Multi-objective optimization of rolling schedule based on cost function for tandem cold mill

In terms of tandem cold mill productivity and product quality, a multi-objective optimization model of rolling schedule based on cost fimction was proposed to determine the stand reductions, inter-stand tensions and rolling speeds for a specified product. The proposed schedule optimization model consists of several single cost fi.mctions, which take rolling force, motor power, inter-stand tension and stand reduction into consideration. The cost function, which can evaluate how far the rolling parameters are from the ideal values, was minimized using the Nelder-Mead simplex method. The proposed rolling schedule optimization method has been applied successfully to the 5-stand tandem cold mill in Tangsteel, and the results from a case study show that the proposed method is superior to those based on empirical formulae.

Application of Crown-Flatness Vector Analysis in Plate Rolling Schedule

A simple plate crown model was introduced,and the crown-flatness vector analysis method was analyzed.Based on the plate rolling technology,the rolling schedule design of elongation phase is divided into three steps.First step is to calculate the reductions of first pass of elongation making full use of the mill capability to decrease the total pass number.The second step is to calculate the pass reduction for the last three or four passes to control crown and flatness by crown-flatness vector analysis method.In the third step,the maximum rolling force limit and the total pass number are adjusted to make the plate gauge at exit equal to target gauge with satisfactory flatness.The on-line application shows that this method is effective.

Practice to improve the plate camber during hot rolling by optimizing rolling schedule

Plate camber is one of the most important problems in hot rolling process which not only lead to lower output caused by increasing of crop loss,but also influence on the efficiency of follow-up shear processes,in severe cases damages of side guides or stands also occurred.In terms of reversible four-high hot rolling mills,the main causes of this problem exist in the following areas,reasons of stands,such as the stiffness difference between the drive side and operation side;reasons of slabs,such as the original wedge or the temperature difference along the width direction;reasons of side guides,such as the error of work pieces centerin.In their essence,it can be concluded that the initial deviation of deformation on both sides will increase as the processing,and then the work piece will deviate the center line of the stand,which will form camber defects in the end. The attempt of improving the plate camber was carried out by design the optimized schedules on the bases of theory of the steady rolling conditions during hot rolling process.In presizing and broadsizing sequence,according to the biting conditions and maximum torque restrictions,the rolling reduction of every pass should be as large as possible for the propose of increasing the negative convexity of load-gap through increasing the rolling force. When rolling process goes to finishing stage,it will be impossible to correct rolling centerline in last serval passes because the work pieces will be too long and thin,while considering the bad impact on plate profile which brought by increasing force.Therefore,the main purpose of finishing sequence should be profile control,and slowing down the speed of camber extension as much as possible by gap tilt adjustment automatically. The results show that in hot rolling process,the degree of final camber is impacted by all the three sequences. It is suggested that the control or even eliminating the defect is expectable by a well designed rolling schedule fundamentally.

KDD-based rolling schedule model for plate mill

A novel method for generating a rolling schedule is presented, which is fundamentally different from the existing ones. KDD (knowledge discovery in database) techniques are applied for discovering association rules between rolling parameters in a large database of rolling operation, and based on these rules, the schedule for the crucial last six finishing passes is generated. Operational evaluation shows that the schedule generated by the new method outperforms that generated by existing methods. It also shows how in this application the human's domain knowledge is applied to speed up the KDD process and to ensure the validity of the knowledge discovered.

Genetic Algorithm-Based Optimization Used in Rolling Schedule

A genetic algorithm-based optimization was used for 1 370 mm tandem cold rolling schedule,in which the press rates were coded and operated.The superiority individual is reserved in every generation.Analysis and comparison of optimized schedule with the existing schedule were offered.It is seen that the performance of the optimal rolling schedule is satisfactory and promising.

Multi-Objective Optimization for Tandem Cold Rolling Schedule

Considering the multivariable, strong-coupled, and nonlinear features of tandem cold rolling mill, a mathematical model of multi-objective optimization was built to facilitate the design of new systems aiming at equating the relative load, preventing slip, and obtaining best shape. BP （back propagation） neural network based on Levenberg- Marquardt algorithm was used for predicting the rolling force. The multi-objective fuzzy theory and method were introduced during the optimization. With an example of 1 370 mm tandem cold rolling mill, the rolling schedule of the common rolling, the single-objective optimization design, and the multi-objective fuzzy optimization design were compared with each other. The results generated from the case study showed that the proposed approach could significantly decreased the values of three objective functions simultaneously and the performance of the optimal rolling schedule was satisfactory and promising. Moreover, the capability and usefulness of fuzzy application in tandem cold rolling schedule were clearly demonstrated.

