Intelligent Prediction and Real-time Monitoring System for Gas Flow Distribution at the Top of Blast Furnace

Abstract

Aiming at the problem of complex internal environment of blast furnace and the difficulty of gas flow distribution (GFD) detection and prediction, an intelligent prediction and real-time monitoring system of blast furnace roof gas flow distribution based on long short-term memory neural network (LSTM) and fuzzy C-mean clustering (FCM) is proposed, which solves the problems of poor stability of traditional GFD model, low accuracy of multi-step prediction and “black box”. The system consists of a GFD identification model and a multi-step prediction model. The system consists of GFD identification model and cross-beam temperature measurement (CBTM) multi-step prediction model. The GFD identification model first uses the blast furnace CBTM information to establish temperature field of blast furnace burden surface, calculates the center and edge gas flow development index, and adopts the FCM algorithm model to identify the blast furnace GFD pattern; the CBTM multi-step prediction model uses the LSTM model to predict the temperature of 29 CBTM points respectively; Finally, the system returns the predicted CBTM data to the GFD identification model to complete the prediction of the GFD model in the future moment. The experiment shows that the system can effectively predict the GFD development pattern within the next 7 hours, the model prediction accuracy reaches 99%, and the correct rate of all kinds of GFD pattern recognition is above 95%, which can achieve better intelligent prediction and real-time monitoring effect than other traditional GFD models, and provide effective help and support for blast furnace operators to analyze the furnace condition.

1. Introduction

The blast furnace is the core equipment in the steel production process, which affects the product quality and energy consumption of the steel industry, and maintaining the stable smooth running of the blast furnace is the common goal pursued by the whole steel industry.¹⁾ The blast furnace top gas flow distribution (GFD) is one of the main factors affecting the production condition of the blast furnace, and a reasonable GFD is conducive to the smooth running of the blast furnace, high production and lower coke ratio, Therefore, it is very important to grasp and predict the GFD in real time. However, the blast furnace is in a “black box” state during operation, and there are thousands of operating parameters involved in the long process of blast furnace production from raw material feeding to product discharging, so the adjustments made by manual analysis of GFD results often have serious lags. To deal with such long delays, field operators generally use empirical estimation methods to predict the state of the GFD, which is highly subjective and makes it difficult to control the GFD state accurately and for blast furnace operators to obtain a satisfactory GFD condition.²⁾ Therefore, intelligent prediction and real-time monitoring about the GFD condition of blast furnace has become a popular research direction in academia and industry.

With the development of detection technology and the increase of application cases of big data artificial intelligence technology in the steel industry,^3,4) The advanced tools and methods have also been applied to the prediction and monitoring of the blast furnace ironmaking process by domestic and foreign scholars, such as autoregressive moving average model,⁵⁾ echo state network,⁶⁾ and image recognition techniques.⁷⁾ In addition, the recently hot deep neural networks are also gradually applied to the blast furnace iron making process. Shenyi Ding et al.⁸⁾ used recurrent neural networks to establish a prediction model for the prediction of the silicon content of blast furnace molten iron and obtained an accuracy of 86%–94%, which is important for controlling the silicon content of molten iron. To monitor the blast furnace condition, Hang Ouyang et al.⁹⁾ proposed a fault detection and identification method based on a multidimensional gated circulation unit (GRU) network, and the application in real blast furnace faults showed that the method is effective.

In terms of GFD prediction, Ping Zhou et al.¹⁰⁾ proposed a method for online estimation of cross-beam temperature measurement (CBTM) temperature based on the idea of time series, and Pu Huang et al.¹¹⁾ established an estimation model of cross thermometry center temperature based on a three-layer long and short-term memory network, and they both obtained the estimated temperature with high accuracy by experimental verification; Jianqi An et al.¹²⁾ used data-level fusion technique to build a model for temperature field of blast furnace burden surface (BFBS). It can show the radial and axial distribution states of blast furnace gas flow respectively, but such models suffer from the problem of noise interference of CBTM temperature data. For this reason, Xiaoyang Wu et al.¹³⁾ used autoregressive moving average model to remove the measurement error of CBTM measurement, and then used regularized limit learning mechanism to build a multi-step prediction model of blast furnace gas flow, which is suitable for multi-step prediction of blast furnace GFD condition, but cannot completely solve the problem that the prediction error keeps superimposing with the increase of the number of prediction steps. In terms of GFD pattern recognition, Lin Shi et al.¹⁴⁾ used image processing techniques to quantify the statistics of infrared monitoring images and proposed a method to identify the distribution characteristics of blast furnace gas flow centers, which can derive important information of GFD patterns; on this basis, Shenghai Zhang¹⁵⁾ divided the continuous gas flow development process into a state vector sequence of the cloth cycle, and used image processing technology, artificial intelligence technology, time series processing technology to explore the correlation between the cloth cycle and the gas flow development, and found a suitable GFD development model. Although the above research results can achieve the prediction and identification of GFD states, there are still several shortcomings as follows, and the optimization and improvement of these problems play an important role in the improvement of model performance.

The main problems include: 1) In the process of blast furnace operation, the temperature data obtained based on the CBTM device always has different degrees of abnormal data, and the construction of an accurate and effective abnormality treatment method can further improve the stability of GFD model prediction and identification; 2) The traditional blast furnace gas flow temperature prediction model mainly uses mathematical models and machine learning models, most of the prediction models are single-step prediction. Although they have high accuracy, they ignore the practicality and stability of the model in engineering, and can only provide prediction results for a very short period of time, which leads to very limited help for practical operation; 3) Although the traditional blast furnace GFD prediction model predicts the top temperature, it does not give specific GFD model results, which does not completely solve the blast furnace “black box. The problem of “black box” is not completely solved. To address the above mentioned problems, this paper intends to use the actual data to study and establish a GFD intelligent prediction and real-time monitoring system by means of the fusion of two algorithms, Long Short Term Memory (LSTM) and Fuzzy C-Means (FCM).

2. System Structure Design

The functional structure of the GFD intelligent prediction and real-time monitoring system is shown in Fig. 1.

Fig. 1. The functional structure diagram of the system. (Online version in color.)

