The use of artificial intelligence technique for the optimisation of process parameters used in the continuous casting of steel

The productivity and quality of a continuous caster depend mainly on process parameters, i.e. casting speed, casting temperature, steel composition and cleanliness of the melt, water flow rates in the different cooling zones, etc. This work presents the development of an algorithm, which incorporates heuristic search techniques for direct application in metallurgical industries, particularly those using continuous casting process for the production of steel billets and slabs. This is done to determine the casting objectives of maximum casting rate as a function of casting constraints. These constraints are evaluated with the aid of a heat transfer and solidification model based on the finite difference technique, which has been developed and integrated with a genetic algorithm. The essential parts of continuous casting equipment, which must be subjected to monitoring, as well as a methodology of mathematical model and physical settlements in each cooling region, are presented. The efficiency of the intelligent system is assured by the optimisation of the continuous casting operation by maximum casting rate and defect-free products. This approach is applied to the real dimension of a steel continuous caster, in real conditions of operation, demonstrating that good results can be attained by using heuristic search, such as: smaller temperature gradients between sprays zones, reduction in water consumption and an increase in casting speed.     

Optimal control of cooling process in continuous casting of steel using a visualization-based multi-criteria approach

This paper is devoted to the application of a new visualization-based multi-criteria approach in an optimal control problem related to the cooling process in the continuous casting of steel. The purpose is to develop such a control that results in steel of the best possible quality, that is, minimizes the defects in the final product. Since the constraints describing technological and metallurgical requirements result in an empty set of the feasible controls of the cooling process, the aim of the study is to find a control that violates the constraints as little as possible. The problem is formulated as a multi-criteria optimization problem and the constraint violations play the role of selection criteria.Our approach is based on the application of both a nonlinear mathematical model of the cooling process that features a system of partial differential equations, and a new decision support technique, called Interactive Decision Maps technique, that uses the on-line visualization of the non-dominated frontier.     

Optimal Control of Continuous Casting by Nondifferentiable Multiobjective Optimization

A new version of an interactive NIMBUS method for nondifferentiable multiobjective optimization is described. It is based on the reference point idea and the classification of the objective functions. The original problem is transformed into a single objective form according to the classification information. NIMBUS has been designed especially to be able to handle complicated real-life problems in a user-friendly way.The NIMBUS method is used for solving an optimal control problem related to the continuous casting of steel. The main goal is to minimize the defects in the final product. Conflicting objective functions are constructed according to certain metallurgical criteria and some technological constraints. Due to the phase changes during the cooling process there exist discontinuities in the derivative of the temperature distribution. Thus, the problem is nondifferentiable.Like many real-life problems, the casting model is large and complicated and numerically demanding. NIMBUS provides an efficient way of handling the difficulties and, at the same time, aids the user in finding a satisficing solution. In the end, some numerical experiments are reported and compared with earlier results.     

MHD analysis in hydromagnetic casting process of clad steel slabs

A novel continuous casting process for clad steel slabs has been developed by suppressing the mixing of molten steels in the mold pool of continuous casting strand with a level DC magnetic field (LMF) installed in the mold. In this process, two molten steels of different chemical composition are discharged by two nozzles into the upper and the lower pools respectively to solidify in the outer and the inner layers as a clad steel slabs. The mechanism of separation into two layers has been elucidated by using a three dimensional MHD analysis. The numerical prediction employing Maxwell's equation, Ohm's law, and the turbulent flow model shows that the mixing of the different type of steels is suppressed by the electromagnetic dividing of the upper and the lower recirculating flows. The principle of the new process has also been verified by steel casting trials of the stainless-steel clad steel slabs with an 8-ton scale pilot continuous casting machine.     

直接配置法求解连续铸钢过程中的最优控制问题

利用描述连续铸钢过程二冷区喷水控制下钢的热传导的半离散化模型 ,我们构造一包含温度梯度约束的最优控制问题 .针对此最优控制问题 ,采用直接配置法进行数值求解 ,得出相应的近似最优控制 .     

