面向鋁電解槽的變論域模糊專家系統(tǒng)英文

1、variable universe fuzzy expert system for aluminum electrolysiscao dan-yang1, zeng shui-ping2, li jin-hong11. college of information engineering, north china university of technology, beijing 100144, china;2. college of mechanical and electrical engineering, north china university of technology, bei

2、jing 100144, chinareceived 4 march 2010; accepted 28 june 2010abstract: in aluminum electrolytic process, the variables affect the current efficiency and the stability of electrolysis cells. alf3addition and aluminum tapping volume are two important factors that affect economic benefits of aluminum

3、electrolytic production. fuzzy logic provides a suitable mechanism to describe the relationship between the process variables and the current efficiency. fuzzy expert system based on mamdani fuzzy inference process for aluminum electrolysis was adopted to adjust alf3 addition and aluminum tapping vo

4、lume. a novel variable universe approach was applied in the system to solve the problem that different electrolysis cells have different universes of variables. the system was applied to 300 ka aluminum electrolysis cells in a aluminum plant. experimental results showed that the electrolyte temperat

5、ure was kept stably between 945 and 955 c, the current efficiency reached 93.5%, and the dc power consumption was 13 000 kwh per ton aluminum.key words: variable universe; fuzzy expert system; aluminum electrolysissteam engine2. mamdani fuzzy expert system has beenapplied in the field of production

6、control in many industries, for example, the application of fuzzy expert system for the early warning of accidents due to driver hypo-vigilance3, the determination of coronary heart disease risk4, and operating room air condition control systems5. despite the wide application of fuzzy expert system,

7、 the technique hasnt been applied in aluminum electrolysis production still.each electrolytic cell has its own unique range of universe of parameters. so, for different electrolytic cells, we cant get very good results even if we use the fuzzy logic control. to settle this question, the variable uni

8、verse fuzzy controller was presented in refs.610. in the premise that the number of control rules is fixed, the universe is changed with the changing error. thus, the contraction of universe is equal to the control rules added, and the precision of the controlled system will be improved. so it was w

9、idely used in various controlled fields.recently, low cryolite ratio and low temperature technology are regarded as the main process operation conditions in the aluminum electrolysis process. modern1 introductionin the aluminum electrolysis production, alumina isusually dissolved into molten cryolit

10、e, which reduces its melting temperature significantly. objectives of the workers are to maximize the current efficiency, and to maintain the stability of the electrolytic cells during aluminum electrolysis. however, the process of aluminum electrolysis production is a nonlinear, multivariable, and

11、strong coupling process due to the influence of process parameters and environmental factors. the relationship between the current efficiency and process parameters is very complex and difficult to describe through a mathematical model. however, the relationship can be constructed using fuzzy logic

12、approach1.as a qualitative approach, fuzzy logic provides a methodology to mimic human expert and allow the use of data and information from expert knowledge. fuzzy expert system has been widely used in the production process control and optimization since mamdani and assilian developed fuzzy logic

13、controller model for afoundation item: project (2009bae85b00) supported by the national key technology r&d program of china; project (phr20100509) supported by funding project for academic human resources development in institutions of higher learning under the jurisdiction of beijing municipality,

14、chinacorresponding author: cao dan-yang; tel: +86-10-88803022-22; e-mail: ufocdydoi: 10.1016/s1003-6326(11)60732-2430cao dan-yang, et al/trans. nonferrous met. soc. china 21(2011) 429436control theory and new method to control the aluminaconcentration are widely used, and a fuzzy expert control meth

15、od has been developed based on on-line intelligent identification1114. however, the research on other parameters such as temperature, aluminum tapping volume and alf3 is very limited. so in this work a variable universe fuzzy expert system was developed for3 variable universe fuzzy logic controlfuzz

16、y system consists of few inputs, outputs, set ofpredefined rules and a defuzzification method with respect to the selected fuzzy inference system.3.1 variable universelet xi= emax i , emin i (i=1, 2, , n) be the universe of the input variable xi (i=1, 2, , n) and let y=umin,umax be the universe of o

