本文探討奇異譜分析法(Singular Spectrum Analysis , SSA)於定常環境振動模態參數識別之應用。奇異譜分析法是藉由奇異值分解萃取出響應資料的主要成分，剔除次要成分進而降噪，得到的主要成分即為各模態的響應資料，進而轉換成頻譜圖可得到模態頻率。吾人利用前人所提之求取系統矩陣方法，因此將奇異譜分析法應用於狀態空間模型上，利用系統矩陣求出系統的動態特性，進而求出系統之模態參數。最後經由數值模擬，驗證本文所探討的方法能有效地識別出結構的主要模態參數及振動反應。

The purpose of this thesis is to discuss the application of Singular Spectrum Analysis (SSA) in Modal-Parameter Identification of stationary ambient vibration. SSA extracts the main components of response data by Singular Value Decomposition (SVD) and removes minor components to reduce noise. The main component obtained is the response data of each mode and converted into a spectrogram to get the modal frequency. Using the method proposed by the predecessors to obtain the system matrix, the SSA is based on the state space model. Using the system matrix to find the dynamic characteristics of the system, then find the modal parameters of the system. Finally, the method verified through numerical simulation discussed in this paper can effectively distinguish the main modal parameters and vibration response of the structure.

[1]Ewins, D. J., Modal Testing: Theory and Practice, Research Studies Press, 1984.
[2]Eykhoff, P., System Identification: Parameter and State Estimation, London, England: Wiley-Interscience, 1974.
[3]Den Hartog, J. P., Mechanical Vibration, New York, U.S.A: McGraw-Hill, 1962.
[4]Ibrahim, S. R., and Pappa, R. S., “Large Survey Testing Using the Ibrahim Time Domain (ITD) Model Identification Algorithm,” Journal of Spacecraft and Rockets, Vol. 19, pp. 459-465, 1982.
[5]Ibrahim, S. R. and Mikulcik, E. C., “A Method for the Direct Identification of Vibration Parameters from Free Response,” Shock and Vibration Bulletin, Vol. 47, Part. 4, pp. 183-198, 1977.
[6]Ibrahim, S. R., Brincker, R. and Asmussen, J. C., “Modal Parameter Identification from Response of General Unknown Random Inputs,” Proceedings of 14th International Modal Analysis Conference, pp. 446-452, 1995.
[7]Juang, J. N. and Pappa, R. S., “An Eigensystem Realization Algorithm for Modal Parameter Identification and Modal Reduction,” Journal of Guidance and Control Dynamics AIAA, Vol.8, No. 5, pp. 620-627, 1985.
[8]Juang, J. N. and Pappa, R. S., “Effects of Noise on Modal Parameter Identification by the Eigensystem Realization Algorithm,” Journal of Guidance and Control Dynamics AIAA, Vol. 9, No. 3, pp. 294-303, 1986.
[9]Juang, J. N., Cooper, J. E. and Wright, J. R., “An Eigensystem Realization Algorithm using Data Correlations (ERA/DC) for Modal Parameter Identification,” Control Theory and Advanced Technology, Vol. 4, No. 1, pp. 5-14, 1988.
[10]Carne, T. G., Lauffer, J. P. and James, G. H., “The Natural Excitation Technique for Modal Parameter Extraction from Operating Wind Turbines,” SAND92-1666.UC-261, Sandia National Laboratories, 1993.
[11]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, pp. 117-122, 1988.
[12]鍾旻軒,資料型隨機子空間識別法於非定常環境振動下之模態參數識別,碩士論文,國立成功大學航空太空工程學研究所, 2019.
[13]蘇芳禾,特徵系統實現法於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學研究所, 2006.
[14]D.S. Broomhead, and G.P. King. Extracting qualitative dynamics from experimental data. Physica D, 20, pp. 217–236, 1986.
[15]D.S. Broomhead, and G.P. King. On the qualitative analysis of experimental dynamical systems. Nonlinear Phenomena and Chaos, Sarkar S(Ed.), Adam Hilger, Bristol, pp. 113—144, 1986.
[16]K. Fraedrich. Estimating dimensions of weather and climate attractors. J. Atmos. Sci. 43, pp. 419–432, 1986.
[17]Bendat, J. S. and Piersol, A. G., Random Data: Analysis and Measurement Procedures, 4th edition, New York: Wiley, 2010.
[18]N.Golyandian, V.Nekrutkin, and A. Zhigljavsky .Analysis of time Series Structure:SSA and related techniques. Chapman and Hall/CRC, 2001.
[19]Yufeng Lu and Jafar saniie, Singular spectrum analysis for trend extraction in ultrasonic backscattered echoes, 2015.
[20]M. Ghil, M.R. Allen, M.D. Dettinger, K. Ide, D. Kondrashov, M.E. Mann, et al. Advanced spectral methods for climatic time series.Rev.Geophys.40(1),pp. 3.1-3.41,2002.
[21]郭采蓉,應用隨機子空間識別法於結構健康診斷:結合穩態圖穩定標準與頻域分解法,碩士論文,國立台灣大學工學院土木工程學研究所,2018.
[22]Nicholson, W. K., Linear Algebra with Applications, 6th edition, New York, U.S.A: McGraw-Hill, 2009.
[23]王建智,資料型隨機子空間法於系統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學研究所, 2017.
[24] Bathe, K. J., Finite Element Procedures in Engineering Analysis, Prentic-Hall, Chap.9, 1982.