Numerical solution to the optimal feedback control of continuous casting process

Using a semi-discrete model that describes the heat transfer of a continuous casting process of steel, this paper is addressed to an optimal control problem of the continuous casting process in the secondary cooling zone with water spray control. The approach is based on the Hamilton–Jacobi–Bellman equation satisfied by the value function. It is shown that the value function is the viscosity solution of the Hamilton–Jacobi–Bellman equation. The optimal feedback control is found numerically by solving the associated Hamilton–Jacobi–Bellman equation through a designed finite difference scheme. The validity of the optimality of the obtained control is experimented numerically through comparisons with different admissible controls. Detailed study of a low-carbon billet caster is presented.     

连续铸钢问题的有限元解法及参数优化

本文介绍连续铸钢二冷区钢坯温度分布的计算以及喷水量的优化，钢铁工艺对二冷区钢坯温度有一定要求，将其量化为求代价泛函最小问题，对状态方程用有限元模拟遗传算法求问题的最小解，确定最佳喷水方案。     

Multiple crane scheduling in a batch annealing process with no-delay constraints for machine unloading

In this work, we focus on the scheduling of multi-crane operations in an iron and steel enterprise for a two-stage batch annealing process. The first stage is the heating process, and the second stage is the cooling process. To start the heating (cooling) stage, a special machine called a furnace (cooler) must be loaded. The real constraints of no-delay machine unloading are defined as follows: once the heating (cooling) is completed, the furnace (cooler) must be unloaded by crane immediately. The goal is to schedule limited machines (furnaces and coolers) operated by multiple cranes to minimize the completion time of the last annealed coil (makespan). We formulate a mixed-integer linear programming model to address this problem. Certain feasible properties are identified to avoid crane conflicts and ensure that the machine unloading no-delay constraints are met. Based on these necessary conditions, we then present a heuristic algorithm with running time in connection with the number of cranes, coils and machines. A lower bound to the problem is also developed. Through theoretical analysis, we show the worst-case bound of our heuristic algorithm. The average performances of the solution approaches are computationally evaluated. The computational results show that the proposed heuristic algorithm is capable of generating good quality solutions.     

Parameters optimization of selected casting processes using teaching–learning-based optimization algorithm

In the present work, mathematical models of three important casting processes are considered namely squeeze casting, continuous casting and die casting for the parameters optimization of respective processes. A recently developed advanced optimization algorithm named as teaching–learning-based optimization (TLBO) is used for the parameters optimization of these casting processes. Each process is described with a suitable example which involves respective process parameters. The mathematical model related to the squeeze casting is a multi-objective problem whereas the model related to the continuous casting is multi-objective multi-constrained problem and the problem related to the die casting is a single objective problem. The mathematical models which are considered in the present work were previously attempted by genetic algorithm and simulated annealing algorithms. However, attempt is made in the present work to minimize the computational efforts using the TLBO algorithm. Considerable improvements in results are obtained in all the cases and it is believed that a global optimum solution is achieved in the case of die casting process.     

A novel Lagrangian relaxation approach for a hybrid flowshop scheduling problem in the steelmaking-continuous casting process

One of the largest bottlenecks in iron and steel production is the steelmaking-continuous casting (SCC) process, which consists of steel-making, refining and continuous casting. The SCC scheduling is a complex hybrid flowshop (HFS) scheduling problem with the following features: job grouping and precedence constraints, no idle time within the same group of jobs and setup time constraints on the casters. This paper first models the scheduling problem as a mixed-integer programming (MIP) problem with the objective of minimizing the total weighted earliness/tardiness penalties and job waiting. Next, a Lagrangian relaxation (LR) approach relaxing the machine capacity constraints is presented to solve the MIP problem, which decomposes the relaxed problem into two tractable subproblems by separating the continuous variables from the integer ones. Additionally, two methods, i.e., the boundedness detection method and time horizon method, are explored to handle the unboundedness of the decomposed subproblems in iterations. Furthermore, an improved subgradient level algorithm with global convergence is developed to solve the Lagrangian dual (LD) problem. The computational results and comparisons demonstrate that the proposed LR approach outperforms the conventional LR approaches in terms of solution quality, with a significantly shorter running time being observed.     

