Evaluation and Prediction Models for Blast Furnace Operating Status Based on Big Data Mining

Abstract

Based on the historical data of a commercial blast furnace (BF), the evaluation and prediction models for the BF comprehensive operating status were established by big data mining methods. Firstly, based on the data resources of the data warehouse of BF ironmaking, clean data were obtained by processing the original data with the problem of null values, outlier data, and blowing-down operations data. Then, the AHP_EWM_TPOSIS evaluation model was built with the combined weight of AHP and EWM and the improved TOPSIS algorithm. Finally, the model evaluation results were verified with the actual production situation, and the comprehensive matching rate reached 94.49%, indicating that the model can accurately judge the comprehensive operating status of BF. The evaluation result was the target parameter for building the BF comprehensive operating status prediction model. The results showed that the stacking model achieved better results than the base models in all indicators. The accuracy index of the deviation between the predicted value and the actual value within ±0.05 reached 94.50%, which meets the practical needs of BF production. The evaluation and prediction models provided timely and accurate furnace condition information to the operators in the BF smelting process, which promoted the long-term stable operation of the BF condition.

1. Introduction

The fluctuation of BF conditions seriously affected the yield, the quality of molten iron, and energy consumption in BF production [1,2,3]. The smooth operation of a BF is the key to obtaining a high quality, high yield, low consumption, and long life. Due to the dynamic time-varying and strong coupling in BF production, there is no specific index that can directly characterize the operation status of a BF [4]. Whether by using the direct observation method, such as by observing iron notch, slag notch, tuyere, and the movement state of a probe, or by using the indirect observation method, such as in analyzing CO₂ curve or judging hot air pressure, blast pressure, blast volume, and shaft temperatures, all of these have the disadvantage of one-sided localization and subjective experience. It is difficult to provide a timely prediction and warning for BF production conditions, and to effectively guide the stable production, because of the time lag of the operation status judgment. The expert experience evaluation system, based on mechanism knowledge and mechanism model, cannot guide the actual BF production well due to the higher constraints of the system, the small amount of data in the model training set, and the subjective nature of an expert’s experience [5,6,7,8,9,10]. The accurate judgment and prediction of BF operating conditions are still the focus and difficulty of current research.

With the development of technology, new technologies and concepts represented by big data bring hope for solving the current problems. Ma Steel comprehensively selected the parameters that characterize the operating state of BF based on mathematical statistics and expert experience. According to a comparison between the real-time operating parameter index and the set parameter index, the BF smooth-running index was established to accurately judge the BF operation status [11]. Li Hongyang used the factor analysis method to extract the hidden common factors in the BF production parameters by considering the 19 status parameters to calculate the BF status index, then the AdaBoost model was used to predict it 3 h in advance, which achieved a better prediction result [12].

Based on the above comments, a study of the evaluation and prediction models is important to estimate and predict the comprehensive operating status of BF. In this study, based on the historical data of a commercial BF, big data mining technologies were used to establish a comprehensive BF evaluation model that integrates furnace condition, yield, quality, and energy consumption, with production indexes as the starting point, by deeply mining the production data of a BF, which could quickly judge the operating status of a BF and accurately predict it in the proceeding hour. Based on the evaluation and prediction results provided by the model, it is used to guide the BF production, which promotes the effective long-term stable operation of BF conditions and achieves high quality, high production, low consumption, and long service life in BF production.

2. Data Preparation

2.1. Research Steps

The research process needs to be established before data preparation. The steps of the research process are shown in Figure 1. Firstly, we established the data warehouse of BF ironmaking based on the big data platform. Then, we selected the data related to BF production and carried out the data processing work to obtain the clean data for model building. Secondly, we built the evaluation model to evaluate the BF comprehensive operating status. Based on this, we took the evaluation results as the target and built the prediction model to predict the BF’s future operating status. Finally, we provided the operators with production information on the evaluation results and predictions in order to guide BF production.

2.2. Data Warehouse of BF Ironmaking

The establishment of the BF ironmaking data warehouse was based on the strong data resource of the BF ironmaking big data platform. The big data platform integrates all data from the BF production process, and provides the complete data services for the life cycle of BF ironmaking, including the basic services of data transmission, data storage, data management, data modeling, data analysis, and intelligent applications. The big data platform realizes the information and intelligence of BF ironmaking [13]. The architecture of BF ironmaking big data platform is shown in Figure 2.

BF ironmaking is a long production process involving many production parameters. The effective management of the whole process data can provide convenient data extraction and analysis for model development. In order to improve the availability of the data, erroneous data correction, data frequency processing, and data association integration were completed on the source data. Based on the dimensions of the collected data, the different production processes were divided into themes and the structure and content of the individual data tables of the BF were designed. Finally, a versatile and efficient data warehouse template was created for BF ironmaking. The architecture of the BF ironmaking data warehouse is shown in Figure 3.

As shown in Figure 3, an operational data store (ODS) stores the massive underlying source data streams by modules. Unified data management (UDM) cleans, transforms, and integrates source data to divide and arrange the data by theme according to the process and business needs of BF production. An application data store (ADS) provides data links between the integration layer and different application scenarios, enabling independent data storage for the applications. A parameter data store (PDS) consolidates the important parameters of interest in BF production, allowing the users or applications to extract metric data in the most convenient way.

2.3. Data Selection and Processing

2.3.1. Data Selection

The data was selected from a 2500 m³ No.4 commercial BF for vanadium–titanium ore smelting. A total of 535 parameter variables were selected based on the data resource for the BF; these parameters contain all the data for the production. The data collection and description of BF are shown in

Table 1. Data collection and description of BF.

