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

【摘要】：熱傳導(dǎo)反問題可以用于材料熱物性參數(shù)和材料表面熱流辨識(shí),因其實(shí)用性強(qiáng)得到廣泛應(yīng)用。但是熱傳導(dǎo)反問題的不適定性使之求解困難,因此熱傳導(dǎo)反問題的求解方法研究對(duì)其應(yīng)用具有舉足輕重的作用。熱傳導(dǎo)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(chǔ)上提出了收斂性更好的分段辨識(shí)方法,研究了分段辨識(shí)方法的計(jì)算精度、計(jì)算效率、對(duì)初始值的依賴性和對(duì)溫度測(cè)量誤差的穩(wěn)定性,并進(jìn)行了實(shí)驗(yàn)驗(yàn)證。首先,通過在非線性熱傳導(dǎo)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(dǎo)方程的求解方法。通過與有限元方法計(jì)算結(jié)果對(duì)比,驗(yàn)證了熱傳導(dǎo)問題計(jì)算方法的有效性。其次,分析了CGM和LMM辨識(shí)材料變熱物性參數(shù)過程中存在的問題,并基于此提出了分段辨識(shí)方法。隨后,利用數(shù)值方法在計(jì)算精度、計(jì)算效率、對(duì)初始值的依賴性和對(duì)溫度測(cè)量誤差的穩(wěn)定性等方面對(duì)比了分段辨識(shí)方法和傳統(tǒng)的CGM和LMM的辨識(shí)結(jié)果,對(duì)比結(jié)果表明,分段辨識(shí)方法在計(jì)算精度、計(jì)算效率和對(duì)初始值的依賴性等方面明顯優(yōu)于CGM和LMM。此外,還利用數(shù)值方法驗(yàn)證了分段辨識(shí)方法進(jìn)行多參數(shù)辨識(shí)和熱流辨識(shí)的有效性。最后,設(shè)計(jì)實(shí)驗(yàn)驗(yàn)證了分段辨識(shí)方法處理真實(shí)溫度數(shù)據(jù)的可行性,利用實(shí)驗(yàn)測(cè)得的溫度歷程,辨識(shí)出了無氧銅的熱導(dǎo)率,并與激光熱導(dǎo)儀所測(cè)試結(jié)果對(duì)比,結(jié)果表明,本文所辨識(shí)出的熱導(dǎo)率在測(cè)試數(shù)據(jù)的誤差范圍內(nèi),并且變化趨勢(shì)相同,證明了該方法利用真實(shí)溫度信號(hào)辨識(shí)變熱物性參數(shù)可行性。另外通過在材料表面加載階躍熱流,記錄材料內(nèi)部溫度歷程,利用分段辨識(shí)方法對(duì)表面突變熱流進(jìn)行辨識(shí),驗(yàn)證了分段辨識(shí)方法對(duì)于熱流辨識(shí)的有效性,同時(shí)驗(yàn)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(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：TB303

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本文編號(hào)：2064226