利用温度测量结果反演三维热传导问题中热源项的算法研究

利用表面温度测量来反演热传导问题中的热源项是一类典型的热传导逆问题,在采用有限体积法对三维稳态热传导问题进行数值求解的基础上,将该热传导逆问题转化为优化问题,基于灵敏度分析建立了反演算法.采用该算法对一典型算例的计算结果表明:建立的算法是有效的,具有较好的抗噪性能.此外,对反演算法中计算收敛准则的选取进行了较深入的分析,结果表明,由于热传导逆问题的不适定性,优化过程中目标函数值越小并不意味着反演结果与真值更为接近,可以通过设定合适的收敛准则来模拟正则化项的作用,克服不适定性的影响.

Estimation of heat source term in three-dimensional heat conduction problem from temperature measurements

Estimation of heat source term in three-dimensional heat conduction problem from temperature measurements is a typical Inverse Heat Conduction Problem(IHCP).In this paper,based on the numerical simulation of three-dimensional steady heat conduction problem with the Finite Volume Method(FVM),this three-dimensional IHCP is converted to an optimization problem,and the inversion method for estimation of heat source term is developed from sensitivity analysis. After applying this method to a typical test case,it can be seen that the estimation method is feasible and is not sensitive to the measurement noise.Moreover,the role of the stop criterion in the estimation process of cases with measurement noise is investigated.By analyzing the change of difference between the estimated heat sources and the exact values along with the decreasing of the objective function,it is shown that the decreasing of the objective function does not certainly mean the closer agreement between the estimated heat sources and exact values due to the ill-posedness of the IHCP.This ill-posedness can be overcome by choosing a proper specification of stop criterion to simulate the regularization effect in IHCP.