- Email: [email protected]
Application of the improved the ELM algorithm for prediction of blast furnace gas utilization rate
Proceedings, 5th IFAC Workshop on Mining, Mineral and Metal Proceedings, Processing 5th IFAC Workshop on Mining, Mineral and Metal Available online at www.sciencedirect.com Processing Shanghai, China, August 23-25, 2018 Proceedings, 5th IFAC Workshop on Mining, Mineral and Metal Proceedings, 5th IFAC Workshop on Mining, Mineral and Metal Shanghai, China, August 23-25, 2018 Processing Processing Shanghai, China, August 23-25, 2018 Shanghai, China, August 23-25, 2018
ScienceDirect
IFAC PapersOnLine 51-21 (2018) 59–64
Application of the improved the ELM algorithm for prediction of blast furnace Application of the improved the ELM algorithm for prediction of blast furnace gasELM utilization ratefor prediction of blast furnace Application algorithm gasELM utilization ratefor prediction of blast furnace Application of of the the improved improved the the algorithm 1,2gas utilization 1,2 rate , Sen utilization Zhang , Yixin Yin1,2, Xiaoli Su1,2 YuFei Ji1,2gas rate YuFei Ji , Sen Zhang1,2, Yixin Yin1,2, Xiaoli Su1,2
, Yixin Yin , Xiaoli Su YuFei Ji , Sen Zhang 1,2 1,2 1,2 , Sen Zhang , Yixin Yinand , Xiaoli Su1,2 YuFei Ji 1,2 1,2 1. School of Automation and Electrical Engineering, Science Technology Zhang ,ofYixin Yin1,2, Xiaoli Su1,2 Beijing, Beijing 100083, P. R. YuFei Ji , Sen University 1. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China 1. School of Automation and Electrical Engineering, University Science and Technology Beijing, Beijing 100083, P. R. China of [email protected], E-mail: [email protected], [email protected], [email protected], 1. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China E-mail: of [email protected], [email protected], [email protected], [email protected], 2. Key Laboratory Knowledge Automation for IndustrialChina Processes of Ministry of Education, School of Automation and E-mail: of [email protected], [email protected], [email protected], [email protected], 2. Key Laboratory Knowledge Automation for Industrial Processes of Ministry of Education, School of Automation and Electrical E-mail: of [email protected], [email protected], [email protected], [email protected], 2. Key Laboratory Knowledge Automation for Industrial Processes of Ministry of Education, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China 2. Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education, School of Automation and Engineering, University of Science and Electrical Technology Beijing, Beijing 100083, P. R. China Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China Abstract: Blast furnace gas utilization rate is one of the indicators for measuring the smooth operation of the blast furnace model gas utilization rate isfurnace one of the measuring smooth operation of the blast Abstract: furnace. TheBlast prediction of the blast gas indicators utilizationfor rate based onthethe extreme learning machine furnace. prediction of theThe blast gas indicators utilization rate based onthethe extreme learning machine Blast furnace gas utilization rateburden isfurnace one of the for measuring smooth operation of the blast Abstract: algorithmThe (ELM) is firstlymodel established. surface characteristics and the indexes of the blast furnace Blast furnace gas utilization rateburden isfurnace one of the for measuring smooth operation of the blast Abstract: furnace. prediction of theThe blast gas indicators utilization rate based onthe the extreme learning machine surface characteristics andisthe indexes of the blast furnace algorithmThe (ELM) isinput firstlymodel established. blast furnace gas utilization rate the output parameter. In most condition are the parameters, and the furnace. The prediction model of the blast furnace gas utilization rate based on the extreme learning machine algorithm (ELM) is firstly established. The burden surface characteristics and the indexes of the blast furnace blast furnace gas utilization rate is the output parameter. In most condition are the input parameters, and the for ELM to ensure satisfactory output. In this paper, the same cases, the(ELM) regular item is introduced surface characteristics andisthe of the blast In furnace algorithm firstlyfactor established. The burden blastELM furnace gasisutilization theindexes output parameter. most condition theisinput parameters, and the cases, the are regular item factor is introduced for to ensure satisfactory In component this paper, the same prediction model based on PCA-ELM algorithm which based onrate theisoutput. principal analysis blast furnace gas utilization rate the output parameter. In most condition are the input parameters, and the cases, the regular item factor is introduced for ELM to ensure satisfactory output. In this paper, the same prediction model based on PCA-ELM algorithm which is based on the principal component analysis method (PCA) and ELM is established secondly. Real production data of the blast furnace isthe used to cases, the regular item factor is introduced for ELM to ensure satisfactory output. In this paper, same prediction model onis PCA-ELM algorithm which isofbased on theofprincipal analysis method (PCA) andbased ELM established secondly. Real production data themodel blastcomponent furnace isthe used to verify the prediction model. By comparing with the results two models, the based on PCAprediction model based onis PCA-ELM algorithm which is based on theofprincipal component analysis method (PCA) and ELM established secondly. Real production data the blast furnace is used to verify the prediction model. By comparing with the results of two models, the model based on the PCAELM algorithm has better accuracy than that based on ELM. method and ELM is By established secondly. Real production data of the blast furnace is used to verifyalgorithm the(PCA) prediction model. comparing theon results ELM has better accuracy than thatwith based ELM.of two models, the model based on the PCAverify the prediction model. By comparing with theon results of two models, the Ltd. model on theleaning PCAKeywords: Blast furnace, Blast furnace burden surface, Blast furnace utilization rate ,rights Extreme © 2018, IFAC (International Federation of that Automatic Control) Hosting bygas Elsevier Allbased reserved. ELM algorithm has better accuracy than based ELM. Blast furnace gas utilization rate, Extreme leaning Keywords: Blasthas furnace, Blastanalysis, furnace burden surface, ELM algorithm better accuracy than Prediction that based on ELM. machine, Principal component Keywords: Blast furnace, Blastanalysis, furnace Prediction burden surface, Blast furnace gas utilization rate, Extreme leaning machine, Principal component Blast furnace gas utilization rate, Extreme leaning Keywords: Blast furnace, Blastanalysis, furnace Prediction burden surface, machine, Principal component machine, Principal component analysis, Prediction Panzhihua blast furnace production. Some concrete measures 1. INTRODUCTION Panzhihua blast furnace production. concrete measures such as using stable and suitableSome charge structure and 1. INTRODUCTION Panzhihua blast furnace production. Some concrete such as using stable and suitable charge structure and improving blast the quality ofproduction. coke. to improve the blastmeasures furnace recent years, with the national government’s great Panzhihua 1. In INTRODUCTION furnace Some concrete measures such as using stable and suitable charge structure improving the quality of coke. to improve the blast furnace 1. INTRODUCTION In recent years, with the national government’s great gas utilization rate were put forward. The above study on the emphasis on environmental protection and rising iron ore such as using stable and suitable charge structure and and thegas quality coke. tois improve the blast furnace In recent years, withisthe national government’s great gas utilization rate wereofput forward. The above study on the emphasis on environmental protection and rising iniron ore improving blast furnace utilization rate mainly used in the lower prices, the steel industry facing great challenges energy improving the rate quality ofput coke. to improve the blast furnace In recent years, with theprotection national and government’s great gas utilization were forward. The above study the emphasis environmental rising ore parameters blast furnaceofgas utilization rate is mainly used in the on lower prices, the on steel industry reduction is facing great challenges iniron energy blast furnace production. The relationship conservation , emission and green production(Pan gas utilization rateutilization were put forward. The above study on the emphasis on environmental protection and rising iniron ore blast furnace gas rate is mainly used in the lower prices, the steel industry is facing great challenges energy parameters of blast furnace production. The relationship conservation , emission reduction and consumption green production(Pan thesegas parameters is rate complicated and there are lower some Yu et al ,2011) Grasping the energy ofenergy blast between blast furnace utilization is mainly used in the prices, the steel industry is facing great challenges in parameters of parameters blast furnace production. The relationship conservation , emission reduction green production(Pan these is complicated there are Yu et al is,2011) Grasping the energy consumption of blast non-independence phenomena. If simplyand rely on the some blast furnaces the key to realizing theand production reduction of between parameters of parameters blast furnace production. The relationship conservation , emission reduction and green production(Pan between these is complicated and there are some Yu et al ,2011) Grasping the energy consumption of blast non-independence phenomena. If simply rely on the could blast furnaces is the key to realizing the production reduction of furnace foreman to make judgment and estimate, there blast furnaces. Among them, the blast furnace gas utilization between these parameters is complicated and there are some Yu et al is,2011) Grasping the energy consumption of blast non-independence phenomena. If simply rely on the blast furnaces the key to realizing the production reduction of furnace foreman to make judgment and estimate, there could blast furnaces. Among them, the blast furnace gas utilization great limited, That could causeIfdelays in rely adjustment, to rate reflects andtheutilization ofreduction main raw non-independence phenomena. simply onthere the led blast furnaces is thethe keyreduction to them, realizing production of be furnace foreman to make judgment and estimate, could blast furnaces. Among the blast furnace gas utilization be great limited, That could cause delays in adjustment, led to rate reflects the reduction and utilization of main raw waste, which is not conducive to the full automation of blast materials for blast furnace production and is an important furnace foreman to make judgment and estimate, there could blast reflects furnaces.the Among them, the blast furnace of gas main utilization be great limited, That could cause delays in adjustment, led to rate reduction and utilization raw waste, which is not conducive to the full automation of blast materials for blast furnace production and is an important (Du Nan cause et al ,2014) index for evaluating blast furnace production of (Anmain Jianqiraw et furnace be great production limited, That could delays adjustment, to rate reflects the reduction and utilization is not conducive to ,2014) the fullinautomation ofled blast materials blast furnace production and is (An an important furnacewhich production (Du Nan et al index for for evaluating blast furnace production Jianqi et waste, al ,2015). Increasing the blast furnace gas utilization rate has waste, which is not conducive to the full automation of blast materials for blast furnace production and is an important In this production paper, the parameters upper surface of the blast index for evaluating the blast furnace production (An emission Jianqi et furnace (Du Nan etofalthe ,2014) al ,2015). Increasing furnace gas utilization rate has great significance for blast energy conservation, furnace (Du Nanunder etofalthe ,2014) In this production paper, the parameters upper surface blast index for evaluating the blast furnace production (An Jianqi et furnace were used firstly, the premise of of thethe