Prediction Model of End-Point Phosphorus Content in EAF Steelmaking Based on BP Neural Network with Periodical Data Optimization

Abstract

The phosphorus (P) content of molten steel is of great importance for the quality of steel products in the electric arc furnace (EAF) steelmaking process. At present, the initial conditions of smelting process in the prediction of end-point P content are still the core part. However, few studies focus on the influence between process data and end-point P content. In this research, the relationships between process data and end-point P content are explored by a BP neural network. Based on the theoretical analysis, influencing factors with high correlation were selected. The prediction model of P content coupled with process data and end-point P content is established. On this basis, the model is optimized with process data of oxygen supply and the time of the first addition of lime. Compared with the practical production data, the results indicate that the hit rate of the model optimized is 87.78% and 75.56% when prediction errors are within $\pm 0.004$ and $\pm 0.003$ of P content. The model established has achieved the effective prediction for end-point P content, and provided a reference for the control of P content in practical production.

1. Introduction

Electric arc furnace (EAF) steelmaking is a heterogeneous reaction process in a high-temperature system that takes scrap as the main raw material. The main objective of EAF steelmaking is to reach the standard of composition and temperature simultaneously [1,2]. Elements in the steel affect the properties of steel [3,4]. A negative impact will be generated when phosphorus (P) content in steel is out of the limit [5,6,7]. Cold conditions cause cracks on the surface of steel due to the excessive P content; this makes the steel exhibit hard brittleness [8]. However, as one of the main sources of P content, the quality of scrap is unpredictable. The content of the original P fluctuates violently in the process of EAF steelmaking process. To obtain qualified and cost-effective steel products, it is necessary to regulate the P content in steel accurately.

At present, the main method to control the end-point P content is widely through molten steel samples [9]. However, the method is inefficient and disadvantageous to guide the production operation. Mathematical modeling is another way to control end-point P content in EAF steelmaking [10]. The mathematical model is quite important for the prediction of P content. But unfortunately, the complexity limits the precision of the model. Therefore, many studies are devoted to predicting the end-point P content by using intelligent model.

The soft sensor models for end-point prediction mainly include the mechanism model [11,12] and the black box model [13,14,15]. Many types of research have been carried out on the control and prediction of end-point P content in the steelmaking process. W. Zhou et al. [16] established a multi-level recursive regression model when combining a multi-level recursive model and multiple regression model. Large amounts of data were used to train the model. The model was applied to the prediction of P content in the steelmaking process, and the result showed the accuracy was more than 84% within the error range of $\pm$0.005%. Based on a backpropagation (BP) neural network, F. He et al. [9] constructed the prediction model of P content in a blast oxygen furnace (BOF). Principal component analysis (PCA) was used to reduce the dimension. The accuracy of the model reached 86.67% under the error range of $\pm$0.004%. S.C. Chang et al. [17] considered the dependencies between elements. Correlations with the process variables were integrated to establish a multi-channel graph convolutional network for the prediction of elements. Experiments demonstrated the superiority and effectiveness of the proposed model. H. Liu et al. [18] used multi-features and GRNN to build a prediction model for end-point elements in BOF. The model was based on flame image processing and could quickly extract the boundary and texture features. The experimental results demonstrated the model was good for the prediction of the end-point elements in the BOF steelmaking process. Z.Y. Lai et al. [19] selected 11 factors to forecast end-point P content by using the grey correlation degree analysis method. The clustering method was used to divide data into different levels, which was a great contribution to building the grey prediction model of end-point content of P. The simulation result showed the built model with cluster was valid. P. Yuan et al. [20] set up the prediction model of end-point composition in EAF steelmaking process. The method of the multidimensional support vector machine algorithm was used to build the model. To improve the accuracy, the model was optimized by subtraction clustering and PCA. Results of the prediction model showed 87% accuracy of P content in the error range of $\pm$0.003%. K.X. Zhou et al. [21] created a prediction model of end-point P content in BOF. A monotone constrained BP neural network algorithm was employed to build the model. The model was constrained by a monotonic relationship and trained by abundant data. The accuracy of this model achieved 94% in the error range of $\pm$0.005%. H.B. Wang et al. [22] combined the clustering algorithm with a neural network to build a prediction model for end-point P content in steelmaking. The data used in the model was classified by clustering. A group method of data handling (GMDH) polynomial neural network was established in each cluster which would be predicted by the model. Compared to the results under different clusters, the optimum solution was obtained. Results showed the accuracy of this model was better than that of the common neural network model. C.R. Li established a BP neural network for predicting the end-point P content of molten steel [23]. J. Liu developed the partial least squares-back propagation (PLS-BP) dimensionality reduction net [24]. S.M. Xie established the model in intelligence to estimate the bath end-point P content [25].

