Spread is a major parameter in the steel wire rod rolling process since it is required for the calculation of material crosssectional area and other rolling characteristics. Therefore, it is important to have a method to predict the spread with high accuracy and less computation time in wire rod rolling. In this study, multiple artificial intelligence (AI) methods including MultiLayer Perceptron (MLP) and Adaptive NeuroFuzzy Inference Systems (ANFIS) are employed to predict the spread. The 3D finite element (FE) analysis is used to generate the input data for the AI model and investigate the effect of different input parameters on the spread in onestand and threestand rolling setups of the wire rod rolling. The results demonstrate that the backward tension and the roll diameter are the most influencing parameters. Due to the use of dimensionless inputs and outputs, the model is independent of geometries and processing conditions which results in the transferability of the model. Furthermore, the ANFIS model provides some level of reasoning for the user by using a rulebased approach. Data fusion is also used to combine all outputs of the trained models and provide a single output for the prediction of spread in new data sets. The reasoning and transferability of the model result in the prediction of spread for a wide range of conditions in the steel wire rod rolling process. The generality and accuracy of the proposed approach are examined by comparing the results of the AI model with the FE analysis and experimental data obtained from the steelmaking company. The findings indicate that there is good agreement between the predicted and the measured values.
Rolling is one of the most widely used forming processes in a steelmaking company. One of the products of the rolling process is the steel wire rod which is a long semifinished product with a round crosssection that has several applications in automotive, construction, and other industries. During the manufacturing process of steel wire rods, the initial billet is heated up to around 1,000°C and passed through many rolling stands. There are some types of rolling stands with different numbers of rollers, and different roll pass types. A tworoll stand with roundoval and ovalround passes is one of the most common types of rolling setup. Each stand is responsible for a part of the deformation. Thus, the large crosssection of the initial input material is decreased by passing through different rolling stands and a long steel product with a small round crosssection is produced at the end of the process [
Prediction of the material crosssection after each stand of the rolling is of great importance in industrial applications since it leads to an accurate and optimized pass design and set up of production lines. In addition, it is necessary to have the crosssection of a sample to calculate strain, strain rate, and other parameters in the rolling process [
Up to now, several FE analysis studies were performed to investigate the roll force, material deformation, strain distribution, strain homogeneity, caliber design, and temperature distribution in wire rod rolling [
On the other hand, empirical models which can be obtained based on experiments are applicable in industrial applications because of their simplicity. The major problem of empirical models is the generality of these equations since they are normally applicable for a specific range and the results may also be affected by the employed machines and other experimental factors. In addition, it is diff icult, timeconsuming, and expensive to experimentally investigate different conditions and parameters such as friction and tension in the rolling process. Therefore, some parameters are not considered in the empirical equations for the prediction of spread in single and multiple rolling stands. Some of the important empirical models in the flat and wire rod rolling process belong to Siebel [
Another approach that has attracted great attention in different industries is based on artif icial intelligence. In the rolling processes, most previous studies are focused to predict the rolling force [
Therefore, a method that can predict the spread in wire rod rolling with low computation time, high accuracy, and generality is favorable for industrial applications. To overcome the challenges of the previous studies, the following objectives are set out. First, finite element (ABAQUS/Explicit^{TM}) software is used to simulate different cases of the 3D wire rod rolling process and investigate the relationship between the input parameters and the output. Second, all the input and output parameters are changed to dimensionless values in which they are not related to a specific rolling stand, so the proposed model can be transferred to other setups and some level of transferability can be achieved which increases the generality of the model. Third, multiple AI methods including MLP and ANFIS are employed to predict the output based on the dimensionless data obtained from FE analysis which results in an accurate and robust prediction. Forth, some level of reasoning is provided for the user by using the ANFIS, thus, the effect of different input parameters can be understood. In addition, data fusion is employed to combine the result of trained MLP and ANFIS models for the prediction of those cases that are out of the range of simulations, thus, the reliability and explainability of this model will be increased.
This study presents a fusion of AI methods to predict the spread in the steel wire rod rolling process. FE analysis is used to simulate several cases to generate the required data for the AI model and find the relationship between inputs and output. For the AI model, MLP is selected since it is a universal approximator and can model any functions regardless of the level of complexity and ANFIS is chosen since it is a rulebased system and provides reasoning [
The proposed model to predict the spread in steel wire rod rolling is shown in
FE analysis is used to simulate the wire rod rolling process and generate data for the AI model. Due to the existence of 3D deformation, complex contact conditions, and elevated temperature in the wire rod rolling, a 3D coupled thermomechanical analysis is performed by using ABAQUS/ Explicit^{TM} to simulate the steel wire rod rolling process [
An 8node coupled thermomechanical element (C3D8RT) with reduction integration and hourglass control is used to mesh the material [
where
The FE analysis part aims to generate data for the prediction system and to investigate the effect of different input parameters on the output. The input parameters are defined as friction, material temperature, roller rotational speed, roll gap, input material size, roller diameter, material strength, backward tension, forward tension, caliber type, and the output parameter is the spread ratio which means the relative difference between initial and final width of material. To design the simulation cases, two setups are considered which are onestand and threestand rolling operations; the geometry of the caliber is also considered as oval and round calibers which is shown in
