Comparison of Different Approaches to the Creation of a Mathematical Model of Melt Temperature in an LD Converter
Abstract
:1. Introduction
2. Materials and Methods
2.1. Regression Model of the Melt Temperature
- -
- the concentration of CO in converter gas (%),
- -
- the concentration of CO2 in converter gas (%),
- -
- the concentration of H2 in converter gas (%),
- -
- the concentration of O2 in converter gas (%),
- -
- the volume flow of converter gas (m3/hour),
- -
- the pressure of converter gas (Pa)
- -
- the lance height (cm),
- -
- the volume flow of oxygen (Nm3/min).
2.2. Deterministic Model of the Melt Temperature
- Deterministic model with feedback;
- Simplified deterministic model without feedback.
2.2.1. The Modeled Processes of Steelmaking
- Scrap melting process;
- The decomposition process of slag-forming additives;
- The process of oxidation of elements C, Si, Fe, Mn, P in the melt and others.
2.2.2. The Heat Balance
2.3. Machine Learning Model of the Melt Temperature
- Support vector regression (SVR);
- Adaptive neuro-fuzzy inference system (ANFIS).
2.3.1. Support Vector Regression
2.3.2. Adaptive Neuro-Fuzzy Inference System
3. Results
3.1. Results of the Regression Model
3.2. Results of the Deterministic Model
- DM1_1—deterministic model with feedback, heat loss coefficient according to the model Equation (41).
- DM1_2—deterministic model with feedback, heat loss coefficient according to the model Equation (42).
- DM1_3—deterministic model with feedback, heat loss coefficient according to the model Equation (43).
- DM2_1—deterministic model without feedback, heat loss coefficient according to the model Equation (41).
- DM2_1—deterministic model without feedback, heat loss coefficient according to the model Equation (42).
- DM2_1—deterministic model without feedback, heat loss coefficient according to the model Equation (43).
3.3. Results of the Machine Learning Model
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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No. Melt | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|
Tmeas (°C) | 1655 | 1648 | 1702 | 1647 | 1656 | 1642 | 1657 | 1668 | 1665 | 1688 |
RM1 Tmod (°C) | 1651 | 1662 | 1713 | 1681 | 1688 | 1646 | 1681 | 1732 | 1680 | 1723 |
(°C) | 4.0 | 14.4 | 11.2 | 33.6 | 31.9 | 3.8 | 24.3 | 64.0 | 15.2 | 35.2 |
(%) | 0.24 | 0.87 | 0.66 | 2.04 | 1.93 | 0.23 | 1.47 | 3.84 | 0.91 | 2.08 |
RM2 Tmod (°C) | 1646 | 1671 | 1709 | 1648 | 1659 | 1632 | 1652 | 1688 | 1689 | 1706 |
(°C) | 9.3 | 22.7 | 6.6 | 1.1 | 3.1 | 9.9 | 4.5 | 19.9 | 23.8 | 18.0 |
(%) | 0.56 | 1.38 | 0.39 | 0.07 | 0.19 | 0.60 | 0.27 | 1.19 | 1.43 | 1.07 |
RM3 Tmod (°C) | 1646 | 1671 | 1709 | 1650 | 1661 | 1632 | 1653 | 1689 | 1688 | 1706 |
(°C) | 9.2 | 22.5 | 7.0 | 3.0 | 4.6 | 9.8 | 3.6 | 20.6 | 23.3 | 17.9 |
(%) | 0.55 | 1.37 | 0.41 | 0.18 | 0.28 | 0.60 | 0.22 | 1.23 | 1.40 | 1.06 |
No. Melt | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|
Tmeas (°C) | 1655 | 1648 | 1702 | 1647 | 1656 | 1642 | 1657 | 1668 | 1665 | 1688 |
DM1_1 Tmod (°C) | 1656 | 1669 | 1694 | 1722 | 1674 | 1622 | 1642 | 1661 | 1631 | 1659 |
(°C) | 0.6 | 20.8 | 8.2 | 75.4 | 17.6 | 19.9 | 14.9 | 7.0 | 33.8 | 29.4 |
