Estimation of heat transfer coefficients and heat flux on the billet surface by an integrated approach

Yu, Yang; Luo, Xiaochuan

doi:10.1016/j.ijheatmasstransfer.2015.07.008

Cited by 35 publications

(7 citation statements)

References 29 publications

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“…where d k � (∇J 1 (h)) k is the gradient, which decides the iterative direction of L-M algorithm, μ is the L-M parameter, the adaptive parameter method [19]…”

Section: Sufficient Descent Levenberg-marquard With Adaptivementioning

confidence: 99%

“…. , P, P � 6) with the time interval ΔT m � 20(s) and choose the maximum iterative number N max � 100. e gradient algorithm (GA), conjugate gradient algorithm (CGA), improved conjugate gradient algorithm (ICGA) [29], LM algorithm [19], sufficient descent Levenberg-Marquard (SD-LM) algorithm, and SD-LMAP are used to estimate the heat transfer coefficient c i , i � 1, 2, . .…”

Section: Simulationmentioning

confidence: 99%

“…Our previous works [19,20] focused on the identification of the heat transfer coefficients of the heat transfer model by the L-M algorithm. Based on the above works, this paper considers the inverse problem of two-dimensional nonhomogeneous parabolic equation associated with the continuous casting.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of Heat Flux in Two-Dimensional Nonhomogeneous Parabolic Equation Based on a Sufficient Descent Levenberg–Marquard Algorithm

Pang

et al. 2021

Journal of Mathematics

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The main work of this paper focuses on identifying the heat flux in inverse problem of two-dimensional nonhomogeneous parabolic equation, which has wide application in the industrial field such as steel-making and continuous casting. Firstly, the existence of the weak solution of the inverse problem is discussed. With the help of forward solution and dual equation, this paper proves the Lipchitz continuity of the cost function and derives the Lipchitz constant. Furthermore, in order to accelerate the convergence rate and reduce the running time, this paper presents a sufficient descent Levenberg–Marquard algorithm with adaptive parameter (SD-LMAP) to solve this inverse problem. At last, compared with other methods, the results of simulation experiment show that this algorithm can obviously reduce the running time and iterative number.

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“…where d k � (∇J 1 (h)) k is the gradient, which decides the iterative direction of L-M algorithm, μ is the L-M parameter, the adaptive parameter method [19]…”

Section: Sufficient Descent Levenberg-marquard With Adaptivementioning

confidence: 99%

Section: Simulationmentioning

confidence: 99%

See 1 more Smart Citation

Estimation of Heat Flux in Two-Dimensional Nonhomogeneous Parabolic Equation Based on a Sufficient Descent Levenberg–Marquard Algorithm

Pang

et al. 2021

Journal of Mathematics

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“…Several optimization methods have been extensively developed to solve this problem, such as gradient method [20], conjugate gradient method [21], [22], Levenberg-Marquardt method (LM) [18], [23], Cao method [24], and Lanbweber method [25]. The basic concept of these optimization methods is to update h for each iteration via the gradient of cost function or the value of cost function.…”

Section: Identification Of Unknown Parameters In Continuous Castmentioning

confidence: 99%

GPU-Based Model Predictive Control of Nonlinear Parabolic Partial Differential Equations System and Its Application in Continuous Casting

2019

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Temperature control of steel billets plays an important role in the quality of steel billets. This paper was motivated by the necessity for setting a value of spray cooling water flow with regard to the accuracy, fast applicability to real-time optimization, and capability of non-steady operation scenarios, especially for the change of casting speed. Therefore, this paper is focused on the GPU-based model predictive control (MPC) for temperature control of steel billets. The system dynamics in MPC is a heat transfer model characterized by the nonlinear parabolic partial differential equations (PDEs). This paper presented two algorithms. First, an adaptive trust-region Levenberg-Marquardt method (ATR-LM) based on the measured surface temperature is presented to estimate the unknown parameters in the heat transfer model. The corresponding experimental results indicate that the presented method can reduce the iteration time. Second, for the purpose of satisfying the real-time requirement, the stream parallel sparse Jacobian method (SP-SJ) is presented to solve the dynamic optimization problem associated with the PDEs. The corresponding experimental results show that the presented method exhibits satisfactory computational performance and achieves satisfactory control performance. INDEX TERMS MPC, PDEs, graphic processing unit (GPU), parallel computation, continuous casting.

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“…In fact, special attention has to be paid to the interface between the polymer and the calibrator where, due to the non-perfect contact between the two physical domains, a temperature discontinuity exists. Numerical methods such as the finite element [5,6,7,8] or finite difference hardly provide a good approximation of the cooling process since they require continuity across the contact boundary. Moreover, such methods do not guarantee local energy conservation at the cell level and may lead to unrealistic evaluation of the heat transfer process.…”

Section: Introductionmentioning

confidence: 99%

A novel heat transfer coefficient identification methodology for the profile extrusion calibration stage

Marques

Clain

Machado

et al. 2016

Applied Thermal Engineering

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A new method to compute heat transfer coefficients of the profile extrusion process calibration stage, in conjunction with a prototype calibration system [1], is proposed. The methodology involves two major ingredients: a numerical modeling code and a fitting procedure. The code, based on the Finite Volume Method, computes the steadystate solution for the heat transfer problem. The software carefully handles discontinuous solutions as well as discontinuities of the velocity and the material characteristics. Fitting procedure introduces alternative algorithms we have tested and assessed in [2]. A real case study demonstrates the advantages of using the new proposed methodology when compared with the previously applied [1].

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Estimation of heat transfer coefficients and heat flux on the billet surface by an integrated approach

Cited by 35 publications

References 29 publications

Estimation of Heat Flux in Two-Dimensional Nonhomogeneous Parabolic Equation Based on a Sufficient Descent Levenberg–Marquard Algorithm

Estimation of Heat Flux in Two-Dimensional Nonhomogeneous Parabolic Equation Based on a Sufficient Descent Levenberg–Marquard Algorithm

GPU-Based Model Predictive Control of Nonlinear Parabolic Partial Differential Equations System and Its Application in Continuous Casting

A novel heat transfer coefficient identification methodology for the profile extrusion calibration stage

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