A Comparative Study of Design of Experiments and Fuzzy Inference System for Plaster Process Control

Transcription

1 Proceedgs of the World Cogress o Egeerg 07 Vol I WCE 07, July 5-7, 07, Lodo, U.K. A Comparatve Study of Desg of Expermets ad Fuzzy Iferece System for Plaster Process Cotrol P. Aegchua, ad B. Phruksapharat, Member, IAENG Abstract Tradtoal process cotrol models suppose certa put cotrol parameters, whch are ot pragmatc. They caot support ucertaty of a dustral process, whch has multfactor volved. The, the resposes of dustral process are cosstet. So, a method that ca hadle ucertaty should be appled to such problems. Desg of expermet (DOE) s oe of the most effcet methods for multfactor expermets. Aother method, called fuzzy logc s owadays a capable methodology may applcatos wth upredctablty. So, these approaches were proposed for a case study factory. k desg of expermets (DOE) was studed ad used to fd the sutable process cotrol parameters. Fuzzy Iferece System (FIS) was cosdered ad represeted by lgustc terms. The, the geerated fuzzy rules were utlzed to extract the fuzzy process cotrol parameters cotuously. The process cotrol parameters were corrected depedg o the FIS system. I ths research, both approaches were compared wth the exstg process parameters. The results dcated that the proposed FIS model acheved better performace tha DOE model for ths applcato. Idex Terms desg of expermet (DOE), fuzzy ferece system (FIS), process cotrol parameters P I. INTRODUCTION ROCESS cotrol meas the methods that are appled to cotrol process varables whe producg a product ad mata the output of a partcular process wth a requred rage. Process cotrol ca be classfed as maual or automatc. Normally, ths classfcato refers to the amout of huma effort eeded to accomplsh a commo fucto. Maual cotrol cossts of ope-loop ad feed-forward cotrol whch volve a lot of physcal adjustmets by operators. Automatc cotrol cossts of closed-loop ad feedback cotrol, whch use a feedback path that samples the output to cotrol the process automatcally []. Automatc feedback cotrol s the most commo form of cotrol. The methods to deal wth process cotrol cosst of classcal ad moder methods. The classcal cotrol methods such as ooff cotrol, proportoal tegral dervatve (PID) cotrol, Mauscrpt receved March, 07; revsed Aprl 0, 07. Prasert Aegchua s wth School of Maufacturg Egeerg, Isttute of Egeerg, Suraaree Uversty of Techology, Nakho Ratchasma, Thalad ( ; fax: ; e- mal: prasert.a@sut.ac.th). Busaba Phruksapharat s wth Departmet of Idustral Egeerg, Faculty of Egeerg, Thammasat Uversty, Ragst Campus, Pathum Tha, 0 Thalad (e-mal: lbusaba@egr.tu.ac.th). etc. are mostly cocered wth mathematcal ad costat varables. Desg of expermet (DOE) method s a crtcally mportat egeerg tool for mprovg a maufacturg process []. Applcato of DOE process cotrol wll produce formato that ca lead to process mprovemet. Referece [3] appled a desg of expermet (DOE) to predct product ad process parameters for a spray dred vacce. The moder cotrol method such as artfcal tellgece (AI) s also developed for hghly complex processes ad radom varables. Process cotrol s wdely used dustry such as power plats, petrochemcal plats, cemet plats, ad may others. Process cotrol empowers automato ad AI methods such as fuzzy logc by whch a few operators ca cotrol a complex process from a cetral cotrol room. Durg the last decade a umber of researchers have cotrbuted ther ovatos ths category. Referece [4] preseted the cosstecy stpulatos ad cotroller desg for structural ad mechacal systems expressed by fuzzy models. The applcato of support vector regresso, FIS ad adaptve euro-fuzzy ferece system (ANFIS) for cemet feess ole motorg has preseted [5]. The applcato of FIS vetory system desg has preseted [6]. Referece [7] preseted the comparso of FIS, FIS wth artfcal eural etworks ad FIS wth adaptve euro-fuzzy ferece system for vetory cotrol. May researches apply smulato for the ma study, but there are very few publcatos regardg comparatve studes, especally the comparso of DOE ad FIS