本文探討小波轉換於定常環境振動下模態參數識別之應用。將系統的定常響應先轉化為近似之自由衰減訊號，再對此訊號進行小波轉換獲得訊號之時頻解析，最終利用系統模態表現於時頻解析之峰脊特徵，識別出各模態的模態參數，即自然頻率，阻尼比及振形。由於各模態的參數是從時頻譜中的峰脊識別而得，小波轉換所使用的尺度是否為模態正確之對應尺度，將直接影響模態參數識別的結果。本文針對模態尺度之決定提出新的作法，直接由小波轉換的時頻解析與各模態峰脊的歷時累加值，來決定系統被激發之主要模態的數目與對應之尺度，再利用小波轉換的相關理論與技術識別模態參數。經數值模擬結果顯示，在定常環境振動情況下本文所提之分析法可得良好的模態參數識別結果，對於雜訊亦有良好之強健性。

In this thesis, a wavelet-based modal parameter estimation technique is proposed to operate on the stationary ambient response of a structural system. Through adequate processing methods, the stationary ambient vibration data is transformed approximately to the free vibration of the analyzed system. The modal parameters of the system (including natural frequencies, damping ratios and mode shapes) are then identified from the ridges in the time-frequency spectrum obtained by the wavelet analysis. Because the modal parameters are identified from the ridges, the scales adopted in the wavelet transform will directly affect the result of modal identification. A new method is proposed to find the modal scale corresponding to the major modes, in which the number of the excited modes and the corresponding modal scales are determined through the wavelet analysis only, and this new method is shown to be robust to noise. Through numerical simulations, applicability and effectiveness of the proposed wavelet-based method of modal parameter identification from stationary ambient vibration data is demonstrated.

參考文獻
[1]Bedewi,N.E.,“The Mathematical Foundation of the Auto and Cross-random Decrement Techniques and the Development of a System Identification Technique for the Detection of Structural Deterioration”,Ph.D Thesis,University of Maryland College Park,1986.
[2]armona,R.A.,Hwang,W.L.,Torresani,B.,Practical Time-frequency Analysis, Academic Press,Inc,1998.
[3]Carmona,R.,Hwang,W.L.,Torresani,B.,“Characterization of Signals by the Ridges of Their Wavelet Transform”,IEEE Transactions on Signal Processing, Vol.45,pp.2586-2589,1997.
[4]Carne,T.G.,Lauffer,J.P.,Gomez,A.J.and Benjannet,H.“ Modal Testing an Immense Flexible Structure Using Natural and Artificial Excitation”,The International Journal of Analytical and Experimental Modal Analysis, The Society of Experimental Mechanics,Oct.,pp.117-122,1988.
[5]Chui C.K.,An Introduction to Wavelets,Academic Press,Inc,1992.
[6]Code,H.A.Jr.,“Methods and apparatus for measuring the damping characteristics of a structures by the random decrement technique”,United States Patent No.3,620,069,1971.
[7]Delprat,N.,Escudie,B.,Guillemain,P.,Ronland-Martinet,R.K.,Ph.Tchamichian, Torresani,B.,“Asymptotic Wavelet and Gabor Analysis: Extraction of Instantaneous Frequencies”,IEEE,Vol.38,pp.644-664,1992.
[8]Grossman,A.,Morlet,J.,“Lecture on Recent Results”,Mathematics and Physics,World Scientific,1985.
[9]Hwang,W.L.,Carmona,R.A.,Torresani,B.,“Characterization of Signals by the Ridges of Their Wavelet Transform”,Preprint,1994.
[10]James,G.H.,Carne,T.G.and Lauffer,J.P.,“The Natural Excitation Technique for Modal Parameter Extraction from Operating Wind Yurbines.”, SAND92-1666.UC-261,Sandia National Aboratories,1993.
[11]Lardies,J.,Gouttebroze,S.,“Identification of Modal Parameters Using the Wavelet Transform”,International Journal of Mechanical Sciences,Vol.44,pp.2263-2283, 2002.
[12]Lardies,J.,Ta,Minh-Nghi,“A Wavelet-Based Approach for the Identification of Damping in Non-Linear Oscillators”,International Journal of Mechanical Sciences,Vol.47,pp.1262-1281,2005.
[13]Mallat,S.,A Wavelet Tour of Signal Processing, Academic Press,Inc,1997.
[14]Morlet,J.,“Sampling Theory and Wave Propagation”,Proceedings of the 51st Annual Meeting Soc,1980.
[15]Pandit,S.M.and Wu,S.M.,Time Series and System Analysis with Applications, John Wiley & Sons,Inc.,New York,1983.
[16]Ruzzene,M.,Fasana, A.,Garibaldi,L.,Piombo,B.,“Natural Frequencies and Dampings Identification Using Wavelet Transform: Application to Real Data”,Mechanical Systems and Signal Processing,Nov.,pp.207-218,1997.
[17]Sheen,Y.T.,Hung,C.K.,“Constructing A Wavelet-Based Envelope Function for Vibration Signal analysis”,Mechanical Systems and Signal Processing,Vol.18, pp.119-126,2004.
[18]Shinozuka,M.,“Simulation of Multivariate and Multidimensional Random Processes”,Journal of the Acoustical Society of America,Vol.49,No.1,pp.357-367,1971.
[19]Slavic,J.,Simonovski,I.,Boltezar,M.,“Damping Identification Using A Continuous Wavelet Transform: Application to Real Data”,Journal of Sound and Vibration,Vol.262,pp.291-307,2003.
[20]Staszewski,w.J.,“Identification of Damping in MDOF Systems Using Time-Scale Decomposition ”,Journal of Sound and Vibration,Vol.203,pp.283-305,1997.
[21]Tom,H.,Wavelet: An Elementary Treatment of Theory and Applications,World Scientific,Inc,1993.
[22]Vandiver,J.K.,Dunwoody,A.B.,Campbell,R.B.and Cook,M.F.,“A Mathematical Basis for the Random Decrement Vibration Signature Analysis Technique”, Journal of Mechanical Design,Apr.,Vol.104,1982.
[23]Yan,B.F.,Miyamoto,A.,Bruhwiler,E.,“Wavelet Transform-Based Modal Parameter Identification Considering Uncertainty”,Journal of Sound and Vibration,Vol.291,pp.285-301,2006.
[24]林章生,相關函數法於非定常環境振動之模態參數識別研究,碩士論文,國立成功大學航空太空工程研究所,2004.
[25]秦前清,楊宗凱,實用小波分析,西安電子科技大學出版社,1994
[26]曹松華,隨機遞減法於非定常環境振動模態參數識別之應用,碩士論文,國立成功大學航空太空工程研究所,2004.
[27]楊福生,小波變換的工程分析與應用,科學出版社,1999.