feature al ,2015). Increasing blast furnace gas utilization rate has great significance for blast energy conservation, emission reduction and energy the consumption reduction. In this paper, the parameters of the upper surface of the blast furnace were used firstly, under the premise of the feature al ,2015). Increasing furnace gas utilization rate has of the furnace's material great significance for energy reduction. conservation, emission extraction In this paper, theblast parameters ofmaterial the uppersurface, surfacethe of the blast reduction and energy consumption furnace were used firstly, under the premise of the feature great significance for energy conservation, emission extraction of the blast furnace's material surface, the material of the blast furnace which have strong correlation The common blast consumption furnace operating parameters, such as parameters reduction and energy reduction. furnace were used firstly, under the premise of the feature extraction ofofthe material surface, the material parameters theblast blastfurnace's furnace which have correlation reduction and energy consumption reduction. The temperature, common blast furnace operating parameters, the blast furnace utilization rate arestrong selected, and the blast blast pressure, and coal injectionsuch rate as is with extraction of the blast gas furnace's material surface, the material parameters of the blast furnace which have strong correlation The common blast furnace operating parameters, such as with the blast furnaceare gastaken utilization rateinput. are selected, and the blast temperature, blastand pressure, and coal the injection rate is furnace conditions as the The material used by Prof. Wu Min others to predict blast furnace parameters of the blast furnace which have strong correlation The temperature, common blast furnace operating parameters, such as with the blast furnace gastaken utilization rate are selected, and the blast blast pressure, coal injection rate is furnace conditions are as the input. The material usedutilization by Prof. Wu Min and others toand predict the blast furnace characteristics and furnace condition data were obtained gas rate. However these operating parameters have with the blast furnace gas utilization rate are selected, andfrom the blast temperature, blastand pressure, and coal the injection rate is furnace conditions are taken as the input. The material used by Prof. Wu Min others to predict blast furnace characteristics and furnace condition data were obtained froma gas utilization rate. However these operating parameters have blast conditions furnace monitoring a steelThe plantmaterial over aused certain degree of lag, as well as a large amount of the furnace are takensystem as theof input. by Prof. Wu Min and others to predict the blast furnace characteristics furnace condition data from gas utilization rate. of However operating parameters have the blast monitoring systemwas of used awere steel plant over ameasurement certain degree lag, asthese well as a large amount of period of furnace time.and The ELM algorithm toobtained establish thea and cumbersome measurement. The infrared characteristics and furnace condition data were obtained from gas utilization rate. of However these operating parameters have the blast furnace monitoring system of a steel plant over aimages certain degree lag, as well as a large amount of period of time. The ELM algorithm was used to establish thea measurement and cumbersome measurement. The infrared mathematical model for predicting thea blast furnace from the flow distribution of as blast gas reacts the blast furnace monitoring system of steel plant overgasa ameasurement certain degree of lag, as well a furnace largeThe amount of period of time. The ELM algorithm was used to establish the and cumbersome measurement. infrared mathematical model for predicting the blast furnace gas images from the flow distribution of blast furnace gas reacts rate The with material surface characteristics center gas distribution characteristics of the blastThe furnace (Shi utilization period of time. ELM algorithm was used to establish and the measurement andflow cumbersome measurement. infrared mathematical model for predicting the blast furnace gas images from the distribution of blast furnace gas reacts utilization rate with material surface characteristics and center gas distribution characteristics of the blast furnace (Shi condition parameters. According toblast the blast furnace Lin et alfrom ,2016).. The coal gas utilization prediction model is furnace mathematical model for predicting the furnace gas images the flow distribution of blast furnace gas reacts utilization rateconditions with material surface to characteristics and center distribution characteristics of the blast (Shi condition parameters. According the blast Lin ettogas alpredict ,2016).. The gas utilization prediction model is furnace field working are complicated, there is a furnace certain used the usecoal of blast furnace gas. Thefurnace analysis of utilization rate with material surface characteristics and center gas distribution characteristics of the blast furnace (Shi Lin et al ,2016).. The coal gas utilization prediction model is furnace condition parameters. According to the blast furnace working are complicated, thereisisimproved, a certain used to predictforthe ofutilization blast furnace The furnace analysisgas of field degree noiseconditions interference, ELM algorithm main reasons theuse low rate gas. of blast furnaceofcondition parameters.the According to the blast furnace Lin et al ,2016).. The coal gas utilization prediction model is working conditions arethe complicated, there a certain used to predictfor the ofutilization blast gas. The furnace analysis of field degree of noise interference, ELM algorithm improved, main reasons the,use low ofmeasured blast dimension reduction is applied toisis the ELM in Panzhihua Iron Steel from furnace the rate field datagas of field PCA working conditions arethe complicated, there isimproved, a certain used to predictfor the use ofutilization blast furnace gas. The furnace analysis of the degree of noise interference, ELM algorithm is main reasons the low rate of blast gas the PCA dimension reduction is applied to the ELM in Panzhihua Iron , Steel from the field measured data of algorithm, and the PCA-ELM prediction model of the blast Panzhihua Steel blast furnace, and the potential of Panzhihua degree of noise interference, the ELM algorithm is improved, main reasons for the, low utilization rate ofmeasured blast furnace gas the PCA dimension reduction is applied to the ELM in Panzhihua Iron Steel from the field data of algorithm, and the PCA-ELM prediction model of the blast Panzhihua Steel blast furnace, and the potential of Panzhihua furnace gas utilization rate is established. By compare the Iron & Steel to increase the blast furnace gas utilization rate the PCA dimension reduction is applied to the ELM in Panzhihua Iron , Steel from the field measured data of algorithm, and the PCA-ELM prediction model of the blast Panzhihua Steel blast furnace, and the potential of Panzhihua furnace gas utilization rate is established. By compare the Iron & Steel to increase the blast furnace gas utilization rate two models from different perspectives. The blast furnace gas (He Shaogang ,2017), and then proceeded from the actual algorithm, and the PCA-ELM prediction model of the blast Panzhihua Steel blast furnace, andfurnace the potential of Panzhihua furnace gas utilization rate is established. By compare Iron & Steel to increase the blast gas utilization rate two models from different perspectives. The blast furnace gas (He Shaogang ,2017), and then proceeded from the actual production with thegas characteristics of furnace gas utilization rate is established. By compare the the Iron Shaogang & Steelconditions, to ,2017), increasecombined the then blast proceeded furnace utilization rate (He and from the actual production conditions, combined with the characteristics of two models from different perspectives. The blast furnace gas two models from different perspectives. The blast furnace gas (He Shaogang ,2017), and then proceeded from the actual production conditions, combined with the characteristics of Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) production conditions, combined with the characteristics of 59 Copyright © 2018, 2018 IFAC Peer review under responsibility of International Federation of Automatic 59 Control. Copyright © 2018 IFAC 10.1016/j.ifacol.2018.09.393 Copyright © 2018 IFAC 59 Copyright © 2018 IFAC 59
IFAC MMM 2018 60 Shanghai, China, August 23-25, 2018
YuFei Ji et al. / IFAC PapersOnLine 51-21 (2018) 59–64
utilization rate prediction model based on PCA-ELM is obtained, and the prediction effects are good.
The over-limit learning machine model can be shown in Fig. 2. It can be seen from the figure that the model of over-limit learning machine includes an input layer, an implicit layer, and an output layer. The neurons in each layers are connected in a fully connected manner (Li Ailian et al ,2015).
. 2. SELECTION OF THE BLAST FURNACE GAS UTILIZATION RATE MODEL In the process of making blast furnace iron, the surface of blast furnace will change with the progresses of reaction process. The shapes of the material surface are the characteristics of the blast furnace material surface, and the material surface characteristics are closely related to the blast furnace production index. According to blast furnace material surface and characteristics analysis, the funnel radius R, the depth of the funnel area h1, the height of the material line to the platform h2, the width of the funnel area l1, and the platform width l2 are used as the input of the blast furnace gas utilization rate prediction model. Since the reduction reactions in the blast furnace are also affected by the furnace condition index at the time. The blast temperature, blast pressure, coal injection rate, oxygen enrichment rate, and permeability index at the same time are also used as the input of the gas utilization rate model. The output of the model is the blast furnace gas utilization rate. In order to reflect the improvement of the ELM algorithm, the result of ELM and the improved PCA-ELM are compared. Figure 1 shows the input and output of gas utilization prediction model of ELM algorithm
Fig. 2. Structure diagram of Overrun Learning Machine The single hidden-layer feed-forward neural network is expressed in Figure 2. the input layer of network contains n neurons corresponding to the input variables 𝑥𝑥𝑖𝑖 = [𝑥𝑥𝑖𝑖1 , 𝑥𝑥𝑖𝑖2 , … , 𝑥𝑥𝑖𝑖𝑖𝑖 ]𝑇𝑇 .The hidden layer contains L neurons. The output layer contains m neurons corresponding to the output variables 𝑦𝑦𝑖𝑖 = [𝑦𝑦𝑖𝑖1 , 𝑦𝑦𝑖𝑖2 , … , 𝑦𝑦𝑖𝑖𝑖𝑖 ]𝑇𝑇 。 The weight matrix between input layer and hidden layer can be expressed as Equation 2-1: 𝑤𝑤11 𝑤𝑤12 ⋯ 𝑤𝑤1𝑛𝑛 𝑤𝑤21 𝑤𝑤22 ⋯ 𝑤𝑤2𝑛𝑛 𝑤𝑤 = [ ⋮ ( 2-1 ) ⋮ ⋱ ⋮ ] 𝑤𝑤𝑙𝑙1 𝑤𝑤𝑙𝑙2 ⋯ 𝑤𝑤𝑙𝑙𝑙𝑙 𝑙𝑙×𝑛𝑛 The weight value between the hidden layer neuron i and the input layer neuron β is expressed in 𝑤𝑤𝑖𝑖𝑖𝑖 . The connection weight matrix β between the hidden layer and the output layer can be expressed as: 𝛽𝛽11 𝛽𝛽21 𝛽𝛽 = [ ⋮ 𝛽𝛽𝑙𝑙1
Fig. 1. Input and output of blast furnace gas utilization rate prediction model of ELM algorithm
𝛽𝛽12 𝛽𝛽22 ⋮ 𝛽𝛽𝑙𝑙2
⋯ 𝛽𝛽1𝑚𝑚 ⋯ 𝛽𝛽2𝑚𝑚 ] ⋱ ⋮ ⋯ 𝛽𝛽𝑙𝑙𝑙𝑙 𝑙𝑙×𝑚𝑚
( 2-2 )
The output weight value between the hidden layer neuron j and the output layer neuron k is expressed in 𝛽𝛽𝑗𝑗𝑗𝑗 .
The Extreme Learning Machine (ELM) is a simple and effective learning algorithm (Huang GB et al.,2004) based on a single hidden layer feed-forward neural network. The overlimit learning machine does not need complicated iterative optimization during the training of the model. It only needs to set the number of neuron nodes in the hidden layer, the weight matrix and hidden layer bias vectors are randomly generated between the input layer and the hidden layer. The output matrix of the hidden node is obtained, the connection weight matrix between hidden layer and output layer is obtained through one-step matrix calculation, and the unique global optimal solution is quickly calculated. Since its introduction, the over-limit learning machine model has been widely used in regression and classification problems due to its advantages such as fast operation speed, strong generalization ability, and not falling into local minimum values(Huang GB et al ,2006; Liang NY et al ,2006).
