Plan view pattern control (PVPC) is a highly effective means to improve the rectangularization of products and increase the yield of plate mills. By optimizing the parameters of PVPC, the effect of PVPC can be further improved. In this paper, a digital model for predicting and controlling crop patterns of plates is proposed based on the radial basis function (RBF) neural network optimized by the dung beetle optimizer (DBO) algorithm. Machine vision technology is used to obtain a digital description of the crop pattern of the rolled plates. An automatic threshold adjustment algorithm is proposed for the image processing of plate pattern photos during the rolling process. The error between the pattern data calculated through machine vision technology and the measured pattern data does not exceed 3 mm. The spread parameters of the RBF are optimized using DBO, and the digital model structure is established. The goodness of fit (R2) and the mean absolute error (MAE) are used as evaluation indicators. The results show that the digital model established based on DBO-RBF has good predictive and control performance, realizing intelligent prediction of the crop pattern of plates and the parameter optimization of PVPC. In practical applications, the crop cutting loss area of irregular deformation at the end of the plate can be reduced by 31%.
Keywords: plate; PVPC; digital model; DBO-RBF; machine vision
Plate products are essential key materials for national economic construction. At present, the competition in the iron and steel industry is becoming increasingly fierce, so improving product yield and reducing resource loss are key to enhancing the competitiveness of plate enterprises [[
The basic principle of the plan view pattern control (PVPC) process is to quantitatively predict the pattern of the rolled plate and then convert it into the abnormal distribution of the plate thickness given at the last pass of the sizing or broadsiding phase according to the "constant volume principle". This abnormal thickness distribution is used to improve the rectangularity of the rolled parts in the later rolling stages, as shown in Figure 1.
There are roughly three research methods for controlling the plan pattern of plates. The first is the analytical method, which is the earliest method of studying the deformation process of plate patterns. On the basis of the law of minimum resistance and the constant volume principle, the theoretical equation for three-dimensional metal flow can be obtained, which lays a foundation for the study of plan view pattern prediction of plates. However, in the derivation of these equations, it is necessary to make assumptions and simplifications, which will inevitably increase the model's error. Moreover, in the plate rolling process, the irregular deformation regions of plates are difficult to express by strict theoretical models.
The second method is physical simulation and industrial testing. Based on theoretical models, this method involves carrying out physical simulation experiment in the laboratory and industrial experiments. The simulations and experimental results are used to improve the accuracy of the model. Hiroyasu Shigemori et al. [[
In recent years, with the development of computer science, finite element simulation technology has become increasingly advanced, and it has been widely used in rolling process simulation. Liu [[
In the context of Made in China 2025 and Industry 4.0, digitalization is in an important position. Digital Twins are thought of as a digital counterpart to physical production artefacts. Therefore, to be useful for every purpose in their environment they have a high resolution [[
The digitization of the iron and steel industry also provides a new idea for the research of plan view pattern control of plates. It is necessary to solve the problem that the traditional mechanism model of PVPC has reached a bottleneck. Some researchers have studied the plan view pattern control of plates by using machine learning algorithms. Zhao [[
At present, there have been few studies on the application of machine learning algorithms to predict the plan view patterns of plates. This is because machine learning algorithms require a large number of data samples and the quality requirements for data samples are very high. Machine vision technology can effectively solve the above two problems. At present, machine vision technology has been applied in the rolling field. Schausberger et al. [[
At present, the image detection devices of plate production lines are normally situated at the finishing area, which cannot provide timely feedback regarding the effect of PVPC. Therefore, because the detection conditions of mill areas are complicated, it is necessary to study the development of image recognition algorithms.
In this paper, according to the requirements of the digitization of plan view pattern control, a machine vision detection device is installed near the mill area and an image processing algorithm is developed to obtain high-quality data according to the actual conditions of plate pattern detection image processing. A combinational optimization machine learning algorithm is proposed for a digital model of plan view pattern control and the digital model is applied to the actual production for verification. In the second section, the development of machine vision detection and image processing algorithms are introduced and the data sets of digital models are established. In the third section, a digital model of PVPC is established by combining DBO and RBF neural network machine learning algorithms. In the fourth section, the influence of plan view pattern control parameters on the irregular pattern of the crop is analyzed, and the PVPC control model is established. Also, the digital model effect is verified at the production site.
