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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。
The inversion of the heat source term in the heat conduction problem by using the surface temperature measurement is a typical inverse problem of heat conduction. Based on the numerical solution of the three-dimensional steady-state heat conduction problem by the finite volume method, this heat conduction inverse problem is transformed into an optimization problem, Based on the sensitivity analysis established inversion algorithm. The calculation results of a typical example using this algorithm show that the established algorithm is effective and has good anti-noise performance. In addition, a more in-depth analysis is made on the selection of convergence criteria in the inversion algorithm. The results show that the smaller the objective function value in the optimization process does not mean that the inversion result is more true than the true value due to the ill-posedness of inverse heat conduction problem Close, we can simulate the role of regularization term by setting appropriate convergence criteria to overcome the impact of ill-posedness.