Currently, mechanism analysis in the static and dynamic algorithms are widely used in the research of control and prediction of P content in the EAF steelmaking process. However, the focus of most studies in the research was the relationship between the initial state and end-point state. The effect of process data was ignored, which is disadvantageous for the promotion of the accuracy of the model. Therefore, analyzing the influencing factors of end-point P content and establishing a prediction model of end-point P content with process data is significant.

2. Model Structure and Method

A BP neural network is one kind of ANN, which adopts a BP learning algorithm [26,27,28]. The network studies and reserves vast input–output mode mapping relationships without revealing the mathematical equations in advance. The error of the BP neural network state is minimized while the weights and thresholds in the network are constantly adjusted by BP. The Vulgaris structure of BP neural network is divided into three layers: input layer, hidden layer, and output layer. The structure of a typical BP neural network is shown in Figure 1.

$X={\left(x_1,x_2,\cdots \cdots x_n\right)}^T$ is the input variables of the network, $n$ is the dimensionality of input variables, $W_{ij}$ are the weights between the input layer and the hidden layer, $b_i$ are the biases in the hidden layer, $W_{jk}$ are the weights between the hidden layer and the output layer, $b_j$ are the biases in the output layer, $Y=\left(Y_1,Y_2,\cdots \cdots Y_m\right)$ is the output eigenvector of the network, and $m$ is the dimensionality of output variables. The mathematical relationship between the three layers of the BP neural network is as follows:

The calculation between the input layer and hidden layer is shown in Equation (1):

$$h=f\left({\sum }_{i=1}^n{W}_{ij}·x_i+b_i\right) .$$

(1)

The calculation between the hidden layer and output layer is shown in Equation (2):

$$Y=f\left(\sum _{i=1}^m{W}_{jk}·h_m+b_j\right) ,$$

(2)

where h is the input of the output layer, $Y$ is the output of the network, and $h_m$ are the input from the hidden layer. $f\left(x\right)$ is the nonlinear function, which is beneficial to strengthening the fitting ability of the neural network.

The prediction result of the BP neural network is evaluated by the error between the actual value and the predicted value. The goal is to decrease the error. Parameters are adjusted in the network during per training to decrease the error. The weights and biases change as in Equations (3) and (4):

$${w_i}^{\prime }=W_i-\eta \frac{\partial E}{\partial W_i}$$

(3)

$${b_i}^{\prime }=b_i-\eta \frac{\partial E}{\partial b_i} ,$$

(4)

where ${w_i}^{\prime }$ is the updated weight of nodes, $W_i$ is the former weight of nodes, E is the error, $\partial E/\partial W_i$ is the gradient of the network, ${b_i}^{\prime }$ is the updated bias of nodes, and $b_i$ is the former bias of nodes.

BP neural network algorithms have been widely used in the end-point prediction and fault diagnosis of steelmaking [29,30]. Features of the BP neural network are the abilities in strong nonlinear mapping and a high degree of self-learning. The characteristics of the BP neural network are beneficial to building the mapping relationship between input and output under the condition of a black box.

3. Modeling

3.1. Selection of Input-Output Variable of Model

Ten relevant input variables were initially selected based on the analysis of the reaction mechanism [31,32] of P content in EAF steelmaking process, as shown in Figure 2.

In

Table 1. Preliminary selection for influencing factors and reasons for end-point phosphorus (P) content in the electric arc furnace (EAF) steelmaking process.

Influencing Factors	Symbol for Factors	Reason for the Selection
Weight of scrap	$x_1$	Main material of EAF, staple source of P
Weight of hot metal	$x_2$
C content in hot metal	$x_3$	Elements in molten steel affecting dephosphorization
Si content in hot metal	$x_4$
Mn content in hot metal	$x_5$
P content in hot metal	$x_6$
Temperature of hot metal	$x_7$	Affecting the temperature of the bath
Consumption of power	$x_8$	Factors of steelmaking
Consumption of oxygen	$x_9$	Oxidant
Consumption of lime	$x_{10}$	Dephosphorization agent

, reasons for the selection of these factors are shown. P content in scrap and hot metal are the main source of P content in molten steel. The dephosphorization reaction is an exothermic reaction [33,34]. Therefore, the temperature is significant for the removal of P. The content of elements (C, Si, Mn, etc.) in hot metal affects the heat of molten steel. Nearly half of the heat comes from oxidation of these elements [35]. Electricity supplied is another source of heat for molten steel. The $FeO$ in the slag mainly comes from the reaction between the iron element in hot metal and the oxygen blown [36]. $FeO$ is one of the oxidants to remove the P element into the slag [31,37,38]. The amount of lime in slag influences the removal of P as it is the staple dephosphorization agent [34].

