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Soft-measuring models of thermal state in iron ore sintering process
Accepted Manuscript Soft-measuring models of thermal state in iron ore sintering process Xiaoxian Huang, Xiaohui Fan, Xuling Chen, Min Gan, Xinze Zhao PII: DOI: Reference:
S0263-2241(18)30734-6 https://doi.org/10.1016/j.measurement.2018.07.095 MEASUR 5779
To appear in:
Measurement
Received Date: Revised Date: Accepted Date:
4 April 2018 19 June 2018 31 July 2018
Please cite this article as: X. Huang, X. Fan, X. Chen, M. Gan, X. Zhao, Soft-measuring models of thermal state in iron ore sintering process, Measurement (2018), doi: https://doi.org/10.1016/j.measurement.2018.07.095
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Soft-measuring models of thermal state in iron ore sintering process Xiaoxian Huang, Xiaohui Fan, Xuling Chen, Min Gan, Xinze Zhao School of Minerals Processing and Bioengineering, Central South University, Changsha 410083, Hunan, China
Abstract: Thermal state of iron ore sintering in iron and steel production cannot be revealed straightforward, which is unfavorable for field operations. In this paper, the soft-measuring models were established to extract the feature points through curve fitting method and evaluate the whole state via random forest algorithm. All the models proposed were validated by the industrial data, and the results show that feature extraction model can identify the variation of reaction zones, and evaluation model possesses a classification accuracy over 95%. The soft-measuring models were integrated into the automatic control system developed for sintering plant. Running results illustrate that the system can enhance the stable control and reduce the power consumption of sintering process. Keywords: Iron ore sintering; Thermal state; Soft-measuring model; Evaluation model
1 Introduction In iron and steel production enterprises, sintering is the most widely used agglomeration method for preparing blast furnace materials. In sintering process, the temperature variation is the main driving force of physical and chemical reaction. Reasonable thermal state is beneficial to improve the sinter quality [1,2]. Therefore, the detection and control of thermal state is the key step for realizing the optimization control of sintering process. Sintering is a high-temperature reaction process, and it belongs to a semi-closed system. To obtain the thermal parameters inside sintering bed, numerical simulation [3-5] and soft-measuring technique are commonly used. But due to the incomplete detection of boundary conditions and long solving time, numerical simulation is not suitable for online application in operation field. Soft-measuring method has lower requirement for the integrity of original data, and its deployment is relatively simple, so it has been widely applied. For the characterization of sintering thermal state, burn through point (BTP) is a most frequently used parameter, which indicates the completion position of sintering reaction. To estimate BTP, the exhaust gas temperature method is widely adopted [6-8], and the negative pressure method and exhaust gas composition method are also reported [9,10]. However, due to the air leakage from shrinkage cracks in sintering bed, the stability and accuracy of BTP are relatively lower. Moreover, the process control based on BTP has the drawback of large time delay. To avoid the above adverse effect, Keihin Iron and Steel Plant proposed the concept of Burn Rising Point (BRP) in early 1990s [11]. It refers to a certain position on the fitting curve of
Corresponding author E-mail address: [email protected] (X.H. Fan)
wind-boxes temperature. Besides, there are some researches that the thermal state was recognized by the cross-section image of sintering bed and the side panel temperature of sinter pallet [12~14]. In the above-mentioned researches, the thermal state of sintering is characterized by single feature point, and the calculation of feature point ignores the moving state of sintering bed. In addition to the above modelling method based on sintering mechanism, artificial neural network (ANN) is a familiar approach for soft-measuring and predicting of thermal sate parameters. Because of the strong nonlinear mapping ability of ANN, it is usually used to establish the relational model between observed data and state parameters [15-17]. In order to overcome the shortcomings of single ANN model, researchers have tried to improve it via the fusion of different algorithms [18-21] and the optimization of evolutionary algorithms [22,23]. Although the accuracy of prediction model is gradually improved with the continuous development of intelligent algorithms, its adaptability still poor because of the feature extraction of process state is being unrecognized. In the present work, the thermal state is proposed to be jointly characterized by Temperature Rising Point (TRP), BRP and BTP according to the reaction rule of sintering bed, and the feature extraction model was established based on time series method. The thermal state parameter (TS) is put forward to describe the stability of sintering state, and the evaluation model based on random forest algorithm was built. The novel soft-measuring models realizes the transparency of sintering bed and they have great significance for improving the optimal control of sintering.
