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研究生: 曾彥凱
Tseng, Yen-Kai
論文名稱: 應用非參數化方法於頻譜估測之模態參數識別研究
Identification of Modal Parameters Using Nonparametric Method for Spectral Estimation
指導教授: 江達雲
Chiang, Dar-Yun
學位類別: 碩士
Master
系所名稱: 工學院 - 航空太空工程學系
Department of Aeronautics & Astronautics
論文出版年: 2020
畢業學年度: 108
語文別: 中文
論文頁數: 143
中文關鍵詞: 非參數化方法洩漏效應
外文關鍵詞: Nonparametric method, leakage effect
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  • 本文主要利用非參數化方法於頻譜估測之模態參數識別。在頻域分析中,大部分的量測訊號透過快速傅立葉轉換,將時間訊號轉換到頻率域上,可能會發生洩漏效應(Leakage effect),造成後續模態參數識別的誤差。本文利用非參數化方法中的Welch's method,來抑制洩漏現象發生,並提出改良多參考點最小二乘複頻域法的加權函數,以及用circular overlap的方式來改良Welch's method以提高識別結果的精度。

    This study aims to identify the modal parameters for spectrum estimation using a nonparametric method. In frequency domain analysis, fast Fourier transform is employed to convert most time signals within measurement data into frequency domain. In this process, the leakage effect is readily observed, resulting in errors in subsequent modal parameter identification. In this thesis, the leakage effect was minimized using the non-parametric method-Welch’s method. Also, we propose a weighting function to improve the poly-reference least squares complex frequency domain method and a circular overlap method to improve the identification accuracy of the Welch’s method.

    摘要 I 致謝 IX 目錄 X 第一章 緒論 1 1.1 引言 1 1.2 研究背景 2 1.3 文獻回顧 5 1.4 研究動機與目的 8 1.5 論文架構 10 第二章 模態分析理論 11 2.1 引言 11 2.2 比例阻尼系統之模態分析 12 2.3 非比例阻尼系統之模態分析 15 2.4 頻響函數 19 第三章 環境振動之頻率域模態參數識別 22 3.1 引言 22 3.2 隨機過程 24 3.2.1定常過程分析 25 3.2.2洩漏效應與窗函數 26 3.2.3 Welch s method 28 3.3多參考點最小二乘複頻域法 32 3.4模態驗證 38 3.4.1穩態圖(Stabilization Diagram) 39 3.4.2模態可信度(Modal Assurance Criterion, MAC) 40 3.4.3盒形圖(Box Plot) 41 第四章 數值模擬 42 4.1引言 42 4.2定常白訊於低阻尼鏈模型之數值模擬 43 4.2.1數值模擬結果與討論 45 4.2.2 Circular Overlap對定常白訊於低阻尼鏈模型之數值模擬 47 4.2.3數值模擬結果與討論 47 4.3定常白訊於高阻尼鏈模型之數值模擬 49 4.3.1數值模擬結果與討論 50 第五章 結論 53 參考文獻 55

