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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 劉進賢(Chein-Shan Liu) | |
| dc.contributor.author | Jheng-Jhang Lin | en |
| dc.contributor.author | 林政璋 | zh_TW |
| dc.date.accessioned | 2021-06-08T01:47:47Z | - |
| dc.date.copyright | 2016-08-24 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2016-08-04 | |
| dc.identifier.citation | [1] CS Liu, Atluri SN. A Fictitious Time Integration Method for the Numerical Solution of the Fredholm Integral Equation and for Numerical Differentiation of Noisy Data, and Its Relation to the Filter Theory. CMES:Comput Model Eng Sci 2009;41:243-261.
[2] CS Liu, Atluri SN. A GL(n,R) Differential Algebraic Equation Method for Numerical Differentiation of Noisy Signal. CMES:Comput Model Eng Sci 2013;92:213-239. [3] CS Liu. Solving an Inverse Sturm-Liouville Problem by a Lie-Group Method. Boundary Value Probl.2008;2008:Article ID 749865,18 pages. [4] CS Liu. Identifying time-dependent damping and stiffness functions by a simple and yet accurate method.J Sound Vib 2008;318:148-65. [5] CS Liu. A Lie-Group Shooting Method for Simultaneously Estimating the Time-Dependent Damping and Stiffness Coefficients. CMES: Comput Model Eng Sci 2008;27:137-49. [6] CS Liu,Chang JR,Chang KH,Chen YW. Simultaneously Estimating the Time-Dependent Damping and Stiffness Coefficients with the Aid of Vibrational Data. CMC:Comput Master Cont 2008;7:97-107. [7] CS Liu. The Lie-Group Shooting Method for Nonlinear Two-Point Boundary Value Problems Exhibiting Multiple Solutions. CMES: Comput Model Eng Sci 2006;13:149-63. [8] Dabroom AM, Khalil HK. discrete-time implementation of high-gain observers for numerical differentiation.Int J Contr 1997;72:1523-37. [9] Ibrir S. Linear time-derivative trackers. Automatica 2004; 40:397-405. [10] Levant A. Robust exact differentiation via sliding mode technique. Automatica 1998; 34:379-84. [11] Levant A. Higher-order sliding modes, differentiation and output-feedback control. Int J Contr 2003;76:924-41. [12] Levant A,Livne M. Exact Differentiation of Signals with Unbounded Higher Derivatives. IEEE Trans Auto Contr 2012;57:1076-80. [13] Wang X, Chen Z, Yang G. Finite-Time-Convergent Differentiator Based on Singular Perturbation Technique. IEEE Trans Auto Contr 2007;52:1731-37. [14] Wang X, Lin H. Wang X, Design and frequency analysis of continuous finite-time-convergent differentiator. Aerospa Tech 2012;18:69-78. [15] Wang X, Shirinzadeh B. Rapid-convergent nonlinear differentiator. Mech Sys Sign Proces 2012;28:414-31. [16] Wang X, Lin H. Design and analysis of a continuous hybrid differentiator. IET Contr Theo Appl 2011;5:1321-34. [17] Han JQ, Wang W. Nonlinear tracking-differentiator. J. Syst. Sci. Math. Sci, 1994;14:177-83(in Chinese) [18] Guo BZ, Han JQ, Xi FB. Linear tracking-differentiator and application to online estimation of the frequency of a sinusoidal signal with random noise perturbation. Int J Sys Sci 2012;33:351-8. [19] Tang Y, Wu Y, Wu M, Hu X, Shen L. Nonlinear Tracking-Differentiator for Velocity Determination Using Carrier Phase Measurements. IEEE J Selec Top Signal Proce 2009;3:716-25. [20] Xue W, Huang Y, Yang X. What Kinds of System Can Be Used as Tracking-Differentiator. Proc. Chinese Control Conference, 2010,pp.6113-6120. [21] Guo BZ, Zhao ZL. On convergence of tracking differentiator and application to frequency estimation of sinusoidal signals. Int J Contr 2011;84:693-701. [22] Guo