Proactive and reactive scheduling of the steelmaking and continuous casting process through adaptive robust optimization

Intelligent Optimization-Based Production Planning and Simulation Analysis for Steelmaking and Continuous Casting Process

Steel-making and continuous casting (SCC) processes are considered the main bottlenecks in the steel industry. We consider planning and scheduling problems in SCC processes and provide an overview of the literature with our commentary. The planning problem has as goal to create out of customer orders production units for the various production processes. The scheduling problem assigns these production units to the production facilities over different time intervals. We review a large number of planning and scheduling papers and propose two basic models for the planning and the scheduling problems that incorporate the most common and essential features. We describe for each problem the respective constraints and objectives as well as the practical implications in an actual production environment. We also analyse the methodologies used in their solutions, including decomposition strategies. In the last section, we present the conclusions of our survey and propose new research directions.

An Efficient Augmented Lagrange Multiplier Method for Steelmaking and Continuous Casting Production Scheduling

The twin-roll strip casting process is a typical steel-strip production method which combines continuous casting and hot rolling process. The production line from molten liquid steel to the final steel-strip is shortened and the production cost is reduced significantly compared to the conventional continuous casting. The twin-roll strip casting process can produce 1-5 mm thin steel strip directly from the molten steel. Furthermore, since the strip casting process has high cooling rate, it can improve the mechanical properties of steel (Liang et al. 1997; Cook et al. 1995). Usually, the molten steel level is controlled at a preset desired level to monitor the normal strip casting operation. During the roll casting process, once the molten metal contacts with the rotating rolls, a thin solidification shell is formed on the surface of each roll. The shell thickness gradually grows from each roll surface, finally contacts with each other and weld together at a position around the roll exit, called the solidification final point. If the molten metal level is higher than the specified value, the solidification final point will occur at a point above the roll exit. That will result in heat cracking and damage to the cooling roll surface in addition to material structural abnormalities of the steel strip. If the molten metal level is lower than the desirable value, the solidification final point will occur at a point below the roll exit. The steel strip surface will have inferior quality due to the breakout and oxidation. Hence, the molten metal level is an important process control parameter to guarantee the solidification final point and rolling strip quality. The molten steel level must maintain within a specific range during the full casting process except the initial startup operating mode by filling the molten steel into the twin roll cylinders from the tundish. Since the strip casting process has nonlinear dynamics uncertainty and coupled behaviors, accurate molten steel level control problem is still an important research topic to guarantee the steel strip quality. Graebe et al. (1995) verified the dynamic model and various nonlinearities appearing in the continuous casting process and proposed different issues that had to be solved in controller design. Hesketh et al. (1993) applied an adaptive control strategy for the mold level control of a continuous steel slab casting. Hong et al. (2001) investigated the modeling and control problem of a twin-roll strip caster. They analyzed different critical dynamics, including molten steel pool leveling, and developed a two-level

Near Optimal Scheduling of Steel-making and Continuous Casting Process Based on Charge Splitting Policy

This article presents a new model to handle the cast break problem caused by small daily disruptions in the processing time of the steelmaking and continuous casting (SCC) production process. In this model, the exact distribution of the uncertain parameters is unknown, and support set, mean, and covariance information is used to describe the uncertain processing time. The problem aims to determine the assignments, sequences, and time points of the charges to be processed on corresponding machines. The main goal is to minimize the expected value of the production objective while reducing the number of cast break occurrences. The problem is solved in two steps. First, a subproblem is developed by fixing the sequences and the assignments of the charges. This subproblem is formulated as a distributionally robust chance-constrained (DRCC) model, in which the constraints are established with certain probabilities even when the uncertain processing times are in their worst cases. A dual approximation method is proposed to convert the model into a semidefinite programming problem so that it can be solved by standard solvers. Additionally, a linear programming approximation method is used to accelerate the solving procedure. A Tabu search algorithm incorporated with a speed-up strategy is also designed to determine the assignments and sequences of the charges. Both simulated data generated from different distributions and actual production data are used to test the efficacy of our model. Results of the numerical experiments show that the schedule obtained from the DRCC model is more robust, i.e., it causes fewer cast breaks than the nominal schedule obtained from a deterministic model.

A continuous ingot casting process was developed to improve the productivity of ingot fabrication. A supplemental charge method in which uranium dendrites were additionally added into molten uranium was introduced for the first time, and a tilting system of a melting crucible to mold was developed. The feasibility of these processes was confirmed by a uranium melting test at the laboratory scale, successfully obtaining a uranium ingot in about 4.6 kg. Based on the results, we scaled up the ingot casting processes at the engineering scale. A rotating continuous feeder was installed for the ceaseless feeding of the dendrites into molten uranium. The tilting system and eight mold crucibles on a turn-table were adopted. The operability of the continuous ingot casting process at the engineering scale was successfully confirmed by a melting test of copper. We consider that the engineering scale equipment can cast above a 50 kg U/batch with the continuous casting processes.

