材料变热物性参数辨识算法与验证

发布时间：2018-06-25 02:57

本文选题：共轭梯度法 + LM方法　；参考：《哈尔滨工业大学》2015年硕士论文

【摘要】：热传导反问题可以用于材料热物性参数和材料表面热流辨识,因其实用性强得到广泛应用。但是热传导反问题的不适定性使之求解困难,因此热传导反问题的求解方法研究对其应用具有举足轻重的作用。热传导反问题求解方法很多,其中共轭梯度法(CGM)和LM算法(LMM)是最常用的迭代算法。本文在分析CGM和LMM的基础上提出了收敛性更好的分段辨识方法,研究了分段辨识方法的计算精度、计算效率、对初始值的依赖性和对温度测量误差的稳定性,并进行了实验验证。首先,通过在非线性热传导偏微分方程中引入基尔霍夫变换,将非线性方程线性化,利用隐式有限差分方法建立了非线性热传导方程的求解方法。通过与有限元方法计算结果对比,验证了热传导问题计算方法的有效性。其次,分析了CGM和LMM辨识材料变热物性参数过程中存在的问题,并基于此提出了分段辨识方法。随后,利用数值方法在计算精度、计算效率、对初始值的依赖性和对温度测量误差的稳定性等方面对比了分段辨识方法和传统的CGM和LMM的辨识结果,对比结果表明,分段辨识方法在计算精度、计算效率和对初始值的依赖性等方面明显优于CGM和LMM。此外,还利用数值方法验证了分段辨识方法进行多参数辨识和热流辨识的有效性。最后,设计实验验证了分段辨识方法处理真实温度数据的可行性,利用实验测得的温度历程,辨识出了无氧铜的热导率,并与激光热导仪所测试结果对比,结果表明,本文所辨识出的热导率在测试数据的误差范围内,并且变化趋势相同,证明了该方法利用真实温度信号辨识变热物性参数可行性。另外通过在材料表面加载阶跃热流,记录材料内部温度历程,利用分段辨识方法对表面突变热流进行辨识,验证了分段辨识方法对于热流辨识的有效性,同时验证了正问题求解方法的可行性。
[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.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB303

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