瞬态热传导区间反演分析

INTERVAL INVERSE ANALYSIS OF TRANSIENT HEAT CONDUCTION PROBLEM

基于区间有限元和矩阵摄动理论,引入同伦技术,建立了瞬态热传导不确定性区间参数反演识别的数值求解模式。利用测量信息和计算信息的区间残差构造同伦函数,将反演识别问题转化为一个优化问题进行求解。时间域上,引入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,并结合区间有限元法,建立了便于敏度分析的不确定性正反演数值模型。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,可对导热系数和热边界条件等宗量的区间范围进行有效的单一和组合识别,并给出了相关的数值算例。数值结果表明了所建数值模型的有效性和可行性,并具有较高的计算精度。

A general numerical model is presented for the interval inverse transient heat conduction problem with interval parameters. The homotopy method and interval finite element method based on the element and interval extension theory were used. The inverse problem was formulated implicitly as an optimization problem with the homotopy functional of squared residues between calculated and measured quantities. A time stepping scheme was used for transient analysis. An eight-point finite element model was given with interval finite element method based on the element. Single and combined identifications can be carried out for thermal parameters and boundary conditions etc., taking account of inhomogeneity and parameters distribution. Satisfactory numerical validation was given. The results show that the proposed numerical model can be applied to solve the inverse heat conduction problem with interval parameters in a transient state, showing its high computational precision and efficiency.