For instance, the roll gap in onestand rolling with oval caliber is changed up to five levels which means the roll gap is changed five times over the range of 5.95 to 11.03 mm (roll gap = 5.95, 7.225, 8.5, 9.775, 11.03 mm) while the other input parameters are kept constant. Thus, the effect of a specific parameter can be understood independently. The same approach is used for other input parameters such as temperature, speed, and so on. These cases are only for onestand rolling with the oval caliber and for onestand rolling with the round caliber the same method is used but the range of changes of inputs and the reference condition are different.
In simulations with threestand rolling, the effect of backward and forward tensions on the spread ratio is studied (
FE analysis is used to simulate different cases of wire rod rolling. Due to the use of different case studies, the effect of all input parameters on the output is investigated and the parameters without any significant effect on the output are removed from the training data set. The total number of training data for oval and round caliber is around 300 cases.
One of the most important parts of an AI model is the preprocessing since it can be used to increase the quality of the data and the transferability of the model. The initial values of inputs and outputs describe limited conditions in the wire rod rolling process. If these data are used for the training section, the generality of the prediction model will be a challenging issue since the trained model cannot be used for other rolling stands that have different geometries and processing conditions.
In this part, the initial raw data are processed to make the data easier to interpret for the MLP and ANFIS models. Furthermore, the other aim of preprocessing for this study is to make the data independent of dimensions which results in the transferability of the model. Thus, the prediction model which is trained based on the results of simulations in specific dimensions and processing conditions of wire rod rolling can be used for other dimensions and processing conditions which increases the generality of the proposed model. By examining some equations from the literature [
where
In the next step, normalization is used to scale the dimensionless data to a specific range. There are some methods such as linear minmax, zscore, and decimal scaling which are normally used in the preprocessing section. In this study, the following linear formula is used for minmax normalization:
where
Artificial neural networks are developed based on the neurons of the human brain and are widely used in different fields. They can be employed to predict the nonlinear behavior of various variables. A typical neural network consists of an input layer, a hidden layer, and an output layer. Each layer contains some neurons or nodes, and each neuron is connected to other neurons. The number of neurons in the input layer is the same as the number of input variables and the number of outputs also defines the number of neurons in the output layer. However, the number of neurons and layers in the hidden layer are designed based on the complexity of the problem. One of the wellknown types of artificial neural networks, which is also used in this study, is feedforward neural networks or multilayer perceptron (MLP). In these types of neural networks, all the existing neurons in one layer are fully connected to the neurons of the next layer and pass the data in a forward direction through the network by using certain weights and biases [
where
The MLP structure for a specific case is shown in
The number of hidden layers and neurons for all MLPs which are found based on the grid search is three hidden layers. The transfer function of all layers is “
The default and used parameters for MLPs are shown in
In this way, four MLPs are used to predict the spread in oval and round calibers of wire rod rolling. The output of MLP2 and MLP4 can be converted to spread ratio by using
Fuzzy logic, which was introduced by Zadeh in 1965 [
For the sake of simplicity, an ANFIS structure of the TS type with two inputs, one output (Y), and five layers is demonstrated in
where
where
where
In the fourth layer, a firstorder linear equation is used to calculate the values of the consequences of each rule and the summation of all of them is the final output in the fifth layer with the following equations:
The input and output variables are the same as what was used for MLP (
The best result is obtained with four MFs and 100 epochs with the particle swarm optimization (PSO) learning for the ANFIS structure. In addition, fuzzy cmeans clustering is used in the structure of ANFIS which classifies the inputs into similar groups. By using this method, the number of rules is decreased in comparison with the grid partitioning. All the parameters used to design the ANFIS are shown in
In this way, four ANFIS models are designed and used to predict the spread in oval and round calibers of wire rod rolling. The same as the MLP models, ANFIS1 and ANFIS2 are used for the oval caliber and the result of them can be converted to spread ratio by using
The data fusion process takes the outputs of all MLP and ANFIS models and combines them to provide a single output. The idea behind using a fusion step is to increase the consistency and accuracy of the prediction model. Since different submodels may have errors in the prediction of some cases, combining the output can decrease the errors and increase the robustness of the model. In the proposed spread prediction model, the fusion of all data is used to predict of spread for those new cases that are out of the range of simulations. Two MLP models and two ANFIS models are designed to predict the spread ratio and α coefficient for each type of caliber. By using the Shinokura equation, the obtained
An unweighted average is used to combine all the inputs of the fusion process to provide a single output for the prediction model. The output of the fusion step is the spread ratio which is then converted to spread by multiplying the initial width of the material. Finally, the obtained spread is added to the initial width of the material, so the maximum width of the material will be obtained after the rolling process. The structure and steps of the model are shown in
Eight models based on MLP and ANFIS are designed to predict the spread in oval and round caliber which means for each caliber four models are considered. The models are trained and examined separately based on the obtained data from the FE analysis. The fusion process is employed when the trained models are used to predict the spread based on the new data which have not been seen by the trained models in training, validation, and test data sets. By using Shinokura’s model and reverse calculation, the output of all models becomes similar, so an unweighted average is used to provide a single output. Since the errors can be decreased by the summation of all models, the robustness and accuracy of the model increase by using the fusion step when it is used in real applications.