17、utput variable y. i=aij (j=1,2, , m) stand for the fuzzy sets xi and j =bj standfor the fuzzy sets y. i and j are regarded as the linguistic variables, so that rs (s=1, 2, , p), fuzzyinference rule set, is formed as follows:aluminum electrolysis to control aluminumvolume and alf3.tapping2 aluminum e

18、lectrolysis processaluminum is produced from aluminaby anelectrolysis process that uses large quantities of electricalenergy to separate aluminum from oxygen in the alumina. for this process, in a modern smelter about 13 500 kwh of electricity is required to produce 1 t aluminum. thers: if x1 is a1j

19、, , and xn is anj then y is bj(1)the so-called variable universe means that someuniverses, such as xi and y, can change along with changing variables xi and y. in refs.610, the details of variable universe method were described. however, the method is not appropriate to multiple electrolysis cells i

20、n aluminum electrolysis. so we present a novel variable universe approach for aluminum electrolysis. in the novelschematic of aluminum electrolyticfig.115.cellisshowninx (k ) =approach, eq.(1) is still used. in addition, leti( k )( k ),emin i emax i (i=1, 2, , n; k=1, 2, , t) be the(k)universe of th

21、e input variable xi (i=1, 2, , n) of they ( k ) = u ( k ) , u ( k )kth electrolytic cell and let be theimin imax ifig.1 aluminum electrolytic celluniverse of output variable y(k) of the kth electrolytic cell.in order to use the same set of rules rs in fuzzy expertalumina is a compound of aluminum an

22、d oxygen.to obtain metal al from alumina, oxygen must be separated by electricity in the smelting process. this reaction takes place in large, carbon-lined steel cells, or pots, through which a direct electrical current is passed. the bottom of each pot acts as a cathode, or negative electrode. carb

23、on blocks are suspended in the pot to serve as an anode, or positive electrode. inside the pot, alumina is dissolved in a molten electrolyte composed mainly of the cryolite. the electrical current passing from the anode to the cathode causes oxygen in the compound to react with the carbon anode to f

24、orm carbon dioxide, while the produced aluminum settles to the bottom of the pot to be siphoned off to casting and fabricating.in aluminum electrolysis production, aluminum tapping volume and alf3 addition are two important factors that affect the current efficiency and the stability of the electrol

25、ytic cell16. meanwhile, aluminum tapping volume and alf3 addition are influenced by electrolyte temperature and superheat degree and aluminum level.(k) and y(k)system, xiwill be convertedintoxand yirespectively:(k )(k ) emin i )(emax i emin i ) + e( xi=(2)xmin ii(k )(k ) emax i emin i( k )( k ) ( y

26、u )(u u )y =min max min + u(3)minu ( k ) u ( k ) maxmin(k) is shown inthe relationship between xi and xifig.2.fig.2 relationship between xi and xi(k)3.2 fuzzy inference systemthe most commonly used fuzzy inference techniquecao dan-yang, et al/trans. nonferrous met. soc. china 21(2011) 429436431is th

27、e so-called mamdani method. the mamdani-stylefuzzy inference process is performed in three steps:1) fuzzification of the input variables;2) fuzzy inference;3) defuzzification of the output variables.r1: if x1 is a13 or x2 is a21, then y is b1;r2: if x1 is a12 and x2 is a22, then y is b2;r3: if x1 is

28、 a11, then y is b3.the first step is to take the inputs, x1 and x2, and determine the degree to which these inputs belong to each of the appropriate fuzzy sets, as shown in fig.4.in the second step, the system is to take the fuzzified inputs, and apply them to the antecedents of the fuzzy rules. if

29、a given fuzzy rule has multiple antecedents, the fuzzy operator (and or or) is used to obtain a single number that represents the result of the antecedent evaluation, as shown in fig.5.the structure of the fuzzy inference systemshown in fig.3.isa a ( x) = min a ( x), a ( x)(4)1 212a a ( x) = max a (

