Intelligent prediction model of matte grade in copper flash smelting process

Available online at www.sciencedirect.comTransactions of●cIENCE@oineor.Nonferrous M etals骂RSociety of ChinaScienceTrans. Noferrous Met. Soc. China 17(2007) 1075-1081Presswww.c5u.du.cn/yxb/Intelligent prediction model of matte grade in copper flash smelting processGUI Wei-hua(桂卫华), WANG Ling-yum(王凌云动), YANG Chun-bua(阳春华),XIE Yong-fang(谢永芳), PENG Xiao-bo(彭晓波)School of Information Science and Engineering, Cenral South University, Changsha 410083, ChinaReceived 26 December 2006; accepted 28 June 2007Abstract: Due to the importance of detecting the matte grade in the copper flash smelting proces the mcchanism model wasestablished according to the multiphase and multi-component mathematic model. Meanwhile this procedure was a complicatedproduen process with caracteristis of large tine delay, Doninarity and so on. A fuzy neural network model was set up througha great deal of production data. Besides a novel constrained gradientdescent: algorithm used to update the parameters was putforward to irnprove the parameters learning eficiency. Ultimately the self-adaptive combination technology was adopted toparaleled integrate two models in order to obtain the prediction model of the matte grade. Indutial data validation shows that theitelligently integrated model is more precise than a single model. It can not only predict the matte grade exactly but also provideoptinal control of the copper flash snelting process with potent guidance.Key words: copper flash smeling process; matte grade; multi phase and multi-gradient descent algoritinHowever, the matte grade is detected later more than 1 h1 Introductionwhen the copper flash smelting process is finished, so itcan not supervise the production manipulation in time.The copper flash smeling process is one of theConsequently it is very signifcant to predict the mattecomplicated pyomeallurgical processes. A lot of fruitfulgrade online for stabilizing the copper fash smeltingresearches have been done for the online mechanismproduction and improving the product quality. WAN etmodel of the copper flash smelting process. Not only theal[5] established the model of the flash smeling fumnacematte grade and distribution of acessory element can bebased on the neural network and adopted it to predict thepredicted[1], but also the online control is realized fortechnological index and yield. WAN et a[6] also set upthe industry{2-3]. But this model is established on thethe dynamic quality model of the nickel flash smeltingrigorous theory of malallurgical physical chemistry. Itprocess by adopting Takagi-Sugeno fuzzy model. Also itsthe practical production there are lots of uncertain factorsstructure and parameter identification were discussed.such as many variations of mineral resources and greatBut these two approaches are not guided according to thefluctuation of the industrial status, so the practicalmechanism of reaction process then the predictedproduction process deviates from the applicabletechnological index will be not precise.condition of the mechanism model. This model can notThe idea of itelligent integrated modeling is uniquesatisfy the requirement of industrial productionwhen it is adopted to deal with the information ofcompletely.complex process that is characterized by intricate intemalFurthermore thnatte grade is one of themechanism such as nonlinearity, uncertainty and largecomprehensive indexes in tbe copper flash smeltingime dclay. Industrial data can be used for systemprocess when the amount of the treated material isideitification and neural network modeling. Theinvariable in the copper flash smelting furmace. Theexperience knowledge can also be taken as the basis ofstable matte grade is important to the smclting,expe中国煤化Ideling, In adtion,converting and the production of suifuric acid[4].the cndustrial process is1H.CNMHGs。