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

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 Tm(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