𝑏𝑏1 𝑏𝑏 𝑏𝑏 = [ 2 ] ⋮ 𝑏𝑏𝑙𝑙 𝑙𝑙×1
Hidden layer offset vector b can be expressed as：
( 2-3 )
Assume that the model input sample set contains Q groups sample ， Corresponding that sample input matrix X and sample output matrix Y . They can be expressed as 𝑥𝑥11 𝑥𝑥12 ⋯ 𝑥𝑥1𝑄𝑄 𝑥𝑥21 𝑥𝑥22 ⋯ 𝑥𝑥2𝑄𝑄 𝑋𝑋 = [ ⋮ ⋮ ⋱ ⋮] 𝑥𝑥𝑛𝑛1 𝑥𝑥𝑛𝑛2 ⋯ 𝑥𝑥𝑛𝑛𝑛𝑛 𝑛𝑛×𝑄𝑄 60
IFAC MMM 2018 Shanghai, China, August 23-25, 2018
𝑦𝑦11 𝑦𝑦12 𝑦𝑦21 𝑦𝑦22 𝑌𝑌 = [ ⋮ ⋮ 𝑦𝑦𝑚𝑚1 𝑦𝑦𝑚𝑚2
YuFei Ji et al. / IFAC PapersOnLine 51-21 (2018) 59–64
⋯ 𝑦𝑦1𝑄𝑄 ⋯ 𝑦𝑦2𝑄𝑄 ⋱ ⋮ ] ⋯ 𝑦𝑦𝑚𝑚𝑚𝑚 𝑚𝑚×𝑄𝑄
Extreme learning machine model will be better stable and generalization ability due to the introduction of regular parameters. The output weight of the model is:
( 2-4 )
𝐼𝐼 𝛽𝛽̂ = 𝐻𝐻𝑇𝑇 ( + 𝐻𝐻𝐻𝐻𝑇𝑇 )
Set the incentive function of the hidden layer to 𝑔𝑔(𝑥𝑥) ，The output of the network T through operations is
𝐶𝐶
𝑇𝑇
( 2-10 )
𝑓𝑓(𝑥𝑥) = 𝑔𝑔(𝑥𝑥)𝛽𝛽 = 𝑔𝑔(𝑥𝑥)𝐻𝐻𝑇𝑇 ( + 𝐻𝐻𝐻𝐻𝑇𝑇 ) 𝐼𝐼
∑𝐿𝐿𝑖𝑖=1 𝛽𝛽𝑖𝑖1 𝑔𝑔(𝑤𝑤𝑖𝑖 𝑥𝑥𝑗𝑗 ∑𝐿𝐿𝑖𝑖=1 𝛽𝛽𝑖𝑖2 𝑔𝑔(𝑤𝑤𝑖𝑖 𝑥𝑥𝑗𝑗
+ 𝑏𝑏𝑖𝑖 ) 𝑡𝑡1𝑗𝑗 𝑡𝑡2𝑗𝑗 + 𝑏𝑏𝑖𝑖 ) = 𝑡𝑡𝑗𝑗 = [ ] ( 2-5) ⋮ ⋮ 𝐿𝐿 𝑡𝑡𝑚𝑚𝑚𝑚 𝑚𝑚×1 [∑𝑖𝑖=1 𝛽𝛽𝑖𝑖𝑖𝑖 𝑔𝑔(𝑤𝑤𝑖𝑖 𝑥𝑥𝑗𝑗 + 𝑏𝑏𝑖𝑖 )] 𝑚𝑚×1
𝐶𝐶
−1
𝑇𝑇
( 2-11 )
Therefore, for a given training sample (𝑥𝑥𝑖𝑖 , 𝑡𝑡𝑖𝑖 ) ， 𝑥𝑥𝑖𝑖 = [𝑥𝑥𝑖𝑖1 , 𝑥𝑥𝑖𝑖2 , … , 𝑥𝑥𝑖𝑖𝑖𝑖 ]𝑇𝑇 ∈ 𝑅𝑅 ， 𝑦𝑦𝑖𝑖 = [𝑦𝑦𝑖𝑖1 , 𝑦𝑦𝑖𝑖2 , … , 𝑦𝑦𝑖𝑖𝑖𝑖 ]𝑇𝑇 ∈ 𝑅𝑅 ， activation function 𝑔𝑔(𝑥𝑥),𝐿𝐿 Hidden nodes, 𝐿𝐿 < 𝑁𝑁, the ELM algorithm can be summarized as:
That above formulas can be abbreviated as
（1）Randomly generate weight matrix of network w ,which between input layer and hidden layer, hidden layer offset vector b；
( 2-6 )
H is the output matrix of the hidden layer in the network： 𝑔𝑔(𝑤𝑤1 𝑥𝑥1 + 𝑏𝑏1 ) 𝑔𝑔(𝑤𝑤2 𝑥𝑥1 + 𝑏𝑏2 ) 𝑔𝑔(𝑤𝑤1 𝑥𝑥2 + 𝑏𝑏1 ) 𝑔𝑔(𝑤𝑤2 𝑥𝑥2 + 𝑏𝑏2 ) 𝐻𝐻 = ⋮ ⋮ [𝑔𝑔(𝑤𝑤1 𝑥𝑥𝑄𝑄 + 𝑏𝑏1 ) 𝑔𝑔(𝑤𝑤2 𝑥𝑥𝑄𝑄 + 𝑏𝑏2 )
−1
The expression of the model output can be directly represented as
𝑇𝑇 = [𝑡𝑡1 , 𝑡𝑡2 , ⋯ , 𝑡𝑡𝑄𝑄 ]𝑚𝑚×𝑄𝑄
𝐻𝐻𝐻𝐻 = 𝑇𝑇
61
⋯ 𝑔𝑔(𝑤𝑤𝐿𝐿 𝑥𝑥1 + 𝑏𝑏𝐿𝐿 ) ⋯ 𝑔𝑔(𝑤𝑤𝐿𝐿 𝑥𝑥2 + 𝑏𝑏𝐿𝐿 ) ⋯ ⋮ ⋯ 𝑔𝑔(𝑤𝑤𝐿𝐿 𝑥𝑥𝑄𝑄 + 𝑏𝑏𝐿𝐿 )] ( 2-7)
（2）Input training samples, establish the network model, calculate the network's hidden layer output matrix 𝐻𝐻； 𝐼𝐼 （3）Get output weight 𝛽𝛽̂ = 𝐻𝐻𝑇𝑇 ( + 𝐻𝐻𝐻𝐻𝑇𝑇 ) 𝐶𝐶
−1
𝑇𝑇。
It can be seen that, compared with the traditional neural network, the over-limit learning machine model does not need to set a large number of parameters in the model process. During the execution of the algorithm, the ELM model randomly generates the weight matrix w between input layer and hidden layer, the bias matrix b of hidden layer, according to the input training sample. It obtains the output weight of hidden layer through one matrix operation. The result is the only global optimal solution that does not require repeated iterations, which greatly improves the computational speed of ( 2-8) the network model. Therefore, compared with the traditional ‖𝐻𝐻𝛽𝛽̂ − 𝑇𝑇‖ = min𝛽𝛽‖𝐻𝐻𝛽𝛽 − 𝑇𝑇‖ BP neural network, the extreme learning machine ELM Among them 𝛽𝛽̂ = 𝐻𝐻 −1 𝑇𝑇 , The inverse matrix of 𝐻𝐻 is matrix greatly reduces the training time and improves the −1 𝐻𝐻 。 generalization performance of the model. It overcomes the The output of ELM algorithm can be directly represented as： disadvantages of BP neural network, which needs to set stopping conditions, the low learning efficiency and easy ( 2-9 ) getting into local minimums through the gradient descent 𝑓𝑓(𝑥𝑥) = 𝑔𝑔(𝑥𝑥)𝛽𝛽 = 𝑔𝑔(𝑥𝑥)𝐻𝐻 −1 𝑇𝑇 When the over-limit learning machine model is applied to method. However, it also found that in most cases, we must practical problems, the possible complex-coexistence add a regular term factor to ensure satisfactory output. problems of the sample data in various application situations PCA-ELM algorithm will cause the output matrix of the model to be unsatisfactory when the ELM model is used. When solve the least-squares Industrial sites are often in poor conditions and the data solution of facial function 𝐻𝐻𝛽𝛽 = 𝑇𝑇，the required generalized obtained is often disturbed by noise. The ELM model is inverse matrix 𝐻𝐻 −1 = 𝐻𝐻𝑇𝑇 (𝐻𝐻𝐻𝐻𝑇𝑇 )−1 due to the existence of expressed as: complex co-existence issues in the sample, leading to 𝐻𝐻𝐻𝐻𝑇𝑇 is 𝐻𝐻𝐻𝐻 + 𝜉𝜉 = 𝑇𝑇, 𝜉𝜉 𝜖𝜖𝜖𝜖(0, 𝜎𝜎 2 ) ( 2-12 ) not a non-singular matrix. That affects the effects of model prediction or classification. In order to solve the problem that When the model is proposed to internal disturbances, training the matrix dissatisfaction rank affects the prediction result with the ELM algorithm is often not satisfied. The solution to during the solution process(Huang et al ,2014; Uemukai the ELM algorithm is as follows: R ,2012)By introducing a regular parameter 𝐶𝐶，and adding 𝑇𝑇 ∑𝑁𝑁 𝑖𝑖=1 𝐻𝐻𝑖𝑖 (𝐻𝐻𝑖𝑖 𝛽𝛽𝑖𝑖 + 𝜉𝜉𝑖𝑖 ) its inverse to the main diagonal of diagonal matrix 𝐻𝐻𝐻𝐻𝑇𝑇 ， 𝛽𝛽̂ = (𝐻𝐻𝑇𝑇 𝐻𝐻)−1 𝐻𝐻𝑇𝑇 𝑇𝑇 = 𝑇𝑇 ∑𝑁𝑁 𝑖𝑖=1 𝐻𝐻𝑖𝑖 𝐻𝐻𝑖𝑖 making disparate singular matrices non-singular. Finding −1 𝑇𝑇 weight vectors 𝛽𝛽̂ by the formula 𝛽𝛽̂ = 𝐻𝐻 𝑇𝑇 ∑𝑁𝑁 𝑖𝑖=1 𝐻𝐻𝑖𝑖 𝜉𝜉𝑖𝑖 = 𝛽𝛽 + 𝑁𝑁 ∑𝑖𝑖=1 𝐻𝐻𝑖𝑖𝑇𝑇 𝐻𝐻𝑖𝑖 Different from traditional neural networks, they needs to adjust input weight and hidden layer bias value, because of the input function approximation theory. The input weights and the offset vector of the hidden nodes in over-limit learning machine are all randomly generated. Therefore, the model of over-limit learning machine is equivalent to find a solution, which called the facial function 𝐻𝐻𝛽𝛽 = 𝑇𝑇 leastsquares solution β：
61
IFAC MMM 2018 62 Shanghai, China, August 23-25, 2018
YuFei Ji et al. / IFAC PapersOnLine 51-21 (2018) 59–64
(2-13) The three aspects of expectation (𝐸𝐸), variance (𝑉𝑉) and mean squared error (𝑀𝑀𝑀𝑀𝑀𝑀) as follows： E(𝛽𝛽̂ ) = 𝛽𝛽
2 V(𝛽𝛽̂ ) = 𝐸𝐸(𝛽𝛽̂ 2 ) − 𝐸𝐸(𝛽𝛽̂ ) =
𝑀𝑀𝑀𝑀𝑀𝑀(𝛽𝛽̂ ) =
𝑝𝑝
𝜎𝜎 2 1 = 𝜎𝜎 2 ∑ ∑𝑃𝑃𝐼𝐼=1 𝐻𝐻𝑖𝑖𝑇𝑇 𝐻𝐻𝑖𝑖 𝜆𝜆𝑖𝑖 𝑖𝑖=1
1 1 𝜎𝜎 2 𝑇𝑇 𝐸𝐸 [(𝛽𝛽̂ − 𝛽𝛽) (𝛽𝛽̂ − 𝛽𝛽)] = . 𝑃𝑃 𝑝𝑝 𝑝𝑝 ∑𝐼𝐼=1 𝐻𝐻𝑖𝑖𝑇𝑇 𝐻𝐻𝑖𝑖 𝑝𝑝
𝜎𝜎 2 1 = ∑ 𝑝𝑝 𝜆𝜆𝑖𝑖 𝑖𝑖=1
(2-14)
The characteristic value of the matrix 𝐻𝐻𝐻𝐻𝑇𝑇 isλ。When the collinearity situation occurs in the matrix 𝐻𝐻， some of the eigenvalues of matrix 𝐻𝐻𝐻𝐻𝑇𝑇 are equal to zero or approach to zero. This will lead to the solution of ELM algorithm has a large variance and mean square error, and the model cannot achieve the desired effect. This study introduced PCA-ELM algorithm (Zhang HG et al ,2015). He applied the Principal Component Analysis (PCA) to the ELM algorithm. By performing principal component analysis on the hidden layer matrix 𝐻𝐻 ， the algorithm not only can get rid of the influence of collinearity but also can reduce the dimension of the matrix 𝐻𝐻，improve the training speed of the model, and reduce the training time。 Use PCA technology handles hidden layer matrix as follows： 𝐻𝐻′ = 𝐻𝐻𝐻𝐻
