非线性热传导反问题参数辨识  

PARAMETERS IDENTIFICATION OF NON-LINEAR INVERSE HEAT CONDUCTION PROBLEM

作　　者：薛齐文[1,2,3] 魏伟[3] 

机构地区：[1]大连交通大学土木与安全工程学院,大连116028 [2]工业装备结构分析国家重点实验室,大连116023 [3]大连交通大学载运工具先进技术重点实验室,大连116028

出　　处：《工程力学》2010年第8期5-9,共5页Engineering Mechanics

基　　金：国家自然科学基金项目(10802015);辽宁省重点实验室基金项目(2008S036);工业装备结构分析重点实验室开放基金项目(GZ0811)

摘　　要：基于一种时域正演精细算法,引入Bregman距离加权函数作为正则项,应用Tikhonov正则化方法,对非线性热传导反问题进行求解。所建正/反演数值模型在便于敏度分析的同时,能够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有效组合识别。该文给出了相关的数值算例,并对信息误差以及不同正则项的计算效率作了探讨,得到满意的计算结果。数值结果表明所提的求解策略在求解非线性热传导反问题时,不仅能够对相关的热学参数进行有效的组合识别,而且具有较高的计算精度、较好的稳定性和一定的抗噪性,采用加权的Bregman距离函数作正则项可以提高计算效率。Tikhonov’s regularization approach has been used to solve non-linear inverse heat conduction problems, using weighted Bregman distances in the construction of regularization terms for the Tikhonov’s function. Combined identifications can be achieved for non-linear inverse heat conduction with source term, thermal diffusivity and boundary conditions etc, facilitating the sensitivity analysis. Satisfactory numerical validation is performed including a preliminary investigation on the effect of noise data and the computational efficiency of different regularization terms. Results show that the proposed method can identify combined thermal parameters and boundary conditions for non-linear inverse heat conduction problems with high computational precision and anti-noisy capability. Moreover, the computational efficiency is improved with the weighted Bregman distances function as regularization terms.

关 键 词：加权Bregman函数 正则化 多宗量 非线性 精细算法 

分 类 号：O482.2[理学—固体物理]