CBTM is a device for detecting the top temperature of the blast furnace. It is located at the throat of the blast furnace. The shape is shown on the left side of Fig. 1. There are 29 temperature measurement points and 4 CBTMs, They are southeast (TES), southwest (TWS), northwest (TWN)and northeast (TEN), TES CBTM is arranged with 8 thermocouples, and 7 thermocouples are arranged in the other directions. In this paper, in order to study the gas flow index, let the center temperature (TC0) be owned by CBTM in each direction, thus the CBTM in each direction has a layout of 8 temperature data. From the right side of Fig. 1, it can be seen that the overall system consists of two models: identification and prediction. The identification model mainly includes calculating the gas flow development index (GFDI) using the CBTM data, analyzing the relationship between the index and the blast furnace operation index, and giving the mode classification method, among them, GFDI is mainly divided into central development index and edge development index to represent the development state of blast furnace top gas flow; then using the FCM algorithm and the affiliation degree to identify the gas flow development mode. The prediction model mainly includes analyzing the influence coefficients of blast furnace parameters on the CBTM points, determining the input parameters of the model, then using the LSTM model to predict the temperature of 29 CBTM points in the future moment respectively, and finally using the GFDI calculation and pattern identification function in the identification module to predict the GFD pattern in the future moment. The identification and prediction models will share a set of blast furnace data, which will improve the efficiency of the system and have positive significance to break the blast furnace information silo.

In the process of constructing the identification model, firstly, the BFBS is divided based on the CBTM data, and the GFDI formula is used to transform the 29 discrete and high-dimensional CBTM data at each moment into the low-dimensional gas flow center and edge development index, and analyze the relationship between this index and the slag iron ratio (SIR), gas utilization rate (GU) and furnace carbon black top pressure (FCBTP) to obtain the GFD model division rule, BFBS is a curved surface formed on the top of the blast furnace after burden distribution, which is located below the CBTM device; SIR is the amount of slag produced by every 1 ton of pig iron produced by blast furnace, which is the core of reasonable slagging system; GU is an important index of blast furnace stability and energy consumption; FCBTP is an important control parameter of blast furnace production. Then the GFDI is used as the input parameter of FCM for experiments, which include the selection of fuzzy factors and the comparison experiments of FCM¹⁶⁾ with K-Means¹⁷⁾ and DBSCAN¹⁸⁾ models. Finally, the applicability of FCM for GFD identification is demonstrated by the metrics of the sum of squares due to error (SSE) and the silhouette coefficients (SC).

In constructing the prediction model, firstly, the anomalous values of blast furnace data were corrected using a combination of box plot and wavelet denoising (BOX-WD), and the Spearman correlation coefficients of each CBTM point were analyzed to obtain the seven parameters with the largest influence coefficients as the input parameters of the model. The input data were then divided into a training set and three test sets in order to test the stability and accuracy of the model, after which model experiments were conducted, which included 1) the selection of time series, the selection of implied layers and hidden units, and the selection of optimizers, and 2) the LSTM¹⁹⁾ model with Support Vector Regression (SVR),²⁰⁾ the Autoregressive Integrated Moving Average model (ARIMA)²¹⁾ and informer²²⁾ model comparison experiments; 3) LSTM multi-step prediction performance testing experiments. Finally the model will prove the applicability, stability and accuracy of LSTM by mean goodness of fit (R²), mean square error (MSE) and mean absolute error (MAE) evaluation metrics on three test sets.

3. Data Preprocessing

3.1. Data Anomalies and Noise Handling

Since blast furnace ironmaking is in a harsh environment of high temperature and pressure, various testing equipment probes often detect anomalies, resulting in the collected data not conforming to the normal state distribution, and therefore they need to be corrected during data processing. In this paper, a combination of BOX-WD is used to process the extreme outliers and noise of blast furnace data.

The blast furnace data of a steel plant in Hegang from March 2022 to March 2023 were collected, and the collection frequency was hourly. The blast furnace test data are shown in Table 1. In this study, in addition to the data involving the 29 CBTM of the blast furnace other variables affecting the GFD, including air volume (FL), air pressure (FY), permeability index (TQZ), air speed (FS), pressure difference (YC), blast kinetic energy (GFDN), Ore-coke ratio (KJ) and tapping interval (TJ) were also considered. According to the blast furnace process theory, it is known that the CBTM temperature cannot be negative and the thermocouple temperature cannot be consistently high above 1300°C. The production data used were found to have abnormal values, therefore, the data preprocessing operation was carried out.

Table 1. Data information of blast furnace.

parameter	mean	std	min	max	unit
TC0	288.3645	95.4468	−9.3	1372	°C
TEN1	147.6849	61.2894	39.1	1372	°C
TEN2	82.1472	41.9635	20.98	1372	°C
…	…	…	…	…	…
TES3	36.7945	7.2931	18.63	84.11	°C
TES4	35.903	5.9535	19.12	64.43	°C
TES5	32.0625	3.9458	17.5	54.3	°C
TES6	31.6234	3.8182	17.37	66.19	°C
TES7	31.2669	3.824	16.96	68.05	°C
FL	5917.1438	176.9419	3614.82	6239.99	m3/min
FY	431.7281	11.4508	267.67	450.19	kpa
YC	172.199	5.4998	118.77	185.45	kpa
TQZ	34.42	1.1746	26.35	40.49	–
FS	258.9009	7.0123	225.3	292.44	m/s
GFDN	13756.7422	980.8828	9644.81	16931.72	N·m/s
KJ	0.42	0.04	0.29	0.58	–
TJ	2.3	0.02	1.9	3.7	h

The box plot^23,24) is used to process the extreme outliers. Taking TC0 as an example, the processing result of TC0 extreme outliers is shown in Fig. 2. As can be seen from Fig. 2, the left graph is the original data graph, the diamond blocks are the outliers, and the right graph is the effect graph with the outliers removed.

Fig. 2. The effect of box plot to handle outliers. (Online version in color.)

