臺灣博碩士論文加值系統

本文係以數值方法來預測中空圓柱之熱邊界。文中使用二階有限差分法（second-order finite difference method）將熱傳導方程式離散化，搭配Savitzky-Golay digital filter 數位濾波器將因量測誤差而受到干擾的溫度平滑化，使誤差降低，接著以逆算法求出邊界條件，最後再以多項式迴歸求出邊界之經驗公式。

文中針對移動視窗的寬度N、量測間距 及模擬誤差 三種不同的狀況進行邊界的逆運算，進而討論所產生的影響。其結果發現量測間距大小不會絕對影響誤差，而透過Savitzky-Golay digital filter 數位濾波器平滑後的溫度，皆明顯的使誤差變小，且平滑的移動視窗越寬，誤差越小，使得逆運算所求出的邊界值更加接近真實解，故使用數位濾波器將溫度平滑化再搭配多項式迴歸求出邊界條件是一個簡單有效的方法。

The purpose of this study aims to predict the thermal boundary of hollow cylinders by using numerical method. First, use second-order finite difference method to make heat equation discretization, and collocate with Savitzky-Golay digital filter to smooth the measurement errors, caused by the interfered temperature, to reduce errors. Then, calculate the boundary condition with backflush. In the end, calculate the empirical formula for the boundary with polynomial regression.

In this study, the research focuses on doing inverse method in the conditions of breadth N of moving window, distance measurement , and simulation error , and discuss the effects. The results shows that measurement space does not completely influence the errors; however, the temperature smoothened by Savitzky- Golay digital filter obviously reduces the errors. The wider the window is, the lower the error is. It is closer to physical solution for the value of the boundary condition conducted by inverse method. Therefore, it is simple and effective way to use Savitzky- Golay digital filter, to smooth the temperature, and collocate with polynomial regression to find out the boundary condition.

摘要.......................................................i
Abstract ................................................ii
目錄 .................................................iii
表目錄 ..................................................iv
圖目錄 ...................................................v
符號說明..................................................ix
第一章 前言...............................................1
1–1 研究動機.........................................1
1–2 文獻回顧.........................................1
1–3 研究方法.........................................3
第二章 數值方法...........................................4
2–1 物理模型.........................................4
2–2 有限差分法.......................................4
2–3 逆解左邊界溫度...................................8
2–4 量測誤差.........................................9
2–5 數位濾波法.......................................9
2–6 多項式迴歸......................................11
第三章 問題描述..........................................13
3–1 簡介............................................13
3–2 範例討論........................................13
第四章 結果與討論........................................17
第五章 結論與建議........................................18
參考文獻..................................................19

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