GMAW Welding Optimization Using Genetic Algorithms

Transcription

1 D. S. Correa e al D. S. Correa, C. V. Gonçalves, Sebasão S. C. Junor and V. A. Ferrares Federal Unversy of Uberlânda Faculy of Mechancal Engneerng Av. João Naves de Ávla, Uberlânda, MG. Brazl dscorrea@mecanca.ufu.br cgoncalvesa@mecanca.ufu.br sscunha@mecanca.ufu.br valarf@mecanca.ufu.br GMAW Weldng Opmzaon Usng Genec Algorhms Ths arcle explores he possbly of usng Genec Algorhms (GAs) as a mehod o decde near-opmal sengs of a GMAW weldng process. The problem was o choose he near-bes values of hree conrol varables (weldng volage, wre feed rae and weldng speed) based on four qualy responses (deposon effcency, bead wdh, deph of peneraon and renforcemen), nsde a prevous delmed expermenal regon. The search for he near-opmal was carred ou sep by sep, wh he GA predcng he nex expermen based on he prevous, and whou he knowledge of he modelng equaons beween he npus and oupus of he GMAW process. The GAs were able o locae nearopmum condons, wh a relavely small number of expermens. However, he opmzaon by GA echnque requres a good seng of s own parameers, such as populaon sze, number of generaons, ec. Oherwse, here s a rsk of an nsuffcen sweepng of he search space. Keywords: Opmzaon,GMAW, genec algorhm, weldng Inroducon The GMAW weldng process s easly found n any ndusry whose producs requres meal jonng n a large scale. I esablshes an elecrc arc beween a connuous fller meal elecrode and he weld pool, wh sheldng from an exernally suppled gas, whch may be an ner gas, an acve gas or a mxure. The hea of he arc mels he surface of he base meal and he end of he elecrode. The elecrode molen meal s ransferred hrough he arc o he work where becomes he deposed weld meal (weld bead). The qualy of he welded maeral can be evaluaed by many characerscs, such as bead geomerc parameers (peneraon, wdh and hegh) and deposon effcency (rao of wegh of meal deposed o he wegh of elecrode consumed). These characerscs are conrolled by a number of weldng parameers, and, herefore, o aan good qualy, s mporan o se up he proper weldng process parameers. Bu he underlyng mechansm connecng hen (weldng parameers and qualy characerscs) s usually no known. 1 The expermenal opmzaon of any weldng process s ofen a very cosly and me consumng ask, due o many knds of nonlnear evens nvolved. One of he mos wdely used mehods o solve hs problem s he Response Surface Mehodology (RSM), n whch he expermener res o approxmae he unknown mechansm wh an approprae emprcal model, beng he funcon ha represens called a response surface model. Idenfyng and fng from expermenal daa a good response surface model requres some knowledge of sascal expermenal desgn fundamenals, regresson modelng echnques and elemenary opmzaon mehods (Myers and Mongomery, 1995). Ths and oher echnques (such as Taguch) provde good resuls over regular expermenal regons,.e., wh no rregular pons. However, s ofen very dffcul o esablsh an arc, and mel-hrough may occur under ceran expermenal pons needed o sasfy he specfc expermenal desgn. The daa obaned may be mpossble o analyze or provde poor resuls, wha ofen forces he expermener o modfy he desgn space (Km and Rhee, 001). Therefore, s mporan o move he expermenal regon closer o he regon of neres, whch show relavely good weld qualy. Ths process s parcularly of neres when expermenaon begns far from he regon of opmal condons. The full facoral desgn Presened a COBEF 003 II Brazlan Manufacurng Congress, 18-1 May 003, Uberlânda, MG. Brazl. Paper acceped Ocober, 003. Techncal Edor: Alsson Rocha Machado can resul n opmal sengs of he weldng process parameers whou dervng a model for he weldng process. Bu as he number of he npu parameers ncreases, he number of expermens exponenally ncreases and he full facoral mehod for he problem becomes unrealsc (Km and Rhee, 001). Recenly, some arcles have red o overcome hese problems wh a new approach for expermenal opmzaon. They sugges usng Genec Algorhms (GAs) o sweep a regon of neres and selec he opmal (or near opmal) sengs o a process. The GA s a global opmzaon algorhm, and he objecve funcon does no need o be dfferenable. Ths allows he algorhm o be used n solvng dffcul problems, such as mulmodal, dsconnuous or nosy sysems. Afer he GAs have found a regular regon, furher expermenal opmzaon can be performed wh convenonal echnques, such as response surface mehodology. Some examples of hs knd of work are See e al (1996), Busacca e al (001) and Km and Rhee (001). The goal of hs arcle s o explore he GAs echnque n he deermnaon of he near-opmal GMAW process parameers, weldng volage (T), wre feed speed (F) and weldng speed (S). The search for he opmum was based on he mnmzaon of an objecve funcon, whch akes no accoun he economc aspecs (deposon effcency, d exp ) and he geomerc characerscs (peneraon, p exp, wdh, w exp, and renforcemen, r exp ) of he bead. Nomenclaure b = number of bs d = deposon effcency, % f = fness F = wre feed speed, m/mn GA = genec algorhms GMAW = gas meal arc weldng = relave o a specfc run (or expermen) Of = objecve funcon N = populaon sze p = deph of peneraon, mm pr = probably r = bead renforcemen, mm RSM = response surface mehodology S = weldng speed, cm/mn T = weldng volage, V V = varable w = bead wdh, mm Superscrps max = relave o maxmum values 8 / Vol. XXVI, No. 1, January-March 004 ABCM

2 GMAW Weldng Opmzaon Usng Genec Algorhms mn = relave o maxmum values o = relave o nal populaon Subscrps exp = relave o expermenal value = relave o arge Genec Algorhms Genec algorhms are a se of compuer procedures of search and opmzaon based on he concep of he mechancs of naural selecon and genecs. Holland (1975) made he frs presenaon of he GA echnques n he begnnng of he 60 s and furher developmen can be creded o Goldberg (1989). The GAs operae over a se of ndvduals, usually represened by a bnary srng comprsed beween 0 and 1. Ths bnary codfcaon s randomly generaed over he search space, where each ndvdual represens a possble problem soluon. When deermnng he soluon whn he search range, he genec algorhm smulaneously consders a se of possble soluons. Ths parallel processng of he algorhm may preven he convergence of one parcular local exreme pon. Anoher characersc of hese algorhms s as he GAs only use he fness value of each srng; he fness funcon does no need o be connuous or dfferenable. The GMAW weldng opmzaon procedure usng genec algorhm s shown n Fgure 1. In hs fgure, nal populaon means he possble soluons of he opmzaon problem, and each possble soluon s called an ndvdual. In hs work, a possble soluon s formed by values of he weldng volage, T o ; he wre feed speed, F o and he weldng speed, S o, whch are shown as a bnary srng. However, hey need o be changed no real numbers when beng appled o he opmzaon problem, snce he expermener ses he weldng equpmen wh real values, nsead of bnary codes. Inal populaon (T o,f o and S o ) Decodng Weldng Expermens ( p exp, d exp,w exp and r exp Fness evaluaon Selecon Crossover Muaon New populaon T, F and S Fgure 1. The GWAW weldng opmzaon procedure usng genec algorhm. Decodng s he process of changng he npu varables ha are coded as a bnary srng no a real number. The bnary codfcaon s used o represen each varable V as a b-b bnary number, whch approxmaes b dscree numbers n he range of he varables, accordng o: where: V mn V and = V max + bn1 b V max V mn (1) max V are he lower and upper bounds of he -h connuous varable and bn s an neger number beween zero and b -1. Each ndvdual, represened by he bnary srng, s ransformed no a real number by Equaon (1) and appled o he opmzaon problem. Afer decodng, he values of each ndvdual obaned (T, F and S), are used o se up he weldng expermen. Whle he expermen s beng conduced, he algorhm sands by unl he weld bead s compleed and he desred responses (p exp, d exp, w exp and r exp ) are measured. Accordng o he resuls of he weldng expermens, he fness value of he prevous weldng condon s calculaed. The fness evaluaon s a necessary procedure o decde he survval of each ndvdual. Indvduals