J. Cent. South Univ. (2013) 20: 1226−1234 DOI: 10.1007/s11771-013-1606-8
Simulation-based multi-objective optimization for roll shifting strategy in hot strip mill LI Wei-gang(李维刚)1,2 1. College of Information Science and Engineering, Northeastern University, Shenyang 110819, China; 2. Automation Division, Central Research Institute, Baosteel Group Corporation, Shanghai 201900, China © Central South University Press and Springer-Verlag Berlin Heidelberg 2013 Abstract: A simulation-based multi-objective optimization approach for roll shifting strategy in hot strip mills was presented. Firstly, the effect of roll shifting strategy on wear contour was investigated by numerical simulation, and two evaluation indexes including edge smoothness and body smoothness of wear contours were introduced. Secondly, the edge smoothness average and body smoothness average of all the strips in a rolling campaign were selected as objective functions, and shifting control parameters as decision variables, the multi-objective method of MODE/D as the optimizer, and then a simulation-based multi-objective optimization model for roll shifting strategy was built. The experimental result shows that MODE/D can obtain a good Pareto-optimal front, which suggests a series of alternative solutions to roll shifting strategy. Moreover, the conflicting relationship between two objectives can also be found, which indicates another advantage of multi-objective optimization. Finally, industrial test confirms the feasibility of the multi-objective approach for roll shifting strategy, and it can improve strip profile and extend same width rolling miles of a rolling campaign from 35 km to 70 km. Key words: hot rolling; roll shifting strategy; roll wear; multi-objective optimization; Pareto-optimal front
1 Introduction Hot rolling is one of the key process of the strip steel production. Schedule-free rolling (SFR) is an effective way to organize production flexibly and maximize production efficiency [1]. The key of SFR is profile and flatness control. As the key factors to affect profile and flatness control, both crown control and wear control abilities in downstream stands of HSM (hot strip mills) are very necessary to implement SFR, such as a large number of the same width strip rolling campaigns in hot rolling. The major methods to control strip crown or work roll wear in the downstream stands in the field of profile and flatness control in hot rolling are adopting the WRS (work roll shifting) technology, adopting the CVC (continuously variable crown) technology, and using high-speed steel work rolls or lubrication rolling technology to alleviate roll wear [2]. In terms of roll contour, limits of SFR are mainly coming from work roll wear, which imposes strong restrictions on rolling schedule. Especially, the effect of increased wear in strip edge zones leads to anomalies in work roll contour and subsequently in strip contour. SFR in a HSM without specific tools to control the roll wear
evolution will bring to a roll contour with pronounced high spots in the case of same width campaign or to an irregular contour in the case of alternate rolling [3]. The rolls in upstream stands of HSM show a very small increase in roll wear, whereas the rolls in downstream stands wear rapidly. There are two forms of work roll wear contours which are recognized as overall and local in downstream stands. The long stroke shifting system with conventional work roll contours can make roll wear dispersive and uniform, and obtain rather smooth local roll contours near strip edges, favorable to decrease body crown and edge drop. The optimized roll shifting strategy is helpful for the improvement of work roll wear contours. To achieve SFR, much attention has been paid to the shifting strategy optimization in the WRS mills with conventional flat rolls [2−9]. KONG et al [5] introduced a cyclic varying step shifting strategy. Its limitation is that the accuracy of objective function and the error range of loaded gap crown model belong to the same order of magnitude, so it is difficult to achieve on-line control. SHAO et al [6] proposed a shifting strategy with varying stroke, but they did not build an optimization model to optimize the shifting strategy for each specific rolling campaign. LI et al [7] presented an optimization
Foundation item: Projects(50974039, 50634030) supported by the National Natural Science Foundation of China Received date: 2012−02−28; Accepted date: 2012−09−01 Corresponding author: LI Wei-gang, PhD Candidate; Tel: +86−21−26641062; E-mail:
[email protected]
J. Cent. South Univ. (2013) 20: 1226−1234
model for roll shifting strategy with varying strokes, but its objective function only evaluated wear contour in the end of a rolling campaign. LI et al [8] established a multi-objective optimization model for roll shifting strategy with varying stroke, and its objective functions evaluated roll comprehensive contour (including wear contour, thermal contour and ground contour) of each strip in a rolling campaign, but the time-consuming computation made it difficult for on-line control. LI et al [9] put forward an optimization solution to roll shifting strategy of alternate rolling, but it was only for alternate rolling campaign. In this work, targeting to these existing problems, a simulation-based multi-objective optimization approach for roll shifting strategy is investigated, which can optimize roll shifting strategy for each specific rolling campaign.
2 Framework of multi-objective optimization for roll shifting strategy In hot rolling process, with the extensions of a rolling campaign, increased roll wear in strip edge zones results in severe local wear low spots at work roll edge and the local high spots at strip contour, causing deterioration of strip contour. The long stroke shifting system can make work roll wear dispersive and uniform by the symmetrical roll contour and periodic shifting. The goal of shifting strategy optimization is to control roll wear evolution in the rolling process, improve roll wear contours, and reduce restrictions on rolling schedule. The block diagram of simulation-based multiobjective optimization for roll shifting strategy is given in Fig. 1. It comprises two main blocks: An optimization engine based on a multi-objective optimization algorithm and an evaluation engine. The optimization engine guides the optimization process. It explores the solution space by iteratively selecting many sets of shifting control parameters for evaluation. The evaluation engine performs an accurate evaluation of roll wear contours. For each set of shifting control parameters, the evaluation engine computes a set of quality criteria which are introduced into the multi-objective optimization algorithm and guide it in the search space towards better solutions. The essence of the proposed roll shifting strategy optimization is simulation-based optimization (SBO), which can be defined as the phenomenon of coupling an optimization method with simulation in order to test many parameters that can maximize the performances of the simulated system. This technique was the subject of many works in the last years [10−12].
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Fig. 1 Block diagram of simulation-based multi-objective optimization for roll shifting strategy
3 Simulation of work roll wear contour Roll shifting strategy affects roll wear contours. The focus of this section is to evaluate the effect of roll shifting strategy on wear contour by numerical simulation. 3.1 Roll shifting strategy with varying stroke To reduce the number of decision variables of shifting strategy optimization problem, a recursive algorithm is developed to obtain roll shifting strategy with varying stroke by several parameters. 1) First phase of a rolling campaign Set the shifting position of the first strip S1=d1
(1)
Start from the second strip, firstly update the shifting step d1: When |Si−1+d1 |>M, then set d1=−d1; and then calculate the i-th strip shifting position: Si=Si−1+d1, 2≤i≤N
(2)
where d1 is the first phase shifting step; M is the maximum shifting stroke; N is the phase switch point, which can be set as N=3·floor (M/d1). 2) Second phase of a rolling campaign Start from the (N+1)-th strip, firstly update the shifting step d2: When |Si−1+d2|>M·exp(−A·(i−N)), then set d2 =−d2; and then calculate the shifting position: Si=Si−1+d2, N