for the plaster process cotrol. So, ths research proposes the comparso of the methodologes of DOE ad FIS models for predctg the target settg of process cotrol varables ad establshg the model of the pragmatc problem wth the fuzzy puts for the process cotrol maufacturg system. The process cotrol problem of a costructo materal compay Thalad was selected as a maufacturg system case study. The plasterboard producto process cossts of varous cotrol parameters ad s qute complcated to cotrol, so requres hghly expereced operators. II. SYSTEM DESCRIPTION AND APPLICATION A. System Descrpto The case study compay s a make-to-stock maufacturer that produces two types of stadard sze plasterboard ISBN: ISSN: (Prt); ISSN: (Ole) WCE 07

2 Proceedgs of the World Cogress o Egeerg 07 Vol I WCE 07, July 5-7, 07, Lodo, U.K. products, recessed edge ad square edge. I the producto process, the ma materal s plaster powder, whch s geerally produced by the calcg process. Gypsum (CaSO 4 H O) s the oldest orgac substace that has bee extesvely used costructo ad buldgs. Plaster or hem-hydrate (CaSO 4 0.5H O) s produced by grdg ad heatg gypsum at 50 degree Celsus to remove 75% of ts combed water from molecules of water to 0.5 molecules of water. The flow dagram of the plaster maufacturg process s llustrated Fg. I ths process, the atural gypsum s crushed ad fed to a vertcal roller mll (VRM). The schematc dagram of VRM s show Fg. The gypsum s groud ad dred sde the VRM to become the plaster powder. VRM s comprsed of a grdg table ad rollers stalled o the table crcumferece. The grdg table rotates wth a accurate fxed rotatoal speed aroud the vertcal axs gog through the ceter. A blower fuctos at the process vet to peumatcally covey plaster to the ext process. A classfer s stalled at the uppermost of the mll to scree the requred partcle sze. The oversze s collected the base ad retured back to the mll by bucket elevators. The plaster s segregated from the hot ar the bag house ad trasported to the storage slo for later packagg or producg plasterboard. The qualty of the plaster s tested by collectg a plaster sample at the slo to test the combed water (). The combed water dcates the percetage of water remag the chemcal bodg of plaster. Normally, combed water s tested by weghg the collected plaster sample before ad after heatg at 50 C for 5 mutes. The combed water value ca be calculated ( wo w ) (%) 00 () w where w o s the sample weght before heatg ad w s the sample weght after heatg. wll cause more effectvely grdg ad s dcated by lower roller mll motor curret ad wll result crease of combed water. Hgh feed rate of gypsum wll produce less effectve grdg ad result decrease of combed water. Lkewse, low ar crculato rate wll cause a lower quatty of groud materal to pass through the classfer ad result crease of combed water. The hgh ar crculato rate wll make a hgh quatty of groud materal pass through the classfer ad result decrease of combed water. A hgh classfer speed wll allow fe partcles to pass through t ad wll result crease of combed water. A low classfer speed wll result decrease of combed water. Hgh temperature sde the mll caused by more heat for cookg of grdg gypsum wll result decrease of combed water. The lower temperature sde the mll resultg from less heat for cookg wll result crease of combed water. Fg. The schematc dagram of vertcal roller mll (VRM). Fg. The flow dagram of plaster maufacturg process. The target for the plaster producto process, recommeded by expert s experece, s 5.8% ad the varato s cotrolled the rage 5.6% to 6.0%. Low combed water dcates too much cookg of the plaster or less water the plaster. Hgh combed water dcates uder cookg of the plaster or hgh water the plaster. The ma factors fluecg the plaster qualty are: the gypsum feed rate, ar crculato rate, the classfer operatg speed ad temperature sde the mll. Lower feed rate of gypsum B. Applcato to Desg of Expermet (DOE) Model Factoral desg was appled to scree factors that may have sgfcat effects o respose(s) because t s the most effcet avalable method