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Multi-objective Optimization of Welding Parameters in Submerged Arc Welding of API X65 Steel Plates
JOURNALOFIRON ANDSTEELRESEARCH,INTERNATIONAL２ ０ １ ５,２ ２( ９):８ ７ ０ Ｇ ８ ７ ８
Mu l t i Ｇ ob e c t i v eOp t imi z a t i ono fWe l d i ngPa r ame t e r si n j Subme r e dAr cWe l d i ngo fAPIX６５S t e e lP l a t e s g MAMORADPOUR, S HHASHEMI, KKHALILI
( Depa r tmen to fMe chan i c a lEng i ne e r i ng,Un i ve r s i t fB i r and,B i r and９７１７５ Ｇ ３７６,I r an) yo j j Ab s t r a c t:Subme r r cwe l d i ng ( SAW)i soneo ft he ma i n we l d i ngp r o c e s s e swi t hh i s i t i onr a t eandh i geda ghdepo gh we l d i ngqua l i t ． T h i sw e l d i n m e t h odi sex t ens i ve l edi n we l d i ngl a r Ｇ d i ame t e rga st r ansmi s s i onp i l i ne sand y g yus ge pe h i Ｇp r e s su r eve s s e l s．I nwe l d i ngo fsuchs t r uc t u r e s,t hes e l e c t i onp r o c e s spa r ame t e r sha sg r e a ti n f l uenc eont hewe l d gh ( be adge ome t r n dc o n s e u e n t l f f e c t s t h ew e l dq u a l i t ． B a s e do nF u z z l o i c a n dN S G A Ｇ I I N o n Ｇ d o m i n a t e dS o r t i n ya q ya y y g g Gene t i cAl r i t hmＧ I I)a l r i t hm,anewapp r oa chwa sp r opo s edf o rwe l dbe adge ome t r r ed i c t i onandf o rp r o c e s s go go yp , , a r a m e t e r so t i m i z a t i o n ． F i r s t d i f f e r e n tw e l d i n a r a m e t e r s i n c l u d i n e l d i n o l t a e c u r r e n ta n ds e e dw e r es e t p p gp gw gv g p t ope r f o rm SAW unde rd i f f e r en tc ond i t i onsonAPIX６５s t e e lp l a t e s．Nex t,t hede s i n e dF u z z o d e lw a su s e df o r g ym r ed i c t i ngt hewe l dbe adge ome t r l i ngo ft hep r o c e s s．Theob t a i ned me anpe r c en t agee r r o ro fpene t r a t i on p yandmode , , dep t h,we l dbe adwi d t handhe i h t f r o mt h ep r o o s e dF u z z o d e lw a s６ ０ ６％ ６ ４ ０％ a n d５ ８ ２％ r e s e c t i v e l g p ym p y． Thep r o c e s spa r ame t e r swe r et henop t imi z edt oa ch i e vet hede s i r edva l ue so fc onvex i t t r a t i oni ndexe ss imu l Ｇ yandpene t ane ous l i ngNSGAＧ I Ia l r i t hm．Asar e su l t,as e to fop t imumve c t o r s( e a chve c t o rc on t a i nscu r r en t,vo l t ageand yus go spe edwi t h i nt he i rs e l e c t edexpe r imen t a ldoma i ns)wa sp r e s en t edf o rde s i r ab l eva l ue so fc onvex i t t r a t i oni n Ｇ yandpene dexe si nt her ange so f( ０ １０６,０ １６８)and ( ０ ３５４,０ ５６１)r e spe c t i ve l i ch wa smo r eapp l i c ab l ei nr e a lc ond i Ｇ y,wh t i ons． Ke r d s:subme r r cwe l d i ng;we l dbe adge ome t r u z z og i c;mu l t i Ｇ ob e c t i veop t imi z a t i on;APIX６５s t e e l geda y;f yl j ywo
Subme r r c we l d i ng ( SAW )i soneo ft he geda mos timpo r t an tandc ommon me t hodso fwe l d i ngi n va r i ousi ndus t r i e s．The SAW i s mo s t l edf o r y us we l d i ng wi t hah i s i t i onand pene t r a t i oni n gh depo l a r t e e ls t ruc t u r e s wh i cha r esu i t ab l ef o rau t o Ｇ ges ma t i cwe l d i ng．Oneo ft he mo s timpo r t an tapp l i c a Ｇ [] t i onso fSAW i s we l d i ng o fp i l i ne１ ．Theh i pe gh manu f a c t u r i ngc o s t so fo i land ga sp i s maket he pe r ed i c t i onandc on t r o lo ft he i rwe l d i ngp r o c e s smo r e p impo r t an t． Oneo ft hema o ri nd i r e c tme t hodst ogua r an t e e j t hede s i r ed we l d i ngqua l i t st oa s s e s st hea c t ua l yi we l dbe adgeome t r o rva r i ouswe l d i ngp r oc e s Ｇ y．Asf s e s,t hewe l dbe adgeome t r sc on t r o l l edbyad us Ｇ yi j t i ng t he e f f e c t i ve pa r ame t e r s du r i ng we l d i ng r oc e s s．Thewe l dbe adgeome t r nc l ude st hedep t h p yi o f pene t r a t i on, we l d be ad he i t and we l d be ad gh wi d t h． Thec ommon me t hodsf o rad us t i ngt hei npu t j r ame t e r so f we l d i ng t o ob t a i n app r op r i a t e we l d pa be adgeome t r r emo s t l r imen t a l,o rba s edon ya yexpe
t e chn i c a lbookso rc a t a l ogs p r ov i ded byi ndus t r i a l compan i e s． Such t e chn i c a lr e commenda t i ons a r e r a lando f t endono tp r ov i dea c cur a t ei n f o rma Ｇ gene , t i onf o rd i f f e r en twe l d i ngcond i t i ons．Howeve rt he us eo fnove lme t hodsanda r t i f i c i a li n t e l l i e Ｇba s ed genc s t emsi sex t r eme l e f u lande f f e c t i vei np r ed i c Ｇ ys yus t i ng we l dbe adgeome t r o rop t imi z a t i ono fi n Ｇ yandf tpa r ame t e r si nva r i ouswe l d i ngp r oc e s s e s．S i i f Ｇ pu gn i c an te f f o r t shavebe en mader e c en t l o rp r ed i c t i ng yf we l d be ad geome t r t imi z i ng t he we l d i ng y and op [ ] r oc e s s pa r ame t e r s１Ｇ７ ．I n such r e s e a r ch, a f t e r p we l d i ngp r o c e s s mode l i ng,s i ng l e Ｇ ob e c t i v eop t imi z a Ｇ j t i on wa sc a r r i edou tt oa ch i e v ede s i r edv a l ueo fe a ch we l dbe adg e ome t r r ame t e r．Fo rexamp l e,Ta r ng ypa andYangop t imi z edt hewe l dbe adhe i t,we l dbe ad gh wi d t handt op Ｇ s i debe ad wi d t hi ng a st ung s t en a r c [ ２] ( GTA)we l d i ngp r o c e s sus i ng Taguch it e chn i que ． Us i ngr eg r e s s i onmode l,Ko l ahanand He i da r ip r ed i c Ｇ , t edde t ho fpene t r a t i on we l dbe adhe i tandwi d t h p gh i ng a s me t a la r c (GMA ) be ad Ｇ on Ｇ l a t e we l d i ng p [] r o c e s s３ ．Theya l soop t imi z edp r oc e s sva r i ab l e si n p
B i o r aphy:M． A．MORADPOUR,Ma s t e r; E Ｇma i l: mo r adpour． mamad＠yahoo． c om; Re c e i v e dDa t e:May２０,２０１４ g
I s sue９ Mu l t i Ｇ ob e c t i veOp t imi z a t i ono fWe l d i ngPa r ame t e r si nSubme r c We l d i ngo fAPIX６５S t e e lP l a t e s j gedAr
o rde rt ode t e rmi net hebe s tva r i ab l es e t sf o ranyde Ｇ s i r ed we l d be ad geome t r r ame t e r s (we l d be ad y pa he i t,wi d t handpene t r a t i on)us i ngs imu l a t edan Ｇ gh ne a l i ng a l r i t hm．Nage sh and Da t t ai nve s t i t ed go ga t heus eo fneu r a lne two rksi np r ed i c t i ng wi d t hand he i to fwe l dbe adandba ck Ｇ s i debe adi nTungs t en gh [ ４] ( ) I ne r tGa s TIG we l d i ngp r o c e s s ．Theya l s oop Ｇ t imi z edt he pr o c e s s pa r ame t e r st oa ch i evet hede Ｇ s i r edc onvex i t ndexus i nggene t i ca l r i t hm．The yi go op t imi z a t i ono fe f f e c t i ve pa r ame t e r sonl a s e rbe am be ad Ｇ on Ｇ l a t e we l d i ng wa sc a r r i ed ou t by Sa t h i p ya [ ５] andJ a l e e lus i ngg r ay Ｇ ba s edTaguch ime t hod ．The lo ft h i sop t imi z a t i onwa st oob t a i nade s i r edva l Ｇ goa ueo fdep t ho fpene t r a t i ont owe l dbe adwi d t hr a t i o． Sudhaka r anandc o Ｇwo rke r sop t imi z edt hee f f e c t i ve r ame t e r sonGTA we l d i ngp r o c e s si no r de rt oob Ｇ pa t a i nt hemax imumdep t ho fpene t r a t i ont owe l dbe ad [] wi d t hr a t i ous i nggene t i ca l r i t hm ６ ．Sa t h i go yaand co Ｇwo rke r sc a r r i edou tt he mode l i ng o fl a s e rbe am we l d i ngby me anso fneu r a lne two rksandop t imi z ed i t spa r ame t e r sf o rde s i r edva l ue so fdep t ho fpene Ｇ t r a t i on,we l dbe adwi d t handt ens i l es t r eng t hbyu Ｇ [] s i nggene t i ca l r i t hm ７ ． go Thema i nd i s advan t ageo fs i ng l e Ｇ ob e c t i veop t i Ｇ j mi z a t i oni st ha ti nde t e rmi n i nganapp r op r i a t eve c t o r o ft hewe l d i ngp r o c e s sva r i ab l e st or e a cht hede s i r ed va l ueo fonepa r ame t e ro fwe l dbe adgeome t r he y,t va l ue so fo t he rpa r ame t e r so f we l dbe ad geome t r y a r ei n o r e d ． T h i s c a nr e s u l t i nu n d e s i r e dw e l d u a l i g q Ｇ , t s edont hep r ev i ousr e s e a r ch t hec onvex i t y．Ba y i ndex ( he i tt owi d t hr a t i oo fwe l dbe ad)andpene Ｇ gh ( t r a t i oni ndex dep t ho f pene t r a t i ont o we l d be ad wi d t hr a t i o)c anbec ons i de r eda simpo r t an tf e a t ur e s o fwe l dbe adgeome t r nsuchr e s e a r ch,t heop t i Ｇ y．I mi z a t i ono f we l d i ng p r o c e s s pa r ame t e r si sc a r r i ed ou ti no r de rt o mi n imi z ec onvex i t ndexo r max i Ｇ yi mi z epene t r a t i oni ndex．Howeve r,t hesho r t c omi ng o ft he s eop t imi z a t i onsi st ha ti nad us t i ngt hewe l d Ｇ j i ngp r o c e s s pa r ame t e r st or e a cht he max imum o r mi n imumva l ueo foneo ft he s ei ndexe s,t heva l ueo f t heo t he ri ndexi si r ed．Th i sr e su l t si ni napp r o Ｇ gno r i a t eva l ue so ft hei r edi ndex,wh i chi nt u rnr e Ｇ p gno su l t si n poo rqua l i t ft he we l dbe ado ri nex t r a yo