wh large fness values are wha he user wans o maxmze. Consderng he mnmzaon of an objecve funcon, durng he evaluaon operaon, a proper fness ndex s assgned o each canddae se n such a way ha he lower he value of he objecve funcon assocaed o an ndvdual canddae, he hgher he fness ndex gven o. The responses used n hs sudy were used o make he fness funcon, Equaon (), as shown below: P p exp() d d exp() w w exp() r r exp() Of() = cp + cd + cw + cr p d w r () where: Of() - Value of he objecve funcon a he expermen; p - Targe (desrable) value for he deph of peneraon; p exp() - Expermenal value for he deph of peneraon a he expermen; d - Targe value for he deposon effcency; d exp() - Expermenal value for he deposon effcency a he expermen; w - Targe value for he bead wdh; w exp() - Expermenal value for he bead wdh a he expermen; r - Targe value for he bead renforcemen; r exp() - Expermenal value for he bead renforcemen a he expermen; cp,cd,cw and cr -Weghs ha gve dfferen saus (mporance) o each response. The responses evaluaed n hs work do no have equal mporance. The mos mporan response s he deph of peneraon, followed by he deposon effcency, bead wdh and renforcemen. In order o ranspose hese sauses o he objecve funcon, weghs were ncluded. These weghs are he values pu n fron of each response erm (0.5, 0.3, 0.1 and 0.1) respecvely. The nex sep s o use each ndvdual fness and he genec operaor (reproducon, crossover and muaon) o produce he nex generaon of he new populaon (T, F and S). The ndvdual evoluon (ha s, he problem soluon) s done by hree operaors (Goldberg,1989): J. of he Braz. Soc. of Mech. Sc. & Eng. Copyrgh 004 by ABCM January-March 004, Vol. XXVI, No. 1 / 9

3 D. S. Correa e al Selecon hs process s responsble for he choce of whch ndvdual, and how many copes of, wll be passed o he nex generaons. An ndvdual s seleced f has a hgh fness value, and he choce s based owards he fes members. Ths sudy used he based roulee wheel selecon o mae Darwn s survval of he fes heory (Goldberg, 1989). Ths selecon approach s based on he concep of selecon probably for each ndvdual proporonal o he fness value. For ndvdual k wh fness f k, s selecon probably, p k, s calculaed as follows: n p = f f (3) k k j j= 1 where n s populaon sze. Then a based roulee wheel s made accordng o hese probables. The selecon process s based on spnnng he roulee wheel n mes. The ndvduals seleced from he selecng process are hen sored n a mang pool. Crossover - hs sep akes wo srngs (parens) from he mang pool and performs a randomly exchange n some porons beween hem o form a new srng (chldren). Afer selecon, crossover proceeds n hree seps. Frs, wo srngs (referred o as parens) are seleced randomly from he mang pool. Second, an arbrary locaon (called he crossover se) n boh srngs s seleced randomly. Thrd, he porons of he srngs followng he crossover se are exchanged beween wo paren srngs o form wo offsprng srngs. Ths crossover does no occur wh all srngs, bu s lmed by he crossover rae. Muaon - n a bnary codng scheme, nvolves swchng ndvdual bs along he srng, changng a zero o one or vce-versa. Ths operaor keeps he dversy of he populaon and reduces he possbly ha he GAs fnd a local mnmum or maxmum nsead of he global opmal soluon, alhough hs s no ever guaraneed. The muaon rae s usually se a a low value o avod losng good srngs. I also provdes nformaon ha dd no exs n he nal sage. The man characersc of he GAs s ha hey operae smulaneously wh a huge se of search space pons, nsead of a sngle pon (as he convenonal opmzaon echnques). Besdes, he applcably of he GAs s no lmed by he need of compung gradens and by he exsence of dsconnues n he objecve funcon (performance ndexes). Ths s so because he GAs work only wh funcon values, evaluaed for each populaon ndvdual. The major drawback n he GAs s he large use of compuaonal effor when compared wh he radonal opmzaon mehods. Expermenal Procedure The am of hs arcle s o fnd he opmum adjuss for he weldng volage, wre feed speed and weldng speed n a GMA weldng process. The