yo、wioaFoundation item: Proijext(60634020) supported by the National Natural Science FounBasie Research and Devclopment Program of ChinaCorrespoadiag uthor: WANG Ling youn; Tel: +86-731-8830394; E-mail: susawlinghotrail.com1076GUI Wei-hua, et al/Trans. Nonferous Met. Soc. China 17(2007)the premise of the mechanism modeling. Therefore thesematte grade when tbe equilibrium model reaches balancediverse information provide convenience for thein the copper flash smelting process.integration of different modeling methods[7- 10].If the temperature, pressure and the amount ofIa this study the tmatte grade of the copper flashsubstance of each element are given in the sealed system,smelting process was predicted. Firstly the mechanismthe equilibrium state of this system will be determined.model based on multiphase and multi-component modelThe key point of equilibrium constant method is that allwas discussed; secondly a fuzzy neural network modelthe chemistry reaction reaches balance at the same timwas set up by production data and rules in order towhen the system reaches balance. The differentovercome the nonlinear dymamic characteristic in thecomponents in each phase are associated with a group ofprocess. Due to the low parameter learming efficiency, acomplex united equations through equilibrium constant.constrained gradient descent algorithm of the parameterThe amount of substance of each component in theleaming was proposed in the fuzzy neural network.equilibrium system can be obtained through solving theunited equations and this is the basic idea of equilibriumFinally the self-adaptive combination technology waadopted to paralleled integrate the two models in order toconstant method. There are Goto method, reaction coursemethod and so on according to the different concreteobtain the prediction model of the matte grade.disposing methods. All the equilibrium constant methods2 Mechanism of matte grade based onare developed based on Brinkley principle. The detailedintroduction of the general principle for equilibriummulti-phase and multi-component modelconstant method can be seen in Ref.[4].The copper flash smelting process is a typicalIn the copper flash smelting process, the foemulti -phase and multicomponent reaction process in theparticles of dry concentrate and flux are mixed with thehermetically sealed container. According to theoxygen-enriched air at the nozzle of the flash smeltingmulti-phase and multi-component mathematic model offurmace, then are injected into the fumace fom the top ofthe copper flash smelting established by the balancethe reaction tower and react. The blending melts of tbeconstant method, the amouat of fine concentrate, slagmolten sulfide and oxide fall down to the bottom of thefioe concentrate, siliceous concentrate, indeterminatereaction tower, then they are gathered, precipitated andmaterial, oxygen-enriched air and the composition ofseparated in the precipitation pool. Finally the matte andeach component are substituted into this mathematicslag are formed respectively.model, respectively. Then the calculated amount ofThe copper flash smelting process is a typicallysubstance of Cu, Fe, S, O, As and Zn elements in thebermietically sealed container pyrometallurgical process.matte are substituted into the mechanism model of matteThis chemical reaction is extremely complicated and thegrade:reaction substances have three pbases such as solid,liquid and gas. Generally the mathematic model of thex(Cu)=mava/ Zm,a;(1)mutiphase and multi-component chemistry equilibriumis established through Brinkley principle that is alsowhere m is the amount of substance of each element, 4;called equilibrium constant method. Its basic idea is thatis the relative atomic mass of each element.The static mathematic model of matte grade basedthe whole components contained in each phase ardivided into independent components and auxiliaryon metal equilibrium equation can reflect the industriatstatus, but there are certain errors in the calculated resultcomponents in the equilibrium system. The elements thatof the model inevitably.compose the independent components should include thewhole elements in this system and the mumber o3 T-S fuzzy neural network identificationindependent components should be equal to the sum ofmodel of matte gradethe knds of elements contained in the system when theindependent component is chosen. So theamount of3.1 T-S fuzzy neural network modelsubstance of the whole auxiliary components in theAlthough the matte grade based on multiphase andequilibrium system can be described as the function ofmulti- component model is established on the basis ofthe amount of substance of independent components.rigon中国煤化工al chemistry, tbereThe amount of substance of the auxiliary componentswille industrial statuscan be obtained as long as the amount of substance of thefluctYHCNMHG