for coductg multfactor expermets. The sgfcat factors ca the be used to develop a model to optmze ad predct the respose [], f eeded. The most commo factoral desg s the two level (or k ) desg. Based o the aalyss of varace (ANOVA), the sgfcat factors are determed ad used to produce the multple regresso predcto model. The multple regresso model represetato of a 4 factoral expermet ca be wrtte as: Yˆ ˆ ˆ A ˆ B ˆ ˆ C ˆ D ˆ A B ˆ 0 j j k k l l j j jk A B jck () jkl A B C D,,,...,4, j,,...,4, k,,...,4, l,,...,4 j k l whereyˆ s the respose, ˆ s the mea of all treatmet 0 combatos, ˆ, ˆ, j ˆ, k ˆ, ˆ, l j ˆ, ad ˆ are half of the jk jkl effect estmated correspodg to sgfcat effects, A, B j, C k, ad D l are coded varables that represet sgfcat ISBN: ISSN: (Prt); ISSN: (Ole) WCE 07

3 Proceedgs of the World Cogress o Egeerg 07 Vol I WCE 07, July 5-7, 07, Lodo, U.K. effects ad take o values betwee - ad +, ad s a radom error term. The radom error terms are assumed to have a ormal dstrbuto, a costat varace, ad are depedet [8]. C. Applcato to Fuzzy Iferece System (FIS) Model The prmtve structure of fuzzy ferece system model s show Fg 3. FIS cossts of three dfferet types: Mamda, Sugeo ad Tsukamoto [9]. The dstcto betwee Mamda ad Sugeo depeds o the outcome of fuzzy rules. Whle Mamda apples fuzzy sets as rule outcome, Sugeo apples lear fuctos as rule outcome. For Tsukamoto, the outcome of each fuzzy rule apples a mootocal membershp fucto. Mamda s selected for ths study. The sgfcat steps to develop FIS are: covertg crsp puts to be fuzzfed puts, fuzzfcato of the fuzzy puts, developg of the rule base ad defuzzfcato by covertg the fuzzfed output to be the crsp output value. FIS s appled may applcatos [0]-[]. Roller Blower Classfer Temperature Iput (crsp) Fuzzfcato terface (fuzzy) Kowledge base Rule base f the rules Database defes membershp Iferece system ut (Decso-makg o the rules) Fuzzy Iferece System Defuzzfcato terface (fuzzy) Fg 3. A scheme of process cotrol fuzzy ferece system. Combed Water Output (crsp) For ths study, fve data sets of the plaster grdg process from August to December of year 06 were vestgated. Each moth the process parameters cossted of 00 data. Four put parameters, roller mll curret (R ), blower hot ar flow curret (B ), classfer speed (C ) ad temperature (T ) were take as the put parameters of the proposed models. The output varable was combed water ( ). Fuzzy logc toolbox of MATLAB was mplemeted to the process cotrol fuzzy ferece system model to calculate combed water (). The process cotrol FIS model s show Fg 4. flow curret (B ), classfer speed (C ) ad temperature (T ), represeted by membershp fuctos, R, B, C ad T, respectvely, ad were set after checkg ad valdato of exstg data. Fuzzy output was combed water ( ), represeted by membershp fuctos,. The uverse of dscourse, membershps fuctos, lgustc values of each varable of fuzzy puts ad fuzzy output are dsplayed Table I. TABLE I Fuzzy Parameters Iputs Output DESCRIPTION OF FUZZY INPUTS AND FUZZY OUTPUT Varables roller mll curret (µr ) blower hot ar flow curret (µb) classfer speed (µc) temperature (µt) combed water (µ) Uverse of dscourse [Rm, Rmax] [Bm, Bmax] [Cm, Cmax] [Tm, Tmax] [m, max] Membershp fuctos Rm, R R, R, R R, Rmax Bm, B B, B, B B, Bmax Cm, c C, C, c C, Cmax Tm, T T, T, T T, Tmax m,,,, max Lgustc values * * VL = very low, L = low, M = medum, H = hgh, VH = very hgh VL, L, M, H, VH The fuzzy rule s terpreted by a order of IF-THEN, accordg to algorthms descrbg what actvty or output should be chose wth respect to the curretly otced formato. A set of fuzzy rules s developed by expert s experece or a huma beg s kowledge, based o each real codto. Ths IF-THEN rule s utlzed by the FIS to evaluate the degree to whch the put data correspods to the rule restrcto. Sce the output, combed water s fuzzy sets, a FIS of Mamda type s selected for evaluatg ad aggregatg the fuzzy rules. The IF-THEN rule ca be descrbed by Cartesa product of the fuzzy puts, x x x 3 x 4 [3]. The relatoshp betwee roller mll curret x, blower hot ar flow curret