双曲传热反问题研究

RESEARCH ON THE INVERSE HYPERBOLIC HEAT CONDUCTION PROBLEMS

该文建立了双曲传热正/反问题求解模型,应用高斯-牛顿方法,对辐射边界进行了识别。空间上采用等参元进行离散,时域上采用时域精细算法进行离散,利用测量信息和计算信息构造最小二乘函数,将多宗量反演识别问题转化为一个优化问题,所建模型可对导热系数和辐射边界等宗量进行有效的单一和组合识别。给出了相关的数值验证,对信息测量误差作了初步探讨。数值结果表明,所建模型能对双曲传热反问题的导热系数和辐射边界条件进行有效的识别,并具有较高的计算精度。

A general numerical model is given to identify parameters of the radiation boundary conditions for inverse hyperbolic heat conduction problems using Gauss-Newton method.The finite element is used for the discretization in the space system and a time stepping scheme is used for transient analysis.The inverse problem is formulated implicitly as an optimization problem with the cost functional of squared residues between calculated and measured quantities.Single and combined identifications can be carried out for thermal parameters and radiation boundary conditions etc.Satisfactory numerical validation is given including a preliminary investigation of effect of noise data on the results.Results show that the proposed numerical model can identify single and combined thermal parameters and radiation boundary conditions for hyperbolic heat conduction problems with precision.