An Online Sintering Batching System Based on Machine Learning and Intelligent Algorithm

Abstract

Aiming at the problem that the accuracy and economy of the traditional off-line batching method are not high, the online batching system (BSMLIA) based on machine learning and intelligent algorithms was put forward from three aspects: real-time, technical requirements and economic benefits. The accurate solution and on-line fast calculation of sintering raw material ratio under the influence of multiple factors are solved. Specifically, a BSMLIA architecture with three levels of data communication layer (DCL), parameter prediction and batching optimization layer (PPBOL), and diagnostic decision layer (DDL) was first designed to realize online monitoring and abnormal diagnosis of sinter performance. Then, the sintering batching adjustment and optimization module (SBAOM) was elaborated. The mixture performance prediction model was developed by MLR and LightGBM algorithm, the model can be based on sinter composition and quality index requirements and current sintering production process parameters to calculate the appropriate mixture performance. In addition, the pre-batching model and the sintering batching model were established to achieve the solution of the lowest raw material cost ratio for a given mixture performance. Finally, the actual production data was used to verify the SBAOM. The results proved that the online batching system can not only quickly calculate the batching plan that meets the requirements, but also reduce the batching cost by RMB 29.54/ton.

1. Introduction

The batching is the process of determining the appropriate raw material ratio according to the physical characteristics, chemical composition and inventory of the current raw materials, aiming at the composition and quality of sinter specified by the sintering process. The effect of batching will directly affect the chemical composition, quality index and the cost of using raw materials. Different from foreign iron and steel enterprises with fixed mineral sources, the raw materials used in sintering production of domestic iron and steel enterprises have problems such as unstable source and supply, miscellaneous varieties and large fluctuation of raw material composition, which makes the structure of the raw materials more complicated. It brings a lot of difficulties to the rapid and accurate ore blending of sintering production.^1,2)

For the vanadium-titanium sintering process, the various iron-containing raw materials used in one-batching process have different chemical compositions (such as iron grade, vanadium, titanium, etc.) and prices.³⁾ The mixture of neutralizing ore, return fines, calcium ash, magnesium ash and coke powder is mixed in the two-batching stage to make the formed mixture have certain Fe, V₂O₅, SiO₂, CaO, MgO, Al₂O₃, S and P components. In addition, the sintered mixture can obtain sinter with some properties under certain production process parameters. Therefore, how to obtain the sinter composition and quality corresponding to the current mixture in time, and how to quickly stabilize the production process when the performance of the sinter fluctuates, which is an urgent problem in sintering production.^4,5)

Sintering batching is a complex process limited by many factors. Many scholars have conducted a lot of useful research on the optimization of sintering ingredients. However, most research methods can only provide the raw material ratio offline, and cannot realize the real-time dynamic adjustment of the ratio. In addition, the quality of sinter is closely related to the original mixture generated in the batching step as well as the operating parameters and state parameters. The above modeling and optimization of batching does not fully consider the influence of the sintering production process parameters on the composition and quality of sinter, which limits their scope of application.

In recent years, machine learning technology has been developed rapidly. Through the learning of historical data, a more realistic model is obtained to realize the mining of the law of interaction between complex multidimensional parameters.^6,7) Moreover, the intelligent algorithm can solve the optimization problem under multiple constraints, and it has been widely studied and applied in the field of sintering batching. Therefore, according to the characteristics of sintering batching in a steel enterprise, this paper adopted the integrated learning method combining multiple models to establish the mixture performance prediction model and the corresponding optimization algorithm. Using a comprehensive integration method from qualitative to quantitative, the ratio calculation model based on linear programming method and intelligent algorithm was organically combined with the mixture performance prediction model based on machine learning, and the sintering batching adjustment and optimization model (SBAOM) was established. The various modeling methods involved in the process were compared and selected.

The remainder of the paper is organized as follows. In Section 2, we present a multi-objective intelligent batching scheme. In Section 3, we explain a mixture performance prediction model based on MLR and BO-LightGBM algorithm. In Section 4, we present an ingredient adjustment and optimization model based on intelligent algorithms. In Section 5, we describe the practical application of the designed optimization system. In Section 6, we give the conclusion.

2. Literature Review

Great progress has been made in the modeling and optimization of batching process since the development of early empirical batching method, which can be divided into the following stages.

2.1. Empirical Batching Method

The empirical batching method is a method based on the mechanism model, which uses artificial experience to make the matching ratio, and then verifies the ore blending scheme by sintering cup experiment. If the quality index does not meet the process requirements, it is still necessary to repeatedly fine-tune the proportion of each raw material based on experience until it meets the requirements. For example, according to the sintering performance and original particle size composition of the external ore powder for sintering, Tang Steel⁸⁾ used sintering cups to test a variety of ore blending structures. After analyzing the sintering process and the performance test results of the sinter, the preferred order of ore blending structure is obtained. The above method has the problems of high labor intensity, high dependence on artificial experience, and low efficiency and so on, which is suitable for determining the proportion of many new iron ore materials.

2.2. Linear Programming Method

The linear programming method is a widely used optimization method, which is mostly used in models where the objective function and constraints are all linear. In the early sintering batching model, the lowest cost was used as the objective function, and the raw material usage ratio and chemical composition index were constrained. By establishing the optimization models of the primary and secondary batching processes, the single-target optimization of the sintering batching was achieved. For example, domestic scholars Yanyun Zhang,⁹⁾ Daoqun Wang,¹⁰⁾ etc. conducted the optimization of ingredients. The batching model using the linear programming method must simplify the sintering batching into a linear relation model. But in the actual production process, the batching process not only needs to meet the requirements of chemical composition of sinter, but also to meet the requirements of physical properties. The batching process is not a simple linear relationship, so a single linear programming method is not applicable.

2.3. Integration Prediction Method

With the deep understanding of sintering mechanism, more and more nonlinear factors were introduced into batching optimization model. Therefore, some scholars proposed to combine the batching model based on linear programming method with the data-driven prediction model, used the data-driven prediction model to predict the quality index of sinter, took the prediction results as feedback information, and adjusted the constraint conditions of batching model through expert rules, so as to calculate and obtain the optimized proportioning. Wang Wei et al.¹¹⁾ established a neural network prediction model of sinter performance index. This model took the lowest cost of sinter as the objective function and adjusted the constraint range of the linear programming model based on the output of the prediction model to achieve the optimal ratio solution. For the batching model established by this kind of integrated prediction method, the batching model and the sinter performance prediction model in the model core are two independent modules. In practical applications, field personnel are required to repeatedly adjust the constraints of the batching model based on the results of the forecast model, which makes it difficult to quickly obtain a satisfactory and optimal raw material ratio.

