| 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 |
| 相關次數: | 點閱:73 下載:3 |
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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.
[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.