Although the box plot can remove the extreme outliers of the data, the blast furnace data processed by the box plot still shows a high-frequency oscillation pattern with strong data noise, and the high-precision prediction model requires data smoothing, so it is also necessary to remove the data noise on the basis of removing the outliers. The wavelet denoising (WD)²⁵⁾ method inherits the low entropy, multi-resolution, de-correlation and base selection flexibility of wavelet transform, and from the signal science point of view, WD can be seen as low-pass filtering, but it is again superior to the traditional low-pass filter because it can successfully retain the signal characteristics after denoising.WD The flow chart is shown in Fig. 3, and it can be seen that WD is actually a combination of feature extraction and low-pass filtering functions.

Fig. 3. The flow chart of WD. (Online version in color.)

WD can choose the db wavelet basis for the one-dimensional blast furnace parameter data; in order to avoid distortion of the signal due to the excessive number of decomposition layers, the number of layers is chosen to be 1; then the wavelet coefficients are wavelet transformed using the threshold function to obtain the denoised data. So far, the blast furnace data were processed by BOX-WD method to get the final results as shown in Fig. 4.

Fig. 4. The effect of BOX-WD in handling data anomalies and noise. (Online version in color.)

As can be seen from Fig. 4, the TC0 temperature data after data preprocessing completely eliminates the abnormal values in the original data while keeping the data change trend unchanged, and removes the noise in the data to the maximum extent, so that the data are smooth and can truly reflect the production process of the blast furnace, which lays the data foundation for the next work of GFD prediction and identification.

3.2. Feature Selection for High-dimensional Data

In this paper, we study the identification and prediction of GFD; however, the collected data samples have a total of 98 dimensions, including temperature, airflow, and pressure data, and some parameters are not relevant to GFD prediction and identification. It is worth noting that the ore/coke charging conditions and the timing of pig iron tapping are also important factors affecting the temperature of the blast furnace top. The adjustment of the distribution and the change of the tapping rhythm will affect the temperature change of the blast furnace top. In this study, through the mining and analysis of the production data of a blast furnace in Hegang, it is found that the standard deviation of the ore coke ratio and the tapping interval during the production process from March 2022 to March 2023 is very small, indicating that the two parameters are almost unchanged, therefore, it is less helpful for the model to predict the temperature of cross temperature measurement. Finality, by fusing data change characteristics and production experience, the characteristic parameters that can best reflect GFD are determined, a total of 35. On this basis, the Spearman correlation coefficient is used to analyze the correlation between the parameters. The correlation coefficient heat map is shown in Fig. 5.

Fig. 5. Heat map of Spearman correlation coefficient for blast furnace data. (Online version in color.)

As can be seen from Fig. 5, the darker the color indicates the greater correlation. Taking TC0 as an example, TEN1, TWN1, TES1, TEN2, TWN2, TEN4 and TES2 have larger correlation coefficients with TC0, and the other target values have only weak correlation strength with the feature parameters. In this paper, the seven features with the largest correlation coefficients for each target value will be selected as the input parameters of the prediction model for each temperature measurement point. Different feature variables are used for each temperature measurement point prediction model because the correlation coefficients of feature variables and target values are ranked differently.

4. GFDI Calculation and Analysis

4.1. Calculation of GFDI

The CBTM data of the furnace top the temperature information of 29 points, which is large and discrete, not conducive to subsequent analysis and processing, and can be transformed into low-dimensional data with small data volume and more information according to the characteristics of the blast furnace production process.

In the furnace top GFD, most of the upper cloth adjustment and the lower air supply adjustment of the blast furnace are carried out around the central gas flow and the edge gas flow.²⁶⁾ In this paper, the gas flow index of blast furnace center and edge is used as an effective feature to judge GFD. According to the development characteristics of the gas flow in the furnace, the BFBS is divided into three parts: The center (C), the edge (P) and the middle part (M) include three, three and two temperature measurement points of CBTM in the radial range of the blast furnace, respectively. In order to make the respective characteristics of the three parts more prominent and reduce the uncertainty of the divided region, each part is divided into several sub-regions corresponding to each CBTM, the BFBS region division diagram is shown in Fig. 6. The CBTM in the northeast direction is illustrated, that is, the three central points (TC0, TEN1, TEN2) correspond to C₀, C₁, C₂ sub-regions, the two middle points (TEN3, TEN4) correspond to M1, M2 sub-regions, and the three edge points (TEN5, TEN6, TEN7) correspond to P₁, P₂, P₃ sub-regions.

Fig. 6. Schematic diagram of BFBS’s dividing areas. (Online version in color.)

The GFD has a strong correlation with the blast furnace charge surface temperature distribution, but the charge surface temperature has a certain uncertainty, and its correlation with the blast furnace working condition is great. In this study, the relative values of center and edge temperature relative to the average temperature of the charge surface are used to represent the center gas flow index and edge gas flow index, and the specific calculation steps are as follows.

Step1: Evenly take out the n CBTM data that can reflect the temperature field of the BFBS, and calculate the average value of the temperature of the whole BFBS.

  

$$T_{AVE}=\frac{\sum _1^n{T}_i}{n}$$(1)

T_AVE reflects the overall temperature level of the current furnace top gas.

Step 2: calculate the weighted average temperature of the center, middle and edge, representing the temperature of the center, middle and edge areas.

  

$$\{\begin{array}{c}{T}_c=W_{c_0}{T}_{c_0}+W_{c_1}{T}_{c_1}+W_{c_2}{T}_{c_2},\mathrm{\hspace{0.17em} }{W}_{c_0}+W_{c_1}+W_{c_2}=1\\ T_M=W_{M_1}{T}_{M_1}+W_{M_2}{T}_{M_2},\mathrm{\hspace{0.17em} }{W}_{M_1}+W_{M_2}=1\\ T_p=W_{p_1}{T}_{p_1}+W_{p_2}{T}_{p_2}+W_{p_3}{T}_{p_3},\mathrm{\hspace{0.17em} }{W}_{p_1}+W_{p_2}+W_{p_3}=1\end{array}$$(2)

Where, T is the average temperature of each sub-region, and W is the weight of each sub-region. The subscripts C₁, C₂, C₃, M₁, M₂, P₁, P₂ and P₃ represent the areas divided by the center, middle and edge areas of BFBS. Which sub-region can better represent the characteristics of the region, its corresponding weight is relatively high. For example, if C₁ is more representative of the central region than C₂, the weight W_C1 corresponding to C₁ is set to be 10% higher than the weight W_C2 corresponding to C₂.