2.4. Intelligent Optimization Method

With the development of artificial intelligence technology, intelligent optimization methods that imitate natural and biological mechanism features have been produced, such as genetic algorithm (GA), differential evolution algorithm (DE), particle swarm optimization (PSO) and ant colony optimization (ACO).^{12,13,14,15,16)} For complex nonlinear problems, these intelligent methods can better solve the optimization problem, so they are widely used in sintering batching optimization research. For example, Xuewei Lv et al.¹⁷⁾ developed a batching optimization model using genetic algorithm, based on the penalty function to flexibly control the priority order of constraints, and realized batching optimization. Zhi Li et al.¹⁸⁾ carried out research on sintering batching optimization using ACO. The simulation results show that based on the improved ACO, the optimization ability is stronger, and it is possible to obtain the batching scheme that is closer to the actual production requirements. To achieve accurate solution of this type of model, it is necessary to obtain a clear objective function and constraint conditions. However, based on traditional modeling methods, it is difficult to accurately establish the corresponding relationship between the physical properties of the sinter and the performance of the mixture, so the output results of the model often deviate from the actual value.

3. System Structure

According to the characteristics of the sintering process and the requirements of the ratio solution, a batching system based on machine learning and intelligent algorithms (BSMLIA) was designed. The system has a three-level layered configuration: data communication layer (DCL), parameter prediction and batching optimization layer (PPBOL) and diagnostic decision layer (DDL), its structure is shown in Fig. 1. The BSMLIA is to be able to quickly and online give the mixture performance and raw material optimal ratio scheme that meet the requirements, under normal production process parameters, when it is detected that the composition and quality of sinter are fluctuating due to abnormal mixture performance.

Fig. 1.

System configuration of BSMLIA.

3.1. DDL

The DDL regularly analyzes and diagnoses the properties of the sintered mixture and the parameters of the sintering process, which can quickly lock the location of the abnormal parameters. The abnormal parameter diagnosis module uses sensitivity analysis to determine the cause. Sensitivity analysis is to determine the influence degree of each input variable x_i on the composition and quality of sinter by measuring the influence of one or more input variables on the change range of the model output y = f(x₁,x₂,...,x_n).¹⁹⁾

3.2. PPBOL

The parameter prediction and batch optimization layer consists of two parts: the sinter composition and quality prediction model (SCQPM)^20,21) and the sintering batching adjustment and optimization model (SBAOM).

The SCQPM can realize the real-time detection and advance prediction of the sinter composition and quality index. By using the composition monitoring model based on Deep Neural Network algorithm and the sinter quality prediction model based on Extra Tree algorithm, the performance of the mixture, the operating parameters and the state parameters of the sintering process are taken as input, which can be used to calculate the chemical composition and quality index of the tail sinter in real time.

The SBAOM can adjust and optimize the performance of the mixture that causes sinter composition and quality fluctuations based on the feedback results of the abnormal parameter diagnosis model. The mixture composition that meets the requirements can be obtained by the mixture performance prediction model based on MLR and LightGBM algorithms when the model diagnosis results are that the mixture performance causes sinter composition or quality anomaly. Then combined with the artificially given ratio constraints, raw material composition and other parameters, the ratio calculation and optimization model based on linear programming (LP) and genetic algorithm (GA) were used to obtain the lowest cost ingredient plan, and the results were fed back to the human-computer interaction interface. The material can be changed quickly after being confirmed by the chief engineer.

3.3. DCL

The data communication layer mainly realizes the reading function of PPBOL and DDL related parameters, and reads the data required for model operation from the Level 3 database through the SQL Server search statement. At the same time, the human-computer interaction module accepts the constraints of the initial raw material ratio, sinter chemical composition and quality index input by the sintering technician, and communicates data with SCQPM and PPBOL.

4. Mixture Performance Prediction Model

The process of the mixture forming sinter through ignition and sintering is complex, and the fluctuation of the mixture performance will have a certain impact on the quality of sinter. Therefore, the calculation model of mixture composition is established to detect and optimize the mixture performance. Based on the influence law of parameters in the sintering history data, a high-efficiency prediction model of mixture performance based on data-driven model is proposed in this study. It is possible to quickly calculate and output the mixture composition (total iron, vanadium pentoxide and basicity) that meets the requirements based on the current sintering process parameters (operation parameters and status parameters) when the requirements of sinter composition and quality indicators are given.

In order to solve the problem that it is difficult to use multiple linear regression model (MLR) for accurate prediction of mixture total iron and vanadium pentoxide, a mixture composition prediction model based on LightGBM algorithm was established. The model was trained and verified using a large amount of production data collected in sintering field, and the hyperparameters of the LightGBM algorithm were selected by using Bayesian optimization technology to make it have higher prediction accuracy. To evaluate the model comprehensively and objectively, statistical indicators such as root mean square error (RMSE) and goodness of fit (R²) were used to compare the performance of the LightGBM model with traditional modeling techniques (such as support vector machine (SVR) and multi-layer perceptron (MLP)).

4.1. Test Setup and Data Analysis

Based on the whole process data of sintering process in a domestic iron and steel enterprise, the relationship between input and output characteristics was established by using the high precision and high speed gradient enhancement framework^22,23) issued by Microsoft according to the influence law between sintering mixture and process parameters, sinter chemical composition and quality index. The correlation ranking of each characteristic with total iron (TFe_HL), vanadium pentoxide (V₂O₅_HL) and basicity (CaO/SiO₂_HL) of the mixture is shown in Fig. 2. It can be seen from Fig. 2 that compared with the CaO/SiO₂_HL, the difference between the related variables of TFe_HL and V₂O₅_HL is more obvious. In particular, the variable nine-roller speed (JGSD), the average fan air volume (FJFLJZ), the average throttle opening (FMKDJZ), the total iron of sinter (TFe), the vanadium pentoxide of sinter (V₂O₅) have higher correlation with TFe_HL and V₂O₅_HL. In addition, the derived variables calculated from the sintering process parameters are introduced in the correlation analysis, which are the average throttle opening (FMKDJZ), the average fan air volume (FJFLJZ), the average flue gas temperature (YDWDJZ), and the average flue negative pressure (YDFYJZ), sintering end position (BTP_m) and sintering end temperature (TmaxInt), the meanings of the remaining variables are shown in Table 1.

