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首页> 外文期刊>Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology >Design, formulation, and solution of multidimensional inverse heat conduction problems
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Design, formulation, and solution of multidimensional inverse heat conduction problems

机译：多维逆导热问题的设计，公式化和解决方案

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摘要

The solution of linear inverse heat conduction problems (IHCP) for the reconstruction of time-dependent, spatially unknown heat fluxes on the boundaries of two- and three-dimensional geometries from several temperature measurements is presented. The solution method is based on the interpretation of the IHCP in the frequency domain. We emphasize the extension of the method to large-scale problems. In particular, we consider the parameterization of the unknown heat fluxes with respect to the number of sensors and their positions and the reduction and stable inversion of the large linear state-space models obtained from semidiscretization of the heat conduction equation. The influence of each of the steps and the choice of their tuning parameters on the quality of the estimated heat flux are discussed. Two- and three-dimensional examples show the good performance of the method with regard to time and space resolution in the presence of noisy measurements.
机译：提出了线性逆导热问题（IHCP）的解决方案，该解决方案可通过多次温度测量在二维和三维几何的边界上重建时间相关的，空间未知的热通量。解决方法基于对IHCP的频域解释。我们强调将方法扩展到大规模问题。特别是，我们考虑了未知热通量相对于传感器数量及其位置的参数化，以及从热传导方程的半离散化获得的大型线性状态空间模型的减少和稳定反演。讨论了每个步骤的影响及其调整参数的选择对估计的热通量的质量的影响。二维和三维示例显示了在存在噪声测量的情况下该方法在时间和空间分辨率方面的良好性能。

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