Step3: Calculate the relative values of the center, middle and edge temperatures relative to the average temperature of the BFBS

  

$$\{\begin{array}{c}{K}_c^{\prime }=\frac{T_c}{T_{AVE}}\\ K_M^{\prime }=\frac{T_M}{T_{AVE}}\\ K_p^{\prime }=\frac{T_p}{T_{AVE}}\end{array}$$(3)

Step4: Normalizing ${\mathrm{K}}_{\mathrm{C}}^{\prime }$ and ${\mathrm{K}}_{\mathrm{P}}^{\prime }$, the center (Kc) and edge gas flow indices (Ke) in one direction of the furnace top are obtained.

  

$$\{\begin{array}{c}Kc=\frac{K_c^{\prime }}{K_c^{\prime }+K_M^{\prime }+K_p^{\prime }}\\ Ke=\frac{K_p^{\prime }}{K_c^{\prime }+K_M^{\prime }+K_p^{\prime }}\end{array}$$(4)

Step5: The average value of the gas flow index in the four directions of the furnace top is used as the final gas flow development index of the blast furnace.

  

$$\{\begin{array}{c}K\_C=(ENKc+ESKc+WSKc+WNKc)/4\\ K\_E=(ENKe+ESKe+WSKe+WNKe)/4\end{array}$$(5)

The center gas flow index K_C and edge gas flow index K_E of the blast furnace are calculated by the above steps, and the quantification of the development level of the center and edge gas flow of the blast furnace is realized.

4.2. GFD Model Division

Although the above can get the level of gas flow center development and edge development, it cannot directly delineate the pattern of GFD yet, therefore, this study continues the research of GFD clustering identification. By integrating the actual data of blast furnace production in an iron and steel plant, the parameters of K_C, K_E, SIR, GU and FCBTP under the same time span are obtained, and the relationships between K_C, K_E and SIR, GU and FCBTP are analyzed to obtain the rules of GFD pattern classification.

Combining data analysis mining and expert experience, the optimal distribution intervals of blast furnace SIR, GU and FCBTP were obtained as 0.25–0.30, 47%–49% and 225–235 kpa, respectively. in addition, the relationship between gas flow development index and blast furnace operation index was also analyzed based on actual blast furnace production data, and the results are shown in Fig. 7.

Fig. 7. The relationship between GFDI and blast furnace operating index. (a) Relationship between GFDI and SIR; (b) Relationship between GFDI and GU; (c) Relationship between GFDI and FCBTP. (Online version in color.)

Fig. 8. The schematic diagram of GFD model division. (Online version in color.)

As can be seen from Fig. 7, when K_C increases and K_E decreases, the SIR shows a decreasing trend, and the GU and the FCBTP show an increasing trend, so the gas flow development index has an approximately linear relationship with the blast furnace operation index. According to the above analysis combined with expert experience, the best state of gas flow development index in the center and edge can be determined. In order to further refine the gas flow development model, this study divides nine typical distribution patterns from A to I according to the development levels in the center and edge, as shown in Fig. 9, which can better reflect the GFD state. According to the obtained GFD patterns, the blast furnace operator can adopt the corresponding fabric system to keep the GFD in the best distribution pattern (A) as much as possible to keep the blast furnace production stable and smooth.

Fig. 9. Memory block structure diagram of LSTM network. (Online version in color.)

In this section, the development indices K_C and K_E of gas flow in the center and edge of blast furnace are obtained, the GFD patterns are analyzed, and the development levels of gas flow in the center and edge of blast furnace are quantified. In order to complete the real-time monitoring function of GFD at the top of blast furnace and open the “black box” of blast furnace, we will continue the research of GFD pattern identification by FCM algorithm on this basis.

5. Model Construction Method and Process

Although noisy data and high-dimensional problems are solved after data processing, GFD advance prediction and pattern recognition are still to be realized. To meet these challenges, a GFD prediction and monitoring system based on LSTM and FCM is proposed.

5.1. Modeling Algorithms

5.1.1. LSTM

LSTM neural network is an improved algorithm based on RecurrentNeural Networks (RNN).²⁷⁾ Three gating units that control information transfer are added to the ordinary RNN, which effectively solves the gradient disappearance or explosion defects that occur in RNNs in long sequences, and the structure of LSTM is shown in Fig. 9.

The three gating units in the LSTM structure are the forgetting gate, the input gate and the output gate, where the forgetting gate keeps the useful information while avoiding the useless information from the previous moment to be passed backward, and the input and output gates serve to read the data and pass the processed data to the next moment. The calculation process is shown below.

  

$$\{\begin{array}{c}{f}_t=\sigma (W_{fx}{x}_t+W_{fh}{h}_{t-1}+b_f)\\ i_t=\sigma (W_{ix}{x}_t+W_{ih}{h}_{t-1}+b_i)\\ g_t=tanh(W_{gx}{x}_t+W_{gh}{h}_{t-1}+b_g)\\ O_t=\sigma (W_{ox}{x}_t+W_{oh}{h}_{t-1}+b_o)\\ C_t=g_i{i}_t+C_{t-1}{f}_t\\ h_t=tanh(C_t)O_t\end{array}$$(6)

Where: W is the weight; b is the bias; σ is the sigmoid function. The input variables at each moment contain the cell state at the previous moment C_t−1; the intermediate state at the previous moment h_t−1; and the input at the current moment x_t; the intermediate variables include the output of the forgetting gate f_t; the output of the input-output gate i_t and O_t, and the output of the input node g_t; the output variables include the cell state C_t and the intermediate state h_t.

In this study, the Keras deep learning framework is used to build the LSTM model using the mean absolute error as the loss function and Adam as the optimizer.

5.1.2. FCM

The FCM algorithm is an improvement of the ordinary C-mean algorithm, which is hard for data partitioning, while FCM is a flexible fuzzy partitioning. Hard clustering classifies each object to be identified strictly into a certain category with an either-or nature, while fuzzy clustering establishes an uncertain description of the sample to the category, which can solve the problem that the object may lie between two or more categories and can reflect objective facts more objectively.

