臺灣博碩士論文加值系統

本論文透過急遽遞減法(Steppest Descent Method)與套裝軟體CFD-RC的結合，配合模擬紅外線溫度感測器所量測的模型表面溫度值為參考，來對複合材料界面之幾何形狀進行預測。
　　本論文有兩個主題。在第二章中，吾人以套裝軟體CFD-RC為基礎,利用急遽遞減法來預測二區複合材料之未知界面幾何形狀 (即一組未知界面形狀，��(x,y))。在第三章中，吾人亦以套裝軟體CFD-RC為基礎,利用急遽遞減法來預測三區複合材料之未知界面幾何形狀(即二組未知界面形狀��1(x,y)及��2(x,y) )。
本研究與之前相關研究不同的是，在進行二區和三區複合材料未知界面形狀之預測時，為了得到梯度方程式(gradient equation)必須利用一重複使用條件(over-utilized condition)方可達成目的。此外，吾人亦假設兩區或三區複合材料之界面為良好接觸(perfect thermal contact)，故求解時需利用兩材料交界面上溫度相同且達到熱平衡之原理來求解。
最後在數值實驗中測試了考慮量測誤差與量測點數改變的情況，此外並於第二章中探討量測位置對於預測結果之影響。數值實驗結果皆證明了急遽遞減法於逆向幾何形狀預測問題中能夠正確預測複合材料內部界面形狀。

A three-dimensional shape identification problem (or inverse geometry problem) in estimating the interfacial geometry for a multiple region domain is solved by using the steepest descent method (SDM) and a general purpose commercial code CFD-RC based on the simulated measured temperature distributions on the surfaces obtained by the imaginary infrared scanners.
The present thesis has two themes, in chapter two the goal is to estimate only one irregular interfacial surface ��(x,y) in a two-layer structure, while in chapter three the objective is to estimate simultaneously two irregular interfacial surfaces ��1(x,y) and ��2(x,y) in a three-layer-structure.
In this work, in order to determine the gradient equation, one of the integral terms obtained from the integration by parts should be over-utilized. This differs from our previous relevant study. Also it is assumed that perfect thermal contact condition is applied to the interfacial surfaces between different materials.
The numerical experiments are performed to test the validity and accuracy of the present shape identification algorithm by using different types of interfaces, initial guesses and measurement errors. Results show that excellent estimations on the unknown geometry of the interfaces can be obtained by the present steepest descent method (SDM).

目 錄

摘 要…………...........................................................................................I

誌 謝........................................................................................................III

目 錄…..………......................................................................................IV

圖 目 錄………......................................................................................VI

符 號 說 明….....................................................................................VIII

第一章 緒 論............................................................................................1

1-1 研究背景與目的…………………………………………………..…1

1-2 文獻回顧…………………………………………………………..…2

第 二 章 反算法於三維兩區複合材料未知界面幾何形狀之預測…..5

2-1 直接解問題(Direct Problem)…………………………………...……5

2-2 反算問題(Inverse Problem) ……………………………………...…..6

2-3急遽遞減法之極小化過程(Conjugate Gradient Method For Minimization)………………………………………………………….....8

2-3-1靈敏性問題與前進步距(Sensitivity Problem and Search Step Size) ..........................................................................................................9

2-3-2 伴隨問題與梯度方程式(Adjoint Problem and Gradient Equation)..................................................................................................11

2-3-3 收斂條件(Stopping Criterion)……………………………..……..14

2-3-4 數值計算流程(Computational Procedure)………………….……15

2-4 結果與討論(Results and Discussion)…………………………..…..16

第 三 章 反算法於三維三區複合材料未知界面幾何形狀之預測…34

3-1 直接解問題(Direct Problem)……………………………………….35

3-2 反算問題(Inverse Problem)……………………………………...…37

3-3 急遽遞減法之極小化過程(Conjugate Gradient Method For Minimization)……………………………………………………...……38

3-3-1 靈敏性問題與前進步距(Sensitivity Problem and Search Step Size)……………………………………………………………………..39

3-3-2 伴隨問題與梯度方程式(Adjoint Problem and Gradient Equation)…………………………………………………………..……44