x, classfer speed x 3, temperature x 4, (IFs) ad combed water y (THEN) are descrbed by 8 rules. The fuzzy reasog of these rules creates fuzzy outputs by utlzg the max-m compostoal operato. Fuzzy combed water ( ( y )) ca be descrbed as RollerMll (3) Process Cotrol μ ( y) ( μ ( μ R R ) μ ) μ B B ) μ ) μ C C ) μ 3 ) μ 3 T T 4 4 )... )) (3) Blower (3) (mamda) 8 rules Classfer (3) (5) Temp (3) Fg 4. The process cotrol FIS model. System Process Cotrol: 4 puts, outputs, 8 rules Fuzzy puts were roller mll curret (R ), blower hot ar where s the mmum operato ad s the maxmum operato. R, B, C, T ad are fuzzy subsets represeted by the accordg membershp fuctos,.e.,,,,,. Normally, the fuzzy output s a R B C T lgustc varable whch requres to be chaged to the crsp varable durg the defuzzfcato process. For ths research, the ceter of gravty method s selected to chage the fuzzy ferece output to crsp values of combed water, y *. Defe rule umber as. The crsp values of ISBN: ISSN: (Prt); ISSN: (Ole) WCE 07

4 Proceedgs of the World Cogress o Egeerg 07 Vol I WCE 07, July 5-7, 07, Lodo, U.K. combed water are computed as y 8 * 8 y( ( y)) ( y) D. Performace Parameters for =,,..., (4) The models ca be evaluated wth the statstcal parameters: the coeffcet of determato (R ), the root mea squared error (RMSE) ad the mea absolute error (MAE) as represeted equatos (5), (6) ad (7). where R RMSE (5) y y y y y y y y (6) MAE, (7) y s the actual output. y s the predcted model output. y s the average of actual output. s the total umber of samples. Actually R has a value betwee zero ad oe ad represets the gap betwee depedet varables ad depedet varables whch terprets the varablty of the predcto. A value for R approachg oe mples a good ft of predctg model ad a value approachg zero mples a poor ft. MAE would dsclose f the results suffer from a bas betwee the predcted ad actual datasets. RMSE s a measure adapted to calculate the error betwee predcted values ad the actual values. RMSE ad MAE are postve umbers wth o upper lmt. III. RESULTS AND DISCUSSION I ths study, statstcally sgfcat factors that affect the performace of process cotrol were screeed based o the DOE techque. A k full factoral desg was appled to study the effects of four factors, roller mll curret (R), blower hot ar flow curret (B), classfer speed (C) ad temperature (T). I addto, combed water () was also used as resposes to evaluate process performace. For four factors, the desg requres 6 rus wth 3 replcates whch are totally 48 rus as show Table II. The aalyss of varace of expermetal desg shows that T are the ma factors affectg the respose (). Moreover, the results also show that the teracto RB, BC, BCT ad RBC have a sgfcat effect to ad the factor T has cotrbuted the hghest effect o the respose. The regresso model of expermet has bee formulated as the follow ad used to predct the results for comparg ISBN: ISSN: (Prt); ISSN: (Ole) wth FIS model. TABLE II 4 EXPERIMENTAL DESIGN (Replcates) Ru R B C T TABLE III THE COMPARISON OF STATISTICAL VALUES OF 5 DATA SETS Data set FIS DOE R Avg RMSE Avg MAE Avg Yˆ T 0.9 BCT (8) RB BC RBC The FIS process cotrol model of the plaster maufacturg system has bee modeled systematcally as well as wth DOE approach. The predcto of combed water of both models compared to actual values represeted that the FIS model outperformed the DOE model (as show Fg 5). The comparso of statstcal values of 5 data sets for each model s dsplayed Table III. The results have valdated wth K-fold cross valdato [4] whch was utlzed for further evaluato of the proposed models effcecy. I ths study, the total 5 data sets were dvded to 5 eve groups, ad the the trag model was executed 5 tmes by leavg oe group out at each tme for checkg the model geeralty. The rage of put data ad output data for each varable s show Table IV. The average accuracy of the models was descrbed WCE 07