The partial correlation analysis of 10 influencing factors is carried out through the obtained data. The obtained correlation coefficients are shown in

Table 2. Partial correlation analysis of process variables.

−	${\mathit{x}}_1$	${\mathit{x}}_2$	${\mathit{x}}_3$	${\mathit{x}}_4$	${\mathit{x}}_5$	${\mathit{x}}_6$	${\mathit{x}}_7$	${\mathit{x}}_8$	${\mathit{x}}_9$	${\mathit{x}}_{10}$
$x_1$	1.00	-	-	-	-	-	-	-	-	-
$x_2$	−0.05	1.00	-	-	-	-	-	-	-	-
$x_3$	−0.03	−0.15	1.00	-	-	-	-	-	-	-
$x_4$	0.02	−0.03	0.05	1.00	-	-	-	-	-	-
$x_5$	0.07	0.10	0.17	−0.18	1.00	-	-	-	-	-
$x_6$	−0.01	0.14	0.02	0.06	0.22	1.00	-	-	-	-
$x_7$	−0.07	0.19	−0.11	0.02	0.51	0.49	1.00	-	-	-
$x_8$	0.07	−0.30	0.08	−0.05	−0.06	−0.08	0.08	1.00	-	-
$x_9$	−0.09	−0.16	0.08	−0.01	−0.05	0.03	−0.02	0.12	1.00	-
$x_{10}$	0.03	0.35	0.19	0.11	0.07	−0.12	0.09	0.05	0.24	1.00
$Y$	0.18	0.19	0.06	−0.04	0.02	−0.05	0.14	0.01	−0.09	0.06

. The coefficients represent the influence degree of each influencing factor on end-point P content. The symbol of $Y$ is used to present the actual end-point P content.

The influencing degrees of the 10 selected factors on end-point P content are shown in Table 2, namely that $\left|X_2\right|>\left|X_1\right|>\left|X_7\right|>\left|X_9\right|>\left|X_{10}\right|=\left|X_3\right|>\left|X_6\right|>\left|X_4\right|>\left|X_5\right|>\left|X_8\right|$. As a result, the weight of scrap, hot metal, and lime consumption show a significant influence on end-point P content. The results of partial correlation analysis agree well with the theory of steelmaking.

3.2. Establishment of Artificial Neural Network Model

A total of 1250 data heats of the 10 influencing factors and the corresponding data of end-point P content had been collected from a steel plant in Hunan, China. Data selected were eliminated from abnormal data through the study of the normal distribution to reduce the noise. A total of 580 data heats were finally picked from the dataset of 1250 data heats used by the BP neural network in this paper. The data of the end-point P content, selected from the 580 data heats, were taken as the output vector while the data of 10 influencing factors were taken as the input vector. All of the datasets were normalized into the range of (0,1) by the normalization function. The normalization of the data is beneficial to reduce the influence on the level of data. To make the actual value be converted into a unified range space, the normalization function was used as Equation (5),

$$x^{\prime }=\frac{x-x_{min}}{x_{max-x_{min}}} ,$$

(5)

where $x^{\prime }$ is the value after normalization, $x$ is the actual value in the dataset, $x_{min}$ is the minimum in the dataset, and $x_{max}$ is the maximum in the dataset.

According to the BP theorem, the BP neural network with the structure of three layers could realize any continuous function with the desired accuracy. Therefore, the BP neural network in this paper adopts a structure of three layers. The activation function in the neural network is to perform a nonlinear transformation of data, which is beneficial for the fitting ability of neural networks. The activation function selected in the network is also crucial. ReLU function, also known as a modified linear element, had been chosen due to the purpose of regression. Features of the function show a different linear variation while on a different side of the coordinate axis. The function is beneficial to preventing the disappearance of gradient under multiple iterations.

All nodes in the hidden layer are connected to the node in the output layer [39]. Parameters of the hidden layer are bonded to determine the best structure of the BP neural network. To ulteriorly confirm the optimum number of hidden layer nodes, MATLAB was employed to establish the model. Under the condition of different node numbers of the hidden layer, the error was compared to determine the optimum number. The training algorithm used in the model is Levenberg–Marquardt [40]. Advantages of the Gauss–Newton algorithm and gradient descent algorithm are combined in the Levenberg–Marquardt algorithm. The algorithm modifies the parameters during execution, which is effective in convergence in the net. The mean square error (MSE) was taken as the basis to determine the optional number of hidden layer nodes.

