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研究生: 張耕華
Chang, Keng-Hua
論文名稱: 應用Welch s Method 於環境振動之模態參數識別
Identification of Modal Parameters from Ambient Vibration Data Using Welch's Method
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: 2019
畢業學年度: 107
語文別: 中文
論文頁數: 103
中文關鍵詞: Welch s method穩態圖模態可信度盒形圖
外文關鍵詞: Welch’s method, stabilization diagram, modal assurance criterion, box plot
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  • 在頻率域中的模態參數識別,量測訊號大部分透過快速傅立葉轉換,將時間訊號轉至頻率域做進一步的分析,可能會遇到頻譜洩漏效應(Leakage phenomenon),造成後續識別模態參數的誤差。故本文利用計算功率頻譜密度函數的方法-Welch s method,得到抑制洩漏現象後之功率頻譜密度函數。針對前人提出的多參考點最小二乘複頻域法進行研究,由於本識別法是藉由提高多項階數來增加模態參數的識別精度,然而在實際識別模態參數時,並無法選擇何階的多項式解所得到識別結果最精確,故在此引入盒形圖以利提取模態參數。

    In frequency domain, the response signal in the modal parameter identification must be converted to the frequency domain by a fast Fourier transform. There may be a leakage phenomenon, which causes errors in identifying modal parameters. Therefore, this thesis uses the method of calculating the power spectral density function-Welch's method to obtain the power spectral density function that reduces the leakage phenomenon. We mainly study the poly -reference least squares complex frequency domain method to apply ambient vibra-tion situation. This identification method increases the Identified accuracy of modal parame-ters by increasing the order of multiple orders. When we identify under realistic ambient vi-bration, the polynomial solution of which order cannot be selected to obtain the most pre-cisely identified result, apply the box plot in this thesis. Therefore, this thesis uses the box plot which is a statistical method to obtain identification result.

    摘要 I Table 1 6-DOF chain model identification result VII Table 2 6-DOF chain model identification result from earthquake data VII Table 3 Non-stationary white noise identification results VIII Figure 1 Earthquake data IX Figure 2 Earthquake data autocorrelation IX Figure 3 Earthquake data spectrogram X Figure 4 Non-stationary white noise response spectrum X 誌謝 XIII 目錄 XIV 第一章 緒論 1 1.1 引言 1 1.2 研究背景 2 1.3 文獻回顧 3 1.4 研究動機與目的 6 1.5 論文架構 8 第二章 模態分析理論 9 2.1引言 9 2.2比例阻尼系統之模態分析 10 2.3非比例阻尼系統之模態分析 13 2.4頻響函數 17 第三章 環境振動之頻率域模態參數識別 20 3.1引言 20 3.2隨機過程 21 3.2.1定常過程分析 22 3.2.2洩漏效應與窗函數 23 3.2.3 Welch s method 24 3.3多參考點最小二乘複頻域法 28 3.4模態驗證 33 3.4.1穩態圖(Stabilization Diagram) 33 3.4.2模態可信度(Modal Assurance Criterion, MAC) 34 3.4.3盒形圖(Box Plot) 35 第四章 數值模擬 36 4.1引言 36 4.2定常白訊之數值模擬 36 4.2.1模擬結果討論 39 4.2.2分段數量對定常白訊於阻尼鏈模型之數值模擬 40 4.2.3模擬結果討論 41 4.3定常白訊於十二倍阻尼鏈模型之數值模擬 41 4.3.1模擬結果討論 42 4.4震訊號於鏈模型之模態參數識別 44 4.4.1模擬結果討論 45 第五章 結論 47 參考文獻 50

    [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] Hougen, J. O., Walsh, R. A., “Pulse Testing Method,” Chemical Engineering Progress, Vol. 57, pp. 69-79, 1961.
    [7] Brigham, E. O., Morrow, R., “The Fast Fourier Transform,” IEEE Spectrum, Vol. 4, pp. 63-70, 1967.
    [8] Peeters, B., Roeck, G. D., “Stochastic System Identification for Operational Modal Analysis: A Review,” Journal of Dynamic Systems, Measurement and Control, Vol.123, pp. 659, 2001.
    [9] Rainieri, C., Fabbrocino, G., Operational Modal Analysis of Civil Engineering Structures, Vol. 142. Springer, New York, 2014.
    [10] 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.
    [11] 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.

    [12] Vold, H., Kundrat, J., Rocklin, G. T., Russell, R., “A Multi-Input Modal Estimation Algorithm for Mini-Computers,” SAE Technical Paper 0148-7191, 1982.
    [13] 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.
    [14] 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.
    [15] 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.
    [16] Peeters, B., Van der Auweraer, H., “Polymax: A Revolution in Operational Modal Analysis,” In 1st International Operational Modal Analysis Conference. Copenhagen, 2005.
    [17] 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.
    [18] 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.
    [19] Caughey, T., O’Kelly, M. E., “Classical Normal Modes in Damped Linear Dynamic Systems,” Journal of Applied Mechanics, Vol. 32, pp. 583-588, 1965.
    [20] Clough, C. W., Penzien, J., “Dynamic of Structure,” 2nd: McGram-Hill. Inc, 1993.

    [21] 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.
    [22] Kirshenboim,J., “Real vs Complex Normal Mode Shapes,” International Modal Analysis Conference, 5 th, London, England, pp. 1594-1599, 1987.
    [23] Wei, M., Allemang, R., Brown, D., “Real-Normalization of Measured Complex Modes,” Proceedings of the fifth International Modal Analysis Conference, pp. 708-12, 1987.
    [24] Henrion, D., Šebek, M., “Polynomial and Matrix Fraction Description,” Retrieved from.
    [25] 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.
    [26] 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.
    [27] Oppenheimer, A. V., Schafer, R.W., Digital Signal Processing, Prentice Hall, 1975.
    [28] Nuttall, A., H., “Some Windows with Very Good Sidelobe Behavior; Application to Discrete Hilbert Transform,” Naval Underwater Systems Center, pp. 84-91, 1980.
    [29] Martin, R. L., “Digital Signal Processing Theory and Background,” Polyhedron, Vol.7, pp. 2243, 1988.
    [30] Avci, K., Nacaroglu, A., “Exponential Window Family,” Signal and Image Processing : An International Journal, Vol.4, pp1-12, 2013.
    [31] Sneddon, I. N., “Fourier Transforms: Courier Corporation,” North Chelmsford, 1995.
    [32] Eckmann, J. P., Ruelle, D., “Ergodic Theory of Chaos and Strange Attractors,” The Theory of Chaotic Attractors, Springer, pp. 273-312, 1985.

    [33] Widanage, W. D., Douce, J. L., Godfrey, K. R., “Effects of Overlapping and Windowing on Frequency Response Function Estimates of Sys-tems with Random Inputs,” IEEE Transactions on Instrumentation and Measurement,Vol. 58, pp. 214-220, 2009.
    [34] 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.
    [35] 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.
    [36] 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.
    [37] Van Loan, C. F., “The Ubiquitous Kronecker Product,” Journal of Computational and Applied Mathematics, Vol. 123, pp. 85-100, 2000.
    [38] Edelman, A., Murakami, H., “Polynomial Roots from Companion Matrix Eigenvalues,” Mathematics of Computation, Vol. 64, pp. 763-776, 1995.
    [39] 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.
    [40] 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.
    [41] Porat, B., Digital Processing of Random Signals: Theory and Methods: Courier Dover Publications, 2008.

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