热力耦合反问题研究  

Research of Inverse Problem of Thermo-mechanical Coupling

作　　者：薛齐文[1,2] 张雪珊[1] 

机构地区：[1]大连交通大学土木与安全工程学院,大连116028 [2]大连理工大学工业装备结构分析国家重点实验室,大连116023

出　　处：《机械工程学报》2010年第18期157-161,168,共6页Journal of Mechanical Engineering

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

摘　　要：引入Bregman距离函数及其加权函数,应用正则化技术,建立一种非定常热力耦合反问题的数值求解模式。利用测量信息和计算信息的残差构造最小二乘函数,将反演识别问题转化为一个优化问题进行求解。时域上采用时域精细算法进行离散,空间上采用八节点等参元技术进行离散,分别建立便于敏度分析的热力耦合正演和反演数值模型。该模型不仅考虑了非均质和参数分布的影响,而且也便于正演和反演问题的敏度分析,可对热导率和热边界条件等宗量进行有效的单一和组合识别。给出相关的数值算例,对信息测量误差以及不同函数形式的计算结果作了探讨。数值结果表明,所建模型能够对非定常热力耦合反问题进行有效的求解,对各宗量进行有效的识别,并具有较高的计算精度、较好的稳定性和一定的抗噪性。Tikhonov＇s regularization approach is used to solve inverse problem of thermo-mechanical coupling in transient state with multi-variables,using Bregman distances and weighted Bregman distances in the construction of regularization terms for the Tikhonov＇s function.The inverse problem is formulated implicitly as an optimization problem by using the residual error between calculated and measured quantities to construct the least square function.A time stepping scheme is used for transient analysis and the eight-node isoparametric element model is given,facilitating sensitivity analysis of direct and inverse problems,and taking account of inhomogeneity and parameters distribution.Single and combined identifications can be carried out for thermal parameters and boundary conditions etc.Satisfactory numerical validation is given,including a preliminary investigation of effect of noise data on the results and the computational efficiency for different regularization terms.Results show that the proposed method can identify single and combined thermal parameters and boundary conditions for thermo-mechanical coupling problems with high computational precision,good stability and certain anti-noise capability.

关 键 词：反问题 多宗量 热力耦合 时域分析 有限元 

分 类 号：O482.2[理学—固体物理]