A Novel MIMO T-S Fuzzy Modeling for Prediction of Blast Furnace Molten Iron Quality With Missing Outputs

For complex and difficult-to-control blast furnace systems with hour-level delay, accurate prediction of molten iron quality plays a very important role in guaranteeing the stable and smooth operation. Recently, some data-driven multi-input multi-output (MIMO) modeling methods have been proposed to model multiple molten iron quality indicators including molten iron temperature, silicon content ([Si]), phosphorus content ([P]), and sulfur content ([S]). However, those data-driven MIMO models ignore the interindicator correlation, which leads to the suboptimal model for the estimation of multiple molten iron quality indicators. Moreover, the above methods do not pay attention to the molten iron quality indicators missing issue, which often occurs on blast furnace. To address the above two issues, this article proposed a novel MIMO Takagi-Sugeno (T-S) fuzzy model by utilizing an output transfer matrix. In the novel method, the interindicator correlation was explicitly modeled by a low-rank learning of the correlation matrix that overcame the great challenge of jointly determining the fuzzy rules of the MIMO T-S model and the interindicator correlation. Moreover, a new complete complementary matrix can be obtained by the output transfer from the original incomplete matrix resulting from molten iron quality indicators missing issues. For the corresponding optimization problem, an effective alternating optimization algorithm is presented, and the convergence of the optimization algorithm is also rigorously proved. The validity of the proposed method is verified by comparison with some related methods on real blast furnace data.