Ladle Furnace Temperature Prediction Model Based on Large-scale Data With Random Forest

Xiaojun Wang

doi:10.1109/JAS.2016.7510247

Volume 4 Issue 4

Oct. 2017

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 15.3, Top 1 (SCI Q1)

CiteScore: 23.5, Top 2% (Q1)
Google Scholar h5-index: 77， TOP 5

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Article Contents

Abstract

Ⅰ. INTRODUCTION

Ⅱ. THERMAL MODEL OF LADLE FURNACE

Ⅲ. THE RANDOM FOREST METHOD

Ⅳ. EXPERIMENTS

Ⅴ. CONCLUSION

References

Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2017 > 4(4): 770-774

Xiaojun Wang, "Ladle Furnace Temperature Prediction Model Based on Large-scale Data With Random Forest," IEEE/CAA J. Autom. Sinica, vol. 4, no. 4, pp. 770-774, Oct. 2017. doi: 10.1109/JAS.2016.7510247

Citation:

Xiaojun Wang, "Ladle Furnace Temperature Prediction Model Based on Large-scale Data With Random Forest," IEEE/CAA J. Autom. Sinica, vol. 4, no. 4, pp. 770-774, Oct. 2017. doi: 10.1109/JAS.2016.7510247

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Ladle Furnace Temperature Prediction Model Based on Large-scale Data With Random Forest

doi: 10.1109/JAS.2016.7510247

Xiaojun Wang

Key Laboratory of Advanced Design and Intelligent Computing, Ministry of Education, Dalian University, Dalian 116622, China

Funds:

the National Natural Science Foundation of China 61702070

More Information

Abstract

Abstract

In ladle furnace, the prediction of the liquid steel temperature is always a hot topic for the researchers. The most of the existing temperature prediction models use small sample set. Today, the precision of them can not satisfy practical production. Fortunately, the large sample set is accumulated from the practical production process. However, a large sample set makes it difficult to build a liquid steel temperature model. To deal with the issue, the random forest method is preferred in this paper, which is a powerful regression method with low complexity and can be designed very quickly. It is with the parallel ensemble structure, uses sample subsets, and employs a simple learning algorithm of sub-models. Then, the random forest method is applied to establish a temperature model by using the data sampled from the production process. The experiments show that the random forest temperature model is more precise than other temperature models.
- Ladle furnace,
- random forest,
- regression tree,
- temperature prediction

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Ⅰ. INTRODUCTION

THE main purpose of ladle furnace treatment is to ensure that the liquid steel has the required temperature when the ladle is taken over at downstream secondary metallurgy units or at a continuous caster. Practically, the liquid steel temperature can not be measured continuously, making it difficult to realize precisely controlling. Therefore, a liquid steel temperature prediction model in ladle furnace is always a hot topic for the researchers [1]-[4].

Some mechanism models of the liquid steel temperature in ladle furnace are proposed in earlier works [5]. However, since the parameters are hard to obtain, mechanism models can not be used efficiently for online precise prediction. Additionally, the operating environment of ladle metallurgy is harsh, especially the high temperatures and corrosive slag associated with the process. Indeed, some of the parameters are estimated by experience. Thus, it is hard to ensure the precision of mechanism models.

To improve the precision of mechanism models, intelligent methods have been used for predicting the temperature of the liquid steel in ladle furnace. Sun et al. [6] use neural network to estimate the liquid steel temperature in ladle furnace. Ensemble models are able to further improve the precision of a single predictor [7]. In recent years, ensemble modeling methods have been used to establish the liquid steel temperature models.

In [1], Tian and Mao propose a new hybrid artificial intelligent technique called the ensemble extreme learning machines to develop a liquid steel temperature model, and demonstrate that their ensemble method can improve the precision. In [3], Lv et al. propose another ensemble temperature model in which a pruning Bagging method based on the negative correlation learning approach is applied to predict the unknown parameters, and simultaneously, to predict the undefined function of the liquid steel temperature model.

