**1. Introduction**

The raw material used in the production of a blast furnace is called burden. It is mainly composed of coke, sinter, and pellet. The prepared burden is loaded into a hopper. After a series of transportation steps on the top of the furnace, it falls onto a rotating chute, when the exit of the hopper opens. Then, the material enters the blast furnace and forms burden layers in the throat. At the bottom, hot air is blown into the furnace to burn the coke, producing carbon monoxide and hydrogen that act as reductants. The rising reductants react chemically with iron oxide in burden and the iron oxide becomes hot metal after the reduction and melting. In the reduction, impurities in iron ore combine with the added flux to form molten slag. Hot metal and slag are discharged from tapholes at the bottom of the furnace. After treatment, molten slag is used as a raw material for cement and hot metal is transported to basic oxygen furnace by torpedo.

Some studies have shown that the charging affects the chemical reaction between the layers and reducing gas in the shaft of the furnace. The layers influence the shape of the cohesive zone and energy utilization efficiency of the furnace [1]. Therefore, the charging system is of great significance for the operation of the blast furnace. Due to the high temperature, high pressure, and dusty environment of the blast furnace, the internal state of the furnace cannot be measured. Even though furnace top temperature detection equipment, cross temperature measurement, and furnace top infrared cameras are already applied in the furnace, they still cannot accurately provide information about the burden layers in the furnace. Simulation technology is a powerful method combining computer, mathematics, physical engineering, and chemical engineering. It is helpful to observe the phenomena that are difficult to be directly measured in practice. Meanwhile, it saves costs, time, and materials in experiments [2].

Many studies have used mathematical models to study the charging system of the blast furnace. Yoshimasa et al. [3] developed a simulation model for the burden distribution of blast furnace charging

and studied the trajectory of the raw material, burden descent, and mixing layer, providing important information for the subsequent model development. Pohang Iron and Steel Company proposed a radial distribution function of the burden and applied it in an actual blast furnace to study the distribution characteristics of the burden and to improve the distribution of the gas flow [4]. Krishman et al. [5] developed a mathematical model for the optimization of bell-less charging, and the calculation results were consistent with the actual data. Saxén and Hinnelä [6] developed a bell-less burden distribution model on the basis radar measurement, and the dependence between the layer thickness and charging variables was modeled by neural networks [7]. Nag [8] proposed a mathematical model of the bell-less top to calculate the trajectory of the burden in charging. Park et al. [9] analyzed the blast furnace charging system by developing a burden descent model and a gas flow model, and compared the results with those from a 1/12-scaled model experiment. Samik et al. [10] proposed a general target methodology to estimate the stock profile in the blast furnace, where the burden distribution is based on experiments in different scaled models of a blast furnace with various materials. Shi et al. [11] proposed a new model of stockline profile formation in which equations were developed for the inner and the outer repose angles by considering the influence of the burden's vertical and horizontal flow.

The above mathematical models were developed based on some assumptions and different operating conditions. Therefore, it is quite difficult to apply them to get accurate results of the burden layer for other furnaces. If a charging model can be combined with a reliable burden surface detection method, the reliability of the calculated burden profile information can be increased. For example, rotating radar detection technology can more accurately measure the height of each point of the burden surface even under severe conditions, such as complete darkness and high-dust atmosphere, than a mechanical stock rod [12]. Therefore, in a black-box environment, vibration, and strong airflow, burden distribution online measurement should be stable and accurate. Considering the limits of the radar method, radar data also includes noise and can only reflect the surface shape of the object. Through the combination of radar, data processing, and the charging mathematical model, the error and noise of radar data can be reduced a lot. Furthermore, the shape of the burden surface and the structure of the burden layers can be better estimated [13].

Some scholars have studied the application of radar in blast furnaces, and some achievements have been made. Liu et al. [14] used radar data containing information of the burden surface situation and cross thermometer data reflecting the trend change of the burden surface with time as the training data for a fuzzy neural network to classify and predict the burden surface. Gao et al. [15] suggested that visualization and simulation is a new technology to monitor the charging system and to help the operation of blast furnaces. Based on the real multi-radar data, Zhu et al. [16] estimated the burden profile by a cubic-curve equation at the end of a multi-loop charging. Furthermore, the burden profile before the next multi-loop charging was calculated by considering the impact of the burden descent. Li et al. [17] used fuzzy c-means clustering to classify a large amount of burden surface radar data and proposed a multiple-model set of the burden surface. The real-time burden surface data were matched with the model to produce the expected burden surface. A reconstruction algorithm based on phased array radar data was proposed by Zhang [13] to extract the data of the blast furnace charging line and it was shown to have high efficiency and high accuracy. Tian et al. [18] developed a radar detection-based model for the prediction of the burden surface shape to develop a charging strategy and the results showed that the proposed model had the advantages of higher prediction accuracy for both local details and global shape than mechanical stock rods. In another publication [19], they proposed an innovative data-driven model for predicting the distribution of the burden descent speed. This model has the ability to better characterize the variability in the radial distribution of the burden descent speed than a pure mathematical model based on Newton's second law. Miao et al. [20] proposed a new calculation method of shape fusion of the material line based on a stacking method, which can directly calculate the shape of the material surface and improve the measurement accuracy by 4.8%, compared to the first principle mathematical model. Li et al. [21] recently presented a similar model to improve the measurement accuracy of the burden profile and to use this in modeling of the burden distribution.

From the above literature and statements, there are no publications presenting a combination of radar data and a mathematical model to test, modify, and improve the model. Therefore, this paper will concentrate on this issue.