2 Process description The typical sintering process is portrayed in Fig.1, the raw materials are filled into the moving pallet after mixing and granulating, and the solid fuels in mixture bed start to burn when the pallet passing through the ignition hood. The negative pressure is formed inside the windboxes caused by the main exhauster, which leading larger amount of gas pass by the materials bed. The convection heat transfer between gas and materials make the solid fuel continues to burn, and the sinter finally formed after the melting and condensing of mixed materials.
Fig.1 Schematic diagram of sintering process The reaction zones in sintering pallet and the curve of exhaust gas temperature in wind-boxes are depicted in Fig. 2, in which the horizontal axis x indicates the length of sintering pallet, the vertical axis y indicates the height of materials bed, and T indicates the exhaust gas temperature.
Fig.2 Relationship between TRP, BRP, BTP and the reaction zone of the sintering process As shown in Fig.2(a), the original mixture zone is at the bottom of materials bed, and there are no physical and chemical changes. The humid mixture zone, also known as the moisture condensed zone, is formed by the condensation of water vapor that meets the cold materials in lower layer. Drying and preheating zone mainly occurs water evaporation, crystallized water decomposition, carbonate decomposition and solid-phase reaction. The temperature of combustion zone is up to 1000~1500℃, and mainly occurs the softening, melting and liquid phase formatting of mixture in this zone. In the sinter zone, the molten materials (liquid phase) condenses, the mineral is crystallized and the sinter is formed. As illustrated in Fig.2(b), the heat generated by upper materials layer is absorbed by humid materials zone at the beginning of sintering, which make the exhaust gas temperature remains stable. When the humid materials zone disappears and the drying and preheating zone reaches the bed bottom, the exhaust gas temperature begins to rise and the slope of temperature curve increase slowly. The inflection point of temperature curve is temperature rising point (TRP). When the drying and preheating zone disappears and the combustion zone reaches the bed bottom, exhaust gas temperature begins to increase drastically. This inflection point of temperature curve is burn rising point (BRP). After the exhaust gas temperature reaches the maximum value, the combustion zone disappears and the gas temperature begins to decrease. The highest point of temperature curve is burn through point (BTP). Therefore, TRP, BRP and BTP are jointly used to describe the thermal state of sintering in this paper, and the feature point extraction models are established separately. Reasonable thermal state means that the reaction zone in sintering bed, especially the drying
and preheating zone and the combustion zone, have appropriate thickness and downward moving speed. Therefore, the leading or lagging state of a single feature point can not reflect the fluctuation of thermal state completely. In this research, the evaluation model is established to classify the thermal state (TS) into normal and fluctuating, which using TRP, BRP, BTP and the corresponding exhaust gas temperature as inputs.
3 Modeling 3.1 Feature extraction According to the definition of TRP, BRP and BTP, their variation trend should be in sequence. It means that the state of TRP, BRP and BTP should be leaded ahead or lagged behind in turn with certain operation parameters. Therefore, the dynamic characteristics that materials bed moving with sintering pallet should be considered, and the corresponding exhaust gas temperature is selected based on time series method. Fig. 3 shows the dynamic characteristics of materials bed, in which D represents the center distance between wind-boxes, and
represents the time
interval that the materials bed moving from one wind-box to other.
Fig.3 Diagram of the materials bed moving with sintering pallet When assembling the data series of exhaust gas temperature, the detection data of adjacent wind-boxes at corresponding time interval are selected, which base on the certain wind-box located in the setting value of characteristic points. The data series is shown in Eq. (1), where N refers to the wind-box number.
Ti TN j t j , , TN 1 t , TN t , i trp, brp, btp; j 2,3, 4
（1）
Apply secondary curve fitting to the data series combined with wind-box distance, the resulting curve equation is expressed in Eq. (2).
fi x ai x 2 bi x ci , i trp, brp, btp
（2）
The solution of each characteristic point shows in Eq. (3) ~ Eq. (5) respectively, where Strp refers to the tangent slope of fitting curve, Tbrp refers to the setting temperature of BRP.
