界效應Boundary effect 8 2.4 極值點位置 Extrema locations 13 2.5 混波現象Mode mixing 14 2.6 其他EMD的問題 16 第三章 混波問題探討 17 3.1 Ensemble Empirical Mode Decomposition, EEMD 17 3.2 Signal-Assisted Empirical Mode Decomposition, SAEMD 19 3.3 Masking Signal-Assisted EMD, MEMD 21 3.4 利用微分運算來改善混波現象 22 3.5 迭代式高斯濾波器,IGDF 24 3.6 傾斜極值篩選法,OEMD 27 第四章 實驗流程設計與實驗結果 31 4.1 實驗流程設計 31 4.2 本研究所使用的模擬訊號 34 4.3 迭代式高斯濾波器實驗結果 35 4.4 傾斜極值篩選法實驗結果 39 4.5 本論文方法實驗結果 49 第五章 結論與未來展望 56 5.1 結論 56 5.2 未來展望 57 參考文獻 58

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