Double-hyperplane fuzzy classifier design for tendency prediction of silicon content in molten iron

Abstract

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.

Introduction

A blast furnace is the key unit for continuous molten iron production under various conditions such as use of coke and hot air. The detailed structure of the blast furnace and its detailed process are shown in Fig. 1. It is very difficult to control a blast furnace because of its complex nonlinear and long time delay characteristics. The silicon content in molten iron not only reflects the thermal state of the blast furnace but also indicates the quality of molten iron. Therefore, if the development trend of the silicon content in molten iron can be predicted accurately, it is of great significance for the automatic control of a blast furnace. With the continuous enhancement of data availability regarding the blast furnace, many data-driven methods have emerged for modeling the silicon content in molten iron.

In the early days, some linear data-driven methods were used to model the silicon content in molten iron [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13]. Then many nonlinear methods were proposed considering the complex nonlinearity of the blast furnace. A neural network is the method most often adopted. Chen et al. [15] proposed the use of a genetic algorithm to optimize the neural network. The complexity of a neural network is closely related to the performance of the model. So to balance them, Saxén et al. [14] presented a predator-prey model that modifies the weight between layers of the neural network by a Kalman filter. The generalization ability of the final model was improved. Obviously, it did not consider that the silicon content of molten iron is affected by the lag time of the blast furnace. In [16], a sparse neural network was obtained with the pruning technique considering the lag time. Unfortunately, sparse neural networks cannot be generated automatically. Later, Nurkkala et al. [17] further improved the performance of the above-mentioned algorithm by using the Pareto boundary. David et al. [18] used a simplified neural network to show that the silicon content of hot metal is positively correlated with the theoretical flame temperature, the pressure blow, and the coke rate, and is negatively correlated with the hot metal rate. Zhou et al. [19] presented a robust data-driven modeling method for the online estimation and control of molten iron quality. In [20], the silicon content prediction model for molten iron is approximated by a Wiener model identification using a linear subspace identification algorithm. In [21], a piecewise linear switching system is used for the blast furnace, and a self-organizing-based model is proposed.

The generalization ability of the model using the empirical risk minimization mentioned above cannot be guaranteed. So some modeling methods based on structural risk minimization are used, such as least-squares support vector machines (SVMs) with radial basis kernels [22], support vector regression with a multiple-function kernel [24], a sliding window [25] or improve its performance by chaos particle swarm optimization [23], ν-SVM [26] that its output with probability, SVM that its output class is coded by binary [27], adaptive least-squares SVM [28]. The fact proved that structural risk minimization–based models are better than empirical risk minimization–based models.

Some fuzzy modeling methods have been proposed that make a model has better interpretability. In [29], the fuzzy method using the Stone-Wilstrath theorem is used to model the relationship between input and output. In [30], the fuzzy c-means clustering model is used to search for the optimal control center of the blast furnace thermal state. To have a more intuitive understanding of the changing trend of silicon content in molten iron, a three classification fuzzy model–based SVM was proposed [31]. Saxén et al. [32] systematically reviewed the development of silicon content prediction models. In addition, there have been some studies on the simultaneous modeling of multiple indexes in molten iron [33], [34].

Recently, blast furnace data were visualized in two dimensions by means of t-distributed stochastic neighbor embedding [35], [36]. It was found that the data for blast furnace problems have a crossing feature, which leads to it being hard to classify them accurately by traditional classifiers such as least-squares and large margin–based classifiers. The discovery of relevant blast furnace data characteristics can well guide the design of classifiers. Li et al. [35] presented a fuzzy classifier with nonparallel hyperplanes (NHFC) that can conquer the intractable problem but that preserves the advantages of fuzzy classifiers. Here we also only focus on whether the silicon content in molten iron increases or decreases. The tendency prediction for the blast furnace is to judge whether the blast furnace is cooling or warming, which is enough for the control of the blast furnace. Therefore, the modeling process can be regarded as a data-driven binary classification modeling problem, and the model has a great guiding role for blast furnace operators. On the basis of the advantage of the fuzzy model, we propose a new nonparallel hyperplane–based fuzzy classifier (i.e., a double-hyperplane fuzzy classifier [DHFC]) that solves two smaller quadratic programming problems by conquering the cross-classification problem.

The contributions of this article are twofold: (1) A DHFC is proposed. The design of the classifier fully takes into account the cross-characteristics of blast furnace data, so it has a good classification effect. (2) The formulation of the proposed classifier is a pair of smaller quadratic programming problems that work faster than an SVM-based fuzzy classifier, which is a large quadratic programming problem.

The remainder of this article is organized as follows. In Section 2, the basic principle of the fuzzy classifier is recalled. In Section 3, the DHFC is introduced. The application and a discussion of the new fuzzy classifier in the blast furnace are given in Section 4. Section 5 provides a summary.