Now, the precision of the most existing temperature models can not meet the requirement of the industrial production. These models are built on small sample sets. Fortunately, the large sample set for building the liquid steel temperature model are accumulated from the practical production process. The large sample set contains more effective information, and provide possibilities to boost the precision of the temperature prediction.

However, the large sample set makes it difficult to these ensemble modeling methods. In [1], the extreme learning machine [8] is selected as the learning algorithm of sub-models and the modified AdaBoost.RT is employed as the ensemble structure. The learning speed of a extreme learning machine is extremely fast, but the modified AdaBoost.RT is a serial ensemble model where a new sub-model relies on former built sub-models. In [3], the pruning process of sub-models is one after another, and Bagging is changed from a parallel ensemble model into a serial ensemble model. Generally, a serial ensemble model is more complex than a single predictor [9].

In this paper, the random forest [10] method is preferred to build the liquid steel temperature prediction model on a large sample set. In the random forest method, Bagging [11] is used in tandem with random feature selection. The random forest is a powerful regression method with low complexity and can be designed very quickly. It is with the parallel ensemble structure, uses sample subsets, and employs a simple learning algorithm of sub-models, i.e., the regression tree [12]. The random forest is expected to fully utilize the large sample set accumulated from ladle furnace system, improve the precision, and meet the requirements of the root mean square errors (RMSE) and the maximum error of the temperature prediction.

The remainder of this paper is organized as follows. In Section Ⅱ, the thermal model of ladle furnace is given to provide a priori knowledge for the random forest temperature model. In Section Ⅲ, the random forest method is presented. In Section Ⅳ, the experimental investigations are brought out, and the random forest temperature model is compared with other ensemble temperature models. In Section Ⅴ, the conclusion of this paper is summarized.

Ⅱ. THERMAL MODEL OF LADLE FURNACE

The thermal model of ladle furnace can be divided into the following parts: the heat gain due to arcing, the heat effects of additions, the heat loss of the refractory wall, and the top surface [4], [5].

"The heat ladle furnace gained is from arcing. The submerged arc operation ensures the heat gain of liquid steel. The following expression is employed to describe the change in temperature due to arcing.

$\begin{equation} \Delta T_{\rm arc}=\eta E \end{equation}$

(1)

where $\eta$ is the thermal efficiency coefficient of arcing. $E$ is the total refining power consumption.

Temperature drop due to heat loss during the heating of refractory can be seen as a one-dimensional transient heat transfer equation for the side wall and bottom wall. It is calculated with the following assumptions and expression.

Initial condition: $t=0$ , $T_{\rm Wall}=T_{\rm Preht}$ .

Boundary condition: $t=t$ , $T_{\rm Wall}=T_{\rm LiqSt}$ .

$\begin{equation} \rho C_P \frac{ d T_{\rm Wall}}{ d t}=\hbar(T_{\rm Wall}-T_{\infty}) \end{equation}$

(2)

where $T_{\rm Preht}$ is the temperature of preheated refractory. $T_{\rm LiqSt}$ is temperature of liquid steel. $T_{\infty}$ is the temperature of the plant environment. $\rho$ is the density of steel (kg/m $^3$ ). $C_P$ is the specific heat of steel (JK $^{-1}$ kg). $\hbar$ is the heat transfer coefficient (J/m $^2$ s). Then $\Delta T_{\rm Wall}$ owing to the refractory heat loss can be calculated.

The temperature change of liquid steel owing to additions is shown as the following expression:

$\begin{equation} \Delta T_{\rm add}=\sum\limits_iW_iQ_i \end{equation}$

(3)

where $i$ designates a specific addition (metal alloy or slag). $W_i$ is the weight of addition $i$ (kg). $Q_i$ is the temperature effect parameter of $i$ (℃/kg).