In order to provide timely feedback on the plan view pattern control effect of the rolled plate, a Gige network camera was installed at the exit of the rolling mill for image acquisition, as shown in Figure 2. Through the LAN and Gige camera link, the plate image data is obtained. Image recognition technology is used to obtain the edge data of the crop pattern of the plate and the recognition results are stored in the local disk.
A harsh rolling environment due to water vapor, dust, and light interference, will affect the clarity of the image acquired by the measuring device, so it is necessary to use the image processing algorithm to treat the acquired image and obtain an accurate plate profile. In this process, an established and widely used image processing algorithm is selected, allowing gray-scale transform, projection transform, threshold processing, contour extraction, and the complete contour point coordinates to be obtained, as shown in Figure 3.
However, in the actual process of extracting contour points of plate images, due to the different temperature of plates at different passes and the different brightness and darkness of workshop light at different times, the values of image pixels will be affected. If a fixed threshold is selected for threshold processing, it is impossible to segment each plate image accurately, thus affecting the extraction of contour points. Therefore, an adaptive threshold adjustment method for plan view pattern image detection of plates is proposed. The algorithm flow is shown in Figure 4.
The principle of this algorithm is to find the outline point coordinates of the plate through the Canny edge detection algorithm, project them into the original plate image, calculate the average pixel value of the point set, and set it as a threshold value for threshold processing, so that each plate image can be automatically adjusted for binarization processing, as shown in Figure 5.
In order to verify the detection accuracy of the algorithm, five images processed by the algorithm are randomly selected. Five edge feature points, A, B, C, D, and E in the plate image, are defined, as shown in Figure 6. Where A is the lower left end point of the plate, B is the lower right end point of the plate, C is the left peak point of the plate, D is the right peak point of the plate, and E is the valley value point of the middle region of the plate. Taking the upper left corner of the plate image as the origin, a rectangular coordinate system plan is established, and the internal midpoint of the five edge feature pixels corresponding to each image is selected as the ideal edge coordinate point and compared with the five edge feature coordinate points extracted by the above image detection algorithm. The comparison results of the first image are shown in Table 1. The deviations of the five images are shown in Table 2. It can be seen that the image detection algorithm is more accurate in locating the edge of the plate, and the final accuracy can be controlled within one pixel.
In the actual rolling process, the crop will show irregular asymmetry, which is because the plate in the rolling process is affected by transverse asymmetric factors, such as the stiffness difference on both sides of the mill, the transverse temperature of the plate, and the deviation of the center line of the plate. Therefore, in the actual collection of 101 contour points in the head–tail deformation area, the middle point is taken as the benchmark and the y values of the left and right symmetrical points are treated as the mean value, as shown in Figure 7.
The actual coordinate data of 51 contour points can be obtained by converting the pixel coordinate system to the actual coordinate system. Match the data obtained from image processing with the plate ID and rolling process data and summarize it into a database for easy selection when establishing a neural network prediction model in the future. In this paper, the data from 1150 plates are selected as the sample for the neural network prediction model for the plan view pattern. Considering the physical model and the actual production situation, 12 main variables were selected and combined with the head–tail contour points of the rolled plate as the data set used, as shown in Table 3. V7, V8, V9, and V10 are the parameters of PVPC. In the actual rolling process, the theoretical model is simplified to a seven-point control method in order to ensure control accuracy, as shown in Figure 8. V11 and V12 can be used as two indexes to evaluate the irregular region of the crop pattern, as shown in Figure 9. The smaller V11 and V12 are the smaller the crop cutting loss area of irregular deformation.
The contour coordinate data of 1150 plates and the corresponding rolling schedule parameters were collected from the hot rolling site as the original data. The main equipment of the plate production line is a two stand four high mill. The main process parameters are shown in Table 4.
