Ironmaking process modeling uncertainty quantification via conformal prediction based on random vector functional link networks

For real-world industrial system modeling, dynamic stochastic errors inevitably exist in data-driven deterministic predictions (i.e., point predictions). The uncertainty of such prediction results directly affects various prediction-based operations for work condition identification and production decision-making. Therefore, a novel interval prediction method quantifying multi-output uncertainty is proposed by combining conformal prediction with random vector functional link networks (RVFLNs), which has fast learning speed and high accuracy performance. The proposed algorithm is used for the reliable prediction of molten iron quality in blast furnace ironmaking process. Firstly, to address the issue that shallow learning models have limited expression capabilities to describe complex nonlinear relationships, the dynamic attention mechanism and semi-supervised autoencoder are utilized to reveal and represent the correlations between different input variables and multi-output variables. Subsequently, the Elastic Net regularization technique is adopted to improve the multicollinearity and overfitting problems of traditional RVFLNs. Further, considering the deterioration of prediction accuracy and credibility caused by uncertain system dynamics, an Empirical Copula function-based Copula prediction uncertainty quantification method is introduced to realize multi-output variables reliable prediction with a given confidence level. Finally, actual blast furnace industrial data is applied to demonstrate the validity, utility, and sophistication of model.