Fig. 2.

Importance ranking of the TFe_HL, V₂O₅_HL and CaO/SiO₂_HL related variables. (Online version in color.)

Table 1. Main parameters and abbreviations of sintering production line.

Category	No.	Parameters and units	Abbreviation	No.	Parameters and units	Abbreviation
Raw material parameters	1	Total iron of mixture (%)	TFe_HL	2	Vanadium pentoxide of mixture (%)	V2O5_HL
	3	Calcium oxide of mixture (%)	CaO_HL	4	Silica of mixture (%)	SiO2_HL
	5	Basicity of mixture	CaO/SiO2_HL	6	Moisture of mixture (%)	HLSF
Operating parameters	7	Round roller speed (r/h)	YGSD	8	nine-roller speed (r/h)	JGSD
	9	Sintering machine speed (m/min)	SJJJS	10	Gas pressure (kpa)	MQYL
	11	Gas flow (m3/h)	MQLL	12	Combustion air pressure (kpa)	ZRFYL
	13	Combustion air flow (m3/h)	ZYFLL	14	Ignition temperature (°C)	DHWD
	15	Material thickness (mm)	LCHD	16	Throttle opening 01 (%)	FMKD01
	17	Throttle opening 02 (%)	FMKD02	18	Fan air volume 01 (m3/h)	FJFL01
	19	Fan air volume 02 (m3/h)	FJFL02	–	–	–
State parameter	20	North flue gas temperature (°C)	YDWDB	21	South flue gas temperature (°C)	YDWDN
	22	North flue negative pressure (kpa)	YDFYB	23	South flue negative pressure (kpa)	YDFYN
	24	Bellows exhaust temperature (°C)	Tem i	25	Bellows negative pressure (kpa)	Pre i
Sinter composition	26	Total iron (%)	TFe	27	Basicity	R
	28	Ferrous oxide (%)	FeO	29	Vanadium pentoxide (%)	V2O5
	30	Calcium Oxide (%)	CaO	31	Silica (%)	SiO2
Sinter quality	32	Drum Index (%)	ZGZS	33	Screening index (%)	SFZS

In this study, the top 34 feature parameters with a relatively large contribution to the predicted values (TFe_HL, V₂O₅_HL, and CaO/SiO₂_HL) in each group were selected as the model input. First, MLR was used to predict the composition of the mixture, as shown in Fig. 3. Based on the MLR algorithm, the R² of the TFe_HL, V₂O₅_HL and CaO/SiO₂_HL prediction models are respectively 0.7412, 0.8126, and 0.8534, and the root mean square error (RMSE) is 0.8467, 0.0245, and 0.0100. From the evaluation indexes and visualization results of the model, it can be seen that the prediction model results of the TFe_HL and V₂O₅_HL deviate greatly from the actual values compared with the CaO/SiO₂_HL. Due to the inherent nonlinear characteristics of the sintering process, it is difficult to obtain accurate results through the linear model for the TFe_HL and V₂O₅_HL. Therefore, nonlinear models such as LightGBM, SVR, and MLP are used to further improve the prediction accuracy.

Fig. 3.

Visualization and prediction of TFe_HL, V₂O₅_HL and CaO/SiO₂_HL. (Online version in color.)

4.2. Modeling Process and Results Discussion

4.2.1. Modeling Process

Unlike traditional statistical models, LightGBM, SVR, and MLP are all data-driven models.^24,25) Without understanding the detailed “internal” structure of the model, the desired output results are obtained by providing input parameters. The sintering process parameters (process parameters, chemical composition and quality index of sinter) with high contribution to the predicted value are taken as input, and the TFe_HL and V₂O₅_HL as output. In the modeling process, the model hyperparameters, the implementation of the algorithm and the training and verification of the model are studied.

A total of several billion pieces of data have been downloaded from the production management system for the sintering process of the steel plant, and more than 13500 sets of data samples used for modeling have been obtained through data sorting. These samples were divided into two parts (training set (D1) and test set (D2)) to train and test various models, to capture the quantitative relationship between the total iron and vanadium pentoxide of the mixture and their respective characteristic parameters. In order to eliminate the influence of each parameter unit during the sintering process, the original data was pre-processed before it was input into the model. In this study, all feature parameters were scaled by using z-score standardized methods to make them comparable without changing the distribution of original data.

4.2.2. Results and Discussion

In this section, LightGBM is used to predict the TFe_HL and V₂O₅_HL. Moreover, the selection of model parameters, the prediction accuracy and the time response of the LightGBM model are mainly discussed.

Taking the modelling process of the TFe_HL as an example, a default benchmark model is first trained based on the historical data, and it is tested for prediction. Then two techniques are used to select the hyperparameters of the model, one is Bayesian Optimization (BO), and the other is Random Search (RS) for comparison purposes. Hyperopt is a tool for adjusting parameters through BO. This method can find better parameters quickly,²⁶⁾ so Hyperopt is used to automatically optimize the hyperparameters of the LightGBM. In addition, the RS process is customized by using random-sample function to realize the selection of model hyperparameters. The root mean square error (RMSE) on the D1 was taken as the objective function during the optimization process, and all calculations for this study were conducted on an Intel Core (TM) I7-6700 CPU 3.5 GHz PC with 8 GB RAM. The results of BO and RS are compared in the optimization process of the TFe_HL prediction model, as shown in Fig. 4.

Fig. 4.

Comparison of distribution in the process of hyperparameters optimization. (Online version in color.)