xtrp
Strp btrp 2 atrp
（3）
xbrp
2 bbrp bbrp 4 abrp Tbrp c
2 abrp bbtp
xbtp
（4）
（5）
2 abtp
In some case, the burning through state cannot be described exactly via initial value of BTP. As shown in Fig.4, the calculation results of initial BTP of No.1 curve and No.2 are the same, but the curve shape of No.2 is gentler, and its maximum temperature is lower. In this study, the initial value of BTP is proposed to be modified by the deviation of actual BTP temperature and ideal BTP temperature, and the curvature radius of fitting curve vertex, as expressed in Eq. (6).
xbtp xbtp
* Tbtp Tbtp
（6）
* Tbtp refers to ideal BTP temperature, ℃;
Where, Tbtp refers to actual BTP temperature, ℃;
is standard deviation of BTP temperature, ℃ ; =1 2abtp is curvature radius of fitting curve vertex.
Fig.4 Diagram of the burn through point in difference states 3.2 Evaluation The evaluation model of sintering thermal state is a typical supervised classification model. The traditional classification algorithms include logistic regression, naïve Bayes algorithm, decision tree classifier, artificial neural network and so on [24]. Random forest (RF) is a comprehensive classification system composed of multiple random decision trees. It has achieved good application results in many fields, because its good generality and insensitivity to outlier and noise data [25,26]. The establishing process of RF-based evaluation model is described as follow. Assume that the original data sample is
x
i1
, xi 2 , xi 6 , TSi , i 1, 2, , N , where N
represents the number of samples, the six-dimensional data set xi1, xi2, …, xi6 indicate TRP, BRP, BTP and its corresponding exhaust gas temperature. TS refers to the thermal state of sintering process, TS y1 , y2 represent the label of normal state and fluctuating state respectively. Fig.
5 shows the sketch map of random forest algorithm, in which n refers to the number of decision trees in random forest.
Fig.5 Sketch map of random forest algorithm There are three main steps of the construction process of random forest: random sampling, decision tree constructing and random forest assembling. (1) Random sampling. The Bagging sampling technique is used to generate n cluster of training subsets from original training data. Each subset is selected randomly and returned to the original dataset in every step, so that the samples are partly duplicated which can avoid the local optimal solution of training decision tree. (2) Decision tree constructing. The decision trees are established through training of each subset, and every tree can grow without any pruning. There are two key procedures for constructing the decision tree: nodes splitting and random characteristic variables selecting. Nodes splitting usually select the attribute with best classification ability from whole attribute set. In this study, the node splitting rule used in this research is minimum Gini coefficient, and the generation process of decision tree is based on the classification and regression tree algorithm (CART). Gini coefficient is calculated by Eq. (7). m
Gini S 1 Pi 2
(7)
i 1
Where, Pi represents the probability that category Cj appears in sample set S. If sample set S is divided into two subsets S1 and S2, the Gini coefficient of this division is:
Ginisplit S
S1 S Gini S1 2 Gini S 2 S S
(8)
The CART algorithm calculates the Gini coefficient of each variable based on Eq. (8), and a variable with minimum Gini coefficient is selected to split. The recursive method is used to construct the decision tree, which leads to the classification principle. The random characteristic variable refers to several attributes that randomly selected to participate in the Gini coefficient comparison during nodes splitting. In this study, the input
variables are randomly selected and grouped, the number of variables in each group is F = log2M + 1, where M represent the number of input variables. A tree is produced by CART algorithm for each variable group and allowed to grow fully without pruning. (3) Random forest assembling. The random forest is formed by assembling the decision trees. When the random forest classifier is used to discriminate or classify new input data, the classification results of all decision trees are aggregated, and which has maximum occurrences number is taken as final output.
4 Results and discussion The soft-measuring model of thermal process established is applied in a sintering field of Chinese iron and steel plant. The setting value of TRP, BRP and BTP of the sintering machine was 28m, 33m and 39m respectively, according to the data analysis of exhaust gas temperature in stable sintering state. The soft-measuring can be divided into three steps: Firstly, the production data are pre-processed by limiting filter and sliding time average method. Secondly, the temperature data list is established respectively based on the setting value of each feature point, and the current value of each feature point is obtained by feature extracting. Finally, the sintering state is evaluated according to the extracted feature points and its corresponding wind-box temperature. 4.1 Validation of feature extraction model During actual sintering process, there is time lag between the feature points since the certain mixture bed is moving along with sintering pallet. It means that when the sintering state is stable, the TRP value of partial mixture bed is leading ahead of setting position, the BRP value will lead after a certain time later, and vice versa. The results of feature extraction model in a stable production period are shown in Fig.6. According to the setting values of each feature point, the distance between TRP and BRP, BRP and BTP is 5m and 6m respectively. While the moving speed of sintering pallet is 1.2m·min-1, the time interval can be set to 4min and 5min.
