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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 柯文俊(Wen-Jiunn Ko) | |
| dc.contributor.author | Gang-Yi Lin | en |
| dc.contributor.author | 林罡亦 | zh_TW |
| dc.date.accessioned | 2021-06-15T01:51:52Z | - |
| dc.date.available | 2010-07-14 | |
| dc.date.copyright | 2009-07-14 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-07-02 | |
| dc.identifier.citation | 參考文獻
[1] S. A. Billings, J.O. Gary and D. H. Owen, Nonlinear System Densign. Peter Peregrinus Ltd, 1985. [2] E. P. Box George, M. J. Gwilym and C. R. Gregory, Time series analysis forecasting and control, Third edition, Prentice Hall, 1994. [3] M. Schetzen, The volterra and wiener theories of nonliner system, New York: Wiley, 1980. [4] S. A. Billings and K. M. Tsang, “Spectral analysis for non-linear systems, part I: parametric non-linear spectral analysis,” Mechanical Systems and Signal Processing, Vol. 3, pp. 319–339, 1989. [5] S. A. Billings and K. M. Tsang, “Spectral analysis for non-linear systems, part II: interpretation of non-linear frequency response functions,” Mechanical Systems and Signal Processing, Vol. 3, pp. 341–359, 1989. [6] S. A. Billings and K. M. Tsang, “Spectral analysis for non-linear systems, part III: case study examples,” Mechanical Systems and Signal Processing, Vol. 4, pp. 3–21, 1990. [7] G. M. Jenkin, Spectral analysis and it’s applications, Holden-Day, 1998 [8] M. Jacob and P. Fortier, “An interpretation of the spectrogram for discrete-time signal,” IEEE, pp. 281–284, 1992 [9] H. V. der Auweraer and B. Peeters, “Discriminating physical poles from mathematical poles in high order system: use and automation of the stabilization diagram,” IEEE, Instrumentation and Measurement Technology Conference, pp. 2193–2198, 2004 [10] S. R. Singiresu, Mechanical vibrations, Prentice Hall, SI edition, 2005. [11] S. K. Mitra, Digital signal processing, Third edition, McGraw-Hill, 2006. [12] J. C. Peyton-Jones and S. A. Billings, “Recursive algorithm for computing the frequency response of a class of non-linear difference equation models,” International Journal of Control, Vol. 50, pp. 1925–1940, 1989 [13] P. Palumbo and L. Piroddi, “ Harmonic analysis of non-linear structures by means of generalised frequency response functions coupled with NARX models,” Mechanical Systems and Signal Processing, Vol. 14, pp. 243–265 [14] X. J. Jing, Z. Q. Lang and S. A. Billings, “Magnitude bounds of generalized frequency response functions for nonlinear volterra systems described by NARX model,” Automatica, Vol. 44, pp. 838 – 845, 2008. [15] J. E. Chance, K. Worden and G. R. Tomlinson, “Frequency domain analysis of NARX neural networks,” Journal of Sound and Vibration, Vol. 213, pp. 915–941, 1998. [16] P. Palumbo and L. Piroddi, “Seismic behaviour of buttress dams: non-linear modelling of a damaged buttress based on ARX/NARX models,” Journal of Sound and Vibration, Vol. 239, pp. 405–422, 2001. [17] X. J. Jing, Z. Q. Lang and S. A. Billings, “Magnitude bounds of generalized frequency response functions for nonlinear Volterra systems described by NARX model,” Automatica, Vol. 