Collaborative Optimization Model of Blast Furnace Raw Materials and Operating Parameters Based on Intelligent Calculation

Abstract

Aiming at the problem of coadjustment of blast furnace raw materials and operation parameters, this paper proposes a cooptimization model of blast furnace batching that integrates Random Forest and NSGA-III (Non-dominated Sorting Genetic Algorithm III) algorithm. First, blast furnace field data were collected for a two-year time span, and a predictive model for CO² emissions and blast furnace permeability was constructed using the Random Forest algorithm; taking the goodness of fit (R²), mean square error (MSE) and mean absolute error (MAE) as the evaluation indexes, the R² of the two prediction models obtained reached 0.93 and 0.96 respectively, and the MSE and MAE tended to be close to the zero value. Then, NSGA-III was used to establish the blast furnace batching optimization model to optimally solve the batching scheme and the corresponding blast furnace operating parameters by taking the lowest batching cost, the lowest carbon dioxide emission and the maximum blast furnace permeability as the objective function, and the composition requirement of raw materials and the range limitation of operating parameters as the constraints; finally, the model was validated using the actual on-site data, and the application results showed that the output of the model conformed to the Finally, the results show that the model output meets the composition requirements and obtains a lower-cost dosage scheme than the original dosage ratio; moreover, this scheme corresponds to a blast furnace with less carbon dioxide emission, better blast furnace permeability and less slag. Therefore, the model can provide an effective reference for field operators to optimize blast furnace batching and operation.

1. Introduction

With the rapid development of the global economy, the demand for steel has been increasing year by year, and the steel industry plays a pivotal role in global industrial production.¹⁾ Blast furnace ironmaking, as an important link in steel production, directly affects the sustainable development of steel enterprises in terms of production efficiency, energy consumption, and environmental impact.²⁾ The burden problem in blast furnace ironmaking is one of the key factors affecting the operation effect of the blast furnace. With the development of technology and the intensification of competition in the steel industry, blast furnace burden optimization also faces new challenges and opportunities. Traditional blast furnace burdening mainly relies on experience and experiments, which cannot meet the needs of modern industry. Additionally, it suffers from problems such as unstable burdening, low efficiency, and high energy consumption.^3,4) Therefore, how to use modern technology to optimize the blast furnace burden and improve smelting efficiency, reduce energy consumption, and ensure environmental safety is an urgent problem that needs to be solved in the current steel industry.

Influenced by multiple factors such as raw material characteristics, furnace conditions and operation level, the blast furnace ironmaking process has significant nonlinearity and uncertainty.⁵⁾ Therefore, the scientific optimization of blast furnace batching process has important theoretical value and practical significance. Some results have been achieved in the technical fields of mathematical modeling,^6,7) artificial intelligence^8,9,10) and optimization algorithms for the optimization of blast furnace dosage.

In terms of optimization algorithms, researchers have used intelligent optimization algorithms such as genetic algorithm (GA), multi-objective evolutionary algorithm (MOEA), and non-dominated sorting genetic algorithm (NSGA) to improve the efficiency and economy of the blast furnace by searching and optimizing the dosage scheme; at present, the optimization models of the dosage process of blast furnace production are mainly classified into two categories: single-objective optimization model and multi-objective optimization model. In the research of single-objective optimization model, the main optimization objective is to minimize the cost.Wang et al. based on metallurgical theory, analyzed the chemical composition of each raw material, and with the objective of minimizing the cost of tons of iron, designed a set of optimization system for the whole process of blast furnace ironmaking, which includes the processes of optimization of sintering batching, analysis of the performance of sintered ore, optimization of the batching of the blast furnace, analysis of the composition of the iron water, etc.¹¹⁾ Tamoghna Mitra et al. used data-driven modeling combined with genetic algorithm to achieve the computation of blast furnace batching with the objective of cost minimization.¹²⁾ In the optimization problem of blast furnace dosage, cost optimization considering single objective alone cannot meet the demand of actual production. For this reason, researchers explored the use of multi-objective optimization methods to deal with blast furnace dosage optimization. Yang et al. established a multi-objective optimization model for the blast furnace ironmaking process based on the conservation of energy and matter, with the energy consumption, cost, and CO² emission of blast furnace ironmaking as the objective function, and blast furnace batching, iron quality parameters, and production indexes as the decision variables.¹³⁾ Zhang Zongwang et al. established a mathematical model for optimization of blast furnace ironmaking with energy consumption and cost as the objective function, and analyzed the effects of coke ratio, blast temperature, and coke oven gas injection on energy consumption and cost.¹⁴⁾

In the blast furnace operation at the actual site, after the adjustment of the blast furnace batching ratio, the blast furnace operation parameters also need to be adjusted to ensure the smooth running of the blast furnace; therefore, some researchers use the optimization model of the batching scheme as the basis, and use machine learning, deep learning and other technologies to analyze and model the blast furnace operation data, and further predict the output, thermal efficiency and other indexes of the blast furnace, in order to achieve the effect of multi-process optimization. Hua Changchun et al. optimized the bi-objective problem consisting of cost and carbon dioxide emissions using a non-dominated sorted multi-objective genetic algorithm, and obtained a uniformly distributed Pareto optimal solution set.¹⁵⁾ Compared with the literature,^11,12,13,14) the literature¹⁵⁾ considered the optimization study of blast furnace process parameters, but there is a problem of uncoordinated matching between raw materials and process parameters, which often leads to a situation where the optimization results output from the model match the actual demand. In the actual production, it is difficult to directly use mathematical models to establish a matching relationship between raw materials and process parameters. In other fields, scholars usually use machine learning methods to find the fitting relationship between parameters and optimize the calculation by optimization algorithms.^16,17,18) In a similar application in the steel sector, the, Li Zhuangnian et al.¹⁹⁾ used six machine learning algorithms, namely, support vector machine, random forest, gradient boosting tree, XGBoost, LightGBM, and artificial neural network, to predict the coke ratio and permeability of the blast furnace, and on the basis of which they used the NSGA-II genetic algorithm to carry out a multi-objective optimization analysis of the blast furnace parameters, and the Pareto optimal solution was obtained; the blast furnace operator can obtain the optimal solution according to this Based on the multi-objective optimization results, the blast furnace operator can select the corresponding blast furnace control parameters for different dosing schemes. Compared with the above model, this literature has enriched the research on the coordination relationship between raw materials and process parameters, but there is a lack of cost constraints of batching.