To reduce the probability of accidental error, the experiment was repeated five times at each node number. The mean value of five times was taken as the specific MSE of the structure training result, and the MSE is shown in Figure 3.

As shown in Figure 3, the changes of MSE are tortuous along with the number of hidden layer neurons. To prevent overfitting, the number of neurons should be under the limit. The optimal number of hidden layers is 11.

The model was trained by the training set containing 400 feature vector times, whereas 180 other data times were used to evaluate the accuracy of the model. Data in the different datasets are selected randomly. The mean value and standard deviation of training data and test data were counted to describe the data distribution, as shown in

Table 3. Mean and standard deviation of input and output data.

Influence Factors	Units	Training Set		Test Set
		Mean	Standard Deviation	Mean	Standard Deviation
Weight of scrap	t	54.44	13.06	52.73	11.37
Weight of hot metal	t	64.47	11.80	63.45	7.68
C content in hot metal	wt%	4.42	0.04	4.42	0.04
Si content in hot metal	wt%	0.32	0.13	0.26	0.15
Mn content in hot metal	wt%	0.33	0.04	0.28	0.06
P content in hot metal	wt%	0.11	0.01	0.10	0.01
Temperature of hot metal	°C	1329.44	32.90	1329.01	38.10
Consumption of power	kw·h	11,514.65	3380.36	7745.28	2036.53
Consumption of oxygen	Nm3	4504.15	571.21	4147.13	604.35
Consumption of lime	kg	2988.23	795.67	2789.43	1046.72

.

In Table 3, the standard deviation between the weight of scrap and the weight of molten iron is similar. The phenomenon is consistent with the complementary relationship between both. The composition of hot metal is related to the previous process and fluctuates. The standard deviation of various components in hot metal would be in the situation in which the value is excessive. Smelting operations like the consumption of power, oxygen, and lime are varied with the composition and temperature of the solution.

The prediction results of the BP neural network obtained after inverse normalization are shown in Figure 4 and Figure 5.

The points between the dotted lines indicate that the errors are within $\pm 0.004$(wt%). Most of the predicted data shown in Figure 4 is concentrated within the error range of $\pm 0.004$(wt%). However, compared to the range of variation from actual value, the margin of relative error is still colossal. Results of the prediction model indicate there is still a gap between the predicted value and the actual result.

Figure 5 indicates that the absolute deviation of the model is 28.89%, 48.33%, 65.56%, 77.22%, and 88.89% when the predictive errors are within $\pm 0.001$ (wt%), $\pm 0.002$ (wt%), $\pm 0.003$ (wt%), $\pm 0.004$ (wt%), and $\pm 0.005$ (wt%), respectively. The absolute deviation when the error is within $\pm 0.004$ (wt%) and below, which affects the guidance of actual production. However, the frequency when the error is within $\pm 0.004$ (wt%) and below is less than 80%. Poor accuracy meant the model is not qualified for the role to regulate the actual production. There is still room for the improvement of the prediction model.

3.3. Improvement of Prediction Model

EAF steelmaking is complex in its internal reaction mechanism. With the progress of smelting, various technological parameters in the molten pool changed. The variation of P content in the molten pool is different in various smelting periods [31,32]. In the early stage of smelting, the dephosphorization reaction is quickly completed due to the combined effect of the addition of lime and oxygen injection. In the middle stage of smelting, other lime is added to adjust the basicity of slag to maintain the equilibrium condition of residual P in the molten pool. In the later stage of smelting, the temperature of the molten pool is raised because of oxygen injection. The rising temperature destroys the equilibrium conditions of P. The recovery of P occurred and P content in molten steel increased [31,38]. In the refining stage, P content in molten steel is further reduced. An empirical model based on real-life measurements could be used to predict the P content in molten steel [41]. From the above analysis, the change of composition in the molten pool is affected by the process operating system. Therefore, consumption of oxygen and lime in different stages are proposed to be taken as input variables of the BP neural network to optimize the prediction model of end-point P content.

(1)

Optimization of the model with consumption of oxygen divided into stages.

There are different laws of oxygen supply in the process of EAF steelmaking. No specific division for oxygen supply is provided in practical production. However, the main oxidation reaction changes during the smelting [32]. The rhythm of different oxygen supplies affects the reaction. According to the smelting cycle in actual production, the oxygen supply is divided into four stages in eight-minute intervals after the observation of selected data. A total of 400 heats of data at each stage are counted as shown in Figure 6.

