# Data-Driven Modelling and Optimization of Energy Consumption in EAF

^{*}

## Abstract

**:**

## 1. Introduction

- By producing different types of steel in the desired quality, the specified process requirements are met.
- By reducing the manufacturing costs, the specified economic requirements are met, which means that the profitability and competitiveness of the products can be increased.
- By limiting excessive pollution, which is regulated by government regulations, the specified environmental requirements are met.
- By limiting physically and mentally demanding work that is unacceptable for the population of a given country above a certain level of social development, the specified health and safety requirements are met.

- By reducing the consumption of loaded materials, refractory materials, energy sources, etc. per ton of product;
- By speeding up and increasing production and thus reducing the costs of maintenance, personnel and other specific production costs;
- By finding cheaper input materials and energy sources.

## 2. Materials and Methods

#### 2.1. Data Description and Pre-Processing

#### 2.2. Selection of the Key Input Variables

#### 2.3. Machine Learning Methods

#### 2.3.1. Linear Regression

#### 2.3.2. K-Nearest Neighbour Method

#### 2.4. Takagi–Sugeno Fuzzy Modeling

#### 2.5. Evolving the Cloud-Based Prediction Model

## 3. Results

#### 3.1. Results of the Selection of Key Input Variables

#### 3.2. Analysis of Models for Energy Consumption Prediction

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Toulouevski, Y.N.; Zinurov, I.Y. Modern Steelmaking in Electric Arc Furnaces: History and Development. In Innovation in Electric Arc Furnaces: Scientific Basis for Selection; Springer: Berlin/Heidelberg, Germany, 2013; pp. 1–24. [Google Scholar] [CrossRef]
- Saboohi, Y.; Fathi, A.; Škrjanc, I.; Logar, V. Optimization of the Electric Arc Furnace Process. IEEE Trans. Ind. Electron.
**2019**, 66, 8030–8039. [Google Scholar] [CrossRef] - Carlsson, L.S.; Samuelsson, P.B.; Jönsson, P.G. Predicting the Electrical Energy Consumption of Electric Arc Furnaces Using Statistical Modeling. Metals
**2019**, 9, 959. [Google Scholar] [CrossRef][Green Version] - Kovačič, M.; Stopar, K.; Vertnik, R.; Šarler, B. Comprehensive Electric Arc Furnace Electric Energy Consumption Modeling: A Pilot Study. Energies
**2019**, 12, 2142. [Google Scholar] [CrossRef][Green Version] - Sung, Y.; Lee, S.; Han, K.; Koo, J.; Lee, S.; Jang, D.; Oh, C.; Jang, B. Improvement of Energy Efficiency and Productivity in an Electric Arc Furnace through the Modification of Side-Wall Injector Systems. Processes
**2020**, 8, 1202. [Google Scholar] [CrossRef] - Echterhof, T. Review on the Use of Alternative Carbon Sources in EAF Steelmaking. Metals
**2021**, 11, 222. [Google Scholar] [CrossRef] - Ahmed, W.; Moazzam, M.; Sarkar, B.; Ur Rehman, S. Synergic Effect of Reworking for Imperfect Quality Items with the Integration of Multi-Period Delay-in-Payment and Partial Backordering in Global Supply Chains. Engineering
**2021**, 7, 260–271. [Google Scholar] [CrossRef] - Mahapatra, A.S.; N Soni, H.; Mahapatra, M.S.; Sarkar, B.; Majumder, S. A Continuous Review Production-Inventory System with a Variable Preparation Time in a Fuzzy Random Environment. Mathematics
**2021**, 9, 747. [Google Scholar] [CrossRef] - Bhuniya, S.; Pareek, S.; Sarkar, B. A supply chain model with service level constraints and strategies under uncertainty. Alex. Eng. J.