８７１
cos t so ft hewho l ewe l d i ngp r oc e s s． Somee f f o r t shavea l r e adybe en madeon mu l t i Ｇ ob e c t i v eo t i m i z a t i o n o fd i f f e r e n t w e l d i n r o c e s Ｇ j p gp [] s e s．Fo ri ns t anc e,Pa i vae ta l．８ c a r r i ed ou tt he mu l t i Ｇ ob e c t i veop t imi z a t i ono fpu l s edga sme t a la r c j we l d i ngp r oc e s s．Mu l t i Ｇ ob e c t i v eo t i m i z a t i o n o fa j p we l d i ngp r oc e s sbyt hee s t ima t i ono ft hePa r e t oop Ｇ [] t ima ls e twa sconduc t edbyTr ev i noe ta l．９ ．Mo r e Ｇ [ [ １０] １１] , ove r Sa t he e she ta l． and Da t t ae ta l． op t i Ｇ mi z edwe l d i ngp r oc e s s e ss epa r a t e l i ng mu l t i Ｇ ob Ｇ yus e c t i veop t imi z a t i on．I nt hel a t t e rr e s e a r ch,expe r i Ｇ j men t a lr e spons e swe r et r ans f o rmedi n t ot he i ri nd i Ｇ v i dua lde s i r ab i l i t l ue s by s e l e c t i ng app r opr i a t e y va de s i r ab i l i t unc t i ont oimp r ovet he we l d qua l i t yf y． , Af t e rwa rds t he ove r a l lde s i r ab i l i t saf unc t i on ya wa sop t imi z edf i na l l t h i nt heexpe r imen t a ldo Ｇ y wi ma i nus i ngPSO ( Pa r t i c l eSwa rm Op t imi z a t i on)a l Ｇ r i t hm wh i l eSa t he e she ta l．sur veyedt heapp l i c a Ｇ go t i ono fde s i r ab i l i t unc t i onapp r oa chcomb i nedwi t h yf f uz z og i cana l i st oop t imi z et hemu l t i l equa l i t yl ys p y ( , cha r a c t e r i s t i c s be ad r e i n f o r c emen t be ad wi d t h, be ad pene t r a t i on and d i l u t i on)o fsubme r r c ged a we l d i ngp r oc e s spa r ame t e r so fSA５１６g r ade７０s t e e l ( ) bo i l e rs t e e l ． I nt hecur r en tr e s e a r ch,t heFuz z og i candda Ｇ yl t a ga t he r i ng t hr ough r e a lexpe r imen t si s us edt o r e s en tanapp r op r i a t emode lf o rp r ed i c t i ngt hewe l d p be adgeome t r nsubme r r cbe ad Ｇ on Ｇ l a t ewe l d Ｇ yi geda p i ngo fAPIX６５s t e e lp l a t e s．Fur t he rmo r e,t oob t a i n t hede s i r edva l ue sf o rbo t hconvex i t t r a Ｇ yand pene t i oni ndexe ss imu l t aneous l Ｇ ob e c t i veop t imi Ｇ y,two j z a t i ono fSAW va r i ab l e si sp r opos edandc a r r i edou t wi t hNSGAＧ I Iapp r oa ch．I nt hetwo Ｇ ob e c t i veop t i Ｇ j mi z a t i on,as e to fop t imumve c t o r si sde t e rmi nedf o r r ope rva l ue so fconvex i t t r a t i oni ndexe s p yand pene ( i ns t e ado fde t e rmi n i nganop t imumve c t o r)．
１ Exp e r imen t a lPr o c e du r e
Di f f e r en texpe r imen t swe r ec a r r i edou ton API X６５s t e e lp l a t e s．Th i ss t e e li swi de l edi nmanu Ｇ yus f a c t ur i ngo fga sando i lt r ansmi s s i onp i l i ne s．The pe chemi c a l compos i t i on and t ens i l ep r ope r t i e sa r e r e s en t edi nTab l e s１and２,r e spe c t i ve l p y．
Tab l e１ Ch emi c a lc ompo s i t i ono fAPIX６５s t e e landt a r e tv a l u e sf r om API５Ls t anda r d g
ma s s％
Con t en t
C
S i
Mn
P
S
Cr
Ni
Al
Cu
V
Ti
Nb
Te s ts t e e l
０ ０７０
０ ２１０
１ ５１５
０ ０１０
０ ００１
０ １６４
０ ０１１
０ ０３９
０ ０１６
０ ０４２
０ ０１４
０ ０４４
API５L
≤０ １６
≤０ ４５
≤１ ６５
≤０ ０２０ ≤０ ０１０
≤０ ０９
≤０ ０６
≤０ ０５
—
—
—
—
J ou r na lo fI r onandS t e e lRe s e a r ch,I n t e r na t i ona l Vo l ２２
８７２
Tab l e２ Ten s i l ep r op e r t i e so fAPIX６５s t e e land t a r e t v a l u e s f r o m A P I５ Ls t a n d a r d g Yi e l ds t r eng t h/MPaUl t ima t e st r eng t h/MPaEl onga t i on/％
Te s ts t e e l API５L
５３８
４５０—６００
６２４
５３５—７６０
３４ ２４
Toi nve s t i t et hee f f e c to fi npu tpa r ame t e r so f ga SAW onwe l dbe adgeome t r i f f e r en texpe r imen t s y,d we r ec onduc t edon５０s t e e lp l a t e so f１００mm wi d t h, , ２００mml eng t h and１４ ３０mmt h i ckne s s．I na l lex Ｇ r imen t s,t hewe l dcu r r en t( I),vo l t age ( V )and pe we l d i ngspe ed ( S)we r ec ons i de r eda st hep r oc e s s va r i ab l e s．Ot he re f f e c t i vepa r ame t e r si nSAW we r e f i xeddu r i nga l lexpe r imen t s．Thewe l dbe adgeome Ｇ , t r i n c l u d i n t h ed e t h o f e n e t r a t i o n w e l d b e a d y g p p he i tandwe l dbe ad wi d t hi si l l us t r a t edi nF i １． gh g Mo r eove r,t he we l d i ngequ i tus edi nt h i sr e Ｇ pmen s e a r chands omeo ft hewe l dedp l a t e sa r eshowni n F i e spe c t i ve l gs．２and３,r y． I no r de rt ode t e rmi net hedep t ho fpene t r a t i on, a l lp l a t e swe r ecu tandpo l i sheda f t e rwe l d i ng．The c r os ss e c t i ons o ft he po l i shed p l a t e s we r et hen e t chedi n３％ n i t a l．Ac a l i rwi t h０ ０５mma c cur a Ｇ pe cy wa sus ednex tt o me a su r et he we l dbe adhe i t gh ( H ),we l dbe ad wi d t h( W )anddep t ho fpene t r a Ｇ t i on ( D)．Theus edexpe r imen t a le l emen t sa r epr e s Ｇ , en t edi nTab l e３．Al s ot heme a su r edwe l dbe adpa Ｇ r ame t e r sa r eg i veni nTab l e４．
F i １ We l db e adg e ome t r g y
F i ２ Subme r e da r cwe l d i ngequ i tu s e di nt h i sr e s e a r ch g g pmen
F i ３ Pho t o r apho ft h ewe l d e dp l a t e s g g Tab l e３ Di f f e r en te l emen t su s e di ns ubme r e d g a r cwe l d i ngo fp l a t e s
Pa r ame t e r P l a t e
El e c t r ode F l ux
Us edt ype
APIX６５s t e e l
S２MO ( Di ame t e r３ ２mm) ( AWSA５ ２３,EN７５６,EN１２０７０)
AMA OP１３９ ( AWSA５ １７ & A５ ２３,DIN３２５２２ & DIN EN７６０)
２ Pr opo s e dFu z z e l y Mod I nt h i sr e s e a r ch,Fuz z og i ct oo l boxo fMATＧ yl LABso f twa r ei sus edt o mode lt hesubme r r c geda be ad Ｇ on Ｇ l a t e we l d i ngp r oc e s sandt op r ed i c t we l d p be adgeome t r nt h i sFuz z t em,f o rc l a s s i f i c a Ｇ y．I ys ys , , t i ono fcur r en t vo l t ageandspe ed e a chl eve lo f t he s epa r ame t e r s( i nc l ude４００,４５０,５００,５５０and ６００Af o rcur r en t,３０,３２,３４and３６Vf o rvo l t age , / ) and３６ ４６and４９cm mi nf o rwe l d i ngspe ed a r es e Ｇ l e c t edt oc en t e ro fas e t．Asar e su l t,t henumbe ro f Fuz z e t sus edf o rc l a s s i f i ng o fcur r en t,vo l t age ys y andwe l d i ngspe edi scons i de r ed５,４and３,r e spe c Ｇ t i ve l so,a c co rd i ngt oagg r ega t i oni n t e r va l so f y．Al ou t tda t a po i n t s,we l d be ad wi d t h,he i tand pu gh t r a t i ona r ec l a s s i f i edt o１２,９and１０s e t s,r e Ｇ pene spe c t i ve l y． I nFuz z l i ng,t hei npu tandou t tva r i a Ｇ y mode pu [ １２] b l e sa r ea l so known a sl i ngu i s t i c va r i ab l e s ． Thus,Fuz z unc t i onsa r eus edt ode f i nel i ngu i s t i c yf va l ue sanda s s i he membe r sh i r e e st oi npu t gnt pdeg andou t u t a r a m e t e r s ．T h e G a u s s i a nf u n c t i o ni s p p us edf o rcur r en tandvo l t agebe c aus eo fi t ssmoo t hＧ ne s s．TheTr ape z o i da lf unc t i oni sus edf o rwe l d i ng spe ed．He r e,t r ape z o i da lf unc t i oni sus edbe c aus ei t cove r smo r er ang e so ft hewe l d i ngs e e da sc omp a r e d p t oc ommonmemb e r s h i un c t i on s．Al s o,t het r i angu l a r pf