In summary, in order to effectively solve the limitations of the single-objective dosage-based optimization model, and to comprehensively and coordinately consider the relationship between the proportioning scheme and the operating parameters. In this study, a combination of Random Forest algorithm and NSGA-III (Non-dominated Sorting Genetic Algorithm III) optimization algorithm was used to synergistically optimize the operating parameters and raw material parameters in the blast furnace ironmaking process. In the research process, the blast furnace batching cost, carbon dioxide emission and blast furnace permeability are taken as the objective functions of the optimization problem; the Random Forest algorithm is used to predict the carbon dioxide emission and the blast furnace permeability, and the mapping relationship between the operating parameters of the blast furnace and the raw material parameters is established; on the basis of which, with the optimal cost of the batching cost as the objective condition, the optimization problem is solved by using the NSGA-III optimization algorithm; finally, the optimization problem is solved by comparing and analyzing real cases. Finally, the feasibility of the proposed method in practical application is verified through comparative analysis of actual cases.

2. Algorithm Selection and Model Construction

2.1. Random Forest

Random Forest (RF) is an integrated learning method that improves prediction accuracy and stability by constructing multiple decision trees and combining their prediction results.²⁰⁾ Random forest is widely used in data mining, classification and regression tasks. Its model framework is shown in Fig. 1.

Fig. 1. Framework of random forest algorithm model. (Online version in color.)

The specific process of the algorithm is as follows:

(1) Self-sampling: the original dataset is sampled with put-back to generate new training subsets. Each subset has the same size as the original dataset.

(2) Decision tree construction: A decision tree is constructed using the training subsets. At each split node, a certain number of features are randomly selected for splitting. This helps to reduce the correlation between the trees.

(3) Repeat tree construction: Repeat the above process several times to generate multiple decision trees.

(4) Fusion of prediction results: The prediction results of all decision trees are voted (classification task) or averaged (regression task) to obtain the final prediction results.

The advantages of random forests include reduced risk of overfitting, improved prediction accuracy, ease of parallelization, and adaptability. The random forest algorithm has performed excellently in blast furnace prediction tasks.^21,22,23) Therefore, in this thesis, we use the random forest algorithm to predict the problem and provide the basis for the subsequent optimization tasks.

2.2. NSGA-III Algorithm

The Non-dominated Sorting Genetic Algorithm III (NSGA-III) is an evolutionary algorithm based on multi-objective optimization.²⁴⁾ It is an improved version of NSGA-II and is particularly suitable for handling optimization problems with multiple conflicting objectives. The main features of NSGA-III are the introduction of reference points and co-evolutionary strategies to maintain the diversity of the population. The flowchart of the algorithm is shown in Fig. 2.

Fig. 2. NSGA-III algorithm flow chart. (Online version in color.)

The following are the main steps of the NSGA-III algorithm:

(1) Initialization of population: the initial population is randomly generated, including a certain number of solutions.

(2) Non-dominated ranking: The solutions are divided into multiple non-dominated layers by performing non-dominated ranking based on the objective function values of the solutions.

(3) Calculate the crowding degree: Within each non-dominated layer, the crowding degree of each solution is calculated. The crowding degree is used to measure how dense the solution is in the objective space and helps to maintain the diversity of the population.

(4) Selection: Parent solutions are selected using roulette wheel selection method or tournament selection method.

(5) Crossover and variation: The selected parent solutions are subjected to crossover and variation operations to generate offspring solutions.

(6) Environment selection: The parent and child solutions are merged to perform non-dominated ranking and calculate the crowding degree. New populations are selected based on the non-dominated stratum and crowding degree.

(7) End condition: The algorithm terminates when the maximum number of iterations is reached or other stopping conditions are satisfied.

2.3. Co-optimization Modeling of Blast Furnace Batching

Compared with the traditional NSGA-II algorithm, the NSGA-III algorithm has the advantages of better convergence, scalability, and robustness, and performs well in multi-objective optimization problems in energy,²⁵⁾ industry,²⁶⁾ and military,²⁷⁾ so in this thesis, we use the NSGA-III algorithm to optimize the ingredient optimization problem. Through multi-objective optimization, we can find a set of solutions that perform superiorly in the objective space and provide more choices for decision makers. Meanwhile, the reference points and co-evolutionary strategy of NSGA-III help to improve the diversity of the population, which leads to a more comprehensive set of solutions.

By combining Random Forest and NSGA-III algorithms, we can fully utilize the advantages of both methods to achieve high-precision prediction and efficient optimization. Specifically, the random forest algorithm provides reliable prediction results for optimization tasks, while the NSGA-III algorithm finds optimal solutions in multi-objective optimization problems.The overall flow of the model is shown in Fig. 3.

