Based on the hot rolling process, a load distribution optimization model is established, which includes rolling force model, thickness distribution model, and temperature model. The rolling force ratio distribution and good strip shape are integrated as two indicators of objective function in the optimization model. Then, the evolutionary algorithm for complex-process optimization (EACOP) is introduced in the following optimization algorithm. Due to its flexible framework structure on search mechanism, the EACOP is improved within differential evolutionary strategy, for better coverage speed and search efficiency. At last, the experimental and simulation result shows that evolutionary algorithm for complex-process optimization based on differential evolutionary strategy (DEACOP) is the organism including local search and global search. The comparison with experience distribution and EACOP shows that DEACOP is able to use fewer adjustable parameters and more efficient population differential strategy during solution searching; meanwhile it still can get feasible mathematical solution for actual load distribution problems in hot rolling process.
With the increasing demand for improving the product quality and control accuracy in hot rolling process, the rolling scheduling problem has become an important issue in the steel industry. According to the principle that nominal motor power should be greater than rolling power, the main purpose of hot rolling scheduling problem consists in determining the final thickness for every rolling pass to set other process parameters [
The hot rolling process has been optimized with rolling theory or heuristics algorithms [
Thus, the major objective pursued in this paper is to formulate a better solution on the rolling scheduling optimization. Based on the evolutionary algorithm for complex-process optimization (EACOP) [
Based on experimental simulation by actual data in hot rolling process, simulation result shows that the application of DEACOP optimizes the gauge reduction for each rolling pass and gives full play to the upstream rolling mill equipment’s ability. Meanwhile, DEACOP algorithm regulates crown index of the downstream mills, so it can further improve the efficiency of plate-shaped regulating.
In order to determine rolling force of each stand, as well as the other settings, the key point of load distribution is that the exit thickness of each stand should be distributed reasonably. Thus, in this section the optimal load distribution with the consideration of overall performance on shape and gauge is proposed. The optimal load distribution of finishing mill group can be divided into three stages [
The first phase requires that the 1st stand’s reduction should be left some room, as the steel billet’s thickness may fluctuate when steel billet goes into rolling mill.
In the second phase, the 2nd and 3rd stands should make full use of equipment power, therefore making the amount of the reduction as large as possible.
In the third phase, the rolling force in the last stage should gradually decrease from the 4th to the last stand, so that the accuracy and performance of the shape and gauge can be synthesized properly. Meanwhile, the relative crown of the last four stands should be equal.
With the consideration of those steps, the objective function is derived as follows, which constructs with the desire of above three stages with DEACOP optimizes load distribution:
The main purpose of load distribution system is seeking a set of data
According to [
Consider the following:
Temperature is an important factor in hot rolling, which can directly impact on the rolling force value of each pass. Equation (
The exit temperature of each finishing mill is denoted as
In this section, the evolutionary algorithm for complex-process optimization based on differential evolutionary strategy (DEACOP) is proposed to solve load distribution problem of the hot rolling scheduling. The DEACOP is innovative strategy embedded in various submethods within the flexible. This algorithm improves path relinking to generate a new combination method which considers a broader area around the population members. Meanwhile DEACOP improves the balance between intensification and diversification with a population-update method. The above strategies can escape from suboptimal solutions and advance the search efficiency. The algorithm consists of five parts: (1) building the initial population, (2) determining similarity solution, (3) differential evolutionary strategy, (4) population update, and (5) deep search feasible solutions. Its principle is to deeply explore new population members near individuals with minimum fitness. The optimization process will be repeatedly executed unless the stop conditions were met.
In this subsection a latin hypercube uniform sampling (LHS) is first used to generate the initial population. To illustrate how LHS works, during the following description we will explain the building process of LHS.
Each side of the test area was divided equally into 10 parts, so test area was divided into 102 small areas. (1, 2, Column of the matrix, such as (7,7), (5,9), (6,3) … (3,1), is fixed on 10 rectangles. A sample was randomly selected in each small rectangle, and then sampling group was composed of 10 samples. The result about LHS works is shown in Figure
LHS
Through LHS procedure, an initial set Pop of Psize diverse vectors is generated, whose size is set as 10 × Nvar (Nvar is defined as a number of variables which need to be optimized). Meanwhile high-quality solution set
The purpose of similarity determining is to help escape from (possible) local optimal area. Algorithm
until the end of the loop
In the traditional EACOP, the reference set was usually based on linear combination method, which has advantage in some aspects. Unfortunately, there is difficult to solutions of complex issue. Thus, an improved differential variation method was introduced as follows:
Besides, the crossover strategy is used for better evolutionary effects. After the crossover operation on
As described in the combination method, we incorporate each member of the reference set with the rest
By the previous steps, the new population members are surrounded by hyperrectangle in accordance with update strategy. For enhancing the search intensification to exploit better feasible solutions, the evolutionary algorithm has implemented
The flow chart of DEACOP.