Machine learning has high requirements for sample quality, which requires further sample screening. In order to make the data more real and objective, the samples with irregular patterns and breakpoints are eliminated, and only the samples with smooth contour coordinates of head and tail are retained. Finally, 1096 samples were selected for subsequent machine learning modeling. In addition, different variables often have different data distributions, so it is necessary to normalize each feature of the sample to make each variable have the same metric scale. In this paper, the min–max processing method [[
Yi = (Xi − X
where, X
An artificial neural network (ANN), also known as a neural network, is a mathematical model based on the basic principles of neural networks in biology. It simulates the processing mechanism of the human brain's nervous system for complex information by understanding and abstracting the brain's structure and external stimulus–response mechanism [[
A radial basis function (RBF) network is a three-layer feedforward neural network with a single hidden layer that can approximate any nonlinear function. It is one of the most widely used and well-performing models [[
In the figure, X is the input feature vector, Y is the output feature value, is the number of hidden layer nodes, d is the center in the hidden layer, and W represents the weights from the hidden layer to the output layer. The model consists of an input layer, a hidden layer, and an output layer. The transformation from the input layer to the hidden layer is nonlinear, while the transformation from the hidden layer to the output layer is linear. In this paper, the RBF neural network selects the Gaussian function [[
(
A strict radial basis function neural network is established using the newrbe function. This network model is a feedforward neural network with a single-layer hidden layer, and the number of hidden layer neurons is equal to the number of samples (1096 hidden layer neurons in this article). Use the input layer feature matrix of the nth sample as the clustering center value of the nth neuron of hidden layer. The transpose matrix of the input feature matrix is set as the weight matrix between the input layer and the hidden layer. The structure of the newrbe function is shown in Equation (
net = newrbe (P, T spread) (
where, P is an RQ-dimensional matrix composed of Q input vectors, T is an SQ-dimensional matrix composed of Q target classification vectors, and spread is the spread rate of the radial basis function.
The dung beetle optimizer (DBO) is a novel swarm optimization algorithm. The DBO algorithm simulates the behaviors of dung beetles, including rolling, breeding, foraging, and stealing, to form an optimization process for finding the optimal solution of a target function. In benchmark function tests, the DBO algorithm has demonstrated better capability in finding optimal solutions compared to other swarm intelligence algorithms [[
The algorithm starts by randomly initializing the positions and fitness values of dung beetle individuals in the search space. After each iteration, individuals of different types of dung beetles update their positions according to their respective position update rules. The fitness values of all individuals are compared, and the information of the current best dung beetle is recorded. This process is repeated until the termination condition is met. Finally, the algorithm outputs the information of the globally best dung beetle individual, obtaining the global optimal solution and its corresponding fitness value. The algorithm flowchart is shown in Figure 11.
In this paper, the RBF network is combined with the DBO algorithm to find the optimal smoothing coefficient for the RBF neural network with the current samples and network structure, in order to obtain a model with the highest accuracy and smoothness. The larger the spread of the radial basis function, the smoother the fitted function and the stronger the network's generalization ability. However, a large spread means that a large number of neurons are required to adapt to rapid changes in the function. If the spread is set too small, it means that many neurons are needed to adapt to slow changes in the function, which can result in poor network performance. The combination with the dung beetle optimization algorithm can effectively solve this problem.
The structure of the RBF neural network is simpler compared to deep learning network structures, allowing for the design of minimal structure models that meet accuracy requirements and making it highly applicable in industrial settings. In order to obtain a robust prediction model for the plan pattern of plates, 10 feature variables that are relevant to the physical model and have a significant impact on the plan pattern of plates are selected as input variables for the plan pattern prediction model. The corresponding coordinates of the plate's crop pattern contour points are combined as the output variable for the plan pattern prediction model. The model structure of RBF is shown in Figure 12.
DBO can achieve fast convergence by gradually obtaining the optimal solution to the problem in the entire population through the local behavior optimization of individuals. By using DBO to optimize the spread parameter of the RBF neural network, the DBO-RBF model has better generalization and learning abilities. It can improve the predictive accuracy of the model. The algorithm flow of DBO-RBF is shown in Figure 13.