The obtained data from a steelmaking company is used for the verification of the FE analysis. When it is verified, the same conditions are used to do other simulations and generate data for the training purpose. Based on the factory data, a sixstand rolling is used for the verification of FE analysis. The input and output areas of the material passed through sixstand rolling are obtained from the existing sensors in the factory and then compared with the output area of the simulations. Based on the verified model, other simulations are done, and the results are investigated to determine the important parameters that have a significant effect on the spread ratio in steel wire rod rolling. In the next step, the results of input parameters that do not have a significant effect on the spread ratio are removed from the input database and the remaining inputs are changed to dimensionless values. By using MLP and ANFIS, an accurate mapping of inputs to the output is achieved for all models.
Based on the obtained data from the steelmaking company, the area of the material crosssection in specific sections is measured by using the sensors. The input and output sections are shown in
The input and output crosssectional areas obtained from the factory are 866.6, 225.6 mm^{2}, respectively. The position of the input crosssection is before the first stand of rolling and the position of the output crosssection is after the sixth stand of rolling which is shown in
As is shown in
The rolling rotational speed also affects the spread ratio at low speed; however, its effect becomes negligible at higher speeds (
The other results of FE analysis and the Shinokura’s model with
Interstand tension is one of the most important variables that can affect the spread ratio. Changing the rotational speed of the rollers and using a looper can result in changing the tension between the rolling stands. In this study, a threestand rolling is considered to study the effect of interstand tension on the spread ratio. If the speed of these three rollers is changed, the tension between the stands, which is a longitudinal force, will be changed. This force can cause a push or pull action in the material and change the spread of rolled material.
For a threestand rolling, backward and forward tensions are defined (
The backward tension is a function of the rotational speed of the first and second roller, therefore, any changes in these speeds will change the interstand tension. To understand the effect of backward tension, the rotational speed of the first roller is changed at five levels while the speed of the other rollers is kept constant. An increase in the speed of the first roller results in the reduction of the backward tension which means the material (between the first and second roller) experiences a lower tension or a pulling force. Thus, the material tends to have higher width after the first stand of rolling. Since the material at the entry section of the second roller has higher width, the width of the material after the second roller increases which is shown in
Based on the simulations of onestand rolling and threestand rolling, it is understood that Shinokura’s model results in large errors for the prediction of the spread ratio when the processing parameters are changed. It can predict the spread ratio when the geometrical parameters are changed, however, selecting the correct
The spread ratio and α coefficient in oval and round calibers are predicted by using separate MLP models with the hyperparameters shown in
The FE analysis results and the predicted values of spread ratio and
The correlation coefficients (R) for training and test data are 0.975 and 0.979 for MLP1 and 0.994 and 0.988 for MLP2, respectively. In addition, the RMSE for test data of MLP1 and MLP2 is 0.009 and 0.034, respectively.
The same as the oval caliber, the results of MLP models (MLP3 and MLP4) for round caliber are obtained. The correlation coefficients (R) for training and test data are 0.992 and 0.996 for MLP3 and 0.997 and 0.995 for MLP4, respectively. In addition, the RMSE of test data sets for MLP3 and MLP4 is 0.005 and 0.014, respectively. Finally, the comparison between R and RMSE of train and test data is shown in
For the ANFIS section, fuzzy cmeans clustering is used instead of the grid partitioning in the structure of ANFIS which decreases the number of rules and the training time.
The best results were achieved by using four clusters/rules for all the ANFIS models. The result of ANFIS models for oval caliber (ANFIS1 and ANIS2) are shown in
The comparison between R and RMSE of train and test data for ANFIS models is shown in
Transferability is one of the most important aspects of AIbased approaches in practical applications. Most models are trained based on specific data sets obtained from experiments, simulations, and so on. By using different algorithms and finding the optimal hyperparameters, it is possible to achieve acceptable accuracy in the test data sets. However, one of the challenging parts of these models is the transferring process from the controlled simulation environment to the practical applications where new data sets have not been examined by the trained models. In addition, it is of interest to obtain information from the AI models which demonstrate how input parameters can affect the output and which parameters have the highest and lowest effects on the output. By using the ANFIS models, some level of reasoning can be achieved which will increase the explainability of the prediction system.
To have a better view of the effect of different input parameters, two other ANFIS models are used with the same hyperparameters shown in
A reference condition is considered in the threestand rolling and only one variable in each graph is changed from its minimum value up to its maximum value while other variables are kept constant, thus, the relative effect of each input parameter on the output can be understood.
This calculation is done for all input parameters and the final output width is normalized to the range of 0 to 1 as well as each input variable. The normalized graphs are then plotted, and a linear regression is done for all curves. The slope of the normalized curves is considered as the relative effect of each input parameter which is shown in
The results of ANFIS models are also shown as colormaps in
To obtain the colormaps, the same reference condition is considered and the other two variables in each graph are increased from their minimum values up to their maximum values. As explained in the FE analysis result section, by increasing the roll diameter and friction the output width increases and by increasing the speed, roll gap (or