3. MODELING AND SIMULIATION Using a blast furnace monitoring system of a steel plant to collect data online for a period of time, Obtains 3000 sets of material characteristics and furnace condition data, and 2500 sets of data are used to establish the blast furnace gas utilization rate prediction model. 500 sets of data are used to test the model. The CO and CO2 content (both volume percentages) of the gas after automatic analysis of the gas mixture on the furnace top in actual measurement and the results obtained from the calculation formula of the blast furnace gas utilization rate are compared after data preprocessing. Using the ELM prediction model and the improved PCA-ELM prediction model for simulation verification, the sigmoid function is used as the activation function and 1000 hidden nodes are used in the ELM prediction model. In the PCA-ELM prediction model, the sigmoid function is still used as the activation function. The numbers of hidden nodes are 500, and the numbers of hidden nodes becomes 450 after dimension reduction. Figures 3 and 4 show the prediction results of the blast furnace gas utilization rate. The blue curves in the two figures represent the raw data of the blast furnace gas utilization rate, and the red curves with “o” represent the prediction results of the two algorithms. Table 1 shows four indicators of the train time, test time, train accuracy, and test accuracy of the two prediction algorithms. The blast furnace gas utilization rate prediction results for each model are shown in the figure below. The performance of each model is shown in the following table: 2 𝜂𝜂 = 𝐶𝐶𝐶𝐶+𝐶𝐶𝑂𝑂
𝐶𝐶𝑂𝑂
2
(2-18)
(2-15 )
𝐻𝐻′ is converted hidden layer matrix, 𝐺𝐺 is conversion matrix。 After dimension reduction for hidden layer matrix 𝐻𝐻 by PCA technology, the solution of PCA-ELM is as follows： 𝑇𝑇 𝑇𝑇 𝛽𝛽̂ = (𝐻𝐻′ 𝐻𝐻′ ) 𝐻𝐻′ 𝑇𝑇 −1
( 2-16 )
Again, from three aspects of PCA-ELM solutions for analysis: expectation, variance, and mean square error as follows. E(𝛽𝛽̂ ) = 𝛽𝛽
2 V(𝛽𝛽̂ ) = 𝐸𝐸(𝛽𝛽̂ 2 ) − 𝐸𝐸(𝛽𝛽̂ ) =
𝑀𝑀𝑀𝑀𝑀𝑀(𝛽𝛽̂ ) = =
𝑝𝑝
𝜎𝜎 2 1 𝑝𝑝𝜎𝜎 2 2 = 𝜎𝜎 ∑ ≤ ∑𝑃𝑃𝐼𝐼=1 𝐻𝐻𝑖𝑖𝑇𝑇 𝐻𝐻𝑖𝑖 𝜆𝜆𝑖𝑖 𝜆𝜆𝑚𝑚𝑚𝑚𝑚𝑚 𝑖𝑖=1
1 1 𝜎𝜎 2 𝑇𝑇 𝐸𝐸 [(𝛽𝛽̂ − 𝛽𝛽) (𝛽𝛽̂ − 𝛽𝛽)] = . 𝑃𝑃 𝑝𝑝 𝑝𝑝 ∑𝐼𝐼=1 𝐻𝐻𝑖𝑖𝑇𝑇 𝐻𝐻𝑖𝑖
𝜎𝜎 2 𝑝𝑝
∑𝑝𝑝𝑖𝑖=1
1
𝜆𝜆𝑖𝑖
≤
𝜎𝜎 2
𝜆𝜆𝑚𝑚𝑚𝑚𝑚𝑚
Fig. 3 Prediction results of the blast furnace gas utilization rate based on ELM
( 2-17 )
From the above formulas, it can get the conclusion that after the PCA treatment, the solution of ELM is improved in terms of variance and mean square error. It also can still maintain an unbiased estimate. 62
IFAC MMM 2018 Shanghai, China, August 23-25, 2018
YuFei Ji et al. / IFAC PapersOnLine 51-21 (2018) 59–64
63
algorithm can well solve the problem of collinearity existing in the ELM algorithm in dealing with fluctuating data. Make it more accurate in the event of significant fluctuations, the PCA-ELM algorithm has a better predictive effect when the furnace conditions change drastically and the industrial environment is complicated.Therefore, in the actual production process, not only need to according to the theoretical algorithm, but also should combined with the specific blast furnace conditions. So that to achieve a better overall grasp of the blast furnace, make blast furnace forward and achieve better economic benefits.
ACKNOWLEDGEMENT This work was supported by the Key Program of National Nature Science Foundation of China under grant No. 61333002, the National Nature Science Foundation of China under grants No. 61673056, the Beijing Natural Science Foundation under grant No. 4182039 and the Beijing Key Discipline Construction Project (XK100080537).
Fig. 4 Comparison results of the blast furnace gas utilization rate based on PCA-ELM Table 1 Prediction Index of The Blast Furnace Gas Utilization Rate Name
Hidden nodes Numbers
Train time
Test time
Train error
Test error
ELM
1000
1.0718
0.022
0.0032
0.0232
PCAELM
500→450
0.1094
0.042
0.0030
REFERENCES Pan Yu, Yu Haibin, Yuan Mingzhe. Blast furnace energy efficiency modeling and analysis [J]. Manufacturing Automation, 2011, (23): 142-144. An Jianqi, Chen Yifei, Wu Min. Prediction method of carbon monoxide utilization in blast furnace based on improved support vector machine [J]. Journal of Chemical Industry and Engineering, 2015, (01): 06-214.
0.0057
At the same time, it is noticed that both algorithms have large prediction errors within the range of 100-120 test sample points. This has a lot to do with the internal working conditions of the blast furnace and the operation of the foreman. Due to its complexity, the blast furnace reaction process depends to some extent on empirical operation. Traditional experience shows that at the stage of lower oxygen enrichment rate, the blast furnace gas utilization rate will increase with the increase of oxygen enrichment rate, but at the stage of higher oxygen enrichment rate, the blast furnace gas utilization rate will gradually decline with the continue increase of oxygen enrichment rate. According to the production records, with the progress of the reaction, in this phase, the oxygen enrichment rate continues to increase, so that the utilization rate of blast furnace gas decreases, and led to the prediction results of the two algorithms have relatively large errors.
LinSHI,You-binWEN,Guang-shengZHAO,etal. RecognitionofBlastFurnaceGasFlowCenterDistributionBased onInfraredImageProcessing[J]. Journal of Iron and Steel Research, 2016, 23(3):203-209. He Shaogang. Current status and analysis of utilization rate of blast furnace gas in Panzhihua Iron and Steel Corporation [J]. Sichuan Metallurgy, 2017(1):13-17. Du Nan. Research on Modeling Method for Prediction of Blast Furnace Condition and Distribution of Gas Flow[D]. Hunan: Central South University, 2014. Huang GB, Zhu QY, Siew C K. Extreme learning machine: a new learning scheme of feedforward neural networks[J]. Proc.int.jointConf.neuralNetw, 2004, 22004, 22004[2017-1008 16:38:00]. Huang GB, Zhu QY, Siew C K. Extreme learning machine: Theory and applications [J]. Neurocomputing, 2006, 70(1– 3)-2006, 70(1–3).2006[2017-10- 31 21:45:00].
4. CONCLUSIONS This paper based on a blast furnace monitoring system online acquisition for a period of time, burden surface characteristics and furnace condition indexes data. Two kinds of prediction algorithms, ELM and PCA-ELM, are used to predict the blast furnace gas utilization rate. By comparing the results of two prediction algorithms, it can be considered that applying PCA to ELM has a good effect in reducing the number of hidden nodes. As a result, the PCA-ELM
Liang NY, Huang GB, Saratchandran P, et al. A Fast and Accurate Online Sequential Learning Algorithm for Feedforward Networks [J].IEEE Transactions on Neural Networks, 2006, 17(6)-2006, 17(6).2006[2017-10-31 21:46:00].
