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系統識別號 U0026-1707201416242400
論文名稱(中文) 利用希伯特-黃轉換分析非線性動力學
論文名稱(英文) Analyzing Nonlinear Dynamics by the Hilbert-Huang Transform
校院名稱 成功大學
系所名稱(中) 光電科學與工程學系
系所名稱(英) Department of Photonics
學年度 102
學期 2
出版年 103
研究生(中文) 簡子婷
研究生(英文) Tzu-Ting Chien
學號 l76014255
學位類別 碩士
語文別 中文
論文頁數 45頁
口試委員 指導教授-魏明達
口試委員-謝文峰
口試委員-吳小華
口試委員-黃勝廣
中文關鍵字 非線性動力學  希伯特-黃轉換 
英文關鍵字 Nonlinear Dynamics  Hilbert-Huang Transform 
學科別分類
中文摘要 本論文以希伯特-黃轉換(Hilbert-Huang transform, HHT)分析非線性動力學,主要研究羅侖茲訊號與泵源調製雷射模型兩個系統。由HHT分析羅侖茲(Lorenz)訊號,可發現本質模態函數(Intrinsic Mode Function)平均頻率依序可得到基頻、二分之一基頻、四分之一基頻的結果。在泵源雷射調製系統中的結果為基頻、五分之一基頻、十分之一基頻等,顯示不同的動態系統有不同的基頻變化,但都由簡單分數的基頻組成。除此之外,本質模態函數的平均瞬時頻率對調製深度的變化趨勢與Lyapunov分析結果相互對應,故HHT可作為判斷混沌訊號閥值的參考工具。
英文摘要 In this thesis, we study the nonlinear dynamics by the Hilbert-Huang Transform (HHT).The main researches including the Lorenz attractor and the laser system with pump modulation. Analyzing the Lorenz system by HHT, the result reveals a regular ratio distribution for the fundamental frequency of 1/2, 1/4, and so on. Using HHT to investigate the pump modulated laser output; the ratio relationship of frequency is 1/5, 1/10, 1/20, etc. It shows that the difference of ratio will appear in separate system. Furthermore, HHT can become a tool to distinguish the threshold of chaotic signal due to the trend of frequency in each intrinsic mode function is similar with the Lyapunov exponent analysis.
論文目次 摘要I
AbstractII
誌謝VI
目錄VII
圖目錄IX
表目錄XI
第一章 序論1
1.1背景1
1.2研究動機與目的4
1.3章節概述4
第二章 希伯特-黃轉換5
2.1 經驗模態分解5
2.2 希伯特轉換7
第三章 羅倫茲動力學模型分析9
3.1 羅倫茲模型9
3.2 HHT 分析11
第四章 雷射非線性動力學研究14
4.1 泵源調製雷射動力學14
4.2 HHT 分析17
4.2.1調製頻率 f1 = 739.06 kHz 分析結果17
4.2.2調製頻率 f2 = 789.56 kHz 分析結果27
4.2.3調製頻率 f3 = 775.11 kHz 分析結果35
第五章 結論與未來展望43
5.1 結論43
5.2 未來展望43
參考文獻44
參考文獻 1.N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N. C. Yen, C. C. Tung and H. H. Liu, “The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-stationary Time Series Analysis,” Proc. R. Soc. Lond. A, 454, 903–995, (1998).
2.N. E. Huang, S. S. P. Shen, Hilbert-Huang Transform and Its Applications, World Science, Singapore, (2005).
3.Z. Wu, N. E. Huang, J. M. Wallace, B. V. Smoliak, X. Chen, “On the Time-varying Trend in Global-mean Surface Temperature,” Climate Dynamics, 37, 759–773, (2011).
4.Z. X. Liu, H. J. Wang, and S. L. Peng, “Texture Classification Through Directional Empirical Mode Decomposition,” Int. Conf. Pattern Recognition, 4, 803–806, (2004).
5.G. Rilling, P. Flandrin, and P. Goncalves, “Detrending and Denosing with Empirical Mode Decompositions,” 12th EUSIPCO, 1581–1584, Wien, Austria, (2004).
6.Y. H. Shiau, and M. C. Wu, “Detecting Characteristics of Information Masked by a Laser-triggered Microwave System via Hilbert–Huang Transform,” Opt. Commu., 283, 1909–1916, (2010).
7.T. Yalcinkaya, and Y. C. Lai, “Phase Characterization of Chaos,” Phys. rev. lett., 79, 3885–3888, (1997).
8.Y. C. Lai, and N. Ye, “Recent Developments in Chaotic Time Series Analysis,” Int. J. Bifurcation Chaos, 13, 1383–1422, (2003).
9.E. N. Lorenz, J. Atmos. Sci., “Deterministic Nonperiodic Flow,” J. Atmos. Sci., 20, 130–141, (1963).
10.S. Kizhner, K. Blank, T. Flatley, N. E. Huang, D. Petrick, and P. Hestnes, “On Certain Theoretical Developments Underlying the Hilbert-Huang Transform,” IEEEAC, USA, (2006).
11.A. G. Fox and T. Li, “Resonant Modes in a Maser Interferometer,” Bell Syst. Tech. J., 40, 453–488, (1961).
12.Y. J. Cheng, P. L. Mussche, and A. E. Siegman, “Cavity Decay Rate and Relaxation Oscillation Frequency in Unconventional Laser Cavities,” IEEE J. Quantum Electro., 31, 391–398, (1995)
13.M. D. Wei, C. H. Chen, H. H. Wu, D. Y. Huang, and C. H. Chen, “Chaos Suppression in the Transverse Mode Degeneracy Regime of a Pump-modulated Nd:YVO4 Laser,” J. Opt. A: Pure Appl. Opt., 11, 045504, (2009).
14.C.H. Chen, P. T. Tai, M. D. Wei, and W. F. Hsieh, “Multibeam-waist Modes in an End-pumped Nd:YVO4 Laser,” J. Opt. Soc. Am. B, 20, 1220–1226, (2003).
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