FCM divides n vectors x_i (i=1,2,...,n) into c fuzzy groups and finds the cluster centers of each group so that the value function of the non-similarity index is minimized. the main difference between FCM and hard clustering is that FCM can be fuzzy partitioned, using the affiliation degree to determine the extent to which the data point belongs to each category. the steps of FCM modeling are as follows.

Step1: Initialize the affiliation matrix u so that it satisfies the constraints.

  

$$\sum _{i=1}^c{u}_{ij}=1,j=1,\mathrm{...},n$$(7)

Step2: Calculate c cluster centers, i=1,...,c.

  

$$c_i=\frac{\sum _{j=1}^n{u}_{ij}^m{x}_j}{\sum _{j=1}^n{u}_{ij}^m}$$(8)

Step3: Calculate FCM objective function J (or sum of squared errors SSE).

  

$$J(U,c_1,\mathrm{...},c_c)=\sum _{i=1}^c{J}_i=\sum _{i=1}^c\sum _j^n{u}_{ij}^m{d}_{ij}^2$$(9)

where is between 0, 1; c_i is the cluster center of fuzzy group i, $d_{ij}=\Vert c_i-x_j\Vert$ is the Euclidean distance between the ith cluster center and the jth data point; and m>=1, it is a weighted index.

Step4: Compute the new U matrix. Return to Step 2 until the objective function (9) is no longer small, then the algorithm stops.

  

$$u_{ij}=\frac{1}{\sum _{k=1}^c{\left(\frac{d_y}{d_{kj}}\right)}^{2/(m-1)}}$$(10)

5.2. System Construction

The GFD forecasting and identification system consists of LSTM-based CBTM forecasting model and identification model based on FCM clustering. There are 29 CBTM to be predicted, firstly, the CBTM forecasting model is formed by 29 multi-input single-output LSTM sub-models, then the gas flow index is calculated, and finally the GFD pattern is identified by FCM. The system construction process is shown in Fig. 10.

Fig. 10. The flow chart of system construction. (Online version in color.)

5.2.1. Input and Output

For the prediction model of LSTM, CBTM data is used as input. Using the current moment t of the CBTM and t-x moments (x=1,2,3...), predict its temperature at the moment t+n (n=1,2,3...) and 80% of the samples in the dataset are used as the training set and the remaining 20% are divided equally into 3 test sets in chronological order. For the FCM identification model, K_C and K_E obtained by the calculation method in Section 4.1 are used as input data, and the gas flow development pattern is used as output data.

5.2.2. Network Structure and Parameter Setting

Based on the above data as model inputs and outputs, a prediction model was built using LSTM to select and determine the number of hidden layers, and the number of cells in each layer of each network. In order to solve the problem of overfitting, a missing layer (dropout layer) was added to the network. The recognition model was established using FCM to determine the number of divided classes, fuzzy factors and other parameters.

To verify the performance of LSTM model and FCM clustering, some popular models were selected for comparison experiments, as shown in Table 2.

Table 2. Competitive methods.

	Competitive methods	Description
Forecast	SVR	It can deal with both regression and classification problems. It does not need time dependence.
	ARIMA	It is a strong baseline when there are enough data. It need time dependence.
	Informer	It is a long time series prediction model based on Transformer’s optimization.It need time dependence.
	LSTM	It is an optimized recursive neural network.It does not need time dependence.
Clustering	K-Means	It is a hierarchical clustering algorithm, which needs to specify the number of clusters.
	DBSCAN	It is a density-based clustering algorithm, which does not need to specify the number of clusters in advance.
	FCM	It is a clustering algorithm based on the function optimization method, and the number of clusters needs to be specified.

For the prediction models without time dependence, the input is the feature parameters consisting of 7 dimensions; for the time-dependent prediction models, the input is the time series of each CBTM point, and the optimal LSTM structure in this dataset is given to get the forecast accuracy of different models. For the recognition models constructed using K-Means and FCM clustering, the number of clusters needs to be determined in advance, while DBSCAN does not, and the recognition effect of the GFD model is given at the end.

5.2.3. Model Evaluation

For the CBTM prediction model, besides paying attention to the model fitting effect and the error loss value between the predicted and true values, the stability of the model is also concerned. Therefore, in this study, R², MSE and MAE evaluation metrics were chosen to evaluate the model on three test sets. As shown in Eqs. (11), (12) and (13).

  

$$R^2=1-{\sum _{k=1}^N[y_P(\mathrm{k})-y_R(\overline{\mathrm{k}})]}^2/{\sum _{k=1}^N[y_R(\mathrm{k})-y_R(\overline{\mathrm{k}})]}^2$$(11)

  

$$MSE=\frac{1}{\mathrm{N}}{\sum _{k=1}^N[y_R(\mathrm{k})-y_P(\mathrm{k})]}^2$$(12)

  

$$MAE=\frac{1}{N}\sum _{k=1}^N\left|y_P(\mathrm{k})-y_R(\mathrm{k})\right|$$(13)

where y_R (k) is the actual value of the kth data point, $y_R(\overline{\mathrm{k}})$ is the mean of the data, y_P (k) is the predicted value, and N is the sample size.

For the GFD pattern recognition model, more attention is paid to the accuracy of clustering, and the rationality of the process. Therefore, the clustering algorithm in this study is evaluated using a combination of SSE, SC and expert experience methods. As shown in Eqs. (14) and (15).

  

$$SSE=\sum _{i=1}^k\sum _{p\in m_i}^{}{\left|p-c_i\right|}^2$$(14)

  

$$SC=\frac{b(i)-a(i)}{max\{a(i),b(i)\}}$$(15)

Where k is the number of clustering families, c_i is the clustering center of the ith family, m_i is all points within the ith family; a (i) is the average of the dissimilarity of the i-vector to other points in the same cluster, and b (i) is the minimum of the average dissimilarity of the i-vector to other clusters.