The proposed AI model is trained based on a specific range of geometries, however, different input material sizes and several calibers with various geometries are used under different processing conditions in the production of the steel wire rods. Due to the existence of many possible cases, it is not an efficient method to do FE analysis for all possible cases and then use them for training of the model. Thus, the FE analysis is done within a specific range and then dimensionless values and fusion of all the models are used to transfer the trained model from a specific domain to other setups of the wire rod rolling. Therefore, the obtained dimensionless values do not belong to specific dimensions and processing conditions. Furthermore, since four AI models are used for each type of caliber, the fusion of all these models can increase the accuracy and reliability of the model.
Based on the obtained experimental data from the steelmaking company, the verification of the FE analysis was done by using a sixstand rolling model. The same model is also used for the verification of the transferability of the proposed model. The input material for the FE analysis was a circular crosssection with a diameter of around 73 mm; however, the input material for the sixstand rolling is a circular crosssection with a diameter of around 20 mm. In addition, the roll gap, size of caliber, rolling speed, and other parameters are different from the initial case that was used for the training of the models. Therefore, this can be considered a good case to examine the transferability aspect of the proposed AIbased method. The schematic view of the sixstand rolling model with the sections used for measurement is shown in
Therefore, the proposed model by employing dimensionless data and data fusion can predict the width of material in the steel wire rod rolling process with high accuracy. Due to the using several AI models, the possibility of error decreases and the reliability of the model increases. In addition, the use of ANFIS provides some level of reasoning and explains how the model predicts the width by demonstrating the effect of each input parameter on the output. Finally, the proposed model shows that it can be transferred to other setups where the dimensions and processing conditions are completely different from what was used in the training section.
There are some limitations and assumptions associated with this study. The number of FE analyses is limited to around 300 cases due to the long FE simulation time of 3D wire rod rolling (especially for the threestand rolling). In addition, it is desired to perform additional FE analysis with more steel grades to elucidate the effect of different steel grades on the spread even though the strength of the material is changed over a wide range. Finally, the number of sensors to obtain the actual crosssectional area of the rolled material is limited to a few stands in the factory which is a limitation to obtaining data about the crosssectional area after all stands of rolling and using them for further examination of the model.
In this study, a method is proposed to predict the spread in the steel wire rod rolling process which is based on the results of FE analysis and employing multiple AI methods. The current AIbased approach is developed to overcome the low accuracy and generality of the available empirical models.
Based on the FE analysis, it is understood that friction, speed, backward tension, forward tension, roller diameter, roll gap, and input material size are the important parameters affecting the spread in the steel wire rod rolling process. For each type of caliber, four models including MLP and ANIFS are separately trained to predict the spread based on the result of FE analysis. The lowest and highest correlation parameters (R) among all models were 0.9708 for ANFIS1 and 0.996 for MLP3, respectively. The lowest and highest RMSE were also 0.009 for MLP1 and 0.055 for ANFIS4, respectively. Due to the use of data fusion for the prediction of new data sets and the dimensionless values for all inputs and outputs, the proposed model is independent of dimensions and processing conditions which makes the model transferable. In addition, the data fusion combines the output of all AI models and provides a single output which increases the accuracy and robustness of the model. Due to the use of ANFIS, it is understood that the most effective input parameters in the wire rod rolling process are roller diameter and backward tension while the rotational speed of the roller is the least important parameter. In addition, the effect of each input parameter on the output is understood which increases the level of reasoning of the model. The transferability of the proposed model was verified by using a sixstand rolling which was not previously used in the training and test data sets. The model could successfully predict the width of material in five sections and the predicted results were in good agreement with the measured values.
The authors would like to acknowledge the financial support provided by POSCO.
Backward Tension
Forward Tension
Geometrical Parameter
Friction
Rolling Velocity
Spread Ratio
Shinokura Coefficient
Mean Height of Caliber
The authors declare that they have no conflict of interests.
Overview of the spread prediction system for the steel wire rod rolling
Schematic view of onestand and threestand wire rod rolling process
Parameters for making the input and output data dimensionless
The structure of MLP3 and MLP4 used for prediction of spread ratio and Shinokura coefficient
The ANFIS structure with two inputs and one output
The structure of the proposed model to predict spread/width in steel wire rod rolling
(a) Positions of the sensors to obtain input and output crosssectional area in the steelmaking company and (b) The model used to simulate the sixstand rolling for the verification
The effect of (a) Friction, (b) Roller rotational speed, (c) Material strength, and (d) Temperature on the spread ratio in onestand rolling of oval caliber
The effect of (a) Roll gap, (b) Material size, and (c) Roller diameter on the spread ratio in onestand rolling of oval caliber
The effect of (a) Backward tension and (b) Forward tension on the spread ratio in threestand rolling of the roundovalround caliber
Comparison between the result of FE analysis and (a), (b) MLP1 and (c), (d) MLP2
The obtained regression results of (a) MLP1 and (b) MLP2
Comparison between the evaluation parameters of all MLP models
Comparison between the result of (a), (b) ANFIS1 and (c), (d) ANFIS2 with their FE analysis
Comparison between the evaluation parameters of all ANFIS models
The relative effect of input parameters on the material width after rolling for oval and round caliber by using the ANFIS model
The effect of input parameters on the material width after rolling for (a) Oval caliber and (b) Round caliber by using ANFIS model
(a) The sixstand rolling used for the verification of the proposed model and (b) Comparison between the result of FE analysis and AI model
Johnson Cook parameters of the used steel
A (MPa)  B (MPa)  C  n  m  

