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  本文選題：共軛梯度法 + LM方法�。� 參考：《哈爾濱工業(yè)大學》2015年碩士論文

【摘要】：熱傳導反問題可以用于材料熱物性參數和材料表面熱流辨識,因其實用性強得到廣泛應用。但是熱傳導反問題的不適定性使之求解困難,因此熱傳導反問題的求解方法研究對其應用具有舉足輕重的作用。熱傳導反問題求解方法很多,其中共軛梯度法(CGM)和LM算法(LMM)是最常用的迭代算法。本文在分析CGM和LMM的基礎上提出了收斂性更好的分段辨識方法,研究了分段辨識方法的計算精度、計算效率、對初始值的依賴性和對溫度測量誤差的穩(wěn)定性,并進行了實驗驗證。首先,通過在非線性熱傳導偏微分方程中引入基爾霍夫變換,將非線性方程線性化,利用隱式有限差分方法建立了非線性熱傳導方程的求解方法。通過與有限元方法計算結果對比,驗證了熱傳導問題計算方法的有效性。其次,分析了CGM和LMM辨識材料變熱物性參數過程中存在的問題,并基于此提出了分段辨識方法。隨后,利用數值方法在計算精度、計算效率、對初始值的依賴性和對溫度測量誤差的穩(wěn)定性等方面對比了分段辨識方法和傳統的CGM和LMM的辨識結果,對比結果表明,分段辨識方法在計算精度、計算效率和對初始值的依賴性等方面明顯優(yōu)于CGM和LMM。此外,還利用數值方法驗證了分段辨識方法進行多參數辨識和熱流辨識的有效性。最后,設計實驗驗證了分段辨識方法處理真實溫度數據的可行性,利用實驗測得的溫度歷程,辨識出了無氧銅的熱導率,并與激光熱導儀所測試結果對比,結果表明,本文所辨識出的熱導率在測試數據的誤差范圍內,并且變化趨勢相同,證明了該方法利用真實溫度信號辨識變熱物性參數可行性。另外通過在材料表面加載階躍熱流,記錄材料內部溫度歷程,利用分段辨識方法對表面突變熱流進行辨識,驗證了分段辨識方法對于熱流辨識的有效性,同時驗證了正問題求解方法的可行性。
[Abstract]:The inverse problem of heat conduction can be used to identify the thermal properties of materials and the heat flux on the surface of materials, because of its strong practicability, it has been widely used. However, the ill-posed heat conduction problem makes it difficult to solve, so the study of the solution method of heat conduction inverse problem plays an important role in its application. There are many methods to solve heat conduction inverse problem, among which conjugate gradient method (CGM) and LM algorithm (LMM) are the most commonly used iterative algorithms. In this paper, based on the analysis of CGM and LMM, a more convergent piecewise identification method is proposed. The computational accuracy, computational efficiency, dependence on initial value and stability of temperature measurement error of the piecewise identification method are studied. The experimental results are verified. Firstly, by introducing Kirchhoff transform into nonlinear partial differential equation of heat conduction, the nonlinear equation is linearized and the solution method of nonlinear heat conduction equation is established by implicit finite difference method. The validity of the method is verified by comparing with the finite element method. Secondly, the problems existing in the identification of variable thermal properties parameters of materials by CGM and LMM are analyzed, and a piecewise identification method is proposed. Then, the piecewise identification method and the traditional CGM and LMM identification results are compared in terms of calculation accuracy, computational efficiency, dependence on initial value and stability of temperature measurement error by numerical method. The piecewise identification method is superior to CGM and LMM in calculation accuracy, computational efficiency and dependence on initial value. In addition, the effectiveness of the piecewise identification method for multi-parameter identification and heat flux identification is also verified by numerical method. Finally, the feasibility of subsection identification method to deal with real temperature data is verified by designing experiments. The thermal conductivity of oxygen free copper is identified by using the temperature history measured in the experiment. The results are compared with those measured by laser thermal conductivity meter. The thermal conductivity identified in this paper is within the error range of the test data and the variation trend is the same. It is proved that the method is feasible to identify the variable thermal properties parameters by using the real temperature signal. In addition, by loading step heat flux on the material surface, recording the temperature history inside the material, and using the subsection identification method to identify the abrupt heat flux on the surface, the effectiveness of the piecewise identification method for the heat flux identification is verified. At the same time, the feasibility of the forward problem solving method is verified.
【學位授予單位】：哈爾濱工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TB303

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本文編號：2064226