**2021**, 60, 6035–6052. [Google Scholar] [CrossRef] - Sarkar, B.; Mridha, B.; Pareek, S. A sustainable smart multi-type biofuel manufacturing with the optimum energy utilization under flexible production. J. Clean. Prod.
**2022**, 332, 129869. [Google Scholar] [CrossRef] - Yadav, D.; Kumari, R.; Kumar, N.; Sarkar, B. Reduction of waste and carbon emission through the selection of items with cross-price elasticity of demand to form a sustainable supply chain with preservation technology. J. Clean. Prod.
**2021**, 297, 126298. [Google Scholar] [CrossRef] - Carlsson, L.S.; Samuelsson, P.B.; Jönsson, P.G. Using Statistical Modeling to Predict the Electrical Energy Consumption of an Electric Arc Furnace Producing Stainless Steel. Metals
**2020**, 10, 36. [Google Scholar] [CrossRef][Green Version] - Logar, V.; Fathi, A.; Škrjanc, I. A Computational Model for Heat Transfer Coefficient Estimation in Electric Arc Furnace. Steel Res. Int.
**2016**, 87, 330–338. [Google Scholar] [CrossRef] - Meier, T.; Logar, V.; Echterhof, T.; Škrjanc, I.; Pfeifer, H. Modelling and Simulation of the Melting Process in Electric Arc Furnaces—Influence of Numerical Solution Methods. Steel Res. Int.
**2016**, 87, 581–588. [Google Scholar] [CrossRef] - Núñez, A.; De Schutter, B.; Sáez, D.; Škrjanc, I. Hybrid-fuzzy modeling and identification. Appl. Soft Comput.
**2014**, 17, 67–78. [Google Scholar] [CrossRef] - Dovžan, D.; Logar, V.; Škrjanc, I. Implementation of an Evolving Fuzzy Model (eFuMo) in a Monitoring System for a Waste-Water Treatment Process. IEEE Trans. Fuzzy Syst.
**2015**, 23, 1761–1776. [Google Scholar] [CrossRef] - Škrjanc, I.; Iglesias, J.A.; Sanchis, A.; Leite, D.; Lughofer, E.; Gomide, F. Evolving fuzzy and neuro-fuzzy approaches in clustering, regression, identification, and classification: A Survey. Inf. Sci.
**2019**, 490, 344–368. [Google Scholar] [CrossRef] - Fathi, A.; Saboohi, Y.; Škrjanc, I.; Logar, V. Comprehensive Electric Arc Furnace Model for Simulation Purposes and Model-Based Control. Steel Res. Int.
**2017**, 88, 1600083. [Google Scholar] [CrossRef] - Hay, T.; Visuri, V.V.; Aula, M.; Echterhof, T. A Review of Mathematical Process Models for the Electric Arc Furnace Process. Steel Res. Int.
**2021**, 92, 2000395. [Google Scholar] [CrossRef] - Lee, B.; Sohn, I. Review of Innovative Energy Savings Technology for the Electric Arc Furnace. JOM
**2014**, 66, 1581–1594. [Google Scholar] [CrossRef] - Barati, M.; Esfahani, S.; Utigard, T. Energy recovery from high temperature slags. Energy
**2011**, 36, 5440–5449. [Google Scholar] [CrossRef] - Lee, B.; Ryu, J.W.; Sohn, I. Effect of Hot Metal Utilization on the Steelmaking Process Parameters in the Electric Arc Furnace. Steel Res. Int.
**2015**, 86, 302–309. [Google Scholar] [CrossRef] - Kirschen, M.; Risonarta, V.; Pfeifer, H. Energy efficiency and the influence of gas burners to the energy related carbon dioxide emissions of electric arc furnaces in steel industry. Energy
**2009**, 34, 1065–1072. [Google Scholar] [CrossRef] - Bisio, G.; Rubatto, G.; Martini, R. Heat transfer, energy saving and pollution control in UHP electric-arc furnaces. Energy
**2000**, 25, 1047–1066. [Google Scholar] [CrossRef] - Meier, T.; Hay, T.; Echterhof, T.; Pfeifer, H.; Rekersdrees, T.; Schlinge, L.; Elsabagh, S.; Schliephake, H. Process Modeling and Simulation of Biochar Usage in an Electric Arc Furnace as a Substitute for Fossil Coal. Steel Res. Int.
