Levenberg-Marquardt算法求解三维圆管稳态导热反问题

Solution of inverse steady-state heat conduction problem using Levenberg-Marquardt method for three-dimensional pipeline

应用Levenberg-Marquardt算法求解三维水平圆管导热反问题,以反演圆管内壁未知的温度分布。使用有限单元法求解三维导热正问题。在周向及轴向上引入插值函数,把内壁温度场的反演转化为内壁有限点温度的反演。分析了圆管内壁两种不同温度分布的反问题,并通过引入随机测量误差,探讨了测量误差对反演结果的影响。数值计算结果表明:所构算法能精确地反演出圆管内壁的温度分布。

An inverse steady state heat conduction problem was solved for estimation of unknown inner wall temperature in a three-dimensional pipeline by using the Levenberg-Marquardt method.The direct heat conduction problem was solved by using the finite element method.The inner wall temperature distribution estimation was transformed into the infinite nodes temperature estimation by the one-dimensional interpolations in the longitudinal and circumferential directions.The inverse analysis for two cases of inner wall temperature were carried out and the effects of measurement errors on the inverse problem were discussed.The numerical results show that the accurate inner wall temperature can be obtained by this method.