opmum adjuss are he ones ha delver he pre-seleced values of four responses: deposon effcency (100%), bead wdh (8.5 mm), deph of peneraon (5.3 mm) and renforcemen (1.5 mm). These values were developed n Correa & Ferrares (001). In oher words, he opmum parameers are hose who delver responses he closes possble of he ced values. And s assumed ha he near opmum pon s whn he followng expermenal regon, defned by he GA search ranges for T, V and S (see n he Table 1). Table 1. GA search ranges. Parameers Range Weldng volage (T), V Wre feed speed (F), m/mn Weldng speed (S), cm/mn The applcaon nvolved n hs work s he weldng of 9.5 mm hck mld seel wh a square-groove bu jon (1. mm roo openng). A sngle pass weldng process was used. The fller meal was an AWS classfcaon ER 70S-6 wh a 1. mm dameer elecrode. The sheldng gas used was 100% CO wh a 13 l/mn flow rae. Insde he expermenal space, he GAs chose, randomly, he nal weldng seup,.e., he parameers values of he frs expermen. Afer (he frs exp.) was done, s response characerscs were measured and fed no he GAs. Then, based n he prevous nformaon, he algorhm chose anoher seup, whch was done and s daa agan fed no he algorhm. The process connued unl he opmum was found,.e., unl he objecve funcon (Eq. ) reached s mnmum. The parameers of GA compuaons are shown on Table. Table. Parameers of GA compuaons. Accuracy (number of bs) 30 Populaon sze 7 Number of generaon allowed 4 Muaon rae 1 % Crossover rae 90 % Type of crossover Sngle In he GA, he populaon sze, crossover rae and muaon rae are mporan facors n he performance of he algorhm. A large populaon sze or a hgher crossover rae allows exploraon of he soluon space and reduces he chances of selng for poor soluon. However, f hey are oo large or hgh, resuls n wased compuaon me explorng unpromsng regons of he soluon space. In hs work, he populaon sze and number of generaon are small n order o manan he oal number of expermens n an accepable level. Abou he muaon rae, f s oo low, many bnary bs ha may be useful are never red. However, f s oo hgh, here wll be much random perurbaon, and he offsprng wll loose he good nformaon of he parens. The 1% value s whn he ypcal range for he muaon rae. The crossover rae s 90 %,.e., 90% of he pars are crossed, whereas he remanng 10% are added o he nex generaon whou crossover. The chosen ype of crossover was sngle, whch means ha a new ndvdual s formed when he paren genes are swapped over a some random sngle pon along her chromosome. Accuracy s he b quany for each varable. Resuls and Dscusson Table 3 presens he sengs and he resulan values of he evaluaed responses for all he expermens performed, as well as he values of he corresponden objecve funcon. 30 / Vol. XXVI, No. 1, January-March 004 ABCM

4 GMAW Weldng Opmzaon Usng Genec Algorhms Table 3. Resuls of all generaons. Run T (V) F (m/mn) S (cm/mn) p exp (mm) d exp (%) w exp (mm) r exp (mm) Objecve Funcon All he expermens performed accordng o he genec algorhm had a relavely good qualy (n he sense of lack of bead defecs) wh no problems of mel-hrough, porosy or cracks. Consderng qualy as closeness o defned arges, he genec algorhm dd no manage o acheve all he esablshed arges. The fnal value of he objecve funcon was 0.11, whch s a relavely low value (compared o s nal value) and can be consdered sasfacory weld qualy, accordng o Km and Rhee (001). And hs fnal value for he objecve funcon repeas self n he las four expermens of he Table 3 wh he same sengs, suggesng ha hs s no some random error (hs sablzaon can be beer seen n he Fgure ). Bu Table 4 shows ha he dscrepancy beween arges and obaned values was que bg for some responses, manly he bead wdh and he bead renforcemen. Objecve Funcon 5,5 5,0 4,5 4,0 3,5 3,0,5,0 1,5 1,0 0,5 0,0-0, Number of Expermens Fgure. Convergence of he genec algorhm. J. of he Braz. Soc. of Mech. Sc. & Eng. Copyrgh 004 by ABCM January-March 004, Vol. XXVI, No. 1 / 31