Type of Data	Data Content	Data Frequency	Number
Non-real-time discrete data	Test data of raw material and fuel	Batches	60
	Test data of slag and iron	Furnaces	21
	Manually entered production data	Hours	13
Real-time continuous data	Operating parameters	Seconds, hours	69
	Temperature of the hearth and bottom of BF	Seconds	156
	Temperature, pressure, and flow of cooling stave of BF	Seconds	216

.

As shown in Table 1, different types of data are collected and stored in different ways during the BF production process. According to the production process and the characteristics of the data type, the BF data are divided into two categories of non-real-time discrete data (non-real-time data) and real-time continuous data (real-time data). Non-real-time discrete data refers to the relevant data recorded during the production, this type of data generally includes raw material and fuel, slag and iron test data, and some manually entered production data. Real-time continuous data refers to the temperature, pressure, and flow data recorded in real-time by monitor equipment.

2.3.2. Data Processing

The production environment of a BF is complex. The constraints of production conditions can lead to variable data quality issues with null values and outlier data [14,15,16,17]. Therefore, the data processing of raw data is required. Considering the characteristics of data types, the targeted works of data processing were completed according to their causes. The data processing methods of null values and outlier data are shown in

Table 2. Data processing methods of null values and outlier data.

Abnormal Data	Data Attribute	Causes of Abnormal Data	Data Processing Method
Null values	Non-real-time discrete data	Artificial data omission or inconsistent data frequency	Considering that the high correlation in adjacent time, filling with the correct value from the previous moment
	Real-time continuous data	Abnormal monitoring equipment or signal interference	Filling with Lagrangian method to maintain data continuity
Outlier data	Non-real-time discrete data	Human input errors or abnormal device storage	Data discrimination: outlier data are first identified by setting artificial thresholds. A box plot is used to further discriminate data that fall within the threshold range. Data outside the extreme outlier (Q3 + 3IQR) are referred to as outlier data. Data processing: updating with the correct values from the previous time.
	Real-time continuous data	Signal interference or sensitivity deterioration of monitoring equipment	Data discrimination: distance-based sliding window anomaly detection algorithm identifies outlier data. Data processing: updating with the linear interpolation method to maintain the continuity of the data.

. The data processing work improves the quality of the data and ensures that this data can be better used for data analysis or data mining. The data processing methods of null values and outlier data are shown in Table 2.

The operations of BF blowing-down cannot be avoided during normal production. The BF production is at a standstill during the BF blowing-down to allow for maintenance works such as changing air outlets, welding, and patching gas systems, etc. The data during BF blowing-down are not useful. So, this part of BF data was deleted according to the production log.

3. Evaluation Model for BF Comprehensive Operating Status

The production index was the target point with furnace condition, yield, quality, and energy consumption to develop the evaluation model for the BF comprehensive operating status. Firstly, the index evaluation system of BF comprehensive operating status was established with the selected characterization parameters. Then, the combination of AHP and EWM based on game theory was used to determine the index weights. Finally, the evaluation model was built using the improved TOPSIS algorithm.

3.1. Related Research Methods

3.1.1. Combined Weighting Based on Game Theory

The analytical hierarchy process (AHP) is based on the evaluator’s knowledge and experience, which is interpretable and systematic [18]. The entropy weighting method (EWM) is objective and reflects the law of the data [19]. A single method of weighting can lead to a less accurate weighting because some aspect of the information is overlooked or overemphasized, thus affecting the judgment of the final rating. Game theory considers the role of different weighting outcomes in the evaluation process. It assumes that the weight vectors are independent in order to find the minimization bias of the combined and sub-vector weights, and balances the differences in the single weights by developing reasonable weight allocation coefficients, thus reducing the information loss of a single assignment. In this study, game theory is applied to the combined weighting of AHP and EWM to obtain the combination weights of evaluation indexes [20]. The steps of the combined weighting method based on game theory are as follows.

Step 1, determine the basic weight vector set of a scheme $w_k=\left\{w_1,w_2,\dots ,w_k\right\},k=1,2,\dots ,K$, then any linear combination of K weight vectors is:

$$w={\displaystyle \sum _{k=1}^K{\alpha }_k{w}_k}({\alpha }_k>0)$$

(1)

where ${\alpha }_k$ is a linear combination of weight coefficients and $w$ is a vector of weights.

Step 2, find the linear combination vector with all other vectors whose extreme differences reach a combined minimum and determine the combined most satisfactory weight vector $w^{\prime }$.

$$w^{\prime }=min{\Vert {\displaystyle \sum _{i=1}^K{\alpha }_k{w}_i^T-w_j^T}\Vert }_2, (j=1,2,\dots K)$$

(2)

Using the matrix differential equation property, the system of linear equations, corresponding to the optimized first order derivative condition equivalent to Equation (2), is obtained as follows:

$${\displaystyle \sum _{i=1}^K{\alpha }_k{w}_i^{}{w}_j^T}=w_i^{}{w}_j^T, (j=1,2,\dots K)$$

(3)

$$\left[\begin{array}{cccc}{w}_1^{}{w}_1^T& w_1^{}{w}_2^T& \cdots & w_1^{}{w}_k^T\\ w_2^{}{w}_1^T& w_2^{}{w}_2^T& \cdots & w_2^{}{w}_k^T\\ ⋮& ⋮& ⋮& ⋮\\ w_k^{}{w}_1^T& \cdots & \cdots & w_k^{}{w}_k^T\end{array}\right]\left[\begin{array}{c}{\alpha }_1\\ {\alpha }_2\\ ⋮\\ {\alpha }_k\end{array}\right]=\left[\begin{array}{c}{w}_1^{}{w}_1^T\\ w_2^{}{w}_2^T\\ ⋮\\ w_k^{}{w}_k^T\end{array}\right]$$

