# SCORN: Sinter Composition Optimization with Regressive Convolutional Neural Network

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## Abstract

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## 1. Introduction

- We are the first to develop a regressive convolutional neural network for the sinter composition optimization problem. In our SCORN model, the input is the single final sintering production, and outputs are the corresponding chemical compositions of the sintered product. SCORN is a single input and multiple outputs RCNN model.
- We have collected sinter production and its burdening compositions from sintering machines in one sintering plant in China. Experimental results indicate that our SCORN model can produce an optimal sinter burdening ratio given a target production. SCORN also achieves higher performance than several regressive approaches.

## 2. Related Work

#### 2.1. Mathematical Statistical Models

#### 2.2. Machine Learning

#### 2.3. Sinter Compositions

## 3. Sintering Process and Characteristic Indexes

#### 3.1. Description of Sintering Process

#### 3.2. Sinter Characteristic Indexes

#### 3.2.1. Chemical Index

#### 3.2.2. Physical Index

## 4. Methods

#### 4.1. Motivation

#### 4.2. Problem

#### 4.3. Notations

#### 4.3.1. Architecture

**Feature Extraction.**The feature extraction module extracts features from the simple numerical target production for the second module. One advantage of the RCNN architecture is that the layers are easily interchangeable, which greatly facilitates transfer learning between layers [17].**Prediction.**This block takes the extracted features from the previous module and feeds them to a fully connected (FC) layer for regression prediction.

#### 4.3.2. Loss Function

#### 4.4. Model Evaluation

## 5. Experimental Setups

#### 5.1. Datasets Description

#### 5.1.1. Sinter Datasets

#### 5.1.2. More Validation Datasets

#### 5.2. Implementation Details

#### 5.3. Results

#### 5.3.1. The Traditional Methods Used for Comparison

**Least Square.**Least squares is a mathematical optimization technique that finds the best functional match for the data by minimizing the sum of squared errors.**KNN.**The nearest-neighbor technique is a well-known and studied technique in statistical learning theory [40]. In essence, the method consists of constructing estimators by averaging the properties of training events of similar characteristics to those of a test event to be classified or whose properties need to be inferred.**RondomForest.**A random forest algorithm is an ensemble approach that relies on CART models [39].**Decision Tree.**In a decision tree model, an empirical tree represents a segmentation of data, which is created by applying a series of simple rules. These models generate a set of rules that can be used for prediction through the repetitive process of splitting [38].**Multilayer Perceptron.**MLPs learn a mapping function from the input space to the target space [42]. Generally, there are three basic layers in the structure of MLPs, the input layer, the number of hidden layers, and the output layers. The three-layer MLP consists of one input node, three hidden layers with [20, 50, 100] hidden nodes, and nine output nodes in each joint.**SVR.**Support vector regression (SVR) works on the principle of structural risk minimization (SRM) from statistical learning theory. The core idea of the SRM theory is to arrive at a hypothesis h, which can yield the lowest true error for the unseen and random sample testing data [43].

#### 5.3.2. Composition Predictions

#### 5.3.3. Significance Analysis

#### 5.4. Parameter Analysis

## 6. Discussion

#### 6.1. Applications and Extensions

#### 6.2. Advantages and Limitations

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The architecture of our proposed SCORN for predicting the compositions of sinter at “production” 1010 ton (Conv: convolution, ReLU: rectified linear units, BN: Batch normalization, AP: average pooling, CCN: cross-channel normalization, MP: max pooling, Drop: dropout and FC: fully connected. The number of features of each layer is represented in the middle of the graph of each layer).

**Figure 4.**Comparison of the actual Tfe component and the predicted Tfe component with our SCORN model. The max error is $\pm 1.4835$.

Factors | Field | Unit | Average/Year | Change Range |
---|---|---|---|---|

Chemical compositions | TFe | % | 56.2 | 53.9–58.6 |

FeO | % | 8.8 | 5.5–12.3 | |

SiO${}_{2}$ | % | 5.7 | 4.7–6.4 | |

CaO | % | 11.6 | 9.7–13.7 | |

RO | - | 2 | 1.6–2.3 | |

MgO | % | 1.5 | 0.9–2.1 | |

S | % | 0.026 | 0.002–0.063 | |

Al${}_{2}$O${}_{3}$ | % | 1.23 | 0.19–1.98 | |

Total iron ore in the sinter | - | 98.35 | 96.88–99.80 |

**Table 2.**Comparison of the actual composition and the predicted composition using our SCORN model (# means the actual number, and P# represents the predicted number).

