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系統識別號 U0026-1401202023290200
論文名稱(中文) 多目標打靶法在動態系統之應用
論文名稱(英文) Applications of Multiple Shooting Optimization Method to Dynamic Systems
校院名稱 成功大學
系所名稱(中) 工程科學系
系所名稱(英) Department of Engineering Science
學年度 108
學期 1
出版年 109
研究生(中文) 徐逸耘
研究生(英文) Yi-Yun Hsu
學號 N96044036
學位類別 碩士
語文別 英文
論文頁數 67頁
口試委員 指導教授-莊哲男
口試委員-廖德祿
口試委員-姚志民
口試委員-吳謂勝
中文關鍵字 多目標打靶法  最佳化  參數估計  動態系統 
英文關鍵字 multiple shooting method  optimization  parameter estimation  dynamic system 
學科別分類
中文摘要 多目標打靶法是用來預估動態系統中未知參數的最佳化方法之一,而含有成本函數、動態方程式以及其他等式與不等式限制條件的動態系統可以被改寫為一約束二次規劃問題,多目標打靶法即可將動態模型切割成數個子區間並建立分塊矩陣,此方法可增加等式限制條件和未知參數,利用壓縮式演算法將分塊矩陣架構簡化成單目標打靶法可解的數學模型。有別於傳統單目標打靶法,多目標打靶法的優點在於增加參數估計的精度並支援平行計算以提升運算效率。
本篇論文利用兩個動態模型系統並加入隨機亂數充當實驗測量誤差來驗證多目標打靶法在參數估計的精度及演算效率,在此,我們用多目標打靶法來估量質量彈簧系統中動態方程式的未知係數,以及基因定序網絡中動態方程式的未知指數和係數,模擬結果顯示多目標打靶法在針對具有實驗誤差的動態系統中具有優秀的最佳化演算能力。
英文摘要 Multiple shooting method is a strategy for calculating unknown parameters in a dynamic system. With a cost function, dynamic equations and extra equality and inequality constraints, a dynamic model can be formulated as a constrained quadratic program. The approach of multiple shooting is to divide the dynamic state time histories into several sub-intervals and construct a block matrix structure which increases equality constraints and unknown parameters. A condensing algorithm is available to rebuild the model into a mathematical form which can be solved by generalized Gauss-Newton method. The benefits of multiple shooting method include gaining high accuracy of optimal parameters than the original single shooting method, and supporting a parallel computation with higher computational efficiency.
In this thesis, we present two dynamic models to demonstrate the accuracy of optimal parameters and the efficiency of computation for the multiple shooting method. The multiple shooting is used to optimize two unknown coefficients in a linear continuous-time or discrete-time model for mass-spring system, and sixty unknown exponents and coefficients in a nonlinear model for a gene regulatory network, respectively. The results show that the multiple shooting is capable of producing good optimal parameters for dynamic systems with measurement errors.
論文目次 中文摘要 i
Abstract ii
Acknowledgements iii
Contents iv
List of Tables v
List of Figures vii
Nomenclature ix
1.Introduction 1
2.Mathematical Theories and Backgrounds 4
2.1 Parameter Estimation 4
2.2 Least Square Approach 6
2.3 Single Shooting Method 7
2.4 Multiple Shooting Method 17
3. Applications of Multiple Shooting Method 23
3.1 Mass-spring System 23
3.2 Gene Regulatory Network 33
4. Conclusions and Prospects 63
References 65
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