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研究生:陳德聰
研究生(外文):Chen Te-Tsung
論文名稱:最佳化控制問題於生醫科技之應用
論文名稱(外文):Optimal control for applications of bio-medical technology
指導教授:黃正弘黃正弘引用關係
指導教授(外文):C.H. HUANG
學位類別:碩士
校院名稱:國立成功大學
系所名稱:造船及船舶機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:中文
論文頁數:79
中文關鍵詞:細胞體積控制急速冷凍最佳化控制共軛梯度法
外文關鍵詞:optimal controlultra-rapid freezingcell volume control
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傳統的設計方法在修改設計的過程當中必需仰賴工程師豐富的設計經驗;而「最佳化設計」則是將工程設計問題先建立一個適當的物理模式(model),並依據該模式架構出數學方程,最後再使用適當的方法求解以得到最佳的設計。大部分工程問題的解析上,可依輸入(Input source)、系統模式以及輸出(Output response)三者間之關係分成兩大類。第一類即是傳統上常用的正算問題(Direct problem),探討不同輸入值對於已知之系統模式所造成的輸出變化為何。然而,在實際的工程應用上,仍舊存在著許多無法直接測得的物理量,因此我們需藉由已知的系統模式和輸出,來推算出輸入量;或者藉由已知的輸入及輸出,來推斷出系統模式,第二類問題即稱為反算問題或逆向問題(Inverse problem)。目前,已有諸多實例應用反算問題之技巧於最佳化控制(Optimal control)設計上。
本論文主要探討最佳化控制理論於生醫科技之應用,可分為兩大主題,第一章為最佳化控制問題於細胞脫水(Dehydration)及復水(Rehydration)過程體積控制之研究。第二章為最佳化控制問題於細胞低溫保存超急速冷凍(Ultra-rapid Freezing)技術之應用。
第一章旨在探討於擴散限制(Diffusion-limited)模式下,欲得到給定時變細胞體積時之最佳邊界控制濃度。本章中吾人將利用共軛梯度法(Conjugate Gradient Method,簡稱CGM)進行最佳化控制之分析。並藉由數值模擬分析來驗證最佳化控制理論之精準能力。
第二章旨在探討最佳化控制理論之共軛梯度法應用在細胞低溫保存的領域上,於要求細胞所需的溫度下,成功地預測出最適當的雷射加熱強度。在這個最佳化控制問題中,我們將進行數值實驗來加以驗證此反算法分析之可靠度。
結果顯示共軛度法之最佳控制技巧能成功的應用於以上兩主題,並且得到很好的控制成果。
An optimal control algorithm for cryoperservation of cells utilizing the conjugate gradient method (CGM) of minimization is applied successfully in the present study in determining the strength of optimal laser heating based on the desired temperature distributions of the cell. The validity of this optimal control analysis is examined by using the numerical experiments. Three different heating times are given and the corresponding optimal control heat fluxes are to be determined. Results show that the optimal boundary heat fluxes can be obtained with any arbitrary initial guesses within a very short CPU time on a Pentium III-600 MHz PC. Finally a 2-D enthalpy method is applied to the phase change problem to calculate the cooling rate of the cell.
摘 要………………………………………………………………………… I
誌 謝………………………………………………………………………… III
目 錄………………………………………………………………………… IV
圖表目錄………………………………………………………………………… VI
符號說明………………………………………………………………………… VIII
第一章 最佳化問題於細胞進行脫水(Dehydration)與復水過程(Rehydration)之體積控制………………………………………………………………………………… 1
1-1 研究背景與目的……………………………………………………… 1
1-2 前言…………………………………………………………………… 2
1-3 直接解問題…………………………………………………………… 4
1-4 最佳化控制問題……………………………………………………… 7
1-5 共軛梯度法之極小化過程…………………………………………… 8
1-6 靈敏性問題與前進步距……………………………………………… 9
1-7 伴隨問題與梯度方程式……………………………………………… 11
1-8 數值計算流程………………………………………………………… 14
1-9 結果與討論…………………………………………………………… 15
1-10 結論…………………………………………………………………… 22
1-11 參考文獻……………………………………………………………… 32
第二章 最佳化控制問題於細胞低溫保存急速冷凍 (Ultra-rapid Freezing) 法之應用………………………………………………………………………………… 34
2-1 研究背景與目的………………………………………………34
2-2 前言……………………………………………………………35
2-3 直接解問題……………………………………………………37
2-4 最佳化控制問題………………………………………………38
2-5 共軛梯度法之極小化過程……………………………………39
2-6 靈敏性問題與前進步距………………………………………40
2-7 伴隨問題與梯度方程式………………………………………42
2-8 數值計算流程…………………………………………………45
2-9 結果與討論……………………………………………………46
2-10 結論……………………………………………………………52
2-11 參考文獻………………………………………………………65
第三章 結語…………………………………………………………… 67
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