非线性热传导逆问题的表面热流辨识方法

摘要

当材料的热物性参数随温度变化时,其内部的热传导方程是一非线性偏微分方程,对应的热传导逆问题称为非线性热传导逆问题.本文建立了非线性热传导逆问题的两种表面热流辨识方法:顺序函数法和共轭梯度法,介绍了这两种辨识方法的基本思想和具体算法推导,并针对典型算例进行了仿真辨识,结果表明:两种辨识方法虽然在算法构造、计算效率方面存在一定的差异,但都能给出较好的辨识结果,并且算法受测量噪声的影响较小,具有较好的鲁棒性.%When the thermal properties of a material, I. E. , the heat conduction coefficient and the heat capacity are temperature dependent, the heat conduction in the material is of nonlinear form and the corresponding Inverse Heat Conduction Problem (IHCP) is called nonlinear IHCP. In this paper, two estimation methods, Sequential Function specification Method(SFM) and Conjugate Gradient Method(CGM) , are developed for the estimation of the time-variable surface heat flux from temperature measurements. The basic idea and detailed algorithm of these two methods are presented and both methods are applied to a typical exemplified case. It can be seen from the result that, although there are some differences of algorithm framework and computational efficiency between the SFM and CGM, both estimation methods are feasible and not sensitive to the measurement noise.