2.2.1. Radar Data Collection

When a rotating radar works, it rotates around the axis of itself to detect the radial data of the burden profile. The radial data includes the height and the radius of the burden surface. Dust, chute shield, and airflow in the throat all interfere with the radar data, producing noise and making the measurement values deviate from the real ones.

#### 2.2.2. Processing of Radar Data

Radar data were collected from a blast furnace of Nanjing Steel. In order to ensure the accuracy and authenticity of the data, the K nearest neighbor algorithm was firstly employed to remove the noise. Then, the Delaunay triangulation algorithm was used to realize the visualization of the 3D surface. The burden profile takes the average values of multiple coordinates extracted from the data. After the above processing, 40 group points were selected as the coordinates of the burden profile. The intersection of the furnace center line and the zero line of the stock line was defined as the origin of the coordinates. These 40 group points were converted into two-dimensional coordinates of the burden profiles.

The 40 groups of radar data were treated and stored in a database, which included the radar data time, burden profile coordinates (x, y), and material type as shown in Figure 9.

**Figure 9.** Radar data structure in the database.

From these 40 group of radar data, burden profiles were extracted and illustrated, as depicted in Figure 10. The radar data are independent points and discontinuous in the radial direction (red points in Figure 10). Therefore, a polyfit regression method was used to find the most consistent curve for these radar data. This not only retains the characteristics of the radar data but also makes the burden profile look continuous and smooth.

**Figure 10.** Radar data calculation of the burden profile function.

When the burden profile function is known, it is modified by the burden descent function. There are two methods to obtain the descent function: The one from the mathematical model (Equations (19)–(21)) and the other from the radar data fitting method.

Considering the difference between these two measurements, the descent velocity function can be calculated by:

$$V\_d = \frac{f(r)\_n - f(r)\_{n-1}}{t\_n - t\_{n-1}},\tag{24}$$

where *<sup>f</sup>*(*r*)*<sup>n</sup>* and *<sup>f</sup>*(*r*)*n*−<sup>1</sup> are the nth burden distribution and the (n <sup>−</sup> 1)th one after the descent, respectively. *tn* and *tn*−<sup>1</sup> define the charging times of the nth and (n − 1)th burden distribution, respectively.

A polyfit regression method was used to obtain the descent functions show in Figure 11. The distribution of the descent function is symmetrical at the centerline of the furnace (x = 0). The red dots in Figure 11 and blue curve express the radar data and the fitted curve, respectively.

**Figure 11.** Method of the burden descent velocity from radar data.
