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Statement of novelty
In this paper, an improved genetic algorithm is designed for the water consumption of the secondary
cooling zone based on the heat transfer model of the off-line bloom caster. This algorithm coupled
with heat transfer model and metallurgical criteria, added dynamic coding method and self-adapting
mutation on the original genetic algorithm, can increase the simulated water distribution adaptively,
improve the efficiency of the simulation process and the convergence ratio, and reduce the reheating
between the zones. In the experimental, it is found that the water consumption after optimization
reduced by 2%, compared to that of before optimization. The maximum surface cooling rate and the
rate of temperature rise reduced, and the equiaxed rate increases. Then a function is built for
explaining the relationship between casting speed and water distribution, which can be the direction
to control the cooling system in manufacturing process. So far, to our knowledge, although a lot of
intelligent algorithms are used to optimize the secondary cooling conditions, but there are few
reports on the simulation of this process with the developed algorithms. In this study, the improved
genetic algorithm to optimize the secondary cooling water distribution is concerned, and the results
show that the developed algorithm can save more water consumption with lower reheating and
cooling rates.
The optimization of the secondary cooling water distribution with improved
genetic algorithm in continuous casting of steels
Y.Y. Zhai
1
; Y. Li
*1
; B.Y. Ma; Z.Y. Jiang
2
1: School of Materials and Metallurgy, Northeastern University, Shenyang 110819, China
2: School of Materials and Mechatronic Engineering, University of Wollongong, Wollongong 2500, Australia
*Corresponding Author: liying@mail.neu.edu.cn (Y. Li)
Abstract
An improved genetic algorithm is presented for the water consumption of the secondary cooling
zone based on the heat transfer model of the off-line bloom caster. This study is to control the
existing cooling system and the steel casting practice in order to produce steel with best possible
quality. The fitness function of IGA (improved genetic algorithm) is founded according to the
metallurgical criteria. This algorithm coupled with heat transfer model and metallurgical criteria,
added dynamic coding method and self-adapting mutation on the original genetic algorithm, can
increase water distribution adaptively and improve the process efficiency. The simulation results of
T91 bloom show that the optimized distribution reduced by 2% of water consumption comparing to
that of before optimization. The maximum surface cooling rate and the rate of temperature rise
reduced, and the equiaxed rate increases. The function is built for explaining the relationship
between the casting speed and water distribution.
Keywords: Continuous casting, Secondary cooling, Water distribution, Genetic algorithm,
Self-adapting mutation
Introduction
Continuous casting technology, a main method in steelmaking industry, has been rapidly
developed in recent years. In this process, liquid steel from tundish is poured into mold to form
billets, blooms or slabs. Since the cooling conditions at the mold and air cooling zone are relatively
stable for a given caster, with only the secondary cooling zone (SCZ) capable of being adjusted
within a wide range, the quality and output of casting is closely related to the SCZ. Given that the
cooling process removes the superheat and the latent heat of fusion at the solidification front, the
main cause of internal crack, surface crack and center segregation is the unreasonable secondary
cooling structure. These defects should be avoided for the sake of competitiveness in manufacturing.
Thus, it is critical to control and optimize the secondary cooling in the whole casting process. It is
not feasible to conduct a lot of experimental trials to calculate the influence of different operational
parameters due to economic reasons. Mathematical models and optimization algorithms are useful
tools for the optimization of water distribution in the SCZ. The heat transfer model is the foundation
of the optimization of the SCZ. This model is an initial boundary problem of partial differential
equation (PDE). It cannot be solved using analytical method and also the computational time
solution is too long. In the secondary cooling process, the value function of metallurgical criterion is
complicated, and the efficiency of general optimization method is low.
The traditional method for solving the optimization problem of the secondary cooling process is
complex nonlinear optimization problem with poor efficiency. Intelligent optimization algorithm
has been rapidly developed in secondary cooling water distribution, which is an important factor
affecting the quality of the bloom. The improper distribution of water will make surface cracks, the
crack in the middle, the center of the crack, the crack corner, bulging and so on. They will seriously
affect the production and product quality finishing process. A number of intelligent optimization
methods used in the secondary cooling process have been developed rapidly. Lally et al. used an
optimization method with heat flow and solidification model to determine the parameters that
maximize the quality of final product of billet and slab casters [1-2]. Santos et al. developed an
intelligent optimization method of genetic algorithm (GA) with finite difference heat transfer model
based on the metallurgical criterion and maximum withdraw speed to control the secondary cooling
zone of slab continuous casting, and heuristic search algorithms were used to minimize the
consumption water and the smooth temperature gradient in the secondary cooling process [3-5]. A
model optimization of billet continuous casting steel secondary cooling with an implicit enthalpy
mathematical solidification was developed to calculate three dimensional and stationary temperature
fields and to decrease center segregation [6]. An approach based on Hamilton-Jacobi-Bellman
equation satisfying the value function has been used to the optimal problem of the SCZ with water
spray control of a low-carbon billet caster [7]. Chakraborti et al. solved the pertinent transport
equations in the mold of continuous caster using a finite volume approach with genetic algorithms.
The results showed significant improvements of the casting velocity and the solidified shell
thickness [8]. Meng et al. proposed an enhanced particle swarm optimization algorithm to optimize
the secondary cooling of billet, which has been reported with good convergence rate and
convergence precision [9].
This study presents an optimization model for controlling the water intensities of the water in the
SCZ of bloom caster. Considering the simulation condition, a heat transfer model of bloom caster is
applied using an analytical solution for the temperature profile. Then an improved genetic algorithm,
which contains byte type dynamic coding method and self-adapting mutation, is used to code the
secondary cooling water distribution. The procedure corresponds to the fitness function determined
by highly conflicting technological and metallurgical requirements. These methods increase the
distribution adaptability and improved the efficiency, comparing with the traditional optimization
methods of solving multi-objective optimization and other non-linear problems. In the present study,
the secondary cooling water distributions are optimized in different casting speeds, and then the
function of second cooling optimal water distribution and casting speed is obtained. This model
improved the equiaxed rate of the bloom and reduced the maximum surface cooling rate and the rate
of temperature rise. As a result, the optimized bloom has better quality.
The Mathematical Optimization Model
The state system used in the present study is a two-dimensional heat transfer model in which the
heat conduction to the withdrawal direction is neglected. It is because that the withdrawal rate of
steel is relatively high and the thermal conductivity is low. The heat transfer model is developed and
applied to calculate the temperature distribution and solid shell thickness profile of bloom
continuous casting. It is the foundation of the optimization of secondary cooling zone. The
optimization module of the water distribution of secondary cooling zone using Genetic Algorithm is
established according to the metallurgical criteria for bloom and target temperature controlling
principle.
Suppose that the cross section of the bloom is a rectangular, Ω=[0, a]×[0, b], which is moving
along the z direction with a constant speed. Let T(x, y, t) be the temperature at the point (x, y, t).
Then T satisfies the following nonlinear heat conduction equation with boundary conditions [10].