63
IFAC MMM 2018 64 Shanghai, China, August 23-25, 2018
YuFei Ji et al. / IFAC PapersOnLine 51-21 (2018) 59–64
Li Ailian, Zhao Yongming, Cui Guimei. ELM blast furnace temperature prediction model based on grey correlation analysis[J]. Journal of Iron and Steel Research, 2015, 27(11)2015, 27(11).2015[2017-10-31 22 : 16:00]. Zhang HG, Zhang S, Yin Y X. A Novel Improved ELM Algorithm for a Real Industrial Application[J]. Mathematical Problems in Engineering, 2014, (2014-4-16), 2014, 2014(2)2014 , 2014(2).2014[2017-10-31 22:18:00]. Uemukai R. Erratum to: Small sample properties of a ridge regression estimator when there exist omitted variables[J]. Statistical Papers, 2012, 53(1)-2012, 53(1).2012[2017-10-31 22:19:00]. Zhang H, Yin Y, Zhang S, et al. An Improved ELM Algorithm Based on PCA Technique[M]. Springer International Publishing, 2015: 95-104[2017-10-31 22:22:00
64
ScienceDirect
IFAC PapersOnLine 51-21 (2018) 59–64
Application of the improved the ELM algorithm for prediction of blast furnace Application of the improved the ELM algorithm for prediction of blast furnace gasELM utilization ratefor prediction of blast furnace Application algorithm gasELM utilization ratefor prediction of blast furnace Application of of the the improved improved the the algorithm 1,2gas utilization 1,2 rate , Sen utilization Zhang , Yixin Yin1,2, Xiaoli Su1,2 YuFei Ji1,2gas rate YuFei Ji , Sen Zhang1,2, Yixin Yin1,2, Xiaoli Su1,2
, Yixin Yin , Xiaoli Su YuFei Ji , Sen Zhang 1,2 1,2 1,2 , Sen Zhang , Yixin Yinand , Xiaoli Su1,2 YuFei Ji 1,2 1,2 1. School of Automation and Electrical Engineering, Science Technology Zhang ,ofYixin Yin1,2, Xiaoli Su1,2 Beijing, Beijing 100083, P. R. YuFei Ji , Sen University 1. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China 1. School of Automation and Electrical Engineering, University Science and Technology Beijing, Beijing 100083, P. R. China of [email protected], E-mail: [email protected], [email protected], [email protected], 1. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China E-mail: of [email protected], [email protected], [email protected], [email protected], 2. Key Laboratory Knowledge Automation for IndustrialChina Processes of Ministry of Education, School of Automation and E-mail: of [email protected], [email protected], [email protected], [email protected], 2. Key Laboratory Knowledge Automation for Industrial Processes of Ministry of Education, School of Automation and Electrical E-mail: of [email protected], [email protected], [email protected], [email protected], 2. Key Laboratory Knowledge Automation for Industrial Processes of Ministry of Education, School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China 2. Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education, School of Automation and Engineering, University of Science and Electrical Technology Beijing, Beijing 100083, P. R. China Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China Abstract: Blast furnace gas utilization rate is one of the indicators for measuring the smooth operation of the blast furnace model gas utilization rate isfurnace one of the measuring smooth operation of the blast Abstract: furnace. TheBlast prediction of the blast gas indicators utilizationfor rate based onthethe extreme learning machine furnace. prediction of theThe blast gas indicators utilization rate based onthethe extreme learning machine Blast furnace gas utilization rateburden isfurnace one of the for measuring smooth operation of the blast Abstract: algorithmThe (ELM) is firstlymodel established. surface characteristics and the indexes of the blast furnace Blast furnace gas utilization rateburden isfurnace one of the for measuring smooth operation of the blast Abstract: furnace. prediction of theThe blast gas indicators utilization rate based onthe the extreme learning machine surface characteristics andisthe indexes of the blast furnace algorithmThe (ELM) isinput firstlymodel established. blast furnace gas utilization rate the output parameter. In most condition are the parameters, and the furnace. The prediction model of the blast furnace gas utilization rate based on the extreme learning machine algorithm (ELM) is firstly established. The burden surface characteristics and the indexes of the blast furnace blast furnace gas utilization rate is the output parameter. In most condition are the input parameters, and the for ELM to ensure satisfactory output. In this paper, the same cases, the(ELM) regular item is introduced surface characteristics andisthe of the blast In furnace algorithm firstlyfactor established. The burden blastELM furnace gasisutilization theindexes output parameter. most condition theisinput parameters, and the cases, the are regular item factor is introduced for to ensure satisfactory In component this paper, the same prediction model based on PCA-ELM algorithm which based onrate theisoutput. principal analysis blast furnace gas utilization rate the output parameter. In most condition are the input parameters, and the cases, the regular item factor is introduced for ELM to ensure satisfactory output. In this paper, the same prediction model based on PCA-ELM algorithm which is based on the principal component analysis method (PCA) and ELM is established secondly. Real production data of the blast furnace isthe used to cases, the regular item factor is introduced for ELM to ensure satisfactory output. In this paper, same prediction model onis PCA-ELM algorithm which isofbased on theofprincipal analysis method (PCA) andbased ELM established secondly. Real production data themodel blastcomponent furnace isthe used to verify the prediction model. By comparing with the results two models, the based on PCAprediction model based onis PCA-ELM algorithm which is based on theofprincipal component analysis method (PCA) and ELM established secondly. Real production data the blast furnace is used to verify the prediction model. By comparing with the results of two models, the model based on the PCAELM algorithm has better accuracy than that based on ELM. method and ELM is By established secondly. Real production data of the blast furnace is used to verifyalgorithm the(PCA) prediction model. comparing theon results ELM has better accuracy than thatwith based ELM.of two models, the model based on the PCAverify the prediction model. By comparing with theon results of two models, the Ltd. model on theleaning PCAKeywords: Blast furnace, Blast furnace burden surface, Blast furnace utilization rate ,rights Extreme © 2018, IFAC (International Federation of that Automatic Control) Hosting bygas Elsevier Allbased reserved. ELM algorithm has better accuracy than based ELM. Blast furnace gas utilization rate, Extreme leaning Keywords: Blasthas furnace, Blastanalysis, furnace burden surface, ELM algorithm better accuracy than Prediction that based on ELM. machine, Principal component Keywords: Blast furnace, Blastanalysis, furnace Prediction burden surface, Blast furnace gas utilization rate, Extreme leaning machine, Principal component Blast furnace gas utilization rate, Extreme leaning Keywords: Blast furnace, Blastanalysis, furnace Prediction burden surface, machine, Principal component machine, Principal component analysis, Prediction Panzhihua blast furnace production. Some concrete measures 1. INTRODUCTION Panzhihua blast furnace production. concrete measures such as using stable and suitableSome charge structure and 1. INTRODUCTION Panzhihua blast furnace production. Some concrete such as using stable and suitable charge structure and improving blast the quality ofproduction. coke. to improve the blastmeasures furnace recent years, with the national government’s great Panzhihua 1. In INTRODUCTION furnace Some concrete measures such as using stable and suitable charge structure improving the quality of coke. to improve the blast furnace 1. INTRODUCTION In recent years, with the national government’s great gas utilization rate were put forward. The above study on the emphasis on environmental protection and rising iron ore such as using stable and suitable charge structure and and thegas quality coke. tois improve the blast furnace In recent years, withisthe national government’s great gas utilization rate wereofput forward. The above study on the emphasis on environmental protection and rising iniron ore improving blast furnace utilization rate mainly used in the lower prices, the steel industry facing great challenges energy improving the rate quality ofput coke. to improve the blast furnace In recent years, with theprotection national and government’s great gas utilization were forward. The above study the emphasis environmental rising ore parameters blast furnaceofgas utilization rate is mainly used in the on lower prices, the on steel industry reduction is facing great challenges iniron energy blast furnace production. The relationship conservation , emission and green production(Pan gas utilization rateutilization were put forward. The above study on the emphasis on environmental protection and rising iniron ore blast furnace gas rate is mainly used in the lower prices, the steel industry is facing great challenges energy parameters of blast furnace production. The relationship conservation , emission reduction and consumption green production(Pan thesegas parameters is rate complicated and there are lower some Yu et al ,2011) Grasping the energy ofenergy blast between blast furnace utilization is mainly used in the prices, the steel industry is facing great challenges in parameters of parameters blast furnace production. The relationship conservation , emission reduction green production(Pan these is complicated there are Yu et al is,2011) Grasping the energy consumption of blast non-independence phenomena. If simplyand rely on the some blast furnaces the key to realizing theand production reduction of between parameters of parameters blast furnace production. The relationship conservation , emission reduction and green production(Pan between these is complicated and there are some Yu et al ,2011) Grasping the energy consumption of blast non-independence phenomena. If simply rely on the could blast furnaces is the key to realizing the production reduction of furnace foreman to make judgment and estimate, there blast furnaces. Among them, the blast furnace gas utilization between these parameters is complicated and there are some Yu et al is,2011) Grasping the energy consumption of blast non-independence phenomena. If simply rely on the blast furnaces the key to realizing the production reduction of furnace foreman to make judgment and estimate, there could blast furnaces. Among them, the blast furnace gas utilization great limited, That could causeIfdelays in rely adjustment, to rate reflects andtheutilization ofreduction main raw non-independence phenomena. simply onthere the led blast furnaces is thethe keyreduction to them, realizing production of be furnace foreman to make judgment and estimate, could blast furnaces. Among the blast furnace gas utilization be great limited, That could cause delays in adjustment, led to rate reflects the reduction and utilization of main raw waste, which is not conducive to the full automation of blast materials for blast furnace production and is an important furnace foreman to make judgment and estimate, there could blast reflects furnaces.the Among them, the blast furnace of gas main utilization be great limited, That could cause delays in adjustment, led to rate reduction and utilization raw waste, which is not conducive to the full automation of blast materials for blast furnace production and is an important (Du Nan cause et al ,2014) index for evaluating blast furnace production of (Anmain Jianqiraw et furnace be great production limited, That could delays adjustment, to rate reflects the reduction and utilization is not conducive to ,2014) the fullinautomation ofled blast materials blast furnace production and is (An an important furnacewhich production (Du Nan et al index for for evaluating blast furnace production Jianqi et waste, al ,2015). Increasing the blast furnace gas utilization rate has waste, which is not conducive to the full automation of blast materials for blast furnace production and is an important In this production paper, the parameters upper surface of the blast index for evaluating the blast furnace production (An emission Jianqi et furnace (Du Nan etofalthe ,2014) al ,2015). Increasing furnace gas utilization rate has great significance for blast energy conservation, furnace (Du Nanunder etofalthe ,2014) In this production paper, the