In order to obtain a DBO-RBF model with fast convergence speed and high computational efficiency, it is necessary to determine the appropriate range interval, population size, and number of iterations. During the evaluation process of the RBF prediction model, MAE (mean absolute error) and R
(
(
where n is the number of samples in the dataset,
From the evaluation index Equations (
The hidden layer of the RBF neural network created based on Equation (
From Table 5, it can be seen that the prediction performance of RBF gradually improves with the increase of the spread parameter. However, when the spread parameter reaches a certain level, the increase of the spread parameter will actually decrease the prediction accuracy. Overall, the optimal spread parameter search interval for the model is between 200 and 250. After determining the search interval, it is necessary to discuss and test the population size and iteration times. Although increasing the number of populations and iterations can avoid the possibility of falling into a local optimal solution due to a small population or failing to find the optimal solution due to a small number of iterations, setting the number of populations and iterations too high may lead to slow convergence speed and a significant increase in calculation time.
The test of the prediction model based on DBO-RBF is carried out without changing the training set samples through the commonly used collocation method of multiple population numbers and iteration times, so as to determine the most suitable collocation parameters. The v.R
From the results in the table, it can be seen that when the population size is 50 and the number of iterations is 150, the prediction accuracy has reached its maximum. So, the population size of the DBO-RBF model was set to 50 and the iteration number was set to 150.
In addition, we have also obtained the optimal parameters of the BP neural network through experiments, as shown in Table 7.
In order to establish a neural network model between the deformation area and the plan view pattern control parameters, and adjust the plan pattern parameters to obtain the most suitable control parameters, eight feature variables that are relevant to the physical model and have a significant impact on the PVPC parameters are selected as input variables for the plan pattern control model, which also combines the corresponding control data as the output variables of the model. The model structure of the RBF network is shown in Figure 14.
The parameter optimization for the PVPC control model is similar to the prediction model. The search range interval, population size, and iteration number of DBO-RBF are determined first. The results are shown in Table 8 and Table 9.
Finally, the search range was determined to be 50–70, and the combination of population size and iteration number was 50–100.
In addition, we have also obtained the optimal parameters of the BP neural network through experiments, as shown in Table 10.
Three algorithms—BP, RBF, and DBO-RBF—were used to train the prediction model of the plate head. The three models were trained after randomly scrambling the dataset samples to generate the training set samples for a total of nine times. Figure 15 shows the distribution of v.R
After the same prediction analysis, the predictive results of the tail plan pattern prediction model and the head model are summarized in Table 12. It shows that the DBO-RBF has the best predictive performance. The v.R
In previous studies, the influence of PVPC parameters on the irregular deformation of the plate crop pattern was mostly explored through experiments based on physical model calculations and finite element simulation analysis. Due to the complex coupling effect between process parameters, it is difficult for physical models to cumulatively predict the head and tail deformation after multiple passes of rolling. Also, finite element simulation requires high modeling levels and parameter settings, and the calculation time is long. This section investigates the influence of PVPC parameters on the deformation of the plate head based on the developed neural network model. The conventional slab was selected and its slab size and rolling schedule are shown in Table 13.
Firstly, verify the correctness of the model. Use the target thickness (V4) as the sole variable for prediction. The values of Hp and Sr as a function of the target thickness are shown in Figure 17. As the target thickness decreases, the total amount of metal flowing to the head part during the rolling process will increase, and Hp and Sr will also increase, which is consistent with the physical phenomenon of the rolling process.
Here we discuss the influence of PVPC parameters on the crop pattern of rolled plates, with reference to the control method. Due to the need to consider the judgment of steel biting signals, V7 is usually set as a fixed value, so only V8, V9, and V10 parameters are adjusted appropriately. As shown in Figure 18, V8, V9, and V10 all have an impact on the crop pattern. Among them, as V8 and V10 gradually increase, Hp shows a trend of first decreasing and then increasing, while Sr shows a trend of gradually decreasing. As V9 gradually increases, Hp shows a decreasing trend, while Sr also shows a decreasing trend. Therefore, for plates with poor head plan view patterns, it is possible to appropriately increase the parameters of V8, V9, and V10 while meeting the equipment requirements to reduce the deformation area at the head end. It can be seen that optimizing the PVPC parameters can effectively reduce the deformation area of the crop pattern.