I s sue９ Mu l t i Ｇ ob e c t i veOp t imi z a t i ono fWe l d i ngPa r ame t e r si nSubme r c We l d i ngo fAPIX６５S t e e lP l a t e s j gedAr Tab l e４ Exp e r imen t a lda t aba s e Te s t No．
Pr o c e s spa r ame t e r
I/A
V/V
１
４００
３０
３
５００
３０
２ ４ ５ ６ ７ ８ ９
１０ １１ １２ １３ １４ １５ １６ １７ １８ １９ ２０ ２１ ２２ ２３ ２４ ２５ ２６ ２７ ２８ ２９ ３０ ３１ ３２ ３３ ３４ ３５ ３６ ３７ ３８ ３９ ４０ ４１ ４２ ４３ ４４ ４５ ４６ ４７ ４８ ４９ ５０
４５０ ５５０ ６００ ４００ ４５０ ５００ ５５０
６００ ４００ ４５０ ５００ ５５０ ６００ ４００ ４５０ ５００ ５５０ ６００ ４００ ４５０ ５００ ５５０ ６００ ４００ ４５０ ５００ ５５０ ６００ ４００ ４５０ ５００ ５５０ ６００ ４００ ４５０ ５００ ５５０ ６００ ４００ ４５０ ５００ ５５０ ６００ ４００ ４５０ ５００ ５５０ ６００
３０ ３０ ３０ ３２ ３２ ３２ ３２
３２ ３４ ３４ ３４ ３４ ３４ ３６ ３６ ３６ ３６ ３６ ３０ ３０ ３０ ３０ ３０ ３２ ３２ ３２ ３２ ３２ ３４ ３４ ３４ ３４ ３４ ３６ ３６ ３６ ３６ ３６ ３０ ３０ ３０ ３０ ３０ ３２ ３２ ３２ ３２ ３２
S/ ( cm∙mi n－１)
Me a sur emen t so fwe l d be adgeome t r y/mm
D
W
H
３６
４ ９０
１５ ７０
２ ４０
３６
６ ００
２０ ００
２ ４５
３６ ３６ ３６ ３６ ３６ ３６ ３６
３６ ３６ ３６ ３６ ３６ ３６ ３６ ３６ ３６ ３６ ３６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４９ ４９ ４９ ４９ ４９ ４９ ４９ ４９ ４９ ４９
５ ７５ ７ ８０ ９ ３０ ４ ７５ ６ ９０ ５ ００ ８ ４０
９ １５ ４ ７０ ６ ６５ ５ ２５ ８ ３５ ８ ２０ ５ １０ ５ １０ ６ ８０ ７ ００ ７ ８５ ３ ６０ ５ １０ ５ ６０ ５ ９０ ７ ２０ ３ ３０ ４ ５５ ５ ２０ ６ ００ ６ ８０ ５ ０５ ４ ６０ ６ ００ ７ ５０ ７ ３０ ５ ００ ５ ６０ ６ ３５ ６ ５０ ７ ３０ ４ ２５ ５ ７０ ６ ６０ ７ ０５ ８ ６０ ５ ４０ ６ １０ ７ １０ ６ ９０ ８ ２０
１７ ７０ ２１ １０ １８ ３０ １７ ３５ １７ ４０ １７ ３０ １８ ５０
２０ ３０ １６ ００ １９ ４５ １８ ４５ １９ ７０ ２２ ５５ １６ ３０ １９ ００ １９ ６０ ２２ ６５ ２３ ２５ １２ ５０ １２ ４５ １３ ９０ １３ １０ １３ ２０ １０ １０ １２ ３０ １２ ７０ １２ ３０ １４ ００ １０ ８０ １１ ９０ １４ ０５ １５ ００ １３ ７５ １１ ３５ １３ ００ １４ ５５ １４ ３０ １４ ７０ １２ ７０ １５ ７０ １６ ００ １８ ００ １７ ４５ １３ ６０ １４ ９０ １５ ５０ １７ １０ １８ ５５
２ ４０ ３ ２０
f unc t i onsi sus edf o rpene t r a t i ondep t h,we l dbe ad he i tandwi d t hbe c aus eo fi t ss imp l i c i t r e c i Ｇ gh yandp s i oni nde t e rmi n i ngt heva l ueo ft heou t u t a r a m e Ｇ p p t e r s．Thec l a s s i f i edi npu tandou t tpa r ame t e r sand pu t he u t i l i z ed membe r sh i unc t i ons a r e shown i n pf , F i s ４－９． A l s o t h ed i f f e r e n t l i n u i s t i cv a l u e sa n d g g t he i rFuz z n t e r va l sa r eshowni nTab l e５． yi
３ ４０ ２ ６０ ２ ３５ ２ ９０ ３ １５
３ ７０ ２ ７０ ２ ９０ ２ ２０ ２ ３５ ２ ５０
F i ４ Cu r r en tmemb e r s h i unc t i on s g pf
２ ５０ ２ ５５ ３ ２５ ３ ４５ ２ ６５ ２ １０ ２ ２０ ２ ３０ ２ ００ ２ ４０ ２ ４０ ２ ４０
F i ５ Vo l t a ememb e r s h i unc t i on s g g pf
２ １０ ２ ２０ ２ ５０ ２ ２０ ２ ２５ ２ ５０ ２ ７０ ２ ４５ ２ １０ ２ ６０ ２ ４０ ２ ５０
F i ６ Sp e e dmemb e r s h i unc t i on s g pf
２ ９０ ２ ４０ ２ ３０ ２ ８０ ２ ６５ ３ １０ ２ ５０ ３ １５ ３ １５ ２ ７５ ３ ３０
８７３
F i ７ Pen e t r a t i onmemb e r s h i unc t i on s g pf
８７４
J ou r na lo fI r onandS t e e lRe s e a r ch,I n t e r na t i ona l Vo l ２２
e l)we r ef edi n t o Fuz z l．Thep r ed i c t ed pa Ｇ y mode r ame t e r sby t h i s mode l we r et hencompa r ed wi t h t hos er e su l t i ngf r om p r a c t i c a lexpe r imen t s．Theob Ｇ t a i nedr e su l t sf o rwe l dbe adgeome t r r omt het e s t yf da t aandt her e su l t ed pe r c en t agee r r o rf r om e a ch r ed i c t i ona r eshowni n Tab l e８．Theave r agepe r Ｇ p , c en t agee r r o ro fdep t ho f pene t r a t i on we l d be ad wi d t handhe i tf r omt hede s i z la r e gh gnedFuz y mode , , ６ ０６％ ６ ４０％ and５ ８２％ r e spe c t i ve l y． F i ８ Be adwi d t hmemb e r s h i unc t i on s g pf
Tab l e５ I npu tandou t tv a r i ab l e swi t ht h e i rf u z z a l u e s pu yv Sys t em va r i ab l e
I npu t s
L i ngu i s t i c va r i ab l e
Cur r en t
L i ngu i s t i cva l ue Ve r ow yl
４２２ ０－４７８ ０
Hi gh
５２２ ０－５７８ ０
Med i um
I no r de rt oe s t ab l i shFuz z l e si nt hede s i yru gned Fuz z t em,t heknowl edgeob t a i nedf r om p r a c t i Ｇ ysys c a lexpe r imen t si sus ed．I nt o t a l,３８s e t so fda t a r e s en t edi n Tab l e４ a r echo s en r andoml r om p y,f wh i cht heFuz z l e sa r ee s t ab l i shed．The１２r e Ｇ yru ma i nedda t as e t sa r eus edt ot e s tt hep r opo s edmod Ｇ e l． Af t e r da t ac l a s s i f i c a t i on, s ome ou t t da t a pu i n t smaybel o c a t edi nt heove r l apr ange so fs e t s． po I tr e su l t si np r oduc i ngs omeru l e sf o ron l e to f yones da t a．Asar e su l t,t henumbe ro fru l e sp r oduc edf o r mode l i ngt hesubme r r cbe ad Ｇ on Ｇ l a t e we l d i ng geda p , i s１３３byus i ng３８s e t so fda t a．I nTab l e６ s omeo f t he s eru l e sa r edemons t r a t ed． I nt h i sr e s e a r ch,Mamdan i ′ si n f e r enc eeng i nei s , us ed．Af t e r en t e r i ng i n f e r enc e eng i ne t hei npu t Fuz z l ue sa r et u rnedi n t oFuz z t t sbyap Ｇ yva you pu l i ng Fuz z l e s． F i na l l z t t sa r e p y y ru y, Fuz y ou pu changedi n t onume r i c a lva l ue so fpene t r a t i ondep t h,
we l dbe ad wi d t handhe i tby me anso fCen t r o i d gh de f uz z i f i c a t i ont e chn i he va r i ous de Ｇ que．Among t f uz z i f i c a t i ont e chn i sava i l ab l ei nFuz z og i ct oo l Ｇ que yl box,t he Cen t r o i dde f uz z i f i c a t i ont e chn i e su l t s quer i n mi n imum ave r ageva l ueo fpe r c en t agee r r o rf o r r ed i c t i on ( Tab l e７)． p I no r de rt oob t a i nt hec apab i l i t fFuz z l yo y mode i np r ed i c t i on o f we l d be ad geome t r heave r age y,t r c en t agee r r o r wa sc a l cu l a t ed．To pe r f o rm t h i s, pe , t heva l ue so fcu r r en t vo l t ageandwe l d i ngspe edi n １２s e r i e so fda t a( r andoml s ent ot e s tt hemod Ｇ ycho
Spe ed
５７５ ０－６２５ ０
Low med i um
３０ ７－３３ ２
Hi i um ghmed Low
２９ ０－３１ ０
３２ ７－３５ ２
３５ ０－３７ ０
２７ ０－４５ ０
Med i um
４４ ０－４８ ０
Ve r r ow ( VVL) yve yl Ve r ow ( VL) yl
２ ７５－４ ２５
Hi gh
Low ( L)
Ou t t s Pene t r a t i on pu
４７２ ０－５２８ ０
Ve r i yh gh
Hi gh
F i ９ Be adh e i tmemb e r s h i unc t i on s g gh pf
３７５ ０－４２５ ０
Low
Low
Vo l t age
Fuz z n t e r va l yi
Low med i um ( LM) Med i um１ (M１)
Med i um２ (M２) Hi i um (HM) ghmed
４７ ０－５１ ０
２ ００－３ ２７
３ ７５－５ ２５
４ ７５－６ ００ ５ ７５－６ ２５
６ ００－７ ２５
６ ７５－８ ２５ Hi ７ ７５－９ ２５ gh (H) Ve r i VH) ８ ７５－１０ ２５ yh gh ( Ve r r i VVH) ９ ７５－１１ ００ yve yh gh ( Ve r r r ow ( VVVL)８ ００－１２ ００ yve yve yl Ve r r ow ( VVL) yve yl ( Ve r ow VL) yl
Wi d t h
Low ( L) Low med i um ( LM) ( Med i um１ M１)
Med i um２ (M２) Hi i um (HM) ghmed
１１ ５０－１２ ５０
１２ ００－１３ ２５
１２ ７５－１４ ２５ １３ ７５－１５ ２５ １４ ７５－１６ ２５ １５ ７５－１７ ２５
１６ ７５－１８ ２５ Hi １７ ７５－１９ ２５ gh (H) Ve r i VH) １８ ７５－２０ ２５ yh gh ( Ve r r i VVH) １９ ５０－２２ ００ yve yh gh ( Ve r e r e r i VVVH)２０ ７５－２４ ７５ yv yv yh gh ( Ve r r ow ( VVL) yve yl ( Ve r l o w V L) y
He i t gh
Low ( L) Low med i um ( LM) Med i um (M)
Hi i um (HM) ghmed Hi gh (H)
Ve r i VH) yh gh ( Ve r r i VVH) yve yh gh (
１ ８０－２ ２０ ２ ００－２ ５０
２ ３０－２ ７０
２ ５０－３ ００ ２ ８０－３ ２０
３ ００－３ ５０
３ ３０－３ ７０ ３ ５０－４ ００
３ ８０－４ ２５
I s sue９ Mu l t i Ｇ ob e c t i veOp t imi z a t i ono fWe l d i ngPa r ame t e r si nSubme r c We l d i ngo fAPIX６５S t e e lP l a t e s j gedAr
８７５
Tab l e６ As amp l eo ff u z z u l e sp r odu c e dt omod e lt h ewe l d i ngp r o c e s so fp l a t e s yr Ru l eNo．
Ru l e s ( Cur r en ti sMed i um)( Vo l t agei sLow)( Spe edi sLow)t hen ( Pene t r a t i oni sM１)(Wi d t hi sVVH)(He i ti sVL) gh ( )( )( ) ( )( )( Cur r en ti sMed i um Vo l t agei sLow Spe edi sLow t hen Pene t r a t i oni sM１ Wi d t hi sVVH He i ti sL) gh
１ ２
( Cur r en ti sHi Vo l t agei sLow)( Spe edi sLow)t hen ( Pene t r a t i oni sMH)(Wi d t hi sVVH)(He i ti sH) gh)( gh ( )( )( ) ( )( )( Cur r en ti sVe r Ｇh i l t agei sLow Spe edi sLow t hen Pene t r a t i oni sH Wi d t hi sMH He i ti sML) y gh Vo gh ( )( )( ) ( )( )( Cur r en ti sLow Vo l t agei sLowＧmed i um Spe edi sLow t hen Pene t r a t i oni sM２ Wi d t hi sM２ He i ti sVL) gh
３
４
５
