Application of artificial neural networks for the prediction of roll force and roll torque in hot strip rolling process

This paper introduces an artificial neural network (ANN) application to a hot strip mill to improve the model’s prediction ability for rolling force and rolling torque, as a function of various process parameters. To obtain a data basis for training and validation of the neural network, numerous three dimensional finite element simulations were carried out for different sets of process variables. Experimental data were compared with the finite element predictions to verify the model accuracy. The input variables are selected to be rolling speed, percentage of thickness reduction, initial temperature of the strip and friction coefficient in the contact area. A comprehensive analysis of the prediction errors of roll force and roll torque made by the ANN is presented. Model responses analysis is also conducted to enhance the understanding of the behavior of the NN model. The resulted ANN model is feasible for on-line control and rolling schedule optimization, and can be easily extended to cover different aluminum grades and strip sizes in a straight-forward way by generating the corresponding training data from a FE model.     

A Nonlinear Control Concept for Rolling Mills

This contribution is concerned with the nonlinear control of a temper rolling mill based on the exact input/output linearization method. The considered subsystem of the temper rolling plant consists of a four‐high mill stand with a hydraulic adjustment system, and bridle rolls in the entry and the exit section. The demand on the temper rolling process is to establish a certain elongation of the steel strip under the action of the roll force and certain predefined backward and forward strip tensions in order to achieve the desired material characteristics and surface properties of the rolled product. The nonlinear control concept to be presented is characterized by the fact that the torques of the bridle rolls are intended as control inputs for the elongation and master speed control, whereas the hydraulic adjustment system and the main mill drive are used to take effect on the strip tensions. After a brief review of the mathematical model of the mill we will focus on the multi‐input nonlinear tension control.     

Optimization model of recrystallization hot rolling of titanium-vanadium steels

An optimization model was built based on the data of a pilot-scale (4.5 MN load, 225 KW power capacity) rolling mill to minimize the austenite grain sizes of Ti–V steels, which prevail at the instant of completion of the static recrystallization during hot rolling. A computer program developed for this optimization model was run for the rolling schedule, which is designed according to the complete recrystallization case. An energy optimization model developed previously was applied to different rolling schedules. The grain size optimization results demonstrate the effectiveness of these modelling approaches in terms of final grain size, final plate thickness, measured and computed roll force and torque values for both the design of the thermomechanical schedules which produce plate with fine-grained microstructures, high strength, and notch toughness and the temperature-reduction schedules of conventional controlled rolling.     

LP modelling of the finishing hot rolling programme for low carbon steel coils

In this paper a mathematical model was developed to optimize the finishing rolling of hot rolled coils by increasing the productivity of the rolling programme, to help achieve the required level of quality assurance and to facilitate production planning and control in the hot rolling mill. A brief account of the technological and planning aspects of the hot rolling processes and mills relevant to strip steel is given. Linear (mixed integer) programming is used to formulate the objective function and the various types of constraints of the model. The model takes into consideration, the general aspects pertinent to hot rolling of low carbon steel and the characteristics of the hot rolling mills as stipulated by the operational codes and guidelines of the relevant establishments. Owing to the flexibility offered by linear programming the model can incorporate any modifications and/or additional requirements, if any, in case of other types of steel and/or other types of mills. The full modelling of the problem required the incorporation of some zero/one variable constraints. Owing to the complexity involved and the need to keep the model as simple as possible, it was decided to exclude these constraints and deal with them externally. HYPER LINDO PC was used to solve the programme. Using available data, in the case under consideration the model showed astonishing results in achieving the objectives. Taking into account the effect on the overall productivity as well as quality improvement, the investigation showed that a net improvement in conforming output to the effect of around 43%, could have been obtained had the model been used in the case under consideration.     

An integrated thermal model of hot rolling

During the heavy plate rolling process, different production steps, i.e., roll passes, descaling passes, and air cooling periods, influence the temperature evolution of the plate. All these relevant aspects are covered by a one-dimensional thermal model proposed in this paper. Experiments were conducted in a rolling mill under realistic rolling conditions to parametrise and validate the model. Using pyrometer measurements, a simple model adaption strategy is developed, which can cope with uncertainties in the initial temperature profile. The model provides accurate predictions of the temperature evolution of the plate during the whole rolling process from the plate’s exit of the furnace to the last pass. Thus, it can be used for scheduling the production process. Based on the model, an observer can be designed.     

基于智能控制的高速线材轧机水冷控制系统优化

针对武汉钢铁集团公司大型轧钢厂当前在高速线材生产线中存在的水冷控制系统可靠性差,轧线温度波动范围大等问题,应用智能计算理论及方法对上述工业控制系统进行系统辨识、建模以及优化.分析比较了基于梯度下降搜索BP算法、径向基函数网络、Levenberg Marquardt BP算法的前馈神经网络对SMS水冷系统的逼近精度、训练速度.研究了采用Levenberg-Marquardt BP算法的前馈神经网络在样本集和测试集上的表现,建立了基于Levenberg-Marquardt BP算法的前馈神经网络水冷控制系统模型.解决了高速线材水冷控制系统可靠性,温度控制精度问题.     

