# Digital Model of Plan View Pattern Control for Plate Mills Based on Machine Vision and the DBO-RBF Algorithm

^{*}

## Abstract

**:**

^{2}) 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%.

## 1. Introduction

## 2. Plan View Pattern Detection and Actual Data Acquisition

#### 2.1. Detection Device

#### 2.2. Image Processing Algorithm

#### 2.3. Data Preprocessing

_{min})/(X

_{max}− X

_{min})

_{min}and X

_{max}are the minimum and maximum values in the input feature vector, respectively.

## 3. Establishment of Digital Model for PVPC Based on DBO-RBF

#### 3.1. Neural Network Algorithm

#### 3.2. Dung Beetle Optimizer

#### 3.3. Establishment of the Plan Pattern Prediction Model

^{2}(goodness of fit) can be chosen as performance metrics for the model [38]. By evaluating these metrics, adjustments can be made to the parameters. The equations for calculating MAE and R

^{2}are as follows:

^{2}is to one, the better the descriptive power of the established prediction model on the dataset.

^{2}(v.R

^{2}) and average MAE (v.MAE) of the test set with 51 output values are used as evaluation indicators, and the test results are shown in Table 5.

^{2}, v.MAE and training time of the test set with 51 output values were used as evaluation indicators, and the results are shown in Table 6.

#### 3.4. Establishment of the Plan Pattern Control Model

## 4. Results and Discussion

#### 4.1. Results of the PVPC Prediction Model

^{2}in the test set of three different network models, and the median result was selected as the stable prediction result. The results indicate that the DBO-RBF model has the best predictive performance and generalization ability. Figure 16 shows the R

^{2}distribution of 51 output values for three different neural network models. From the R

^{2}distribution of the three models, it can be seen that the predictive performance of the middle contour point is better than that of the edge contour point, and DBO-RBF shows the highest predictive performance. In addition, from Table 11, it can be further seen that the average absolute error distribution of DBO-RBF is more concentrated. From this perspective, DBO-RBF has better predictive performance.

^{2}and v.MAE of the head section prediction model were 0.9902 and 10.54 mm. The v.R

^{2}and v.MAE of the tail part prediction model were 0.9894 and 10.57 mm.

#### 4.2. Analysis Based on the PVPC Prediction Model

#### 4.3. Prediction Results of the PVPC Control Model

^{2}and MAE of L2_b were 0.96679 and 9.0289 mm; the R

^{2}and MAE of Dh_b were 0.97014 and 0.1294 mm; and the R

^{2}and MAE of G_b were 0.98642 and 0.0201 mm.

#### 4.4. Data Analysis Based on PVPC Control Model

## 5. Conclusions

- (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%.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Image before and after image processing: (

**a**) before image processing, and (

**b**) after image processing.

**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.

**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.

**Figure 19.**Prediction effect in RBF and DBO-RBF of PVPC parameters: (

**a**) L2_b, (

**b**) Dh_b, and (

**c**) G_b.

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 |

Group | 1 | 2 | 3 | 4 | 5 | Average Deviation |
---|---|---|---|---|---|---|

Deviation (pi) | 0.6 | 1 | 1 | 0.4 | 0.8 | 0.76 |

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 | mm^{2} |

V13-V63 | h1-h51 | Y-value of plate contour points | mm |

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 6 − 60 × 1500 − 2500 × 6000 − 53,000 | mm | |

Plate size range (Thick × Width × Length) | mm |

Spread | v.R^{2} | 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 |

Population Size | Iterations | v.R^{2} | 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 |

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 |

Spread | v.R^{2} | 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 |

Population Size | Iterations | v.R^{2} | 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 |

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 |

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 |

Index | v.R^{2} | 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 |

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 |

Parameter | Models | R^{2} | 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 |

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 |

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 |

Group | Number | Sr (mm^{2}) |
---|---|---|

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 |

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## Share and Cite

**MDPI and ACS Style**

Jiao, Z.; Gao, S.; Liu, C.; Luo, J.; Wang, Z.; Lang, G.; Zhao, Z.; Wu, Z.; He, C.
Digital Model of Plan View Pattern Control for Plate Mills Based on Machine Vision and the DBO-RBF Algorithm. *Metals* **2024**, *14*, 94.
https://doi.org/10.3390/met14010094

**AMA Style**

Jiao Z, Gao S, Liu C, Luo J, Wang Z, Lang G, Zhao Z, Wu Z, He C.
Digital Model of Plan View Pattern Control for Plate Mills Based on Machine Vision and the DBO-RBF Algorithm. *Metals*. 2024; 14(1):94.
https://doi.org/10.3390/met14010094

**Chicago/Turabian Style**

Jiao, Zhijie, Shiwen Gao, Chujie Liu, Junyi Luo, Zhiqiang Wang, Guanyu Lang, Zhong Zhao, Zhiqiang Wu, and Chunyu He.
2024. "Digital Model of Plan View Pattern Control for Plate Mills Based on Machine Vision and the DBO-RBF Algorithm" *Metals* 14, no. 1: 94.
https://doi.org/10.3390/met14010094