( Cur r en ti sLow)( Vo l t agei sLowＧmed i um)( Spe edi sLow)t hen ( Pene t r a t i oni sMH)(Wi d t hi sMH)(He i ti sVL) gh ( Cur r en ti sMed i um)( Vo l t agei sLowＧmed i um)( Spe edi sLow)t hen ( Pene t r a t i oni sML)(Wi d t hi sMH)(He i h t sVL) g i ( )( )( ) ( )( )( Cur r en ti sVe r Ｇ l o w V o l t a e i sH i h Ｇ m e d i u m S e e d i sL o w t h e n P e n e t r a t i o n i sL W i d t h i sM １ H e i h t i y g g p g sL)
６
７
８
( Cur r en ti sVe r Ｇh i Vo l t agei sHi Ｇmed i um)( Spe edi sLow)t hen ( Pene t r a t i oni sMH)(Wi d t hi sVVVH)(He i ti sVL) y gh)( gh gh ( )( )( ) ( )( )( ) Cur r en ti sVe r Ｇ l o w V o l t a e i sH i h S e e d i sL o w t h e n P e n e t r a t i o n i sML W i d t h i sM １ H e i h t i sL y g g p g
９
１０
Tab l e７ Pe r c en t a ee r r o ro fFu z z e lp r e d i c t i on g ymod wi t hd i f f e r en td e f u z z i f i c a t i onme t hod s No． １
De f uz z i f i c a t i on me t hod
Me anpe r c en t agee r r o r /％ o fFuz z l ymode
B i s e c t o r
１５ ５４
Lom
１８ ３３
Cen t r o i d
２ ３
６ ０９
Mom
４ ５
→
f ＝ [ f１( x), x),．．．, x)] ∈ F, f２( fm (
１６ ４９
Som
Me a sur edby /mm ope r a t o r
D
W
H
１３ ０６
Pr ed i c t edbyFuz z r c en t agee r r o r y Pe mode l o fp r ed i c t i on/％
D
W
H
D
W
H
２
５ ７５ １７ ７０ ２ ４０ ６ ２９ １８ ３０ ２ ３５ ９ ６９ ３ ３８ ２ ０８
１７
５ １０ １９ ００ ２ ５５ ５ ６２ １８ ００ ２ ４７ １０ １９ ５ ２６ ３ １３
１０ １８ ２３ ２７ ２９ ３１ ３５ ３９ ４３ ５０
→
９ １５ ２０ ３０ ３ ７０ ８ ２８ ２１ ２０ ３ ３０ ９ ５０ ４ ４３ １０ ８１ ６ ８０ １９ ６０ ３ ２５ ６ ３２ ２１ ００ ２ ７９ ７ ０５ ７ １４ １４ １５ ５ ６０ １３ ９０ ２ ３０ ５ ４１ １１ ３０ ２ １７ ３ ３９ １８ ７０ ５ ６５ ４ ５５ １２ ３０ ２ ４０ ４ ７１ １２ ００ ２ ３７ ３ ５１ ２ ４３ １ ２５ ６ ００ １２ ３０ ２ ２０ ６ １１ １４ ２０ ２ ４０ １ ８３ １５ ４４ ９ ０９ ５ ０５ １０ ８０ ２ ２０ ４ ３８ １０ ９０ ２ ２８ １３ ２６ ０ ９２ ３ ６３ ７ ３０ １３ ７５ ２ ４５ ７ ０９ １４ ９０ ２ ４７ ２ ８７ ８ ３６ ０ ８１ ６ ５０ １４ ３０ ２ ５０ ７ ０１ １４ ６０ ２ ４７ ７ ８４ ２ ０９ １ ２０ ６ ６０ １６ ００ ２ ８０ ６ ６０ １６ ４０ ２ ８２ ０ ００ ２ ５０ ０ ７１
８ ２０ １８ ５５ ３ ３０ ７ ９２ １７ ４０ ２ ７３ ３ ４１ ６ １９ １７ ２７
３ Mu l t i Ｇ ob e c t i v eOp t imi z a t i on j Thec onc ep to f mu l t i Ｇ ob e c t i veop t imi z a t i oni s j ba s edont hef a c tt ha tmanyr e a l Ｇwo r l dop t imi z a t i on r ob l emsi nvo l ves imu l t aneousop t imi z a t i ono fmu l Ｇ p t i l eo b e c t i v e sw h i c ha r eo f t e n i nc o n f l i c tw i t he a c h p j o t he r．I n mu l t i Ｇ ob e c t i veop t imi z a t i onc a s e s,t he r e j mayno tbeones o l u t i on wh i chi sop t ima lwi t hr e Ｇ , spe c tt oa l lob e c t i v e s r a t h e r t h e r e a r e a s e t o f s o l u Ｇ j t i onswi t ha l t e rna t i vet r ade Ｇ o f f swhena l lob e c t i ve s j a r econs i de r ed．The s es e to fs o l u t i onsa r eknowna s [ １３] Pa r e t o Ｇ op t ima ls o l u t i ons ． De f i n i t i on １ (Mu l t i Ｇ ob e c t i ve op t imi z a t i on): j Thema i ngoa lo fmu l t i Ｇ ob e c t i veop t imi z a t i oni st o j → ∗ ∗ ∗ ∗ x２ ,．．．, xn ] t o f i ndve c t o rx ＝ [ x１ ,
( １)
st heob e c t i v ev e c t o r;Er xi st hed e c i s i onv e c t o r;fi e Ｇ j ; e no t e s r e s e n t sc on s t r a i n t si np r ob l em and X andF d p [ １４] d e c i s i ons a c eandob e c t i v es a c e,r e s e c t i v e l p j p p y ． De f i n i t i on２ ( Pa r e t oDomi nanc e):Fo ranytwo → → → , , ti ss a i dt ha tu domi Ｇ ob e c t i veve c t o r s uandv i j → → → na t e sv ( fandon l f u＜v)i yi , , ∀j ∈ { １,． ． ． ． ． m} : uj ≤vj ∧ ∃j ∈ { １,． m} : ( uj ＜vj ２) Ac co rd i ngt o Pa r e t o domi nanc e,t he de c i s i on →
Tab l e８ Re s u l t so fwe l db e adg e ome t r r e d i c t i on s yp byFu z z e lf o rt e s tda t a ymod P l a t e No．
mi nf( x)＝ { f１( x), x),．．．, x)} f２( fm ( wi t hr e spe c tt o E( x)＝ {e１( x), e２( x),．．．, ek( x)} ≤０ → , , , , whe r e x ＝ [ x１ x２ ．．．xn ] ∈ X,
→
→
→ → ve c t o radomi na t e sde c i s i onve c t o rb ( a＜b)i fand →
→
→
on l ff ( a)＜f ( b)． yi De f i n i t i on３ (Pa r e t o op t ima l i t c i s i on y): A de ve c t o rx∈Xi ss a i dt ha ti snon Ｇ domi na t edr ega rd i ng fandon l f t oas e tS⊆Xi yi ( The r edoe sno tex i s t s∈S:s≺x． ３) , , snon Ｇ domi n a t e dr e a r d i ngt oX i ti s Al s oi fxi g s a i dt ha txi sPa r e t o Ｇ op t ima l．Mo r e ov e r,as e to fd e c i Ｇ s i onv e c t o r st ha ti snon Ｇ domi n a t e dr e a r d i ngt o X,i s g , knowna sPa r e t o Ｇ op t ima ls e t andt hec o r r e s i ngob Ｇ pond →
e c t i v ev e c t o r sa r eknowna sPa r e t o Ｇ op t ima lFr on t． j Toso l ve mu l t i Ｇ ob e c t i veop t imi z a t i onpr ob l ems j (MOPs),manyevo l u t i ona r l r i t hmsp r opos edi n ya go [ １５ Ｇ １６] t hel i t e r a t ur e sr e c en t l ．Howeve r,i nt h i spa Ｇ y r,t heNon Ｇ domi na t edSo r t i ngGene t i cAl r i t hmＧ pe go [ ] I I( NSGAＧ I I)pr opos edbyDeb１７ i sus edf o ri t sr o Ｇ [ ] bus t ne s sandpopu l a r i t nso l v i ng MOPs１８ ． yi
３ １ Non Ｇ domi na t e ds o r t i ngg ene t i ca l o r i t hmＧ I I g ３ １ １ Non Ｇdomi na t eds o r t i ng Tocompa r et heso l u t i onsa c co rd i ngt ot hedomＧ i nanc econc ep t,e a chso l u t i oni scompa r ed wi t ha l l , o t he rso l u t i ons．Then t hes e to fso l u t i onsno tdomＧ i na t edbyanyso l u t i oni sdeno t eda st heso l u t i onso f
８７６
J ou r na lo fI r onandS t e e lRe s e a r ch,I n t e r na t i ona l Vo l ２２
t hef i r s tPa r e t oFr on t( r ank＝１)．Thes amep r oc e Ｇ dur ei sapp l i edt ot her e s to fs o l u t i onst ode t e rmi ne t hes e c ondPa r e t oFr on t( r ank＝２)．Th i sp r o c edur e con t i nuedt i l la l ls o l u t i onst obec l a s s i f i edt ot hePF１ t oPFP Pa r e t oFr on t s,andt henumbe ro ft hePa r e t o Fr on tt ha ti sa s s i n e dt oas o l u t i o nd e t e r m i n e st h e g Pa r e t o domi nanc er ank o ft ha ts o l u t i on．F i １０ g showsanexemp l a rs e to fs o l u t i onsi ntwod imen Ｇ ( s i ona l ob e c t i ve spa c e c l a s s i f i ed i n t o ３ Pa r e t o j Fr on t sPF１ ,PF２ andPF３)．
F i １０ Pa r e t oFr on t sf o rane x emp l a rs e to fs o l u t i on s g
３ １ ２ Cr owdi ngdi s t anc efac t o r Thec r owd i ngd i s t anc ei sadens i t s t ima t i ono f ye so l u t i ons su r r ound i ng a pa r t i cu l a rs o l u t i on． The c r owd i ngd i s t anc e( f o rapa r t i cu l a rs o l u t i oni nanon Ｇ domi na t eds e t)i sde t e rmi ned byt heave r ages i de l eng t ho facubo i d( who s eve r t i c e sa r et head a c en t j so l u t i onso ft ha tpa r t i cu l a rs o l u t i on wi t hr e spe c tt o e a ch ob e c t i ve f unc t i on)． F i １１ shows cubo i d j g wh i chi sf o rmedbyad a c en to fs o l u t i oni．Thepe r Ｇ j ime t e ro ft h i scubo i di sp r opo r t i ona lt oc r owd i ng d i s t anc eo fs o l u t i oni．I ti swo r t hno t i ngt ha tani n Ｇ f i n i t eva l uea st hec r owd i ngd i s t anc eva l uea s s i o gnst t heex t r emes o l u t i ons ( t hes o l u t i on wi t hh i s t ghe va l ueandt hes o l u t i onwi t hsma l l e s tva l uer ega rd i ng t oe a chob e c t i vef unc t i on)i nanon Ｇ domi na t eds e t． j
F i １１ Cr owd i nge s t ima t i onf o rt h es o l u t i oni g
３ １ ３ Impl emen t a t i onof NSGAＧ II Thef i r s ts t ep o f NSGAＧ I Iimp l emen t a t i oni s i n i t i a l i z a t i on．I nt h i ss t ep,ar andom pa r en tpopu l a Ｇ