Fig.6 Relationship between characteristic points of thermal state (a) TRP and BRP; (b) BRP and BTP As illustrated in Fig.6(a), there is a good linear relationship between TRP value and the BRP
value after 4min, namely, the position that drying and preheating zone and combustion zone reach the bottom of sintering pallet has a good consistency. As shown in Fig.6(b), although the data points are relatively scattered due to the air leakage of sintering machine, there is still a good linear relationship between BRP value and the BTP value after 5min. That is to say, the position of the combustion zone reaches pallet bottom correlate well with the position of combustion reaction finished. The variation trend between feature points accords with the internal reaction rules of sintering bed, the feature extraction model has a good recognition capacity for sintering thermal state. 4.2 Validation of evaluation model The data samples for modeling are collected from sintering field. The 400 groups of data samples are randomly selected as training set and 100 groups are used as testing set. The number of decision trees in random forest is set to 500. The evaluation results for the testing set are listed in Table 1. The evaluation model of thermal state has high classification ability, and the accuracy can reach 95%. Table 1 Results of the evaluation model for sintering state Items
Normal state
Fluctuating state
Total number in testing set
63
37
Number of correct classification
60
37
Classification accuracy (%)
95
100
Since the final output of random forest classifier is determined through voting, the performance of evaluation model can be analyzed according to the output distribution of decision trees in the random forest, as shown in Fig.7. The number of decision tree in random forest is 500, while the thermal state evaluation is a binary classification problem. Therefore, the data samples are distributed on the straight line of x + y = 500. When data samples appear on the ends of line, it means that one of output result plays a dominant role in random forest. When data samples occupy the intersection point of two lines, it illustrates that two kinds of output are close in random forest. In Fig.7, the test samples are mainly distributed at both ends of straight line x + y = 500, and most of them are correctly classified. Few samples are shown at the intersection, including two incorrect classified samples. The results show that the classification performance of evaluation model based on random forest algorithm is remarkable.
Fig.7 Performance analysis of evaluation model for sintering state 4.3 Application of soft-measuring models Based on the soft-measuring models established above, an automatic control system for iron ore sintering production was developed in Visual C# and applied in a domestic sintering plant. The major function of this system is to realize the visualization of thermal state and stabilize the production automatically via intelligent control models. The intelligent control models are based on the combination of expert system and fuzzy logic control, and its control strategy are the expert controller is activated while the sintering state is fluctuating and the fuzzy controller is activated while process state is steady. The Graphical User Interface (GUI) of this system is shown in Fig.8.
Fig.8 GUI of automatic control system Since this system was put into closed-loop running in a domestic sintering plant, BTP stability and sinter quality indices were improved, and the power consumption of per ton sinter was reduced by 2 kWh. Suppose an annual production of 2.5 million tons and power price of 0.7 RMB per kWh, the system directly reduces energy costs by 3,500,000 RMB per year for the sintering plant.
5 Conclusions Iron ore sintering is a complicated system that interior thermal state cannot be revealed straightforward. In accordance with the reaction rules of sintering process, the soft-measuring models coupled with feature extraction and comprehensive evaluation were established. Feature extraction model was established via piecewise fitting method and time series-based
method. Evaluation model of thermal state was established based on random forest algorithm. Validation by production data shows that the feature extraction model can identify the variations of reaction zones very well, and the classification accuracy of evaluation model is about 95%. Application results show that the automatic control system based on the novel soft-measuring models can enhance the stable control and reduce the power consumption of sintering. Work continues to further improve the generality of the proposed model, considering that some model parameters of feature extraction model and the data samples of state evaluation model were collected from sintering experts and field operators.
