3.2. Multiple-Decision Ore Allocation Algorithm Based on OLS Analysis
The calculation of the furnace charge needs to analyze the composition of feed materials such as sinter and lump ore, which is an important part of production. Therefore, the analysis and optimization of sinter composition based on data mining requires a complete calculation model of blast furnace charge composition. Sintering production has a decisive impact on blast furnace ironmaking production from the perspectives of raw materials, smelting costs, slag discharge, and environmental protection. Calculation of the incoming charge requires analysis of the composition of the incoming materials, such as sinter and lump ore.
The calculation model for blast furnace charge is mainly composed of two parts: sinter calculation and lump ore calculation. The sinter calculation is based on the available iron ore and its quantity, the slag agent and its quantity, and fuel and its quantity to calculate the composition of sinter and prepare the data for lump ore calculation. The lump ore calculation is to calculate the composition of the blast furnace charge based on the sinter and its amount, the available high-grade lump ore and pellets, and the comprehensive blast furnace fuel, and finally obtain the composition of the blast furnace charge.
In order to calculate the composition of iron in sinter, the formula is as follows.
Among them, IFe is the Fe mineral composition of sinter, MFe is the Fe content of each raw material, Draw is the dry ratio obtained by subtracting the moisture ratio of each raw material from the wet ratio, D is the total dry ratio, and Rraw is the burning loss of each raw material. Among them, Rraw is represented by a number from 0–100 in the company, which is converted into a percentage and added to the calculation when used. According to this formula, replace the elements represented by IFe and MFe with CaO, MgO, SiO2, TiO2, Al2O3, P, Mn, Na2O, K2O, and Zn one by one to get the content of the corresponding elements in the sinter. For example, replacing it with ICaO and MCaO can calculate the content of CaO in the sinter. The final composition ratio is obtained by combining the amounts of iron, coal, and coke in the feed. It will be used to calculate information such as iron grade, basicity of blast furnace slag, and magnesium to aluminum ratio of the feed. The comprehensive measurement model of sinter and blast furnace charge composition has a better effect than the traditional artificial ore blending method.
Theoretically, in order to achieve the best ratio of raw materials in the blast furnace charge, the calculation model can be used in reverse. However, the company’s calculation model is one-way, and it cannot complete the reverse calculation from the result to the raw material ratio. As shown in
Figure 2 below, the forward calculation is from the raw material wet ratio to the raw material dry ratio, and the sinter composition is calculated according to the formula. After the composition of the sinter is calculated, the composition of the furnace charge is calculated, and finally the basicity and magnesium-aluminum ratio of the blast furnace slag are obtained. However, in order to calculate the ore composition from the raw material composition, it is necessary to calculate the burning loss during the sintering process by means of unit consumption. The purpose of back-projection is to calculate the ratio, and the process of calculating the back-projection ratio is still used, so back-projection is not established.
Figure 2 below is a flow chart of the steps for calculating the composition of raw materials and the steps for inferring the ratio in reverse.
Taking
Ca1 as an example, the formula for calculating the mineral composition in
Section 2.1.
Among them, the constant MCa is the known calcium content of iron ore fines, R1 is the known residual amount of iron ore fines, D1 is the dry ratio of iron ore fines, and d is the total amount. The total amount only needs to be calculated when the dry ratio of each raw material is known, but the purpose of this equation is to find the dry ratio of iron ore powder. Therefore, the above equation has no solution, and the equation system for inverting the dry mix ratio is not established.