Efficiency of a DC magnetic field used for braking the flow within a continuous casting mould

The continuous casting technology provides about 90 percent of the world steel production. The application of DC magnetic fields in form of so-called electromagnetic brakes is considered for an effective flow control with substantial capabilities to improve the product quality or to enhance the productivity of the process. The main effect of the DC magnetic field is supposed to result in a uniform reduction of the maximum velocities in the discharging jet from the submerged entry nozzle and to damp violent turbulent fluctuations. However, the electromagnetic braking of such highly turbulent and complex flows is complicated phenomenon and has not been understood fully until now. We present numerical and experimental investigations focusing on the fluid flow in the continuous casting mould under the influence of a transverse magnetic field. Numerical calculations were performed using the software package CFX with an implemented RANS-SST turbulence model. the non-isotropic nature of the MHD turbulence was taken into account by specific modifications of the turbulence model. Corresponding experimental investigations were carried out at the mock-up LIMMCAST at HZDR. The comparison between our numerical calculations and the experimental results display a very well agreement. An important outcome of this study is the feature that the magnetic field does not provide a continuous reduction of the velocity fluctuations at the nozzle port. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Verified reduction of a model for a continuous casting process

The casting of metals is known to involve the complex interaction of turbulent momentum and heat transfer in the presence of solidification, and it is believed that computational fluid dynamical (CFD) techniques are required to model it correctly. Here, using asymptotic methods, we demonstrate that the key quantities obtained in an earlier CFD model for a particular continuous casting process – ostensibly for a pure metal, but equally for an alloy of eutectic composition – can be recovered using a much simpler model that takes into account just the heat transfer, requiring the numerical solution of a two-phase Stefan problem. Combining this with a more recent asymptotic thermomechanical model for the same continuous casting process, we postulate that it should be possible, with the additional help of algebraic manipulation, to reduce a model that takes into account turbulent momentum and heat transfer in the melt and the thermomechanics in the solid shell to one formulated in terms of only heat transfer, without adversely affecting model predictions.     

Simulation of capacity expansion and sequencing alternatives for a sheet metal producer

We present a simulation case study carried out for a make-to-order aluminium sheet producer located in Istanbul, Turkey. We are concerned with a subsystem of the factory consisting of continuous casting, cold rolling, and annealing processes. Two simulation models are developed: (1) a combined model for studying the casting process only; (2) a discrete event model for comparing capacity expansion alternatives and order sequencing rules in the subsystem. Operational characteristics of the real system and past data are extensively analysed for modelling and validation purposes. Capacity expansion and sequencing alternatives are evaluated in an experimental design setting with the objectives of satisfying the demand, balancing the process loads, and keeping the work-in-process inventory under control.     

3-D transient analytical solution based on Green’s function to temperature field in friction stir welding

Friction stir welding (FSW) is a relatively modern welding process, which not only provides the advantages offered by fusion welding methods, but also improves mechanical properties as well as metallurgical transformations due to the pure solid-state joining of metals. The FSW process is composed of three main stages; penetrating or preheating stage, welding stage and cooling stage. The thermal history and cooling rate during and after the FSW process are decisive factors, which dictate the weld characteristics. In the current paper, a novel transient analytical solution based on the Green’s function method is established to obtain the three-dimensional temperature field in the welding stage by considering the FSW tool as a circular heat source moving in a finite rectangular plate with cooling surface and non-uniform and non-homogeneous boundary and initial conditions. The effect of penetrating/preheating stage is also taken into account by considering the temperature field induced by the preheating stage to be the non-uniform initial condition for the welding stage. Similarly, cooling rate can be calculated in the cooling stage. Furthermore, the simulation of the FSW process via FEM commercial software showed that the analytical and the numerical results are in good agreement, which validates the accuracy of the developed analytical solution.     