t i onP０i sc r e a t ed．Fo rt h i sr e a son,r andom va l ue s c i s i onve c t o r st opa r en tt he a r ea s s i ot heN de gnedt nex tgene r a t i on．Co r r e spond i ngob e c t i veva l ue sa r e j ( c a l cu l a t edandt he popu l a t i oni sso r t ed ba s ed on non Ｇ domi na t edso r t i ngandc r owd i ngd i s t anc eva l ue f o re a chnon Ｇ domi na t eds e t)． ( １) Ma i nl oopo fNSGAＧ I I Thema i nl oopo fNSGAＧ I Is t a r t swi t ht heva r i Ｇ a t i oni nt hepopu l a t i on．Theb i na r ournamen ts e Ｇ yt l e c t i oni sus edt os e l e c tpa r en t sf r om Pt．Byapp l Ｇ y i ng mu t a t i onandc r os sove rope r a t o r st ot hos epa r Ｇ , r ec r e a t ed． en t so f f spr i ngpopu l a t i onQ０ o fs i z eN a Bycomb i n i ngPt wi t hQt,t hepopu l a t i ons i z ewi l lbe ti sne c e s s a r ochoos e N so l u t i onsf r om２N ２N ．I yt ( so l u t i ont of o rm t henex tpopu l a t i on Pt＋１ )．Fo r t h i sr e a son,non Ｇ domi na t edso r t i ng app l i e st ot he cur r en t popu l a t i on,andso l u t i onsen t e ri nt ot he nex tpopu l a t i onba s edont he i ro rde ro fPa r e t odomi Ｇ nanc er ank．I ft heen t r anc eo fas e to fso l u t i onswi t h oexc e edN ,t r t i cu l a rr ankl e adsPt＋１t heso l u t i ons pa ( o ft ha ts e t wi t hh i rc r owd i ngd i s t anc eva l ue)i s ghe chos ent o bet he membe ro f Pt＋１ andt her e s to f t hema r er emoved．Thema i nl oopo fNSGAＧ I Icon Ｇ t i nue sun t i las t opp i ngc r i t e r i oni sme t．Th i spr oc e Ｇ [ ] dur ei sshowni nF i １２１８ ． g
F i １２ Imp l emen t a t i ono fNSGAＧ I I g
( ２)B i na r ournamen ts e l e c t i on yt Theb i n a r ou r n ame n ts e l e c t i oni su t i l i z e dbyNS Ｇ yt GAＧ I Ia st hes e l e c t i onf o rv a r i a t i ons t a e ． F o r t h i sr e a Ｇ g s on,twos o l u t i on sa r ep i c ke dr andoml r om c u r r e n t yf o u l a t i o n ．T h es o l u t i o nw i t hb e t t e rP a r e t od o m i n a n c e pp r anki ss e l e c t e d．I ft hetwos o l u t i on ss ha r et hes amePa Ｇ r e t or ank,s o l u t i onwi t hh i rc r owd i ngd i s t an c ev a l u e ghe i ss e l e c t e d．I fbo t hs o l u t i on ss ha r et hes ame Pa r e t o domi n an c er ankandt hes amec r owd i ngd i s t an c ev a l u e, on eo ft hemi ss e l e c t e dr andoml y．
３ ２ Mu l t i Ｇ ob e c t i v eop t imi z a t i ono fwe l d i ngpr o c e s s j r ame t e r s pa I nt h i spape r,t he NSGAＧ I Ia l r i t hmi sus ed go
I s sue９ Mu l t i Ｇ ob e c t i veOp t imi z a t i ono fWe l d i ngPa r ame t e r si nSubme r c We l d i ngo fAPIX６５S t e e lP l a t e s j gedAr
f o rt he mu l t i Ｇ ob e c t i veop t imi z a t i ono ft hep r o c e s s． j Thec onvex i t ndex ( he i tt o wi d t hr a t i oo fwe l d yi gh be ad)and pene t r a t i oni ndex ( t r a t i ondep t ht o pene we l dbe ad wi d t hr a t i o)a r ec ons i de r eda sob e c t i ve j f unc t i ons．Thewe l d i ngcu r r en t,vo l t ageandspe ed a r ec on s i d e r e da sd e c i s i onv a r i a b l e s．Fo rt h eph a s eo f i n i t i a l i z a t i oni nNSGAＧ I Ia l r i t hm, t h ec u r r e n t,v o l t a e go g andwe l d i ngs e e da r ec ho s e nr a ndoml nt h er a ng eo f p yi [ ３７５,６２５],[ ２９,３７]a nd [ ２７,５１],r e s e c t i v e l p y．The a s s i e dnumb e rt opopu l a t i oni nd i v i du a l sa ndnumb e r gn o fi t e r a t i on sa r e５０a nd１００,r e s e c t i v e l ec r o s s ov e r p y．Th andt h e mu t a t i onr a t e sa r ec on s i d e r e dt ob e０ ７and ０ ３,r e s e c t i v e l i sl e a d st o７０％ o ft h ec h i l d r e n p y．Th r odu c e dbyc r o s s o v e rop e r a t o ra nd３０％ o ft h em p r o Ｇ p du c e dbymu t a t i onop e r a t o r．Th eimp l eme n t a t i ono ft he c r o s s o v e ra ndmu t a t i onop e r a t o r sc a nb es umma r i z e da s twon e x ts ub s e c t i on s． ３ ２ １ Cr o s s ove r Theus edc r o s s ove rope r a t o rf o rt h i sp r ob l em c anbeexp r e s s eda s: → → ( C１ ＝ ( α)P１ ＋ ( １－α) ４) → → ( ) ( ) ( C２ ＝ １－α P１ ＋ α ５) → → ep r e s en tde c i s i onve c t o ro fpa r Ｇ whe r e,P１ andP２ r → → en t s;C１ and C２ r ep r e s en tde c i s i on ve c t o ro fch i l Ｇ d r en;andαi sar andomva l uei n( ０,１)． ３ ２ ２ Mu t a t i on Th eu s e dmu t a t i onop e r a t o rc a nb es umma r i z e da s: ( ) １ Cho o s eon ee l eme n to fv a r i a b l ev e c t o ro fp a r Ｇ e n tr a ndoml i t ht h ep r ob a b i l i t f１/d,wh e r edi s yw yo t henumb e ro fv a r i a b l e s( d＝３i nt h i sp r ob l em)． ( ２)As s i andomva l uef o rs e l e c t ede l emen t gnar ([ , i napp r opr i a t er angef o rt ha te l emen t ３７５ ６２５] ,[ , ] , f o rcu r r en t ２９ ３７ f o rvo l t age and [ ２７,５１]f o r we l d i ngspe ed)．
４ Re s u l t sandDi s c u s s i on
As men t i oned above,t he ave r age pe r c en t age e r r o ro f pene t r a t i on dep t h, we l d be ad wi d t h and he i tf r omt hede s i z la r e６ ０６％ , gh gnedFuz y mode ６ ４０％ and ５ ８２％ , r e spe c t i ve l ． T h i s d emon Ｇ y s t r a t e st ha tt he pr opo s ed Fuz z li sr e l i ab l e． y mode Mo r eove r,t heimp l emen t a t i ono ft he NSGAＧ I Iap Ｇ oa cht os o l vet h i sop t imi z a t i on p r ob l em p r e s en t s pr t hePa r e t o Ｇ op t ima ls e tshowni nF i １３a st heso l u Ｇ g t i ons e tf o rt h i s pa r t i cu l a rp r ob l em．Th i ss e ti n Ｇ c l ude s５０po i n t swi t hd i f f e r en tva l ue so fwe l d i ngi n Ｇ tpa r ame t e r s (wi t h i ns e l e c t ed expe r imen t a ldo Ｇ pu ma i n),r e su l t i ngi nd i f f e r en tva l ue so fc onvex i t yand t r a t i oni ndexe sr ang i ng f r om ０ １０６ t o０ １６８ pene and０ ３５４t o０ ５６１r e spe c t i ve l ． T a b l e９s h o w st he y va l ue so fpr o c e s sva r i ab l e sr e l a t edt oe a ch Pa r e t o Ｇ op t ima landt he i rc o r r e spond i ng va l ue so fpene t r a Ｇ t i onandc onvex i t ndexe s．Cons i de r i ngt hede s i r ed yi
８７７
va l ue so fconvex i t t r a t i oni ndexe sandi n yand pene t urn,t hewe l dbe adgeome t r equ i r ed,anyve c t o r yr o ft hep r oc e s spa r ame t e r sshowni nTab l e９cou l dbe Tab l e９ SAW p r o c e s spa r ame t e r sandc o r r e s i ng pond c onv e x i t F１)andp en e t r a t i on ( F２)i nd e x e s y( a ch i e v e dbyNSGAＧ I Ia l o r i t hm g
No．
F１
F２
１
０ １０６
０ ３５４
３
０ １０８
０ ３５８
２ ４ ５ ６ ７ ８ ９
１０ １１ １２ １３ １４ １５ １６ １７ １８ １９ ２０ ２１ ２２ ２３ ２４ ２５ ２６ ２７ ２８ ２９ ３０ ３１ ３２ ３３ ３４ ３５ ３６ ３７ ３８ ３９ ４０ ４１ ４２ ４３ ４４ ４５ ４６ ４７ ４８ ４９ ５０
０ １０７ ０ １０８ ０ １０９ ０ １１０ ０ １１１ ０ １１１ ０ １１２
０ １１３ ０ １１３ ０ １１４ ０ １１５ ０ １１６ ０ １１７ ０ １１８ ０ １１９ ０ １２０ ０ １２１ ０ １２２ ０ １２２ ０ １２３ ０ １２５ ０ １２６ ０ １２８ ０ １３０ ０ １３２ ０ １３４ ０ １３５ ０ １３８ ０ １４０ ０ １４１ ０ １４３ ０ １４５ ０ １４６ ０ １４７ ０ １４８ ０ １４９ ０ １５１ ０ １５２ ０ １５３ ０ １５５ ０ １５６ ０ １５９ ０ １６１ ０ １６３ ０ １６４ ０ １６６ ０ １６７ ０ １６８
０ ３５７ ０ ３６２ ０ ３６６ ０ ３６８ ０ ３７１ ０ ３７７ ０ ３８０
０ ３８６ ０ ３８８ ０ ３９２ ０ ３９５ ０ ３９６ ０ ３９９ ０ ４０３ ０ ４０８ ０ ４１１ ０ ４１６ ０ ４１７ ０ ４１９ ０ ４２３ ０ ４２５ ０ ４２８ ０ ４３０ ０ ４３４ ０ ４３５ ０ ４３６ ０ ４３７ ０ ４４２ ０ ４４４ ０ ４５４ ０ ４６３ ０ ４７７ ０ ４８３ ０ ４８６ ０ ４８９ ０ ４９１ ０ ４９３ ０ ５０５ ０ ５０６ ０ ５１７ ０ ５１９ ０ ５３０ ０ ５３４ ０ ５４４ ０ ５４８ ０ ５５６ ０ ５５９ ０ ５６１
/A Vo /V Cur r en t l t age ６０７ ３
３３ ７
５９９ ３
３３ ７
６０７ ３ ５８９ ９ ５８３ ２ ５７９ ７ ５７３ ４ ５６９ ２ ５６７ ４
５７０ ９ ５６８ ０ ５６８ ６ ５５７ ３ ５７０ ５ ５６８ １ ５６８ １ ５７３ ４ ５６７ ７ ５７９ ４ ５８８ ７ ５７２ ２ ５７９ ３ ５７５ ３ ５７５ ４ ５７８ ７ ５７４ ５ ５７２ ５ ５９９ ８ ６００ ４ ６００ １ ６０３ ０ ６０５ ２ ６０６ ９ ６０８ １ ６０９ ０ ６０８ ３ ６０２ ０ ６０２ ９ ６０５ １ ６０３ ７ ６０２ ５ ６０２ ７ ６０２ ７ ５９０ ２ ６０２ ６ ６０２ ８ ５８８ ３ ６０２ ７ ６０２ ０ ６０９ ０
３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７
３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３０ ４ ３０ ２ ３０ ３ ３０ ４ ３０ ４ ３０ ７ ３０ ２ ３０ ２ ３０ ２ ３０ １ ３０ ５ ３０ ２ ３０ ３ ３０ １ ３０ １ ２９ ６ ３０ ３ ３０ ３ ３０ ３ ３０ ８ ３０ １ ３０ ２ ３０ ２
Spe ed/ ( cm∙mi n－１) ３５ ０ ３５ １ ３５ ９ ３５ ８ ３６ ３ ３５ ０ ３５ ０ ３６ ３ ３５ ９
３６ ６ ３６ ６ ３６ ７ ３５ ０ ３６ ８ ３６ ８ ３６ ９ ３７ １ ３７ ０ ３７ ２ ３７ ４ ３７ ３ ３７ ４ ３７ ５ ３７ ５ ３７ ６ ３７ ６ ３７ ７ ３８ ０ ３８ ０ ３７ ７ ３７ ９ ３７ ９ ３７ ７ ３７ ７ ３７ ３ ３８ ０ ３８ １ ３８ １ ３８ １ ３８ １ ３８ １ ３８ １ ３８ １ ３８ １ ３８ １ ３８ １ ３８ ２ ４４ ５ ３８ ２ ３８ ２
J ou r na lo fI r onandS t e e lRe s e a r ch,I n t e r na t i ona l Vo l ２２
８７８
F i １３ Re s u l to fNSGAＧ I Iimp l emen t a t i on g