(4)

Step 3, the vector of weight coefficients $\left[{\alpha }_1,{\alpha }_2,\dots {\alpha }_k\right]$ is normalized. The calculation formula is:

$${\alpha }_k^{\ast }=\frac{\left|{\alpha }_k^{}\right|}{{\displaystyle \sum _{k=1}^K\left|{\alpha }_k^{}\right|}}$$

(5)

Step 4, calculate the final weight vector $w^{\ast }$.

$$w^{\ast }={\displaystyle {\sum }_{k=1}^K{\alpha }_k^{\ast }}{w}_k^T$$

(6)

3.1.2. Improved TOPSIS Algorithm

TOPSIS, as a comprehensive evaluation method, can make full use of the information of the original data to accurately reflect the gap between the evaluation objects, so as to obtain their relative pros and cons [21]. TOPSIS usually uses the Euclidean distance to calculate similarity. The Euclidean distance is the linear distance between two points in space, and it does not consider the correlation between indexes. The evaluation results calculated with Euclidean distance cannot truly reflect the advantages of each sample. In this study, we improved the problem by using the Mahalanobis distance instead of the Euclidean distance in order to solve the problem of index correlation [22,23]. Compared with the Euclidean distance, the Mahalanobis distance can better reflect the correlation between indexes. The establishment steps are as follows.

Step 1, establish the multi-index decision matrix:

$$R={(r_{ij})}_{m\times n}=\left[\begin{array}{cccc}{r}_{11}& r_{12}& \cdot \cdot \cdot & r_{1n}\\ r_{21}& r_{22}& \cdot \cdot \cdot & r_{2n}\\ \cdot \cdot \cdot & \cdot \cdot \cdot & \cdot \cdot \cdot & \cdot \cdot \cdot \\ r_{m1}& r_{m2}& \cdot \cdot \cdot & r_{mn}\end{array}\right]$$

(7)

where $r_{ij}$ is the initial value of the jth index of the ith evaluation object.

Step 2, construct the forward decision matrix.

According to the attribute characteristics of the evaluation indexes, the evaluation indexes of the BF can be divided into three categories: the extremely large indexes, the extremely small indexes, and the intermediate indexes. The different interval directions of the evaluation indexes could make the analysis confusing. In order to simplify the analysis, all the indexes were converted into extremely large indexes. The specific method is as follows.

The extremely small indexes converted to extremely large indexes:

$${\overline{x}}_i=\max (x_i)-x_i$$

(8)

The intermediate indexes converted to extremely large indexes:

$${\overline{x}}_i=1-\frac{\left|x_i-x_{best}\right|}{\max \left\{\left|x_i-x_{best}\right|\right\}}$$

(9)

Construct the forward decision matrix:

$$R^{\prime }={(r_{ij}^{\prime })}_{m\times n}=\left[\begin{array}{cccc}{r^{\prime }}_{11}& {r^{\prime }}_{12}& \cdot \cdot \cdot & {r^{\prime }}_{1n}\\ {r^{\prime }}_{21}& {r^{\prime }}_{22}& \cdot \cdot \cdot & {r^{\prime }}_{2n}\\ \cdot \cdot \cdot & \cdot \cdot \cdot & \cdot \cdot \cdot & \cdot \cdot \cdot \\ r_{m1}^{\prime }& r_{m2}^{\prime }& \cdot \cdot \cdot & r_{mn}^{\prime }\end{array}\right]$$

(10)

where $x_i$ is the ith sample value of the evaluation object, ${\overline{x}}_i$ is the value of the extremely large indexes after $x_i$ conversion, $x_{best}$ is the optimal value of the intermediate indexes, and $r_{ij}^{\prime }$ is the positive value of the jth index of the ith evaluation object.

Step 3, construct the standardized decision matrix:

$$v_{ij}=\frac{R_{ij}^{\prime }}{\sqrt{{\displaystyle \sum _{i=1}^m{R}_{ij}^{\prime }{}^2}}}$$

(11)

$$V={(v_{ij})}_{m\times n}=\left[\begin{array}{cccc}{v}_{11}& v_{12}& \cdot \cdot \cdot & v_{1n}\\ v_{21}& v_{22}& \cdot \cdot \cdot & v_{2n}\\ \cdot \cdot \cdot & \cdot \cdot \cdot & \cdot \cdot \cdot & \cdot \cdot \cdot \\ v_{m1}& v_{m2}& \cdot \cdot \cdot & v_{mn}\end{array}\right]$$

(12)

where $v_{ij}$ is the standardized value of the jth indicator of the ith evaluation object.

Step 4, construct the standardized weighted decision matrix:

$$Z={(z_{ij})}_{m\times n}=w_i{v}_{ij}=\left[\begin{array}{cccc}{w}_1{v}_{11}& w_2{v}_{12}& \cdot \cdot \cdot & w_n{v}_{1n}\\ w_1{v}_{21}& w_2{v}_{22}& \cdot \cdot \cdot & w_n{v}_{2n}\\ \cdot \cdot \cdot & \cdot \cdot \cdot & \cdot \cdot \cdot & \cdot \cdot \cdot \\ w_1{v}_{m1}& w_2{v}_{m2}& \cdot \cdot \cdot & w_n{v}_{mn}\end{array}\right]$$

(13)

where $z_{ij}$ is the weighted standardized value of the jth indicator of the ith evaluation object and $w_i$ is the value of the combination weight.

