Output space transfer based multi-input multi-output Takagi–Sugeno fuzzy modeling for estimation of molten iron quality in blast furnace

Abstract

The molten iron quality (MIQ) in the blast furnace (BF) needs on-site sampling and laboratory tests, which is very unfavorable to the control. To estimate multiple molten iron quality indicators (MIQIs) such as molten iron temperature (MIT), silicon content ([Si]), phosphorus content ([P]) and sulfur content ([S]) in real-time, some data-driven multi-input multi-output (MIMO) modeling methods have lately been developed. However, those modeling methods ignore the inter-indicator correlation. Moreover, the above modeling methods do not consider the processing strategy for the samples with missing indicators. To conquer the above two problems in the process of modeling, this paper proposed an output space transfer based MIMO Takagi–Sugeno (T–S) fuzzy modeling method for the four MIQIs. Through sparse learning of the correlation matrix, the inter-indicator correlation is specifically modeled. Due to the full use of inter-indicator correlation, the impact of missing indicators on modeling accuracy is greatly reduced. An effective alternative optimization algorithm is also provided for the corresponding intractable optimization problem. The actual data test shows that the proposed method can greatly improve the accuracy of multiple MIQIs estimations.