BZ, Zhao ZL. On Finite-Time Stable Tracking Differentiator without Lipschitz Continuity of Lyapunov Function.Proc. Chinese Control Conference, 2010,pp.354-358. [23] Xinhua Wang n , Bijan Shirinzadeh. High-order nonlinear differentiator and application to aircraft control [24] L. Dong , A. Alotaibi , S.A. Mohiuddine , S. N. Atluri.Computational Methods in Engineering: A Variety of Primal & Mixed Methods, with Global & Local Interpolations, for Well-Posed or Ill-Posed BCs [25] L. Wei, J. Griffin, THE PREDICTION OF SEAT TRANSMISSIBILITY FROM MEASURES OF SEAT IMPEDANCE [26] Liu CS,Chang CW.A real-time Lie-group differential algebraic equations method to solve the inverse nonlinear vibration problems. Inv Pro Sci Eng, [27] 陳柏穎：利用李群微分代數方程法即時重建作用於非線性結構之外力，國立台灣大學碩士論文。(2014) [28] Wu, A.L., Loh, C.H., Yang, J.N.: Input force identification: application to soil-pile interaction. Journal of Structural Control and Health Monitoring 16, 223-240 (2009) [29] Starek L., Inman, D.J.: A symmetric inverse vibration problem with overdamped modes. Journal of Sound and Vibration 181, 893-903 (1995) [30] Mukherjee, S., Roy, B., Dutta, S.: Solution of the Duffing-van der Pol oscillator equation by a differential transform method. Physica Scripta 83, 015006 (2011) [31] Masri, S. F., Chassiakos, A. G., Caughey, T. K.: Identification of nonlinear dynamic systems using neural networks. Journa of Applied Mechanics 60, 123-133 (1993) [32] Liu, C.-S.: An iterative method for solving nonlinear inverse vibration problems. Nonlinear Dynamics 74, 685-699 (2014) [33] Liu, C.-S.: A state feedback controller used to solve an ill-posed linear system by a iterative algorithm. Communication of Numerical Analysis, vol. 2013, Article ID cna-00181, 22 pages. [34] Liu, C.-S.: Identifying time-dependent damping and stiffness functions by a simple and yet accurate method. Journal of Sound and Vibration 318, 148-165 (2008) [35] Huang, C.H.: A generalized inverse force vibration problem for simultaneously estimating the time-dependent external forces. Applied Mathematical Modelling 29, 1022-1039 (2005) [36] Fern’andez, F. M.: Comment on 'solution of the Duffing-van der Pol oscillator equation by a differential transform method'. Physica Scripta 84, 037002 (2011) [37] Chen, Y. W.: Application of the characteristic time expansion method for estimating nonlinear restoring forces. Journal of Applied Mathematics 2013, ID 841690, 13 pages (2013) [38] Cheung YK, Jin WG, Zienkiewicz OC. Direct solution procedure for solution of harmonic problems using complete non-singular, Trefftz functions. Commun Appl Numer Methods 1989;5:159–69. [39] Liu, C.-S. (2008a): Solving an inverse Sturm-Liouville problem by a Lie-group method. Boundary Value Problems, vol. 2008, Article ID 749865. [40] Liu, C.-S. (2008b): Identifying time-dependent damping and stiffness functions by a simple and yet accurate method. J. Sound Vib., vol. 318, pp. 148-165. [41] Liu, C.-S. (2008c): A Lie-group shooting method for simultaneously estimating the time-dependent damping and stiffness coefficients. CMES: Computer Modeling in Engineering & Sciences, vol. 27, pp. 137-149. [42] Liu, C.-S.; Atluri, S. N. (2008): A novel time integration method for solving a large system of non-linear algebraic equations. CMES: Computer Modeling in Engineering & Sciences, vol. 31, pp. 71-83. [43] Liu, C.-S. (2008d): A time-marching algorithm for solving non-linear obstacle problems with the aid of an NCP-function. CMC: Computers, Materials & Continua, in press. [44] Liu, C.-S. (2008e): A fictitious time integration method for two-dimensional quasilinear elliptic boundary value problems. CMES: Computer Modeling in Engineering & Sciences, in press. [45] 蔡孟芹：化為偏微分方程的李群微分代數方法識別非線性結構外力，國立台灣大學碩士論文。(2015) | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/19180 | - |