Deep search step is shown as follows: firstly, create a new solution
According to description about above five parts subsection, all of subsections will be integrated to build an evolutionary algorithm. Optimization steps of DEACOP are shown as follows.
Set initial parameters that include variable dimension vars,
This step uses a latin hypercube uniform sampling to generate initial set of diverse solutions. But the set should meet constraint condition about optimization problem.
Check for similarity solutions. This step uses Algorithm
Make differential evolutionary computation in reference to the actual individuals of concentration.
Associate population-update strategy with
Escape from suboptimal solution. If the parent
Repeatedly perform Step
Until stopping criterion is met, go into Step
In order to clarify this algorithm procedure, a flow chart was shown in Figure
In order to validate the effectiveness of DEACOP optimization for load distribution of the hot rolling,
Set parameters for optimization.
Model parameters | Value | DEACOP parameters | Value |
---|---|---|---|
|
1520 |
|
10 |
|
35.3 |
|
10 |
|
5.9 |
|
70 |
|
1061 |
|
20 |
|
0.016 |
|
10−4 |
|
7 | ITTM | 150 |
The process of DEACOP algorithm optimization for load distribution of the hot rolling is shown as follows.
The load distribution model considering flatness is established based on the actual production process parameters.
First of all, thickness value
Use DEACOP to optimize mathematic model of load distribution. According to constraint condition of modeling details, the process parameters which are calculated by optimizing variable must satisfy actual production requirements.
Until stopping criterion is met, go back to Step
In this part, we have considered three methods for optimizing load distribution, including, experience distribution, EACOP, and DEACOP. Meanwhile, the results generated through those algorithms were compared and analyzed. Under constraints conduction and objective function, as we can notice that top three stands’ reduction must be as large as possible. For the desire of rolling force, the first stand rolling force
Comparison of rolling force distribution.
Methods | Variables (/KN) | ||||||
---|---|---|---|---|---|---|---|
|
|
|
|
|
|
| |
Classic | 22438.8 | 20054.3 | 24530.9 | 17842.8 | 12593.2 | 12170 | 8941.5 |
EACOP | 20356.8 | 22629.6 | 22048.6 | 17446.9 | 15130.7 | 12136.4 | 9184.9 |
DEACOP | 21845.7 | 23648.4 | 23646.4 | 15963.3 | 13472.2 | 9813.8 | 9148.4 |
Relative crown of each stand.
Methods | Variables (×103) | ||||||
---|---|---|---|---|---|---|---|
|
|
|
|
|
|
|
|
Classic | 1.4 | 1.7 | 3 | 3.1 | 2.6 | 2.9 | 2.8 |
EACOP | 1.2 | 1.9 | 2.6 | 2.9 | 3.1 | 2.9 | 2.8 |
DEACOP | 1.2 | 1.9 | 2.6 | 2.9 | 2.9 | 2.8 | 2.8 |
According to reference with the constraints conduction and objective function in actual rolling process, Figure
Thickness distribution of each stand.
Methods | Variables (/mm) | ||||||
---|---|---|---|---|---|---|---|
|
|
|
|
|
|
| |
Classic | 24.9662 | 18.3946 | 12.7358 | 9.7047 | 8.0254 | 6.718 | 5.9 |
EACOP | 25.8395 | 18.2928 | 13.1485 | 10.0799 | 8.04719 | 6.7393 | 5.9 |
DEACOP | 25.2135 | 17.3832 | 12.1914 | 9.5458 | 7.797 | 6.7361 | 5.9 |
Comparison of rolling force distribution.
The thickness distribution of every stand is shown in Table
Judgment with Shohet formula.
In this paper, The DEACOP which has a flexible frame structure embedding in various submethods has been introduced. This algorithm was presented to optimize the rolling schedule and show its superior ability of global searching. Moreover, it can not only escape from suboptimal solutions, but also advance the search efficiency.
According to the experimental results within actual data in hot rolling process, the DEACOP still can get feasible and better mathematical solution and validate the real-time application even by fewer adjustable parameters, which is more suitable for the actual load distribution problems. With this algorithm, the optimized rolling schedule can make full use of the upstream finishing mill equipment which controls top three stands’ reduction and improves the total rolling consumption. The rolling force of the last four stands which control exit thickness can be used as an important means of shape control. Therefore, the improvement of efficiency in plate-shaped regulating by DEACOP is recommended as an important issue for further investigation.
The authors gratefully acknowledge the support by the National Natural Science Foundation of China (61074085, 51205018), China Postdoctoral Science Foundation Funded Project (2012M510321), and Fundamental Research Funds for the Central Universities (FRF-TP-12-104A, FRF-SD-12-008B). The authors heartily appreciate the data support from Ansteel Company in Liaoning Province, China. Meanwhile, great thanks also go to former researchers for their excellent work, which gives great help for our academic study.