Details
| Original language | English |
|---|---|
| Pages (from-to) | 41-61 |
| Number of pages | 21 |
| Journal | Computers and Mathematics with Applications |
| Volume | 148 |
| Early online date | 18 Aug 2023 |
| Publication status | Published - 15 Oct 2023 |
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
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Computers and Mathematics with Applications, Vol. 148, 15.10.2023, p. 41-61.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A machine learning approach coupled with polar coordinate based localized collocation method for inner surface identification in heat conduction problem
AU - Chu, Wen Hui
AU - Fu, Zhuo Jia
AU - Tang, Zhuo Chao
AU - Xu, Wen Zhi
AU - Zhuang, Xiao Ying
N1 - 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 ).
PY - 2023/10/15
Y1 - 2023/10/15
N2 - 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.
AB - 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.
KW - Effective thermal conductivity
KW - Internal boundary detection
KW - Inverse heat conduction problem
KW - Neural network
KW - Polar coordinate based generalized finite difference method
UR - http://www.scopus.com/inward/record.url?scp=85168091698&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2023.07.031
DO - 10.1016/j.camwa.2023.07.031
M3 - Article
AN - SCOPUS:85168091698
VL - 148
SP - 41
EP - 61
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
SN - 0898-1221
ER -