Acknowledgments This work was supported by the National Natural Science Foundation of China [Grant No. 51474237 and No. U1660206]
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Highlights [27]
Sintering thermal state was proposed to be jointly described by TRP, BRP and BTP Feature points was extracted via piecewise fitting and time series-based approach Evaluation model was established based on random forest algorithm Soft-measuring models can identify and classify the interior thermal state exactly Automatic control system can enhance stable control and reduce energy consumption
S0263-2241(18)30734-6 https://doi.org/10.1016/j.measurement.2018.07.095 MEASUR 5779
To appear in:
Measurement
Received Date: Revised Date: Accepted Date:
4 April 2018 19 June 2018 31 July 2018
Please cite this article as: X. Huang, X. Fan, X. Chen, M. Gan, X. Zhao, Soft-measuring models of thermal state in iron ore sintering process, Measurement (2018), doi: https://doi.org/10.1016/j.measurement.2018.07.095
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Soft-measuring models of thermal state in iron ore sintering process Xiaoxian Huang, Xiaohui Fan, Xuling Chen, Min Gan, Xinze Zhao School of Minerals Processing and Bioengineering, Central South University, Changsha 410083, Hunan, China
Abstract: Thermal state of iron ore sintering in iron and steel production cannot be revealed straightforward, which is unfavorable for field operations. In this paper, the soft-measuring models were established to extract the feature points through curve fitting method and evaluate the whole state via random forest algorithm. All the models proposed were validated by the industrial data, and the results show that feature extraction model can identify the variation of reaction zones, and evaluation model possesses a classification accuracy over 95%. The soft-measuring models were integrated into the automatic control system developed for sintering plant. Running results illustrate that the system can enhance the stable control and reduce the power consumption of sintering process. Keywords: Iron ore sintering; Thermal state; Soft-measuring model; Evaluation model
1 Introduction In iron and steel production enterprises, sintering is the most widely used agglomeration method for preparing blast furnace materials. In sintering process, the temperature variation is the main driving force of physical and chemical reaction. Reasonable thermal state is beneficial to improve the sinter quality [1,2]. Therefore, the detection and control of thermal state is the key step for realizing the optimization control of sintering process. Sintering is a high-temperature reaction process, and it belongs to a semi-closed system. To obtain the thermal parameters inside sintering bed, numerical simulation [3-5] and soft-measuring technique are commonly used. But due to the incomplete detection of boundary conditions and long solving time, numerical simulation is not suitable for online application in operation field. Soft-measuring method has lower requirement for the integrity of original data, and its deployment is relatively simple, so it has been widely applied. For the characterization of sintering thermal state, burn through point (BTP) is a most frequently used parameter, which indicates the completion position of sintering reaction. To estimate BTP, the exhaust gas temperature method is widely adopted [6-8], and the negative pressure method and exhaust gas composition method are also reported [9,10]. However, due to the air leakage from shrinkage cracks in sintering bed, the stability and accuracy of BTP are relatively lower. Moreover, the process control based on BTP has the drawback of large time delay. To avoid the above adverse effect, Keihin Iron and Steel Plant proposed the concept of Burn Rising Point (BRP) in early 1990s [11]. It refers to a certain position on the fitting curve of
Corresponding author E-mail address: [email protected] (X.H. Fan)
wind-boxes temperature. Besides, there are some researches that the thermal state was recognized by the cross-section image of sintering bed and the side panel temperature of sinter pallet [12~14]. In the above-mentioned researches, the thermal state of sintering is characterized by single feature point, and the calculation of feature point ignores the moving state of sintering bed. In addition to the above modelling method based on sintering mechanism, artificial neural network (ANN) is a familiar approach for soft-measuring and predicting of thermal sate parameters. Because of the strong nonlinear mapping ability of ANN, it is usually used to establish the relational model between observed data and state parameters [15-17]. In order to overcome the shortcomings of single ANN model, researchers have tried to improve it via the fusion of different algorithms [18-21] and the optimization of evolutionary algorithms [22,23]. Although the accuracy of prediction model is gradually improved with the continuous development of intelligent algorithms, its adaptability still poor because of the feature extraction of process state is being unrecognized. In the present work, the thermal state is proposed to be jointly characterized by Temperature Rising Point (TRP), BRP and BTP according to the reaction rule of sintering bed, and the feature extraction model was established based on time series method. The thermal state parameter (TS) is put forward to describe the stability of sintering state, and the evaluation model based on random forest algorithm was built. The novel soft-measuring models realizes the transparency of sintering bed and they have great significance for improving the optimal control of sintering.