Before performing OLS fitting, we need to determine the method of changing materials. Situation 1: In actual production, after the laboratory detects that a certain element index of the sinter product does not meet the requirements for entering the blast furnace, the iron ore blending personnel need to adjust the raw materials to bring the composition of the sinter back to the ideal range. In the second case, when a raw material is insufficient, other raw materials need to be used instead, so the raw materials that have not been replaced must be adjusted to finally keep the composition of the sintered ore reasonable. So we can increase the ratio of one ingredient and adjust the ratio of other ingredients by weight. We use the np.linspace algorithm to generate the arithmetic sequence of the adjusted raw material ratio and the np.random.normal normal noise algorithm to generate a wide range of raw material ratios. We use the above Formula (1) to calculate the composition of the blast furnace charge, and we finally encapsulate the raw material ratio and sinter composition in a set of data in a DataFrame. When
n is determined as the adjustment step size of the main mineral powder, the weighted adjustment formula of the remaining mineral powder is as follows:
Among them, M1 is the proportion of mineral powders that are actively adjusted, and M2 is the proportion of other mineral powders after weighting. As shown in the table below, mineral powder 1 was adjusted by −0.3%, and then the remaining mineral powders were increased accordingly according to their weights. Combined with the trend of change in sinter raw materials obtained by OLS algorithm fitting analysis, the above formula is used to calculate the composition of a blast furnace charge and is applied to multiple decision-making processes. The algorithm of the OLS least squares method is:
- (1)
We need to use the OLS algorithm to fit the ratio and each component of the sintered ore one by one. Among them, x is the ore powder to be mainly adjusted, and y is the composition of sintered ore.
- (2)
Import the DataFrame data source in Python, specify x and y for fitting, and establish the mapping relationship between x and y in the program through the fit() method.
- (3)
Obtain the OLS fitting report through the summary() method, and count the slopes in all OLS reports. Sintering ore blending should not only consider the influence of composition but also factors such as price and equipment operation. In the company’s sintering ore blending process, the items that need to be considered in weight are listed in
Table 1 below:
In the decision-making process, there will also be situations where certain raw materials account for an excessively large proportion, which is obviously unreasonable. For example, Brazil card powder is high quality and suitable for adding in large quantities, but its price is about 30% more expensive than other raw materials. Apparently, the addition of too much Brazil card powder will lead to a substantial increase in the cost of ore blending and ultimately reduce the cost performance of sintered ore. However, it is reasonable to use more high-quality ore powder under the condition of ensuring cost performance. We use the single product price of sinter ore, that is, the price per 1% of TFe, to measure the cost performance of sinter ore. Therefore, when the cost performance of sintered ore is reduced by 5%, no more high ore powder will be added.
Taking SiO2 as an example, in fact, because the SiO2 content of dolomite powder and limestone powder is too different, in order to quickly adjust SiO2 to the target value, it is necessary to set a large step size adjustment to make the plan quickly approach the target value and set the standard step size to cover the mineral blending plan close to the target value, then set a small step size to fine-tune the ore blending plan to meet the accuracy requirements.
In order to make the ore blending plan quickly reach the final adjustment accuracy of sinter composition required by the enterprise within 0.005, the gradient descent method is adopted, and the adjustment step size of the raw material amount that can reach the target the fastest is obtained after many experiments and adjustments: the step size is 0.3% The adjustment ratio for large step size adapts to the change in SiO2 content of different iron ore powders and optimizes the scheme with 0.18% as the standard step adjustment ratio. Accompanied by a 0.07% step adjustment ratio for precise adjustment. The model will adjust the large, medium, and small adjustment steps according to the distance between the currently judged sinter composition and the target value and use various raw materials flexibly to quickly make the sinter composition reach the target value together.
In actual production, the sintering ore blending scheme often cannot reach the theoretical value required by the production line. Therefore, when the composition of the mineral blending plan tends to be stable, the system should stop continuing the mineral blending.
In order to express more intuitively the 1.2 OLS analysis-based multiple decision-making ore allocation algorithm, the main solution steps are as follows:
- (1)
Maintain the raw material warehouse and update information such as available raw materials, storage volume, raw material composition, and price.
- (2)
Set the ratio of raw materials used in the current production line and the ratio of blast furnace charge as a benchmark for the ore blending plan.
- (3)
Set the target element target value of the blast furnace charge.
- (4)
Start by solving the decision and getting the result.