6. Results and Analysis

To address the problems of the conventional blast furnace GFD prediction and identification models mentioned in the introduction, a multi-algorithm fusion of BOX-WD, LSTM and FCM was used to establish a blast furnace GFD intelligent prediction and real-time monitoring system. In the experimental process, (1) the data preprocessed and unprocessed data are used as the input of the blast furnace CBTM prediction model, respectively, to test the performance of the model based on LSTM algorithm; (2) the parameters of the LSTM algorithm model are determined and compared with the traditional machine learning model and the latest popular informer model; (3) the fuzzy factors of the FCM model are determined and compared with other popular clustering algorithms for comparison.

All the above experiments were implemented in Python on a computer with AMD Ryzen7 4800 H 3.6 GHz and 16 GB RAM. To measure the merit of the experimental results, R², MSE, MAE, SSE, SC and training time were used as the evaluation criteria for each prediction model.

6.1. Data Processing Method Based on BOX-WD Method

The actual production data of a blast furnace in a steel plant of HSC was selected, and the data sampling frequency was 1 hour (h). In order to verify the effect of BOX-WD algorithm model on outliers, 4000 sets of experimental data were selected, and the two sets of experimental data, pre-processed and unprocessed, were divided into training set and test set in the ratio of 3:1, respectively. The model performance was tested using two sets of experimental data (preprocessed and unprocessed), and the test results are shown in Table 3.

Table 3. The prediction effect comparison of the model in the raw data and processed data.

model	Train time/s	Test time/s	R2	MSE	MAE
processed data	11.3356	4.5093	0.987	0.8357	0.5635
raw data	12.6589	5.9306	0.536	6.308	2.4068

As can be seen from Table 3, the two experimental data sets are close in terms of model training and testing time, but the performance metrics (R², MSE, and MAE) obtained in the model testing are very different, and the performance of the model using the pre-processed experimental data is significantly better than that of the model using the original data. This shows that the original data improves the accuracy of the prediction model after removing outliers and noise through the BOX-WD model, which proves the effectiveness of the BOX-WD model for blast furnace data processing.

6.2. CBTM Prediction Model Based on LSTM Algorithm

6.2.1. Optimization of CBTM Prediction Model Based on LSTM Algorithm

In the network structure setting of LSTM, the selection of input feature time series is performed first, and then, LSTM deep neural network models with different parameters and structures are proposed. Taking TC0 as an example, the method of determining the best LSTM network for predicting TC0 is described.

(1) Selection of Time Series

A time series with the detection results from the past moment (t-x) to the current moment (t) as input and the future moment (t+n) as output was created by using the shift() function in Pandas based on historical CBTM data. A 2-layer hidden layer and a 64-unit LSTM regressor were used for the input feature selection. Table 4 shows the loss values and the number of iterations of the model corresponding to different x values.

Table 4. Loss and iterations of different x values.

Evaluation	x values
	1	2	3	4	5
Train loss	0.0286	0.0260	0.0350	0.0376	0.0337
Test loss	0.0098	0.0092	0.0128	0.0145	0.0128
Iterations	43	35	39	65	97

As can be seen from Table 4, when the value of x is 2, the regressor model obtains the smallest loss value with the least number of iterations.

(2) Selection of Parameters

The results of the selection of the number of implied layers and hidden cells are shown in Table 5 and Fig. 11.

Table 5. LSTM model’s loss of different network structure.

Layer count	20 units learning_rate=0.01 batch_size=50			20 units learning_rate=0.001 batch_size=100
	Train loss	Test loss	State	Train loss	Test loss	State
2	0.0675	0.0683	Shake	0.0217	0.0133	Steady
4	0.1527	0.1132	Shake	0.0358	0.0206	Steady

Fig. 11. Loss changes in different network structures. (a) Shake; (b) Steady. (Online version in color.)

From Table 5, the best performance of the model in the test set is obtained when the number of hidden layers of the network is 2, the learning_rate is 0.001, and the batch_size is 100. As can be seen from Fig. 11, when the batch size of the network is 50 and the learning_rate is 0.01, the loss results are oscillated. The reason for this phenomenon is that when the learning rate is large, the gradient descent direction of the model fluctuates during the training process, which makes the loss value oscillate.

The results of the optimiser selection are shown in Table 6.

Table 6. Selection of optimizer in different LSTM network structures.

Target	SGD	Adadelta	Adam
Train loss	0.7447	0.8101	0.1153
Test loss	0.5489	0.6578	0.0791
Iterations	200	200	100

As can be seen from Table 6, when “Adam” is used as the optimiser of the LSTM, the loss function of the LSTM model in the test set is the smallest, and the network converges the fastest.

6.2.2. Comparison of the LSTM Algorithm with Other Model Algorithms

The LSTM was compared with other algorithmic models and the results are shown in Table 7 and Fig. 12.

Table 7. Test results of LSTM and other models on three test sets.

Target	Model	Test1	Test2	Test3	AVG
R2	LSTM	0.998	0.997	0.996	0.997
	ARIMA	0.995	0.993	0.996	0.995
	SVR	0.712	0.697	0.983	0.797
	Informer	0.586	0.552	0.459	0.512
MSE	LSTM	0.578	0.512	0.580	0.556
	ARIMA	0.736	0.764	0.850	0.783
	SVR	9.662	8.569	2.039	6.757
	Informer	12.876	11.467	15.524	13.289
MAE	LSTM	0.529	0.608	0.707	0.615
	ARIMA	0.821	0.986	0.896	0.901
	SVR	4.416	3.301	1.449	3.055
	Informer	10.483	10.018	13.855	11.452
Training Time	LSTM	10.356	10.153	10.869	10.459
	ARIMA	125.503	117.853	135.365	126.240
	SVR	0.367	0.286	0.392	0.348
	Informer	20.175	19.635	22.803	20.871

Fig. 12. Comparison of the prediction results of LSTM and other models on three test sets. (a) Test1 test results; (b) Test2 test results; (c) Test3 test results. (Online version in color.)

From the test results in Table 7 and Fig. 12, it can be seen that the overall performance and stability of the LSTM-based TC0 prediction model is better. Although the R² metrics of the ARIMA model and the LSTM model were not significantly different, the LSTM model had a shorter training time and faster convergence than the ARIMA model. In addition, the results of the informer model, which also utilises the deep learning algorithm, did not yield better performance, due to the differences in the applicability of the informer model to different data, which was less applicable to the blast furnace CBTM data. In summary, the LSTM-based CBTM prediction model is more accurate and stable.