Switched system modeling and robust steering control of the tail end phase in a hot strip mill

In this article, a robust steering control for the last phase of the rolling process in a hot strip mill is proposed. This phase, called tail end phase, may be modelled as a linear switched system. The switchings make the system unstable and the task of the tail end steering control consists in guaranteeing the safety of the industrial plant. The system involves a two time scales dynamics. Hence, the singular perturbation method is used in order to design the control law. The controller has to take into account the physical variations of the rolled products and an uncertainty in the switching time. Results concerning the ArcelorMittal hot strip mill of Eisenhüttenstadt are presented.     

Feedforward Control Strategies for Hot Rolling in a Reversing Plate Mill

This contribution is devoted to a new feedforward control concept for the thickness control in a hot rolling mill. The core of this concept is an accurate forward slip model for the calculation of the entry thickness profile. This forward slip is derived by means of the fundamental equations of hydrodynamics for a viscoplastic material in the roll gap. The proposed control strategy advantageously uses the additional information of the rolled plate in form of this entry thickness profile. Simulated and measured data demonstrate the feasibility of the forward slip model and the control concept. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Using a Facility Location Algorithm to Determine Optimum Cast Bloom Lengths

The dimensions of a bloom, which is a rectangular piece of steel, are critical for efficiently and effectively rolling the bloom into a finished structural shape (I-beam) for sale to the customer. To achieve maximum productivity and yield, the bloom size (thickness, width and length) to be rolled on a finishing mill into a structural shape must be determined by steel deformation experts. Suppose, for a particular finishing mill, these ‘rolled' blooms are all produced from a ‘cast' bloom of the same cross-section but with many different lengths. It is necessary to consolidate the many ‘cast' bloom length-metallurgical grade combinations to a number that can be managed by the casting operation and bloom stockyard without significantly impacting productivity and yield. An uncapacitated facility location problem formulation and algorithm were used to solve this problem. The way in which this approach was used to solve a real-world application is discussed.     

Thermal analysis of hot strip rolling using finite element and upper bound methods

Thermal analysis of hot rolling process has been studied in this work. A finite element method has been coupled with an upper bound solution assuming, triangular velocity field, to predict temperature field during hot strip rolling operation. To do so, an Upwind Petrov–Galerkin scheme together with isoparametric quadrilateral elements has been employed to solve the steady-state heat transfer equation. A comparison has been made between the published and the model predictions and a good agreement was observed showing the accuracy of the proposed model.     

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.     

Microstructure analysis on IN 718 alloy round rod by FEM in the hot continuous rolling process

Based on physical metallurgy rules and experiential equations, models for microstructure analysis on IN 718 alloy in the round rod hot continuous rolling process has been developed using the finite element method (FEM) on the software ANSYS/LS-DYNA. The dynamic and metadynamic recrystallization models in and after deformation, the grain growth models in the compensated reheating process for IN 718 alloy are regressed, and corresponding processes are involved in these models. For a real rolling practice, the calculated central grain sizes were examined and are in good agreement with the measured ones. The element in the center of the workpiece is a typical one possessing the maximum of the effective strain, the temperature and the grain size in the rolling process. In the hot continuous rolling process, the relationship between the final grain size of the typical element and the inlet velocity of the first stand has been regressed by FE analysis, and the lower rolling speed is beneficial to the grain refinement.     

A consistent implementation for inelastic materials in an ALE formulation for steady state rolling contact

The numerical analysis of rolling contact for rubber materials is a challenging task, especially due to the many nonlinearities inherent to the material, large deformations, friction, and energy dissipation, among others. Industrial applications can be found in ball bearings, rollers, and most commonly in tires of vehicles, applications where reliable numerical simulations lead to the improvement of durability, performance and safety. While a transient analysis stands as a practical and powerful tool for the simulation of rotating bodies, the large amount of computational resources required represents its biggest disadvantage. An alternative frequently used lays in a steady state simulation by means of an Arbitrary Lagrangian Eulerian (ALE) formulation, where the rotational velocity and axial loads are assumed to remain constant. Within this framework, the reference configuration is neither attached to the material particles nor fixed in space and special attention should be paid to the history variables of inelastic materials. In this work, a viscoelastic material model is implemented in an in-house finite element code, based on a generalized Maxwell model. The implementation takes into consideration the contribution of all elements connected in circumferential direction and a consistent linearization is made for each of them, leading to an assembled stiffness matrix with more non-zero values than a standard one. This approach is combined with smeared reinforcement embedded in base elements. The reinforcing layers are described by a hyperelastic material model, providing additional advantages for the modeling and simulation of reinforced rollers and tires. Numerical results for different examples show the capabilities of this implementation and the efficiency of the numerical algorithms is discussed. Important remarks and an outlook for further research concludes this presentation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