The fluctuations in the consumption of oxygen in different stages are shown in Figure 6. The tread for the consumption of oxygen in different heat is in flux. In

Table 4. Characteristic statistics of oxygen supply in different stages of 400 heats.

	Total Oxygen Consumption (m3)	Oxygen Consumption in Stage 1 (m3)	Oxygen Consumption in Stage 2 (m3)	Oxygen Consumption in Stage 3 (m3)	Oxygen Consumption in Stage 4 (m3)
Mean	4514	709	1431	1325	1050
Maximum	6250	1557	2097	1975	2869
Minimum	3058	231	518	463	0
Standard deviation	528	170	255	239	515

, characteristic statistics of oxygen supply in different stages are calculated. The average value of oxygen supply in each stage is 709.85 m³, 1431.58 m³, 1325.44 m³, and 1050.16 m³, respectively. The consumption of oxygen supply is high in the middle period and low in the anterior and posterior periods. The oxygen supply is consistent with reality. Compared to other stages, the difference in oxygen supply between the maximum and minimum is the largest, and the standard deviation is at maximum in stage 4. The great fluctuation of oxygen supply in stage 4 happens due to the different smelting cycles in each heat. As the oxygen supply changes in different stages, the phased treatment of oxygen supply is beneficial to improve the accuracy of the prediction model.

The number of variables changes along with the oxygen supply divided into four stages to 14. The structure of the BP neural network needs to be determined again. The same method as mentioned above in Section 3.2 was used to determine the optimal network structure. The optimal structure of hidden layers is 12.

The model optimized was trained and the prediction result is shown in Figure 7 and Figure 8.

In Figure 7, the predicted data are evenly distributed throughout the range of actual values. The predicted value and actual value show a similar trend. Figure 7 indicates that the absolute deviation of the model is 30.56%, 48.89%, 68.33%, 81.11%, and 92.22% when the predictive errors are within $\pm 0.001$ (wt%), $\pm 0.002$ (wt%), $\pm 0.003$ (wt%), $\pm 0.004$ (wt%), and $\pm 0.005$ (wt%), respectively. Within all the ranges of absolute deviation, the frequency is improved compared with the results without optimization. The result in Figure 8 shows the improvement of the model with the consumption of oxygen divided into stages. However, the improvement of the model is limited as the increase is less than 4%. In particular, the frequency when the error is within $\pm 0.004$ (wt%) and below is poor for meeting the requirements in actual production.

(2)

Optimization of the model with the time of the first addition of lime.

As the remover of P, the amount of lime added plays the strongest correlation role with end-point P content in the EAF steelmaking process [42]. The flow properties of molten pool change in different smelting stages [43]. According to the flow characteristic of the molten pool, lime is added in batches. The first addition of lime affects the formation of slag, which influences the smelting [44]. This paper selects the time of the first addition of lime for the further optimization of the model. The time of the first addition of lime in all heats was gathered, as shown in Figure 9.

In Figure 9, the trend for the time of the first addition of lime was fluctuant. The time of the first addition of lime constantly changes with different heat. In

Table 5. Characteristic statistics of time of the first addition of lime.

	Mean (min)	Maximum (min)	Minimum (min)	Standard Deviation (min)
Time of lime first added	27.36	48.00	17.00	10.20

, the characteristic statistic of time of the first addition of lime is calculated. To further optimize the model, the time of the first addition of lime is selected as one of the characteristic factors.

The input variables are changed from 14 to 15. The structure of the BP network needs to be determined as before. The method of Section 3.2 was used. The optimal structure of hidden layer is 14.

The model optimized was trained and tested. Results of the prediction are shown in Figure 10 and Figure 11.

In Figure 10, the predicted data are evenly distributed in the space between two imaginary lines. Compared with previous results, the predicted value and actual value show a further similar trend. Under the absolute deviation, the model is optimized after the time of the first addition of lime. Figure 10 indicates that the absolute deviation of the model is 33.89%, 50%, 75.56%, 87.78%, and 95.56% when the predictive errors are within $\pm 0.001$ (wt%), $\pm 0.002$ (wt%), $\pm 0.003$ (wt%), $\pm 0.004$ (wt%), and $\pm 0.005$ (wt%), respectively. In all the ranges of error, the improvements in frequency appear to be in accordance with the results previously obtained. In particular, the frequency when the error is within $\pm 0.004$ (wt%) is improved from 81.11% to 87.78%.

