基于Levenberg-Marquardt算法的内部缺陷导热反问题研究

Inverse Heat Conduction Problem of Inherent Defect Based on the Levenberg-Marquardt Method

在传热学的基础上,建立了三维的物理和数学模型,同时对LM(Levenberg-Marquardt)方法进行了修正。根据修正后的模型进行了导热反问题模拟研究,计算结果显示修正后的模型收敛速度更快;同时利用修正后的导热反问题的数学模型对材料内部不同性质缺陷的位置、几何形状及导热率对反问题求解的影响进行了分析,发现修正后的模型如果同时对缺陷位置、几何形状和导热率进行求解时,效果不好,但是对缺陷位置、几何形状与导热率分别进行求解时,可以获得比较好的结论;而测量误差对该方法求解结果有所影响,特别是对导热率影响较大。

A three-dimensional physical and mathematical heat transfer model was built based on the heat transfer theory and the modified Levenberg-Marquardt method. An inverse heat conduction problem was studied based on the modified model. And the computational results show that the new model converges better than the old one. The effects of position, size and the thermal conductance of the defect on the computational results were analyzed according to the different defect. And the results show that the modified model is more suitable to calculate the position, size of the defect and the thermal conductance of the defect respectively than together. And the results are affected by the temperature measurement errors, especially the thermal conductance of defect.