Fig. 3. Blast furnace co-optimization model structure. (Online version in color.)

3. Algorithm Introduction

3.1. Data Collection and Pre-treatment

From the collected blast furnace database, the whole production line data of an iron and steel plant is selected, covering more than 3000 blast furnace raw material parameters, status parameters, operation parameters and inspection parameters, etc. The time span is from January 2021 to December 2022, and the amount of data is up to several billions of items. Through on-site research and communication with the furnace manager, the performance of the blast furnace raw materials is an important parameter affecting the quality of the molten iron, and when the performance of the blast furnace raw materials changes, the on-line parameters of the blast furnace (including the status parameters and operating parameters) will fluctuate in real time. At the same time, the plant has a strict quality limitation interval when selecting raw materials, and the quality of raw materials does change in actual production, but the fluctuation is small; moreover, since the quality of some raw materials can not be accurately accessed in real time, it is proposed to determine the selection of 4 raw material parameters, 13 state parameters and 7 operating parameters as the data set of this study, as shown in Table 1. In order to predict the blast furnace permeability and carbon dioxide emissions, 24 parameters from the collected data are extracted, and the total number of integrated data reaches more than seventeen thousand.

Table 1. Blast furnace parameters.

Parameter type	No.	Parameter	Abbreviations	No.	Parameter	Abbreviations
Material parameters	1	Sintered ore/t	SJK	2	pellet ore/t	QTK
	3	Lump ore/t	KK	4	Coking coal/t	JT
state parameter	5	Standard wind speed m·s−1	BZFS	6	Actual wind speed m·s−1	SJFS
	7	Furnace top pressure/kPa	LDYL	8	Blast kinetic energy/kg·m·s−1	GFDN
	9	Furnace gas volume m3/(min·m2)	LFMQL	10	Burning temperature/°C	RSWD
	11	Breathability/m3·min−1·kpa−1	K	12	CO2 emissions/t	CO2
	13	Gas-tight box temperature/°C	QMXWD	14	Full furnace temperature difference/°C	QLWC
	15	Gas utilization/%	MQLYL	16	Seat temperature/°C	YZWD
	17	Furnace top temperature/°C	LDWD	18	Hot-air pressure/kPa	SFYL
	19	Differential pressure/kPa	YC
operating parameter	20	Cold air flow/m3·min−1	LFLL	21	Blower humidity g/m3	GFSD
	22	Hot air temp/°C	RFWD	23	Coal injection volume/t	PML
	24	Oxygen-enriched rate/%	FYL

As the data collected at the sintering site is prone to deviations and missing values, it is necessary to pre-process the data before feature extraction. Blast furnace data collection devices are often susceptible to interference from external factors, resulting in missing values or exceeding upper limits during the collection and transmission process. Data cleaning is an integral part of data analysis and can help us to find and correct errors, missing and abnormalities in the data and improve the quality and reliability of the data.²⁸⁾ In this paper, we first deal with the missing values in the data, for a small number of missing to take the filling method, with the mean value of the data to fill, you can maintain the overall distribution and trend of the data to a certain extent; for a large number of consecutive missing data, the deletion method is used directly to ensure the quality and reliability of the data.

After the initial cleaning of the dataset, the dataset is normalized in this paper due to the large differences in the magnitude and order of magnitude of each feature parameter. The normalization process is to reduce each feature parameter in the dataset to the same scale range for better data analysis and modeling. The following normalization methods are commonly used:

3.1.1. Min-Max Standardization

Min-Max standardization is a linear transformation of the original data to map the input data to the interval [0,1] through normalization by setting the minimum and maximum values of the data as Min and Max. Its calculation formula is shown as follows:

  

$$x=\frac{x-min}{max-min}$$(1)

In the equation: min is the minimum value in the input data; max is the maximum value in the input data.

3.1.2. Z-Score Standardization

The method is applied to the case where the maximum and minimum values of the original data are unknown, and is based on the mean and standard deviation of the data for normalization. The data are converted to a form conforming to the standard normal distribution after the Z-Score standardization process. That is, the mean value is 0 and the standard deviation is 1. The calculation formula is shown below:

  

$$x=\frac{x-\mu }{\sigma }$$(2)

In the equation: μ represents the mean of the input data, σ represents the standard deviation of the input data.

For this paper, there are some parameters in the blast furnace data that require specific range requirements, so we standardize the data using Min-Max normalization, which is easy to use and applicable to most machine learning algorithms. Through normalization, we convert each feature parameter in the dataset into a range of values with the same scale, which makes the features comparable with each other and allows for better data analysis and modeling.

The normalized data is examined using box plots to check the distribution and identify possible outliers. Box plots can be used to display statistics such as median, quartiles, minimum and maximum values of the data, as well as outliers of the data.²⁹⁾ In this study, box plots were used to analyze the data collected. As shown in the left panel of Fig. 4, it can be clearly seen that there are some outliers in the data, for the outliers we repair the data according to the missing data, and the repaired data is shown in the right panel of Fig. 4. The rectangular box in the Fig. 4 indicates the upper and lower quartiles of the data, which contains 50% of the data between the quartiles, and the height of the box reflects the degree of fluctuation of the data to some extent. A short line in the middle of the box indicates the median of the data; the two lines above and below the box indicate the minimum and maximum values of the data, respectively: the hollow rectangle is the mean of the data, and the solid rhombus is the outliers in the data.

Fig. 4. Blast furnace data box diagram. (a) Raw data (b) Post-processing data. (Online version in color.)

