材料热传导系数随温度变化函数的反演方法

Estimation of temperature-dependent function of thermal conductivity for a material

材料热传导系数的反演是一类典型的热传导逆问题。针对材料热传导系数随温度变化的情况,本文将材料的热传导系数值按温度区间分段离散,建立了通过材料边界点的温度测量来反演各温度区间热传导系数值的遗传算法和伴随方程法。通过典型算例分析和考虑测量噪声、系统噪声的反演计算结果分析表明:所建立的两种反演算法都是可行有效的,受测量随机噪声和系统噪声的影响较小,具有较好的鲁棒性。

Estimation of thermal conductivity of a material is a typical Inverse Heat Conduction Problem（IHCP）.Especially,when the thermal conductivity of a material is a function of temperature,the temperature range should be divided into several segments and let the thermal conductivity of the material to be a constant in every segment,and then these constants need to be estimated from the measurement information of boundary points.In this paper,two estimation methods,Genetic Algorithms（GA） and Adjoint Equation Method（AEM）,are developed for the temperature-dependent thermal conductivity inversion problem.After applying these two inversion methods to some typical cases and analyzing the influence of measurement random noise and system noise,it is found that both inversion methods are feasible,effective,robust and not too sensitive to the measurement noise and system noise.Both methods are of bright prospect in engineering practice.