It can be observed from Fig. 4 that BO and RS attempt different hyperparameters. Since the selection of hyperparameters by RS is carried out without considering the previous results, the distribution of parameter samples is close to the domain space defined in this study. BO, however, uses a completely different approach from RS when looking for the optimal parameter. It works by learning the shape of the objective function to find the parameter that increases the result to the global maximum. BO first assumes an acquisition function based on the prior distribution, and updates the prior distribution after testing the objective function with new sampling points each time. Then, the posterior distribution gives the location where the global maximum value may occur.²⁷⁾ In the process of hyperparameter search, the model loss changes of BO and RS are shown in Fig. 5, and the optimal hyperparameters and evaluation results are shown in Table 2.

Fig. 5.

Comparison of validation losses. (Online version in color.)

Table 2. Comparison of the optimal hyperparameters.

Parameters and objectives	BO	RS
boosting_type	gbdt	gbdt
colsample_bytree	0.5566	0.4000
learning_rate	0.0297	0.0288
min_child_samples	20	13
min_child_weight	12	13
num_leaves	144	149
reg_alpha	0.3110	0.1000
reg_lambda	0.2421	0.9000
subsample	0.8364	1.0
subsample_for_bin	160000	160000
iterations	403	247
RMSE	0.4173	0.4177

It can be seen from Fig. 5 that the verification loss of BO is lower than the loss value of RS. And Table 2 shows that the Bayesian optimized LightGBM model (BO-LightGBM) has a lower RMSE index in the D1, but it also takes more iterations to reach the best index. It is difficult to say that BO is better for this particular problem because the difference in the evaluation indicators (RMSE) obtained by the LightGBM model under the two parameter optimization techniques is small. Nevertheless, in order to obtain a more accurate prediction model, we obtained the optimal parameter set by using BO and RS, and established a prediction model. Furthermore, the model was tested by using a data set D2 which not included in the training set. The comparison between the predicted and actual values of the TFe_HL and V₂O₅_HL based on BO-LightGBM model is shown in Fig. 6. The evaluation index results of benchmark model, RS model and BO model are shown in Table 3.

Fig. 6.

Predicted TFe_HL and V₂O₅_HL on the D2 from BO-LightGBM. (Online version in color.)

Table 3. Performance summary of the original model and the two optimized models.

Prediction model	Benchmark model		RS model		BO model
	R2	RMSE	R2	RMSE	R2	RMSE
TFe	0.8073	0.7306	0.8347	0.6766	0.8378	0.6704
V2O5	0.8699	0.0200	0.8602	0.0200	0.8776	0.0200

It can be seen from Table 3 that the performance of the LightGBM model based on Bayesian optimization is significantly improved. The R² of the TFe_HL and V₂O₅_HL based on the BO-LightGBM model on the test set D2 were 0.8378 and 0.8776, respectively. Compared with V₂O₅_HL, the R² index of TFe_HL is relatively low, which is closely related to the characteristics of the metallurgical process flow and the quality of the data itself. However, even such model accuracy can still play an important guiding role in sintering production. In addition, the RMSE of the two models are 0.6704 and 0.0200, and the values are relatively small, which indicates that the BO-LightGBM model is more robust. The on-line construction time of the TFe_HL and V₂O₅_HL prediction model is 6.42 s and 5.18 s, respectively, this time is acceptable for the long process sintering process. Therefore, this set of models can be nested in the metallurgical industry MES system for application.

4.3. Comparison between Models

The BO-LightGBM models determined for the prediction of TFe_HL and V₂O₅_HL were compared with the SVR and MLP models in terms of prediction accuracy. As mentioned earlier, the input data of the SVR and MLP models are the same as the BO-LightGBM models, and the prediction results of the three models are shown in Fig. 7. It can be seen from the figure that the prediction results of the V₂O₅_HL based on the BO-LightGBM model is closer to the actual value; for the prediction results of the TFe_HL, the deviation between the predicted value of the MLP model and the measured value is significantly greater than that of the SVR and BO-LightGBM models. However, it is difficult to judge which prediction accuracy is higher between the SVR and BO-LightGBM models through Fig. 7, so the relative error distributions on the D2 of the three models that predict the TFe_HL are compared, as shown in Fig. 8.

Fig. 7.

Difference between estimation obtained by the three models and measured value. (Online version in color.)

Fig. 8.

Relative error distribution of models on the D2. (Online version in color.)

It can be seen from Fig. 8 that the performance of BO-LightGBM is better than the SVR model, because the maximum relative error of the SVR model on the D2 is significantly higher than that of the BO-LightGBM model. The R², RMSE and calculation time of each model on the D2 are summarized, as shown in Table 4.

Table 4. Summary of component forecasting modeling for various models.

Prediction model	SVR			MLP			BO-LightGBM
	R2	RMSE	Time	R2	RMSE	Time	R2	RMSE	Time
TFe	0.7806	0.7796	11.15 s	0.7121	0.8930	16.61 s	0.8368	0.6723	10.04 s
V2O5	0.3433	0.0443	5.64 s	0.4611	0.0401	6.23 s	0.8720	0.0195	5.18 s

It can be seen from the table that the BO-LightGBM models are significantly better than the SVR and MLP models in terms of prediction accuracy and model robustness, and the BO-LightGBM models training time are shorter. In order to apply the model to the MES system, the training time response of the TFe_HL and V₂O₅_HL models is also an important consideration. However, the comparison between the algorithms is the calculation time of the real-time CPU. The BO-LightGBM models have the shortest training time and can be completed in about 10 s, so it is very suitable for real-time modeling and online prediction of the mixture composition in the sintering process.

The above research results prove the ability of artificial intelligence to model the complex and highly nonlinear relationships of the sintering process parameters. The BO-LightGBM-based TFe_HL and V₂O₅_HL prediction models and the MLR-based CaO/SiO₂_HL prediction model can provide guidance for online modeling and prediction of the performance of the sintering mixture.

5. Pre-batching and Sintering Batching Model

The batching in the sintering process includes two steps: pre-batching (first batching) and sintering batching (second batching). The first batching is the process of mixing iron ore raw materials of different origins and different grades at a certain ratio to form a neutralized ore; the second batching is the process of mixing the raw materials such as neutralized ore, return fines, solvent and fuel in a certain proportion, and forming the mixture through adding water and stirring. In order to produce qualified sinter, it is necessary to ensure that the iron grade, basicity and other properties of the mixture meet certain requirements in the batching process. Therefore, the pre-batching and sintering batching model is established. Aiming at the problem of solving the sintering ratio under multi-constrained conditions, the application effects of a variety of intelligent algorithms are compared and tested, and the rapid batching calculation and optimization of the given mixture performance are realized.