Step 5 is the proximity calculation.

Firstly, determine the positive ideal solution $X^{+}=\left\{x_1{}^{+},x_2{}^{+},x_3{}^{+},\cdot \cdot \cdot ,x_n{}^{+}\right\}$ and negative ideal solution $X^{+}=\left\{x_1{}^{+},x_2{}^{+},x_3{}^{+},\cdot \cdot \cdot ,x_n{}^{+}\right\}$ of each evaluation index.

$$\{\begin{array}{l}{x}_j{}^{+}=\left\{\underset{1\le i\le m}{\max }{x}_{ij}|j\in J_B,\hspace{1em}\underset{1\le i\le m}{\min }{x}_{ij}|j\in J_C\right\}\hfill \\ x_j{}^{-}=\left\{\underset{1\le i\le m}{\min }{x}_{ij}|j\in J_B,\hspace{1em}\underset{1\le i\le m}{\max }{x}_{ij}|j\in J_C\right\}\hfill \end{array}$$

(14)

Secondly, calculate the Mahalanobis distance from each evaluation sample sequence to the positive ideal solution $X^{+}$ and the negative ideal solution $X^{-}$, namely $D^{+}$ and $D^{-}$:

$$\{\begin{array}{l}{D}_i{}^{+}=\sqrt{(X_i-X^{+})\Lambda {\epsilon }^{-1}{\Lambda }^{\mathrm{T}}{(X_i-X^{+})}^{\mathrm{T}}}\hfill \\ D_i{}^{-}=\sqrt{(X_i-X^{-})\Lambda {\epsilon }^{-1}{\Lambda }^{\mathrm{T}}{(X_i-X^{-})}^{\mathrm{T}}}\hfill \end{array}$$

(15)

where $X_i=\left\{x_{i1},x_{i2},x_{i3},\cdot \cdot \cdot ,x_{im}\right\}$ and $\epsilon$ is the correlation coefficient matrix, $\Lambda =\mathrm{diag}(w_1,w_2,\cdot \cdot \cdot ,w_n)$.

The correlation coefficient between indexes was calculated using the Deng correlation degree, and the calculation formula is:

$${\gamma }_{ik}=\frac{\underset{i}{\min }\underset{j}{\min }\left|x_{ik}-x_{ij}\right|+\underset{i}{\rho \max }\underset{j}{\max }\left|x_{ik}-x_{ij}\right|}{\left|x_{ik}-x_{ij}\right|+\underset{i}{\rho \max }\underset{j}{\max }\left|x_{ik}-x_{ij}\right|}$$

(16)

where $\rho$ is the resolution, here $\rho$ = 0.5.

The correlation coefficient matrix $\epsilon$ is:

$$\epsilon =\left[\begin{array}{cccc}{\gamma }_{11}& {\gamma }_{12}& \cdot \cdot \cdot & {\gamma }_{1n}\\ {\gamma }_{21}& {\gamma }_{22}& \cdot \cdot \cdot & {\gamma }_{2n}\\ \cdot \cdot \cdot & \cdot \cdot \cdot & \cdot \cdot \cdot & \cdot \cdot \cdot \\ {\gamma }_{m1}& {\gamma }_{m2}& \cdot \cdot \cdot & {\gamma }_{mn}\end{array}\right]$$

(17)

Thirdly, calculate the degree of closeness of each sample based on the positive ideal solution and the negative ideal solution:

$$D_i=\frac{D_i{}^{-}}{D_i{}^{+}+D_i{}^{-}},\hspace{1em}i=1,2,\cdot \cdot \cdot ,m$$

(18)

where, according to the size of the value $D_i$, the comprehensive operation of BF is sorted, and the larger value of $D_i$, the better the BF operation is.

3.2. Evaluation Model Based on AHP_EWM_TPOSIS

3.2.1. BF Evaluation Index System

BF ironmaking features a long process sequence, complex internal reaction mechanism, large hysteresis, strong coupling, and non-linearity. The melting process of a vanadium-titanomagnetite BF is more complex in comparison with that of a BF with common ores. Based on the data resources of the BF data warehouse, and combined with BF process theory and actual production demand, 33 parameters were selected with the assistance of the operators and experts from the BF site as the evaluation index of the BF comprehensive operating status. The evaluation indexes of the BF comprehensive operating status are shown in

Table 3. Evaluation indexes of the BF comprehensive operating status.

Production Processes	Parameter Name	Parameter Description	Number
BF charging	Theoretical iron content, coke ratio, coal ratio	Charging information of BF, including iron content and fuel	3
BF blast	Blast volume, blast temperature, oxygen enrichment volume, actual wind speed, permeability index, gas utilization rate, blast kinetic energy, gas volume index, theoretical combustion temperature	Blast information of BF, including flow, pressure, gas utilization rate and other calculation parameters	9
BF cooling	Heat load, copper cold proportion, inlet water temperature	Cooling information of BF	3
BF monitoring (top, stack, belly, hearth, and bottom)	Top temperature, top pressure, temperature center/edge	Temperature and pressure of BF top	3
	Pressure difference, proportion upper pressure difference, proportion lower pressure difference	Pressure of BF main body	3
	Cooling stave temperature 19 m, cooling stave temperature 26 m	BF cooling stave temperature (furnace bosh and body)	2
	Hearth temperature 8 m, hearth temperature 10 m, bottom temperature first floor, bottom temperature second floor	BF hearth and bottom temperature	4
Molten iron and slag	Iron flow velocity, molten iron temperature, molten iron [Si + Ti], molten iron [S], slag CaO/SiO2, slag MgO/Al2O3	Tapping information and composition information of molten iron and slag	6

.