r ame t e r so f we l d be ad geome t r t r a t i on pa y (pene dep t h,be ad wi d t h and he i t)i n op t imi z a t i on gh r oc e s sgavet hede s i r edva l ue sf o rt he s epa r ame t e r s p s imu l t aneous l s i r edwe l d i ngpa r ame t e r sc an y．Thede r educ et hecos t sf r om l ow qua l i t l d i ngp r oc e s Ｇ y we ( s e s．Thee f f e c t so fon l t h r e em a i nv a r i a b l e s v o l t Ｇ y age,cur r en tand we l d i ngspe ed)we r econs i de r ed． Ont h i sba s i s,t heop t imi z a t i on wa sconduc t edf o r t hef i xedi n i t i a lcond i t i onssuch a sspe c i f i ed ba s e me t a lwi t hknownchemi c a lcompos i t i onandt ens i l e r ope r t i e s,f i xed e l e c t r ode and powde r (we l d i ng p consumab l e s)．I fanyo ft he s epa r ame t e r schanged, t heou t t so fwe l d i ngp r oc e s swou l dno tne c e s s a r i l pu y r ema i nt hes ame．
i n t r oduc eda st her e su l to fop t imi z a t i on．S i nc et he max imumo fpene t r a t i oni ndexandmi n imumo fcon Ｇ , vex i t i n d e xa r et h ed e s i r e dv a l u e s t h ev e c t o rt h a t y c aus e st he h i s t va l ue o f pene t r a t i on i ndexe s ghe ( wh i chi st hede s i r edva l ueo ft h i si ndex)c anno tbe t hef avo r ab l eone,be c aus ei tb r i ngsabou tt heh i ghＧ ( e s tva l uef o rc onvex i t ndex wh i chi sno tde s i r a Ｇ yi b l e)and v i c eve r s a．Thus,ba s ed ont he de s i r ed shapeo ft hewe l dbe adgeome t r ft he s eve c Ｇ y,oneo t o r sc anbeus ed．
Thes uppl l i nes t e e landt he yof APIX６５pipe he lpon we ldi ng expe r imen t sby Sadid Pipeand Equ ipmen tCompany ( I ran)andt hehe lponimpl e Ｇ men t i ng t he mu l t i Ｇ o b e c t i ve opt imi za t i on by Mr． j Hamo onNi ko oar egr ea t l knowl edged． yac
Anewapp r oa ch,ba s edonFuz z og i candNS Ｇ yl GAＧ I Ia l r i t hmf o rwe l dbe adgeome t r r ed i c t i on go yp andf o rp r o c e s spa r ame t e r sop t imi z a t i on,wa sp r e s Ｇ en t ed． Re a l expe r imen t a l da t a we r e ga t he r ed t hr ought hesubme r r cbe ad Ｇ on Ｇ l a t ewe l d i ngo f geda p f i f t t e e lp l a t e s．The me t a l l u r i c a lf e a Ｇ y API X６５s g t ur e sandme chan i c a lp r ope r t i e so fwe l deds t ruc t ur e s a r eaf unc t i ono ft hewe l dbe adgeome t r Ｇ y．Thede s i r edwe l dbe adgeome t r nt u rnc anbea ch i evedby yi , r oc e s spa r ame t e r sop t imi z a t i on wh i ch gua r an t e e s p t hea c c ep t ab l e we l d i ngqua l i t i s t i ngp r ob Ｇ y．Theex l emsi ns i ng l e Ｇ ob e c t i veop t imi z a t i ono fe f f e c t i vepa Ｇ j r ame t e r so fwe l d i ngp r o c e s sl e adt ot heus eo fmu l t i Ｇ ob e c t i veop t imi z a t i ont e chn i ndo i ngs o,Fuz z j que．I y l og i c wa sus edf o r mode l i ngt heSAW p r o c e s s．I n , o rde rt oa ch i evede s i r ed we l dbe ad geome t r Ｇ y NS GAＧ I Ia l r i t hm wa st henus edf o r mu l t i Ｇ ob e c t i ve go j op t imi z a t i ono fe f f e c t i vepa r ame t e r si nt he we l d i ng , r oc e s s．Vo l t age cu r r en tand we l d i ngspe ed we r e p cons i de r eda st hep r o c e s spa r ame t e r sandt heop t imi Ｇ z a t i onpr o c e s swa spe r f o rmedi no r de rt oa ch i evet he r ope rva l ue sf o rbo t ho fc onvex i t t r a t i on p yandpene i ndexe ss imu l t aneous l t e rmi n i nganapp r op r i Ｇ ybyde a t eve c t o ro fwe l d i ngp r o c e s sva r i ab l e s．Thr e ema i n
[ ４] D． S． Na e s h,G． L． Da t t a,App l．So f tCompu t．１ ０( ２ ０ １ ０)８ ９ ７ Ｇ ９ ０ ７． g [ ] , , ５ P． Sa t h i Y． J a l e e l Advanc ei nPr oduc t i onEng i ne e r i ng & ya M．
５ Conc l u s i on s
Re f e r enc e s: [ １] N．Mur ugan, V．Guna r a t e r．Pr o c e s s．Te chno l．１６８ j,J．Ma ( ２００５)４７８ Ｇ ４８７．
[ ２] Y． S． T a r ng,W．H． Ya ng,I n t． J． Adv．Ma nu f． T e c hno l． １４ ( １９９８) ５４９ Ｇ ５５４． [ ３] F． Ko l ahan,M． He i da r i,Eng i ne e r i ngandTe chno l ogy５９ ( ２００９) No． １１,１３８ Ｇ １４１．
Managemen t５ ( ２０１０)No． １１,２２５ Ｇ ２３４． [ ６] R． Sudhaka r an,V．Mur ugan,K．M．Kuma r,R． J aya r am,A． Pushpa r a Pr ave en,N． Pr abhu,Eur ope anJ our na lo fSc i en Ｇ j,C．
t i f i cRe s e a r ch６２ ( ２０１１)No． １,７６ Ｇ ９４． [ ７] P． Sa t h i Panne e r s e l vam,M．Y．J a l e e l, Ma t e r．De s．３６ ya,K． ( ２０１２) ４９０ Ｇ ４９８．
[ ８] A． P． Pa i va,S． C． Co s t a,E． J． Pa i va,P． P． Ba l e s t r a s s i,J． R． Fe r Ｇ r e i r a, I n t． J． Adv．Manu． Te chno l．５０ ( ２０１０)１１３ Ｇ １２５．
[ ９] L．M． Tr ev i no,F．A．Va l de s,V． Lope z,R．Al e o,Expe r tSys Ｇ j t emswi t hApp l i c a t i ons３８ ( ２０１１)８０４５ Ｇ ８０５３．
[ １０] M． Sa t he e sh,J． R． Dha s,I JST Tr ans a c t i onso fMe chan i c a lEn Ｇ i ne e r i ng３７ ( ２０１３)１７５ Ｇ １８７． g [ １１] S． Da t t a,S． S．Mah a a t r a,Th eJ ou r n a lo fEng i n e e r i ngRe s e a r c h７ p ( ２０１０)No． １,４２ Ｇ ５２．
[ １２] A． Zadeh,I n f o rma t i onSc i enc e s８ ( １９７５)１９９ Ｇ ２４９． [ １３] N． Sr i n i va s,K． Deb,Evo l u t i ona r t a t i on２ ( １９９４)２２１ Ｇ yCompu ２４８． [ １４] E． Z i t z l e r,Evo l u t i ona r r i t hmsf o rMu l t i ob e c t i veOp t imi Ｇ yAl go j z a t i on:Me t hodsandApp l i c a t i ons,ETH Zur i ch,１９９９．
[ o l u t i on a r t a t i on３ ( １９９５) １５] C．M． Fon s e c a,P． J． F l emi ng,Ev yCompu No． １,１ Ｇ １６． [ １６] R． T．Ma r l e r,J． S．Ar o r a,S t r uc t．Mu l t i d i s c． Op t im． ２６ ( ２００４) ３６９ Ｇ ３９５． [ １７] K．Deb,A． Pr a t ap,S．Ag r awa l,T．Meya r i van,Evo l u t i ona r y Compu t a t i on６ ( ２００２)１８２ Ｇ １９７．
[ １８] K．Deb,Pr o c．Gene t i cand Evo l u t i ona r t a t i on Con f． y Compu At l an t a( ２００８)６３３ Ｇ ６４０．
JOURNALOFIRON ANDSTEELRESEARCH,INTERNATIONAL２ ０ １ ５,２ ２( ９):８ ７ ０ Ｇ ８ ７ ８
Mu l t i Ｇ ob e c t i v eOp t imi z a t i ono fWe l d i ngPa r ame t e r si n j Subme r e dAr cWe l d i ngo fAPIX６５S t e e lP l a t e s g MAMORADPOUR, S HHASHEMI, KKHALILI
( Depa r tmen to fMe chan i c a lEng i ne e r i ng,Un i ve r s i t fB i r and,B i r and９７１７５ Ｇ ３７６,I r an) yo j j Ab s t r a c t:Subme r r cwe l d i ng ( SAW)i soneo ft he ma i n we l d i ngp r o c e s s e swi t hh i s i t i onr a t eandh i geda ghdepo gh we l d i ngqua l i t ． T h i sw e l d i n m e t h odi sex t ens i ve l edi n we l d i ngl a r Ｇ d i ame t e rga st r ansmi s s i onp i l i ne sand y g yus ge pe h i Ｇp r e s su r eve s s e l s．I nwe l d i ngo fsuchs t r uc t u r e s,t hes e l e c t i onp r o c e s spa r ame t e r sha sg r e a ti n f l uenc eont hewe l d gh ( be adge ome t r n dc o n s e u e n t l f f e c t s t h ew e l dq u a l i t ． B a s e do nF u z z l o i c a n dN S G A Ｇ I I N o n Ｇ d o m i n a t e dS o r t i n ya q ya y y g g Gene t i cAl r i t hmＧ I I)a l r i t hm,anewapp r oa chwa sp r opo s edf o rwe l dbe adge ome t r r ed i c t i onandf o rp r o c e s s go go yp , , a r a m e t e r so t i m i z a t i o n ． F i r s t d i f f e r e n tw e l d i n a r a m e t e r s i n c l u d i n e l d i n o l t a e c u r r e n ta n ds e e dw e r es e t p p gp gw gv g p t ope r f o rm SAW unde rd i f f e r en tc ond i t i onsonAPIX６５s t e e lp l a t e s．Nex t,t hede s i n e dF u z z o d e lw a su s e df o r g ym r ed i c t i ngt hewe l dbe adge ome t r l i ngo ft hep r o c e s s．Theob t a i ned me anpe r c en t agee r r o ro fpene t r a t i on p yandmode , , dep t h,we l dbe adwi d t handhe i h t f r o mt h ep r o o s e dF u z z o d e lw a s６ ０ ６％ ６ ４ ０％ a n d５ ８ ２％ r e s e c t i v e l g p ym p y． Thep r o c e s spa r ame t e r swe r et henop t imi z edt oa ch i e vet hede s i r edva l ue so fc onvex i t t r a t i oni ndexe ss imu l Ｇ yandpene t ane ous l i ngNSGAＧ I Ia l r i t hm．Asar e su l t,as e to fop t imumve c t o r s( e a chve c t o rc on t a i nscu r r en t,vo l t ageand yus go spe edwi t h i nt he i rs e l e c t edexpe r imen t a ldoma i ns)wa sp r e s en t edf o rde s i r ab l eva l ue so fc onvex i t t r a t i oni n Ｇ yandpene dexe si nt her ange so f( ０ １０６,０ １６８)and ( ０ ３５４,０ ５６１)r e spe c t i ve l i ch wa smo r eapp l i c ab l ei nr e a lc ond i Ｇ y,wh t i ons． Ke r d s:subme r r cwe l d i ng;we l dbe adge ome t r u z z og i c;mu l t i Ｇ ob e c t i veop t imi z a t i on;APIX６５s t e e l geda y;f yl j ywo
