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It is very difficult to control a blast furnace efficiently because of the characteristics of the closed smelting and the system's large delay. It is very helpful for blast furnace control to establish a model that can accurately predict the tendency of silicon content in molten iron. In this article, a nonparallel hyperplane–based fuzzy classifier is proposed reconciling the model accuracy with the model interpretability. Each hyperplane is as close as possible to one class of samples and as far as possible from the other class of samples. This leads to two small quadratic programming problems instead of a large one as a support vector machine–based fuzzy classifier. This makes our classifier faster than a support vector machine–based fuzzy classifier. We evaluate the proposed method on blast furnace data and synthetic data, which verifies the effectiveness. [ABSTRACT FROM AUTHOR]

The accurate prediction of molten iron quality in blast furnace (BF) can effectively improve the smelting efficiency and operation stability, which plays an important role in energy saving, emission reduction, and economic benefits improving. With the improvement of BF information acquisition technology and data storage technology, some data-driven modeling methods for simultaneously predicting multiple molten iron quality indexes have been presented. However, these modeling processes do not explore the use of the correlation information among multiple molten iron quality indexes, resulting in the suboptimal models. In addition, they do not pay attention to the molten iron quality indexes missing issue, which may lead to a great decline in modeling accuracy. To avoiding the above disadvantage, this article presents a novel multiple-input–multiple-output random vector functional-link networks. An output space transfer matrix is exploited, which not only makes full use of the correlation among all the molten iron quality indexes, but also greatly reduces the impact of index missing. For the corresponding tricky optimization problem, an alternative optimization algorithm is given, the convergence of which is guaranteed. A simulation of an actual BF data illustrates the proposed method. [ABSTRACT FROM AUTHOR]

For complex blast furnace smelting systems with large time delay, accurate prediction of molten iron quality indicators plays an important guiding role in blast furnace control. 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 (MIT), silicon content ([Si]), phosphorus content ([P]) and sulfur content ([S]). However, those data-driven MIMO models do not consider the inter-indicator correlation, which leads to the suboptimal model for the estimation of multiple molten iron quality indicators. This paper proposed a novel MIMO Takagi-Sugeno (T-S) fuzzy model with taking full account of the inter-indicator correlation. In the novel method, the inter-indicator correlation was explicitly modeled by a low-rank learning in a latent space that overcame the great challenge of jointly determining the fuzzy rules of MIMO T-S model and the inter-indicator correlation. For the corresponding optimization problem, an effective alternating optimization algorithm is presented. The validity of the proposed method is verified by simulation and comparison with some related methods on real blast furnace data. [ABSTRACT FROM AUTHOR]

The final product quality of blast furnace (BF) smelting, i.e., the molten iron quality (MIQ), cannot be measured in real-time, which has become one of the important factors restricting the automation of BF. Although some data-driven soft sensing methods have been presented recently, two issues still need to be solved to meet the demand for on-site applications. The first issue is that the data-driven modeling process cannot overlook the correlation among multiple MIQ indexes (MIQIs). The second issue is that the data-driven modeling method can tolerate the missing of MIQIs, which can appear due to some factors. To address the above two issues, this article proposed an output space transfer (OST)-based multiinput–multioutput (MIMO) random vector functional-link networks (RVFLNs) for simultaneously modeling multiple MIQIs. Through sparse learning of the OST matrix, the interindicator correlation is reasonably modeled. Due to the full use of interindicator correlation, the impact of missing indicators on modeling accuracy is greatly reduced. For the corresponding knotty optimization problem, an effective alternative optimization algorithm is presented. The actual data test shows that the proposed method can greatly improve the accuracy of multiple MIQIs estimation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]