44, pp. 838 – 845, 2008. [18] H. Hu, “A classical perturbation technique which is valid for large parameters” Journal of Sound and Vibration, Vol. 269, pp. 409–412, 2004. [19] Z. G. Xiong and H. Hu, “Comparison of two Lindstedt–Poincare-type perturbation methods”, Journal of Sound and Vibration, Vol. 278, pp. 437–444, 2004. [20] H. Hu, “A classical perturbation technique that works even when the linear part of restoring force is zero”, Journal of Sound and Vibration, Vol. 271, pp. 1175–1179, 2004. [21] H. Hu, “More on generalized harmonic oscillators,” Journal of Sound and Vibration, Vol. 250, pp. 567–568, 2002. [22] H. Hu, “A modified method of equivalent linearization that works even when the non-linearity is not small,” Journal of Sound and Vibration, Vol. 276, pp. 1145–1149, 2004. [23] H. Hu, “A note on the frequency of nonlinear conservative oscillators,” Journal of Sound and Vibration, Vol. 286, pp. 653–662, 2005. [24] H. Hu and J. H. Tang, “A convolution integral method for certain strongly nonlinear oscillators,” Journal of Sound and Vibration, Vol. 285, pp. 1235–1241, 2005. [25] Z. G. Xiong and H. Hu, “Simplified continuousfinite element method for a class of nonlinear oscillating equations,” Journal of Sound and Vibration, Vol. 287, pp. 367–373, 2005. [26] Z. G. Xiong, H. Hu and Q. Tang “A modified eigenfunction expansion approximation for nonlinear oscillating equations,” Journal of Sound and Vibration, Vol. 290, pp. 1315–1321, 2006. [27] C. Sheng, S. A. Billings and W. Luo, “Orthogonal least squares methods and their application to nonlinear system identification,” International Journal of Control, Vol. 50(5), pp. 1873–1896, 1989. [28] Q. M. Zhu and S. A. Billings, “Parameter estimation for stochastic nonlinear rational models,” International Journal of Control, Vol. 57(2), pp 309–333, 1993. [29] 柯文俊，“由狀態空間系統萃取結構系統矩陣與模態參數”，國立台灣大學工程科學及海洋工程學研究所博士論文，2002。 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/43360 | - |
| dc.description.abstract | 由於現實生活中的力學系統都含有非線性因子，其中的差別僅在於非線性程度的多寡，因此自然界的振動現象皆為非線性振動。而非線性系統之振盪頻率是隨著振幅而改變，且對於真實系統來說皆有阻尼存在，因此使得估計其非線性振盪頻率更加困難；但系統之自然振頻是系統本質上的，不受到其他因素影響，因此本文提出一套識別流程直接估計非線性系統之線性模態參數。
本文首先透過單自由度以及三自由度的非線性具阻尼系統以數值模擬的方式模擬其輸出入響應資料，對此輸出入響應以系統識別技術中的含外變數的非線性自我迴歸模型(NARX model)結合伏爾泰拉級數(Volterra series)針對非線性振動系統之輸出響應做分析，主要用來檢驗本文所提出的識別程序於結構振動問題上的可行性。分析過程中並以時間歷時圖、功率頻譜密度圖、時譜圖及模態穩定圖來輔助觀察分析。最後探討兩組不同結構的實驗例，一為懸臂鋼樑，另一為機車車架結構，懸臂鋼樑主要用於檢驗自由響應資訊之系統識別。機車車架結構則分別為衝擊錘激振以及強迫激振儀激振作用下的結構系統識別，以檢驗NARX方法於未知雜訊干擾及複雜結構下的能力。由數值以及實驗資料識別結果顯示，本文所採用之識別技術能有效的從結構振動量測資料中萃取出線性模態參數。 | zh_TW |
| dc.description.abstract | Since the real mechanical systems have nonlinear factors, the only differences are the extent of nonlinearity, so the vibration phenomenon actually are nonlinear. Since the real system has damping, so the oscillation frequency of non-linear system change with amplitude. Thus it’s difficult to estimate the oscillation frequency of a non-linear systems. However, the natural frequency of any system is natural and is not influenced by other factors. This article purposes a set of identification process to estimate the linear modal parameters of nonlinear systems.