Compositions | # 1 | P# 1 | # 2 | P# 2 | # 3 | P# 3 | # 4 | P# 4 | # 5 | P# 5 | # 6 | P# 6 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

TFe % | 56.98 | 56.86 | 57.22 | 56.94 | 57.08 | 56.94 | 56.90 | 56.95 | 56.91 | 56.85 | 56.82 | 56.85 |

Feo % | 7.7 | 8.7 | 8.9 | 8.65 | 9 | 8.65 | 8.4 | 8.65 | 8.40 | 8.70 | 8.90 | 8.69 |

SiO${}_{2}$ % | 5.52 | 5.46 | 5.39 | 5.46 | 5.47 | 5.47 | 5.38 | 5.47 | 5.39 | 5.46 | 5.54 | 5.46 |

CaO % | 11.03 | 11.11 | 10.85 | 11.01 | 11.05 | 11.01 | 10.85 | 11.01 | 11.22 | 11.11 | 11.52 | 11.10 |

Ro | 2 | 2.04 | 2.01 | 2.02 | 2.02 | 2.02 | 2.02 | 2.02 | 2.08 | 2.04 | 2.08 | 2.03 |

MgO % | 1.55 | 1.27 | 1.52 | 1.20 | 1.49 | 1.20 | 1.5 | 1.20 | 1.61 | 1.27 | 1.53 | 1.26 |

S % | 0.86 | 1.12 | 0.85 | 1.13 | 0.88 | 1.13 | 0.89 | 1.13 | 0.86 | 1.12 | 0.86 | 1.12 |

Al${}_{2}$O${}_{3}$ % | 0.032 | 0.022 | 0.024 | 0.021 | 0.026 | 0.021 | 0.027 | 0.021 | 0.028 | 0.022 | 0.028 | 0.023 |

Total iron ore | 98.87 | 98.31 | 98.73 | 98.27 | 98.77 | 98.27 | 98.30 | 98.27 | 98.81 | 98.30 | 98.99 | 98.29 |

**Table 3.**Comparison of the SCORN models and the different methods (the variances of ${R}^{2}$ values are negligible because of their small values).

Method | SVR | KNN | R Forest | Decision Tree | OLS | MLP | SCORN |
---|---|---|---|---|---|---|---|

RMSE | 3.06 ± 0.33 | 0.50 ± 0.02 | 0.46 ± 0.01 | 0.46 ± 0.01 | 0.48 ± 0.01 | 0.49 ± 0.01 | 0.40 ± 0.01 |

MAE | 1.18 ± 0.08 | 0.33 ± 0.01 | 0.31 ± 0.01 | 0.31 ± 0.01 | 0.33 ± 0.01 | 0.34 ± 0.01 | 0.33 ± 0.01 |

${R}^{2}$ | 0.9865 | 0.9998 | 0.9998 | 0.9998 | 0.9997 | 0.9997 | 0.9999 |

Datasets | Pentagon | Corpus Callosum | Mandible |
---|---|---|---|

Geodesoc regress | 0.0223 | 0.0234 | 0.0873 |

ShapeNet | 0.3911 | 0.3854 | 0.1738 |

SCORN | 0.9923 | 0.9996 | 0.8191 |

Evaluation | drop = 0.5 | drop = 0.6 | drop = 0.7 | drop = 0.8 |
---|---|---|---|---|

Traning Loss | 1.5056 | 1.0434 | 1.0056 | 1.0397 |

Traning RMSE | 1.7353 | 1.4446 | 1.4182 | 1.4420 |

Evaluation | 0.0001 | 0.0005 | 0.001 |
---|---|---|---|

Traning Loss | 1.0056 | 0.9723 | 1345 |

Traning RMSE | 1.4182 | 1.3945 | 51.86 |

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## Share and Cite

**MDPI and ACS Style**

Li, J.; Guo, L.; Zhang, Y.
SCORN: Sinter Composition Optimization with Regressive Convolutional Neural Network. *Solids* **2022**, *3*, 416-429.
https://doi.org/10.3390/solids3030029

**AMA Style**

Li J, Guo L, Zhang Y.
SCORN: Sinter Composition Optimization with Regressive Convolutional Neural Network. *Solids*. 2022; 3(3):416-429.
https://doi.org/10.3390/solids3030029

**Chicago/Turabian Style**

Li, Junhui, Liangdong Guo, and Youshan Zhang.
2022. "SCORN: Sinter Composition Optimization with Regressive Convolutional Neural Network" *Solids* 3, no. 3: 416-429.
https://doi.org/10.3390/solids3030029