钢筋混凝土旧工业厂房结构加固方案优选

当前人们选择旧工业厂房结构加固方案效率低下,且所考虑的因素较为片面,为了全面、高效地解决这一问题,通过综合考虑安全性、经济性、时间性、可行性和适用性等因素,以加固效果显著的工程案例为标准,以全面的18个参数为评价指标,构建了一种基于蛛网面积相似和形状相似的结构加固方案优选模型。该模型中首先运用熵权法确定18个指标权重,并将参数值归一化处理,随后运用Python计算蛛网结构相似度,检索出与目标范例最为相似的源范例。最后以结构加固效果显著的工程为例,验证了该模型能有效减少主观误差,具有较强的实用性,并以此模型优选出了某轧钢厂房结构加固方案。     

Posterior simulation via the exponentially tilted signed root log-likelihood ratio

We explore the use of importance sampling based on exponentially tilted signed root log-likelihood ratios for Bayesian computation. Approximations based on exponentially tilted signed root log-likelihood ratios are used in two distinct ways; firstly, to define an importance function with antithetic variates and, secondly, to define suitable control variates for variance reduction. These considerations give rise to alternative simulation-consistent schemes to other importance sampling techniques (for example, conventional and/or adaptive importance sampling) for Bayesian computation in moderately parameterized regular problems. The schemes based on control variates can also be viewed as usefully supplementing computations based on asymptotic approximations by supplying external estimates of error. The methods are illustrated by a censored regression model and a more challenging 12-parameter nonlinear repeated measures model for bacterial clearance.     

混合优化RBF-BP网络的板形缺陷识别

针对传统板形模式识别方法存在精度低、鲁棒性弱的问题,提出了一种混合优化RBF-BP组合神经网络板形模式识别方法。首先利用自组织映射网络(SOM)对样本聚类,利用聚类后的网络拓扑结构确定RBF的中心,并计算RBF的宽度,克服了传统聚类算法随机选取中心导致聚类结果不稳定的问题。然后利用遗传算法(GA)良好的全局搜索能力优化整个网络的权值。RBF-BP组合神经网络是由一个RBF子网和一BP子网串联构成的,该网络同时具备BP神经网络能较好地预测未知样本的能力以及RBF神经网络的逼近速度快的优点。并以某900HC可逆冷轧机板形识别为应用背景,在MATLAB2010a环境下进行仿真实验,结果表明混合优化RBF-BP组合神经网络的板形模式识别方法能够识别出常见的板形缺陷,提高了板形缺陷识别精度并具有较好的鲁棒性,可以满足板带轧机高精度的板形控制要求。     

Scheduling a hot rolling mill

This paper presents a heuristic algorithm to schedule a hot rolling mill in the aluminum industry. One problematic issue is the tight coupling between the homogenizing furnaces and the mill, which needs to be integrated into the heuristic design. The latter also takes into account standard technological constraints like alloy hardness transitions, roll wear, homogenization code compatibilities and width transitions. The objective is to minimize the idle time on the mill and penalties for soft constraint violations related to production quality. The heuristic is divided into two phases. First, batches of ingots are constructed for the furnaces. These batches, called blocks, are then sequenced on the mill. Numerical results are reported on test instances derived from real-world data.     

An Eulerian‐Lagrangian Concept for the Numerical Simulation of Flat Steady‐State Hot Rolling Processes

For the finite element analysis of stationary flat hot rolling processes, a new and efficient mathematical model was developed. The method is based on an intermediary Eulerian‐Lagrangian concept, where an Eulerian coordinate is employed in the rolling direction, while Lagrangian coordinates are used in the direction of the thickness and width of the strip. This approach yields an efficient algorithm, where the time is eliminated as an independent variable in the steady‐state case. Further, the vector of independent field variables consists of a velocity component in Eulerian and of displacement components in Lagrangian directions. Due to this concept, the free surface deformations can be accounted for directly and the problems encountered with pure Eulerian or Lagrangian models now appear with reduced complexity and can thus be tackled more easily. The general formalism was applied to different practical hot rolling situations, ranging from thick slabs to ultra‐thin hot strips. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Selective proper orthogonal decomposition model reduction for forming simulations

Robot-based incremental sheet metal forming is a cost-effective and flexible method for prototype and low batch size production. The simulation of such processes is very challenging and elaborate from the computational point of view. To reduce the computational effort model reduction techniques such as proper orthogonal decomposition (POD) can be applied. But the reduction of highly non-linear models in solid mechanics for example forming simulation still leads to problems of efficiency and accuracy. Therefore, the aim of this paper is to present an alternative way to use POD for forming processes. The presented selective POD (SPOD) method is used to split the model into two domains depending on the degree of plastic strain. Only the domain with approximately linear elastic behavior will be reduced by using POD. Utilizing the SPOD method for the example of forming a horizontal flute reduces the computational time up to around 30 per cent. High accuracy with approximation errors smaller than one per mill is achieved. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)