3.2. Feature Selection

Feature selection can select the most relevant features from raw data, which not only reduces the time required for model training and prediction, and improves model accuracy, but also prevents overfitting. In this study, we analyzed the correlation between features and screened out feature variables with poor correlation with the target variable. Common correlation analysis methods include Pearson correlation coefficient, Spearman correlation coefficient, and Kendall correlation coefficient. Pearson correlation coefficient is suitable for analyzing data with linear correlations, Spearman correlation coefficient is suitable for handling non-normally distributed data or variables that are not linearly related, while the Kendall method is mostly used to calculate categorical data. The data in the blast furnace smelting process is continuous and exhibits complex nonlinear features.³⁰⁾ Therefore, Spearman correlation coefficient is used in this paper to analyze the magnitude of correlation between features.The heat map of Spearman correlation coefficient is shown in Fig. 5.

Fig. 5. Spearman correlation coefficient heat map.

As shown in Fig. 5, the results of the correlation analysis are visualized in this paper using a heat map. From the Fig. 5, we can see the correlation magnitude between each feature and CO₂ emission and blast furnace permeability, and the valve seat temperature and gas utilization rate features with the worst correlation with these two target vectors are filtered out. At the same time, it can also be seen that there is a large correlation between the features. In order to avoid having redundant features that lead to slower training and poorer accuracy of the model, this paper then uses random forest to rank the importance of the remaining features for the regression task. In terms of feature selection, random forests can be used to evaluate the importance of different features for a classification or regression task, helping us to identify which features are the most useful or most relevant.³¹⁾ In a random forest, each decision tree is constructed based on different random samples and random features, and the relative importance of each feature can be obtained by averaging the importance scores of all decision trees. These importance scores can be used to select the features with the most predictive power, or to reduce the dimensionality by removing unimportant features to improve the performance and generalization of the model.

As shown in Fig. 6, the top 10 features of the blast furnace permeability prediction model are YC, LFLL, RSWD, LFMQL, PML,GFDN, LDYL, FYL, RFWD, and SJFS. The top 10 important features of CO₂ emission prediction model are RFYL, FYL, QLWC, GFSD,LDYL, RSWD, LDWD, RFWD, LFMQL, and PML. Talking with the field staff, among the blast furnace operating parameters that can be manually adjusted are YC, LFLL, PML, FYL, GFSD, and RFWD. Combined with the random forest feature importance ranking and Spearman correlation analysis, these six operating parameters and four raw material parameters were identified as the inputs to the blast furnace prediction model and the decision variables for the optimization model.

Fig. 6. Random forest feature importance ranking. (a) Blast furnace permeability prediction model (b) CO₂ emission projection model.

3.3. Model Building and Training

After feature selection, six blast furnace operating parameters and four raw material parameters were used as inputs to the model, and blast furnace permeability and carbon dioxide emission were used as outputs of the model. The blast furnace permeability prediction model and carbon dioxide emission prediction model were established using the random tree integration algorithm, and the model construction included three parts: the division of data sets, the optimization of model hyperparameters, and the evaluation of the model.

3.3.1. Data Set Partitioning

Random sampling was used to divide the samples in the dataset into a training set and a test set in the ratio of 8:2.

3.3.2. Optimization of Model Hyperparameters

In this study, a blast furnace permeability and CO₂ emission prediction model was developed using the sklearn machine learning algorithm library in python. The hyperparameters such as the number of decision trees (n_estimators), the maximum depth of the tree (Max_depth), the minimum number of samples that can be split by nodes (Min_samples_split), and the minimum number of samples of leaf nodes (Min_samples_leaf) are optimized by using a combination of grid search and cross-validation. In this study, mean_test_score is used as the evaluation metric to measure the performance of the model. The largest mean_test_score value is recorded as the optimal hyperparameter. This approach is widely used in the field of machine learning and has been shown to have good performance in many tasks. The optimization results are shown in Fig. 7.

Fig. 7. Results of hyperparameter optimization of random forest algorithm. (a) Blast furnace permeability prediction model (b) CO₂ emission projection model.

In Fig. 7, the x, y, and z axes are N_estimators, Max_depth, and mean_test_score, respectively, and the color and size of the spheres in the figure indicate Min_samples_split and Min_samples_leaf, respectively. in the process of hyperparameter optimization of the model, the two prediction models with mean_ test_score values of the two prediction models reached a maximum of 0.931 and 0.958, respectively, and the corresponding optimal model hyperparameters were determined, as shown in Table 2.

Table 2. Parameters of random forest model.

Models	N_estimators	Max_depth	Min_samples_split	Min_samples_leaf
Breathability prediction	150	20	2	1
CO2 emission projections	150	20	2	1

3.3.3. Evaluation of Models

In order to more accurately evaluate the model performance and the generalization ability of practical applications, the established blast furnace permeability and carbon dioxide prediction models were tested using test set samples, and the goodness of fit (R²), mean squared error (MSE), and mean absolute error (MAE) were used to evaluate the model. The model performance is shown in Table 3 and Fig. 8.

Table 3. Random forest prediction evaluation.

Evaluation indicators	R2	MSE	MAE
Breathability prediction	0.930	0.152	0.125
CO2 emission projections	0.960	0.203	0.273

Fig. 8. Scatter plot of prediction results. (a) Blast furnace permeability prediction model (b) CO₂ emission projection model. (Online version in color.)

According to Table 3, the prediction performance of both models is relatively accurate, with the goodness of fit (R²) reaching 0.93 and 0.96, respectively, when comparing the model prediction results with the actual values. Therefore, the established blast furnace permeability and carbon dioxide prediction models can accurately fit the blast furnace operating parameters and raw material parameters, which is beneficial for further blast furnace coordinated optimization and has important guiding significance for operators to adjust the charging method and operating parameters in a timely manner on site.