The heat loss from the top surface is mainly due to the radiation loss of liquid slag surface and furnace cover. Moreover, the radiation loss of liquid slag surface is owing to the temperature of liquid slag, quantification of slag and surface area. It is difficult to obtain the quantification of liquid slag exactly. And the temperature of liquid steel (replacing the slag temperature in mechanism model) is changing continually during the ladle furnace metallurgy process. Therefore, it is hard to calculate the heat loss from the top surface exactly using the traditional mechanism model. The heat loss is obtained by calculating the energy change of the cooling water in this paper.

$\begin{equation} \Delta T_{\rm Surf}=\frac{f_{\rm Surf}C_wQ_w\Delta T_w}{C_PW} \end{equation}$

(4)

where $f_{\rm Surf}$ is the heat loss coefficient of slag surface and furnace cover. $C_w$ is specific heat of cooling water (JK $^{-1}$ kg). $Q_w$ is the flux of cooling water (L/s). $\Delta T_w$ is the temperature change of cooling water. $W$ is the weight of liquid steel.

The complete thermal model for the prediction of temperature in ladle furnace can be described as the total effect of the above factors" [4]:

$\begin{equation} \Delta T=\Delta T_{\rm arc}+\Delta T_{\rm Wall}+\Delta T_{\rm add}+\Delta T_{\rm Surf}. \end{equation}$

(5)

Ⅲ. THE RANDOM FOREST METHOD

A combination of many simple but different predictors can reduce the complexity and achieve better performance which can not be achieved by an individual model [10], [13]. Employing the regression tree as the learning algorithm of sub-models, the random forest is a modified version of Bagging [10]. In the random forest, Bagging [11] is used in tandem with random feature selection. A tree is grown on the new training set using the random selection of features at each node to determine the split. The random forest is always better than Bagging. Because of the law of large numbers the fandom forest do not over fit [10].

The random forest can reduce the complexity in three aspects:

1) It is with the parallel ensemble structure. A parallel ensemble is with the parallel computing procedure and the construction of a sub-model on each sample subset proceeds with no communication necessary from the other CPU's [13].

2) Sub-models are built on sample subsets in which the sizes of training samples are decreased dramatically. The generating procedure of the bootstrap replications, i.e., sample subsets, is straightforward, simple and quick, which keeps the complexity low.

3) Considering its simplicity, the regression tree is employed as the learning algorithm of sub-models.

Thus, we focus on building a random forest temperature prediction model.

To further improve the precision of the temperature prediction, in stead of the simple average, the generalized ensemble method is adopted, which is defined using the terminology of Perrone and Cooper [14]. The detailed calculation process is also showed in [15].

"Consider the ensemble model that consists of $P$ sub-models takes the form:

$\begin{align} f_E(X)=\sum\limits_{i=1}^{P}\beta_i f_i(X) =g(X)+\sum\limits_{i=1}^{P}\beta_i\varepsilon_i(X) \end{align}$

(6)

where $\beta_i$ is the weight of the $i$ th sub-model, with $\sum_{i=1}^{P}\beta_i=1$ ; $g(X)$ is the true function to be estimated; $\varepsilon_i(X)=f_i(X)-g(X)$ is the error of the $i$ th sub-model; and $f_i(X)$ is the sub-model.

One considers the covariance matrix $\Gamma$ which is with size $P \times P$ and the entries are as follows:

$\begin{equation} \Gamma_{ij}=E [\varepsilon_i(X)\varepsilon_j(X)] \end{equation}$

(7)

where in practice one works with a finite-sample approximation

$\begin{equation} \Gamma_{ij}=\frac{1}{N}\sum\limits_{k=1}^N[f_i(X_k)-Y_k][f_j(X_k)-Y_k] \end{equation}$

(8)

and $N$ is the number of the training samples. The ensemble error equals:

$\begin{align} \nonumber J_E=&\ E [\{f_E(X)-g(X)\}^2]\\ \nonumber =&\ E \left[\left(\sum\limits_{i=1}^{P}\beta_i\varepsilon_i\right) \left(\sum\limits_{j=1}^{P}\beta_j\varepsilon_j\right)\right]\\ \nonumber \approx &\ \sum\limits_{i=1}^P\sum\limits_{j=1}^P\beta_i\beta_j\Gamma_{ij}\\ =&\ \beta^{T}\Gamma\beta. \end{align}$

(9)

An optimal choice of $\beta$ follows then from:

$\begin{align} &\min\limits_{\beta}\frac{1}{2}\beta^{T}\Gamma\beta\\ & {\rm s.t.\quad} \sum\limits_{i=1}^P\beta_i=1. \end{align}$

(10)

Then, with Lagrange multiplier $\lambda$ ,

$\begin{equation} \ell(\beta, \lambda)=\frac{1}{2}\beta^{T}\Gamma\beta -\lambda\left(\left(\sum\limits_{i=1}^P\beta_i\right)-1\right) \end{equation}$

(12)

one obtains the conditions for optimality:

$\begin{align} \begin{cases} \displaystyle \frac{\partial\ell}{\partial\beta}=\Gamma\beta-\lambda 1_v=0\\[4mm] \displaystyle \frac{\partial\ell}{\partial\lambda}=1_v^{T}\beta-1 \end{cases} \end{align}$

(13)

with optimal solution

$\begin{equation} \beta=\frac{\Gamma^{-1}1_v}{1_v^{T}\Gamma 1_v} \end{equation}$

(14)

with $1_v=[1, \ldots, 1]^{T}$ " [15].

Ⅳ. EXPERIMENTS

A The Preparations of the Experiment

The 1714 samples of production are used. The number of the main factors that affect the temperature is 10. They are the weight of the liquid steel, the number of the ladle, the ladle states, the temperature of the empty ladle, the refining time, the initial temperature, the refining power consumption, the volume of argon purging, the time interval of temperature testing, and the heat effects of additions.

95 % of the data are randomly selected to train the model, and the others are testing data. The data are normalized in the range [0, 1]. Any model is constructed from training set using 10-fold cross-validation.

To demonstrate the potential and necessity of the random forests for the temperature prediction in ladle furnace on large sample set, the following temperature models are compared with the random forest temperature model: the modified AdaBoost.RT based ensemble extreme learning machines proposed by Tian et al. in [1] and the pruned Bagging based on the negative correlation learning proposed by Lv et al. in [3].

For each of the three temperature models, the modeling process is repeated 20 times and the statistical results of obtained performances is presented. The RMSE and the maximum error are employed as the index to quantify the precision, i.e., the accuracy on training set and the generalization on testing set, of the temperature prediction.

All programs are compiled by MATLAB and run on the computer with Pentium (R) Dual-Core CPU, 2.00 GB EMS memory, Microsoft Windows XP professional system.

B The Temperature Model Based on the Random Forest

When the temperature is estimated with the random forest, we find it useful to set the re-sampling rate as 63 %. Breiman [10] demonstrates that the random forest is insensitive to the number of features selected to split each node. Usually, selecting 1 or 2 features gives near optimum results. Thus, 2 features are selected in this experiment. Methods to prune back the trees are not considered. The minimum leaf-node size is set as for all regression trees.

In the modified AdaBoost.RT temperature model, the structure, the parameters of the extreme learning machine, and the training error are the same as [1]. In the pruned Bagging temperature model, 80 % samples are selected from the training set to generate each sample subset. The number of nodes in the hidden layer is 20. Fig. 1 shows the performance of the random forest, the modified AdaBoost.RT and the pruned Bagging temperature models with different numbers of sub-models.

Figure 1. The performance of the random forest, the pruned Bagging and the modified AdaBoost.RT temperature models with different numbers of submodels.