30、 x), a ( x)(5)1 212fig.3 structure of fuzzy inference systemnow, the result of the antecedent evaluation can beapplied to the membership function of the consequent. then, aggregation is the process of unification of thefor example, a simple two-inputproblem includes three rules:andone-outputfig.4 me

31、mbership function and fuzzy setsfig.5 rule evaluation432cao dan-yang, et al/trans. nonferrous met. soc. china 21(2011) 429436outputs of all rules. we take the membership functions ofall rule consequents and combine them into a single fuzzy set. the input of the aggregation process is the list of con

32、sequent membership functions, and the output is one fuzzy set for each output variable, as shown in fig.6.the last step in the fuzzy inference process is defuzzification. fuzziness helps us to evaluate the rules, but the final output of a fuzzy system has to be a crisp number. the input for the defu

33、zzification process is the aggregate output fuzzy set and the output is a single number. there are several defuzzification methods, but the most popular one is the centroid technique. it finds the point where a vertical line would slice the aggregate set into two equal masses. mathematically this ce

34、ntre of gravity (cog) can be expressed as:table 1 fuzzy input and output variablesparametertypelinguistic expressionelectrolytetemperature (x1) superheat degree (x2) aluminum level (x3) aluminum tappingvolume (y1)alf3 addition (y2)very low, low, medium,high, very highlow, medium, highlow, medium, hi

35、ghinputinputinputoutputlow, medium, highoutputlow, medium, highta ble 2 universe of input and output variables parametermin.max.electrolyte temperature (x1)/c9250222 880098035273 10070superheat degree (x )/c2baluminum level (x3)/cmaluminum tapping volume (y1)/kga a ( x) xdxcog =(6)ba a ( x)dxalf add

36、ition (y )/kg324 design of variableuniversefuzzyexpertformulasaregatheredinasuitableway.thesystem for aluminum electrolysismemberships of input and output are shown in fig.7.forelectrolytetemperature(x1)membership functions will bethefuzzy4.1 fuzzificationin the variable universe fuzzy expert system

37、, four parameters were chosen as input, two parameters were chosen as output, and the linguistic expressions are given in table 1. the system assesses electrolyte temperature (x1), superheat degree (x2), and aluminum level (x3) all together in the electrolytic cell and adjusts aluminum tapping volum

38、e (y1) and alf3 addition (y2) in order to enhance the current efficiency and the stability of the electrolytic cell 16. the universes of the input and output variables are listed in table 2.the development of membership functions is also based on discussion with the aluminum electrolytic production

39、experts in the aluminum electrolytic plants. all the membership functions of fuzzy input and output variables are of linear form, such as triangular and trapezium. the linear membership functions are simple, easy to calculate and appropriate in describing the fuzzy input and output variables in the

40、aluminum electrolytic production. as the membership functions of parameters are taken in triangle and trapezium, their mathematical1, 925 x1 933very low ( x1 ) = 939 x1 , 933 x1 9396 x 933 1 , 933 x1 9396low ( x1 ) = 1, 939 x1 944950 x1 , 944 x 95016 x1 944, 944 x1 9506medium ( x1 ) = 1, 950 x1 9559

41、61 x1 , 955 x 96116 x 955 1 , 955 x1 9616high ( x1 ) = 1, 961 x1 966972 x1 , 966 x 97216fig.6 aggregation of rule outputscao dan-yang, et al/trans. nonferrous met. soc. china 21(2011) 429436433fig.7 membership for five fuzzy variablesx3 23, 23 x3 24 x 9661, 966 x1 972very high ( x1 ) = medium ( x3 )

42、 = 1, 24 x3 2561, 972 x 98026 x3 , 25 x3 261x 25, 25 x 26( x ) = 32for superheat degree (x2),functions will bethefuzzymembershiphigh 31, 26 x2 27for aluminum tapping volumemembership functions will be(y1), the fuzzy1, 0 x2 6low ( x2 ) = 8 x2 , 6 x2 8 21, 2 880 y1 2 910( y ) = x2 6 2 980 y, 6 x2 8low

