Estimation of the Total Heat Exchange Factor for the Reheating Furnace Based on the First-Optimize-Then-Discretize Approach and an Improved Hybrid Conjugate Gradient Algorithm

Zhi Yang (), Xiaochuan Luo, Pengbo Liu, Jinwei Qiao and Ming Liu
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Zhi Yang: School of Mechanical & Automotive Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
Xiaochuan Luo: College of Information Science and Engineering, Northeastern University, Shenyang 110819, China
Pengbo Liu: School of Mechanical & Automotive Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
Jinwei Qiao: School of Mechanical & Automotive Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
Ming Liu: School of Mechanical & Automotive Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China

Mathematics, 2022, vol. 10, issue 21, 1-20

Abstract: The total heat exchange factor is one of the most important thermal physical parameters in the heat transfer model for a reheating furnace machine. In this paper, a novel general strategy, which is combined with the first-optimize-then-discretize (FOTD) approach and an improved hybrid conjugate gradient (IHCG) algorithm, is proposed to identify the total heat exchange factor by solving a nonlinear inverse heat conduction problem (IHCP). Firstly, a nonlinear IHCP with the Dirichlet-type boundary condition T m ( t ) = T ( 0 , t ) is built to determine the unknown total heat exchange factor w ( t ) . Secondly, the analysis of the Fréchet gradient of the cost functional is given and the gradient is proved as Lipschitz continuous by the FOTD approach. Thirdly, based on the gradient information by FOTD, a new IHCG algorithm, whose global convergence is proved by us, is proposed for fast solving of the optimization problem. Finally, simulation experiments are given to verify the effectiveness of the proposed strategy. Compared with the first-discretize-then-optimize (FDTO) approach, the FOTD approach can reduce running time and iteration number. Compared with other CG algorithms, the proposed IHCG algorithm has better convergence performance. The experimental data by the thermocouples experiments from a reheating furnace are also given to identify the total heat exchange factor.

Keywords: first-optimize-then-discretize; hybrid conjugate gradient algorithm; inverse heat conduction problem; lipschitz continuity; nonlinear PDEs; total heat exchange factor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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