臺灣博碩士論文加值系統

為了更進一步了解近年來發展出來的簡化熱板法，其量測穩態熱傳導係數之精確度，本研究首先建立一可模擬量測的數值模型來加以分析。依此模型所求出的溫度在待測物中的分佈，可得模擬量測到的熱傳導係數與在模型中指定的熱傳導係數之比值。此比值可用於實際量測時因以多維系統模擬一維量測所引起之系統誤差的修正，以得到更精確之熱傳導係數。此外，對於量測的隨機誤差也可以利用這個數值模型，藉著變動可能的量測誤差，例如溫度量測的誤差、加熱器控制的誤差、以及溫度感測器偏移放置，來求出量測熱傳導係數的不確定性，藉此提供實際量測可信範圍之參考。雖然從數值模型的分析可以找到量測的系統誤差，但這個誤差卻是所要量測的熱傳導係數之函數。因此，本研究利用類神經網路來解決這個困難，就是以數值模型模擬出眾多在不同條件下的量測結果，用來建構這個類神經網路。這個類神經網路在量測時可以從量測參數與量測數據直接預測出正確的熱傳導係數，而不須修正其系統誤差。最後，應用上述的精確度分析結果以及針對以簡化熱板法所製成的儀器雛型的缺點加以修正，重新設計與製造一新式的熱傳導係數量測儀器，期能以精準的溫度控制及所建構出來的類神經網路，使此簡化熱板量測法更具實用價值。

In order to better understand the accuracy of a newly developed simplified hot plate method in measuring steady-state thermal conductivity, a numerical model for simulating the measurement is devised and verified by experimental results to perform the accuracy analysis. The ratios of the thermal conductivity derived from the temperature distribution solutions to that given in the numerical model are obtained and shown. They can be used to correct the systematic error of measurement introduced by the one-dimensional approximation in real applications. Furthermore, the measurement uncertainty due to power control, misalignment of the temperature sensors, and the limitation of sensing devices is also investigated using the numerical model. The results are suitable for the estimation of confidence range in practical measurements. Although the systematic error derived from this study can be use to calibrate the measured thermal conductivity, it is a function of the variable to be measured. Therefore to solve the problem, artificial neural networks (ANNs), which are trained using a variey of simulated measurement given by the numerical model, are used. A trained ANN can be used to predict directly the correct thermal conductivity without calibration using the measurement data. Finally, applying the results of accuracy analysis together with the correction of a prototype using the simplified hot plate method, a new device is designed and built with an accurate temperature control system and a well constructed ANN to promote the practical value of the measuring method.

摘要 ……………………………………………………………………. .i
英文摘要 ………………………………………………………………. ii
圖形目錄 …………………………………………………………….....vi
表目錄 ………………………………………………………………. .viii
符號說明………………………………………………………………. .ix
第一章 緒論 ……………………………………………………….….1
1.1 研究背景與動機 ………………………………………….….1
1.1.1 暫態量測法 ……………………………………….…..1
1.1.2 穩態量測法 ……………………………………….… 2
1.1.3 本研究使用之量測法 …………………………….….4
1.2 研究目標 ………………………………………………….….5
1.3 本論文概要 ……………………………………………….….7
第二章 簡化熱板法之熱傳導係數量測儀器 ..……………………... 8
2.1 簡化熱板法 …………………………………………...…8
2.2 計算熱傳導係數之方法 …………………………………...10
2.3 低溫側溫度分佈近似函數 ………………………………...10
2.3.1 以直角座標描述溫度分佈 …………………………..11
2.3.2 以極座標描述溫度分佈 ……...……………………...11
2.4 簡化熱板法量測熱傳導係數存在之問題 ……....………..13
第三章 數值模型 .…………………………………………………...15
3.1 分析模式 .…………………………………………………..15
3.1.1 統御方程式 .………………………………………...15
3.1.2 模型之離散化 ………………………………………16
3.1.3 初始條件與邊界條件 ………………………………18
3.2 熱傳遞率 …………………………………………………….20
3.3 尺寸收斂分析 ...……………………...…………………….21
3.4 系統誤差分析 …….……………………………………….21
3.5 隨機誤差分析 ……………………………...........................22
3.5.1 溫度量測與加熱器功率控制之不確定性 ……..…22
3.5.2 鐵氟龍板偏移造成 之不確定性 ………………23
3.5.3 熱傳導係數之不確定性 ……………………………24
第四章 模型實驗驗證與誤差分析結果 ……………………………25
4.1 模型實驗驗證 ……………………………………………...25
4.1.1 量測實驗 ……………………………………………25
4.1.2 數值模型實驗 ………………………………………26
4.2 誤差分析結果 ……………………………………………...29
4.2.1 系統誤差 ……………………………………………29
4.2.2 等向性與非等向性材料k值比之比較 ……………33
4.2.3 隨機誤差分析結果 .………………………………..34
第五章 類神經網路系統模擬 ………………………………………37
5.1 ANN應用實例 ……………………………..……………...37
5.2 ANN之建構 …………………………………...…………...38
5.3 倒傳遞演算法 ……………………………………………...40
5.4 ANN訓練結果 ………………………………………….…42
5.5 線性回歸預測結果 ………………………………………...46
5.6 簡化實驗次數之線性預測法 ……………………………...47
第六章 新型熱傳導係數量測儀器 …………………………………51
6.1 儀器之量測原理 …………………………………………...52
6.2 PID控制方法 ……………………………………………....53
6.3 量測實驗步驟 ……………………………………………...54
6.4 結果與討論 ………………………………………………...55
第七章 結論與未來展望 ……………………………………………58
參考文獻 ………………………………………………………………60
附錄A 直角座標與極座標描述溫度分佈之量測k值的不確定性計算
方法 …………………………………………………………64
附錄B 用控制容積法運算統御方程式係數 ………………………70
附錄C 計算熱傳導係數誤差之C語言程式 ………………………95
附錄D 類神經網路模擬之C語言程式 …………………………..115
附錄E 驗證ANN模擬參數所得的熱傳導係數誤差值之C語言程式
………………………………………………………………126

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