5.1. Pre-batching Model

According to the process theory, the total iron content of the neutralized ore has a direct relationship with the grade of the sinter, and the SiO₂ of the neutralized ore will affect the basicity of the sinter. In addition, for iron and steel enterprises smelting vanadium and titanium ore, they attach great importance to the vanadium content of the sinter, and the vanadium component mainly comes from the vanadium concentrate powder added. Therefore, the Fe, SiO₂ and V₂O₅ components are selected as the calculation variables in the first batching calculation model.

The mixing of various iron-containing raw materials has only physical changes in the process of the first batching, so the composition of the neutralized ore should be a linear weighted sum of the chemical composition of various raw materials. Due to the variety of iron-containing raw materials participating in the ingredients and the price differences, the relationship between the neutralized ore composition and the price has become an important factor affecting the ratio of raw materials. The optimization goal of the first batching is to obtain the lowest batching cost when the main component indexes of the neutralized ore meet the requirements, so the calculation model of the first batching is described as:   

$$\{\begin{array}{l}TFe\_neu=\sum _{i=1}^m{z}_{i}TF{e}_i\hfill \\ Si{O}_2\_neu=\sum _{i=1}^m{z}_{i}Si{O}_{2i}\hfill \\ V_2{O}_5\_neu=\sum _{i=1}^m{z}_i{V}_{\text{2}}{O}_{\text{5}i}\hfill \\ F\_neu(Z)=\sum _{i=1}^m{z}_i{p}_i\hfill \\ minF\_neu(Z)\hfill \end{array}$$(1)

Among them, z_i is the ratio of various iron-containing raw materials; TFe_neu, SiO₂_neu and V₂O₅_neu are the iron grade, SiO₂ and V₂O₅ of the neutralized ore, respectively; TFe_i, SiO_2i and V₂O_5i(i = 1,2,...,m) are the iron grade, SiO₂ and V₂O₅ content of the i-th iron-containing raw material. p_i is the price of the i-th iron-containing raw material, and F_neu(Z) is the cost of the neutralized ore.   

$$\text{s}\text{.}t.\{\begin{array}{l}\sum _{i=1}^m{z}_i=1\hfill \\ {[z_i]}_{\text{min}}\le z_i\le {[z_i]}_{\text{max}}\hfill \\ {[TFe\_ne{u}_{Set}]}_{\text{min}}\le TFe\_neu\le {[TFe\_ne{u}_{Set}]}_{\text{max}}\hfill \\ {[Si{O}_2\_ne{u}_{Set}]}_{min}\le Si{O}_2\_neu\le {[Si{O}_2\_ne{u}_{Set}]}_{max}\hfill \\ {[V_2{O}_5\_ne{u}_{Set}]}_{min}\le V_2{O}_5\_neu\le {[V_2{O}_5\_ne{u}_{Set}]}_{max}\hfill \end{array}$$(2)

Considering the stock of raw materials, the ratio of various iron-containing raw materials is restricted during the batching process, where [z_i]_min and [z_i]_max represent the lower limit and upper limit of the ratio of the i-th raw material, respectively. In addition, the chemical components TFe_neu, SiO₂_neu and V₂O₅_neu of the neutralized ore need to meet certain requirements, and [TFe_neu_Set]_min, [TFe_neu_Set]_max, [SiO₂_neu_Set]_min, [SiO₂_neu_Set]_max, [V₂O₅_neu_Set]_min and [V₂O₅_neu_Set]_max are set values, respectively.

5.2. Sintering Batching Model

The process of the mixture through ignition and sintering to form sinter is complex, during which the fluctuation of the mixture performance will have a certain impact on the sinter quality. Therefore, the mixture composition calculation model is established to detect and optimize the mixture performance. The return fines used in the second batching is sinter with unqualified particle size. In order to save costs, the ratio will be fine-tuned according to the amount of ore returned, but generally all will be used. The significance of the second batching is to check whether the mixture composition obtained by mixing the neutralized ore, the return fines, the solvent and the fuel in a certain ratio meets the requirements. The description of the ratio calculation model is as follows:   

$$\{\begin{array}{l}TF{e}_H=y_{1}TFe\_neu+y_{2}TF{e}_r\\ V_2{O}_{5H}=y_1{V}_2{O}_5\_neu+y_2{V}_2{O}_{5r}\\ Si{O}_{2H}=y_{1}Si{O}_2\_neu+y_{2}Si{O}_{2r}+\sum _{j=3}^n{y}_{j}Si{O}_{2f_j}\\ Ca{O}_H=y_{1}CaO\_neu+y_{2}Ca{O}_r+\sum _{j=3}^n{y}_{j}Ca{O}_{f_j}\\ \hspace{1em}{R}_H=Ca{O}_H/Si{O}_{2H}\end{array}$$(3)

Among them, TFe_H, V₂O_5H, SiO_2H, CaO_H and R_H are calculated values of iron grade, V₂O₅, SiO₂, CaO and basicity of the mixture, respectively; TFe_r, V₂O_5r, SiO_2r and CaO_r are the iron grades, V₂O₅, SiO₂ and CaO of the return fines; y_j(j = 1,2,...,n) represent the ratio of neutralized ore, return fines and non-ferrous raw materials (flux, fuel, etc.); SiO_2fj and CaO_fj represent the SiO₂ and CaO content of the j-th non-ferrous raw material.   

$$s.t.\{\begin{array}{l}TF{e}_H-TF{e}_{H\text{Set}}\Rightarrow 0\hfill \\ V_2{O}_{5H}-V_2{O}_{5H\text{Set}}\Rightarrow 0\hfill \\ {\text{R}}_H-{\text{R}}_{H\text{Set}}\Rightarrow 0\hfill \\ \sum _{j=1}^n{y}_j=1\hfill \\ {[y_j]}_{min}\le y_j\le {[y_j]}_{max}\hfill \end{array}$$(4)

In the batching process, the importance of each chemical component of the mixture is different. In order to meet the requirements of blast furnace ironmaking for iron grade, V₂O₅ and basicity of the sinter, strict constraints are established for the iron grade, V₂O₅ and basicity of the mixture composition, so that the above composition approximates the given mixture composition setting value, which is given by the mixture performance prediction model established in section 4. The amount of each raw material is also limited in the sintering batching model, [y_j]_min and [y_j]_max are used as the lower limit value and upper limit value of the ratio.