Three algorithms—BP, RBF, and DBO-RBF—were used to train the PVPC control model. The three models were trained together a total of nine times after randomly scrambling the dataset samples to generate training set samples each time. The median result was selected as the stable prediction result. Figure 19 shows the scatter plots of the results predicted by the different neural networks. From the graph, it can seen that the sample results predicted by DBO-RBF are closer to the standard line. The stable prediction results of the three neural networks are summarized in Table 14. Among them, DBO-RBF showed the best predictive performance. The R
The digital control model was applied in order to verify the actual optimization performance. A group of seven slabs with the same specifications were selected from the same batch and the specific parameters are shown in Table 15.
The seven slabs were divided into three groups as shown in Table 16. The first group of slabs were rolled with the original PVPC parameters settings; The second group of slabs were rolled with the PVPC parameters optimized based on experience; The third group of slabs were rolled with optimized PVPC parameters calculated through the developed PVPC control model. The parameters are shown in Table 16.
We collected images of the head of each rolled plate using the image acquisition device, used the proposed image processing algorithm to extract the coordinates of irregular contour points, and performed corresponding calculations. We also measured the two characteristic lengths of the irregular area of the plate after crop shearing, and deviation is within 3 mm between the measured results and image processing results. The irregular area values of seven rolled plates are shown in Table 17.
The table shows the best optimization effects on the irregularly cropped areas after rolling with the developed digital model. Figure 20 shows the control results of the irregular areas with different control methods. The irregularly cropped areas can be reduced by 31% with the digital control model.
In this paper, machine vision is used as a significant tool to accurately measure the plan view pattern data of plates. Using this dataset, a neural network-based model for predicting the plan view pattern of plates and a control model were proposed and improved using the dung beetle optimization algorithm. The main results of this article are as follows:
- (
1 ) An automatic threshold adjustment algorithm is proposed for image processing of plates' pattern photos during the rolling process. It can accurately perform binary processing to obtain accurate edge contour point data. The error between the pattern data calculated through machine vision technology and the measured pattern data does not exceed 3 mm. - (
2 ) Compared to the radial basis function model, the digital twin model proposed in this paper has higher prediction accuracy. For the prediction of head part contour points, the average goodness of fit increased from 0.98532 to 0.99021, and the average mean absolute error decreased from 11.03 mm to 10.54 mm. For the prediction of tail contour points, the average goodness of fit increased from 0.98103 to 0.98949, and the average mean absolute error decreased from 11.29 mm to 10.57 mm. In the PVPC control model, for the prediction results of PVPC parameters, the DBO-RBF model delivers the best performance. The goodness of fit of short stroke projection length, dynamic reduction, and further dynamic reduction are 0.96679, 0.97014, and 0.98462, respectively. The mean absolute error of short stroke projection length, dynamic reduction, and further dynamic reduction are 9.1007 mm, 0.1294 mm, and 0.0217 mm, respectively. - (
3 ) The developed digital PVPC control model has been applied to practical production. Compared to traditional empirical optimization, the PVPC control model reduces the irregularly cropped pattern by 31%.
Graph: Figure 1 Rolling process of PVPC: (a) PVPC sizing rolling, and (b) PVPC broadsiding rolling.
Graph: Figure 2 Schema of camera installation position.
Graph: Figure 3 Image before and after image processing: (a) before image processing, and (b) after image processing.
Graph: Figure 4 Flow chart of automatic threshold adjustment algorithm.
Graph: Figure 5 Schema of image processing algorithm.
DIAGRAM: Figure 6 Schematic diagram of feature contour points.
Graph: Figure 7 Outline point coordinate processing diagram.
Graph: Figure 8 Cross section of plate. The red line in the picture represents the contour line of the steel plate after PVPC technology is applied, the black line represents the simplified contour line, and the red points are the feature points set in the seven point control method to define variables.
Graph: Figure 9 Parameter extraction of crop pattern deformation. The black line represents the actual contour of the edges of the rolled steel plate, while the red line represents the contour of the edges of the cut steel plate.
Graph: Figure 10 Schema of RBF network neural structure.
Graph: Figure 11 Flow chart of DBO algorithm.
Graph: Figure 12 Network structure of the plan pattern prediction model.
Graph: Figure 13 Flow chart of DBO-RBF algorithm.
Graph: Figure 14 Network structure of the plan pattern control model.