4. Optimization Model

4.1. Determining Decision Variables

In order to achieve the coordinated optimization of blast furnace charging and operation, the model needs to calculate the optimal blast furnace operating parameters while outputting the corresponding ratio scheme that meets the requirements. Based on the input of the prediction model in the previous section and the actual situation on site, this study selected decision variables as shown in Table 4. The decision variables mainly include six blast furnace operating parameters and four raw material parameters.

Table 4. Decision variables.

Decision variables (raw materials)	Symbols	Decision variables (blast furnace operation)	Symbols
SJK	x1	PML	x5
QTK	x2	LFLL	x6
KK	x3	RFWD	x7
JT	x4	FYL	x8
		YC	x9
		GFWD	x10

4.2. Objective Functions

As the country pays increasing attention to environmental protection, carbon dioxide emissions have become an important indicator of concern for steel enterprises. Maximizing the reduction of carbon dioxide emissions has become a crucial task in optimizing the charging process. Blast furnace permeability is one of the important control parameters of the blast furnace, which has a significant impact on the composition and quality of pig iron. Insufficient permeability can affect the progress of reactions in the furnace, causing deviations in the composition of pig iron from the target. Based on on-site investigations and previous research, this study aims to determine the cost of charging, carbon dioxide emissions, and blast furnace permeability as the three objective functions of the charging optimization model. The charging cost and carbon dioxide emissions are minimized, while the blast furnace permeability is maximized. Since it is difficult to mathematically model and explain carbon dioxide emissions and blast furnace permeability, this study uses the trained prediction model as the objective function. The specific formulas are as follows:

  

$$minF\_(Z)=\sum _i^n{x}_i{p}_i$$(3)

  

$$maxF\_(K)=f_1(x_1,x_2,x_3\cdot \cdot \cdot x_n)$$(4)

  

$$minF\_(c{o}_2)=f_2(x_1,x_2,x_3\cdot \cdot \cdot x_n)$$(5)

In the formulas, minF_(Z), maxF_(K) and minF_(co₂) are the lowest cost, the maximum blast furnace permeability, and the minimum CO₂ emissions, respectively. x_i(i=1,2,···,n) denotes the allotment of the i raw material and p_i denotes the price of the i raw material. f₁(x₁,x₂,x₃…x_n), f₁(x₁,x₂,x₃…x_n) are the trained blast furnace permeability prediction model and CO₂ emission prediction model, respectively.

4.3. Binding Conditions

In the process of blast furnace smelting, some constraints need to be added when building a multi-objective optimization model in order to ensure that the quality of smelting meets the standard. In this paper, constraints are imposed from the molten iron composition, slag composition and batching ratio. The specific constraints are as follows:

1) Iron composition constraints:

  

$$d_c^L\le {\lambda }_c\times \sum _{i=1}^n{c}_i{X}_i\le d_c^H$$(6)

This section considers elements such as S, P, Ti, Mn, etc. In the formulas, c_i is the content of an element of the i raw fuel, $d_c^H$, $d_c^L$ are the upper and lower limits of the element’s iron composition requirements, respectively, and λ_c indicates the distribution rate of the element in the iron. The distribution rates of each element in ironmaking production are shown in Table 5.

Table 5. Distribution rate of each element in iron production.

	Fe/%	s/%	p/%	Ti/%	Mn/%	Ni/%
Pig iron	0.9975	0.07	1	0.1	0.7	0.9
Furnace slag	0.0025	0.88	0	0.9	0.3	0.1
Gas	0	0.05	0	0	0	0

2) Composition constraints on slag.

  

$$Si{O}_{2r}=10\times [Si]\times 60/28$$(7)

In the formulas, SiO_2r is the amount of SiO₂ needed for the Si content in reduced pig iron; [si] is the silicon content of the iron.

  

$$Z_A=(Ca{O}_A+(Si{O}_{\text{2}A}-Si{O}_{\text{2}r})+A{l}_2{O}_{\text{3}A}+Mg{O}_A)/0.96$$(8)

In the formula, Z_A is the total amount of slag, which is the sum of the amounts of various raw materials entering the slag; CaO_A, SiO_2A, Al₂O_3A and MgO_A represents the total amount of CaO, SiO₂, Al₂O₃ and MgO in the raw materials.

  

$$\text{st}.\{\begin{array}{l}A{l}_{\text{2}}{O}_{\text{3}L}\le A{l}_{\text{2}}{O}_{\text{3}A}/Z_A*100\%\le A{l}_{\text{2}}{O}_{\text{3}H}\\ Mg{O}_L\le Mg{O}_A/Z_A*100\%\le Mg{O}_H\\ A/S_L\le A{l}_{\text{2}}{O}_{\text{3}A}/(Si{O}_{\text{2}\mathrm{A}}-Si{O}_{\text{2}\mathrm{r}})\le A/S_H\\ M/A_L\le Mg{O}_A/A{l}_2{O}_{3\mathrm{A}}\le M/A_H\\ R_{\text{2}L}\le Ca{O}_A/(Si{O}_{\text{2}\mathrm{A}}-Si{O}_{\text{2}\mathrm{r}})\le R_{\text{2}H}\end{array}$$(9)

In the formula, Al₂O_3H, Al₂O_3L represent the maximum and minimum mass percentages of Al₂O₃ required in the slag during production, respectively; MgO_H and MgO_L represent the maximum and minimum mass percentages of MgO required in the slag during production, respectively; A/S_H and A/S_L represent the maximum and minimum values of Al₂O₃/SiO₂ respectively; M/A_H and M/A_L represent the maximum and minimum values of MgO/Al₂O₃, respectively; R_2H and R_2L represent the maximum and minimum values of slag basicity required in production, respectively.

