The purpose of this paper is to develop a transform method and a deep learning model to identify the inner surface shape based on the measurement temperature at the outer boundary of the pipe.,The training process is assisted by the finite element method (FEM) simulation which solves the direct problem for the data preparation. To avoid re-meshing the domain when the inner surface shape varies, a new transform method is proposed to transform the shape identification problem into the effective thermal conductivity identification problem. The deep learning model is established to set up the relationship between the measurement temperature and the effective thermal conductivity. Then the unknown geometry shape is acquired by the mapping between the inner shape and the effective thermal conductivity through the inverse transform method.,The new method is successfully applied to identify the internal boundary of a pipe with eccentric circle, ellipse and nephroid inner geometries. The results show that as the measurement points increased and the measurement error decreased, the results became more accurate. The position of the measurement point and mesh density of the FEM model have less effect on the results.,The deep learning model and the transform method are developed to identify the pipe inner surface shape. There is no need to re-mesh the domain during the computation progress. The results show that the proposed method is a fast and an accurate tool for identifying the pipe inner surface.

中文翻译：

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基于深度学习和有效热导率变换的热传导问题管道内表面识别

本文的目的是开发一种变换方法和深度学习模型，以根据管道外边界处的测量温度来识别内表面形状。训练过程辅以有限元法（FEM）模拟解决了数据准备的直接问题。为了避免内表面形状变化时重新划分域，提出了一种新的变换方法，将形状识别问题转化为有效的热导率识别问题。建立深度学习模型，建立测量温度与有效热导率之间的关系。然后通过逆变换方法通过内部形状与有效导热系数之间的映射得到未知的几何形状。新方法已成功应用于识别具有偏心圆、椭圆和肾形内部几何形状的管道的内部边界。结果表明，随着测量点的增加和测量误差的减小，结果变得更加准确。有限元模型的测量点位置和网格密度对结果的影响较小。,开发了深度学习模型和变换方法来识别管道内表面形状。在计算过程中不需要重新划分域。结果表明，所提出的方法是一种快速、准确的管道内表面识别工具。结果表明，随着测量点的增加和测量误差的减小，结果变得更加准确。有限元模型的测量点位置和网格密度对结果的影响较小。,开发了深度学习模型和变换方法来识别管道内表面形状。在计算过程中不需要重新划分域。结果表明，所提出的方法是一种快速、准确的管道内表面识别工具。结果表明，随着测量点的增加和测量误差的减小，结果变得更加准确。有限元模型的测量点位置和网格密度对结果的影响较小。,开发了深度学习模型和变换方法来识别管道内表面形状。在计算过程中不需要重新划分域。结果表明，所提出的方法是一种快速、准确的管道内表面识别工具。在计算过程中不需要重新划分域。结果表明，所提出的方法是一种快速、准确的管道内表面识别工具。在计算过程中不需要重新划分域。结果表明，所提出的方法是一种快速、准确的管道内表面识别工具。