As shown in Table 3, these index parameters are highly relevant to the 4# vanadium-titanium BF; they contain the main parameters and reflect the comprehensive situation of the BF production operation. By focusing on and regulating these parameters, the BF operators can achieve control of the 4# BF operation. The evaluation index system of the BF comprehensive operating status is shown in Figure 4.

As shown in Figure 4, 33 indexes were divided into three categories of the BF operating parameters, the BF state parameters, and the BF economic and technical index parameters. The BF operating parameters refer to the production parameters that the operators focus on and control when adjusting the furnace conditions, which comprehensively reflect the operating conditions of the BF. The BF state parameters include various sensor parameters for monitoring BFs, such as temperature and pressure. They are the result variables of operating parameters and reflect the operating condition of the BF. The economic and technical index parameters are used to characterize the results of the BF operation, and generally include economic and technical parameters such as yield and coke rate.

3.2.2. Combination Indexes Weights Analysis

The combination weights of the BF evaluation indexes are shown in

Table 4. Weights of the BF evaluation indexes.

Objective	Evaluation Indexes	AHP	EWM	Combination
BF comprehensive operating status (X)	Blast volume (X11_1)	0.0503	0.0245	0.0326
	Blast temperature (X11_2)	0.0191	0.0123	0.0144
	Oxygen enrichment volume (X11_3)	0.0260	0.1405	0.1044
	Actual wind speed (X11_4)	0.0206	0.0159	0.0174
	Permeability index (X11_5)	0.0303	0.0317	0.0313
	Gas utilization rate (X11_6)	0.0281	0.0020	0.0102
	Blast kinetic energy (X11_7)	0.0327	0.0343	0.0338
	Gas volume index (X11_8)	0.0412	0.0251	0.0302
	Theoretical combustion temperature (X11_9)	0.0365	0.0163	0.0227
	Heat load (X21_1)	0.0251	0.0343	0.0314
	Copper cold proportion (X21_2)	0.0105	0.0036	0.0058
	Inlet water temperature (X21_3)	0.0398	0.0037	0.0151
	Iron flow velocity (X31_1)	0.0434	0.0333	0.0365
	Molten iron temperature (X31_2)	0.0203	0.0002	0.0065
	Molten iron [Si + Ti] (X31_3)	0.0203	0.0569	0.0453
	Molten iron [S] (X31_4)	0.0255	0.0408	0.0360
	Slag CaO/SiO2 (X31_5)	0.0322	0.0250	0.0273
	Slag MgO/Al2O3 (X31_6)	0.0379	0.0652	0.0566
	Top temperature (X21_1)	0.0102	0.0406	0.0310
	Top pressure (X21_2)	0.0117	0.0198	0.0172
	Temperature center/edge (X21_3)	0.0267	0.0185	0.0211
	Pressure difference (X22_1)	0.0409	0.0142	0.0226
	Proportion upper pressure difference (X22_2)	0.0205	0.0479	0.0393
	Proportion lower pressure difference (X22_3)	0.0310	0.0180	0.0221
	Cooling stave temperature 19 m (X22_4)	0.0270	0.0284	0.0280
	Cooling stave temperature 26 m (X22_5)	0.0409	0.0368	0.0381
	Hearth temperature 8 m (X23_1)	0.0303	0.0528	0.0457
	Hearth temperature 10 m (X23_2)	0.0151	0.0251	0.0219
	Bottom temperature first floor (X23_3)	0.0214	0.0235	0.0228
	Bottom temperature second floor (X23_4)	0.0214	0.0185	0.0194
	Theoretical iron content (X31_1)	0.0882	0.0333	0.0506
	Coke ratio (X31_2)	0.0485	0.0032	0.0175
	Coal ratio (X31_3)	0.0267	0.0538	0.0452

.

As shown in Table 4, the AHP method has a relatively balanced distribution of weights based on the production experience of experts. The weights for blast volume, theoretical iron content, and the coke ratio are higher, which is consistent with the BF’s goal of smooth operation, high production, and low consumption. The EWM method has a very variable distribution of weights based on the original data itself. The weights of oxygen enrichment volume, blast volume, and coal ratio are relatively large, because in case of BF fluctuations in the actual production process, it is preferred to ensure stable and smooth furnace conditions by reducing the volume of blast volume, oxygen and coal injection, and the extent of the reduction in these parameters is large. The comparison shows that the AHP and EWM methods differ significantly in the weighting of some indexes, such as oxygen enrichment volume, theoretical iron content and coal ratio, which should be given more attention. The combined weighting method based on game theory assigns new weights to these indexes. The final weighting results are more scientific and correspond to the actual production conditions of the BF. The combined weighting method balances the importance of subjective weights (AHP) and objective weights (EWM) by minimizing the deviation between the weights of the two weighting methods. The combination weights reflect the characteristics of the indexes themselves, while making effective use of the original information in the data of the indexes.

3.2.3. Evaluation Results and Discussion

The values of the BF comprehensive operating status (GL04_Score) were graded and defined based on the actual production conditions and process experiences. The description of the evaluation level can provide an intuitive view of the BF comprehensive operating status. The evaluation level of the BF comprehensive operating status is shown in

Table 5. Evaluation level of the BF comprehensive operating status.