3) Proportion constraints on raw materials.

  

$$\text{st}\text{.}\{\begin{array}{l}{X}_{ZL}\le X_Z\le X_{ZH}\\ SJ{K}_L\le X_{SJK}/X_Z*100\%\le SJ{K}_H\\ QT{K}_L\le X_{QTK}/X_Z*100\%\le QT{K}_H\\ K{K}_L\le X_{KK}/X_Z*100\%\le K{K}_H\\ J{B}_L\le JB\le J{B}_H\\ M{B}_L\le MB\le M{B}_H\end{array}$$(10)

In the formula, SJK_H and SJK_L represent the maximum and minimum percentages of sinter to be added during production, respectively; X_SJK represents the amount of sinter added; X_ZH and X_ZL represent the maximum and minimum amounts of iron ore required to be added to the blast furnace, respectively; X_Z represents the total amount of iron ore added to the blast furnace; QTK_H and QTK_L represent the maximum and minimum percentages of pellet to be added during production, respectively; X_QTK represents the amount of pellet added; KK_H and KK_L represent the maximum and minimum percentages of lump ore to be added during production, respectively; X_KK represents the amount of lump ore added; JB_H and JB_L represent the maximum and minimum percentages of coke rate required during production, respectively; JB represents the coke rate required during production; MB_H and MB_L represent the maximum and minimum percentages of coal rate required during production, respectively; MB represents the coal rate required during production.

4.4. Optimization Model Construction

In this study, the multi-objective non-dominated sorting genetic algorithm NSGA-III is used to optimally solve the blast furnace dosage problem. For the algorithm implementation, the NSGA-III algorithm interface in the open-source toolkit geatpy was invoked using Python language to ensure the generality and reusability.

The decision variables of the optimization model include six blast furnace operating parameters and four raw material parameters, as described in Section 4.1. The objective function of the optimization includes three key metrics: batching cost, CO₂, and K. The compositional requirements in Section 4.3 are used as the constraints set in the blast furnace batching optimization.

In the NSGA-III solving process, the default strategy provided by the geatpy library function was adopted for the parameters such as the coding method of the decision variables and the genetic operator; and according to the scale of the problem, the appropriate population size and the number of iteration generations were set, and the specific parameter settings are shown in Table 6. Meanwhile, the changes of the objective function value during the iteration process were recorded to observe the convergence status of the algorithm. Finally, the computed pareto frontier results were used to provide the staff with decision-making suggestions for different dosage programs.

Table 6. Parameters of NSGA-III optimization algorithm.

Parameters	Iteration	Population	Crossover rate	Variation rate
NSGA-III	100	100	0.7	0.9

5. Experimental Results and Analysis of Blast Furnace Dosage Co-optimization Model

As an example, Table 7 shows the chemical composition test values and prices of raw materials for a certain steel plant in 2022.

Table 7. Composition and price of raw fuel used in blast furnace.

Raw materials	Ingredients									Price
	Tfe	FeO	SiO2	CaO	MgO	Al2O3	S	P	TiO2
SJK	55.45	9.50	5.49	11.22	1.91	2.14	0.031	0.07	0.11	561.80
QTK	63.85	0.50	3.18	3.72	1.65	0.75	0.005	0.02	0.60	849.20
KK	63.07	0	2.57	0.03	0.05	1.36	0.027	0.084	0.05	645.20
JT	0	0	6.19	0	0.07	4.36	0.80	0.04	0.80	2127.00
MF	0	0	4.51	0	0.083	3.14	0.30	0.02	0.30	1122.70

Applying the proposed blast furnace dosage co-optimization model for optimization solution, the total amount of iron ore into the furnace is 100 tons, the coke ratio is set to 300 (kg/t), and the coal ratio is set to 120 (kg/t) according to the actual production requirements on site. The specific constraints are shown in Table 8. The Pareto frontier obtained after solving is shown in Fig. 9. the red, blue, and green points represent the mapping of each Pareto front point on each axis plane.

Table 8. Constraints on the composition of each element in the blast furnace.

Ingredient	S	P	Ti	Mn	Binary alkali	MgO	Al2O3	Al2O3/SiO2	MgO/Al2O3
Max	0.027	0.14	0.06	0.44	1.30	0.10	0.18	0.55	0.60
Min	0	0	0	0	1.00	0.05	0.10	0.40	0.40

Fig. 9. The pareto front obtained from the blast furnace dosage co-optimization model.

Three sets of solutions obtained from the optimization are selected and converted into the raw materials required for producing one ton of iron, as shown in Table 9. The calculated charging results are similar or close to the original plant data, which indicates that the charging optimization method proposed in this study is feasible and reliable.

Table 9. NSGA-III algorithm optimized pareto optimal solutions.

Raw materials and parameters	Raw data	Optimization1	Optimization2	Optimization3
SJK/t	0.754	0.760	0.751	0.754
QTK/t	0.601	0.596	0.594	0.600
KK/t	0.153	0.151	0.156	0.153
JT/t	0.324	0.324	0.322	0.325
PML/t	0.125	0.118	0.120	0.114
LFLL	6088	5284	6588	6334
RFWD	1206	1144	1000	1079
FYL	5.97	6.52	5.10	5.00
YC	176.90	172.00	170.00	170.00
GFWD	25.33	24.60	19.00	14.20

As shown in Table 10, comparing the pig iron composition data before and after optimization, the pig iron composition is very close to the original plant data and meets the production requirements.

