# 臺灣博碩士論文加值系統

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 本文提出一種混合拉氏轉換法（Laplace transform technique）和有限 差分法（Finite difference method）的數值方法，並配合最小平方法（ Least-squares scheme）來預測未知的邊界溫度。首先利用拉氏轉換法處 理系統之時間域而後再以有限差分法處理系統轉換後之空間域，最後再以 數值逆拉氏轉換法來求取系統之溫度值。拉氏轉換法的優點是可以求得在 某一特定時間的溫度值，而不需要由初始時間慢慢的求解。最小平方法的 應用在於使數值結果能較快地收斂。本文將探討熱電偶（Thermocouple） 的安置位置與數量對預測結果的影響。由本文之結果可知此數值方法能夠 精確地、有效地預測出未知的邊界溫度。再者量測誤差對預測值的影響也 將在文中加以討論。由數值結果顯示在考慮量測誤差時本文之數值方法仍 可以正確地預測出未知的表面溫度。因此本文之混合數值方法可成功地被 應用來解析本文之逆向熱傳導問題。
 The present study introduces a numerical method to analyze inverse heat conduction problem concerning the prediction of the surface behavior. The numerical algorithm combines the Laplace transform technique and the finite difference method in conjunction with the least square scheme. Time-dependent terms in the governing equation are removed by using the Laplace transform technique, and then the resulting differential equation are solved by using the finite difference method. Temperature distributions in the domain are obtained by using the numerical inversion of Laplace transform. Due to the application of the Laplace transform technique, the temperature can be calculated at a specific time without step-by-step computation in the time domain. By using the least square scheme, the convergence of iteration is fast and stable. In the estimation of the unknown boundary temperature, various examples are illustrated to show the applicability and efficiency of the present numerical method. The influences of measurement time intervals and thermocouple locations are investigated. It can be seen from various illustrated examples that the present numerical method can accurately and efficiently estimate the unknown boundary temperature and the thermocouple can be located far from the estimated surface. In addition, the effect of the measurement error and noises on measurements will be investigated. It is fount that the present numerical method can also estimate the boundary surface well while the measurement error and noises are considered. Thus, it can be concluded that the present numerical method can successfully be to analyze inverse heat conduction problem applied.
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