450  428.6  0.524  0.416  0.1  25  0.001 
Physical properties of the used steel
Item  Value 

Coefficient of thermal expansion (K^{−1})  2.16e5 
Poisson ratio  0.3 
Specific heat capacity (J·kg^{−1}. K^{−l})  628 
Density (kg·m^{−3})  7,536 
Coefficient of heat conduction (W·m^{−2}·K^{−1})  11,000 
Thermal Conductivity (W·m^{−1}·K^{−1})  28.9 
Different cases for simulation of wire roll rolling in onestand rolling
Num.  Caliber  Friction  Temperature  Speed  Roll gap  Material size  Roller diameter  Material strength 

1  Oval  6 Levels  5 Levels  6 Levels  5 Levels  5 Levels  6 Levels  5 Levels 
2  Round  6 Levels  5 Levels  6 Levels  5 Levels  5 Levels  6 Levels  5 Levels 
Input parameter ranges in onestand rolling for the oval caliber
Input  Friction  Temperature (ºC)  Speed (RPM)  Roll Gap (mm)  Material Size^{*} (mm)  Roller Diameter (mm)  Material Strength^{**} 

Range  0.2 to 0.6  800 to 1,200  6 to 72  5.9 to 11.03  36.21 to 36.76  366 to 854  0.5 to 15 
Ref. condition  0.4  1,000  24  8.5  36.65  610  1 
Material size means the radius of the input material.
These factors are applied to the stressstrain curve of the material. Thus, the strength of a case with a factor of 0.5 is half of the strength of the other case with a factor of 1.
Case studies for simulation of wire roll rolling in threestand rolling
Num.  1^{st} Roller  2^{nd} Roller  3^{rd} Roller  1^{st} Roller Speed  3^{rd} Roller Speed 

