# Gaussian Process-Based Hybrid Model for Predicting Oxygen Consumption in the Converter Steelmaking Process

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

- (1)
- The amount of input materials, such as the carbon, silicon, manganese, phosphorus, sulfur content of hot metal.
- (2)
- The control parameters of blowing, e.g., lance position, and blowing pattern.
- (3)
- The final smelting targets, e.g., oxygen consumption highly depends on the carbon target.
- (4)
- The equipment conditions, e.g., converter lining and internal converter geometry.

#### 2.1. Reaction-Based Linear Model

#### 2.2. Gaussian Process Regression with Noise

#### 2.3. HyGPR with K-Means Clustering

## 3. Experiments and Discussion

#### 3.1. Data Set

- (1)
- The weight of hot metal (Fe).
- (2)
- The weight of impurity elements, e.g., carbon (C), silicon (Si), manganese (Mn), sulphur (S) and phosphorus (S) which are the products of the weights of hot metal and the element percentages.
- (3)
- Five additional materials (AM) for steelmaking, of which the real compositions are secreted.

#### 3.2. Evaluation Metrics

#### 3.3. Results and Analysis

## 4. Conclusions

- (1).
- The online prediction model involving dynamic operating parameters, such as the position of oxygen lance, the pressure of oxygen blowing and the duration of oxygen blowing.
- (2).
- The prediction model to forecast slopping events, which is very important to reduce production costs and environmental impacts.
- (3).
- In this study, we assume that the noise of the steelmaking process is a Gaussian distribution. However, when it comes to the small-sample and high-dimensional data set, the assumption is incorrect. So it needs to develop a non-Gaussian prediction model applied in other environments.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**HyGPR model with K-means clustering. MLR: multiple linear regression; GPR: Gaussian process regression.

**Figure 4.**Forecasting results with candidate clusters: (

**a**) $\mathrm{Q}=1$; (

**b**) $\mathrm{Q}=2$; (

**c**) $\mathrm{Q}=3$; (

**d**) $\mathrm{Q}=4$; (

**e**) $\mathrm{Q}=5$.

Parameters | Mean. | Std. | Minimum | Maximum |
---|---|---|---|---|

Fe (t) | 276.8450 | 252.7000 | 289.8000 | 21.6711 |

C (t) | 12.1259 | 0.5061 | 10.3288 | 14.0078 |

Si (t) | 0.9477 | 0.4456 | 0.0318 | 2.332 |

Mn (t) | 0.4332 | 0.2047 | 0.1252 | 2.2066 |

P (t) | 0.2431 | 0.0221 | 0.1736 | 0.4119 |

S (t) | 0.0023 | 0.0022 | 0 | 0.0343 |

AM1 (t) | 1.7980 | 1.4659 | 0 | 9.908 |

AM2 (t) | 1.7487 | 1.6683 | 0 | 8.172 |

AM3 (t) | 14.1139 | 2.5374 | 5.9610 | 28.937 |

AM4 (t) | 4.1623 | 1.3636 | 0 | 9.66 |

AM5 (t) | 0.7833 | 1.6976 | 0 | 11.994 |

O2 (10^{3}m^{3}) | 13.7823 | 0.8079 | 11.0480 | 15.913 |

Cluster Count | RMSE (10^{3}m^{3}) | MAE (10^{3}m^{3}) | MAPE (%) | CPU Time (S) |
---|---|---|---|---|

Q = 1 | 0.64 | 0.49 | 3.56 | 62.47 |

Q = 2 | 0.64 | 0.48 | 3.51 | 27.62 |

Q = 3 | 0.63 | 0.49 | 3.55 | 19.82 |

Q = 4 | 0.63 | 0.48 | 3.52 | 13.32 |

Q = 5 | 0.64 | 0.53 | 3.90 | 15.49 |

**Table 3.**Performance evaluation of compared models on the test set (The best metrics are highlighted in bold).

Model | RMSE (10^{3}m^{3}) | MAE (10^{3}m^{3}) | MAPE (%) |
---|---|---|---|

MLR | 0.70 | 0.54 | 3.95 |

SVM | 0.69 | 0.53 | 3.92 |

ANN | 0.68 | 0.52 | 3.84 |

HyGPR | 0.63 | 0.48 | 3.52 |

Model | RMSE (10^{3}m^{3}) | MAE (10^{3}m^{3}) | MAPE (%) | HRI (%) | CPU (S) |
---|---|---|---|---|---|

GPR | 0.63 | 0.49 | 3.59 | 92.42% | 75.74 |

HyGPR | 0.63 | 0.48 | 3.52 | 96.08% | 14.14 |

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**MDPI and ACS Style**

Jiang, S.-L.; Shen, X.; Zheng, Z.
Gaussian Process-Based Hybrid Model for Predicting Oxygen Consumption in the Converter Steelmaking Process. *Processes* **2019**, *7*, 352.
https://doi.org/10.3390/pr7060352

**AMA Style**

Jiang S-L, Shen X, Zheng Z.
Gaussian Process-Based Hybrid Model for Predicting Oxygen Consumption in the Converter Steelmaking Process. *Processes*. 2019; 7(6):352.
https://doi.org/10.3390/pr7060352

**Chicago/Turabian Style**

Jiang, Sheng-Long, Xinyue Shen, and Zhong Zheng.
2019. "Gaussian Process-Based Hybrid Model for Predicting Oxygen Consumption in the Converter Steelmaking Process" *Processes* 7, no. 6: 352.
https://doi.org/10.3390/pr7060352