2 Process description The typical sintering process is portrayed in Fig.1, the raw materials are filled into the moving pallet after mixing and granulating, and the solid fuels in mixture bed start to burn when the pallet passing through the ignition hood. The negative pressure is formed inside the windboxes caused by the main exhauster, which leading larger amount of gas pass by the materials bed. The convection heat transfer between gas and materials make the solid fuel continues to burn, and the sinter finally formed after the melting and condensing of mixed materials.
Fig.1 Schematic diagram of sintering process The reaction zones in sintering pallet and the curve of exhaust gas temperature in wind-boxes are depicted in Fig. 2, in which the horizontal axis x indicates the length of sintering pallet, the vertical axis y indicates the height of materials bed, and T indicates the exhaust gas temperature.
Fig.2 Relationship between TRP, BRP, BTP and the reaction zone of the sintering process As shown in Fig.2(a), the original mixture zone is at the bottom of materials bed, and there are no physical and chemical changes. The humid mixture zone, also known as the moisture condensed zone, is formed by the condensation of water vapor that meets the cold materials in lower layer. Drying and preheating zone mainly occurs water evaporation, crystallized water decomposition, carbonate decomposition and solid-phase reaction. The temperature of combustion zone is up to 1000~1500℃, and mainly occurs the softening, melting and liquid phase formatting of mixture in this zone. In the sinter zone, the molten materials (liquid phase) condenses, the mineral is crystallized and the sinter is formed. As illustrated in Fig.2(b), the heat generated by upper materials layer is absorbed by humid materials zone at the beginning of sintering, which make the exhaust gas temperature remains stable. When the humid materials zone disappears and the drying and preheating zone reaches the bed bottom, the exhaust gas temperature begins to rise and the slope of temperature curve increase slowly. The inflection point of temperature curve is temperature rising point (TRP). When the drying and preheating zone disappears and the combustion zone reaches the bed bottom, exhaust gas temperature begins to increase drastically. This inflection point of temperature curve is burn rising point (BRP). After the exhaust gas temperature reaches the maximum value, the combustion zone disappears and the gas temperature begins to decrease. The highest point of temperature curve is burn through point (BTP). Therefore, TRP, BRP and BTP are jointly used to describe the thermal state of sintering in this paper, and the feature point extraction models are established separately. Reasonable thermal state means that the reaction zone in sintering bed, especially the drying
and preheating zone and the combustion zone, have appropriate thickness and downward moving speed. Therefore, the leading or lagging state of a single feature point can not reflect the fluctuation of thermal state completely. In this research, the evaluation model is established to classify the thermal state (TS) into normal and fluctuating, which using TRP, BRP, BTP and the corresponding exhaust gas temperature as inputs.
3 Modeling 3.1 Feature extraction According to the definition of TRP, BRP and BTP, their variation trend should be in sequence. It means that the state of TRP, BRP and BTP should be leaded ahead or lagged behind in turn with certain operation parameters. Therefore, the dynamic characteristics that materials bed moving with sintering pallet should be considered, and the corresponding exhaust gas temperature is selected based on time series method. Fig. 3 shows the dynamic characteristics of materials bed, in which D represents the center distance between wind-boxes, and
represents the time
interval that the materials bed moving from one wind-box to other.
Fig.3 Diagram of the materials bed moving with sintering pallet When assembling the data series of exhaust gas temperature, the detection data of adjacent wind-boxes at corresponding time interval are selected, which base on the certain wind-box located in the setting value of characteristic points. The data series is shown in Eq. (1), where N refers to the wind-box number.
Ti TN j t j , , TN 1 t , TN t , i trp, brp, btp; j 2,3, 4
（1）
Apply secondary curve fitting to the data series combined with wind-box distance, the resulting curve equation is expressed in Eq. (2).
fi x ai x 2 bi x ci , i trp, brp, btp
（2）
The solution of each characteristic point shows in Eq. (3) ~ Eq. (5) respectively, where Strp refers to the tangent slope of fitting curve, Tbrp refers to the setting temperature of BRP.
xtrp
Strp btrp 2 atrp
（3）
xbrp
2 bbrp bbrp 4 abrp Tbrp c
2 abrp bbtp
xbtp
（4）
（5）
2 abtp
In some case, the burning through state cannot be described exactly via initial value of BTP. As shown in Fig.4, the calculation results of initial BTP of No.1 curve and No.2 are the same, but the curve shape of No.2 is gentler, and its maximum temperature is lower. In this study, the initial value of BTP is proposed to be modified by the deviation of actual BTP temperature and ideal BTP temperature, and the curvature radius of fitting curve vertex, as expressed in Eq. (6).
xbtp xbtp
* Tbtp Tbtp
（6）
* Tbtp refers to ideal BTP temperature, ℃;
Where, Tbtp refers to actual BTP temperature, ℃;
is standard deviation of BTP temperature, ℃ ; =1 2abtp is curvature radius of fitting curve vertex.
