基于时域精细积分算法的瞬态传热多宗量反演  

Precise Integral Algorithm Based Solution for Transient Inverse Heat Conduction Problems With Multi-Variables

作　　者：王一博[1] 杨海天[2] 邬瑞锋[2] 

机构地区：[1]清华大学工程力学系,北京100084 [2]大连理工大学工程力学系

出　　处：《应用数学和力学》2005年第5期512-518,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10172024;10272064);973NKBRSF基金资助项目(G1999032805);教育部重点基金资助项目(99149);教育部骨干教师基金资助项目(2000_65);归国留学人员启动基金资助项目(1999_363);工业装备结构分析国家重点实验室开放基金资助项目(GZ9814)

摘　　要：　基于有限元法和精细积分算法,提出了一种求解瞬态热传导多宗量反演问题的新方法·　采用有限元法和精细积分算法分别对空间、时间变量进行离散,可以得到正演问题高精度的半解析数值模型,由此建立了多宗量反演的计算模式,并给出敏度分析的计算公式·　对一维和二维的热物性参数、热源项、边界条件等进行了单宗量和多宗量的反演求解,初步考虑了初值和噪音等对反演结果的影响。By modeling direct transient heat conduction problems via finite element method (FEM) and precise integral algorithm, a new approach is presented to solve transient inverse heat conduction problems with multi_variables. Firstly, the spatial space and temporal domain are discretized by FEM and precise integral algorithm respectively. Then, the high accuracy semi_analytical solution of direct problem can be got. Finally, based on the solution, the computing model of inverse problem and expression of sensitivity analysis are established. Single variable and variables combined identifications including thermal parameters, boundary conditions and source_related terms etc. are given to validate the approach proposed in 1_D and 2_D cases. The effects of noise data and initial guess on the results are investigated. The numerical examples show the effectiveness of this approach.

关 键 词：热传导 反问题 多宗量 精细积分算法 有限元 

分 类 号：O241[理学—计算数学]