基于瞬态热传导反问题反演材料随温度变化的导热系数

Inversion of Temperature-dependent Thermal Conductivity Based on Transient Inverse Heat Conduction Problems

基于瞬态热传导反问题,给出反演材料随温度变化的导热系数的一种新方法。在正问题中,采用有限元方法获得测点的温度值。在反问题中,将反演参数作为优化变量,将测点温度计算值与测量值之间的残差作为优化目标函数,通过极小化目标函数进行数值求解。将复变量求导法引入瞬态热传导反问题,计算灵敏度矩阵的各系数。通过几个算例说明了算法的有效性与精度,并研究了测量误差对反演结果的影响。结果表明,给出的反问题求解方法可同时反演多个参数,可以反演具有函数形式的导热系数,亦可不必事先知道导热系数随温度变化的函数形式、反演指定温度处的导热系数。当测量数据准确时,可得到高精度的反演结果;当测量数据存在一定误差时,仍然可以得到较满意的反演结果,说明该文方法具有较好的鲁棒性。

A new method was represented for estimating temperature-dependent thermal conductivity by solving transient inverse heat conduction problems.In the direct problem,the measurement temperatures were obtained by a finite element method.In the inverse problem,the inverted parameters were treated as the optimization variables,and the errors to be minimized were the differences between the calculated temperatures and the measured ones.The solutions were obtained by minimizing the objective function.The complex-variable-differentiation method was introduced into transient inverse heat conduction problems,for the precise calculation of sensitivity coefficient.Examples were given to demonstrate the effectiveness and accuracy of the inverse approach.The results show that muti-parameters can be simultaneously retrieved by the proposed approach.The prior information on the functional form of the thermal properties is not necessary for the proposed approach.Accurate results can be obtained with accurate measurement data,and satisfactory results can be obtained with certain measurement errors,which further indicates the robustness of the proposed approach.