Dynamics-based optimization of rolling schedule aiming at dual goals of chatter suppression and speed increase for a 5-stand cold tandem rolling mill

In the process of cold tandem rolling,chatter instability leads to serious impacts on enhancing rolling speed,improving product quality,reducing production cost and realizing intellectualization.Chatter occurs with the rolling speed up to a certain threshold value,but the critical speed is determined by both product specifications and rolling schedules.A 5-stand cold tandem rolling mill whose first three stands and subsequent two stands,respectively,have four and six rolls was investigated by formulating its dynamic equations with the corresponding structure-process coupling.By applying the stability-based calculation model about the critical rolling speed in each stand,the system dynamic responses around the critical rolling speed were simulated,and the system eigenvalues which represent instability and characteristic frequencies were figured out.Thereafter,via combining the critical rolling speeds with the system dynamic behavior,a dynamics-based optimization model of rolling schedule for the 5-stand cold tandem system was proposed for the purposes of both the chatter suppression and rolling speed increase.In the optimization model,eight rolling technique parameters(four strip thicknesses and four tensions between the upstream and downstream stands)were taken as design variables,and the constraint conditions were set as no chatter instability in all five stands,and the optimization goal was to maximize the outlet speed of the final stand.The pattern search method was introduced to solve the optimization model.By applying such a dynamics-based optimization model for the 5-stand cold tandem rolling process,the chatter instability was suppressed effectively and the rolling efficiency was improved considerably;therefore,such an optimization model is expected to be valuable for intelligent manufacturing of rolling process.

Robust multi-objective optimization of rolling schedule for tandem cold rolling based on evolutionary direction differential evolution algorithm

According to the actual requirements,profile and rolling energy consumption are selected as objective functions of rolling schedule optimization for tandem cold rolling.Because of mechanical wear,roll diameter has some uncertainty during the rolling process,ignoring which will cause poor robustness of rolling schedule.In order to solve this problem,a robust multi-objective optimization model of rolling schedule for tandem cold rolling was established.A differential evolution algorithm based on the evolutionary direction was proposed.The algorithm calculated the horizontal angle of the vector,which was used to choose mutation vector.The chosen vector contained converging direction and it changed the random mutation operation in differential evolution algorithm.Efficiency of the proposed algorithm was verified by two benchmarks.Meanwhile,in order to ensure that delivery thicknesses have descending order like actual rolling schedule during evolution,a modified Latin Hypercube Sampling process was proposed.Finally,the proposed algorithm was applied to the model above.Results showed that profile was improved and rolling energy consumption was reduced compared with the actual rolling schedule.Meanwhile,robustness of solutions was ensured.

OptiLam:Design of Optimised Rolling Schedules

Nowadays it is known that the thermomechanical schedules applied during hot rolling of flat products provide the steel with improved mechanical properties.In this work an optimisation tool,OptiLam (OptiLam v.1),based on a predictive software and capable of generating optimised rolling schedules to obtain the desired mechanical properties in the final product is described.OptiLam includes some well-known metallurgical models which predict microstructural evolution during hot rolling and the transformation austenite/ferrite during the cooling.Furthermore,an optimisation algorithm,which is based on the gradient method,has been added,in order to design thermomechanical sequences when a specific final grain size is desired.OptiLam has been used to optimise rolling parameters,such as strain and temperature.Here,some of the results of the software validation performed by means of hot torsion tests are presented,showing also the functionality of the tool.Finally,the application of classical optimisation models,based on the gradient method,to hot rolling operations,is also discussed.

Rolling horizon scheduling algorithm for dynamic vehicle scheduling system

Dynamic exclusive pickup and delivery problem with time windows (DE-PDPTW), aspecial dynamic vehicle scheduling problem, is proposed. Its mathematical description is given andits static properties are analyzed, and then the problem is simplified asthe asymmetrical travelingsalesman problem with time windows. The rolling horizon scheduling algorithm (RHSA) to solve thisdynamic problem is proposed. By the rolling of time horizon, the RHSA can adapt to the problem'sdynamic change and reduce the computation time by dealing with only part of the customers in eachrolling time horizon. Then, its three factors, the current customer window, the scheduling of thecurrent customer window and the rolling strategy, are analyzed. The test results demonstrate theeffectiveness of the RHSA to solve the dynamic vehicle scheduling problem.

