Application of a hybrid nonlinear algorithm driven by machine learning and feature importance identification for temperature control prediction of the bath smelting process

Senyuan Yang; Bo Yu; Jianxin Pan; Wuliang Yin; Hua Wang; Kai Yang; Qingtai Xiao; Senyuan Yang; Bo Yu; Jianxin Pan; Wuliang Yin; Hua Wang; Kai Yang; Qingtai Xiao

doi:10.3934/math.2025588

AIMS Mathematics

2025, Volume 10, Issue 6: 13104-13129. doi: 10.3934/math.2025588

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Application of a hybrid nonlinear algorithm driven by machine learning and feature importance identification for temperature control prediction of the bath smelting process

1.
State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming 650093, China
2.
Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming 650093, China
3.
Faculty of Science and Technology, Beijing Normal – Hong Kong Baptist University, Zhuhai, Guangdong 519087, China
4.
Research Center for Mathematics, Advanced Institute of Natural Sciences, Beijing Normal University, Zhuhai, Guangdong 519087, China
5.
School of Electrical and Electronic Engineering, The University of Manchester, Manchester M13 9PL, UK

Received: 31 December 2024 Revised: 15 May 2025 Accepted: 20 May 2025 Published: 06 June 2025
MSC : 62M20, 90C26, 92B20

Temperature control in bath smelting processes is crucial for optimizing the efficiency and quality of metal extraction, especially for nickel and copper. Traditional prediction methods often fail to account for the nonlinear and complex nature of these processes. This work introduces a novel hybrid nonlinear analysis algorithm combining the random forest–least squares support vector machine (RF-LSSVM) and random forest–relevance vector machine (RF-RVM) models to enhance the accuracy of temperature prediction. Utilizing 868 datasets collected from an oxygen-enriched top-blown furnace, key parameters such as the feeding amount (X₁), oxygen pressure (X₂), oxygen flow (X₃), total air flow (X₇), and lance windpipe back pressure (X₅) were analyzed. The RF-LSSVM model achieved superior predictive performance, with a mean absolute error (MAE) of 7.58 and a root mean square error (RMSE) of 9.82 for matte temperature (Y₁), and an MAE of 10.47 and an RMSE of 13.31 for slag temperature (Y₂). Comparatively, traditional methods showed higher errors, with MAE values of up to 23.64 and RMSE values as high as 59.14 in some cases. Additionally, the RF-RVM model performed significantly better than conventional models, with MAE and RMSE improvements of approximately 10~20%. These results demonstrate that the hybrid models effectively capture the intricate dynamics of the smelting process, offering a robust and adaptive framework for real-time temperature prediction. The improved accuracy in temperature control leads to enhanced smelting efficiency, reduced energy consumption, and higher quality of the extracted metals, ultimately benefiting the metallurgical industry by enabling more precise and sustainable production processes.
- bath smelting,
- temperature prediction,
- machine learning,
- hybrid models,
- oxygen-enriched top-blown furnace
Citation: Senyuan Yang, Bo Yu, Jianxin Pan, Wuliang Yin, Hua Wang, Kai Yang, Qingtai Xiao. Application of a hybrid nonlinear algorithm driven by machine learning and feature importance identification for temperature control prediction of the bath smelting process[J]. AIMS Mathematics, 2025, 10(6): 13104-13129. doi: 10.3934/math.2025588

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Abstract

Temperature control in bath smelting processes is crucial for optimizing the efficiency and quality of metal extraction, especially for nickel and copper. Traditional prediction methods often fail to account for the nonlinear and complex nature of these processes. This work introduces a novel hybrid nonlinear analysis algorithm combining the random forest–least squares support vector machine (RF-LSSVM) and random forest–relevance vector machine (RF-RVM) models to enhance the accuracy of temperature prediction. Utilizing 868 datasets collected from an oxygen-enriched top-blown furnace, key parameters such as the feeding amount (X₁), oxygen pressure (X₂), oxygen flow (X₃), total air flow (X₇), and lance windpipe back pressure (X₅) were analyzed. The RF-LSSVM model achieved superior predictive performance, with a mean absolute error (MAE) of 7.58 and a root mean square error (RMSE) of 9.82 for matte temperature (Y₁), and an MAE of 10.47 and an RMSE of 13.31 for slag temperature (Y₂). Comparatively, traditional methods showed higher errors, with MAE values of up to 23.64 and RMSE values as high as 59.14 in some cases. Additionally, the RF-RVM model performed significantly better than conventional models, with MAE and RMSE improvements of approximately 10~20%. These results demonstrate that the hybrid models effectively capture the intricate dynamics of the smelting process, offering a robust and adaptive framework for real-time temperature prediction. The improved accuracy in temperature control leads to enhanced smelting efficiency, reduced energy consumption, and higher quality of the extracted metals, ultimately benefiting the metallurgical industry by enabling more precise and sustainable production processes.

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