Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/74634
標題: 應用熱傳逆算法預測邊界溫度分佈和邊界幾何形狀
作者: 陳朝光
林錦鴻
關鍵字: 逆問題
逆向熱傳
逆向矩陣
未知幾何邊界
出版社: 國立中興大學工學院;Airiti Press Inc.
摘要: This paper applied the reversed matrix method to analyze the inverse heat transfer problem, which estimates the boundary temperatures and irregular boundary configurations. A finite-difference method is used to discretize the governing equations and then a linear inverse model is contracted to identify the unknown boundary conditions. The present approach is to rearrange the matrix forms of the differential governing equations so the unknown conditions can be represented explicitly. Then, the linear least-squares-error method is adopted to find the solutions. The results show that only few measuring points at discrete grid points are needed to estimate the unknown quantities even when measurement errors are considered. In contrast to the traditional approach, the advantages of this method are that no prior information is needed on the functional form of the unknown quantities, no initial guesses are required, no iterations. In the calculating process are necessary, and the inverse problem can be solved in a linear domain. Furthermore, the existence and uniqueness of the solutions can be easily identified. The results show that the proposed methods can solve the engineering inverse problems efficiently and effectively.
本文應用逆向矩陣法預測平板邊界的溫度分布及不規則幾何外形之幾何逆問題分析。首先,有限差分法將欲求解之逆問題的統後方程式離散化以建構一線性矩陣方程式。藉由重新排列逆問題之矩陣方程式,使得未知狀態之式得以明確表示出來;再以少數點之溫度資料代入此線性逆模型中,利用線性最小均方根誤差法將問題最佳化以解此逆模型。本方法在分析物理問題時,不需預設未知條件之解的形式,計算時可以避開以往傳統方法所不可避免的疊代程序,也因此不需襖始猜測值。僅利用一次之運算過程,即可直接解出未知條件。在計算上較一般傳統方法快速、簡潔、精確,且其解之唯一性很容易驗證。由數值結果顯示,即使在考慮量測誤差的情況下,仍可精準地的預出未知之邊界條件或外形。本文所提的逆向矩陣法可應用於一維、二維甚至三維之問題,將可成為研究逆問題之一有效方法。
URI: http://hdl.handle.net/11455/74634
ISSN: 1017-4397
Appears in Collections:第13卷 第2期
工學院

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