At first in this thesis, it is to simulate the output response on both a single and three degrees of freedom of the non-linear systems with damping by using numerical simulation. We can compute the output response of a nonlinear vibration system using system identification techniques by the mathematical model of Nonlinear AutoRegressive with eXogenous inputs model combined with Volterra series to estimate the linear modal parameters of nonlinear systems. Besides, in the analytic process, it also utilizes power spectral density diagram, time frequency analysis diagram and modal stabilization diagram to assist the reach. Finally, NARX method is applied to the two experimental examples, cantilever beam and framed structure of motorcycle. cantilever beam used to test the free response of the system identification information. Framed structure of motorcycle were excitation by hammer and shaker to discuss the identification ability of NARX method under some noise disturbance. By comparing the numerical and the experimental data, for system identificationtechnique involved can work well to estimate the linear modal parameters of nonlinear systems | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T01:51:52Z (GMT). No. of bitstreams: 1 ntu-98-R96525025-1.pdf: 7583102 bytes, checksum: 8497c1367b19ce8d3ccf7fb1968a09b3 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | 中文摘要 I
英文摘要 II 目錄 III 簡稱術語對照表 VII 圖目錄 VIII 表目錄 XIV 符號說明 XVI 第一章 導論 1 1.1 研究目的……………………………………………………… 1 1.2 文獻回顧……………………………………………………… 2 1.3 論文架構……………………………………………………… 4 第二章 非線性振動系統之研究方法及特性 6 2.1 線性振動以及非線性振動…………………………………… 6 2.1.1 線性振動…………………………………………………… 6 2.1.2 非線性振動………………………………………………… 7 2.2 非線性振動系統之週期與振盪頻率之關係………………… 7 2.3 非線性振動系統的定量分析………………………………… 10 2.3.1 古典微擾法………………………………………………… 10 2.3.2 Lindstedt-Poincare法…………………………………… 12 2.4 數值解法……………………………………………………… 16 第三章 NARX模型之系統識別理論 17 3.1 NARMAX與NARX模型………………………………………… 17 3.2 伏爾泰拉級數………………………………………………… 18 3.3 伏爾泰拉級數與NARX模型…………………………………… 20 3.4 估計振動系統之線性模態參數……………………………… 22 第四章 廣義頻率響應函數 25 4.1 頻率響應函數………………………………………………… 25 4.2 廣義頻率響應函數…………………………………………… 26 4.3 計算連續時間之廣義頻率響應函數………………………… 28 4.4 計算離散時間之廣義頻率響應函數………………………… 31 第五章 振動系統之數值模擬例 34 5.1 圖形化資訊分析準則………………………………………… 34 5.2 單自由度系統模擬例………………………………………… 36 5.2.1 單自由度線性具阻尼系統自由振動……………………… 36 5.2.2 單自由度線性具阻尼系統強迫振動……………………… 40 5.2.3 單自由度非線性具阻尼系統自由振動…………………… 44 5.2.4 單自由度非線性具阻尼系統強迫振動…………………… 51 5.3 三自由度系統模擬例………………………………………… 55 5.3.1 三自由度非線性具阻尼系統之自由振動………………… 56 5.3.2 三自由度非線性具阻尼系統之強迫振動………………… 61 第六章 實際結構識別之應用 67 6.1 垂直懸臂鋼…………………………………………………… 67 6.1.1 懸臂鋼樑之理論分析……………………………………… 68 6.1.2 懸臂鋼樑識別結果探討…………………………………… 71 6.2 機車車架之衝擊錘激振實驗………………………………… 75 6.2.1 機車車架之圖形化資訊…………………………………… 78 6.2.2 機車車架之識別結果探討………………………………… 83 6.3 機車車架之強迫振動儀激振實驗…………………………… 90 第七章 結論與展望 103 7.1 結論…………………………………………………………… 103 7.2 展望…………………………………………………………… 104 參考文獻 106 附錄 108 | |
| dc.language.iso | zh-TW | |
| dc.subject | 非線性系統之線性模態參數 | zh_TW |
| dc.subject | 系統識別 | zh_TW |
| dc.subject | 含外變數的非線性自我迴歸數學模型 | zh_TW |
| dc.subject | NARX | en |
| dc.subject | linear modal parameters of nonlinear systems | en |
| dc.subject | System identification | en |
| dc.title | 應用含外變數的非線性自我迴歸模型估算非線性系統之線性模態參數 | zh_TW |
| dc.title | Application of Nonlinear Autoregressive with Exogenous Input Model to Estimate the Linear Modal Parameters of Nonlinear Systems | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 甯攸威,陳國在 | |
| dc.subject.keyword | 系統識別,含外變數的非線性自我迴歸數學模型,非線性系統之線性模態參數, | zh_TW |
| dc.subject.keyword | System identification,NARX,linear modal parameters of nonlinear systems, | en |
| dc.relation.page | 113 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-07-03 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 工程科學及海洋工程學研究所 | zh_TW |
| 顯示於系所單位： | 工程科學及海洋工程學系 | |
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