5.3. Ratio Calculation and Optimization Methods

Combined with the characteristics of the sintering process, the strategy of stratification optimization is adopted. According to the objective function and constraint conditions of the pre-batching and sintering batching models, the DE and GA are called twice to solve the raw material ratio. First, the ratio of iron ore raw material that meets the main component indexes of the neutralized ore and the lowest batching cost is calculated; then, according to the composition of given mixture, the ratio of neutralized ore, return fines, solvent and fuel is optimized.

DE is a method to solve optimization problems through cooperation and competition among individuals within a population. Its essence is a greedy genetic algorithm based on real number coding and with the idea of preserving excellent individuals.²⁸⁾ The GA is a type of randomized search method that borrows from the evolutionary laws of the biological world. During the search process, it can automatically acquire and accumulate knowledge about search space, and adaptively control the search process to obtain the best solution.^29,30) Since the adaptability of various intelligent algorithms in different application fields is different, the DE and GA algorithms are compared and analyzed in this study. The mechanism and calculation flow of the two algorithms are given.

5.3.1. DE

(1) Initial population. The initial population {x_i(0)|$x_{j,i}^L$≤x_j,i(0)≤$x_{j,i}^U$,i=1,2,...,NP;j=1,2,...,D} is randomly generated. Among them, x represents the ratio of each raw material, x_i(0) represents the i-th individual of the 0-th generation in the population, and x_j,i(0) is the j-th “gene” on the x_i(0) individual. NP is the population size and D is the dimension of the solution space.

(2) Crossover operation. The individual mutation is realized through the difference strategy, that is, two different individuals in the population are randomly selected, and the vector difference is scaled to perform vector synthesis with the individual to be mutated, thereby generating a new generation of population, as shown in Eq. (5).   

$$v_i(\mathrm{g}+1)=x_{r1}(\mathrm{g})+F\cdot (x_{r2}(\mathrm{g})-x_{r3}(\mathrm{g})),i\ne r_1\ne r_2\ne r_3$$(5)

In the formula, F is the scaling factor, and x_i(g) is the i-th individual in the g-th generation population.

(3) Mutation operation. Perform cross operations between individuals on the g-th generation population {x_i(g)} and its mutated intermediate product {x_i(g+1)}, as shown in Eq. (6).   

$$u_{j,i}(\mathrm{g}+1)=\{\begin{array}{l}{v}_{j,i}(\mathrm{g}+1),\hfill \\ x_{j,i}(\mathrm{g}),\hfill \end{array}\begin{array}{l}\mathrm{\hspace{0.17em} } \text{if}\mathrm{\hspace{0.17em} } rand(0,1)\le \text{CR}\mathrm{\hspace{0.17em} } \text{or}\mathrm{\hspace{0.17em} } j=j_{rand}\hfill \\ \mathrm{\hspace{0.17em} } \text{otherwise}\hfill \end{array}$$(6)

Among them, CR is the cross probability, j_rand is a random integer of [1,2,...,D].

(4) Selection operation. The objective functions of individuals u_i(g+1) and x_i(g) are compared, and the greedy algorithm is used to select the individual x_i(g+1) who enters the next generation population, as shown in Eq. (7).   

$$x_i(\mathrm{g}+1)=\{\begin{array}{l}{u}_i(\mathrm{g}+1),\hfill \\ x_i(\mathrm{g}),\hfill \end{array}\begin{array}{l}\mathrm{\hspace{0.17em} } \text{if}\mathrm{\hspace{0.17em} } f(u_i(\mathrm{g}+1))\le f(x_i(\mathrm{g}))\hfill \\ \mathrm{\hspace{0.17em} } \text{otherwise}\hfill \end{array}$$(7)

5.3.2. GA

(1) Encoding. Binary encoding is used in this study.

Assuming that the solution of the optimization problem is (x₁,x₂,...,x_n), x represents the ratio of each raw material. The encoding length corresponding to each decision variable is (l₁,l₂,...,l_n), and each individual (chrom) is encoded as a binary string of length chrom_lenth = ${\sum }_{i=1}^n{l}_i$. When initializing the population, pop_num (population number) individuals will be randomly coded, and pop_num binary strings of length chrom_lenth will be generated as the initial population.

(2) Decoding. Its purpose is to get the actual value of the solution corresponding to each individual. The coding segment corresponding the decision variable x_m of an individual (chrom) to is from the individual’s position ${\sum }_{i=1}^{m-1}{l}_i$ to position ${\sum }_{i=1}^m{l}_i$. The binary bit corresponding to the end position is not included, and then the code segment is converted to the corresponding decimal value $x_m^{dec}$. If the value range of x_m is [$x_m^{min}$,$x_m^{max}$], the actual value after decoding is $x_m^{val}$=$x_m^{min}$+$x_m^{dec}$*($x_m^{max}$−$x_m^{min}$)/($2^{l_m}$−1). Finally, the optimization problem solution ($x_1^{val}$,$x_2^{val}$,...,$x_n^{val}$) corresponding to each individual can be obtained.

(3) Solve the fitness. We can get pop_num solutions after decoding, and then bring these solutions into the objective function in turn. And we get the fitness values corresponding to these solutions after that, which are recorded as fit₁,fit₂,...,fit_n.

(4) Duplication. The chrom_best with the best fitness is found as the best individual in the current population, and then pop_num-1 individuals and the optimal individual chrom_best are selected from the population to form the replicated population.

(5) Cross. It takes place in other individuals outside the optimal individual. First, pop_num-1 random numbers between 0 and 1 are generated in an orderly manner, the positions of the random numbers less than the cross probability are recorded, and the individuals corresponding to these positions are selected for cross operation.

(6) Mutation. It is also performed in individuals other than the optimal one. First, connect the pop_num-1 individuals participating in the mutation operation into a string with a length of (pop_num−1)*chorm_lenth, and then generate (pop_num−1)*chorm_lenth random numbers between 0 and 1 at a time, record the positions of random numbers that are less than the probability of mutation, and all mutations occur at these positions.

