基于数据驱动模型求解热传导反问题

Solving the inverse heat conduction problem based on data driven model

热传导反问题求解在工程领域具有重要的应用价值。本文发展数据驱动模型识别了管道内壁几何形状和皮肤肿瘤生长参数等热传导反问题。在管道内壁几何形状识别问题中,首先采用随机生成模型结合有限元法求解热传导正问题,并采用有效导热系数转化的思想,建立机器学习模型,求解了测点温度与有效导热系数之间的抽象映射关系,进而实现管道内壁几何形状的识别。然后,应用数据驱动模型识别了皮肤肿瘤的生长参数,分别讨论了不同测量误差对计算结果的影响。数值算例表明,本文提出的数据驱动模型能够准确估算肿瘤的生热率和血液灌注率。这些工作显示了数据驱动模型在求解热传导反问题方面具有广阔的应用前景。

Inverse heat conduction problems(IHCP)have good application values in engineering.In this paper,a data-driven model is developed to solve the IHCP,such as the inner wall identification of the pipe and growth parameter estimation of the skin tumor.For the pipe inner wall identification problem,we used a stochastic model and the finite element method to solve the direct heat conduction problems.By using the effective thermal conductivity transformation,the relationship between the measurement temperature and effective thermal conductivity is established by a machine learning model and the shape of the inner wall of the pipe is identified.Then the data-driven model is used to identify the growth parameters of the skin tumor and the influences of different measurement errors on the results are discussed.The numerical results show that the proposed method can accurately estimate the heat generation rate and blood perfusion rate of the tumors.They also show that the data-driven model has broad application prospects in solving the IHCP.