# Real-Time Control of Sintering Moisture Based on Temporal Fusion Transformers

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## Abstract

**:**

## 1. Introduction

## 2. Sintering and Water Addition Process Mechanism

## 3. Model Architecture

#### 3.1. Gated Residual Networks

#### 3.2. Variable Selection Network

#### 3.3. Interpretable Multi-Head Attention

^{[19]}. Where $Q=[{q}_{1},{q}_{2},\dots ,{q}_{D}]$, $K=[{k}_{1},{k}_{2},\dots ,{k}_{D}]$ and $V=[{v}_{1},{v}_{2},\dots ,{v}_{D}]$, using the normalization function and the scaled dot product as the scoring function, the result of the self-attention is:

#### 3.4. Temporal Fusion Decoder

#### 3.4.1. Local Enhanced Sequence Layer

#### 3.4.2. Static Enrichment Layer

#### 3.4.3. Temporal Self-Attention Layer

#### 3.4.4. Position-Wise Feedforward Layer

#### 3.5. Quantile Regression Loss Function

## 4. TFT Sintering Mositure Model

#### 4.1. Data Pre-Processing

^{2}, the volume of the mixed hopper is in tons, and the measuring accuracy of the moisture meter is 0.001). They contain the plant’s sintering system measurement data from January 2018 to April 2018. The data were collected every 4 s, totaling 1,636,000 entries (as shown in Table 1), in which the amount of artificial added water is the predicted output variable of the model, and the remaining variables include the amount of each type of material in the sintering process with real-time moisture measurements as input variables.

#### 4.2. TFT Network Architecture and Training Result Analysis

#### 4.3. Comparative Analysis with Existing Models

#### 4.4. Interpretability Analysis

#### 4.4.1. Characteristic Importance Analysis

#### 4.4.2. Analysis of Model Validity under Abnormal Operating Conditions

#### 4.4.3. Analysis of Quantile Forecasting Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

TFT | Temporal Fusion Transformers |

LSTM | Long short-term memory |

PSO-LSTM | Particle swarm optimization–long short-term memory |

## References

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**Figure 5.**Correlation of mixture volume with water addition (where Du denotes dust ash, Si denotes sinter return, Li denotes limestone, Do denotes dolomite, Qu denotes quicklime, Ir denotes iron-tempering return, Bl denotes blast-furnace ash, Fi denotes mineral powder, Pu denotes pulverized coal, and Mo denotes moisture measurements).

**Figure 6.**Multi-step prediction fit (P50_step = 1 denotes the prediction result corresponding to the 50% quartile at one time step in backward prediction, P50_step = 2 denotes the prediction result corresponding to the 50% quartile at two time steps in backward prediction, P90_step = 1 denotes the prediction result corresponding to the 90% quartile at one time step in backward prediction, and P90_step = 2 denotes the prediction result corresponding to the 90% quartile at two time steps in the backward prediction).

**Figure 9.**Distribution of importance of characteristics (Du denotes dust ash, Si denotes sinter return, Li denotes limestone, Do denotes dolomite, Qu denotes quicklime, Ir denotes iron ore return, Bl denotes blast-furnace ash, Fi denotes mineral powder, Pu denotes coal dust, and Mo denotes moisture measurement).

Time (s) | Limestone (t/h) | Quicklime (t/h) | ⋯ | Moisture (%) | Added Water (t/h) |
---|---|---|---|---|---|

0 | 229 | 76 | ⋯ | 7.4 | 115 |

4 | 232 | 67 | ⋯ | 7.4 | 115 |

8 | 237 | 56 | ⋯ | 7.4 | 114 |

12 | 230 | 54 | ⋯ | 7.5 | 113 |

16 | 224 | 62 | ⋯ | 7.4 | 113 |

⋯ | ⋯ | ⋯ | ⋯ | ⋯ | ⋯ |

Model Parameters | Value |
---|---|

Learning rate | 0.001 |

Number of iterations | 15 |

Number of attention heads | 4 |

Encoding time step | 168 |

Total time step | 192 |

Number of single batches | 36 |

Time Interval (s) | RMSE | RMSEr | R |
---|---|---|---|

0 | 3.5651 | 0.0298 | 0.9940 |

4 | 4.0208 | 0.0334 | 0.9924 |

8 | 4.4209 | 0.0367 | 0.9907 |

12 | 4.6186 | 0.0383 | 0.9899 |

16 | 4.4401 | 0.0369 | 0.9895 |

⋯ | ⋯ | ⋯ | ⋯ |

Times (s) | True Added Water | P50 Added Water | P90 Added Water |
---|---|---|---|

0 | 114 | 114.4302 | 114.9393 |

4 | 114 | 114.4522 | 114.9517 |

8 | 114 | 114.4081 | 114.9467 |

12 | 114 | 114.4565 | 114.9686 |

16 | 115 | 115.5932 | 116.1918 |

⋯ | ⋯ | ⋯ | ⋯ |

Model | ${\mathit{R}}^{2}$ | RMSE | RMSEr |
---|---|---|---|

LSTM | 0.8923 | 10.5703 | 0.0878 |

Transformer | 0.8582 | 12.1254 | 0.1007 |

PSO-LSTM | 0.9836 | 4.3081 | 0.0358 |

TFT | 0.9881 | 3.5851 | 0.0298 |

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**MDPI and ACS Style**

Chen, X.; Cheng, J.; Zhou, Z.; Lu, X.; Ye, B.; Jiang, Y.
Real-Time Control of Sintering Moisture Based on Temporal Fusion Transformers. *Symmetry* **2024**, *16*, 636.
https://doi.org/10.3390/sym16060636

**AMA Style**

Chen X, Cheng J, Zhou Z, Lu X, Ye B, Jiang Y.
Real-Time Control of Sintering Moisture Based on Temporal Fusion Transformers. *Symmetry*. 2024; 16(6):636.
https://doi.org/10.3390/sym16060636

**Chicago/Turabian Style**

Chen, Xinping, Jinyang Cheng, Ziyun Zhou, Xinyu Lu, Binghui Ye, and Yushan Jiang.
2024. "Real-Time Control of Sintering Moisture Based on Temporal Fusion Transformers" *Symmetry* 16, no. 6: 636.
https://doi.org/10.3390/sym16060636