5 Proceedgs of the World Cogress o Egeerg 07 Vol I WCE 07, July 5-7, 07, Lodo, U.K. by R, RMSE ad MAE as show Table V. The results showed that FIS model represeted better performace tha DOE model Actual Fg 5. The predcto of combed water of the proposed models compared to actual values. TABLE IV THE RANGE OF INPUT DATA AND OUTPUT DATA Parameters Mmum Maxmum Average SD Iput R B C T Output (FIS) (DOE) Note: SD = Stadard devato TABLE V THE K-FOLD CROSS VALIDATION RESULTS OF EACH MODEL FIS DOE R K K K K K Avg RMSE K K K K K Avg MAE K K K K K Avg IV. CONCLUSION A comparatve study of DOE model ad FIS model were doe for solvg the problem of process cotrol of the plaster maufacturg system wth ucerta codtos. Roller mll curret (R), blower hot ar flow (B), classfer speed (C), temperature (T) were puts ad combed water was the output of the system. k desg of expermet (DOE) was appled to fd the sutable process cotrol parameters. A aalyss of varace resulted that T was the ma factors affectg the respose (). Moreover, the teracto RB, BC, BCT ad RBC have a sgfcat effect to ad the FIS DOE factor T has cotrbuted the hghest effect o the respose. For FIS model, lgustc values were adapted for all fuzzy puts ad output. Fuzzy rules were desged based o the hstorcal experece of the case study plat. The results have show that FIS model acheved better performace tha the DOE model. From ths study, the predcto of combed water for plaster process cotrol of FIS model was more accurate tha the DOE model. However, FIS model requred a lot of hstorcal data ad formato from the experts. Although the DOE model performed less accurately predctg results, but t represeted the ma factors ad the teracto those have sgfcat effect to the respose. For future study, the hybrd method, whch combes of DOE model ad FIS model would be recommeded. Ths hybrd method ca use the beefcal performace of the DOE model frst step for selectg ma factors ad teracto betwee each factor. The, the FIS model ca easly utlze the secod step for predctg the process cotrol respose. REFERENCES [] D.R. Patrck, ad S.W. Fardo, Idustral process cotrol systems. New York: Delmar Publshers, Albay, 997. [] D. C. Motgomery, Itroducto to statstcal qualty cotrol. NJ: Wley, Hoboke, 03. [3] G. Kaoja, G. J. Wllems, H.W. Frjlk, G. F.A. Kerste, P. Soema, ad J.P. Amorj, A Desg of Expermet approach to predct product ad process parameters for a spray dred flueza vacce, Iteratoal Joural of Pharmaceutcs, vol. 5, pp. 098-, 06. [4] C.W. Che, Stablty codtos of fuzzy systems ad ts applcato to structural ad mechacal systems, Advaces Egeerg Software, vol. 37, pp , 006. [5] A.K. Pa, ad H.K. Mohata, Soft sesg of partcle sze a grdg process: Applcato of support vector regresso, fuzzy ferece ad adaptve euro fuzzy ferece techques for ole motorg of cemet feess, Powder Techology, vol. 64, pp , 04. [6] P. Aegchua, ad B. Phruksapharat, Ivetory system desg by fuzzy logc cotrol: A case study, Advaced Materals Research, vol. 8, pp , 03. [7] P. Aegchua, ad B. Phruksapharat, (05, September). Comparso of fuzzy ferece system (FIS), FIS wth artfcal eural etworks (FIS + ANN) ad FIS wth adaptve euro-fuzzy ferece system (FIS + ANFIS) for vetory cotrol. Joural of Itellget Maufacturg. [Ole]. pp. -9. [8] K. Kazem, B. Zhag, L.M. Lye, Q. Ca,ad T. Cao, Desg of expermet (DOE) based screeg of factors affectg mucpal sold waste (MSW) compostg, Waste Maagemet, vol. 58, pp. 07 7, 06. [9] O. Castllo, ad P. Mel. Type- fuzzy logc theory ad applcatos. Berl: Sprger-Verlag, 008. [0] R. Maa, M. Slva, R. Araujo, ad U. Nues, Electrcal vehcle modelg: A fuzzy logc model for regeeratve brakg, Expert Systems wth Applcatos, vol. 4, pp , 05. [] Z. Zhag, Q. Fag, ad X. Gu, Fuzzy ferece system based automatc Brustrom stage classfcato for upper-extremty rehabltato, Expert Systems wth Applcatos, vol. 4, pp , 04. [] L. Abdullah, Modelg of health related qualty of lfe usg a tegrated fuzzy ferece system ad lear regresso, Proceda Computer Scece, vol. 4, pp , 04. [3] E.H. Mamda ad S. Assla, A expermet lgustc sythess wth fuzzy logc cotroller, Iteratoal Joural of Ma Mache Studes,vol. 7, pp. 3, 975. [4] P.I. Good, Resamplg methods: A practcal gude to data aalyss. Brkhauser, Bosto Lucky, 999. ISBN: ISSN: (Prt); ISSN: (Ole) WCE 07