5 D. S. Correa e al Table 4. Comparson beween arge and obaned values. Targe Values Fnal Values Dfference (%) Deph of peneraon (mm) Deposon effcency (%) Bead wdh (mm) Bead renforcemen (mm) The dscrepancy beween arge and fnal values can no be creded o nsuffcen generaons, snce he Fgure shows a good paern of sablzaon for he objecve funcon. In addon, Fgures 3, 4 and 5 show ha he sablzaon also exss when consderng he ndvdual values of he seng parameers. The weldng volage had a mnor varaon n s las values, bu nohng sgnfcan n erms of praccal purposes. The wre feed speed and he weldng speed presened good sablzaon n her fnal values. I should be sad ha maybe a hgher populaon sze would allow a beer sweepng of he search space. An evaluaon on he nfluence of new values for he GA parameers (oher han presened n Table ) should be consdered n fuure works. Weldng Volage (V) Weldng Speed (cm/mn) 7,4 7,0 6,6 6, 5,8 5,4 5, Number of Expermens Fgure 5. Convergence of he weldng speed. The explanaon for he GA nably n accomplshng all arges can be creded o he weghs used n he objecve funcon (Equaon ). As seen, he mos mporan responses are he deph of peneraon (0.5 wegh) and he deposon effcency (0.3 wegh) and he mnmzaon process was led by hese ones. Bu a look n Table 3 reveals ha here are oher compromses avalable, such as expermen, where lower deposon effcency gves room o beer adjused bead wdh and bead renforcemen. A fnal noe on he GA opmzaon s abou s nner mechansm of random search. Fgure 6 shows he expermenal regon ha should be nvesgaed and he pons suggesed by he GA. These pons are no equally dsrbued n he search space, as n a convenonal sascal projec would be. And many of he pons are concden, whch reduces even more he swep regon. So, here s a chance of exsng non-esed pons wh even a beer compromse beween he responses Number of Expermens Fgure 3. Convergence of he weldng volage Wre Feed Speed (m/mn) Fgure 6. Search space and he pons analyzed by he GA Number of Expermens Fgure 4. Convergence of he wre feed speed. Concluson The possbly of a GMAW weldng opmzaon procedure usng genec algorhm s nvesgaed n hs work; more specfcally, he deermnaon of he near-opmal GMAW process parameers, weldng volage (T), wre feed speed (F) and weldng speed (S). The search for he opmum was based on he mnmzaon of an objecve funcon, whch akes no accoun he economc aspecs (deposon effcency) and he geomerc characerscs (peneraon, wdh and renforcemen) of he bead. I was found ha he GA can be a powerful ool n expermenal weldng opmzaon, even when he expermener does no have a 3 / Vol. XXVI, No. 1, January-March 004 ABCM

6 GMAW Weldng Opmzaon Usng Genec Algorhms model for he process. The mos mporan response (deph of peneraon) had a dfference from s arge lower han 4%. However, he opmzaon by GA echnque requres a good seng of s own parameers, such as populaon sze, number of generaons, ec. Oherwse, here s a rsk of an nsuffcen sweepng of he search space. In addon, s suggesed he use of convenonal sascal projecs o nvesgae he space around he condons found by he GA, n order o oban models and/or perform a fne-unng of he opmal parameers. References Busacca, P. G., Marseguerra, M. And Zo, E., 001, Mulobjecve Opmzaon by Genec Algorhms: Applcaon o Safey Sysems, Relably Engneerng and Sysem Safey, No. 7, pp Correa, D. S. & Ferrares, V. A., 001, Meodologa de Cuso da Não Qualdade Aplcada na Soldagem, Anas do XVI Congressso Braslero de Engenhara Mecânca, Uberlânda, Brazl. Goldberg, D. E., 1989, Genec Algorhms n Search, Opmzaon and Machne Learnng, Addson-Wesley, 435p. Holland, J. H., 1975, Adapaon n Naural and Arfcal Sysem, Ann Arbor, MI: Unversy of Mchgan Press, 406p. Km, D. and Rhee, S., 001, Opmzaon of Arc Weldng Process Parameers usng a Genec Algorhm, Weldng Journal, July, pp Myers, R. H. and Mongomery, D. H., 1995, Response Surface Mehodology, John Wley & Sons, USA, 705p. See, S., Boullar, L. and Langenhove, L., 1996, Opmsng a Producon Process by a Neural Nework/Genec Algorhm Approach, Engng. Applc. Arf. Inell., Vol. 9, No. 6, pp J. of he Braz. Soc. of Mech. Sc. & Eng. Copyrgh 004 by ABCM January-March 004, Vol. XXVI, No. 1 / 33