High-Precision Prediction of Oxygen and Carbon Powder Consumption in Electric Arc Furnace Steelmaking: A Whale Optimization Algorithm-Enhanced Multi-Output Hybrid Stacking Approach

A novel Whale Optimization Algorithm-Enhanced Multi-Output Hybrid Stacking (WOA-MOHS) model is proposed for accurately predicting the total amount of oxygen and carbon powder consumed in the steelmaking process of the electric arc furnace (EAF). The core innovation of this work lies in a hybrid modeling strategy in which the proposed method first constructs a mechanistic model based on thermodynamic principles and mass balance equations governing decarburization and oxidation reactions, and a data-driven multi-output stacking ensemble model is then constructed to correct its residual errors. In this ensemble model, the base learners include CatBoost, Random Forest, Extra Trees, Deep Neural Network, and Convolutional Neural Network algorithms. The meta-learner uses the K-Nearest Neighbors algorithm. The hyperparameters of all models are optimized using the WOA. In addition, five other modeling strategies, including single-output and multi-output machine learning models, hybrid models, and hyperparameter-optimized hybrid models. The results show that WOA-MOHS achieves the best performance across all evaluation metrics, with an R² of 0.83 for oxygen consumption and 0.94 for carbon powder consumption. When tested on new production data not used during model training, the WOA-MOHS model maintains excellent generalization ability, achieving a 93 pct hit rate (relative error less than 5 pct) for oxygen consumption and an 85 pct hit rate (relative error less than 5 pct) for carbon powder consumption. This study provides a valuable reference for oxygen injection and carbon powder addition operations in the EAF process, as well as new insights into modeling material addition predictions in the steelmaking process.