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Estimating sensor number and spacing for inverse calculation of thermal boundary conditions using the conjugate gradient method

机译：使用共轭梯度法估算传感器数和间隔，用于使用共轭梯度法计算热边界条件

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摘要

The conjugate gradient method is a popular tool for solving inverse heat transfer problems which arise for example from the estimation of unknown thermal boundary conditions or temperature dependent material properties. Depending on the desired accuracy of the results, input data of numerous temperature sensors need to be considered. However, due to limited access and available space many systems offer only a few temperature measurement spots. Therefore, this paper focuses on the question how changes in the number of temperature measurements affect the inversely estimated boundary condition. This behavior is studied by two numerical test cases with different boundary conditions, thermal properties and geometries, investigating also varying resolutions of the boundary condition and the effect of measurement errors. The results of both test cases show, that for undisturbed measurement data as well as superimposed measurement errors, fewer temperature readings than unknowns are sufficient to accurately estimate the boundary condition. Also, after exceeding a threshold in sensor number, only little improvement of inverse estimated results can be observed in both test cases. To transfer these findings on further inverse heat transfer scenarios, the key heat conduction parameters are summarized in a characteristic parameter, the Fourier number. This number supports the estimation of necessary sensor count in future inverse investigations with varying thermal parameters, geometries and investigation time.
机译：共轭梯度方法是用于求解逆传热问题的流行工具，其例如从未知的热边界条件或温度依赖性材料特性的估计产生。根据结果​​的所需精度，需要考虑许多温度传感器的输入数据。但是，由于访问和可用空间有限，许多系统只提供几个温度测量点。因此，本文重点介绍了质疑温度测量数量的变化会影响反向估计的边界条件。这种行为由具有不同边界条件，热性能和几何形状的两个数值测试用例研究，研究了边界条件的不同分辨率和测量误差的效果。两个测试用例的结果表明，即对于未受干扰的测量数据以及叠加的测量误差，比未知数更少的温度读数足以准确估计边界条件。此外，在超过传感器编号中超过阈值之后，在两个测试用例中只能观察到逆估计结果的几乎没有提高。为了在进一步的逆传热场景上转移这些发现，关键的热传导参数总结在特征参数，傅立叶号。该数字支持在未来的逆调查中估计必要的传感器计数，其具有不同的热参数，几何和调查时间。

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