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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

Author

Listed:
  • Zhi Yang

    (School of Mechanical & Automotive Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
    Shandong Institute of Mechanical Design and Research, Jinan 250353, China)

  • Xiaochuan Luo

    (College of Information Science and Engineering, Northeastern University, Shenyang 110819, China
    State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China)

  • Pengbo Liu

    (School of Mechanical & Automotive Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
    Shandong Institute of Mechanical Design and Research, Jinan 250353, China)

  • Jinwei Qiao

    (School of Mechanical & Automotive Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
    Shandong Institute of Mechanical Design and Research, Jinan 250353, China)

  • Ming Liu

    (School of Mechanical & Automotive Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
    Shandong Institute of Mechanical Design and Research, Jinan 250353, China)

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.

Suggested Citation

  • Zhi Yang & Xiaochuan Luo & Pengbo Liu & Jinwei Qiao & Ming Liu, 2022. "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," Mathematics, MDPI, vol. 10(21), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4074-:d:960628
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    References listed on IDEAS

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    1. Jianguo Zhang & Yunhai Xiao & Zengxin Wei, 2009. "Nonlinear Conjugate Gradient Methods with Sufficient Descent Condition for Large-Scale Unconstrained Optimization," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-16, July.
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