Optimal Scheduling Strategy of Source-Load-Storage Based onWind Power Absorption Benefit

In recent years,the proportion of installed wind power in the three north regions where wind power bases are concentrated is increasing,but the peak regulation capacity of the power grid in the three north regions of China is limited,resulting in insufficient local wind power consumption capacity.Therefore,this paper proposes a two-layer optimal scheduling strategy based on wind power consumption benefits to improve the power grid’s wind power consumption capacity.The objective of the uppermodel is tominimize the peak-valley difference of the systemload,which ismainly to optimize the system load by using the demand response resources,and to reduce the peak-valley difference of the system load to improve the peak load regulation capacity of the grid.The lower scheduling model is aimed at maximizing the system operation benefit,and the scheduling model is selected based on the rolling schedulingmethod.The load-side schedulingmodel needs to reallocate the absorbed wind power according to the response speed,absorption benefit,and curtailment penalty cost of the two DR dispatching resources.Finally,the measured data of a power grid are simulated by MATLAB,and the results show that:the proposed strategy can improve the power grid’s wind power consumption capacity and get a large wind power consumption benefit.

Rolling optimization algorithm based on collision window for single machine scheduling problem

Focusing on the single machine scheduling problem which minimizes the total completion time in the presence of dynamic job arrivals, a rolling optimization scheduling algorithm is proposed based on the analysis of the character and structure of scheduling. An optimal scheduling strategy in collision window is presented. Performance evaluation of this algorithm is given. Simulation indicates that the proposed algorithm is better than other common heuristic algorithms on both the total performance and stability.

Algorithm research of the SQP method used in roll schedule calculation for Baosteel's 5m heavy plate

Loading distribution for heavy plate mill is to find optimal control solutions under the granted performance indicators and constraints including mill capacity and hypothesis of rolling models.The solutions are quite different for different performance indicators.In the article,the performance indicators and sequential quadratic programming(SQP for short below) methods employed in 5 000 mm heavy plate mill of BaoSteel are penetratingly analyzed.Generally,the SQP method is an effective and fast way to solve the nonlinear programming problems with small or medium scale constraints.Early in 1976,Han put forward the SQP method for the first time and Powell made it perfect and accomplished the algorithm in 1977.In fact, SQP method was to turn a nonlinear programming problem to a series of sub set of quadratic programming problems.In the algorithm,each iteration step is to solve one quadratic programming problem.The optimal solutions will be gradually approached after quadratic programming problems were totally solved.When solving the quadratic programming problem,the active set strategy were employed which turned the constrained quadratic programming problem to unconstrained quadratic programming problem.The active set strategy made the whole quadratic programming problem be solved by a least square problem.And finally, the matrix of the least square problem would be decomposed by Q matrix and R matrix.After Q matrix and R matrix were obtained,the optimal solutions would be finally found.For loading distribution,the performance indicators were composed by plate shape and draft of each pass.Plate shape is represented by rolling force gradually reduced pass by pass with a tunable factor.The mill capacity is another performance indicator represented by draft of each pass.For heavy plate mill,the mill capacity here is the motor moment. For heavy draft,the motor would be overloaded especially for the first several passes;for small draft,the motor would be loaded slightly.All these would not be permitted to happen when calculating the loading distribution.The mill capacity indicator made the loading of mill just be in the middle,not too much and not too low.In the article,these two performance indicators were analyzed in detail.Examples of loading distribution results with different performance indicators were given by the SQP method.When making changes to the performance indicators,there would be different solutions to the loading distribution.For the optimal solutions to the mill,there was supposed to make changes to the factors of the performance indicators or upgrade the accuracy of the mathematical models of the rolling process.

Optimization of Pass Schedule in Hot Strip Rolling

Rolling schedule not only determines the rolling process to be going smoothly, but also affects the shape accuracy and structure properties of finished strip. In order to gain good strip crown and flatness, the calculation formulas of the most suitable rolling force and bending force are deduced. By taking relatively equal load of rolling power and good shape as objective functions, the optimization mathematical models of finish rolling schedule are established. By contrast, the rolling schedules after optimization can improve the rolling mill working status and ensure the strip crown and flatness to be good. At the same time, the setting value of bending force is improved and this leaves more space for on-line shape control.

Real-time scheduling strategy for microgrids considering operation interval division of DGs and batteries

Real-time scheduling as an on-line optimization process must output dispatch results in real time. However, the calculation time required and the economy have a trade-off relationship. In response to a real-time scheduling problem, this paper proposes a real-time scheduling strategy considering the operation interval division of distributed generators(DGs) and batteries in the microgrid. Rolling scheduling models, including day-ahead scheduling and hours-ahead scheduling, are established, where the latter considers the future state-of-charge deviations. For the real-time scheduling, the output powers of the DGs are divided into two intervals based on the ability to track the day-ahead and hours-ahead schedules. The day-ahead and hours-ahead scheduling ensure the economy, whereas the real-time scheduling overcomes the timeconsumption problem. Finally, a grid-connected microgrid example is studied, and the simulation results demonstrate the effectiveness of the proposed strategy in terms of economic and real-time requirements.

