摘 要
　　本文研究是利用小波轉換來偵測結構物的缺陷，結構都有其固定的物理特性，其物理性質在破壞處因為其物理性質的改變，會有不連續點產生。基於利用小波轉換方法偵測結構破壞時所造成之模態不連續性，進而預測缺陷存在以及其位置，並且利用奇異性指數來分辨破壞程度以及是否為真正的破壞點。文中以一具破損的交叉懸臂樑為例，利用有限元素(ANSYS)分析方法，進行模態振型分析，再以小波轉換偵測破損；在實驗分析方面，主要是先量測交叉破損樑的振動訊號，利用小波包節點範數來轉換振動訊號，依此獲得模態振形參數，再以小波轉換分析，測得實驗樑的破損位置。
　　以本文所提之缺陷預測方法偵測懸臂樑破損，對於不同破壞程度的缺陷、位置，都有很好的檢測能力，並且可以有效分辨交叉破損樑的交叉位置跟破壞位置的不同。由軟體模擬及實驗量測皆證明了此方法的可行性，文中所提出的缺陷位置預測方法將可進一步應用於現實中的其他結構物。

Abstract
　This article study wavelet transforms to detect the defect of structure. All Structures have there physical characteristics. Property will change, and formed in-continuity point. With wavelet transformation, we can detect this in-continuity mode of structure. Further more, we can point out its location. Then, with singular index, we will know the level of damage and identify the two defects.
　We use one damaged cantilever beam for example, with finite element method analysis to precede vibration mode, then use wavelet transformation to detect the damage. As for the experimental analysis, first, we measure the damaged cross beam, get their vibration signal, with wavelet packet node norm to transform the vibration signal. So we can get the parameters of vibration mode. After that we can use wavelet transformation analysis get the damage position of experienented beam.
　For the cantilever beam, we can use the similar method. All different king of damage for the sophisticated beam, this analysis method can identify their position and type of defect, with small error and uncertainty. It also can identify the cross beam position of damage and of crossing. The software（ANSYS）analysis result confirm the experiment data. And the method have its application or other structures.

參考文獻
【1】Meyer Y., “Wavelets Algorithms and Application,” Siam, 1993.
【2】Pandey,A.K., Biswas, M., Samman, M.M., “ Damage detection from
changes in curvature mode shapes,”. Journal of Sound andVibration
Vol.145 (2),321–332 , 1991.
【3】Pandey,A.K.,Biswas, M., “Damage detection in structures using changes
in flxibility,” Journal of Sound and Vibration ,Vol.169 (1),3–17,1994.
【4】Ratcliffe,C.P., “ Damage detection using a modified Laplacian operator
on mode shape data,” Journal of Sound and Vibration
Vol.204(3),503–517, 1997.
【5】Jeong,H., Jang, Y.S., “ Fracture source location in a thin plate
using the wavelet transform of dispersive waves,” IEEE Transactions
on Ultrasonics,Ferroelectrics,and Frequency Control ,Vol.47,612–619, 2000.
【6】Kim,Y.Y.,Kim, E.H., “Effectiveness of the continuous wavelet transform
in the analysis of some dispersive elastic waves,
” Journal of the Acoustical Society of America ,Vol. 110,86–94, 2001.
【7】Liew,K.M.,Wang,Q., “Application of wavelet theory for crack identication
in structures,” Journal of Engineering Mechanics,
Vol.124 (2),152-157, 1998.
【8】Deng,X.,Wang, Q., “Crack detection using spatial measurements and
wavelet,” International Journal of Fracture, Vol. 91,L23–L28, 1998.
【9】Wang,Q., Deng,X., “Damage detection with spatial wavelets,”
International Journal of Solids and Structures Vol.36,3443-3468, 1999.
【10】Kim,Y.Y.,Lee, H.C.,Lee, Y.W., “Damage detection in a beam via the
wavelet transform of mode shapes,” The Korean Society of
Mechanical Engineers, Vol.24 (4),916–925, 2000.
【11】Mallat S., “A Wavelet Tour Of Signal Processing,
” Academic Press, USA, 1998.
【12】J.C. Hong,Y.Y. Kim,H.C. Lee, Y.W. Lee, “Damage detection using the
Lipschitz exponent estimated by the wavelet transform: applications to
vibration modes of a beam,” International Journal of Solids and
Structures, Vol. 39, 1803-1816, 2002
【13】A Chukwujekwu Okafor , A Dutta, “Structural damage detection in beams
by wavelet transforms,” Smart Mater. Struct. Vol. 9, 906-917, 2000.
【14】黎文明, “快速傅立葉轉換,” 復漢出版社, 台灣, 1985.
【15】胡昌華, 張軍波, 夏軍, 張偉, “基於MATLAB的系統分析與設計：小波分析,
” 西安電子科技大學出版社, 中國大陸,1999.
【16】飛思科技產品研發中心, “MATLAB6.5輔助小波分析與應用,”電子工業出版社,
北京,2003.
【17】蔡展榮, “小波基礎理論與應用課程講義,"
國立成功大學空間及測量工程學系研究所, 2002.
【18】許有村, “小波理論在機械結構破壞點偵測上的應用”,
國立台灣大學機械工程研究所, 碩士論文, 中華民國八十七年六月.
【19】林昆達,“小波理論與類神經網路在橋樑非破壞檢測之應用,”
私立中原大學土木工程研究所, 碩士論文, 中華民國九十年七月.
【20】廖翊宏,“小波轉換應用於樑的破損偵測之研究,”
國立成功大學造船暨船舶機械工程研究所, 碩士論文, 中華民國九十二年六月.　
【21】王柏村, “振動學,” 全華科技, 台灣, 1996.
【22】潘威成, “以模態實驗方法研究懸臂樑的振動行為 ,”
國立成功大學土木工程研究所, 中華民國八十九年七月.
【23】單維彰, “凌波初步,” 全華科技, 台灣, 2000.
【24】王木百村, “實驗模態分析,” 課程講義, 台灣, 1996.
【25】惠汝生, “自動量測系統-LabVIEW,” 全華出版社, 台灣, 2002.
【26】蕭子健, “LabVIEW分析篇,” 高立出版社, 台灣, 2000.
【27】蕭子健, “LabVIEW進階篇,” 高立出版社, 台灣, 2000.
【28】吳志偉, “小波轉換在橋樑非破壞檢測之應用,”
私立中原大學土木工程研究所, 碩士論文, 中華民國九十年七月.
【29】張智星, “MATLAB程式設計與應用,” 清蔚科技, 台灣, 2000.
【30】賴育良, 林啟豪, 謝忠祐, “ANSYS電腦輔助工程分析,” 儒林出版社, 台灣, 2000.