Fig.4 Diagram of the burn through point in difference states 3.2 Evaluation The evaluation model of sintering thermal state is a typical supervised classification model. The traditional classification algorithms include logistic regression, naïve Bayes algorithm, decision tree classifier, artificial neural network and so on [24]. Random forest (RF) is a comprehensive classification system composed of multiple random decision trees. It has achieved good application results in many fields, because its good generality and insensitivity to outlier and noise data [25,26]. The establishing process of RF-based evaluation model is described as follow. Assume that the original data sample is
x
i1
, xi 2 , xi 6 , TSi , i 1, 2, , N , where N
represents the number of samples, the six-dimensional data set xi1, xi2, …, xi6 indicate TRP, BRP, BTP and its corresponding exhaust gas temperature. TS refers to the thermal state of sintering process, TS y1 , y2 represent the label of normal state and fluctuating state respectively. Fig.
5 shows the sketch map of random forest algorithm, in which n refers to the number of decision trees in random forest.
Fig.5 Sketch map of random forest algorithm There are three main steps of the construction process of random forest: random sampling, decision tree constructing and random forest assembling. (1) Random sampling. The Bagging sampling technique is used to generate n cluster of training subsets from original training data. Each subset is selected randomly and returned to the original dataset in every step, so that the samples are partly duplicated which can avoid the local optimal solution of training decision tree. (2) Decision tree constructing. The decision trees are established through training of each subset, and every tree can grow without any pruning. There are two key procedures for constructing the decision tree: nodes splitting and random characteristic variables selecting. Nodes splitting usually select the attribute with best classification ability from whole attribute set. In this study, the node splitting rule used in this research is minimum Gini coefficient, and the generation process of decision tree is based on the classification and regression tree algorithm (CART). Gini coefficient is calculated by Eq. (7). m
Gini S 1 Pi 2
(7)
i 1
Where, Pi represents the probability that category Cj appears in sample set S. If sample set S is divided into two subsets S1 and S2, the Gini coefficient of this division is:
Ginisplit S
S1 S Gini S1 2 Gini S 2 S S
(8)
The CART algorithm calculates the Gini coefficient of each variable based on Eq. (8), and a variable with minimum Gini coefficient is selected to split. The recursive method is used to construct the decision tree, which leads to the classification principle. The random characteristic variable refers to several attributes that randomly selected to participate in the Gini coefficient comparison during nodes splitting. In this study, the input
variables are randomly selected and grouped, the number of variables in each group is F = log2M + 1, where M represent the number of input variables. A tree is produced by CART algorithm for each variable group and allowed to grow fully without pruning. (3) Random forest assembling. The random forest is formed by assembling the decision trees. When the random forest classifier is used to discriminate or classify new input data, the classification results of all decision trees are aggregated, and which has maximum occurrences number is taken as final output.
4 Results and discussion The soft-measuring model of thermal process established is applied in a sintering field of Chinese iron and steel plant. The setting value of TRP, BRP and BTP of the sintering machine was 28m, 33m and 39m respectively, according to the data analysis of exhaust gas temperature in stable sintering state. The soft-measuring can be divided into three steps: Firstly, the production data are pre-processed by limiting filter and sliding time average method. Secondly, the temperature data list is established respectively based on the setting value of each feature point, and the current value of each feature point is obtained by feature extracting. Finally, the sintering state is evaluated according to the extracted feature points and its corresponding wind-box temperature. 4.1 Validation of feature extraction model During actual sintering process, there is time lag between the feature points since the certain mixture bed is moving along with sintering pallet. It means that when the sintering state is stable, the TRP value of partial mixture bed is leading ahead of setting position, the BRP value will lead after a certain time later, and vice versa. The results of feature extraction model in a stable production period are shown in Fig.6. According to the setting values of each feature point, the distance between TRP and BRP, BRP and BTP is 5m and 6m respectively. While the moving speed of sintering pallet is 1.2m·min-1, the time interval can be set to 4min and 5min.
