Silicon Content Prediction in Blast Furnace Ironmaking Process Based on Closed-Loop Multiobjective Evolutionary Ensemble Learning

Silicon content prediction of hot metal is crucial for the stable and efficient operation of blast furnace (BF) ironmaking. As an emerging and promising data-driven modeling method, multiobjective evolutionary ensemble learning (MOEEL) has been successfully applied to silicon content prediction task. However, most existing MOEEL algorithms use an open-loop framework with two independent stages, that is, base learner training and ensemble, which lacks information exchange between the two stages and limits their prediction performance. To address this issue, this article proposes a closed-loop MOEEL (CL-MOEEL) algorithm. In CL-MOEEL, multikernel support vector regression (MKSVR) is used as the base learner, and the ensemble model (EM) is directly encoded as a solution in the population based on a variable-length encoding scheme. In this way, CL-MOEEL can simultaneously optimize EM structure and base learner parameters, and utilize the ensemble results as feedback information to guide the training process of the base learners. In addition, a knowledge-guided selection (KGS) method and two novel variable-length crossover operators are proposed to generate promising offspring solutions. Experimental results on both benchmark and practical industrial datasets show that the proposed method outperforms other powerful prediction methods. In the task of silicon content prediction, CL-MOEEL achieves a root mean square error (RMSE) of 0.083, an $R^{2}$ of 0.74, and a hit rate (HR) of 80.71%. Furthermore, the analysis of its complexity and feasibility highlights its strong potential for application in practical industrial processes.