Graph: Figure 15 The boxplot for the v.R2 value in multiple training sessions.
Graph: Figure 16 The scatter plot for the R2 value in multiple training sessions.
Graph: Figure 17 The Tar_thk influence on the Hp and Sr.
Graph: Figure 18 PVPC parameters influence on the Hp and Sr: (a) L2_b, (b) Dh_b and (c) G_b.
Graph: metals-14-00094-g018b.tif
Graph: Figure 19 Prediction effect in RBF and DBO-RBF of PVPC parameters: (a) L2_b, (b) Dh_b, and (c) G_b.
Graph: metals-14-00094-g019b.tif
Graph: Figure 20 Comparison of head parts with different optimization methods.
Table 1 Contrast deviation of contour point coordinates.
ID Ideal Pixel Coordinates Textual Algorithm Deviation (pi) A1 (53, 599) (53, 599) 0 B1 (1063, 599) (1062, 599) 1 C1 (203, 377) (203, 378) 1 D1 (896, 391) (896, 391) 0 E1 (704, 399) (704, 398) 1 Average deviation: 0.6
Table 2 Five groups of contour point deviation.
Group 1 2 3 4 5 Average Deviation Deviation (pi) 0.6 1 1 0.4 0.8 0.76
Table 3 Parameter description of the dataset.
Index Parameter Description Unit V1 Plt_thk The plate thickness before rolling mm V2 Plt_wid The plate width before rolling mm V3 Plt_len The plate length before rolling mm V4 Tar_thk Target thickness mm V5 Ratio_width Broadening ratio after completion of rolling - V6 Ratio_length Extension ratio after completion of rolling - V7 L1_b Prestroke length (PVPC parameter) mm V8 L2_b Short stroke projection length (PVPC parameter) mm V9 Dh_b Dynamic reduction (PVPC parameter) mm V10 G_b Further dynamic reduction (PVPC parameter) mm V11 Hp Maximum height of crop pattern mm V12 Sr Irregular area of crop pattern mm2 V13-V63 h1-h51 Y-value of plate contour points mm
Table 4 Parameter description of the stand dataset.
Items Roughing Mill Finishing Mill Unit Maximum rolling force 50,000 40,000 kN Work roll diameter Φ900/Φ850 Φ850/Φ800 mm Work roll length 2800 2690 mm Backup roll diameter Φ1800/Φ1700 Φ1600/Φ1500 mm Backup roll length 2740 2590 mm Rated speed of motor 0-50-120 0-60-145 rpm Main motor power 2 × 4200 2 × 4200 kW Rated rolling torque 2 × 1700 2 × 1470 kN·m Slab size range (Thick × Width × Length) 150 − 260 × 1665 − 2570 × 1000 – 2700 mm Plate size range (Thick × Width × Length) mm
Table 5 Effect of spread of RBF.
Spread v.R2 v.MAE (mm) 10 0.90322 16.7342 50 0.93588 13.5319 100 0.95656 13.0510 150 0.97780 12.8796 200 0.98236 11.3574 250 0.98227 11.3587 300 0.98105 11.5419 350 0.97553 12.5201 400 0.96725 13.0107 500 0.95689 13.1065 600 0.92725 15.0107
Table 6 Effect of population size and iterations of Plan Pattern Prediction Model.
Population Size Iterations v.R2 v.MAE (mm) Training Time (s) 30 50 0.98747 11.1523 353 30 100 0.98792 11.0967 701 50 100 0.98841 11.0396 1112 50 150 0.98955 10.8762 1537 50 200 0.98955 10.8762 2196 100 200 0.98955 10.8762 3914 100 500 0.98955 10.8762 9894
Table 7 Plan Pattern Prediction Model parameters based on BP.
Parameters Value Number of hidden layers 2 Number of hidden neurons 25–25 learning rate 0.02 dropout ratio 0.1 hidden layer activation function sigmoid function optimization function optimization function loss function MSE
Table 8 Effect of spread parameter of RBF.
