二维瞬态非线性热传导反问题的混合多宗量反演新方法  

A New Method for Solving Two-dimensional Transient Nonlinear Inverse Heat Conduction Problems for Inverting Hybrid Multi Parameters

作　　者：张博文[1] 梅杰 张春云 彭海峰[1] 崔苗[1] 高效伟[1] ZHANG Bowen;MEI Jie;ZHANG Chunyun;PENG Haifeng;CUI Miao;GAO Xiaowei(Dalian University of Technology,Dalian 116024,Liaoning Province,China)

机构地区：[1]工业装备结构分析国家重点实验室(大连理工大学)

出　　处：《中国电机工程学报》2020年第1期156-164,共9页Proceedings of the CSEE

基　　金：国家自然科学基金项目(51576026);中国博士后基金(2016M601305);中央高校基本科研业务费(DUT17LK04)~~

摘　　要：热传导反问题在航空航天、核电工程、石油化工等领域有着广泛的研究。其求解算法可分为2大类,梯度法与随机法,梯度法则具有收敛速度快,计算效率高等优点,更加适合于工程应用。但是其灵敏度矩阵的准确确定至关重要。将复变量求导法引入求解二维瞬态非线性热传导问题的ABAQUS有限元软件中,并通过ABAQUS用户子程序(user element subroutine,UEL)将复变量有限元法实数化,进而利用ABAQUS求解器求解所需的灵敏度矩阵,然后采用梯度法对热传导反问题进行求解。最后给出算例证明了该方法在求解二维热传导反问题的有效性、精度与效率等性能。Inverse heat conduction problems have been widely used in aerospace,nuclear power engineering,petrochemical and other fields.The solution algorithms can be classified into two categories:random method and gradient method.The gradient methods have the advantages of fast convergence and high efficiency,which is more suitable for engineering applications.The accurate determination of sensitivity matrix is very important.In this paper,the complex variable derivative method was first introduced into ABAQUS for solving two-dimensional transient nonlinear heat conduction problems,and the complex variables finite element method was reformulated based on traditional finite element method through ABAQUS UEL(user element subroutine).Then the inverse heat conduction problem was solved by gradient method based on the sensitivity matrix calculated by ABAQUS standard solver.Finally,some examples were given to verify the effectiveness,accuracy and efficiency of the method for solving two-dimensional inverse heat conduction problem.

关 键 词：热传导反问题 复变量求导法 ABAQUS 梯度法 瞬态热传导 

分 类 号：TM621[电气工程—电力系统及自动化]