连铸中的自由边界问题的边界元解法

本文应用边界元法求解钢铁生产中连铸工艺出现的自由边界问题。首先,对较一般的连铸过程的数学模型进行简化并给出相应的边界积分方程,以及叙述了用边界元法求解该问题的步骤。然后,我们给出了一个计算实例,并对该方法的收敛快慢、对初值的敏感性和对区域形状的适应性等问题进行了探讨。最后,针对一种简化的模型,将数值解与解析解进行比较,两者吻合较好。     

基于PCA-GA-SVM的火成岩分类方法研究

在地质科学中,正确的岩石分类有助于研究岩石的成因、形成条件、演化过程和工程设计等.由于地质条件的多样性、变异性及复杂性,人们很难对岩石样本进行准确的分类.通过主成分分析法(PCA)从影响火成岩分类的众多氧化物评价指标中提取出主成分,用遗传算法(GA)优化支持向量机参数,并采用支持向量机方法(SVM)对实际火成岩公开数据进行训练,建立了火成岩岩石分类的PCA-GA-SVM模型,同时结合火成岩实际数据将预测结果和基于Levenberg-Marquardt算法改进的BP神经网络模型(LM-BP)的预测结果做了比较.结果表明:基于PCA-GA-SVM模型得到的火成岩分类预测结果精度较LM-BP神经网络有很大的提高,与实际分类相符,有广泛的应用前景.     

Recent progress on contactless inductive flow tomography

The contactless inductive flow tomography (CIFT) is a technique to reconstruct the velocity in electrically conducting melts using magnetic fields. One of its application could be the velocity reconstruction in the mould of the continuous casting process. In this paper, we present the numerical investigation and first measurements of the induced magnetic field taken in our lab on a small model of a continuous casting mould. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On convergence of a discrete problem describing transport processes in the pressing section of a paper machine including dynamic capillary effects: One-dimensional case

This work presents a proof of convergence of a discrete solution to a continuous one. At first, the continuous problem is stated as a system of equations which describe the filtration process in the pressing section of a paper machine. Two flow regimes appear in the modeling of this problem. The model for the saturated flow is presented by the Darcy’s law and the mass conservation. The second regime is described by the Richards’ approach together with a dynamic capillary pressure model. The finite volume method is used to approximate the system of PDEs. Then, the existence of a discrete solution to the proposed finite difference scheme is proven. Compactness of the set of all discrete solutions for different mesh sizes is proven. The main theorem shows that the discrete solution converges to the solution of the continuous problem. At the end we present numerical studies for the rate of convergence.     

FEM analysis for residual stress prediction in hot rolled steel strip during the run-out table cooling

With the increasing demand of higher quality hot rolled strips, flatness defects occurred on the strips during the cooling process on the run-out table have received significant attention and should be considered in the online shape control model. Non-uniform temperature distribution and cooling across the strip width are the main reasons why the strip becomes unflatten after cooling process although the strip is rolled flat at the finishing mill. A thermal, microstructural and mechanical coupling analysis model for predicting flatness change of steel strip during the run-out table cooling process was established using ABAQUS Finite Element Software. In this model, Esaka phase transformation kinetics model was employed to calculate the phase transformation, and coupled with temperature calculation by means of the user subroutine program HETVAL. An elasto-plasticity constitutive model of the material, in which conventional elastic and plastic strains, thermal strain, phase transformation strain and transformation induced plastic strain were taken into account, was derived and realized using the user subroutine program UMAT. The conclusion that the flatness of the steel strip will develop to edge wave defect under the functions of the different thermal and microstructural behaviors across strip width direction during the run-out table cooling procedure was acquired through the analysis results of this model. The calculation results of this analysis model agree with the actual measurements and observation, therefore this model has a high accuracy. To better control the flatness quality of hot rolled steel strip, the shape compensation control strategy of slight center wave rolling is proposed based on the analysis result. This control strategy has been verified by actual measurements, and applied in actual production.     

Economic and economic-statistical design of a chi-square chart for CBM

In this paper, the economic and economic-statistical design of a χ² chart for a maintenance application is considered. The machine deterioration process is described by a three-state continuous time Markov chain. The machine state is unobservable, except for the failure state. To avoid costly failures, the system is monitored by a χ² chart. The observation process stochastically related to the machine condition is assumed to be multivariate, normally distributed. When the chart signals, full inspection is performed to determine the actual machine condition. The system can be preventively replaced at a sampling epoch and must be replaced upon failure; preventive replacement costs less than failure replacement. The objective is to find the optimal control chart parameters that minimize the long-run average maintenance cost per unit time. For the economic-statistical design, an additional constraint guaranteeing the occurrence of the true alarm signal on the chart before failure with given probability is considered. For both designs, the objective function is derived using renewal theory.