Degree of Closeness ${\mathit{D}}_{\mathit{i}}$ (GL04_Score)	Rating Level	Description of BF Comprehensive Operating Status
(0.9, 1]	A+	Stable BF conditions and efficient production
(0.8, 0.9]	A	Stable BF conditions and normal production
(0.7, 0.8]	B+	Basically stable BF conditions and slight fluctuations in production
(0.6, 0.7]	B	Basically stable BF conditions and fluctuations in production
(0.4, 0.6]	C	Stable fluctuations in BF conditions and abnormal production
[0, 0.4]	D	Abnormal stable BF conditions and abnormal production

.

The evaluation results of the BF operating status at different times during BF production were selected to test the adjustment effect of the actual BF operating status. The results of the evaluation of the BF operating status and the main indicators for the hours T1, T2, and T3 are shown in

Table 6. BF operating status and main indicators at different times.

Time	Score of Evaluation (GL04_Score)	Rating Level	Blast Volume/m3‧h−1	Fuel Ratio/kg‧t−1	Theoretical Iron Content/t	Gas Utilization Rate/%
T1	0.9248	A+	5450	504	275.21	47.2
T2	0.7659	B+	5325	510	254.16	46.5
T3	0.5545	C	4008	526	170.24	43.3

. As shown in Table 6, the T1 time has a low fuel ratio and a high gas utilization rate, whilst the BF has sufficient airflow and a high theoretical iron content. The BF production is in a stable and efficient state. At the time of T2, in the absence of a large change in the blast volume, the fuel ratio is relatively high and the amount of iron is relatively low, but there is not much deviation from the optimum range. The BF production is normal and stable. At the time of T3, the BF is operating abnormally due to changes in the raw material and fuel, whilst the fuel ratio remains high and other BF indicators are at historically low levels. The BF production is in abnormal furnace status at this time. Therefore, the evaluation results based on the AHP_EWM_TPOSIS model have a high degree of matching with the actual blast furnace operating status.

The data on the BF operating status for one shift (8 h) was selected for evaluation. The evaluation results and the BF key parameters are shown in Figure 5. Referring to the production log, it was found that the furnace condition becomes worse as the pressure difference increases, whilst the operators improve the situation by reducing the blast volume. Then, the pressure difference returned to normal and the blast volume was increased until the BF operating status returned to a stable production level. During this period, the key parameters, such as top temperature, top pressure, and gas utilization rate, all showed large fluctuations, and the fluctuation trend was consistent with the evaluation scores. It can be seen that the evaluation model can accurately judge the BF operating status, and the scores of the model provided timely and accurate information for the furnace conditions with the operators.

On the basis of this, we compared the evaluation results of the BF operating status under different weighting methods during the shift time period, and the results are shown in Figure 6. As can be seen from Figure 6, there are differences in the results of the AHP and EWM weighting methods. The EWM method showed a volatile trend, while the AHP method showed a flat trend. The combined weighting method, based on game theory, can balance the difference in weights between the AHP and EWM methods, reduce the information loss of separate weighting, and its evaluation results can more truly reflect the trend change in the BF, further validating the effectiveness of the combined weighting method.

In order to further verify the effectiveness of the model, a total of 744 groups of the BF actual production data in March 2023 were selected to test the practical application of the model. The model of AHP-EWM-TPOSIS was used to evaluate the BF operating status. The difference level, d, is introduced when judging the actual situation, which represents the deviation between the evaluation results and the actual situation. The larger the absolute value, the greater the deviation. The model evaluation matching result is shown in

Table 7. Result of the model evaluation matching.

Item	d = −3	d = −2	d = −1	d = 0	d = 1	d = 2	d = 3
Number of Matching/n	3	19	56	596	51	17	2
Proportion/%	0.40	2.55	7.53	80.11	6.85	2.29	0.27

.

It can be seen from Table 7 that there were 596 groups of complete matching (d = 0), accounting for 80.11%, and 106 groups of reliable matching (d = ±1), accounting for 14.38%, and the comprehensive matching rate (|d| ≤ 1) was 94.49%. The evaluation model established in this study had a high degree of matching and accurately judged the BF operating status. The evaluation results could provide real-time and effective information for operators in the optimization process of the BF smelting process, avoiding operators’ decision-making mistakes, and ensuring the stable and smooth operation of BF.

4. Prediction Model Based on Stacking Algorithm

The evaluation result of the evaluation model for the BF operating status is the end-of-hour result. It is a good characterization for the BF operating status, but the operators are equally concerned about the future BF operating status. Therefore, the BF operation evaluation result (GL04_Score) as the target parameter, and the integrated learning algorithm of stacking, were used to build the BF comprehensive operating status prediction model, which predicted the BF operating status in the proceeding hour and provided the trend of the BF operating status for the operators.

4.1. Model Principle of Stacking

The BF production process is complex, and its data distribution is diverse, with a certain regularity and randomness. The feature redundancy is greatly reduced by screening important feature variables with the feature engineering. However, it is difficult for a single model to accurately capture the complex production situation of BF and achieve better prediction results. Therefore, the stacking ensemble learning algorithm was used to predict the BF comprehensive operating status [24]. As a typical representative of the combined strategy learning method, it generally consists of a homogeneous or heterogeneous base model and a two-layer structure of the model used for combined learning. In this study, the individual learners of the five base models of Random Forest [25], Extra Trees [26], Gradient Boosting [27], Neural Network [28], and Support Vector Machines [29] were selected as the first layer learner, and the AdaBoost [30] was selected as the second layer learner. The algorithmic structure of the stacking model is shown in Figure 7.