DownLoad: Full-Size Img PowerPoint

shows that the performance of the random forest is sensitive to the number of sub-models. On both the training and the testing sets, as number of sub-models increases, the RMSE and the max error of the random forest temperature model reduce. The performance of the random forest with more than 450 sub-models can meet the requirements of the RMSE (less than $3$ ℃) and the maximum error (less than $10$ ℃) of the temperature prediction. Thus, the random forest with 450 sub-models is used for the temperature prediction.

Fig. 1 also shows that on both the training and the testing sets, as the number of sub-models increases, the RMSE and the max error of the modified AdaBoost.RT and the pruned Bagging temperature models reduce. With less than 500 sub-models, the modified AdaBoost.RT temperature model can not meet the requirements of the RMSE and the maximum error. With more than 400 sub-models, the pruned Bagging temperature model can meet the requirement of the RMSE on both the training and the testing sets, and meet the requirement of the maximum error on the training set. However, with less than 500 sub-models, the pruned Bagging temperature model cannot meet the requirement of maximum error on the testing set. The detailed results of the temperature models based on the random forest, the modified AdaBoost.RT and the pruned Bagging (with 450 sub-models) are presented in Table Ⅰ. On both the training and the testing sets, the RMSE and the maximum error of the temperature estimated with the random forest are less than those of the temperature estimated with the pruned Bagging and the modified AdaBoost.RT. The curve of the temperature estimated with the random forest (450 sub-models) is showed in Fig. 2. Here, the real temperature means the true temperature in practical production process. Based on the random forest, the curve of the real temperature is fitted effectively by the predictive curve.

Table Ⅰ. THE DETAILED RESULTS OF THE TEMPERATURE MODELS BASED ON THE RANDOM FOREST, THE MODIFIED ADABOOST.RT AND THE PRUNED BAGGING (℃)

Temperature model	Training		Testing
Temperature model	RMSE	Maximum error	RMSE	Maximum error
Random forest	2.3	8.9	2.8	7.6
Modified AdaBoost.RT	3.4	15.1	3.7	11.2
Pruned Bagging	4.2	17.9	4.3	13.7

| Show Table

DownLoad: CSV

Figure 2. The curve of the temperature estimated with the random forest on the testing set.

DownLoad: Full-Size Img PowerPoint

To summarize, with the large sample set accumulated from the production process in ladle furnace, only the temperature model estimated with the random forest meets the requirements of the temperature prediction on both the training and the testing sets:

1) The RMSE of the temperature prediction is lower than $2.8$ ℃.

2) The maximum error of the temperature prediction is lower than $8.9$ ℃.

The precision, i.e., the accuracy and the generalization, of the random forest based liquid steel temperature model can satisfy industrial production in ladle furnace.

Ⅴ. CONCLUSION

The main contribution of this paper is to significantly improve the precision of the liquid steel temperature prediction in ladle furnace by the random forest method on the large sample set accumulated from the production process.

The experiments demonstrate that the random forest outperforms the pruned Bagging and the modified AdaBoost.RT in the precision of the temperature prediction.

On the training set, the RMSE of the random forest temperature model is $2.3$ ℃ which is less than the pruned Bagging's $3.4$ ℃ and the modified AdaBoost.RT's $4.2$ ℃; the maximum error of the random forest temperature model is $8.9$ ℃ which is less than the pruned Bagging's $15.1$ ℃ and the modified AdaBoost.RT's $17.9$ ℃.

On the testing set, the RMSE of the random forest temperature model is $2.8$ ℃ which is less than the pruned Bagging's $3.7$ ℃ and the modified AdaBoost.RT's $4.3$ ℃; the maximum error of the random forest temperature model is $7.6$ ℃ which is less than the pruned Bagging's $11.2$ ℃ and the modified AdaBoost.RT's $13.7$ ℃.

Only the random forest temperature model meet the requirements of the RMSE (less than $3$ ℃) and the maximum error (less than $10$ ℃) and satisfy industrial production in ladle furnace.

References(15)

References

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