三维非稳态热传导逆问题反演算法研究

利用表面温度测量来反演热传导方程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非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，建立了伴随方程法和共轭梯度法这两类反演算法. 采用这两类算法对一个典型算例的计算结果表明:建立的两类反演算法是有效的，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. 

INVERSE ESTIMATION OF HEAT SOURCE TERM IN THREE-DIMENSIONAL TRANSIENT HEAT CONDUCTION PROBLEM

Inverse estimation of heat source term inthree-dimensional heat conduction problem from surface temperaturemeasurements is a typical Inverse Heat Conduction Problem (IHCP). In thispaper, based on the three-dimensional (3D) numerical simulation of transientheat conduction problem with the Finite Volume Method (FVM), the 3Dtransient IHCP is generally converted into an optimization problem toinversely estimate the heat source with Adjoint Equation Method (AEM) andConjugate Gradient Method (CGM). A typical case has been shown that the twoestimation methods are feasible and not sensitive to the measurement noise.Moreover, the selection of stopping criterion for the inverse estimationalgorithm is further investigated. The results demonstrate that the closeragreement between the estimated and exact heat sources hasn't made with thedecreasing value of the objective function due to the ill-posedness of theIHCP, which can be overcome with the proper stopping criterion to simulatethe regularization effect in the IHCP.