Fig.6 Relationship between characteristic points of thermal state (a) TRP and BRP; (b) BRP and BTP As illustrated in Fig.6(a), there is a good linear relationship between TRP value and the BRP
value after 4min, namely, the position that drying and preheating zone and combustion zone reach the bottom of sintering pallet has a good consistency. As shown in Fig.6(b), although the data points are relatively scattered due to the air leakage of sintering machine, there is still a good linear relationship between BRP value and the BTP value after 5min. That is to say, the position of the combustion zone reaches pallet bottom correlate well with the position of combustion reaction finished. The variation trend between feature points accords with the internal reaction rules of sintering bed, the feature extraction model has a good recognition capacity for sintering thermal state. 4.2 Validation of evaluation model The data samples for modeling are collected from sintering field. The 400 groups of data samples are randomly selected as training set and 100 groups are used as testing set. The number of decision trees in random forest is set to 500. The evaluation results for the testing set are listed in Table 1. The evaluation model of thermal state has high classification ability, and the accuracy can reach 95%. Table 1 Results of the evaluation model for sintering state Items
Normal state
Fluctuating state
Total number in testing set
63
37
Number of correct classification
60
37
Classification accuracy (%)
95
100
Since the final output of random forest classifier is determined through voting, the performance of evaluation model can be analyzed according to the output distribution of decision trees in the random forest, as shown in Fig.7. The number of decision tree in random forest is 500, while the thermal state evaluation is a binary classification problem. Therefore, the data samples are distributed on the straight line of x + y = 500. When data samples appear on the ends of line, it means that one of output result plays a dominant role in random forest. When data samples occupy the intersection point of two lines, it illustrates that two kinds of output are close in random forest. In Fig.7, the test samples are mainly distributed at both ends of straight line x + y = 500, and most of them are correctly classified. Few samples are shown at the intersection, including two incorrect classified samples. The results show that the classification performance of evaluation model based on random forest algorithm is remarkable.
Fig.7 Performance analysis of evaluation model for sintering state 4.3 Application of soft-measuring models Based on the soft-measuring models established above, an automatic control system for iron ore sintering production was developed in Visual C# and applied in a domestic sintering plant. The major function of this system is to realize the visualization of thermal state and stabilize the production automatically via intelligent control models. The intelligent control models are based on the combination of expert system and fuzzy logic control, and its control strategy are the expert controller is activated while the sintering state is fluctuating and the fuzzy controller is activated while process state is steady. The Graphical User Interface (GUI) of this system is shown in Fig.8.
Fig.8 GUI of automatic control system Since this system was put into closed-loop running in a domestic sintering plant, BTP stability and sinter quality indices were improved, and the power consumption of per ton sinter was reduced by 2 kWh. Suppose an annual production of 2.5 million tons and power price of 0.7 RMB per kWh, the system directly reduces energy costs by 3,500,000 RMB per year for the sintering plant.
5 Conclusions Iron ore sintering is a complicated system that interior thermal state cannot be revealed straightforward. In accordance with the reaction rules of sintering process, the soft-measuring models coupled with feature extraction and comprehensive evaluation were established. Feature extraction model was established via piecewise fitting method and time series-based
method. Evaluation model of thermal state was established based on random forest algorithm. Validation by production data shows that the feature extraction model can identify the variations of reaction zones very well, and the classification accuracy of evaluation model is about 95%. Application results show that the automatic control system based on the novel soft-measuring models can enhance the stable control and reduce the power consumption of sintering. Work continues to further improve the generality of the proposed model, considering that some model parameters of feature extraction model and the data samples of state evaluation model were collected from sintering experts and field operators.
Acknowledgments This work was supported by the National Natural Science Foundation of China [Grant No. 51474237 and No. U1660206]
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Highlights [27]
Sintering thermal state was proposed to be jointly described by TRP, BRP and BTP Feature points was extracted via piecewise fitting and time series-based approach Evaluation model was established based on random forest algorithm Soft-measuring models can identify and classify the interior thermal state exactly Automatic control system can enhance stable control and reduce energy consumption