According to the above-mentioned flow, the steps 2 to 6 are executed in turn to iterate the population until the end condition is satisfied.

6. Test and Application Analysis

For a certain iron and steel enterprise, the types of raw materials used in sintering production process are relatively stable, and the relationship between the mixture properties corresponding to different raw material structures and the sintering production process parameters has been effectively recorded for a long time. In the sintering production process, the raw material unloading system will be affected by factors such as the silo level, raw material moisture and weather temperature, and there will be fluctuations in the unloading weight, which will lead to changes in the batching structure, resulting in abnormal sinter composition and quality. In addition, due to the supply problem of partial raw material, when the overall structure of the batching scheme remains unchanged, it is often necessary to replace and fine-tune one or several raw materials to obtain the sinter quality that meets the production requirements. Aimed at above problems, the SBAOM was constructed based on the influence rule of the mixture performance, the sintering process parameters, the sinter composition and quality in the historical production process of the iron and steel enterprises, first quickly calculate the mixture performance that meets the requirements, then the lowest cost raw material ratio can be obtained through the pre-batching and sintering batching model.

Taking the fine-tuning of the raw material ratio of the steel plant on April 1, 2019 as an example, the effectiveness of this research method was verified through test and applications. When the unloading system is abnormal (or the raw material ratio is fine-tuned), the average value of the sintering process parameters two hours before the material is changed can reflect the operation of the sintering machine at that time. The composition and quality of sinter required by the ironmaking process on that day are shown in Table 5, and the average value of the sintering process parameters two hours before the change is shown in Table 6.

Table 5. Chemical composition and quality requirements for sinter.

Serial number	Composition and quality of sinter
1	TFe ≥ 54.5%
2	V2O5 ≥ 0.245%
3	2.1 ≤ R ≤ 2.15
4	Drum index ≥ 76.5%

Table 6. Process parameters for current sintering production.

Category	No.	Abbreviations and units	value	No.	Abbreviations and units	value
Raw material parameters	1	HLSF (%)	9.40	–	–	–
Operating parameters	2	YGSD (r/h)	432.40	3	JGSD (r/h)	591.54
	4	SJJJS (m/min)	2.21	5	MQYL (kpa)	4.70
	6	MQLL (m3/h)	1676	7	ZRFYL (kpa)	5.30
	8	ZYFLL (m3/h)	1146	9	DHWD (°C)	1155
	10	LCHD (mm)	700	11	FMKDJZ (%)	78.36
	12	FJFLJZ (m3/h)	5611.88	–	–	–
State parameter	13	YDWDJZ (°C)	131.21	14	YDFYJZ (kpa)	−13.58
	15	Tem 1 (°C)	82.17	16	Tem 2 (°C)	83.05
	17	Tem 3 (°C)	78.53	18	Tem 5 (°C)	72.18
	19	Tem 7 (°C)	69.32	20	Tem 9 (°C)	68.35
	21	Tem 11 (°C)	72.42	22	Tem 13 (°C)	94.70
	23	Tem 15 (°C)	161.88	24	Tem 16 (°C)	218.45
	25	Tem 18 (°C)	324.52	26	Tem 20 (°C)	349.25
	27	Tem 21 (°C)	367.40	28	Tem 22 (°C)	294
	29	Pre 1 (kpa)	−11.94	30	Pre 2 (kpa)	−12.69
	31	Pre3 (kpa)	−12.38	32	Pre 5 (kpa)	−12.91
	33	Pre 7 (kpa)	−13.33	34	Pre 9 (kpa)	−13.33
	35	Pre 11 (kpa)	−13.19	36	Pre 13 (kpa)	−13.25
	37	Pre 15 (kpa)	−11.93	38	Pre 16 (kpa)	−13.17
	39	Pre 18 (kpa)	−12.78	40	Pre 20 (kpa)	−12.10
	41	Pre 21 (kpa)	−12.22	42	Pre 22 (kpa)	−11.74
	43	BTP_m (m)	75.35	44	TmaxInt (°C)	372

Through the information in Tables 5 and 6, the mixture performance prediction model was applied to obtain the mixture composition that meets the requirements, as shown in Table 7.

Table 7. Prediction results of mixture performance.

Mixture composition	Predicted value
TFe/%	50.39
V2O5/%	0.24
R	2.23

According to the given mixture composition, the ratio calculation and optimization model was used to calculate the ratio of raw materials that meet the requirements. The chemical composition inspection value and price of raw materials used by the factory in the process of first batching on the same day are shown in Table 8.

Table 8. Chemical composition and price of raw materials in the 1st-proportion.

Raw materials	Chemical composition/%								Price/RMB
	TFe	SiO2	CaO	MgO	V2O5	Al2O3	S	P
T1	63.99	3.38	1.15	4.17	0.53	0.7	0.27	0.07	980
T2	65.52	2.25	1.08	2.98	0.52	1.37	0.08	0.03	1120
T3	58.38	4.09	0.96	1.43	0.40	1.98	0.13	0.13	844
T4	65.61	6.22	1.53	0.68	0.03	2.27	0.17	0.02	1360
T5	61.4	3.56	0.32	0.14	0.04	2.25	0.02	0.11	1050
T6	60.84	5.62	0.39	0.13	0.03	2.54	0.02	0.08	1280
T7	54.55	6.57	0.35	0.28	0.03	2.32	0.02	0.06	730
T8	43.06	9.03	10.4	5.56	0.66	3.98	0.35	0.21	0

Since the iron-containing raw materials used in first batching will be affected by the stock of the material yard, the allowable range of each raw material ratio and the limited range of the neutralized ore components are shown in Table 9. In the second batching, the chemical composition and price of the used neutralized ore are determined by the first batching, and the raw material composition and price except the neutralized ore are shown in Table 10.

Table 9. Restricted interval of the raw material ratio and the neutralized ore component.

Raw materials	Restricted interval		Composition of the neutralized ore	Restricted interval
	Lower limits/%	Upper limits/%		Lower limits/%	Upper limits/%
T1	10	15	TFe	60.5%	61.5%
T2	20	30	SiO2	4.2%	4.5%
T3	3	8	V2O5	0.28	0.3
T4	10	15	–	–	–
T5	15	25	–	–	–
T6	5	15	–	–	–
T7	5	10	–	–	–
T8	5	10	–	–	–

Table 10. Performance and price of raw materials in the 2nd-proportion.