parameters upper surface blast index for evaluating the blast furnace production (An Jianqi et furnace were used firstly, the premise of of thethe feature al ,2015). Increasing blast furnace gas utilization rate has great significance for blast energy conservation, emission reduction and energy the consumption reduction. In this paper, the parameters of the upper surface of the blast furnace were used firstly, under the premise of the feature al ,2015). Increasing furnace gas utilization rate has of the furnace's material great significance for energy reduction. conservation, emission extraction In this paper, theblast parameters ofmaterial the uppersurface, surfacethe of the blast reduction and energy consumption furnace were used firstly, under the premise of the feature great significance for energy conservation, emission extraction of the blast furnace's material surface, the material of the blast furnace which have strong correlation The common blast consumption furnace operating parameters, such as parameters reduction and energy reduction. furnace were used firstly, under the premise of the feature extraction ofofthe material surface, the material parameters theblast blastfurnace's furnace which have correlation reduction and energy consumption reduction. The temperature, common blast furnace operating parameters, the blast furnace utilization rate arestrong selected, and the blast blast pressure, and coal injectionsuch rate as is with extraction of the blast gas furnace's material surface, the material parameters of the blast furnace which have strong correlation The common blast furnace operating parameters, such as with the blast furnaceare gastaken utilization rateinput. are selected, and the blast temperature, blastand pressure, and coal the injection rate is furnace conditions as the The material used by Prof. Wu Min others to predict blast furnace parameters of the blast furnace which have strong correlation The temperature, common blast furnace operating parameters, such as with the blast furnace gastaken utilization rate are selected, and the blast blast pressure, coal injection rate is furnace conditions are as the input. The material usedutilization by Prof. Wu Min and others toand predict the blast furnace characteristics and furnace condition data were obtained gas rate. However these operating parameters have with the blast furnace gas utilization rate are selected, andfrom the blast temperature, blastand pressure, and coal the injection rate is furnace conditions are taken as the input. The material used by Prof. Wu Min others to predict blast furnace characteristics and furnace condition data were obtained froma gas utilization rate. However these operating parameters have blast conditions furnace monitoring a steelThe plantmaterial over aused certain degree of lag, as well as a large amount of the furnace are takensystem as theof input. by Prof. Wu Min and others to predict the blast furnace characteristics furnace condition data from gas utilization rate. of However operating parameters have the blast monitoring systemwas of used awere steel plant over ameasurement certain degree lag, asthese well as a large amount of period of furnace time.and The ELM algorithm toobtained establish thea and cumbersome measurement. The infrared characteristics and furnace condition data were obtained from gas utilization rate. of However these operating parameters have the blast furnace monitoring system of a steel plant over aimages certain degree lag, as well as a large amount of period of time. The ELM algorithm was used to establish thea measurement and cumbersome measurement. The infrared mathematical model for predicting thea blast furnace from the flow distribution of as blast gas reacts the blast furnace monitoring system of steel plant overgasa ameasurement certain degree of lag, as well a furnace largeThe amount of period of time. The ELM algorithm was used to establish the and cumbersome measurement. infrared mathematical model for predicting the blast furnace gas images from the flow distribution of blast furnace gas reacts rate The with material surface characteristics center gas distribution characteristics of the blastThe furnace (Shi utilization period of time. ELM algorithm was used to establish and the measurement andflow cumbersome measurement. infrared mathematical model for predicting the blast furnace gas images from the distribution of blast furnace gas reacts utilization rate with material surface characteristics and center gas distribution characteristics of the blast furnace (Shi condition parameters. According toblast the blast furnace Lin et alfrom ,2016).. The coal gas utilization prediction model is furnace mathematical model for predicting the furnace gas images the flow distribution of blast furnace gas reacts utilization rateconditions with material surface to characteristics and center distribution characteristics of the blast (Shi condition parameters. According the blast Lin ettogas alpredict ,2016).. The gas utilization prediction model is furnace field working are complicated, there is a furnace certain used the usecoal of blast furnace gas. Thefurnace analysis of utilization rate with material surface characteristics and center gas distribution characteristics of the blast furnace (Shi Lin et al ,2016).. The coal gas utilization prediction model is furnace condition parameters. According to the blast furnace working are complicated, thereisisimproved, a certain used to predictforthe ofutilization blast furnace The furnace analysisgas of field degree noiseconditions interference, ELM algorithm main reasons theuse low rate gas. of blast furnaceofcondition parameters.the According to the blast furnace Lin et al ,2016).. The coal gas utilization prediction model is working conditions arethe complicated, there a certain used to predictfor the ofutilization blast gas. The furnace analysis of field degree of noise interference, ELM algorithm improved, main reasons the,use low ofmeasured blast dimension reduction is applied toisis the ELM in Panzhihua Iron Steel from furnace the rate field datagas of field PCA working conditions arethe complicated, there isimproved, a certain used to predictfor the use ofutilization blast furnace gas. The furnace analysis of the degree of noise interference, ELM algorithm is main reasons the low rate of blast gas the PCA dimension reduction is applied to the ELM in Panzhihua Iron , Steel from the field measured data of algorithm, and the PCA-ELM prediction model of the blast Panzhihua Steel blast furnace, and the potential of Panzhihua degree of noise interference, the ELM algorithm is improved, main reasons for the, low utilization rate ofmeasured blast furnace gas the PCA dimension reduction is applied to the ELM in Panzhihua Iron Steel from the field data of algorithm, and the PCA-ELM prediction model of the blast Panzhihua Steel blast furnace, and the potential of Panzhihua furnace gas utilization rate is established. By compare the Iron & Steel to increase the blast furnace gas utilization rate the PCA dimension reduction is applied to the ELM in Panzhihua Iron , Steel from the field measured data of algorithm, and the PCA-ELM prediction model of the blast Panzhihua Steel blast furnace, and the potential of Panzhihua furnace gas utilization rate is established. By compare the Iron & Steel to increase the blast furnace gas utilization rate two models from different perspectives. The blast furnace gas (He Shaogang ,2017), and then proceeded from the actual algorithm, and the PCA-ELM prediction model of the blast Panzhihua Steel blast furnace, andfurnace the potential of Panzhihua furnace gas utilization rate is established. By compare Iron & Steel to increase the blast gas utilization rate two models from different perspectives. The blast furnace gas (He Shaogang ,2017), and then proceeded from the actual production with thegas characteristics of furnace gas utilization rate is established. By compare the the Iron Shaogang & Steelconditions, to ,2017), increasecombined the then blast proceeded furnace utilization rate (He and from the actual production conditions, combined with the characteristics of two models from different perspectives. The blast furnace gas two models from different perspectives. The blast furnace gas (He Shaogang ,2017), and then proceeded from the actual production conditions, combined with the characteristics of Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) production conditions, combined with the characteristics of 59 Copyright © 2018, 2018 IFAC Peer review under responsibility of International Federation of Automatic 59 Control. Copyright © 2018 IFAC 10.1016/j.ifacol.2018.09.393 Copyright © 2018 IFAC 59 Copyright © 2018 IFAC 59
IFAC MMM 2018 60 Shanghai, China, August 23-25, 2018
YuFei Ji et al. / IFAC PapersOnLine 51-21 (2018) 59–64
utilization rate prediction model based on PCA-ELM is obtained, and the prediction effects are good.
The over-limit learning machine model can be shown in Fig. 2. It can be seen from the figure that the model of over-limit learning machine includes an input layer, an implicit layer, and an output layer. The neurons in each layers are connected in a fully connected manner (Li Ailian et al ,2015).
. 2. SELECTION OF THE BLAST FURNACE GAS UTILIZATION RATE MODEL In the process of making blast furnace iron, the surface of blast furnace will change with the progresses of reaction process. The shapes of the material surface are the characteristics of the blast furnace material surface, and the material surface characteristics are closely related to the blast furnace production index. According to blast furnace material surface and characteristics analysis, the funnel radius R, the depth of the funnel area h1, the height of the material line to the platform h2, the width of the funnel area l1, and the platform width l2 are used as the input of the blast furnace gas utilization rate prediction model. Since the reduction reactions in the blast furnace are also affected by the furnace condition index at the time. The blast temperature, blast pressure, coal injection rate, oxygen enrichment rate, and permeability index at the same time are also used as the input of the gas utilization rate model. The output of the model is the blast furnace gas utilization rate. In order to reflect the improvement of the ELM algorithm, the result of ELM and the improved PCA-ELM are compared. Figure 1 shows the input and output of gas utilization prediction model of ELM algorithm
Fig. 2. Structure diagram of Overrun Learning Machine The single hidden-layer feed-forward neural network is expressed in Figure 2. the input layer of network contains n neurons corresponding to the input variables 𝑥𝑥𝑖𝑖 = [𝑥𝑥𝑖𝑖1 , 𝑥𝑥𝑖𝑖2 , … , 𝑥𝑥𝑖𝑖𝑖𝑖 ]𝑇𝑇 .The hidden layer contains L neurons. The output layer contains m neurons corresponding to the output variables 𝑦𝑦𝑖𝑖 = [𝑦𝑦𝑖𝑖1 , 𝑦𝑦𝑖𝑖2 , … , 𝑦𝑦𝑖𝑖𝑖𝑖 ]𝑇𝑇 。 The weight matrix between input layer and hidden layer can be expressed as Equation 2-1: 𝑤𝑤11 𝑤𝑤12 ⋯ 𝑤𝑤1𝑛𝑛 𝑤𝑤21 𝑤𝑤22 ⋯ 𝑤𝑤2𝑛𝑛 𝑤𝑤 = [ ⋮ ( 2-1 ) ⋮ ⋱ ⋮ ] 𝑤𝑤𝑙𝑙1 𝑤𝑤𝑙𝑙2 ⋯ 𝑤𝑤𝑙𝑙𝑙𝑙 𝑙𝑙×𝑛𝑛 The weight value between the hidden layer neuron i and the input layer neuron β is expressed in 𝑤𝑤𝑖𝑖𝑖𝑖 . The connection weight matrix β between the hidden layer and the output layer can be expressed as: 𝛽𝛽11 𝛽𝛽21 𝛽𝛽 = [ ⋮ 𝛽𝛽𝑙𝑙1
Fig. 1. Input and output of blast furnace gas utilization rate prediction model of ELM algorithm
𝛽𝛽12 𝛽𝛽22 ⋮ 𝛽𝛽𝑙𝑙2
⋯ 𝛽𝛽1𝑚𝑚 ⋯ 𝛽𝛽2𝑚𝑚 ] ⋱ ⋮ ⋯ 𝛽𝛽𝑙𝑙𝑙𝑙 𝑙𝑙×𝑚𝑚
( 2-2 )
The output weight value between the hidden layer neuron j and the output layer neuron k is expressed in 𝛽𝛽𝑗𝑗𝑗𝑗 .
The Extreme Learning Machine (ELM) is a simple and effective learning algorithm (Huang GB et al.,2004) based on a single hidden layer feed-forward neural network. The overlimit learning machine does not need complicated iterative optimization during the training of the model. It only needs to set the number of neuron nodes in the hidden layer, the weight matrix and hidden layer bias vectors are randomly generated between the input layer and the hidden layer. The output matrix of the hidden node is obtained, the connection weight matrix between hidden layer and output layer is obtained through one-step matrix calculation, and the unique global optimal solution is quickly calculated. Since its introduction, the over-limit learning machine model has been widely used in regression and classification problems due to its advantages such as fast operation speed, strong generalization ability, and not falling into local minimum values(Huang GB et al ,2006; Liang NY et al ,2006).