Spread v.R2 v.MAE (mm) 10 0.86945 3.9413 20 0.95163 3.2748 30 0.95572 3.2124 40 0.96637 3.1471 50 0.96866 3.1293 60 0.9692 3.0974 70 0.96875 3.1264 80 0.96774 3.1486 100 0.96025 3.1897 200 0.95689 3.2103 300 0.92725 3.4937
Table 9 Effect of population size and iterations of Plan Pattern Control Model.
Population Size Iterations v.R2 v.MAE (mm) Training Time (s) 30 50 0.96975 5.1012 141 30 100 0.96975 5.1012 274 50 100 0.97104 5.0973 409 50 150 0.97216 5.0604 613 50 200 0.97216 5.0604 837
Table 10 Plan Pattern Control Model parameters based on BP.
Parameters Value Number of hidden layers 2 Number of hidden neurons 20–20 learning rate 0.02 dropout ratio 0.1 hidden layer activation function sigmoid function optimization function optimization function loss function MSE
Table 11 The value distribution of v.MAE in multiple training sessions.
v.MAE (mm) BP RBF DBO-RBF ≤12 mm 132 136 145 12–18 mm 65 60 55 18–24 mm 14 17 15 24–30 mm 6 5 4 >30 mm 2 1 0
Table 12 Comparison of the different models.
Index v.R2 v.MAE (mm) head BP 0.95374 13.35 RBF 0.98532 11.03 DBO-RBF 0.99021 10.54 tail BP 0.95590 12.12 RBF 0.98103 11.29 DBO-RBF 0.98949 10.57
Table 13 Slab data summary.
Parameters Values Plt_thk/mm 220 Plt_wid/mm 2065 Plt_len/mm 2447 Tar_thk/mm 11.6 Ratio_width 1.11 Ratio_length 17.14
Table 14 Results comparison of models.
Parameter Models R2 MAE (mm) L2_b DBO-RBF 0.96679 9.0289 RBF 0.95531 9.1007 BP 0.93514 9.2986 Dh_b DBO-RBF 0.97014 0.1294 RBF 0.96038 0.1457 BP 0.93507 0.1601 G_b DBO-RBF 0.98642 0.0201 RBF 0.97875 0.0217 BP 0.94113 0.0243
Table 15 Summary table of slab data.
Items Data material AISI-1045 Start rolling temperature/°C 1100 Plt_thk/mm 220 Plt_wid/mm 2165 Plt_len/mm 2522 Tar_thk/mm 19 Ratio_width 1.11 Ratio_length 10.43
Table 16 PVPC parameters settings.
Optimization Method Number L2_b (mm) Dh_b (mm) G_b (mm) Not optimized 1-1 605 6.2 0.35 Experience optimization 2-1 605 6.4 0.54 2-2 605 6.4 0.54 2-3 605 6.4 0.54 Model optimization 3-1 649.4 6.57 0.75 3-2 649.4 6.57 0.75 3-3 649.4 6.57 0.75
Table 17 The measurement results of Sr after rolling.
Group Number Sr (mm2) 1 1-1 903,271.99 2 2-1 730,173.10 2-2 749,710.71 2-3 728,490.90 Average value 736,124.90 3 3-1 624,578.69 3-2 609,294.65 3-3 642,866.66 Average value 625,580.00
Conceptualization, Z.J. and C.H.; methodology, Z.J., S.G. and C.L.; software, S.G. and G.L.; validation, S.G., C.L., J.L. and Z.W.(Zhiqiang Wang); formal analysis, C.L., J.L. and Z.W. (Zhiqiang Wang); investigation, Z.Z. and Z.W. (Zhiqiang Wu); data curation, S.G. and C.L.; writing—original draft preparation, Z.J., S.G., J.L. and Z.W. (Zhiqiang Wang); writing—review and editing, Z.J., S.G., Z.Z. and Z.W. (Zhiqiang Wu); visualization, C.L., J.L. and Z.W. (Zhiqiang Wang); supervision, Z.J., C.H., Z.Z. and Z.W. (Zhiqiang Wu) All authors have read and agreed to the published version of the manuscript.
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.
The authors declare no conflicts of interest.
By Zhijie Jiao; Shiwen Gao; Chujie Liu; Junyi Luo; Zhiqiang Wang; Guanyu Lang; Zhong Zhao; Zhiqiang Wu and Chunyu He
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