Roll shifting strategy with varying stroke and step in hot strip mill

A new roll shifting strategy with varying stroke and varying step was investigated,Two characteristic parameters including cat ear height and gap contour smoothness were introduced to assess the effect of shifting strategy on roll wear,and the relation between characteristic parameters and shifting strategy was established.Both varying stroke and varying step can reduce cat ear height and gap contour smoothness,so the shifting strategy with varying stroke and varying step is better than the one with either varying stroke or varying step,Based on the effect of shifting control parameters on characteristic parameters of roll wear,the selection principle of these shifting control parameters was gained.A case study was conducted to validate the proposed roll shifting strategy,reducing uncontrollable quartic loading gap contour,improving strip profile and extending rolling length of a rolling campaign.

Slab and Level 2 Automation Design Guidelines for Optimum Metallurgy and Productivity for Plate and Steckel Mills

Many new steel plate processing facilities have been built in the past 10 years around the world with many more being planned for the future.This is especially true in developing countries such as China,India and Brazil.Many of these facilities are plate mills with either one or two stands or a Steckel mill,typically only one stand designed for the production of structural plate steels.Unfortunately,there is a lack of understanding with both the mill builders of the world and the mill owners on the importance of properly matching up the available slab supply (either new as part of a new plate/Steckel mill complex or part of an already existing) with the desired end plate product mix.Many mill builders and owners around the world believe that you can take any slab of any dimension and make any plate dimension you want.While this is basically true with today’s Level 2 automation systems,it does not always result in optimum metallurgy/mechanical properties or productivity.This less than optimum condition results in mechanical property failures,shape issues,productivity losses and in general a less than desirable costly processing operation.It is important to the overall optimization of a steel processing facility that the proper slab dimensions be used to produce the proper final plate dimensions along with achieving the required mechanical properties.The critical nature of this selection will be dependent on the final plate thickness and overall mechanical property requirements.Proper mechanical property,shape and overall microstructure are heavily dependent on the ability to properly work the entire cross section of the slab through the rolling process.Many mechanical property,shape and microstructural issues are a result of improper working of the entire cross section during rolling.The ability for a given mill to properly work the entire cross section is dependent on proper slab selection (total reduction ratio) and a proper rolling schedule either generated manually by the operator or by the mills Level 2 automation system.The proper working and more importantly the true metallurgy of the slab being rolled does not occur until any dimensional rolling passes have been completed.In fact,dimensional rolling passes may create a negative situation that will have to be overcome in the remainder of the rolling schedule.This paper will discuss the importance of proper slab selection for a given plate dimension and final product.Examples and guidelines will be given related to proper slab selection for final plate dimensions and mechanical property requirements.

Metallurgical Optimization of Microalloyed Steels for Oil and Gas Transmission Pipelines

The production of microalloyed steels for oil and gas transmission pipelines has increased significantly over the past years.With more and more countries developing their own capabilities to produce pipeline steels to support their own internal pipeline infrastructure development,there has been an increase of steel producers working to develop their own capabilities to produce microalloyed steels for this application.However,to achieve the desired mechanical property attributes for transmission pipeline applications utilizing a cost effective approach requires metallurgical optimization of the microalloyed steels.To achieve metallurgical optimization a basic understanding is required in the design of a cost effective alloy and then the proper processing of that alloy design to achieve the optimum microstructure/mechanical properties.In this sense,many producers in the world,especially those who have only recently,in the past 10 years,developed their capability to produce microalloyed transmission pipeline steels still do not achieve metallurgical optimization of their alloy and process.This results in yield losses due to failures,inefficient processing causing productivity losses and additional expensive additions of alloys to compensate for failures and process inefficiencies.Since the supplier of plate/coil has the largest percentage effect on the final cost of the pipe,the steel producer must understand proper alloy,microstructure,and process design to produce a uniform and stable plate/coil to be used in pipe production.This means that strength,toughness and microstructure must be uniform down the length,across the width and through the cross section.Metallurgical optimization is achieved when this uniformity is achieved with a cost effective approach.Counter to that,non-uniformity results in pipe forming,welding,expansion,mechanical property and production issues resulting in downgraded pipe and cost overruns in pipemaking.This paper will describe targets for plate/coil uniformity for pipe production and show examples of pipe issues when uniformity cannot be achieved.Key plate/coil attributes will be identified along with guidelines on alloy design and key processing parameters and targets that need to be considered to work toward metallurgical optimization.Examples will be used to illustrate the thought process in alloy/process design for metallurgical optimization.