6.2.3. Multi-step Prediction Performance Tests Based on the LSTM CBTM Prediction Model

According to the experiments in Section 6.2, the CBTM prediction model built using the LSTM and ARIMA algorithms has a good fitting accuracy. However, the multi-step prediction accuracy of the model still needs to be considered. To this end, multi-step prediction models based on the LSTM and ARIMA algorithms are developed separately, and their performance is verified and compared.

The multi-step prediction model uses data with a sampling period of 1 h. The prediction step of the multi-step prediction model is also set at 1 h in the experiment, which is consistent with the actual production data collection period of the blast furnace. In order to measure the prediction effectiveness of the multi-step prediction model for CBTM measurement, MSE and MAE were used as evaluation indexes in conjunction with the requirements of the field experts, and the output of the multi-step prediction model was considered valid when MSE<1 and MAE<1 were satisfied at the same time. The results of the accuracy comparison of the prediction model outputs with different step sizes are shown in Table 8 and Fig. 13. The detailed prediction performance results of the prediction model are shown in Table 9.

Table 8. Comparison table of multi-step prediction results.

Step	MSE		MAE
	LSTM	ARIMA	LSTM	ARIMA
1	0.368	0.736	0.519	0.736
2	0.421	0.875	0.645	0.802
3	0.528	1.093	0.719	0.927
4	0.692	1.325	0.799	0.957
5	0.672	1.258	0.777	1.378
6	0.714	1.577	0.750	1.487
7	0.752	1.869	0.790	1.558
8	1.188	2.535	0.915	1.783
9	1.378	2.891	0.943	1.853
10	1.166	3.355	1.007	1.903
11	0.945	3.964	0.799	2.014
12	0.923	4.574	0.827	2.189
13	0.950	5.231	0.843	2.258
14	1.805	5.978	1.011	2.356
15	1.169	6.739	0.923	2.439
16	1.557	7.853	1.006	2.591
17	1.690	8.952	1.046	2.703
18	1.723	10.016	1.086	2.895
19	1.656	11.967	0.926	2.902
20	1.738	13.726	0.933	2.986

Fig. 13. Comparison chart of multi-step prediction results. (a) MSE; (b) MAE. (Online version in color.)

Table 9. Detailed prediction results of different multi-step prediction models (°C).

Step	True value	ARIMA		LSTM
		Predicted value	Error	Predicted value	Error
1	352	350.24	0.50%	350.94	0.30%
2	337	333.29	1.10%	335.32	0.50%
3	324	315.90	2.50%	321.41	0.80%
4	316	305.89	3.20%	312.21	1.10%
5	327	310.32	5.10%	322.10	1.50%
6	301	278.73	7.40%	295.58	1.90%
7	294	266.66	9.30%	287.24	2.30%
8	285	251.66	11.70%	277.31	2.70%
9	298	252.11	15.40%	287.57	3.50%
10	336	257.04	23.50%	319.87	4.80%
11	341	240.06	29.60%	320.20	6.10%
12	325	200.85	38.20%	296.08	8.90%

It can be seen from Table 8 that the MSE and MAE of the multi-step prediction model of cross temperature measurement based on LSTM algorithm are less than 1 in 7 steps, which indicates that the output result of the model in 7 steps is effective, while the output result of ARIMA algorithm is effective only in 2 steps. According to Fig. 13, in the experimental test within 20 steps, the MSE index of the LSTM algorithm model generally fluctuates in the range of 0–2, while the MSE index based on the ARIMA algorithm model increases with the number of steps. The error increases significantly, especially when the step size is greater than 9. It can be seen from Table 9 that the multi-step prediction results based on the LSTM model are close to the real values from the first step to the 7th step, and the relative error growth rate becomes larger from the 8th step. However, the prediction results of the first two steps of the ARIMA model are still close to the real value, from the third step, with the increase of the number of steps, the prediction results deviate from the real value, and the error even reaches 38.2% at the 12th step, this is unacceptable for practical applications, which proves that the ARIMA model is not suitable for CBTM multi-step prediction; In contrast, the LSTM algorithm model is more suitable for multi-step prediction of CBTM, and the maximum prediction step is 7.

6.3. GFD Recognition Model Based on FCM Algorithm

Using more than 2000 central and marginal gas flow index sample sets, the GFDI sample set is shown in Fig. 14. On the basis of setting the GFD category to 9 categories, the GFD recognition model is constructed by clustering algorithm, and the fuzzy factors are selected.

Fig. 14. GFDI sample data set. (Online version in color.)

6.3.1. Parameter Selection

For the fuzzy factor m of FCM algorithm, it is the parameter of the flexibility of FCM algorithm, if m is too large, the clustering effect will become poor, while if m is too small the algorithm will be close to the hard clustering algorithm, for this reason different fuzzy factors were chosen to construct the gas flow recognition model, the performance of the algorithm model was tested using SSE and iteration number, the experimental results are shown in Table 10 and Fig. 15.

Table 10. SSE and iteration times of different fuzzy factors.

Target	Fuzzy factor m
	2	3	4
SSE	0.68	0.14	0.03
Iterations	20	26	34

Fig. 15. Clustering results of different fuzzy factors. (a) Unclustered; (b) Clustering results when m=2; (c) Clustering results when m=3; (d) Clustering results when m=4. (Online version in color.)

As can be seen from Table 10, the SSE and the number of iterations of the FCM algorithm are different under different fuzzy factors. When the fuzzy factor increases, the model SSE decreases and the number of iterations increases. It can be seen from Fig. 15. When m = 4, the upper left corner area of the graph changes from two categories to one category, and the green area increases significantly. Combined with the content of Section 3.2, it can be seen that the clustering results obtained at this time are inconsistent with the actual production process. The reason is that the fuzzy factor is too large to increase the membership degree, thus expanding the scope of the category. Therefore, the fuzzy factor m = 3 is determined.

6.3.2. Comparison of Fuzzy C Clustering with Other Algorithms

The FCM algorithm was compared with the K-Means clustering algorithm based on hierarchical partitioning and the DBSCAN algorithm based on density partitioning, and the results are shown in Table 11

Table 11. Comparison of FCM and other clustering algorithms. (Online version in color.)