𝑏𝑏1 𝑏𝑏 𝑏𝑏 = [ 2 ] ⋮ 𝑏𝑏𝑙𝑙 𝑙𝑙×1
Hidden layer offset vector b can be expressed as：
( 2-3 )
Assume that the model input sample set contains Q groups sample ， Corresponding that sample input matrix X and sample output matrix Y . They can be expressed as 𝑥𝑥11 𝑥𝑥12 ⋯ 𝑥𝑥1𝑄𝑄 𝑥𝑥21 𝑥𝑥22 ⋯ 𝑥𝑥2𝑄𝑄 𝑋𝑋 = [ ⋮ ⋮ ⋱ ⋮] 𝑥𝑥𝑛𝑛1 𝑥𝑥𝑛𝑛2 ⋯ 𝑥𝑥𝑛𝑛𝑛𝑛 𝑛𝑛×𝑄𝑄 60
IFAC MMM 2018 Shanghai, China, August 23-25, 2018
𝑦𝑦11 𝑦𝑦12 𝑦𝑦21 𝑦𝑦22 𝑌𝑌 = [ ⋮ ⋮ 𝑦𝑦𝑚𝑚1 𝑦𝑦𝑚𝑚2
YuFei Ji et al. / IFAC PapersOnLine 51-21 (2018) 59–64
⋯ 𝑦𝑦1𝑄𝑄 ⋯ 𝑦𝑦2𝑄𝑄 ⋱ ⋮ ] ⋯ 𝑦𝑦𝑚𝑚𝑚𝑚 𝑚𝑚×𝑄𝑄
Extreme learning machine model will be better stable and generalization ability due to the introduction of regular parameters. The output weight of the model is:
( 2-4 )
𝐼𝐼 𝛽𝛽̂ = 𝐻𝐻𝑇𝑇 ( + 𝐻𝐻𝐻𝐻𝑇𝑇 )
Set the incentive function of the hidden layer to 𝑔𝑔(𝑥𝑥) ，The output of the network T through operations is
𝐶𝐶
𝑇𝑇
( 2-10 )
𝑓𝑓(𝑥𝑥) = 𝑔𝑔(𝑥𝑥)𝛽𝛽 = 𝑔𝑔(𝑥𝑥)𝐻𝐻𝑇𝑇 ( + 𝐻𝐻𝐻𝐻𝑇𝑇 ) 𝐼𝐼
∑𝐿𝐿𝑖𝑖=1 𝛽𝛽𝑖𝑖1 𝑔𝑔(𝑤𝑤𝑖𝑖 𝑥𝑥𝑗𝑗 ∑𝐿𝐿𝑖𝑖=1 𝛽𝛽𝑖𝑖2 𝑔𝑔(𝑤𝑤𝑖𝑖 𝑥𝑥𝑗𝑗
+ 𝑏𝑏𝑖𝑖 ) 𝑡𝑡1𝑗𝑗 𝑡𝑡2𝑗𝑗 + 𝑏𝑏𝑖𝑖 ) = 𝑡𝑡𝑗𝑗 = [ ] ( 2-5) ⋮ ⋮ 𝐿𝐿 𝑡𝑡𝑚𝑚𝑚𝑚 𝑚𝑚×1 [∑𝑖𝑖=1 𝛽𝛽𝑖𝑖𝑖𝑖 𝑔𝑔(𝑤𝑤𝑖𝑖 𝑥𝑥𝑗𝑗 + 𝑏𝑏𝑖𝑖 )] 𝑚𝑚×1
𝐶𝐶
−1
𝑇𝑇
( 2-11 )
Therefore, for a given training sample (𝑥𝑥𝑖𝑖 , 𝑡𝑡𝑖𝑖 ) ， 𝑥𝑥𝑖𝑖 = [𝑥𝑥𝑖𝑖1 , 𝑥𝑥𝑖𝑖2 , … , 𝑥𝑥𝑖𝑖𝑖𝑖 ]𝑇𝑇 ∈ 𝑅𝑅 ， 𝑦𝑦𝑖𝑖 = [𝑦𝑦𝑖𝑖1 , 𝑦𝑦𝑖𝑖2 , … , 𝑦𝑦𝑖𝑖𝑖𝑖 ]𝑇𝑇 ∈ 𝑅𝑅 ， activation function 𝑔𝑔(𝑥𝑥),𝐿𝐿 Hidden nodes, 𝐿𝐿 < 𝑁𝑁, the ELM algorithm can be summarized as:
That above formulas can be abbreviated as
（1）Randomly generate weight matrix of network w ,which between input layer and hidden layer, hidden layer offset vector b；
( 2-6 )
H is the output matrix of the hidden layer in the network： 𝑔𝑔(𝑤𝑤1 𝑥𝑥1 + 𝑏𝑏1 ) 𝑔𝑔(𝑤𝑤2 𝑥𝑥1 + 𝑏𝑏2 ) 𝑔𝑔(𝑤𝑤1 𝑥𝑥2 + 𝑏𝑏1 ) 𝑔𝑔(𝑤𝑤2 𝑥𝑥2 + 𝑏𝑏2 ) 𝐻𝐻 = ⋮ ⋮ [𝑔𝑔(𝑤𝑤1 𝑥𝑥𝑄𝑄 + 𝑏𝑏1 ) 𝑔𝑔(𝑤𝑤2 𝑥𝑥𝑄𝑄 + 𝑏𝑏2 )
−1
The expression of the model output can be directly represented as
𝑇𝑇 = [𝑡𝑡1 , 𝑡𝑡2 , ⋯ , 𝑡𝑡𝑄𝑄 ]𝑚𝑚×𝑄𝑄
𝐻𝐻𝐻𝐻 = 𝑇𝑇
61
⋯ 𝑔𝑔(𝑤𝑤𝐿𝐿 𝑥𝑥1 + 𝑏𝑏𝐿𝐿 ) ⋯ 𝑔𝑔(𝑤𝑤𝐿𝐿 𝑥𝑥2 + 𝑏𝑏𝐿𝐿 ) ⋯ ⋮ ⋯ 𝑔𝑔(𝑤𝑤𝐿𝐿 𝑥𝑥𝑄𝑄 + 𝑏𝑏𝐿𝐿 )] ( 2-7)
（2）Input training samples, establish the network model, calculate the network's hidden layer output matrix 𝐻𝐻； 𝐼𝐼 （3）Get output weight 𝛽𝛽̂ = 𝐻𝐻𝑇𝑇 ( + 𝐻𝐻𝐻𝐻𝑇𝑇 ) 𝐶𝐶
−1
𝑇𝑇。
It can be seen that, compared with the traditional neural network, the over-limit learning machine model does not need to set a large number of parameters in the model process. During the execution of the algorithm, the ELM model randomly generates the weight matrix w between input layer and hidden layer, the bias matrix b of hidden layer, according to the input training sample. It obtains the output weight of hidden layer through one matrix operation. The result is the only global optimal solution that does not require repeated iterations, which greatly improves the computational speed of ( 2-8) the network model. Therefore, compared with the traditional ‖𝐻𝐻𝛽𝛽̂ − 𝑇𝑇‖ = min𝛽𝛽‖𝐻𝐻𝛽𝛽 − 𝑇𝑇‖ BP neural network, the extreme learning machine ELM Among them 𝛽𝛽̂ = 𝐻𝐻 −1 𝑇𝑇 , The inverse matrix of 𝐻𝐻 is matrix greatly reduces the training time and improves the −1 𝐻𝐻 。 generalization performance of the model. It overcomes the The output of ELM algorithm can be directly represented as： disadvantages of BP neural network, which needs to set stopping conditions, the low learning efficiency and easy ( 2-9 ) getting into local minimums through the gradient descent 𝑓𝑓(𝑥𝑥) = 𝑔𝑔(𝑥𝑥)𝛽𝛽 = 𝑔𝑔(𝑥𝑥)𝐻𝐻 −1 𝑇𝑇 When the over-limit learning machine model is applied to method. However, it also found that in most cases, we must practical problems, the possible complex-coexistence add a regular term factor to ensure satisfactory output. problems of the sample data in various application situations PCA-ELM algorithm will cause the output matrix of the model to be unsatisfactory when the ELM model is used. When solve the least-squares Industrial sites are often in poor conditions and the data solution of facial function 𝐻𝐻𝛽𝛽 = 𝑇𝑇，the required generalized obtained is often disturbed by noise. The ELM model is inverse matrix 𝐻𝐻 −1 = 𝐻𝐻𝑇𝑇 (𝐻𝐻𝐻𝐻𝑇𝑇 )−1 due to the existence of expressed as: complex co-existence issues in the sample, leading to 𝐻𝐻𝐻𝐻𝑇𝑇 is 𝐻𝐻𝐻𝐻 + 𝜉𝜉 = 𝑇𝑇, 𝜉𝜉 𝜖𝜖𝜖𝜖(0, 𝜎𝜎 2 ) ( 2-12 ) not a non-singular matrix. That affects the effects of model prediction or classification. In order to solve the problem that When the model is proposed to internal disturbances, training the matrix dissatisfaction rank affects the prediction result with the ELM algorithm is often not satisfied. The solution to during the solution process(Huang et al ,2014; Uemukai the ELM algorithm is as follows: R ,2012)By introducing a regular parameter 𝐶𝐶，and adding 𝑇𝑇 ∑𝑁𝑁 𝑖𝑖=1 𝐻𝐻𝑖𝑖 (𝐻𝐻𝑖𝑖 𝛽𝛽𝑖𝑖 + 𝜉𝜉𝑖𝑖 ) its inverse to the main diagonal of diagonal matrix 𝐻𝐻𝐻𝐻𝑇𝑇 ， 𝛽𝛽̂ = (𝐻𝐻𝑇𝑇 𝐻𝐻)−1 𝐻𝐻𝑇𝑇 𝑇𝑇 = 𝑇𝑇 ∑𝑁𝑁 𝑖𝑖=1 𝐻𝐻𝑖𝑖 𝐻𝐻𝑖𝑖 making disparate singular matrices non-singular. Finding −1 𝑇𝑇 weight vectors 𝛽𝛽̂ by the formula 𝛽𝛽̂ = 𝐻𝐻 𝑇𝑇 ∑𝑁𝑁 𝑖𝑖=1 𝐻𝐻𝑖𝑖 𝜉𝜉𝑖𝑖 = 𝛽𝛽 + 𝑁𝑁 ∑𝑖𝑖=1 𝐻𝐻𝑖𝑖𝑇𝑇 𝐻𝐻𝑖𝑖 Different from traditional neural networks, they needs to adjust input weight and hidden layer bias value, because of the input function approximation theory. The input weights and the offset vector of the hidden nodes in over-limit learning machine are all randomly generated. Therefore, the model of over-limit learning machine is equivalent to find a solution, which called the facial function 𝐻𝐻𝛽𝛽 = 𝑇𝑇 leastsquares solution β：
61
IFAC MMM 2018 62 Shanghai, China, August 23-25, 2018
YuFei Ji et al. / IFAC PapersOnLine 51-21 (2018) 59–64
(2-13) The three aspects of expectation (𝐸𝐸), variance (𝑉𝑉) and mean squared error (𝑀𝑀𝑀𝑀𝑀𝑀) as follows： E(𝛽𝛽̂ ) = 𝛽𝛽
2 V(𝛽𝛽̂ ) = 𝐸𝐸(𝛽𝛽̂ 2 ) − 𝐸𝐸(𝛽𝛽̂ ) =
𝑀𝑀𝑀𝑀𝑀𝑀(𝛽𝛽̂ ) =
𝑝𝑝
𝜎𝜎 2 1 = 𝜎𝜎 2 ∑ ∑𝑃𝑃𝐼𝐼=1 𝐻𝐻𝑖𝑖𝑇𝑇 𝐻𝐻𝑖𝑖 𝜆𝜆𝑖𝑖 𝑖𝑖=1
1 1 𝜎𝜎 2 𝑇𝑇 𝐸𝐸 [(𝛽𝛽̂ − 𝛽𝛽) (𝛽𝛽̂ − 𝛽𝛽)] = . 𝑃𝑃 𝑝𝑝 𝑝𝑝 ∑𝐼𝐼=1 𝐻𝐻𝑖𝑖𝑇𝑇 𝐻𝐻𝑖𝑖 𝑝𝑝
𝜎𝜎 2 1 = ∑ 𝑝𝑝 𝜆𝜆𝑖𝑖 𝑖𝑖=1
(2-14)
The characteristic value of the matrix 𝐻𝐻𝐻𝐻𝑇𝑇 isλ。When the collinearity situation occurs in the matrix 𝐻𝐻， some of the eigenvalues of matrix 𝐻𝐻𝐻𝐻𝑇𝑇 are equal to zero or approach to zero. This will lead to the solution of ELM algorithm has a large variance and mean square error, and the model cannot achieve the desired effect. This study introduced PCA-ELM algorithm (Zhang HG et al ,2015). He applied the Principal Component Analysis (PCA) to the ELM algorithm. By performing principal component analysis on the hidden layer matrix 𝐻𝐻 ， the algorithm not only can get rid of the influence of collinearity but also can reduce the dimension of the matrix 𝐻𝐻，improve the training speed of the model, and reduce the training time。 Use PCA technology handles hidden layer matrix as follows： 𝐻𝐻′ = 𝐻𝐻𝐻𝐻