| dc.description.abstract | 二階微分之噪音訊號被寫為二階常微分方程式，當作一種特殊實例未知外力在二階線性系統之回復，轉換成線性拋物線型的偏微分方程式。之後運用格林第二恆等式推導出以伴隨崔維茲頻譜函數表示之邊界積分方程。我們發現一種弱型式的方法可回復外力，之後，從給定之噪音中發展弱型式二階運算子(WFSOD)計算訊號的二階導數，只有訊號本身是具體指定，不需要此噪音訊號之一階導數，最後，在大時間區間和大噪音之下使用弱型式方法回復非線性系統之外力。 | zh_TW |
| dc.description.abstract | The second-order differential of a noisy signal is written as a second-order ordinary differential equation, being a special case of the recovery of unknown external force in a second-order linear system, which is transformed into a linear parabolic type partial differential equation. Then the Green second identity is employed to derive a boundary integral equation in terms of the adjoint Trefftz spectral functions. We find a weak-form method to recover the external force and then a weak-form second-order differentiator(WFSOD) is developed to compute the second-order differential from a given noisy signal, of which only the signal itself is specified, without needing of its first-order differential. Finally, the weak-form method is used to recover the external forces of nonlinear systems within a large time interval and under a large noise. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T01:47:47Z (GMT). No. of bitstreams: 1 ntu-105-R03521247-1.pdf: 5396491 bytes, checksum: 37a2c413c19e2e00877324e1eef4a30e (MD5) Previous issue date: 2016 | en |
| dc.description.tableofcontents | 口試委員會審定書 i
中文摘要 iii ABSTRACT iv 目錄 v 圖目錄 vii 第一章 緒論 1 1.1 前言 1 1.2 論文架構 3 第二章 理論基礎 4 2.1 邊界值問題(Boundary Value Problem) 4 2.1.1 函數內積及正交性質(orthogonality) 5 2.1.2 格蘭-史密特(Gram-Schmidt)正交化法過程問題 6 2.1.3 史特姆-李奧維爾邊界值問題(Sturm-Liouville problem) 7 2.2 傅立葉級數(Fourier series) 8 2.3 格林第二恆等式(The Green's second identity) 8 2.4 虛擬時間積分法(Fictitious Time Integration Method) 9 2.5 崔維茲法(Trefftz method) 11 2.6 共軛梯度法(conjugate gradient method) 11 2.7 尤拉法(Euler's method) 19 2.8 龍格-庫塔法(Runge-Kutta methods) 20 2.9 杜芬微分方程式(Duffing Differential Equation) 21 第三章 弱型式之數值微分運算子推導 23 3.1 ODE轉換成PDE 23 3.2 邊界積分法在虛擬時間領域 24 3.3 頻譜函數υ(t,τ) 26 3.4 弱型式方法 30 3.5 數值演算法 32 3.6 噪音信號之數值微分子 33 第四章 數值算例 34 4.1 線性系統(Linear) 34 4.1.1 算例一WFFOD弱型式一階微分運算子 34 4.1.2 算例二WFSOD弱型式二階微分運算子 41 4.1.3 算例三 線性動力系統方程 48 4.2 非線性系統之外力回復 55 4.2.2 算例四 杜芬振盪器 55 4.2.3 算例五 杜芬-Van der Pol 振盪器 62 4.2.4 算例六 座椅 69 第五章 結語與未來展望 76 5.1 結語 76 5.2 未來展望 77 REFERENCE 78 | |
| dc.language.iso | zh-TW | |
| dc.title | 利用弱型式之數值微分運算子重建非線性系統之外力 | zh_TW |
| dc.title | To recover external forces of nonlinear systems using weak-form numerical differentiators | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 郭仲倫(Chung-Lun Kuo),陳永為(Yung-Wei Chen) | |
| dc.subject.keyword | 弱型式二階微分運算子,非線性反算振動問題,伴隨崔維茲測試函數,格林第二恆等式,弱型式方法,頻譜函數, | zh_TW |
| dc.subject.keyword | weak-form second-order differentiator,Nonlinear inverse vibration problem,Adjoint Trefftz test functions,Green’s second identity,weak-form method,spectral functions, | en |
| dc.relation.page | 82 | |
| dc.identifier.doi | 10.6342/NTU201601896 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2016-08-04 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 土木工程學研究所 | zh_TW |
| 顯示於系所單位： | 土木工程學系 | |
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