As shown in Figure 7, the description of the stacking algorithmic is as follows:

(1)

The training set data are divided into five parts, each part of them includes the validation set and test set.

(2)

We traversed the five basic models to make a prediction for the test set of each part and each sample generated five kinds of prediction results. The five results were averaged and spliced, and we used the results of the five models predicted on the training set as the new features for the next layer.

(3)

We used the learning model to fit and predict the data set after the combination of new features and target parameters and, finally, to obtain the prediction result.

4.2. Model Building

4.2.1. Feature Variables Engineering

Autocorrelation Analysis of Target Feature

In addition to being affected by process parameters, the BF operating status (GL04_Score) also has a strong correlation with time series data. The autocorrelation function (ACF) was used to analyze the correlation of the target variable. ACF describes the relationship between variables in the same series at different time intervals over time, i.e., the correlation between two variables at time t and time t + t′. The higher the correlation value, the stronger the dependence between the two variables. The Autocorrelation function values of the target feature are shown in Figure 8.

As shown in Figure 8, the autocorrelation function values of the target variable (GL04_Score) decrease from 1 as the delay time increases. The ACF value is still greater than 0.9 when the autocorrelation window is four hours, indicating that the target variable itself has a strong autocorrelation. In the actual production, the operators focus on the first 4 h of the operating status to keep track the changes in the BF. Therefore, the new features of the first four-hourly values, GL04_Score1, GL04_Score2, GL04_Score3 and GL04_Score4, should be added to the set of feature variables.

Principal Component Analysis

The hearth and bottom part of the BF contain the temperature information of different heights and directions, a total of 156 feature variables. The cooling part of BF contains the temperature information of different heights and directions, as well as the flow and pressure information of cooling water in different directions, for a total of 172 feature variables [31]. The data types of these feature variables are similar and highly correlated. The analysis of a single feature variable has little significance for BF production, so the two parts of the data need to be integrated for analysis as a whole. In this study, principal component analysis (PCA) was selected for the data dimensionality reduction. PCA can map data from high to low dimensions to reduce the dimensionality of features while retaining as much information as possible about the data [32]. The results of dimensionality reduction are shown in Figure 9.

As shown in Figure 9, the eigenvalue threshold is set to 1 according to the objective of the data analysis. For the hearth and bottom of the BF, 10 independent feature variables (FCA1_1–FCA1_10) were extracted from the 156 feature variables, and the cumulative variance reached 95.226%. For the cooling part of the BF, 16 independent feature variables (FCA2_1–FCA2_16) were extracted from the 172 feature variables, and the cumulative variance reached 86.273%. The combined information of the two parts reached 90.750%, which met the condition for data mining. As a result, the number of features was reduced from 328 to 26 by PCA dimensionality reduction, which achieved the purpose of compressing the data with minimal loss of information and reduced the feature redundancy of the model.

Feature Variables Selection

The BF smelting process is time-varying and highly coupled. The input feature variables of the model by a single feature selection method do not allow the model to achieve good prediction results. Therefore, a combination of multiple feature selection methods was used to select the feature variables [33,34]. Firstly, the set of feature variables was initially selected by correlation analysis of Spearman and maximum information coefficient (MIC). Then, the set of feature variables was further screened by the ironmaking process and production experience. Finally, a random forest recursive feature elimination method (REF) was used to obtain the set of final feature variables for the model prediction.

Spearman and MIC correlation analysis were used to analyze the non-linear data of the BF. The results of Spearman and MIC correlation analysis are shown in Figure 10 and Figure 11.

As shown in Figure 10 and Figure 11, taking the union of the selected sets of feature variables by Spearman and MIC correlation analysis methods resulted in a total of 43 feature variables being selected. These feature variables were initially selected only in terms of relevance and there are still issues of redundancy between the variables. Therefore, further screening based on process and production experience was required. The result of the feature variables after screening based on process and production experience is shown in

Table 8. Result of the feature variables after screening.

Production Processes	Feature Name	Number of Features
Autocorrelated variables	GL04_Score1, GL04_Score2, GL04_Score3, GL04_Score4	4
Raw material and fuel	GL04_Pellet_SiO2, GL04_Pellet_TiO2, GL04_Pellet_Compressive, GL04_Consumption_Coal, GL04_Consumption_Coke, GL04_Consumption_Sinter	6
BF operation	GL04_XFZDWPJ, GL04_TQXZS, GL04_RFYL, GL04_PCML, GL04_N2ZXFX, GL04_LFYL, GL04_LFLL, GL04_LDYL, GL04_LDDW, GL04_GFDNKG, GL04_FYLL, GL04_FYL, GL04_FSBZ, GL04_COZXFX, GL04_CO2ZXFX, GL04_Charging_Ironhour, GL04_Charging_CokeRate	17
Hearth part of BF	FAC1_1, FAC1_2	2
Cooling part of BF	FAC2_1	1

.

As shown in Table 8, 30 feature variables were obtained after screening. In order to select the most useful features of the model from the original feature variables, the set of feature variables was further selected by REF. The result of the feature variables selection by REF is shown in Figure 12.

As shown in Figure 12, the number of features added started at 2 and the model cross-validation score rapidly increased to a high point. The score peaked when the number of feature variables reached 20, and then decreased slightly and began to stabilize. The final number of feature variables selected was determined to be 20. The result of the final feature variables is shown in

Table 9. Result of final feature variables.