The prediction result of the model before and after the optimization is shown in Figure 12.

The accuracy of the model is gradually improved after optimization as shown in Figure 12. The precision of the model is improved obviously when the error is within $\pm 0.003$ (wt%), and $\pm 0.004$ (wt%). Precision of the model is enhanced by 10.56% when the error is within $\pm 0.004$ (wt%). Meanwhile, the promotion of the model is up 10% to 75.56% when the error is within $\pm 0.003$ (wt%). The precision when the error is within $\pm 0.004$ (wt%) and below are acceptable for actual production, which is effective to meet the requirements in actual production. Results show the addition of process data is beneficial to promoting the precision of the model and making the influencing factors of P more complete.

However, the promotion when the error is within $\pm 0.001$ (wt%) and $\pm 0.002$ (wt%) is only 5% and 1.67%. The reason the promotion is at a low level is due to the complex situation in EAF steelmaking. As multiple factors in the EAF steelmaking process should be selected but missed, the noise in dataset also contributes to the error in the model. To further improve the accuracy of the model, a more detailed analysis of the factors would be conducted, and the dataset would be checked more carefully.

Based on the established model, features of the neural network are saved. A system for predicting end-point P content is developed. The interface of the system is shown in Figure 13.

A total of 30 heats are tested in the system, and the results are shown in

Table 6. Results for prediction system of end-point P content.

Heat No.	Actual Value (wt%)	Predicted Value (wt%)	Absolute Deviation (wt%)	Heat No.	Actual Value (wt%)	Predicted Value (wt%)	Absolute Deviation (wt%)
1	0.0141	0.0120	0.0021	16	0.0057	0.0076	−0.0019
2	0.0123	0.0096	0.0027	17	0.0088	0.0068	0.0020
3	0.0113	0.0085	0.0028	18	0.0085	0.0113	−0.0028
4	0.0057	0.0079	−0.0022	19	0.0077	0.0070	0.0007
5	0.0101	0.0106	−0.0005	20	0.0096	0.0099	−0.0003
6	0.0114	0.0125	−0.0011	21	0.0086	0.0107	−0.0021
7	0.0172	0.0163	0.0009	22	0.0121	0.0093	0.0028
8	0.0064	0.0085	−0.0021	23	0.0106	0.0103	0.0003
9	0.0049	0.0074	−0.0025	24	0.0074	0.0096	−0.0022
10	0.0061	0.0086	−0.0025	25	0.0092	0.0102	−0.0010
11	0.0064	0.0109	−0.0045	26	0.0135	0.0171	−0.0036
12	0.0037	0.0058	−0.0021	27	0.0179	0.0114	0.0065
13	0.0059	0.0087	−0.0028	28	0.0098	0.0132	−0.0034
14	0.0070	0.0107	−0.0037	29	0.012	0.0147	−0.0027
15	0.0119	0.0086	0.0033	30	0.0066	0.0101	−0.0035

. Units for actual value, predicted value, and absolute deviation are provided in weight percentage (wt%). The frequency of the model when the errors are within $\pm 0.004$ (wt%), and $\pm 0.003$ (wt%) is 90.00%, and 76.67%, respectively. Absolute deviation of the system is qualified for the actual production. Furthermore, as the model is established based on the mathematics of steelmaking, the model is suitable for other steel plants with specific adjustments.

4. Discussion

Compared to the model without optimization, the accuracy of the prediction model is improved when process data was used. To explore further, the mechanism of dephosphorization in EAF steelmaking process is necessary to be analyzed deeply.

The reaction of dephosphorization during the steelmaking process is the interface reaction, which mainly takes place at the slag–steel interface [38]. According to the molecular theory of slag structure, P in molten pool is generally oxidized to be $CaO·P_2{O}_5$ [31,37,38] into the slag, as shown in Equations (6)–(9).

$$\left(FeO\right)=\left[O\right]+\left[Fe\right]$$

(6)

$$2\left[P\right]+5\left[O\right]=P_2{O}_5$$

(7)

$$P_2{O}_5+3\left(CaO\right)=3CaO·P_2{O}_5$$

(8)

$$5\left[O\right]+2\left[P\right]+3\left(CaO\right)=3CaO·P_2{O}_5 .$$

(9)

