**1. Introduction**

In modern integrated iron and steel works, oxygen is one of the most important energy resources used in various production processes, such as oxygen-rich combustion for ironmaking, converter blowing for steelmaking, and flame cutting for casting [1]. Statistically, about 20% [2] plant-wide electric power is used to produce the oxygen, and more than 50% [2] oxygen is used in the steelmaking process. To precisely monitor for oxygen consumption not only improves the process controlling performance in the steelmaking process, but also benefits making a satisfactory schedule for oxygen production to achieve the goal of energy saving and economic profits [3].

Traditionally, the main task of the steelmaking process is to produce various grades of steel by removing impurities in hot metal, such as excess carbon, silicon, manganese and phosphorus [4]. The primary steelmaking equipment is called the basic oxygen furnace (BOF) also known as Linz–Donawitz (LD) or oxygen converter (as shown in Figure 1). Theoretically, converter steelmaking is a complex process including melting, purifying, and alloying which are carried out at approximately 1600 ◦C (2900 ◦F) in melting conditions. First, the hot metal at 1200–1300 ◦C, an amount of scrap steel and calcined lime are charged into a converter, which produces violent reactions on the surface of the hot metal and slags. Then, oxygen from a lance is blown onto the liquid metal bath surface within typically 15 min, which continuously increases temperature and reduces the carbon-rich hot metal to

low-carbon steel between 0–1.5 percent. The slag-gas emulsion is formed during blowing and will decrease in the later period of blowing. Finally, specified chemical compositions and temperatures are reached by initiating numerous chemical reactions in sequence or simultaneously. In addition, the flux of burnt lime, dolomite and other chemical materials are added to further remove impurities and protect the lining of the converter. In fact, because each reaction couples and interplays with others [5], the process of converter steelmaking is very complex, and the condition of oxygen consumption is hard to be monitored in actual environments. However, with the current trend of Industry 4.0, the industrial process tends to be more expensive, which requires higher system reliability and performance. Therefore, it is needed to find an access to forecast the volume of oxygen consumption, which can boost the control performance of steelmaking process and the operational performance of oxygen distribution to a new level.

**Figure 1.** Converter steelmaking process.

With rapid developments of industrial automation and information systems, the industry has established big-data platforms and has collected a vast amount of valuable data [6]. Hence, a considerable number of researchers have used data-driven methodologies to predict these parameters that are hard to directly collect or calculate in the complex process [7,8], such as semiconductor [9], petrochemical [10], and energy process [11]. With concerns on the converter steelmaking process, many efforts have been devoted into predicting the end-point temperature and carbon content [12] in past decades, but the studies on forecasting oxygen consumption have seldom been reported. Since a large number of complex chemical reactions and physical changes in the steelmaking process exist, the exact amount of oxygen required to complete the steelmaking process cannot be calculated directly. Traditionally, these unmeasurable variables were estimated by constructing explicit knowledge models, i.e., material balance, heat balance, kinetics and other theories [13]. However, there are still many unknown factors in the converter steelmaking process, which may cause low precision and unreliability. Therefore, to develop its theoretical model is a high-cost and high-challenge task. However, industrial data produced in the steelmaking process provide a potential way to forecast these unmeasurable variables. These data-driven models complete the prediction task by building the mapping relationship between the input-output data without knowledge about the process. Owing to these advantages, a wide range of data-driven models are applied in the steel industry. Saxén et al. [14] reviewed a variety of prediction models for the silicon content of hot metal produced in blast furnaces. Liu et al. [15] applied a least squares support vector machine (LS-SVM) model to investigate several real-time prediction problems in the converter steelmaking process. Tian and Mao [16] proposed an ensemble extreme learning machine (ELM) to forecast the temperature of liquid steel in the ladle furnace. Han and Liu [17] proposed an ELM with optimized parameters to predict the endpoint carbon content and temperature of liquid steel. Laha et al. [18] compared a number of machine learning models for predicting yield steel in a steelmaking work, and verified that the support vector regression (SVR) is the most powerful one. However, the data-driven model is a black-box lack of interpretation. Therefore, many researchers paid more attention to the hybrid model based on theory and data. Yang et al. [19] developed a hybrid model to predict the electricity demand in the fused magnesia smelting process, in which its mechanism is formulated by a linear model and the unknown factors are modeled by neural networks. Chen et al. [20] proposed a hybrid model combined with a finite element method and an artificial neural network (ANN) to predict the degree of void closure produced in the cold rolling process. Lei and Su [21] developed an SVR-based hybrid model to forecast the mold level of the continuous casting production process.

The remaining sections of the paper are organized as follows. Section 2 provides the details of the proposed Gaussian process-based hybrid model named HyGPR. The experimental setup and results are analyzed and discussed in Section 3. Finally, Section 4 draws conclusions of this study and identifies several topics for future studies.