(%) | 0.04 | 1.26 | 0.48 | 4.58 | 1.06 | 1.21 | 0.90 | 0.42 | 2.03 | 1.74 |
DM1_2 Tmod (°C) | 1653 | 1668 | 1684 | 1723 | 1674 | 1624 | 1644 | 1664 | 1633 | 1656 |
(°C) | 1.9 | 19.8 | 18.3 | 75.9 | 17.7 | 18.4 | 13.3 | 4.3 | 32.4 | 31.7 |
(%) | 0.11 | 1.20 | 1.08 | 4.61 | 1.07 | 1.12 | 0.80 | 0.26 | 1.95 | 1.88 |
DM1_3 Tmod (°C) | 1641 | 1657 | 1700 | 1721 | 1670 | 1630 | 1649 | 1665 | 1636 | 1659 |
(°C) | 14.0 | 8.7 | 2.3 | 74.1 | 13.8 | 11.9 | 7.6 | 3.1 | 28.7 | 29.0 |
(%) | 0.85 | 0.53 | 0.14 | 4.50 | 0.84 | 0.72 | 0.46 | 0.18 | 1.72 | 1.72 |
No. Melt | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|
Tmeas (°C) | 1655 | 1648 | 1702 | 1647 | 1656 | 1642 | 1657 | 1668 | 1665 | 1688 |
DM2_1 Tmod (°C) | 1654 | 1658 | 1768 | 1669 | 1633 | 1616 | 1619 | 1642 | 1625 | 1687 |
(°C) | 0.9 | 10.2 | 66.0 | 22.3 | 23.2 | 25.8 | 37.6 | 25.9 | 40.4 | 1.2 |
(%) | 0.06 | 0.62 | 3.88 | 1.35 | 1.40 | 1.57 | 2.27 | 1.55 | 2.42 | 0.07 |
DM2_2 Tmod (°C) | 1638 | 1649 | 1718 | 1660 | 1621 | 1621 | 1621 | 1644 | 1631 | 1673 |
(°C) | 17.0 | 1.2 | 16.2 | 13.4 | 34.7 | 21.3 | 36.0 | 24.1 | 34.5 | 14.8 |
(%) | 1.03 | 0.07 | 0.95 | 0.81 | 2.10 | 1.30 | 2.17 | 1.44 | 2.07 | 0.88 |
DM2_3 Tmod (°C) | 1639 | 1651 | 1717 | 1659 | 1621 | 1621 | 1621 | 1644 | 1631 | 1674 |
(°C) | 15.6 | 2.5 | 15.4 | 12.5 | 34.6 | 21.5 | 36.3 | 24.4 | 34.2 | 14.4 |
(%) | 0.94 | 0.15 | 0.90 | 0.76 | 2.09 | 1.31 | 2.19 | 1.46 | 2.06 | 0.86 |
No. Melt | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|
Tmeas(°C) | 1655 | 1648 | 1702 | 1647 | 1656 | 1642 | 1657 | 1668 | 1665 | 1688 |
ANFIS Tmod (°C) | 1640 | 1635 | 1621 | 1619 | 1635 | 1635 | 1640 | 1625 | 1617 | 1624 |
(°C) | 14.8 | 12.4 | 80.2 | 27.5 | 20.2 | 6.8 | 16.5 | 42.7 | 47.5 | 63.2 |
(%) | 0.89 | 0.75 | 4.71 | 1.67 | 1.22 | 0.41 | 0.99 | 2.56 | 2.85 | 3.74 |
SVR Tmod (°C) | 1655 | 1669 | 1648 | 1650 | 1657 | 1665 | 1675 | 1671 | 1646 | 1648 |
(°C) | 0.4 | 21.9 | 53.9 | 3.1 | 1.5 | 23.3 | 18.6 | 3.9 | 18.7 | 39.3 |
(%) | 0.02 | 1.33 | 3.17 | 0.19 | 0.09 | 1.42 | 1.12 | 0.24 | 1.12 | 2.33 |
Model | Average Absolute Deviation (°C) | Average Relative Deviation (%) |
---|---|---|
RM1 | 23.8 | 1.43 |
RM2 | 11.9 | 0.71 |
RM3 | 12.2 | 0.73 |
DM1_1 | 22.7 | 1.37 |
DM1_2 | 23.4 | 1.41 |
DM1_3 | 19.3 | 1.17 |
DM2_1 | 25.4 | 1.52 |
DM2_2 | 21.3 | 1.28 |
DM2_3 | 21.1 | 1.27 |
ANFIS | 33.2 | 1.98 |
SVR | 18.5 | 1.10 |
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Laciak, M.; Kačur, J.; Terpák, J.; Durdán, M.; Flegner, P. Comparison of Different Approaches to the Creation of a Mathematical Model of Melt Temperature in an LD Converter. Processes 2022, 10, 1378. https://doi.org/10.3390/pr10071378
Laciak M, Kačur J, Terpák J, Durdán M, Flegner P. Comparison of Different Approaches to the Creation of a Mathematical Model of Melt Temperature in an LD Converter. Processes. 2022; 10(7):1378. https://doi.org/10.3390/pr10071378
Chicago/Turabian StyleLaciak, Marek, Ján Kačur, Ján Terpák, Milan Durdán, and Patrik Flegner. 2022. "Comparison of Different Approaches to the Creation of a Mathematical Model of Melt Temperature in an LD Converter" Processes 10, no. 7: 1378. https://doi.org/10.3390/pr10071378