deviates fomindependent components was acquired. Hence theequilibrium system, the charge material and oxygen-multiphase and multi- component equilibrium modelenriched air are not mixed homogeneously, and thebased on Brinkley principle can be used to compute thedistribution temperature is lack of balance in the reactionGUI Wei hua, et al/Trans. Nonferrous Met. Soc. China 17(2007)077tower in the practical production. So there is a greatwhere x(i=l, 2,-, n) and y are imput and outputdifference between the practical reaction and idealvariables respectively; Aj (=1,2, *". p) is the fuzzy setchemical equilibrium. The exact analytic solution can notthat is defined as the universe of discourse U; ay is thebe obtained through the mechanism model. Howeverconsequent parameter of the rule; n is the number ofthere is a great deal of industrial data and expertinput variables and p is the oumber of rules.experience in the production field. The stable productionThe node in the fourth layer performs thedata that have the characteristic of sensitivity and realdefuzzification operation that applies centroid method. w:time implicate the mechanism and rule of the reactionis the connective weight between the rule layer and theprocess and can reflect the reaction practice to a certaindefuzzification layer. Its output expression isextent. It is feasible to adopt fuzzy neural network to setup the prediction model of the matte grade.(3)The ielligent model of matte grade is establishedby T-S fuzzy neural network that is widely adopted in thecomplicated nonlinear system modeling process. Thewhere μj=μnHa, --.- Hn is the membershipfuzzy neural network integrates the neural network withfunction of the universe of discourse U,the fuzzy logic. It not only has the strong structuralknowledge expression capability of fuzzy logic inference,3.2 Constrainedgradient descent algorithm ofbut also has the powerful self-learming capability andmodel's parameter updatingdata processing capability of neural network.BP algorithm and gradient descent algorithm areThe predicted matte grade is influenced by manyusually adopted to update the membership functionfactors that have nonlinear relationship with the matteparameters of fuzzy neural network[12- -14]. Always theygrade in the copper fash smeling process. However,re prone to fall into the local minimum in thethere are a great deal of industrial data that can beparameters' learning process of fuzzy neural networkanalyzed in the industrial field. Meanwhile theowing to the intrinsic limitation of gradient descentconvenience of the data acquirement and the correlationalgorithm. Besides if the surrounding area of the solutionamong variables should be regarded. The correlation notis smooth, the parameters will leam more slowly. Due toonly among variables but also between variables andthe low parameters leaming efficiency of conventionalmatte grade was studied. The variables that have lessT-S fuzzy neural network model, the establisbed networkcorrelation with the matte grade will be eliminated.model can not satisfy the industrial process with theTherefore the complexity of the model can be reducedcharacteristic of large time delay for real time. In order topotentially under the premise of not losing importantimprove the conventional parameters leamning algorithm,input variables information. The input variables of thethe constrained gradient descent algorithm is proposed tofuzzy neural network model are the amount of ait,update the model's parameters. This learning algorithmoxygen in the reaction tower, flux, dust, cupreous ratio ofnot only reserves the merit of the traditional gradientdry fine concentrate, slag fine concentrate, siliceousdescent algorithm, but also improves its scarcity.concentrate and indeterminate material.Generally speaking, the validity of fuzzy logic ruleUsually the fuzzy neural network model is amust be guaranteed, i.e. the membership grade of thefour-layer feedforward network[1]. The nodes in thecrossover point of two membership function curvesfirst layer transmit the input information to the next layerwhose centers are adjacent must be bigger than 0.5 whiledirectly. Each node in the second layer acts as adesigning the fuzzy logic rule of T-S fuzzy neuralmembership function. The Gaussian function is selectednetwork, namely the E completeness of fuzzy logic mustas a membership function that divides the inputbe 0.5[15]. In order to guarantee this trait of fuzzy logicinformation. The nodes in the third layer perform therules and each logic rule to exert its self-functionfuzzy T-norm operations, and each node represents a rule.effectively according to the inputs of the model, aThe antecedent rules are fuzy variables and theconstraint function is proposed next.in the membership function layer of TS fuzzyconsequents are equations described through preciseneurstion is chosen as thevariables. The rule is expressed as follows:中国煤化工memRulej:THCNMH GIfx isAynxzisA2j " andxn is AmpThen=l,2, .n;j=1,2, "",P(4)y=Co; +Qj所+Q2jX2 +..