Subme r r c we l d i ng ( SAW )i soneo ft he geda mos timpo r t an tandc ommon me t hodso fwe l d i ngi n va r i ousi ndus t r i e s．The SAW i s mo s t l edf o r y us we l d i ng wi t hah i s i t i onand pene t r a t i oni n gh depo l a r t e e ls t ruc t u r e s wh i cha r esu i t ab l ef o rau t o Ｇ ges ma t i cwe l d i ng．Oneo ft he mo s timpo r t an tapp l i c a Ｇ [] t i onso fSAW i s we l d i ng o fp i l i ne１ ．Theh i pe gh manu f a c t u r i ngc o s t so fo i land ga sp i s maket he pe r ed i c t i onandc on t r o lo ft he i rwe l d i ngp r o c e s smo r e p impo r t an t． Oneo ft hema o ri nd i r e c tme t hodst ogua r an t e e j t hede s i r ed we l d i ngqua l i t st oa s s e s st hea c t ua l yi we l dbe adgeome t r o rva r i ouswe l d i ngp r oc e s Ｇ y．Asf s e s,t hewe l dbe adgeome t r sc on t r o l l edbyad us Ｇ yi j t i ng t he e f f e c t i ve pa r ame t e r s du r i ng we l d i ng r oc e s s．Thewe l dbe adgeome t r nc l ude st hedep t h p yi o f pene t r a t i on, we l d be ad he i t and we l d be ad gh wi d t h． Thec ommon me t hodsf o rad us t i ngt hei npu t j r ame t e r so f we l d i ng t o ob t a i n app r op r i a t e we l d pa be adgeome t r r emo s t l r imen t a l,o rba s edon ya yexpe
t e chn i c a lbookso rc a t a l ogs p r ov i ded byi ndus t r i a l compan i e s． Such t e chn i c a lr e commenda t i ons a r e r a lando f t endono tp r ov i dea c cur a t ei n f o rma Ｇ gene , t i onf o rd i f f e r en twe l d i ngcond i t i ons．Howeve rt he us eo fnove lme t hodsanda r t i f i c i a li n t e l l i e Ｇba s ed genc s t emsi sex t r eme l e f u lande f f e c t i vei np r ed i c Ｇ ys yus t i ng we l dbe adgeome t r o rop t imi z a t i ono fi n Ｇ yandf tpa r ame t e r si nva r i ouswe l d i ngp r oc e s s e s．S i i f Ｇ pu gn i c an te f f o r t shavebe en mader e c en t l o rp r ed i c t i ng yf we l d be ad geome t r t imi z i ng t he we l d i ng y and op [ ] r oc e s s pa r ame t e r s１Ｇ７ ．I n such r e s e a r ch, a f t e r p we l d i ngp r o c e s s mode l i ng,s i ng l e Ｇ ob e c t i v eop t imi z a Ｇ j t i on wa sc a r r i edou tt oa ch i e v ede s i r edv a l ueo fe a ch we l dbe adg e ome t r r ame t e r．Fo rexamp l e,Ta r ng ypa andYangop t imi z edt hewe l dbe adhe i t,we l dbe ad gh wi d t handt op Ｇ s i debe ad wi d t hi ng a st ung s t en a r c [ ２] ( GTA)we l d i ngp r o c e s sus i ng Taguch it e chn i que ． Us i ngr eg r e s s i onmode l,Ko l ahanand He i da r ip r ed i c Ｇ , t edde t ho fpene t r a t i on we l dbe adhe i tandwi d t h p gh i ng a s me t a la r c (GMA ) be ad Ｇ on Ｇ l a t e we l d i ng p [] r o c e s s３ ．Theya l soop t imi z edp r oc e s sva r i ab l e si n p
B i o r aphy:M． A．MORADPOUR,Ma s t e r; E Ｇma i l: mo r adpour． mamad＠yahoo． c om; Re c e i v e dDa t e:May２０,２０１４ g
I s sue９ Mu l t i Ｇ ob e c t i veOp t imi z a t i ono fWe l d i ngPa r ame t e r si nSubme r c We l d i ngo fAPIX６５S t e e lP l a t e s j gedAr
o rde rt ode t e rmi net hebe s tva r i ab l es e t sf o ranyde Ｇ s i r ed we l d be ad geome t r r ame t e r s (we l d be ad y pa he i t,wi d t handpene t r a t i on)us i ngs imu l a t edan Ｇ gh ne a l i ng a l r i t hm．Nage sh and Da t t ai nve s t i t ed go ga t heus eo fneu r a lne two rksi np r ed i c t i ng wi d t hand he i to fwe l dbe adandba ck Ｇ s i debe adi nTungs t en gh [ ４] ( ) I ne r tGa s TIG we l d i ngp r o c e s s ．Theya l s oop Ｇ t imi z edt he pr o c e s s pa r ame t e r st oa ch i evet hede Ｇ s i r edc onvex i t ndexus i nggene t i ca l r i t hm．The yi go op t imi z a t i ono fe f f e c t i ve pa r ame t e r sonl a s e rbe am be ad Ｇ on Ｇ l a t e we l d i ng wa sc a r r i ed ou t by Sa t h i p ya [ ５] andJ a l e e lus i ngg r ay Ｇ ba s edTaguch ime t hod ．The lo ft h i sop t imi z a t i onwa st oob t a i nade s i r edva l Ｇ goa ueo fdep t ho fpene t r a t i ont owe l dbe adwi d t hr a t i o． Sudhaka r anandc o Ｇwo rke r sop t imi z edt hee f f e c t i ve r ame t e r sonGTA we l d i ngp r o c e s si no r de rt oob Ｇ pa t a i nt hemax imumdep t ho fpene t r a t i ont owe l dbe ad [] wi d t hr a t i ous i nggene t i ca l r i t hm ６ ．Sa t h i go yaand co Ｇwo rke r sc a r r i edou tt he mode l i ng o fl a s e rbe am we l d i ngby me anso fneu r a lne two rksandop t imi z ed i t spa r ame t e r sf o rde s i r edva l ue so fdep t ho fpene Ｇ t r a t i on,we l dbe adwi d t handt ens i l es t r eng t hbyu Ｇ [] s i nggene t i ca l r i t hm ７ ． go Thema i nd i s advan t ageo fs i ng l e Ｇ ob e c t i veop t i Ｇ j mi z a t i oni st ha ti nde t e rmi n i nganapp r op r i a t eve c t o r o ft hewe l d i ngp r o c e s sva r i ab l e st or e a cht hede s i r ed va l ueo fonepa r ame t e ro fwe l dbe adgeome t r he y,t va l ue so fo t he rpa r ame t e r so f we l dbe ad geome t r y a r ei n o r e d ． T h i s c a nr e s u l t i nu n d e s i r e dw e l d u a l i g q Ｇ , t s edont hep r ev i ousr e s e a r ch t hec onvex i t y．Ba y i ndex ( he i tt owi d t hr a t i oo fwe l dbe ad)andpene Ｇ gh ( t r a t i oni ndex dep t ho f pene t r a t i ont o we l d be ad wi d t hr a t i o)c anbec ons i de r eda simpo r t an tf e a t ur e s o fwe l dbe adgeome t r nsuchr e s e a r ch,t heop t i Ｇ y．I mi z a t i ono f we l d i ng p r o c e s s pa r ame t e r si sc a r r i ed ou ti no r de rt o mi n imi z ec onvex i t ndexo r max i Ｇ yi mi z epene t r a t i oni ndex．Howeve r,t hesho r t c omi ng o ft he s eop t imi z a t i onsi st ha ti nad us t i ngt hewe l d Ｇ j i ngp r o c e s s pa r ame t e r st or e a cht he max imum o r mi n imumva l ueo foneo ft he s ei ndexe s,t heva l ueo f t heo t he ri ndexi si r ed．Th i sr e su l t si ni napp r o Ｇ gno r i a t eva l ue so ft hei r edi ndex,wh i chi nt u rnr e Ｇ p gno su l t si n poo rqua l i t ft he we l dbe ado ri nex t r a yo
８７１
cos t so ft hewho l ewe l d i ngp r oc e s s． Somee f f o r t shavea l r e adybe en madeon mu l t i Ｇ ob e c t i v eo t i m i z a t i o n o fd i f f e r e n t w e l d i n r o c e s Ｇ j p gp [] s e s．Fo ri ns t anc e,Pa i vae ta l．８ c a r r i ed ou tt he mu l t i Ｇ ob e c t i veop t imi z a t i ono fpu l s edga sme t a la r c j we l d i ngp r oc e s s．Mu l t i Ｇ ob e c t i v eo t i m i z a t i o n o fa j p we l d i ngp r oc e s sbyt hee s t ima t i ono ft hePa r e t oop Ｇ [] t ima ls e twa sconduc t edbyTr ev i noe ta l．９ ．Mo r e Ｇ [ [ １０] １１] , ove r Sa t he e she ta l． and Da t t ae ta l． op t i Ｇ mi z edwe l d i ngp r oc e s s e ss epa r a t e l i ng mu l t i Ｇ ob Ｇ yus e c t i veop t imi z a t i on．I nt hel a t t e rr e s e a r ch,expe r i Ｇ j men t a lr e spons e swe r et r ans f o rmedi n t ot he i ri nd i Ｇ v i dua lde s i r ab i l i t l ue s by s e l e c t i ng app r opr i a t e y va de s i r ab i l i t unc t i ont oimp r ovet he we l d qua l i t yf y． , Af t e rwa rds t he ove r a l lde s i r ab i l i t saf unc t i on ya wa sop t imi z edf i na l l t h i nt heexpe r imen t a ldo Ｇ y wi ma i nus i ngPSO ( Pa r t i c l eSwa rm Op t imi z a t i on)a l Ｇ r i t hm wh i l eSa t he e she ta l．sur veyedt heapp l i c a Ｇ go t i ono fde s i r ab i l i t unc t i onapp r oa chcomb i nedwi t h yf f uz z og i cana l i st oop t imi z et hemu l t i l equa l i t yl ys p y ( , cha r a c t e r i s t i c s be ad r e i n f o r c emen t be ad wi d t h, be ad pene t r a t i on and d i l u t i on)o fsubme r r c ged a we l d i ngp r oc e s spa r ame t e r so fSA５１６g r ade７０s t e e l ( ) bo i l e rs t e e l ． I nt hecur r en tr e s e a r ch,t heFuz z og i candda Ｇ yl t a ga t he r i ng t hr ough r e a lexpe r imen t si s us edt o r e s en tanapp r op r i a t emode lf o rp r ed i c t i ngt hewe l d p be adgeome t r nsubme r r cbe ad Ｇ on Ｇ l a t ewe l d Ｇ yi geda p i ngo fAPIX６５s t e e lp l a t e s．Fur t he rmo r e,t oob t a i n t hede s i r edva l ue sf o rbo t hconvex i t t r a Ｇ yand pene t i oni ndexe ss imu l t aneous l Ｇ ob e c t i veop t imi Ｇ y,two j z a t i ono fSAW va r i ab l e si sp r opos edandc a r r i edou t wi t hNSGAＧ I Iapp r oa ch．I nt hetwo Ｇ ob e c t i veop t i Ｇ j mi z a t i on,as e to fop t imumve c t o r si sde t e rmi nedf o r r ope rva l ue so fconvex i t t r a t i oni ndexe s p yand pene ( i ns t e ado fde t e rmi n i nganop t imumve c t o r)．
