| 研究生: |
陳季聰 Chen, Chi-Tsung |
|---|---|
| 論文名稱: |
連續式小波分析法於紊流訊號拆解之發展研究 Improvement of Continuous Wavelet Transform for The Turbulent Signal Decomposition |
| 指導教授: |
鄭育能
Jeng, Yih-Nen |
| 學位類別: |
博士 Doctor |
| 系所名稱: |
工學院 - 航空太空工程學系 Department of Aeronautics & Astronautics |
| 論文出版年: | 2005 |
| 畢業學年度: | 93 |
| 語文別: | 英文 |
| 論文頁數: | 128 |
| 中文關鍵詞: | 強化連續式小波轉換法,頻譜窗型濾波法,低速紊流數據解析,Hurst分析法 |
| 外文關鍵詞: | Enhanced Morlet transform, Hurst analysis., Gaussian window of spectrum, low speed turbulent flow |
| 相關次數: | 點閱:86 下載:2 |
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本文提出一種強化的連續式小波轉換法,又名強化型Morlet 轉換法,以增強小波係數圖對數據解析的精準和明晰度。此法是在對數據串做Morlet 轉換之前,作取窗型濾波使數據保留特定頻率而移除其他頻率的重要性,其過程如下:1.應用一種新的疊代型濾波器,移
除數據串的非周期性和低頻部分;2.應用一種新的快速Fourier 轉換法,求得低頻誤差極小的頻譜;3.針對於Morlet 轉換的尺度函數,計算其對應的波長和頻率,應用高斯函數取窗型濾波,以得到一組與此對應頻率為主的頻譜;4.取逆Fourer 轉換,求時變數據串;5. 對
此特定數據串,做Morlet 轉換求該應於該尺度函數之小波係數;6.重複步驟3-5,求所有需要的小波係數圖。對於要檢驗之通過鈍頭體之低速委流之紊流流場,本文應用Hurst 分析法,證明此一流場數據是一種「黑色雜訊型的隨機數據」,換句話說,流場具有經過某些轉
變程序後重複的記憶性,它不是一種完全無法預測的隨機過程,而含有複雜的規則在其中,這和早期學者的說法一致。經使用新的小波係數圖對數據作分析後發現下列新的訊息:1.紊流流場之能量次序流動,即從某一頻率之擾動轉換到比較高頻或較低頻的過程,包含有
不規則次序的頻率融合和分裂的階段;2.尾流流場中的渦漩成對結合成低頻渦漩或渦漩裂解成高頻波現象,可用頻率融合和分裂過程解釋之;3.從鈍頭體斜邊形成的渦漩分離層,在尾流區中有斷續出現的現象;4.數個已知的尾流性質也可用小波係數圖做詳細的說明。總之,
本文所發展的強化型連續式小波轉換法,可以做為一種新的詳細紊流流場之分析工具,可以應用到其它方法,也可以直接應用到其它需要解析複雜數據串的學門之中。
The continuous wavelet transform, which is named as the Morlet transform, is enhanced to improve the visibility of the resulting wavelet coefficient plot. The enhancing procedure involves:1. use an iterative filter basing the Gaussian smoothing to remove the non-periodic, smooth, and
low frequency part; 2. use a modified fast Fourier transform algorithm with small low frequency error to obtain an accurate spectrum; 3. use a Gaussian windowing procedure to re-scale the spectrum for a given scale function of the Morlet transform, where scale function is related to the wavelength of the original data string, a rule to determine the characteristic length of the window
is proposed; 4. perform the inverse Fourier transform of the re-scaled spectrum to time domain; 5.evaluate the wavelet coefficient at the scale function; 6. repeat item 3-5 for all desired scale function. The Hurst analysis is employed to show that a low speed turbulent flow over a blunt body is a black noise random process. It confirms the classical assumption that the flow structure
has the memory of repeating itself after some intermediate procedures. The proposed enhancement of the Morlet transform is then employed to obtain the wavelet coefficient plots of the examined turbulent flow field. From these plots, several new features are found: 1. the energy cascades from a wave mode to a higher or lower mode involve series of frequency merging and splitting steps; 2. the mechanisms of vortex pairing and energy dissipation to high frequency modes can be explained by the frequency merging and splitting procedure; 3. the shedding vortex
street is not a segmental discontinuous process; and 4. many known phenomena can be reasonably explained in terms of the energy level of wave components and the frequency shift and the frequency merging-splitting procedures. On the whole the present proposed method of calculating
the wavelet coefficient plot provides a new tool to looking the detailed turbulent structure and other data string involving complicated information.
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