Table 10. Comparison of iron composition.

Ingredients (%)	Max	Min	Original	Optimization1	Optimization2	Optimization3
S	0.027	0	0.023	0.023	0.022	0.023
Ti	0.060	0	0.052	0.051	0.051	0.052
P	0.140	0	0.093	0.093	0.092	0.092
Mn	0.440	0	0.370	0.370	0.370	0.370

As shown in Table 11, the slag composition data before and after optimization are compared, and the changes in slag composition are not significant and are within the range required on site.

Table 11. Slag composition comparison.

Ingredients (%)	Max	Min	Original	Optimization1	Optimization2	Optimization3
Binary alkali	1.30	1.00	1.18	1.19	1.18	1.19
MgO	0.10	0.05	0.09	0.09	0.09	0.09
Al2O3	0.18	0.10	0.15	0.14	0.15	0.14
Al2O3/SiO2	0.55	0.40	0.44	0.42	0.45	0.44
MgO/Al2O3	0.60	0.40	0.50	0.60	0.50	0.60

As shown in Table 12, the cost per ton of iron for the selected charging schemes is reduced compared to the original plant charging method. The three sets of results focus on the goals of charging cost, blast furnace permeability, and carbon dioxide emissions. Moreover, the slag production of the three optimized charging schemes is lower than the original plant charging data.

Table 12. Comparison of optimization results.

Indicators	Cost/RMB	K	CO2/t	Slag volume/t
Original	1863.6	33.10	25.59	27.30
Optimization1	1854.3	32.00	18.40	26.60
Optimization2	1855	36.40	25.00	27.00
Optimization3	1850.9	34.00	23.50	26.90

6. Conclusion

A collaborative optimization model combining random forest and NSGA-III algorithms is proposed to address the problem of coordinated adjustment of raw materials and operating parameters in blast furnaces, achieving coordinated optimization of raw materials and operating parameters.

(1) This study collected on-site data from blast furnaces over a two-year period and corrected outliers in the data using box plots. Six blast furnace operating parameters (including pressure difference, cold air flow rate, pulverized coal injection rate, oxygen enrichment rate, blast humidity, and hot air temperature) and four raw material parameters (including sinter, pellet, lump ore, and coke) were selected as input variables for the prediction model and decision variables for the optimization model using Spearman correlation coefficient and random forest feature ranking method.

(2) A random forest algorithm was used to construct prediction models for carbon dioxide emissions and blast furnace permeability, and the optimal parameter set of the models was obtained using a combination of grid search and cross-validation. The goodness of fit (R²), mean squared error (MSE), and mean absolute error (MAE) were used as evaluation indicators. The R² of the two prediction models reached 0.93 and 0.96, respectively, and the MSE and MAE approached zero.

(3) Using the proposed blast furnace batching co-optimization model, the optimized batching scheme and the corresponding Pareto frontiers of the blast furnace operating parameters are obtained. Based on actual on-site data, the model output results were found to meet the composition requirements while having lower costs than the original charging scheme. The model also reduced carbon dioxide emissions, improved blast furnace permeability, and reduced slag production. Therefore, the model can provide effective reference for on-site operators to optimize blast furnace operations.

Acknowledgement

Thanks are give to the Tangshan talent funding project (B202302007), the Tangshan city applied basic research science and technology plan project (21130233C), the Technology Innovation Center of Tangshan Digital Cultural Tourism Industry.

Data Availability and Access

The raw data used in this study, including Blast furnace dosing program and operating parameter data, are proprietary and subject to confidentiality agreements. Access to the data can be requested from the corresponding author upon agreement with the data owner and compliance with applicable regulations.

Competing Interests

On behalf of all authors, the corresponding author states that there is no conflict of interest.

