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研究生:黎明璟
研究生(外文):Ming Ching Lee
論文名稱:利用連續小波轉換檢測模擬樑之裂縫
論文名稱(外文):Crack Detection in Model Beam Using Continuous Wavelet Transform
指導教授:洪士林洪士林引用關係
指導教授(外文):Shih Lin Hung
學位類別:碩士
校院名稱:國立交通大學
系所名稱:土木工程系
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:中文
論文頁數:68
中文關鍵詞:連續小波轉換
外文關鍵詞:Continuous Wavelet Transform
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應用小波轉換於模擬樑的裂縫檢測已在許多研究中被討論,此篇論文的目的在於檢視此法的可行性。利用小波為破壞檢測工具的主要因素是小波可調整其在時間域的區間大小以獲得一個訊號的區域資訊。利用Lipschitz exponent 定義模擬樑的模態函數之”健康狀況”,區域破壞的資訊可以被具有適當vanishing moments的小波淬取出來。當解析度足夠高的時候,在小波轉換最大值發生的位置,即是破壞位置。在數值分析中,首先觀察模擬樑的前六個模態函數之小波轉換,並利用Mexican hat wavelet為母波。接下來,利用連續小波轉換檢測不同程度的破壞,破壞分別以減少10%,20%,30%,40%的斷面高度模擬。最後,不同母波的檢測能力也被討論,分別是Mexican hat, Db2 and Sym2 小波。分析結果顯示,並沒有特定的模態特別有利於破壞檢測, 而即使在破壞只有10% 的時候,小波仍能在某些模態檢測出裂縫,而只要vanishing moment為二以上的小波都具有良好的檢測能力,即使波形不同。 因此,小波轉換檢測技術在檢測實際的破壞應有很好的能力。

This work investigates the feasibility of using the continuous wavelet transform (CWT) to detect cracks in a model beam, which has been widely discussed in many researches recently. The reason of employing wavelets as a damage detection tool is that wavelets can adapt its size in time to focus on the local structures of a signal. Lipshcitz exponent is used to define the “health” condition of the mode shapes of a model beam, and the damage information can be extracted by wavelets with proper vanishing moments. The damage location can be identified using the wavelet modulus maxima in the finer scale. In the numerical examples, the CWT of the first six mode shapes of a model beam with Mexican hat wavelets is observed first. Then we inspect the CWT with Mexican hat wavelets in different damage levels which are simulated by reducing 10%,20%,30% and 40% cross section height respectively. At last, the detection abilities of different mother wavelets, Mexican hat, Db2 and Sym2 wavelets, are examined. The result shows that not a specific mode dominates the detection ability and the CWT can detect defects which are extremely minor with proper mode shapes, moreover, different families of wavelets with 2 vanishing moments can equally perceive the damage, for proper scales. The CWT technique may be promisingly applied to the real discrete vibration data.

Content
摘要 I
Abstract II
Acknowledgement IV
Contents V
List of Figures VI
Chapter 1 Introduction 1
1.1 Background and previous works 1
1.2 Organization 4
Chapter 2 Wavelet Transform 6
2.1 Basic concept 6
2.1.1 Basis Vectors 6
2.1.2 Inner Products, Orthogonality, and Orthonormality 6
2.2 Fourier Transform 7
2.3 Windowed Fourier transform 8
2.4 Continuous Wavelet transform 11
2.5 Real wavelets 13
Chapter 3 Detection of singularities 15
3.1 Lipschitz exponent 15
3.2 Singularity detection using Fourier analysis 17
3.3 Wavelet analysis for singularities 18
3.3.1 Wavelet vanishing moments 19
3.3.2 Multiscale differential operator 20
3.3.3 Regularity Measurements with wavelets 20
3.4 Wavelet transform modulus maxima 22
3.5 Maxima propagation 24
Chapter 4 Numerical example 25
4.1 Wavelet selection 25
4.2 Crack detection in model beam using wavelet analysis 26
4.2.1 Wavelet analysis for different mode shapes 27
4.2.2 Different damage levels 28
4.2.3 Different wavelet families 29
Chapter 5 Conclusion 29
References: 30

References:
1. A. K. PANDEY, M. BISWAS and M. M. SAMMAN,” Damage detection from changes in curvature mode shapes”, Journal of Sound and vibration 142,321-332, 1991.
2. S.Mallat and W.L.Hwang. “Singularity detection and processing with wavelets.” IEEE Trans.Info.Theory,38(2) 617-643,1992.
3. Gerald Kaiser,”A friendly guide to wavelets”,1994.
4. N.Stubbs,J.T.Kim and R.F.Charles.”Field verification of a nondestructive damage localization and severity estimation algorithm”. Proceedings XIII International Modal Analysis Conference,Nashville,U.S.A,1995.
5. Mallat, S,”A Wavelet Tour of Signal Processing”, Academic Press, New York,1998.
6. R.P.C.Sampaio,”Damage detection using the frequency - response-function curvature method”,Journal of sound and vibration,226(5) 1029-1042,1999.
7. Wang, Q., Deng, X,”Damage detection with spatial wavelets”, International Journal of Solids and Structures 36, 3443—3468, 1999.
8. Quek, S.T., Wang, Q., Zhang, L., Ang, K.K.”Sensitivity analysis of crack detection in beams by wavelet technique.” International Journal of Mechanical Sciences, 43, 2899—2910 , 2001
9. Albert Boggess and Francis J.Narcowich,”A first course in wavelets with Fourier analysis”,2001.
10. J.-C.Hong, Y.Y.Kim, H.C.Lee and Y.W.Lee. “Damage detection using the Lipschitz exponent estimated by the wavelet transform: applications to vibration modes of a beam.”International Journal of Solid and Structures,39,1803-1816, 2002.
11. Robi Polikar
http://engineering.rowan.edu/%7epolikar/WAVELETS/WTtuorial.html

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