3. MODELING AND SIMULIATION Using a blast furnace monitoring system of a steel plant to collect data online for a period of time, Obtains 3000 sets of material characteristics and furnace condition data, and 2500 sets of data are used to establish the blast furnace gas utilization rate prediction model. 500 sets of data are used to test the model. The CO and CO2 content (both volume percentages) of the gas after automatic analysis of the gas mixture on the furnace top in actual measurement and the results obtained from the calculation formula of the blast furnace gas utilization rate are compared after data preprocessing. Using the ELM prediction model and the improved PCA-ELM prediction model for simulation verification, the sigmoid function is used as the activation function and 1000 hidden nodes are used in the ELM prediction model. In the PCA-ELM prediction model, the sigmoid function is still used as the activation function. The numbers of hidden nodes are 500, and the numbers of hidden nodes becomes 450 after dimension reduction. Figures 3 and 4 show the prediction results of the blast furnace gas utilization rate. The blue curves in the two figures represent the raw data of the blast furnace gas utilization rate, and the red curves with “o” represent the prediction results of the two algorithms. Table 1 shows four indicators of the train time, test time, train accuracy, and test accuracy of the two prediction algorithms. The blast furnace gas utilization rate prediction results for each model are shown in the figure below. The performance of each model is shown in the following table: 2 𝜂𝜂 = 𝐶𝐶𝐶𝐶+𝐶𝐶𝑂𝑂
𝐶𝐶𝑂𝑂
2
(2-18)
(2-15 )
𝐻𝐻′ is converted hidden layer matrix, 𝐺𝐺 is conversion matrix。 After dimension reduction for hidden layer matrix 𝐻𝐻 by PCA technology, the solution of PCA-ELM is as follows： 𝑇𝑇 𝑇𝑇 𝛽𝛽̂ = (𝐻𝐻′ 𝐻𝐻′ ) 𝐻𝐻′ 𝑇𝑇 −1
( 2-16 )
Again, from three aspects of PCA-ELM solutions for analysis: expectation, variance, and mean square error as follows. E(𝛽𝛽̂ ) = 𝛽𝛽
2 V(𝛽𝛽̂ ) = 𝐸𝐸(𝛽𝛽̂ 2 ) − 𝐸𝐸(𝛽𝛽̂ ) =
𝑀𝑀𝑀𝑀𝑀𝑀(𝛽𝛽̂ ) = =
𝑝𝑝
𝜎𝜎 2 1 𝑝𝑝𝜎𝜎 2 2 = 𝜎𝜎 ∑ ≤ ∑𝑃𝑃𝐼𝐼=1 𝐻𝐻𝑖𝑖𝑇𝑇 𝐻𝐻𝑖𝑖 𝜆𝜆𝑖𝑖 𝜆𝜆𝑚𝑚𝑚𝑚𝑚𝑚 𝑖𝑖=1
1 1 𝜎𝜎 2 𝑇𝑇 𝐸𝐸 [(𝛽𝛽̂ − 𝛽𝛽) (𝛽𝛽̂ − 𝛽𝛽)] = . 𝑃𝑃 𝑝𝑝 𝑝𝑝 ∑𝐼𝐼=1 𝐻𝐻𝑖𝑖𝑇𝑇 𝐻𝐻𝑖𝑖
𝜎𝜎 2 𝑝𝑝
∑𝑝𝑝𝑖𝑖=1
1
𝜆𝜆𝑖𝑖
≤
𝜎𝜎 2
𝜆𝜆𝑚𝑚𝑚𝑚𝑚𝑚
Fig. 3 Prediction results of the blast furnace gas utilization rate based on ELM
( 2-17 )
From the above formulas, it can get the conclusion that after the PCA treatment, the solution of ELM is improved in terms of variance and mean square error. It also can still maintain an unbiased estimate. 62
IFAC MMM 2018 Shanghai, China, August 23-25, 2018
YuFei Ji et al. / IFAC PapersOnLine 51-21 (2018) 59–64
63
algorithm can well solve the problem of collinearity existing in the ELM algorithm in dealing with fluctuating data. Make it more accurate in the event of significant fluctuations, the PCA-ELM algorithm has a better predictive effect when the furnace conditions change drastically and the industrial environment is complicated.Therefore, in the actual production process, not only need to according to the theoretical algorithm, but also should combined with the specific blast furnace conditions. So that to achieve a better overall grasp of the blast furnace, make blast furnace forward and achieve better economic benefits.
ACKNOWLEDGEMENT This work was supported by the Key Program of National Nature Science Foundation of China under grant No. 61333002, the National Nature Science Foundation of China under grants No. 61673056, the Beijing Natural Science Foundation under grant No. 4182039 and the Beijing Key Discipline Construction Project (XK100080537).
Fig. 4 Comparison results of the blast furnace gas utilization rate based on PCA-ELM Table 1 Prediction Index of The Blast Furnace Gas Utilization Rate Name
Hidden nodes Numbers
Train time
Test time
Train error
Test error
ELM
1000
1.0718
0.022
0.0032
0.0232
PCAELM
500→450
0.1094
0.042
0.0030
REFERENCES Pan Yu, Yu Haibin, Yuan Mingzhe. Blast furnace energy efficiency modeling and analysis [J]. Manufacturing Automation, 2011, (23): 142-144. An Jianqi, Chen Yifei, Wu Min. Prediction method of carbon monoxide utilization in blast furnace based on improved support vector machine [J]. Journal of Chemical Industry and Engineering, 2015, (01): 06-214.
0.0057
At the same time, it is noticed that both algorithms have large prediction errors within the range of 100-120 test sample points. This has a lot to do with the internal working conditions of the blast furnace and the operation of the foreman. Due to its complexity, the blast furnace reaction process depends to some extent on empirical operation. Traditional experience shows that at the stage of lower oxygen enrichment rate, the blast furnace gas utilization rate will increase with the increase of oxygen enrichment rate, but at the stage of higher oxygen enrichment rate, the blast furnace gas utilization rate will gradually decline with the continue increase of oxygen enrichment rate. According to the production records, with the progress of the reaction, in this phase, the oxygen enrichment rate continues to increase, so that the utilization rate of blast furnace gas decreases, and led to the prediction results of the two algorithms have relatively large errors.
LinSHI,You-binWEN,Guang-shengZHAO,etal. RecognitionofBlastFurnaceGasFlowCenterDistributionBased onInfraredImageProcessing[J]. Journal of Iron and Steel Research, 2016, 23(3):203-209. He Shaogang. Current status and analysis of utilization rate of blast furnace gas in Panzhihua Iron and Steel Corporation [J]. Sichuan Metallurgy, 2017(1):13-17. Du Nan. Research on Modeling Method for Prediction of Blast Furnace Condition and Distribution of Gas Flow[D]. Hunan: Central South University, 2014. Huang GB, Zhu QY, Siew C K. Extreme learning machine: a new learning scheme of feedforward neural networks[J]. Proc.int.jointConf.neuralNetw, 2004, 22004, 22004[2017-1008 16:38:00]. Huang GB, Zhu QY, Siew C K. Extreme learning machine: Theory and applications [J]. Neurocomputing, 2006, 70(1– 3)-2006, 70(1–3).2006[2017-10- 31 21:45:00].
4. CONCLUSIONS This paper based on a blast furnace monitoring system online acquisition for a period of time, burden surface characteristics and furnace condition indexes data. Two kinds of prediction algorithms, ELM and PCA-ELM, are used to predict the blast furnace gas utilization rate. By comparing the results of two prediction algorithms, it can be considered that applying PCA to ELM has a good effect in reducing the number of hidden nodes. As a result, the PCA-ELM
Liang NY, Huang GB, Saratchandran P, et al. A Fast and Accurate Online Sequential Learning Algorithm for Feedforward Networks [J].IEEE Transactions on Neural Networks, 2006, 17(6)-2006, 17(6).2006[2017-10-31 21:46:00].
63
IFAC MMM 2018 64 Shanghai, China, August 23-25, 2018
YuFei Ji et al. / IFAC PapersOnLine 51-21 (2018) 59–64
Li Ailian, Zhao Yongming, Cui Guimei. ELM blast furnace temperature prediction model based on grey correlation analysis[J]. Journal of Iron and Steel Research, 2015, 27(11)2015, 27(11).2015[2017-10-31 22 : 16:00]. Zhang HG, Zhang S, Yin Y X. A Novel Improved ELM Algorithm for a Real Industrial Application[J]. Mathematical Problems in Engineering, 2014, (2014-4-16), 2014, 2014(2)2014 , 2014(2).2014[2017-10-31 22:18:00]. Uemukai R. Erratum to: Small sample properties of a ridge regression estimator when there exist omitted variables[J]. Statistical Papers, 2012, 53(1)-2012, 53(1).2012[2017-10-31 22:19:00]. Zhang H, Yin Y, Zhang S, et al. An Improved ELM Algorithm Based on PCA Technique[M]. Springer International Publishing, 2015: 95-104[2017-10-31 22:22:00
64