三维稳态传热系统边界温度场的共轭梯度反演

华侨++梁晓斌++章广祥++范健学

摘 要：本文采用共軛梯度法（conjugate gradient method，CGM），研究了三维稳态导热系统边界温度分布的反演问题。利用有限差分法（finite difference method，FDM）求解传热正问题。以测点处的温度测量值与传热正问题计算值之间的偏差作为输入信息进行共轭梯度计算，获得待反演边界的温度补偿量，对待反演边界温度分布的猜测值进行修正。讨论了待反演边界温度分布的初始猜测值、测点数目以及测量误差对反演结果的影响，证实了共轭梯度法在三维传热系统边界条件反演中的有效性。

关键词：有限差分；共轭梯度；三维稳态；传热学反问题

Conjugate Gradient Inversion of Boundary Temperature Distribution for Three-Dimensional Steady State Heat Transfer System

Hua Qiao， Liang Xiaobin，Zhang Guangxiang， Fan Jianxue

Key Laboratory of Low-grade Energy Utilization Technologies and Systems， Chongqing University， Ministry of Education， Chongqing 400044， PR China

Abstract： In this paper， the conjugate gradient method is used to study the inversion of boundary temperature distribution in a three-dimensional steady-state heat transfer system. The direct problem is solved by Finite Difference Method. The error between the measured temperature and the calculated value of the heat transfer problem is calculated as conjugate gradient. The temperature compensation of the boundary to be retrieved is obtained and the guess value of the inversion boundary temperature distribution is corrected. The influence of the initial guess value， the number of measuring points and the measurement error on the inversion results are discussed， and the validity of the conjugate gradient method in the inversion of the boundary conditions of the three-dimensional heat transfer system has been proved.

Key words： finite difference； conjugate gradient； three-dimensional steady-state； inverse heat transfer problem