**2017**, 88, 1600458. [Google Scholar] [CrossRef] - Gandt, K.; Meier, T.; Echterhof, T.; Pfeifer, H. Heat recovery from EAF off-gas for steam generation: Analytical exergy study of a sample EAF batch. Ironmak. Steelmak.
**2016**, 43, 581–587. [Google Scholar] [CrossRef] - Glavan, M.; Gradišar, D.; Atanasijević-Kunc, M.; Strmčnik, S.; Mušič, G. Input variable selection for model-based production control and optimisation. Int. J. Adv. Manuf. Technol.
**2013**, 68, 2743–2759. [Google Scholar] [CrossRef] - Van De Wal, M.; De Jager, B. Review of methods for input/output selection. Automatica
**2001**, 37, 487–510. [Google Scholar] [CrossRef][Green Version] - May, R.; Dandy, G.; Maier, H. Review of Input Variable Selection Methods for Artificial Neural Networks. In Artificial Neural Networks-Methodological Advances and Biomedical Applications; BoD—Books on Demand: Norderstedt, Germany, 2011. [Google Scholar]
- Li, K.; Peng, J.X. Neural input selection-A fast model-based approach. Neurocomputing
**2007**, 70, 762–769. [Google Scholar] [CrossRef] - Breiman, L. Better subset regression using the nonnegative garrote. Technometrics
**1995**, 37, 373–384. [Google Scholar] [CrossRef] - Chong, I.G.; Jun, C.H. Performance of some variable selection methods when multicollinearity is present. Chemom. Intell. Lab. Syst.
**2005**, 78, 103–112. [Google Scholar] [CrossRef] - Székely, G.J.; Rizzo, M.L.; Bakirov, N.K. Measuring and testing dependence by correlation of distances. Ann. Stat.
**2007**, 35, 2769–2794. [Google Scholar] [CrossRef] - Tibshirani, R. Regression Shrinkage and Selection via the Lasso. J. R. Stat. Soc.
**1996**, 58, 267–288. [Google Scholar] [CrossRef] - Freedman, D. Statistical Models: Theory and Practice; Cambridge University Press: Cambridge, UK, 2009. [Google Scholar]
- Montgomery, D.C.; Peck, E.A.; Vining, G.G. Introduction to Linear Regression Analysis; John Wiley & Sons: Hoboken, NJ, USA, 2012. [Google Scholar]
- Friedman, J.H.; Bentley, J.L.; Finkel, R.A. An Algorithm for Finding Best Matches in Logarithmic Expected Time. ACM Trans. Math. Softw.
**1977**, 3, 209–226. [Google Scholar] [CrossRef] - Chen, G.H.; Shah, D. Explaining the Success of Nearest Neighbor Methods in Prediction. Found. Trends Mach. Learn.
**2018**, 10, 1–250. [Google Scholar] [CrossRef] - Takagi, T.; Sugeno, M. Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern.
**1985**, SMC-15, 116–132. [Google Scholar] [CrossRef] - Kennedy, J.; Eberhart, R. Particle swarm optimization. In Proceedings of the ICNN’95-International Conference on Neural Networks, Perth, WA, Australia, 27 November–1 December 1995; Volume 4, pp. 1942–1948. [Google Scholar] [CrossRef]
- Andonovski, G.; Mušič, G.; Blažič, S.; Škrjanc, I. On-line Evolving Cloud-based Model Identification for Production Control. IFAC-PapersOnLine
**2016**, 49, 79–84. [Google Scholar] [CrossRef] - Blažič, A.; Škrjanc, I.; Logar, V. Soft sensor of bath temperature in an electric arc furnace based on a data-driven Takagi–Sugeno fuzzy model. Appl. Soft Comput.
**2021**, 113, 107949. [Google Scholar] [CrossRef]

