三維穩態傳熱系統邊界溫度場的共軛梯度反演

華僑++梁曉斌++章廣祥++范健學

摘 要：本文采用共軛梯度法（conjugate gradient method，CGM），研究了三維穩態導熱系統邊界溫度分布的反演問題。利用有限差分法（finite difference method，FDM）求解傳熱正問題。以測點處的溫度測量值與傳熱正問題計算值之間的偏差作為輸入信息進行共軛梯度計算，獲得待反演邊界的溫度補償量，對待反演邊界溫度分布的猜測值進行修正。討論了待反演邊界溫度分布的初始猜測值、測點數目以及測量誤差對反演結果的影響，證實了共軛梯度法在三維傳熱系統邊界條件反演中的有效性。

關鍵詞：有限差分；共軛梯度；三維穩態；傳熱學反問題

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