3-3-3 收斂條件(Stopping Criterion)…………………………………....49

3-3-4 數值計算流程(Computational Procedure).....................................50

3-4 結果與討論(Results and Discussion)………………………..……..51

第 四 章 結 語……………………………………………..…………70

參 考 文 獻……………………………………………………………71














圖目錄

圖 2-1. 二區複合材料之(a)幾何形狀座標示意圖 (b)網格分布圖…………………………………………………………….....23

圖2-2. 範例一中之(a)正解 與(b)當�� = 0.0, = 0.015 m , 量測面為Sbottom時之預測形狀��(x,y)……………….……….…........24

圖2-3. 範例一中當量測面為Sbottom,且�� = 0.0,與 = 0.015時之 (a) 量測面溫度 (b)預測面溫度................................................25

圖2-4. 範例一當中�� = 0.0之 (a)�n = 0.085 m ,且量測面為Sbottom與(b) = 0.015 m ,且量測面為Stop時之預測形狀.......26

圖2-5. 範例一中當量測面為Sbottom且(a)�n�� = 0.17 (b) �� = 0.34 時之預測形狀圖……………………………………………………... 27

圖2-6. 範例二中之(a)正解 與(b)當�� = 0.0, = 0.015 m , 量測面為Sbottom時之預測形狀 ��(x,y)….…………………………....28

圖2-7. 範例二中當量測Sbottom,且�� = 0.0,與 = 0.015時之 (a) 量測面溫度 (b) 預測面溫度.........................................................29

圖2-8. 範例二中當量測面為Sbottom且(a)�n�� = 0.17 (b) �� = 0.34 時之預測形狀........................................................................................30

圖2-9. 範例三中之(a)正解 與(b)當�� = 0.0, = 0.015 m , 量測面為Sbottom時之預測形狀 ��(x,y)………….....………………....31

圖2-10. 範例三中當量測Sbottom,且�� = 0.0,與 = 0.015時之 (a) 量測 面溫度 (b) 預測面溫度......................................................32

圖2-11. 範例三中當量測面為Sbottom且(a)�n�� = 0.17 (b) �� = 0.34 時之預測形狀……………………………………………………..…..33

圖3-1. 三區複合材料之(a)幾何形狀座標示意圖 與(b)網格分布圖...............................................................................................57

圖3-2. 範例一中接合面之(a)正解與(b) (��1,�n��3) = (0,0)時之預測形狀................................................................................................58

圖3-3. 範例一中當(��1,�n��3) = (0,0)時，Sbottom之(a) 量測溫度與(b) 預測溫度………………………………………………....……59

圖3-4.範例一中之當(��1,�n��3) = (0,0)時，Stop之(a) 量測溫度與(b) 預測溫度........................................................................................60

圖3-5. 範例一中當(a) (��1,�n��3) = (0.2,0.2)時與(b) (��1,�n��3) = (0.4,0.4)時之接合面預測形狀....................................................................61

圖3-6. 範例二中接合面之(a)正解與(b) (��1,�n��3) = (0,0)時之預測形狀……………………................................................................62

圖3-7. 範例二中之當(��1,�n��3) = (0,0)時，Sbottom之(a)量測溫度與 (b)預測溫度……………………………………….……………...63

圖3-8. 範例二中之當(��1,�n��3) = (0,0)時，Stop之(a)量測溫度與 (b)預測溫度……………………………………………….…….......64

圖3-9. 範例二中當(a) (��1,�n��3) = (0.2,0.2)時與(b) (��1,�n��3) = (0.4,0.4)時之接合面預測形狀...............................................................65

圖3-10. 範例三中接合面之(a)正解與(b) (��1,�n��3) = (0,0)時之預測形狀................................................................................................66

圖3-11. 範例三中之當(��1,�n��3) = (0,0)時，Sbottom之(a) 量測溫度與(b) 預測溫度………………………………………………….…...67

圖3-12. 範例三中之當(��1,�n��3) = (0,0)時，Stop之(a) 量測溫度與(b) 預測溫度………………………….…………………………...68

圖3-13. 範例三中當(a) (��1,�n��3) = (0.2,0.2)時　與(b) (��1,�n��3) = (0.4,0.4)時之預測形狀………………………………………...69

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