Therefore, as the dephosphorization required, [P] should be oxidized by the oxidant to $P_2{O}_5$ and react with the dephosphorization agent to be stable compounds. The stable compounds are removed into the slag. [P] is oxidized to $P^{5+}$ and combined with $O^{2-}$ at the slag interface to be $P{O}_4^{3-}$ complex ions. The reaction of the process is shown in Equation (10):

$$2\left[P\right]+5\left(F{e}^{2+}\right)+8\left(O^{2-}\right)=2P{O}_4^{3-}+5\left[Fe\right] .$$

(10)

The equilibrium constant $K_{\theta }$ of the reaction in the standard state is

$$K_{\theta }=\frac{a_{\left(P{O}_4^{3-}\right)}^2}{a_{\left[P\right]}^2{a}_{\left(F{e}^{2+}\right)}^5{a}_{O^{2-}}^8}=\frac{x{\left(P{O}_4^{3-}\right)}^2}{f_P^{2}w{\left[P\right]}_{\%}^{2}x{\left(F{e}^{2+}\right)}^{5}x{\left(O^{2-}\right)}^8}·\frac{{\gamma }_{P{O}_4^{3-}}^2}{{\gamma }_{F{e}^{2+}}^5{\gamma }_{O^{2-}}^8},$$

(11)

where $a_{P{O}_4^{3-}}$ is the activity of $P{O}_4^{3-}$, $a_{\left[P\right]}$ is the activity of [P], $a_{\left(F{e}^{2+}\right)}$ is the activity of $F{e}^{2+}$, $a_{O^{2-}}$ is the activity of $O^{2-}$, ${\gamma }_{P{O}_4^{3-}}$ is the activity coefficient of $P{O}_4^{3-}$, $x\left(P{O}_4^{3-}\right)$ is the mole fraction of $P{O}_4^{3-}$, $f_P$ is the activity coefficient of [P], $w{\left[P\right]}_{\%}$ is the mass fraction of [P], ${\gamma }_{F{e}^{2+}}$ is the activity coefficient of $F{e}^{2+}$, $x\left(F{e}^{2+}\right)$ is the mole fraction of $F{e}^{2+}$, ${\gamma }_{O^{2-}}$ is the activity coefficient of $O^{2-}$, and $x\left(O^{2-}\right)$ is the mole fraction of $O^{2-}$.

The P distribution ratio, $L_P$, is widely used to measure the dephosphorization ability of slag [32,45],

$$L_p=\frac{x\left(P{O}_4^{3-}\right)}{w{\left[P\right]}_{\%}},$$

(12)

where $x\left(P{O}_4^{3-}\right)$ is the content of $P{O}_4^{3-}$ in the slag, $w{\left[P\right]}_{\%}$ is the mass fraction of [P] in the molten steel.

Equations (11) and (12) could be combined, the expression of equilibrium distribution coefficient $L_p$ between slag and molten steel is deduced and shown in Equation (13)

$$L_p=K^{\frac{1}{2}}·\frac{x{\left(F{e}^{2+}\right)}^{2.5}x{\left(O^{2-}\right)}^4{\gamma }_{F{e}^{2+}}^{2.5}{\gamma }_{O^{2-}}^4{f}_p}{{\gamma }_{P{O}_4^{3-}}} ,$$

(13)

where $x\left(P{O}_4^{3-}\right)$ is the mass fraction of $P{O}_4^{3-}$, $w{\left[P\right]}_{\%}$ is the mole fraction of [P], $K_{\theta }$ is equilibrium constant of Equation (8), ${\gamma }_{F{e}^{2+}}$ is the activity coefficient of $F{e}^{2+}$, $x\left(F{e}^{2+}\right)$ is the mole fraction of $F{e}^{2+}$, $f_P$ is the activity coefficient of [P], ${\gamma }_{O^{2-}}$ is the activity coefficient of $O^{2-}$, $x\left(O^{2-}\right)$ is the mole fraction of $O^{2-}$, and ${\gamma }_{P{O}_4^{3-}}$ is the activity coefficient of $P{O}_4^{3-}$.

The larger $L_p$ indicates the low level of P content in molten steel. Equation (13) indicates that the partition ratio is closely related to the temperature of liquid steel, activity of $FeO$ in slag, basicity of slag, and slag amount in molten steel. The improvement of temperature is adverse for dephosphorization as the process is an exothermic reaction [32,33,34]. The content of $FeO$ in slag provides a necessary environment for dephosphorization, the increase of $FeO$ in slag is beneficial to dephosphorization. However, Notman [46] considers that there is an optimum $FeO$ content (approximately 14–16%) for dephosphorization process, higher content of $FeO$ would cause a decline in the dephosphorization ratio instead. The basicity of slag is expressed as follows,

$$R=\frac{\%CaO}{\%Si{O}_2} ,$$

(14)

where R is slag basicity, (%$CaO$) is the mass percent of $CaO$ in slag, and (%$Si{O}_2$) stands for the mass percent of $Si{O}_2$ in slag.

