多宗量一维瞬态非线性热传导反问题的正则解

详细信息

A CANONICAL SOLUTION FOR UNIDIMENSIONAL NON-LINEAR INVERSE PROBLEM OF HEAT CONDUCTION IN TRANSIENT STATE WITH MULTI-VARIABLES

(1. School of Traffic and Transportation, Dalian Jiaotong University, Dalian 116028, China; 2. State Key Lab of Structural Analysis for Industrial Equipment Dept. of Engineering Mechanics, Dalian University of Technology, Dalian 116023, China)

摘要: 基于一种时域正演精细算法，引入Bregman距离函数作为Tikhonov函数的正则项，建立了求解多宗量一维瞬态非线性热传导反问题的数学模型，可对非线性内热源强度、导温系数和边界条件等多个热学参数进行组合识别。对信息测量误差作了初步探讨，数值验证给出令人满意的结果。
- 多宗量 /
- 正则化 /
- 精细算法 /
- Bregman距离 /
- 反问题
Abstract: A general numerical model to identify multi-variables of the unidimensional non-linear inverse problem of heat conduction in transient state is presented by a precise algorithm for direct heat conduction, based on Bregman distances in the construction of regularization terms in Tikhonov’s function. Combination of identifications can be carried out for non-linear source term, thermal diffusivity and boundary conditions etc. Satisfactory numerical results including a preliminary investigation of effect of noise data and initial value on the results are given as well.
- multi-variables /
- regularization /
- precise algorithm /
- Bregman distances /
- inverse problem