Production Processes	Feature Name	Feature Description	Number of Features
Autocorrelation variable	GL04_Score1, GL04_Score2, GL04_Score3, GL04_Score4	Four hours values of GL04_Score	4
BF operation	FAC1_1, FAC1_2	PCA of furnace hearth and bottom part	2
	GL04_Charging_Ironhour, GL04_Charging_CokeRate	BF charging information	2
	GL04_LDDW, GL04_LDYL, GL04_XFZDWPJ	BF top temperature and pressure	3
	GL04_CO2ZXFX	BF roof gas detection information	1
	GL04_FSBZ, GL04_FYL, GL04_FYLL, GL04_GFDNKG, GL04_LFLL, GL04_PCML, GL04_RFYL, GL04_TQXZS	BF blast parameters information, including coal injection, air supply	8

.

As shown in Table 9, the number of feature variables was reduced from 535 to 20 by the process of feature variables selection. The number of model input feature variables was significantly reduced from the original variables. The final feature variables contain important operational information about the BF operating status. These variables are consistent with those that are important in the practical production of BF. By focusing on and adjusting these variables, operators are able to control the operating status of the BF.

4.2.2. Model Prediction and Analysis

Considering that the BF ironmaking data has a significant time series character, the model data set was split chronologically in a ratio of 9:1. The front 90% of the data was used as the training set for model training, and the remaining 10% was used as the test set for model testing. The impact of feature selection on the predictive effectiveness of the model was analyzed, while the properties of the stacking algorithm were compared with the predictive performance of other models. The prediction and evaluation results of different models are shown in

Table 10. Prediction and evaluation results of different models.

Feature Selection	Model	R2	RMSE	±0.02%	±0.03%	±0.05%
Without feature selection (535)	Neural Network	0.8388	0.0682	59.15	74.61	82.86
	Extra Trees	0.8639	0.0627	64.11	75.86	85.69
	Random Forest	0.8709	0.0610	66.49	79.77	86.49
	SVM	0.8799	0.0588	68.95	79.93	90.04
	Gradient Boosting	0.8946	0.0551	70.57	81.87	91.18
	Stacking	0.9075	0.0516	71.20	83.61	91.56
With feature selection (20)	Neural Network	0.9135	0.0498	64.37	79.79	86.59
	Extra Trees	0.9146	0.0495	68.35	81.64	87.88
	Random Forest	0.9222	0.0423	69.18	85.89	93.20
	SVM	0.9253	0.0452	72.41	85.28	93.33
	Gradient Boosting	0.9304	0.0404	75.58	85.80	93.85
	Stacking	0.9353	0.0409	75.87	87.97	94.50

, and the prediction results of the stacking model are shown in Figure 13 and Figure 14.

As shown in Table 10, the evaluation indicators of all the models with feature selection were higher than those without feature selection, indicating that the combination of multiple feature selection methods can have a positive effect on improving the model prediction performance. The stacking algorithm had a better performance than the base models in all indicators, and provided an accurate prediction of the BF operating status. The R² of the stacking algorithm reached 0.9353, the indicator of prediction accuracy error within ±0.03 reached 87.97%, and the accuracy indicator within ±0.05 reached 94.50%. The prediction results of the stacking model are shown in Figure 13 and Figure 14. As can be seen from Figure 13 and Figure 14, the stacking algorithm showed satisfactory predictive performance. When the BF conditions fluctuate, the model can accurately predict the BF operating status and capture the changing trends. The prediction error (±0.05) was within the acceptable range and met the practical requirements of BF production. Therefore, the prediction model based on the stacking algorithm in this study can provide the accurate BF operating status in the proceeding hour for the operators, which is of great significance in guiding BF production.

It should be noted that the results are only applicable to the No.4 vanadium–titanium ore smelting BF. However, the analysis process, including the data processing and the BF operating status evaluation and prediction, is generally applicable to all types of BF. Therefore, it can be used as a general and effective system to accurately judge and predict BF production status.

5. Conclusions

The aim of this study was to achieve the purpose of BF production guidance by mining the historical production data. This study combined big data mining techniques with machine learning to build evaluation and prediction models for BF comprehensive operating status. The following conclusions were obtained.

(1)

Based on the data resources of the BF ironmaking data warehouse, the original variables related to the BF parameters were selected, and the cleaned data for the models were obtained by dealing with the null values, outlier data, and blowing-down operations data.

(2)

Combined with BF process theory and actual production demand, 33 parameters characterizing the BF operating status were selected to establish the index evaluation system. The index weights were determined by a combination of AHP and EWM. The evaluation model was built using the improved TOPSIS algorithm. The model was able to accurately evaluate the BF operating status, and the evaluation results match the actual production situation. The comprehensive matching rate reached 94.49%, which can provide timely and effective information for the operators.

(3)

The BF comprehensive operating status prediction model was built by using the BF operation evaluation result as the target parameter. The feature extraction of variables was achieved by feature construction and PCA dimensionality reduction, and the final input feature variables were determined using a combination of multiple feature selection algorithms and production process experience. The stacking model was selected for prediction, and the results showed that the stacking model achieved better results than the base models in all indicators. The accuracy index of the deviation between the predicted value and the actual value within ±0.05 reached 94.50%, which meet the practical needs of BF production.

(4)

The evaluation and prediction models provided timely and accurate information and grasped the trends in the furnace conditions for operators in the BF smelting process. This has important practical implications for the production process, which effectively promoted the long-term stable operation of BF conditions, and achieved the purpose of high quality, high yield, low consumption, and long life in BF production.

(5)

The evaluation and prediction models for BF operating status have achieved a satisfactory application performance. However, there are still some in-depth optimization works to be done. In terms of model prediction, we can try to make predictions for the proceeding two or three hours to achieve a longer-term trend for the BF operating status.