With the increase of R, the content of $CaO$ goes up accordingly. The high level of $CaO$ is conducive to the dephosphorization. The amount of slag is related to the capacity of P in the slag, and a large capacity of P is beneficial to dephosphorization.

Reactions of oxygen in each stage are different. The oxygen blown reacts with elements with strong reducibility like $S\mathrm{i}$ at the initial stage. The reaction of decarburization becomes the major in the middle stage. Moreover, the reaction occurs mainly on the surface of molten steel after the decarburization. The variation of oxygen supply in different stages is due to the missions of oxygen in different smelting. The oxygen blown affects the temperature of molten steel, and the content of $FeO$. The variation is bonded to the removal of P. The stirring caused by oxygen jet impinging in the molten pool is of great importance for the dynamic conditions of dephosphorization [2]. The action of stirring plays a role in strengthening the oxygen supply from gas to liquid iron and mass transfer in solid lime.

Lime and other slag are determined by the content of Si and $\mathrm{P}$ in hot metal, scrap, pig iron, and the basicity of slag. In actual production, the quantity and time of the addition of lime directly affect the speed of slagging. High basicity of slag formation in time is the necessary condition in which to strengthen the dephosphorization. However, a large amount of lime added inevitably led to the falling temperature in the molten pool. Decline of temperature leads to the forming of slag uneasily and mass transfer in solid lime obstructively. Rate of mass transfer decreased is harmful to dephosphorization. Therefore, lime is generally added in batches in the single slag operation. The previous lime added contributes to improving the $FeO$ content of primary slag. Others are good for reducing the smelting point and viscosity of slag. Under normal circumstances, lime is added in two batches. The first batch of lime is added together with the oxygen blowing at the same time. The second batch of lime is added at the beginning of the carbon flame while P content is at a low level at that time. The purpose of the second batch of lime is to adjust slag basicity, improve liquidity, and remove other elements in molten steel.

5. Conclusions

In this paper, the influence of process data on the prediction of end-point P content in EAF steelmaking is studied. The ANN combined with the selected factors is used to establish the prediction model of end-point P content. The model established is trained and used to predict P content. Result of the prediction is carried out. The precision of the model is 28.89%, 48.33%, 65.56%, 77.22%, and 88.89% when the predictive errors are within $\pm 0.001$ (wt%), $\pm 0.002$ (wt%), $\pm 0.003$ (wt%), $\pm 0.004$ (wt%), and $\pm 0.005$ (wt%), respectively.

To further improve the accuracy of the model, process data is in view. Oxygen supply in stages and time of the first addition of lime are selected. The model precision is improved by refining the input data, and the factors of the improvement are analyzed through mechanism. After the optimization with oxygen, consumption is divided into stages. The precision of the model is 30.56%, 48.89%, 68.33%, 81.11%, and 92.22% when the predictive errors are within $\pm 0.001$ (wt%), $\pm 0.002$ (wt%), $\pm 0.003$ (wt%), $\pm 0.004$ (wt%), and $\pm 0.005$ (wt%), respectively. Furthermore, the accuracy of the model improved after time of the first addition of lime was added. The precision of the model is 33.89%, 50.00%, 75.56%, 87.78%, and 95.56% when the predictive errors are within $\pm 0.001$ (wt%), $\pm 0.002$ (wt%), $\pm 0.003$ (wt%), $\pm 0.004$ (wt%), and $\pm 0.005$ (wt%), respectively.

The precision of the model is improved gradually after the optimization. The promotion when the error is within $\pm 0.005$ (wt%) is inconspicuous because of its already high accuracy. The promotion of the model when the errors are within $\pm 0.001$ (wt%), $\pm 0.002$ (wt%) are also indistinctive due to the complex situations arising in EAF steelmaking. The evident promotions of the model happen when the errors are within $\pm 0.003$ (wt%), and $\pm 0.004$ (wt%), as the increases are 10.56% and 10%. The promotion is attributed to the factors increased, which makes the related characteristic more complete. The accuracy of the model when the errors are within $\pm 0.004$ (wt%) and below is satisfied for the actual production for its particular function in operation instruction.

In further work, a study of model optimization would focus on the aspects of algorithm optimization and selecting of puissant influencing factors, so as to improve the accuracy and reduce the fluctuation of the model.