43、 11 , 2 910 y1 2 980270medium ( x2 ) = 1, 8 x2 12 y 2 91014 x1, 2 910 y1 2 9802 , 12 x 14702212medium ( y1) = 1, 2 980 y1 3 020 x3 080 y1 , 3 020 y 30802, 12 x2 14high ( x2 ) = 21601, 14 x 352 y 3 0201, 3 020 y1 3 080high ( y1 ) = 60for aluminum level (x3), thefunctions will befuzzymembership1, 3 08

44、0 y 310011, 22 x3 23for alf3 addition (y2), the fuzzy membershipfunctions will bexlow ( 3 ) = 24 x3 , 23 x3 24434cao dan-yang, et al/trans. nonferrous met. soc. china 21(2011) 429436function maximum (max). therefore, it is also known asmin-max rule. we can make use of the 45 rules, as shown in fig.4

45、 and fig.5.1, 0 y2 5low ( y2 ) = 35 y2 , 5 y2 3530 y2 54.3 defuzzificationthe centroid of gravity (cog) method is the most widely adopted deffuzification method. the centroid defuzzification method finds a point representing the centre of gravity of the aggregated fuzzy sets according to eq.(6) and

46、fig.6., 5 y2 3530medium ( y2 ) = 65 y2 , 35 y 65230 35 y2, 35 y2 65high ( y2 ) = 301, 65 y 7025 experimental resultsfor each electrolytic cell, it has own universes ofinput and output variables. so we translate input variablethe variable universe fuzzy expert system has beenapplied to 300 ka aluminu

47、m electrolysis cells in a aluminum electrolysis plant for one year. the system makes use of electrolyte temperature, superheat degree, and aluminum level to control aluminum tapping volume and alf3 addition of electrolysis cell according to 45 fuzzy rules. fig.8 shows the the average current efficie

48、ncy of 4 test cells is increased to 93.5% in 12 months. compared with the whole plant, the current efficiency is enhanced by 0.8%. fig.9 shows that the average dc consumption per ton aluminum for 4 test cells is reduced to 13 000 kwh in 12 months, which is reduced by 135 kwh.the results show that th

49、e current efficiency is improved and dc power consumption is reduced after the system runs normally. this system maintains the electrolyte temperature between 945 and 955 c, so the current efficiency is greater than 93.5%, and dc power consumption per ton aluminum is less than 13 100 kwh.the fuzzy e

50、xpert system makes use of 45 fuzzy rules which are adaptive to give decisions for different cells. however, the system cannot update the standard(k)(k)xiinto xi, and output variable yinto y through eqs.(2)and (3), where i=1, 2, , n; k=1, 2, , t; n is thenumber of variables; t is the number of cells.

51、 thus we can only use a set of fuzzy rules to infer for each cell.4.2 fuzzy inferencethe relationship between fuzzy input and fuzzy output variables in the system is developed using mamdani fuzzy ifthen rules. the fuzzy rules are developed based on interviews with experienced production personnel in

52、 aluminum electrolytic plants. the fuzzy rules are also developed based on industrial data and literatures.according to fuzzification, electrolyte temperature (x1) is divided into five fuzzy sets, superheat degree (x2) and aluminum level (x3) are respectively divided into three fuzzy sets. we can ob

53、tain 45 rules for decision of aluminum tapping volume (y1) and alf3 addition (y2) based on eq.(1). the fuzzy rules can be seen in table 3.the mamdani fuzzy inference is based on an implication function minimum (min) and aggregationtable 3 fuzzy rules of aluminum electrolysisinput variableoutput vari

54、ableno.electrolytetemperature (x1)superheat degree(x2)aluminum level(x3)aluminum tappingvolume (y1)alf3 addition(y2)1234 404142434445very lowvery low very low very low very high very high very high very high very high very highhighhigh high medium medium medium medium low low lowhighmedium low high low medium high low medium h