Dynamic Prediction with Statistical Uncertainty Evaluation of Phosphorus Content Based on Functional Relevance Vector Machine

Abstract

In the steelmaking process, inaccurate composition of raw materials, experimental process parameter control, and other factors bring about large statistical uncertainty to the phosphorus content prediction of molten steel. Meanwhile, lots of models mainly predict the end‐point phosphorus content, but the composition change during the whole production process is still in the gray box condition, where the exact refining state is unknown. These two problems increase the difficulty in process parameter optimization and control. In order to improve the phosphorus content control in the steelmaking process, this work proposes the functional relevance vector machine (FRVM) method. This method smooths the time series of process parameters to continuous functions by functional data analysis to predict the phosphorus content change during the whole production process, and estimates the probabilistic distributions of regression weights based on the Bayesian framework to directly output the probabilistic confidence interval of the phosphorus content. The real‐world steelmaking dataset validates that the mean relative prediction error of phosphorus content by the FRVM method is less than 18.04% during the whole production process and the end‐point hit rate is 86.46% when the prediction error is within ±0.005 wt%.