A machine learning approach coupled with polar coordinate based localized collocation method for inner surface identification in heat conduction problem

authored by: Wen Hui Chu, Zhuo Jia Fu, Zhuo Chao Tang, Wen Zhi Xu, Xiao Ying Zhuang
Abstract: In the present work, we developed the Neural Networks (NNs) for identifying unknown surface shape of inner wall in the two-dimensional pipeline based on the temperature at uniformly distributed measuring points. The steady-state governing equation is transformed into the anisotropic heat conduction equations, and the irregularly shaped inner boundary is identified by the estimation of circumferential distribution of the effective thermal conductivity of the furnace. After the unhomogenized technique for the effective thermal conductivity model, the meshless generalized finite difference method on a radial is derived to effectively solve the direct problem for training data. The NNs are introduced to calculate the effective thermal conductivity for further detection of unknown internal boundary. Several numerical examples are provided to demonstrate the efficiency and accuracy of the proposed solver.
Organisation(s): Institute of Photonics
External Organisation(s): Hohai University
Tongji University
Type: Article
Journal: Computers and Mathematics with Applications
Volume: 148
Pages: 41-61
No. of pages: 21
ISSN: 0898-1221
Publication date: 15.10.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Modelling and Simulation, Computational Theory and Mathematics, Computational Mathematics
Electronic version(s): https://doi.org/10.1016/j.camwa.2023.07.031 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{a449a96bcbf54e1a8ff9c242cc3d9c4c,
title = "A machine learning approach coupled with polar coordinate based localized collocation method for inner surface identification in heat conduction problem",
abstract = "In the present work, we developed the Neural Networks (NNs) for identifying unknown surface shape of inner wall in the two-dimensional pipeline based on the temperature at uniformly distributed measuring points. The steady-state governing equation is transformed into the anisotropic heat conduction equations, and the irregularly shaped inner boundary is identified by the estimation of circumferential distribution of the effective thermal conductivity of the furnace. After the unhomogenized technique for the effective thermal conductivity model, the meshless generalized finite difference method on a radial is derived to effectively solve the direct problem for training data. The NNs are introduced to calculate the effective thermal conductivity for further detection of unknown internal boundary. Several numerical examples are provided to demonstrate the efficiency and accuracy of the proposed solver.",
keywords = "Effective thermal conductivity, Internal boundary detection, Inverse heat conduction problem, Neural network, Polar coordinate based generalized finite difference method",
author = "Chu, {Wen Hui} and Fu, {Zhuo Jia} and Tang, {Zhuo Chao} and Xu, {Wen Zhi} and Zhuang, {Xiao Ying}",
note = "Funding Information: The work described in this paper was supported by the National Science Fund of China (Grant No. 12122205 ) and the Six Talent Peaks Project in Jiangsu Province of China (Grant No. 2019-KTHY-009 ). ",
year = "2023",
month = oct,
day = "15",
doi = "10.1016/j.camwa.2023.07.031",
language = "English",
volume = "148",
pages = "41--61",
journal = "Computers and Mathematics with Applications",
issn = "0898-1221",
publisher = "Pergamon Press",
}

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