1  Oval  Round  Oval  5 Levels  5 Levels 
2  Round  Oval  Round  5 Levels  5 Levels 
Equations to make the input and output parameters dimensionless
Parameter  Equation  

Inputs (Without unit)  Backward tension ( 

Forward tension ( 

Geometrical parameter ( 

Friction  
Input (With unit)  Velocity (m/s) (V)  
Outputs (Without unit)  Spread ratio (S_{r})  
Shinokura coefficient  α 
Stress_{Z} means stress in the rolling direction obtain from FE analysis.
Inputs and outputs of all MLPs for the prediction of spread in oval and round caliber
Case  MLP  Inputs  Output  

Oval caliber  MLP1  G_{r}  T_{in}  T_{out}  V  S_{r}  
MLP2  A  
Round caliber  MLP3  G_{r}  T_{in}  T_{out}  V  S_{r}  
MLP4  A 
Parameters of the MLP structure used to design all MLP models
Network Parameters  Values 

Type of network  Feedforward neural network 
Data division  Manual 
Training algorithm  LevenbergMarquardt 
Performance  Mean square error (MSE) 
Hidden layers for MLP1  7107 
Hidden layers for MLP2  1076 
Hidden layers for MLP3  756 
Hidden layers for MLP4  756 
Transfer functions for hidden layers  Tangential sigmoid 
Learning rate  0.001 (default) 
Epochs  100 
Train, validation, and test data  70%  15%  15% 
Parameters of the ANFIS structure used to design all ANFIS models
Parameters  Values 

Type of system  Type1 Sugeno 
Clustering type  Fuzzy cmeans clustering 
Data division  Manual 
Training algorithm  Particle swarm optimization (PSO) 
Number of MFs/clusters  4 
Type of MFs  Gaussian 
Epochs  100 
Train and test data  75% and 25% 
The results of the proposed model for the prediction of width in sixstand rolling
Prediction method  Sec. 1  Sec. 2  Sec. 3  Sec. 4  Sec. 5 

Reference (mm)  24.38  32.16  18.98  24.1  15.36 
MLP1 (mm)    31.51    25.59   
MLP2 (mm)    32.24    23.41   
ANFIS1 (mm)    31.54    23.79   
ANFIS2 (mm)    31.64    23.85   
MLP3 (mm)  24.68    19.42    15.08 
MLP4 (mm)  24.62    18.64    15.12 
ANFIS3 (mm)  24.38    19.97    15.57 
ANFIS4 (mm)  24.38    18.2    16.08 
Fusion (mm)  24.52  31.73  19.06  24.16  15.46 
Error between Ref. and Fusion (%)  0.57  −1.3  0.42  0.26  0.69 