References

• 1)   B.  Rahmatmand,  A.  Tahmasebi,  H.  Lomas,  T.  Honeyands,  P.  Koshy,  K.  Hockings and  A.  Jayasekara: Fuel, 336 (2023), 127077. https://doi.org/10.1016/j.fuel.2022.127077
• 2)   R.  Liu,  W. G.  Zhao,  S.  Liu,  X. J.  Liu,  X.  Li,  Z. F.  Zhang,  J.  Zhao and  Q.  Lyu: ISIJ Int., 63 (2023), 1714. https://doi.org/10.2355/isijinternational.ISIJINT-2023-099
• 3)   F.  Yan,  X. M.  Zhang,  C. J.  Yang,  B.  Hu,  W. D.  Qian and  Z. H.  Song: The Canadian Journal of Chemical Engineering, 8 (2022), 101. https://doi.org/10.1002/cjce.24790
• 4)   K.  Nakano,  H.  Sakai,  Y.  Ujisawa,  K.  Kakiuchi,  K.  Nishioka,  K.  Sunahara,  Y.  Matsukura and  H.  Yokoyama: ISIJ Int., 62 (2022), 2424. https://doi.org/10.2355/isijinternational.ISIJINT-2022-117
• 5)   J. P.  Li,  X. J.  Liu,  X.  Li,  Q.  Lyu and  Y. N.  Qie: ISIJ Int., 63 (2023), 835. https://doi.org/10.2355/isijinternational.ISIJINT-2022-505
• 6)   X. B.  Yu and  Y. S.  Shen: Chem. Eng. Sci., 248 (2022), 117185. https://doi.org/10.1016/j.ces.2021.117185
• 7)   H. Y.  Li,  X. P.  Bu,  X. J.  Liu,  X.  Li,  H. W.  Li,  F. L.  Liu and  Q.  Lyu: ISIJ Int., 61 (2021), 108. https://doi.org/10.2355/isijinternational.ISIJINT-2020-249
• 8)   W. X.  Hong,  W.  Qin,  Y. N.  Sun,  Y. L.  Lv and  J.  Zhang: J. Intell. Manuf., 3 (2023), 1. https://doi.org/10.1007/s10462-021-09958-2
• 9)   X. L.  Su,  S.  Zhang,  Y. X.  Yin and  W. D.  Xiao: Int. J. Mach. Learn. Cybern., 10 (2019), 2739. https://doi.org/10.1007/s13042-018-0897-3
• 10)   X. P.  Wang,  T. H.  Hu and  L. X.  Tang: IEEE Transactions on Neural Networks and Learning Systems, 33 (2021), 2080. https://doi.org/10.1109/TNNLS.2021.3059784
• 11)   B. X.  Wang,  W.  Chen,  Y. Z.  Zhang,  Y.  Chen and  Y. H.  Zhu: Ironmak. Steelmak., 44 (2017), 59. https://doi.org/10.1080/03019233.2016.1156222
• 12)   T.  Mitra,  F.  Pettersson,  H.  Saxén and  N.  Chakraborti: Mater. Manuf. Process., 32 (2017), 1179. https://doi.org/10.1080/10426914.2016.1257133
• 13)   Y.  Yang,  L.  Zhang,  Y.  Yuan,  J.  Sun,  Z.  Che and  Z.  Qiu: Journal of Environmental Management, 347 (2023), 119102. https://doi.org/10.1016/j.jenvman.2023.119102
• 14)   Z. W.  Zhang,  X. R.  Che and  H. B.  Zhang: Journal of Process Engineering, 17 (2017), 178 (in Chinese).
• 15)   C. C.  Hua,  Y. J.  Wang,  J. P.  Li,  Y. G.  Tang,  Z. G.  Lu and  X. P.  Guan: Journal of Chemical Engineering, 67 (2016), 1040 (in Chinese).
• 16)   P. K.  Tipu,  V. R.  Panchal and  K. S.  Pandya: Advanced Engineering Optimization Through Intelligent Techniques: Select Proceedings of AEOTIT 2022, Singapore, Springer Nature Singapore, (2023), 165.
• 17)   Y.  Huang,  Z.  Huo,  G.  Ma,  L.  Zhang,  F.  Wang and  J.  Zhang: Journal of Building Engineering, 68 (2023), 106070. https://doi.org/10.1016/j.jobe.2023.106070
• 18)   P. Z.  Li,  Q.  Xue,  Z. T.  Zhang,  J.  Chen and  D. P.  Zhou: Computers & Operations Research, 159 (2023), 106360. https://doi.org/10.1016/j.cor.2023.106360
• 19)   Z. N.  Li,  M. S.  Chu,  Z. G.  Liu and  B. F.  Li: Journal of Northeastern University (Natural Science Edition), 41 (2020), 1262 (in Chinese).
• 20)   K. N.  Fang,  J. B.  Wu,  J. P.  Zhu and  B. C.  Jian: Statistics and Information Forum, 26 (2011), 32 (in Chinese).
• 21)   S. H.  Luo and  T. X.  Chen: IEEE Access, 8 (2020), 196112. https://doi.org/10.1109/ACCESS.2020.3034566
• 22)   G.  Yang,  X.  Han,  C. H.  Wang,  Y.  Ding,  K.  Liu,  D.  Tian and  L.  Yao: Analytical Methods, 36 (2017), 5365. https://doi.org/10.1039/C7AY01389B
• 23)   L.  Sun,  L. Z.  Yin,  Z. H.  Jiang,  Y. J.  Guan and  X. M.  Xu: IOP Conf. Ser.-Mater. Sci. Eng., 768 (2020), 072062. https://doi.org/10.1088/1757-899X/768/7/072062
• 24)   A. M.  Usman,  U. K.  Yusof and  S.  Naim: IEEE Access, 8 (2020), 76333. https://doi.org/10.1109/ACCESS.2020.2987057
• 25)   Y.  Hou,  N. Q.  Wu,  Z. W.  Li,  Y. X.  Zhang,  T.  Qu and  Q. H.  Zhu: Swarm and Evolutionary Computation, 57 (2020), 100714. https://doi.org/10.1016/j.swevo.2020.100714
• 26)   J.  Mao,  X.  Wang,  H. Y.  Chen,  K.  Zhang and  Y. X.  Bai: China Mechanical Engineering, 29 (2018), 2335.
• 27)   J. F.  Nie,  X. J.  Chen and  Q.  Su: Acta Armamentarii, 42 (2021), 1771.
• 28)   J.  Zhao,  S. F.  Chen,  X. J.  Liu,  X.  Li,  H. Y.  Li and  Q.  Lyu: Int. J. Miner. Metall. Mater., 28 (2021), 1001. https://doi.org/10.1007/s12613-021-2301-7
• 29)   B. K.  Mahanta and  N.  Chakraborti: Steel Res. Int., 89 (2018), 1800121. https://doi.org/10.1002/srin.201800121
• 30)   H. Y.  Zhu,  B. C.  He and  X. M.  Zhang: ACS Omega, 7 (2022), 41296. https://doi.org/10.1021/acsomega.2c05029
• 31)   D.  Conn,  T.  Ngun,  G.  Li and  C. M.  Ramirez: Journal of Statistical Software, 91 (2019), 1. https://doi.org/10.18637/jss.v091.i09