**Figure 2.**Linear models of electrical energy consumption (as a percentage of the maximum value) as a function of total scrap weight (

**top left**), total oxygen (

**top right**), total carbon (

**bottom left**), and tapping temperature (

**bottom right**), respectively.

**Figure 4.**Linear models of electrical energy consumption as a function of the quotient of tapping temperature and total scrap weight (

**left**) and the quotient of total oxygen and total carbon (

**right**).

**Figure 5.**Prediction of electrical energy consumption with the k-NN model (

**left**) and the linear regression model (

**right**) compared to measurements of electrical energy consumption.

**Figure 6.**Prediction of electrical energy consumption with the evolving model (

**left**) and fuzzy model (

**right**) compared to measurements of electrical energy consumption.

**Figure 8.**Electrical energy consumption as a function of melting time for two different maximum transformer tap levels in the profile.

Charging | Melting | ||
---|---|---|---|

Description | Unit | Description | Unit |

Total scrap weight | $\left[\mathrm{kg}\right]$ | Melting time | $\left[\mathrm{s}\right]$ |

Hotheel start | $\left[\mathrm{kg}\right]$ | Delays | $\left[\mathrm{s}\right]$ |

Scrap weight in basket 1 | $\left[\mathrm{kg}\right]$ | Temperature | $\left[{}^{\circ}\mathrm{C}\right]$ |

Scrap weight in basket 2 | $\left[\mathrm{kg}\right]$ | Total oxygen | $\left[\mathrm{N}{\mathrm{m}}^{3}\right]$ |

Scrap weight in basket 3 | $\left[\mathrm{kg}\right]$ | Total carbon | $\left[\mathrm{kg}\right]$ |

Type of charged scrap | Hotheel end | $\left[\mathrm{kg}\right]$ | |

Slag weight | $\left[\mathrm{kg}\right]$ |

Variable | Influential Factor |
---|---|

Total scrap weight | 0.8571 |

Scrap weight in basket 1 | 0.7679 |

Total carbon | 0.6429 |

Scrap weight in basket 2 | 0.5714 |

Scrap weight in basket 3 | 0.5357 |

Mean temperature | 0.5179 |

Tapping temperature | 0.4286 |

Total oxygen | 0.1786 |

Variable | Influential Factor |
---|---|

Tapping temperature/total scrap weight | 0.9143 |

Mean temperature/scrap weight in baskets 1 and 2 | 0.6000 |

Chemical energy | 0.5143 |

Total oxygen/total carbon | 0.5143 |

Scrap weight in baskets 3 | 0.4571 |

Method | RMSE (%) | ${\mathit{R}}^{2}$ |
---|---|---|

k-NN method | 3.177 | 0.443 |

Linear regression | 3.171 | 0.445 |

Evolving model | 3.118 | 0.464 |

Fuzzy model | 2.910 | 0.533 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tomažič, S.; Andonovski, G.; Škrjanc, I.; Logar, V. Data-Driven Modelling and Optimization of Energy Consumption in EAF. *Metals* **2022**, *12*, 816.
https://doi.org/10.3390/met12050816

**AMA Style**

Tomažič S, Andonovski G, Škrjanc I, Logar V. Data-Driven Modelling and Optimization of Energy Consumption in EAF. *Metals*. 2022; 12(5):816.
https://doi.org/10.3390/met12050816

**Chicago/Turabian Style**

Tomažič, Simon, Goran Andonovski, Igor Škrjanc, and Vito Logar. 2022. "Data-Driven Modelling and Optimization of Energy Consumption in EAF" *Metals* 12, no. 5: 816.
https://doi.org/10.3390/met12050816