    [1] Ewins, D. J., Modal Testing: Theory and Practice, Vol. 15: Research Studies Press Letchworth, 1984.
    [2] Söderström, T., Stoica, P., System Identification, Prentice-Hall,1989.
    [3] Heylen, W., Lammens S., Sas, P., “Modal Analysis Theory and Testing, ” KULeuven (ISBN:90-73802-61-X), 1998.
    [4] Maia, N. M. M., Silva, J. M. M., Theoretical and Experimental Modal Analysis, Taunton: Research Studies Press, 1997.
    [5] Phil, M., Zaveri, K., “Modal Analysis of Large Structures: Multiple Exciter Systems,” Brüel and Kjær Theory and Application Handbook BT 0001-12, 1985.
    [6] Caughey, T., O’Kelly, M. E., “Classical Normal Modes in Damped Linear Dynamic Systems,” Journal of Applied Mechanics, Vol. 32, pp. 583-588, 1965.
    [7] Clough, C. W., Penzien, J., “Dynamic of Structure,” 2nd: McGram-Hill. Inc, 1993
    [8] Hougen, J. O., Walsh, R. A., “Pulse Testing Method,” Chemical Engineering Progress, Vol. 57, pp. 69-79, 1961.
    [9] Brigham, E. O., Morrow, R., “The Fast Fourier Transform,” IEEE Spectrum, Vol. 4, pp. 63-70, 1967.
    [10] Rainieri, C., Fabbrocino, G., Operational Modal Analysis of Civil Engineering Structures, Vol. 142. Springer, New York, 2014.
    [11] Spitznogle, F. R., Quazi, A. H., “Representation and Analysis of Time‐Limited Signals Using a Complex Exponential Algorithm,” The Journal of the Acoustical Society of America, Vol. 47, pp. 1150-1155, 1970.
    [12] Smith, W., “Least-Squares Time-Domain Method for Simultaneous Identification of Vibration Parameters from Multiple Free-Response Records,” The 22nd Structures, Structural Dynamics and Materials Conference, 1981.
    [13] Vold, H., Kundrat, J., Rocklin, G. T., Russell, R., “A Multi-Input Modal Estimation Algorithm for Mini-Computers,” SAE Technical Paper 0148-7191, 1982.
    [14] Richardson, M. H., Formenti, D. L., “Parameter Estimation from Frequency Response Measurements Using Rational Fraction Polynomials,” Proceedings of the 1st International Modal Analysis Conference, pp. 167-186, 1982.
    [15] Van Der Auweraer, H., Guillaume, P., Verboven, P., Vanlanduit, S., “Application of a Fast-Stabilizing Frequency Domain Parameter Estimation Method,” Journal of Dynamic Systems, Measurement, and Control, Vol. 123, pp. 651-658, 2001.
    [16] Guillaume, P., Verboven, P., Vanlanduit, S., Van Der Auweraer, H., Peeters, B., “A Poly-Reference Implementation of the Least-Squares Complex Frequency-Domain Estimator,” Proceedings of IMAC, pp. 183-192, 2003.
    [17] Van der Auweraer, H. and Peeters, B., “Discriminating Physical Poles from Mathematical Poles in High Order Systems: Use and Automation of the Stabilization Diagram”, Proceedings of the IEEE Instrumentation and Measurement Technology Conference, Como, Italy, May, pp. 2193–2198, 2004.
    [18] Peeters, B., Van der Auweraer, H., “Polymax: A Revolution in Operational Modal Analysis,” In 1st International Operational Modal Analysis Conference. Copenhagen, 2005.
    [19] 張耕華, “應用Welch’s Method於環境振動之模態參數識別,” 國立成功大學航空太空工程學系學位論文, 2019.
    [20] IEEE Power System Harmonic Working Group Report, “Bibliography of Power System Harmonics,PartⅠ,” IEEE Trans.Power Apparatus and System, Vol.PAS-103, no.9, Sept., pp. 2460-2469, 1984.
    [21] Oppenheim, A.V. and Schafer, R.W,  “Discrete-time signal processing, New Jersey:Prentice-Hall,1989”
    [22] Welch, P. D., “The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging over Short, Modified Periodograms,” IEEE Transactions on Audio and Electroacoustics,Vol.15,pp.70-73,1967.
    [23] Phani, A. S., “On the Necessary and Sufficient Conditions for the Existence of Classical Normal Modes in Damped Linear Dynamic Systems, ” Journal of Sound and Vibration, Vol.264, pp. 741-745, 2003.
    [24] Kirshenboim,J., “Real vs Complex Normal Mode Shapes,” International Modal Analysis Conference, 5 th, London, England, pp. 1594-1599, 1987.
    [25] Wei, M., Allemang, R., Brown, D., “Real-Normalization of Measured Complex Modes,” Proceedings of the fifth International Modal Analysis Conference, pp. 708-12, 1987.
    [26] Henrion, D., Šebek, M., “Polynomial and Matrix Fraction Description,” Retrieved from.
    [27] Singer, N. C., Seering, W. P., “Preshaping Command Inputs to Reduce System Vibration,” Journal of Dynamic Systems, Measurement and Control, Vol. 112, pp. 76-82, 1990.
    [28] 林昱勳, “多參考點最小二乘複頻域法於模態干涉系統之模態參數識別研究,” 國立成功大學航空太空工程學系學位論文, 2017.
    [29] Martin, R. L., “Digital Signal Processing Theory and Background,” Polyhedron, Vol.7, pp. 2243, 1988.
    [30] Sneddon, I. N., “Fourier Transforms: Courier Corporation,” North Chelmsford, 1995.
    [31] Eckmann, J. P., Ruelle, D., “Ergodic Theory of Chaos and Strange Attractors,” The Theory of Chaotic Attractors, Springer, pp. 273-312, 1985.
    [32] Nuttall, A., H., “Some Windows with Very Good Sidelobe Behavior; Application to Discrete Hilbert Transform,” Naval Underwater Systems Center, pp. 84-91, 1980
    [33] Kurt Barbé, Rik Pintelon, and John Schoukens, “Welch Method Revisited: Nonparametric Power Spectrum Estimation Via Circular Overlap,” IEEE Transaction on signal processing, Vol. 58, NO.2, 2010
    [34] Widanage, W. D., Douce, J. L., Godfrey, K. R., “Effects of Overlapping and Windowing on Frequency Response Function Estimates of Systems with Random Inputs,” IEEE Transactions on Instrumentation and Measurement,Vol. 58, pp. 214-220, 2009.
    [35] Antoni, Jérôme, Schoukens, Johan, “A Comprehensive Study of the Bias and Variance of Frequency-Response-Function Measurements: Optimal Window Selection and Overlapping Strategies,” Automatica, Vol. 43, pp1723-1736, 2007.
    [36] Peeters, B., Van der Auweraer, H., Guillaume, P., and Leuridan, J., “The PolyMAX Frequency-Domain Method:A New Standard for Modal Parameter Estimation?,” Shock and Vibration, Vol. 11, pp. 395-409, 2004.
    [37] 姚明逸, “多參考點最小二乘複頻域法於環境振動之模態參數識別,” 國立成功大學航空太空工程學系學位論文, 2018.
    [38] Peeters, B., Guillaume, P., Van der Auveraer, H., et al., Automotive and aearospace application of the polyMAX modal parameter estimation method, Proc. of the 〖22〗^nd IMAC, Dearborn(ML),USA, Jan., 2004
    [39] Van Loan, C. F., “The Ubiquitous Kronecker Product,” Journal of Computational and Applied Mathematics, Vol. 123, pp. 85-100, 2000.
    [40] Edelman, A., Murakami, H., “Polynomial Roots from Companion Matrix Eigenvalues,” Mathematics of Computation, Vol. 64, pp. 763-776, 1995.
    [41] Kane, C., Marsden, J. E., Ortiz, M. M., West, “Variational Integrators and the Newmark Algorithm for Conservative and Dissipative Mechanical Systems,” International Journal for Numerical Methods in Engineering, Vol. 49, pp. 1295-1325, 2000.
    [42] Martin, R., “Noise Power Spectral Density Estimation Based on Optimal Smoothing and Minimum Statistics,” IEEE Transactions on Speech and Audio Processing, Vol. 9, pp. 504-512, 2001.
    [43] Porat, B., Digital Processing of Random Signals: Theory and Methods: Courier Dover Publications, 2008.

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