本文應用開迴路與閉迴路狀態觀測器於模態參數識別之研究，考慮系統響應資料在含有雜訊影響的情況下，如何有效地利用特徵系統實現法來識別系統結構的模態參數。研究發現，閉迴路狀態觀測器利用輸出誤差反饋來修正系統狀態的觀念雖然可使估測輸出與原系統較為接近，但參數識別的結果卻不盡理想。因此進一步利用馬可夫參數以及系統響應資料的相關性來提升閉迴路狀態觀測器於模態參數識別之有效性。經由數值模擬驗證，本文所探討的理論方法在噪訊比10%的情況下仍能有效識別系統的模態參數。

This thesis employs open-loop and closed-loop state observers for identification of modal parameters based on the Eigensystem Realization Algorithm. Although the estimated output of the closed-loop state observer agrees well with the true response, it is difficult to identify the modal parameters accurately under noisy conditions. This problem can be overcome by further introducing the correlation method coupled with the closed-loop state observer. Through numerical simulations, the applicability of the proposed method for identification of modal parameters is confirmed.

[1]Kennedy, S. R. and Pancu, C. D. P. “Use of Vectors in Vibration Measurement and Analysis”, Journal of Aeronautics Sciences, Vol. 14, No. 11, 1974, pp. 603-625.
[2]Levy, E. “Complex curve fitting[J]”, IRE Transaction on Automatic Control, 1959,4(3):37-43.
[3]Ibrahim, S. R. and Mikulcik, E. C., “The Experimental Determination of Vibration Parameters from Time Responses”, Shock and Vibration Bulletin, Vol. 46, Part 5, Aug. 1976, pp. 183-198.
[4]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, Sept. 1977, pp. 183-198.
[5]Pappa, R. S. and Ibrahim, S. R., “A Parametric Study of Ibrahim Time Domain Modal Analysis”, Shock and Vibration Bulletin, Vol. 51, Part 3, 1981, pp. 43-72.
[6]Vold, H. and Rocklin, G. F., “The Numerical Implementation of a Multi-Input Modal Estimation Method for Mini-Computers”, International Modal Analysis Conference Proceedings, Nov. 1982.
[7]Pandit, S. M. and Wu, S. M., “Time Series and System Analysis with Applications”, John Wiley & Sons, Inc., New York, 1983.
[8]Pandit, S. M. and Mehta, N. P., “Data Dependent Systems Approach to Modal Analysis Via State Space”, Transactions ASME, Journal of Dynamic Systems, Measurement and Control, Vol. 107, 1985, pp. 132-137.
[9]Pandit, S. M. and Mehta, N. P., “Data Dependent Systems Approach to Modal Analysis, Part I: Theory”, Journal of Sound and Vibration, Vol. 122, No. 3, 1988, pp. 413-422.
[10]Beck, J. L., “Determining Models of Structures from Earthquake Records”, Report No. EERL 78-01, California Institute of Technology, Pasadena, 1978.
[11]Beck, J. L. and Jennings, P. C., “Structural Identification Using Linear Models and Earthquake Records”, Earthquake Engineering and Structural Dynamics, Vol. 8, 1980, pp. 145-160.
[12]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, 1985, pp.620-627.
[13]Juang, J. N. and Pappa, R. S., “Effects of Noise on Modal Parameters Identified by the Eigensystem Realization Algorithm”, Journal of Guidance and Control Dynamics, AIAA, Vol. 9, No. 3, 1986, pp.294-303.
[14]Ho, B. L. and Kalman, R. E., “Effective Construction of Linear State-Variable Models from Input/Output Data”, Proceedings of the 3rd Annual Allerton Conference on Circuit and System Theory, 1965, pp. 449-459
[15]Ho, Zeiger, H. P. and McEwen, A. J., “Approximate Linear Realizations of Given Dimension Via Ho’s Algorithm”, IEEE Transactions on Automatic Control, Vol. AC-19, No. 2, April 1974, pp. 153-153.
[16]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, 1988, pp.5-14.
[17]Juang, J. N., Phan, M., Horta, L. G. and Longman R. W., “Identification of Observer/Kalman Filter Markov Parameters: Theory and Experiments”, Journal of Guidance, Control and Dynamics, Vol. 16, No. 2, Mar.-Apr. 1993, pp. 320-329.
[18]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. 1988, pp. 117-122.
[19]James, G. H., Carne. T. G. and Lauffer, J. P., “The Natural Excitation Technique for Modal Parameter Extraction from Operating Wind Turbines.” SAND92-1666. UC-261, Sandia National Aboratories, 1993.
[20]Chiang, D.Y. and Cheng M.S., “Model parameter identification from ambient response”, 1999, AIAA Journal, Vol. 37, pp. 513-515.
[21]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研究所, 2006.
[22]Chiang, D.Y., and Lin, C.S., “Identification of Model Parameters from Nonstationary Ambient Vibration Data Using Correlation Technique”, Journal of AIAA, Vol. 46, No. 11, Nov. 2008, pp.2752-2759.
[23]Lin, Y. K., Probabilitstic Theory of Structural Dynamics, McGraw-Hill, New York, 1967.
[24]Bendat, J. S. and Piersol, A. G., Random Data: Analysis and Measurement Procedures, John Wiley, New York, 2000.
[25]Davis, W.R. and Bucciarelli, L.L, “Nonstationary Spectral Analysis for Linear Dynamic System”, AIAA Journal, Vol. 13, No. 1, 1975, pp. 543-545.
[26]Shinozuka, M., “Random Process with Evolutionary Power”, J. Eng. Mech. Div., ASCE, Vol. 96, EM4, 1970, pp. 543-545.
[27]Ewins, D. J., Modal Testing: Theory and Practice, Research Studies Press, 1984.
[28]Juang, J. N., Applied System Identification, Prentice-Hall, Inc, 1994.
[29]Bathe, K. J., Finite Element Procedures in Engineering Analysis, Prentic-Hall, 1982, Chap. 9.
[30]Shinozuka, M., “Simulation of Multivariate and Multidimensional Random Processes”, Journal of the Acoustical Society of America, Vol. 49, No. 1. 1971, pp. 357-367.
[31]Newland, D. E., An Introduction to Random Vibrations and Spectral Analysis, 1975.
[32]Kirshenboim, J., “Real vs. Complex Mode Shapes”, Proceeding of 5th International Modal Analysis Conference, London, England, 1987, pp. 1594-1599.
[33]Ward Heylen, Stefan Lammens and Paul Sas, Modal Analysis Theory and Testing, 2nd ed., Katholieke Universiteit Leuven, Faculty of Engineering, Dept. of Mechanical Engineering, Division of Production Engineering, Machine Design and Automation, 1998.