良榮論文最終 - 吳順德教授- 國立臺灣師範大學

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Abstract 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. Keywords: Empirical Mode Decomposition, mode mixing, iterative Gaussian diffusive filter, OEMD III
目錄致謝 ............................................................................................................................... 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 IV
Page 1 and 2: 國立臺灣師範大學機電科
Page 3: 中文摘要 1998 年黃鍔等人
Page 7 and 8: 圖 24 迭代式高斯濾波器流
Page 9 and 10: 第一章序論訊號處理中的
Page 11 and 12: 第二章經驗模態分解法與
Page 13 and 14: 當作新的原始訊號繼續步
Page 15 and 16: (2.7)式假設原始訊號可以
Page 17 and 18: 圖 3 邊界效應[6] 圖 4 具有
Page 19 and 20: 圖 5 奇偶函數擴充[6] Zhao Z
Page 21 and 22: 7. 重複步驟 2~6 直到找到 IM
Page 23 and 24: 圖 8 混波現象 2[10] Rilling a
Page 25 and 26: 第三章混波問題探討本論
Page 27 and 28: 圖 11 是 EEMD 對於模擬訊號
Page 29 and 30: 圖 13 SAEMD 實驗結果[27] 3.3 M
Page 31 and 32: 3. 其振幅比為: 4. 透過微分
Page 33 and 34: 圖 17 一般一階濾波器的頻
Page 35 and 36: 3.6 傾斜極值篩選法,OEMD 若
Page 37 and 38: 5. 接下來和傳統 EMD 一樣,
Page 39 and 40: 第四章實驗流程設計與實
Page 41 and 42: 若直接採用迭代式高斯濾
Page 43 and 44: 4.3 迭代式高斯濾波器實驗
Page 45 and 46: 將三個模擬訊號拆解時所
Page 47 and 48: 4.4 傾斜極值篩選法實驗結
Page 49 and 50: 訊號一訊號二訊號三訊
Page 51 and 52: s 1 (t) s 1 (t) IMF1 IMF1 IMF2 IMF3
Page 53 and 54: s 2 (t) s 2 (t) IMF1 IMF2 IMF2 IMF1
Page 55 and 56:
s 3 (t) IMF2 IMF1 20 10 0 0 2 4 6 8
Page 57 and 58:
point 則可以克服這個問題,
Page 59 and 60:
訊號一訊號二訊號三訊
Page 61 and 62:
60 50 40 30 20 10 0 300 250 200 150
Page 63 and 64:
本章最後整理出表 13,是第
Page 65 and 66:
2. 透過本篇論文的設計流
Page 67 and 68:
sign ls,” Proceedings of The Roya
Page 69:
[24] Y. N. Jeng, P. G. Huang and Y.
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良榮論文最終 - 吳順德教授- 國立臺灣師範大學

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