基于伴随方程法的材料热传导系数反演方法

建立利用材料内部温度场的测量结果反演材料热传导系数随时间和空间位置变化函数的伴随方程法,参考迭代正则化的思想在优化过程中给目标函数设置停止准则.对典型算例计算表明,方法在测量噪声较小情况下能得出较为合理的反演结果.但在有测量噪声的情况下,反演结果与真值在边界x=0和L处存在着一定偏差.当测量噪声较大时,反演结果与真值的偏差较为明显,且初值选取会对反演结果有相当大的影响.

Thermal Conductivity Inversion with Adjoint Equation Method

A typical inverse heat conduction problem(IHCP) is converted to an optimization problem.An inversion algorithm of adjoint equation method(AEM) is developed.In order to treat ill-posedness of IHCP,a stop criteria used in iterative regularization method is employed.In a typical case,the inversion method of AEM is feasible and not very sensitive to measurement noise as noise level is relatively low.As measurement noise presents,difference between estimated thermal conductivities and exact values at boundaries x=0 and x=L is significant,which is due to the fact that gradient of objective function with respect to the change of thermal conductivity at boundaries is relatively small.Moreover,further research shows that as noise level rises,significant difference between estimated and exact values of thermal conductivity presents and initial value has great influence on estimated values.