As can be seen from Table 11, although the SC of DBSCAN is larger than that of K-Means, the DBSCAN algorithm cannot specify the number of classifications in advance, and cannot meet the demand of dividing the gas flow recognition model into 9 classes; in addition, the SSE of FCM is reduced by nearly double than that of K-Means, indicating that the accuracy of FCM is better, so finally we think that FCM is more suitable for the recognition of GFD.

6.3.3. Results of GFD Recognition Model Based on FCM Algorithm

According to the production data on site, the GFD recognition model based on the FCM algorithm was used to identify the gas flow state, where the gas flow is divided into categories corresponding to the cluster centre results are shown in Table 12, and the GFD model recognition results are shown in Table 13.

Table 12. Cluster center.

Classification	K_C	K_E
A	0.69093	0.16175
B	0.66817	0.14991
C	0.61385	0.18897
D	0.64575	0.17385
E	0.50064	0.33215
F	0.74867	0.11561
G	0.71907	0.13396
H	0.42637	0.27167
I	0.77711	0.10122

Table 13. Identification results of GFD.

Classification	Number of samples	Number of identification samples	Identification accuracy
A	526	522	99.24%
B	365	361	98.90%
C	314	308	98.09%
D	272	266	97.79%
E	215	206	95.81%
F	157	151	96.17%
G	96	95	98.96%
H	34	33	97.06%
I	21	20	95.24%

As can be seen from Table 13, the blast furnace GFD identification model has an accuracy rate of over 95%, which can meet the production requirements and provide effective guidance for blast furnace production.

6.4. Functional Design and Implementation of the GFD Prediction and Monitoring System

The CBTM multi-step prediction model and the GFD pattern recognition model have achieved good results in off-line data testing. In order to make the models better serve the actual operating units of blast furnace production and maximise the value of the models, the above 2 models were integrated and a GFD intelligent prediction and real-time monitoring system was developed using Python and JavaScript languages. The system functions mainly include: BFBS shape visualisation, real-time monitoring and prediction of key indicators, etc. The visualisation interface is shown in Figs. 16 and 17.

Fig. 16. Real-time monitoring interface of GFD. (Online version in color.)

Fig. 17. Prediction Interface of GFD. (Online version in color.)

Figure 16 shows the interface of the real-time gas flow development monitoring system, which is capable of displaying real-time data of the blast furnace, with the average level of BFBS temperature, central and marginal GFDI, and the current gas flow development pattern respectively, the above four aspects are highlighted as the key indicators of the monitoring system; the feed line and BFBS shape information is presented in the form of two-dimensional charts; the bottom of the interface has the function of querying the historical information of SIR, central and marginal gas flow index and other indicators.

Figure 17 shows the GFD forecast screen, displaying the GFD forecast information for the next 7 hours, with the central and marginal gas flow index forecast results on the left and the corresponding GFD identification results; on the right, the central and marginal GFDI trend graphs for the next 7 hours.

7. Conclusion

This study takes the GFD of blast furnace top as the object, summarizes the development of blast furnace process parameter model in recent years, draws experience and integrates advantages. Due to the large lag and ‘black box’ characteristics of the blast furnace production process, the GFD of blast furnace is modeled based on a large number of historical data in the production process. The intelligent prediction and real-time monitoring system of GFD on the top of blast furnace is constructed by integrating classical blast furnace production theory, big data technology and intelligent algorithm. The real-time monitoring, prediction and pattern recognition functions of GFD in complex industrial scenarios of blast furnace production are realized. The main contributions of this paper are as follows.

(1) A multi-step prediction model based on the LSTM algorithm for CBTM measurement was constructed. The performance of the model was evaluated on different data sets by selecting evaluation metrics such as R², MSE and MAE, and the accuracy and stability of the model were demonstrated. At the same time, the model was tested for multi-step prediction performance, and the validity of the prediction results within 7 steps was verified, achieving accurate multi-step prediction of CBTM measurement.

(2) The gas flow development indices of the centre and edge were calculated, and the gas flow distribution patterns were classified. On this basis, a GFD pattern recognition model based on the FCM algorithm was constructed, and the SSE and SC evaluation indexes combined with expert experience were selected to evaluate the model, and the applicability of the model for GFD recognition was verified. The accuracy of the model for all types of GFD patterns reached over 95%, which can meet the requirements for blast furnace production guidance.

(3) A GFD intelligent prediction and real-time monitoring system has been constructed by integrating a CBTM multi-step prediction model and a GFD identification model. The system covers functions such as visualisation of BFBS shape, real-time monitoring of key indicators and forecasting of core parameters; the establishment of the system solves the defects of the traditional GFD model such as poor stability and low accuracy of multi-step prediction, and is of great significance in assisting the site operator to understand the internal state of the blast furnace intuitively.

Acknowledgement

Thanks are give to the financial supports from the Hebei natural science foundation grant project (E2020209208), the Tangshan city applied basic research science and technology plan project (21130233C).

Nomenclature

GFD: gas flow distribution

CBTM: cross-beam temperature measurement

BFBS: blast furnace burden surface

GFDI: gas flow development index

TES: the southeast direction of cross-beam temperature measurement

TWS: the southwest direction of cross-beam temperature measurement

TWN: the northwest direction of cross-beam temperature measurement

TEN: the northeast direction of cross-beam temperature measurement

FL: air volume

FY: air pressure

TQZ: permeability index

FS: air speed

YC: pressure difference

GFDN: blast kinetic energy

KJ: ratio of external standard of ore-to-coke

TJ: iron tapping interval

SIR: slag iron ratio

GU: gas utilization rate

FCBTP: furnace carbon black top pressure

K_C: the center gas flow index

K_E: the edge gas flow index

LSTM: Long Short Term Memory

FCM: Fuzzy C-Means

BOX-WD: box plot and wavelet denoising

WD: wavelet denoising

SVR: Support Vector Regression

ARIMA: Autoregressive Integrated Moving Average model

SSE: squares due to error

SC: silhouette coefficients

R²: mean goodness of fit

MSE: mean square error

MAE: mean absolute error

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