In this paper, for the first time, using a three-dimensional (3D) thermo-elastoplastic model, the effects of cooling rate and casting speed on the continuous casting (CC) process are studied. Some significant parameters such as solidified shell thickness, mushy zone thickness, metallurgical length, and residual stress in the CC process under different cooling rates and casting speeds are investigated. All analyses are performed using the meshless local Petrov–Galerkin (MLPG) method. The effective heat capacity method is employed to simulate the phase change process. The von Mises yield function with isotropic hardening is used to simulate the stress state, and material parameters are assumed as temperature dependent. To demonstrate the accuracy and efficiency of the present 3D MLPG method in thermo-mechanical analysis of highly nonlinear solidification problems, the obtained results are compared with an exact analytical solution. Several numerical examples for different cooling rates and casting speeds are provided to investigate their effects on the CC process parameters, as well as on the stress, displacement, and temperature fields induced in the cast material. The results from the analyses can be very useful for the optimal design of CC processes.

A Rescheduling Method for Operation Time Delay Disturbance in Steelmaking and Continuous Casting Production Process

In the steelmaking and continuous casting (SMCC) production process, the operation time delay often occurs which may lead to planned casting break or processing conflict so that the initial scheduling plan becomes unrealizable. Existing rescheduling methods with disturbances firstly classify the disturbances according to the disturbance type and disturbance quantity only by artificial experience or rules, and then directly adjust initial scheduling plan with corresponding rescheduling method. Those methods don’t analyze the influence degree of disturbances to the initial scheduling plan in detail, so the adjustment degree of initial scheduling plan is always too greater, which leads to the poor continuity and stability of initial scheduling plan. In this paper, the relation among operation time delay, planned casting break and processing conflict is deeply analyzed. Then a novel prediction method for abnormal condition of scheduling plan with operation time delay disturbance in SMCC production process is proposed including disturbance identification of operating time delay based on event-driven mechanism, analysis on charges based on reachability matrix, analysis on influence degree of disturbance and abnormal condition decision of initial scheduling plan. As a result, the real-time application shows that the proposed prediction method can timely and accurately predict the abnormal condition of the scheduling plan with operation time delay disturbance in SMCC production process, which can only adjust the affected charges that must to be rescheduled in the initial scheduling plan and reduce the frequency of complete rescheduling. The initial scheduling plan can also maintain the good continuity and stability.

The paper presents the results of physical modelling aimed at determining the cracking susceptibility of the selected steel grade under conditions characteristic of the continuous casting process. The material used for investigation was steel grade S355J2G3 [1]. For a study on the physical modelling of the continuous steel casting process, the GLEEBLE 3800 [2, 3], a metallurgical process simulator, was employed. The obtained results allowed establishing conditions for a continuous steel casting process that could cause cracks to form in the material being cast. Research on one of technological conditions for steelworks was carried out taking into account the problem of cracking during rolling in the initial group of the bar rolling mill.

A particle swarm approach for optimization of secondary cooling process in slab continuous casting

Multistage Adaptive Optimization for Steelmaking and Continuous Casting Scheduling under Processing Time Uncertainty

The Hazelett continuous casting and rolling process represents a leading-edge production method for cold-rolled aluminum sheet and strip billets in the world. Its solidification microstructure significantly influences the quality of billets produced for cold rolling of aluminum sheets and strips. In this study, employing the CAFE (Cellular Automaton-Finite Element) method, we developed a coupled computational model to simulate the solidification microstructure in the Hazelett continuous casting process. We investigated the impact of nucleation parameters, casting temperature, and continuous casting speed on the microstructural evolution of the continuous casting billet. Through integrated metallographic analyses, we aimed to elucidate the controlling mechanisms underlying the Hazelett continuous casting process and its resultant microstructure. The results demonstrate that the equiaxed rate of grains increases with an increase in nucleation density, and the grain size decreases under constant cooling strength. With other nucleation parameters held constant, the grain size decreases as undercooling increases, and the columnar crystal zone expands. The nucleation density of the Hazelett continuous casting aluminum alloy has been determined to range between 1011 m-3 and 1013 m-3, and the undercooling ranges between 1 °C and 2.5 °C. The solidified grain structure can be controlled between 35 μm and 72 μm. The grain size of the continuous casting billet increases with an increase in pouring temperature and decreases as the casting speed increases. Elevating the pouring temperature positively impacts the fraction of high-angle grain boundaries and promotes the dendritic to equiaxed grain transition. Moreover, there exists potential for further optimization of continuous casting process parameters.

The production scheduling of steelmaking and continuous casting(SCC) is the key to eliminate waste for steel enterprise, and its accuracy and efficiency is determined by modeling and solving algorithm. In this paper, multi-object optimization model of SCC is established to realize the target of punctual casting, no conflict between equipment for one furnace and maximum operating start time of converter, and a new algorithm based on cuckoo search algorithm(CSA) is proposed to solve it. To minimize solve duration, bird's nest coding that is object to constrain of unique equipment and process sequence is proposed. Industry production data are applied to validate modeling and solving algorithm, showing that proposed algorithm will solve the scheduling model in 7.594 seconds, which meets the requirement that management and scheduling should be solved in 60 seconds with high accuracy. In general, proposed CSA is feasible and effective in solving problems of SCC.