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工程力学  2014 

瞬态热传导区间反演分析

DOI: 10.6052/j.issn.1000-4750.2012.09.0713, PP. 237-241

Keywords: 区间反演,热传导,不确定性,同伦技术,精细算法

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Abstract:

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。

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