+ryXxn(2where Cg and σy are the center and width of Gaussian1078GUI Wei hua, et al/Trans. Nonferrous Met. Soc. China 17(2007)membership function respectively. From Fig.1, it can beseen that the crossover point Xxo of that two curves can bef=1In2(σg + Ouy+)+Cy -CuU+1)≥c(11)obtained through the following equation when twoWhen considering the proposed constrainedcrossed membership functions whose centers aregradient desccnt algorithm, the membership functionadjacent operate on the input variable x simultaneously:parameters of fuzzy logic are not updated in accordanceH(xro)=Hum(&xo)(5)with this algorithm firstly, but updated by adopting theconventional unconstrained gradient descent algorithm.If the updated parameters are in the feasible region asthendefined in Eqn.(1), then they are deemed acceptable.Xxo =CyOu+) -C1(+1)0重(6)Otherwise these parameters need to be updated again byusing the constrained gradient descent algorithm until the01(U+1) -σg .updated parameters are in the feasible region.For a group of training data {x}，the inputx is1.0the n dimension vector {x,Xx2, .., x}, j is the desiredoutput and y is the practical output of the model. Thefollowing objective function is defined as the队，performance index of the training data, where L is thegroup number of the training data:。0.6(y-沪(12)旨0.4{”For Gaussian membership function, the training0.process of fuzzy neural network is that the membershipfunction parameters Cy and Oy are regulated continuouslythrough minimizing the value of the objective function E.Universe of discourseThe parameters of membership function are updated byusing the following conventional gradient descentFig.1 Two Gaussian membership function adjacent to junctionalgorithm frstly:The membership grade of the crossover point mustCg(k+1)=cy(k)-nc(y-)not be smaller than 0.5, i.e. μa (x;o)≥0.5. So thefollowing expression can be obtained:H;W,2[x-Cy(k)](x;o -cg)2.≤ln2(7)u; -σ(k)(13)。σy(k+1)=σg(k)-ηo(v-)(x;0 -Cu(+1)户-≤In2(8)w,之u-二u,m,2[x-Cg(k)]2ij+I) .u;-暗(k)(14)From the above bilateral neighborhood of thecrossover point Xxo0 in Fig.1, it can be seen that the span of(创the satisfied x can be expressed as the following twowhere k is the kth training epoch; ne and n。are theinequations:learing step size.Next, the completeness value of fuzzy logic must bex≤√In2oy+Cy(9)verified. not less than 0.5 at least. At the kth training中国煤化Ibe obtained accordingx≥←√in20σu+) +Ciu+)(10)HCNMHGIncorporating the two constraint conditions of thef =√In2(σg(k+ 1)+ Ou+H){k +1))+Eqns.(9) and (10), the constraint function f can beobtained as follows:cy(k+1)- C(+)(<+1)20(15)GUI Wei -bua, et al/Trans. Nonferrous Met. Soc. China 17(2007)1079If Eqn.(15) is satisfied and the performance index offactors such as variation of mine resource.the objective function E achieves the appointed value atTherefore it is necessary to adopt inelligentthe kth training epoch, the updated parameters at theintegrated modeling method to estalish the itelligentcurrent epoch are feasible solutions. Otherwise theprediction model of the matte grade. The mechanismparameters must be updated again in accordance with themodel should be paralleled integrated with the fuzzyfollowing algorithm,neural network model and the optimal integrated model1) Keeping ogy(k+1) invariable, i.e. the width ofis established through determining the weights 0Gaussian membership function is invariable, cj(k+1) isdifferent submodels in real time. Then their advantagescan complement each other and the matte grade can berecalculated as follows:predicted exactly. The frame of the integrated model isCy(k +1)=cg(k)+ne;(16)shown in Fig.2 and the integrated model is expressed as: dcyfollows:2) Keeping crj(k+1) invariable, i.c. the centery= m.YxI + W2yk2 :(0