Raw materials	Chemical composition/%								Burning loss/%	Price/RMB
	TFe	SiO2	CaO	MgO	V2O5	Al2O3	S	P
Return fines	54.80	4.94	11.05	1.9	0.292	1.75	0.03	0.06	0.00	0
Coke powder	0.00	7.89	1.25	0.35	0.00	4.56	0.40	0.00	81.50	895
Limestone powder	0.00	1.10	49.78	3.86	0.00	0.90	0.02	0.00	41.50	215.5
Calcium ash	0.00	3.40	72.89	5.23	0.00	2.80	0.07	0.00	12.50	337.61
Magnesium ash	0.00	1.30	43.92	32.51	0.00	1.85	0.07	0.00	17.50	324.79

First, the optimization calculation of the first batching was performed by DE and PSO algorithms, and the results were compared with the actual ratio and performance of the sintering plant used on the same day, the results are shown in Table 11. Then, the DE and PSO algorithms were also used to optimize the calculation of the second batching according to the interval limitation of the raw materials used and the constraints on the performance of the mixture. The constraint conditions of the raw material ratio and composition are shown in Table 12, and the ratio calculation results of the second batching and mixture performance are shown in Table 13.

Table 11. Ratio and performance in the 1st-proportion.

Raw materials	Ratio/%			Composition and price	Performance
	Actual ratio	DE	PSO		Actual ratio	DE	PSO
T1	13.06	11.53	14.86	TFe/%	61.21	60.60	60.97
T2	23.99	25.68	20.93	SiO2/%	4.36	4.48	4.32
T3	4.99	4.49	7.93	CaO/%	1.49	1.75	1.42
T4	11.04	10.51	10.16	MgO/%	2.27	2.36	2.50
T5	21.97	21.07	24.77	V2O5/%	0.28	0.29	0.28
T6	10.93	7.62	5.1	Al2O3/%	1.98	2.03	1.95
T7	7.01	9.42	9.9	S/%	0.12	0.13	0.13
T8	7.01	9.69	6.34	P/%	0.08	0.08	0.08
–	–	–	–	Price/RMB	1010.76	968.87	982.86

Table 12. Ratio limits of the raw material and constraints of the mixture composition.

Raw materials	Restricted interval		Mixture composition	Constraint condition
	Lower limits/%	Upper limits/%
Return fines	10.00	15.00	TFe	The approximation is 50.39%
Coke powder	4.40	4.50	V2O5	The approximation is 0.24%
Limestone powder	5.00	5.50	R	The approximation is 2.23%
Calcium ash	5.50	6.00	SiO2	Greater than 4.2%, less than 4.5%
Magnesium ash	1.00	1.50	CaO	Greater than 9.5%, less than 10.5%
Neutralized ore	70.00	80.00	–	–

Table 13. Ratio and performance in the 2nd-proportion.

Raw materials	Ratio/%			Composition and price	Performance
	Actual ratio	DE	PSO		Actual ratio	DE	PSO
Return fines	11.5	13.02	14.78	TFe/%	50.39	50.24	50.30
Coke powder	4.43	4.3	4.34	SiO2/%	4.32	4.43	4.33
Limestone powder	5.13	4.91	4.93	CaO/%	9.63	9.71	9.75
Calcium ash	5.66	5.59	5.76	MgO/%	2.47	2.50	2.39
Magnesium ash	1.24	1.05	0.99	V2O5/%	0.24	0.24	0.24
Neutralized ore	72.03	71.13	69.21	Al2O3/%	2.06	2.09	2.03
–	–	–	–	S/%	0.11	0.12	0.12
–	–	–	–	P/%	0.06	0.06	0.06
–	–	–	–	R	2.23	2.1	2.26
–	–	–	–	Price/RMB	781.85	770.5	752.31

From the above test results, it can be seen that the mixture performance of the batching scheme calculated by the GA is closer to the actual ratio scheme, and the lower batching cost is obtained. Therefore, it is considered that the GA based pre-batching and sintering batching model is more suitable for solving the field batching scheme.

To sum up, the SBAOM can not only give the mixture composition close to the actual ratio quickly, but also obtain lower batching cost. The ratio of iron ore and non-ferrous raw material is obtained by the above calculations, and the requirements of chemical composition and quality index, as well as the stock of raw materials, cost constraints and so on, are considered to realize the rapid adjustment and optimization of sintering batching. This method can effectively solve many limitations of the current off-line batching model, and provide scientific and rapid decision guidance for the small-scale changing material operation in sintering production.

7. Conclusion

The characteristics of non-linearity, complexity and large hysteresis of the sintering process make the solution of the sintering raw material ratio extremely complicated. In addition, the original mixture, the operating parameters and state parameters are closely related. The above characteristics bring great difficulties to the rapid solution of raw material ratios in the process of first batching and second batching, so we have developed a BSMLIA to solve this problem. The main contributions are:

(1) The design of the BSMLIA system architecture has been completed. This system can quickly provide online mixture performance that meets the requirements and the optimal ratio of raw materials.

(2) Appropriate algorithm models are selected for different prediction target parameters, and a mixture performance prediction model was developed using the method of multi-model integration such as MLR and LightGBM algorithms. This model not only ensures the prediction accuracy of the mixture performance, but also shortens the response time of the model in practical applications.

(3) The optimal hyperparameter set of the LightGBM algorithm was obtained using BO technology. By comparing the mixture forecast model based on the BO-LightGBM algorithm with other algorithm models, the superiority of this algorithm model in mixture performance prediction is proved.

(4) The actual production data were applied to verify the SBAOM. The results show that the system can quickly calculate the batching scheme which meets the performance requirements of the sinter and has a lower cost. In addition, the mixture performance of the batching scheme calculated by GA is closer to the actual batching scheme, and the batching cost is reduced by RMB 29.54/ton.

Acknowledgement

Thanks are give to the financial supports from the key program of national nature science foundation of China (U1360205), the Hebei province high-end iron and steel metallurgical joint research fund project (E2019209314), the science and technology project of Hebei education department (BJ2021099).

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