A two-stage multiobjective evolutionary ensemble learning for silicon prediction in blast furnace

Silicon content of molten iron is an important indicator in the blast furnace ironmaking process. Accurate prediction of silicon content is very important for monitoring the operating condition of the blast furnace and the quality of the molten iron. However, accurate and effective online prediction of silicon content is a challenging task due to the complex and high-dimensional nonlinear relationship between silicon content and process variables. Therefore, a two-stage multiobjective evolutionary ensemble learning algorithm is proposed to achieve a high-accuracy and low-complexity prediction model using support vector machine (SVR) as the base learner. In the first stage, a non-dominated sorting differential evolution algorithm with dynamic resource allocation (DRA-NSDE) is proposed to generate a set of non-dominated solutions (SVRs) with the objectives of accuracy and complexity. In the second stage, a stacking method based on clustering and differential evolution (CDE-Stacking) is proposed to select base learners with better diversity and construct the ensemble model. The effectiveness of the proposed DRA-NSDE and CDE-Stacking strategies is verified through a series of numerical experiments. The experimental results show that the proposed algorithm outperforms the rival methods on both the UCI benchmark data set and the actual blast furnace data set. In addition, the analysis of model complexity shows that the proposed model can achieve higher prediction accuracy with relatively low model complexity, which indicates that the algorithm is very suitable for the online prediction of silicon content in actual blast furnace ironmaking process.