Precise Integral Algorithm Based Solution for Transient Inverse Heat Conduction Problems With Multi-Variables
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摘要: 基于有限元法和精细积分算法，提出了一种求解瞬态热传导多宗量反演问题的新方法．采用有限元法和精细积分算法分别对空间、时间变量进行离散，可以得到正演问题高精度的半解析数值模型，由此建立了多宗量反演的计算模式，并给出敏度分析的计算公式．对一维和二维的热物性参数、热源项、边界条件等进行了单宗量和多宗量的反演求解，初步考虑了初值和噪音等对反演结果的影响，数值算例验证了该方法的有效性．Abstract: By modeling direct transient heat conduction problems via finite element method (FEM) and precise integral algorithm, a new approach is presented to solve transient inverse heat conduction problems with multi-variables. Firstly, the spatial space and temporal domain are discretized by FEM and precise integral algorithm respectively. Then, the high accuracy semi-analytical solution of direct problem can be got. Finally, based on the solution, the computing model of inverse problem and expression of sensitivity analysis are established. Single variable and variables combined identifications including thermal parameters, boundary conditions and source-related terms etc. are given to validate the approach proposed in 1-D and 2-D cases. The effects of noise data and initial guess on the results are investigated. The numerical examples show the effectiveness of this approach.
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Key words:
- heat conduction /
- inverse problem /
- multi-variables /
- precise integral algorithm /
- finite element
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