１ Exp e r imen t a lPr o c e du r e
Di f f e r en texpe r imen t swe r ec a r r i edou ton API X６５s t e e lp l a t e s．Th i ss t e e li swi de l edi nmanu Ｇ yus f a c t ur i ngo fga sando i lt r ansmi s s i onp i l i ne s．The pe chemi c a l compos i t i on and t ens i l ep r ope r t i e sa r e r e s en t edi nTab l e s１and２,r e spe c t i ve l p y．
Tab l e１ Ch emi c a lc ompo s i t i ono fAPIX６５s t e e landt a r e tv a l u e sf r om API５Ls t anda r d g
ma s s％
Con t en t
C
S i
Mn
P
S
Cr
Ni
Al
Cu
V
Ti
Nb
Te s ts t e e l
０ ０７０
０ ２１０
１ ５１５
０ ０１０
０ ００１
０ １６４
０ ０１１
０ ０３９
０ ０１６
０ ０４２
０ ０１４
０ ０４４
API５L
≤０ １６
≤０ ４５
≤１ ６５
≤０ ０２０ ≤０ ０１０
≤０ ０９
≤０ ０６
≤０ ０５
—
—
—
—
J ou r na lo fI r onandS t e e lRe s e a r ch,I n t e r na t i ona l Vo l ２２
８７２
Tab l e２ Ten s i l ep r op e r t i e so fAPIX６５s t e e land t a r e t v a l u e s f r o m A P I５ Ls t a n d a r d g Yi e l ds t r eng t h/MPaUl t ima t e st r eng t h/MPaEl onga t i on/％
Te s ts t e e l API５L
５３８
４５０—６００
６２４
５３５—７６０
３４ ２４
Toi nve s t i t et hee f f e c to fi npu tpa r ame t e r so f ga SAW onwe l dbe adgeome t r i f f e r en texpe r imen t s y,d we r ec onduc t edon５０s t e e lp l a t e so f１００mm wi d t h, , ２００mml eng t h and１４ ３０mmt h i ckne s s．I na l lex Ｇ r imen t s,t hewe l dcu r r en t( I),vo l t age ( V )and pe we l d i ngspe ed ( S)we r ec ons i de r eda st hep r oc e s s va r i ab l e s．Ot he re f f e c t i vepa r ame t e r si nSAW we r e f i xeddu r i nga l lexpe r imen t s．Thewe l dbe adgeome Ｇ , t r i n c l u d i n t h ed e t h o f e n e t r a t i o n w e l d b e a d y g p p he i tandwe l dbe ad wi d t hi si l l us t r a t edi nF i １． gh g Mo r eove r,t he we l d i ngequ i tus edi nt h i sr e Ｇ pmen s e a r chands omeo ft hewe l dedp l a t e sa r eshowni n F i e spe c t i ve l gs．２and３,r y． I no r de rt ode t e rmi net hedep t ho fpene t r a t i on, a l lp l a t e swe r ecu tandpo l i sheda f t e rwe l d i ng．The c r os ss e c t i ons o ft he po l i shed p l a t e s we r et hen e t chedi n３％ n i t a l．Ac a l i rwi t h０ ０５mma c cur a Ｇ pe cy wa sus ednex tt o me a su r et he we l dbe adhe i t gh ( H ),we l dbe ad wi d t h( W )anddep t ho fpene t r a Ｇ t i on ( D)．Theus edexpe r imen t a le l emen t sa r epr e s Ｇ , en t edi nTab l e３．Al s ot heme a su r edwe l dbe adpa Ｇ r ame t e r sa r eg i veni nTab l e４．
F i １ We l db e adg e ome t r g y
F i ２ Subme r e da r cwe l d i ngequ i tu s e di nt h i sr e s e a r ch g g pmen
F i ３ Pho t o r apho ft h ewe l d e dp l a t e s g g Tab l e３ Di f f e r en te l emen t su s e di ns ubme r e d g a r cwe l d i ngo fp l a t e s
Pa r ame t e r P l a t e
El e c t r ode F l ux
Us edt ype
APIX６５s t e e l
S２MO ( Di ame t e r３ ２mm) ( AWSA５ ２３,EN７５６,EN１２０７０)
AMA OP１３９ ( AWSA５ １７ & A５ ２３,DIN３２５２２ & DIN EN７６０)
２ Pr opo s e dFu z z e l y Mod I nt h i sr e s e a r ch,Fuz z og i ct oo l boxo fMATＧ yl LABso f twa r ei sus edt o mode lt hesubme r r c geda be ad Ｇ on Ｇ l a t e we l d i ngp r oc e s sandt op r ed i c t we l d p be adgeome t r nt h i sFuz z t em,f o rc l a s s i f i c a Ｇ y．I ys ys , , t i ono fcur r en t vo l t ageandspe ed e a chl eve lo f t he s epa r ame t e r s( i nc l ude４００,４５０,５００,５５０and ６００Af o rcur r en t,３０,３２,３４and３６Vf o rvo l t age , / ) and３６ ４６and４９cm mi nf o rwe l d i ngspe ed a r es e Ｇ l e c t edt oc en t e ro fas e t．Asar e su l t,t henumbe ro f Fuz z e t sus edf o rc l a s s i f i ng o fcur r en t,vo l t age ys y andwe l d i ngspe edi scons i de r ed５,４and３,r e spe c Ｇ t i ve l so,a c co rd i ngt oagg r ega t i oni n t e r va l so f y．Al ou t tda t a po i n t s,we l d be ad wi d t h,he i tand pu gh t r a t i ona r ec l a s s i f i edt o１２,９and１０s e t s,r e Ｇ pene spe c t i ve l y． I nFuz z l i ng,t hei npu tandou t tva r i a Ｇ y mode pu [ １２] b l e sa r ea l so known a sl i ngu i s t i c va r i ab l e s ． Thus,Fuz z unc t i onsa r eus edt ode f i nel i ngu i s t i c yf va l ue sanda s s i he membe r sh i r e e st oi npu t gnt pdeg andou t u t a r a m e t e r s ．T h e G a u s s i a nf u n c t i o ni s p p us edf o rcur r en tandvo l t agebe c aus eo fi t ssmoo t hＧ ne s s．TheTr ape z o i da lf unc t i oni sus edf o rwe l d i ng spe ed．He r e,t r ape z o i da lf unc t i oni sus edbe c aus ei t cove r smo r er ang e so ft hewe l d i ngs e e da sc omp a r e d p t oc ommonmemb e r s h i un c t i on s．Al s o,t het r i angu l a r pf
I s sue９ Mu l t i Ｇ ob e c t i veOp t imi z a t i ono fWe l d i ngPa r ame t e r si nSubme r c We l d i ngo fAPIX６５S t e e lP l a t e s j gedAr Tab l e４ Exp e r imen t a lda t aba s e Te s t No．
Pr o c e s spa r ame t e r
I/A
V/V
１
４００
３０
３
５００
３０
２ ４ ５ ６ ７ ８ ９
１０ １１ １２ １３ １４ １５ １６ １７ １８ １９ ２０ ２１ ２２ ２３ ２４ ２５ ２６ ２７ ２８ ２９ ３０ ３１ ３２ ３３ ３４ ３５ ３６ ３７ ３８ ３９ ４０ ４１ ４２ ４３ ４４ ４５ ４６ ４７ ４８ ４９ ５０
４５０ ５５０ ６００ ４００ ４５０ ５００ ５５０
６００ ４００ ４５０ ５００ ５５０ ６００ ４００ ４５０ ５００ ５５０ ６００ ４００ ４５０ ５００ ５５０ ６００ ４００ ４５０ ５００ ５５０ ６００ ４００ ４５０ ５００ ５５０ ６００ ４００ ４５０ ５００ ５５０ ６００ ４００ ４５０ ５００ ５５０ ６００ ４００ ４５０ ５００ ５５０ ６００
３０ ３０ ３０ ３２ ３２ ３２ ３２
３２ ３４ ３４ ３４ ３４ ３４ ３６ ３６ ３６ ３６ ３６ ３０ ３０ ３０ ３０ ３０ ３２ ３２ ３２ ３２ ３２ ３４ ３４ ３４ ３４ ３４ ３６ ３６ ３６ ３６ ３６ ３０ ３０ ３０ ３０ ３０ ３２ ３２ ３２ ３２ ３２
S/ ( cm∙mi n－１)
Me a sur emen t so fwe l d be adgeome t r y/mm
D
W
H
３６
４ ９０
１５ ７０
２ ４０
３６
６ ００
２０ ００
２ ４５
３６ ３６ ３６ ３６ ３６ ３６ ３６
３６ ３６ ３６ ３６ ３６ ３６ ３６ ３６ ３６ ３６ ３６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４６ ４９ ４９ ４９ ４９ ４９ ４９ ４９ ４９ ４９ ４９
５ ７５ ７ ８０ ９ ３０ ４ ７５ ６ ９０ ５ ００ ８ ４０
９ １５ ４ ７０ ６ ６５ ５ ２５ ８ ３５ ８ ２０ ５ １０ ５ １０ ６ ８０ ７ ００ ７ ８５ ３ ６０ ５ １０ ５ ６０ ５ ９０ ７ ２０ ３ ３０ ４ ５５ ５ ２０ ６ ００ ６ ８０ ５ ０５ ４ ６０ ６ ００ ７ ５０ ７ ３０ ５ ００ ５ ６０ ６ ３５ ６ ５０ ７ ３０ ４ ２５ ５ ７０ ６ ６０ ７ ０５ ８ ６０ ５ ４０ ６ １０ ７ １０ ６ ９０ ８ ２０
１７ ７０ ２１ １０ １８ ３０ １７ ３５ １７ ４０ １７ ３０ １８ ５０
２０ ３０ １６ ００ １９ ４５ １８ ４５ １９ ７０ ２２ ５５ １６ ３０ １９ ００ １９ ６０ ２２ ６５ ２３ ２５ １２ ５０ １２ ４５ １３ ９０ １３ １０ １３ ２０ １０ １０ １２ ３０ １２ ７０ １２ ３０ １４ ００ １０ ８０ １１ ９０ １４ ０５ １５ ００ １３ ７５ １１ ３５ １３ ００ １４ ５５ １４ ３０ １４ ７０ １２ ７０ １５ ７０ １６ ００ １８ ００ １７ ４５ １３ ６０ １４ ９０ １５ ５０ １７ １０ １８ ５５
２ ４０ ３ ２０
f unc t i onsi sus edf o rpene t r a t i ondep t h,we l dbe ad he i tandwi d t hbe c aus eo fi t ss imp l i c i t r e c i Ｇ gh yandp s i oni nde t e rmi n i ngt heva l ueo ft heou t u t a r a m e Ｇ p p t e r s．Thec l a s s i f i edi npu tandou t tpa r ame t e r sand pu t he u t i l i z ed membe r sh i unc t i ons a r e shown i n pf , F i s ４－９． A l s o t h ed i f f e r e n t l i n u i s t i cv a l u e sa n d g g t he i rFuz z n t e r va l sa r eshowni nTab l e５． yi
３ ４０ ２ ６０ ２ ３５ ２ ９０ ３ １５
３ ７０ ２ ７０ ２ ９０ ２ ２０ ２ ３５ ２ ５０
F i ４ Cu r r en tmemb e r s h i unc t i on s g pf
２ ５０ ２ ５５ ３ ２５ ３ ４５ ２ ６５ ２ １０ ２ ２０ ２ ３０ ２ ００ ２ ４０ ２ ４０ ２ ４０
F i ５ Vo l t a ememb e r s h i unc t i on s g g pf
２ １０ ２ ２０ ２ ５０ ２ ２０ ２ ２５ ２ ５０ ２ ７０ ２ ４５ ２ １０ ２ ６０ ２ ４０ ２ ５０
F i ６ Sp e e dmemb e r s h i unc t i on s g pf
２ ９０ ２ ４０ ２ ３０ ２ ８０ ２ ６５ ３ １０ ２ ５０ ３ １５ ３ １５ ２ ７５ ３ ３０
８７３
F i ７ Pen e t r a t i onmemb e r s h i unc t i on s g pf
８７４
J ou r na lo fI r onandS t e e lRe s e a r ch,I n t e r na t i ona l Vo l ２２
e l)we r ef edi n t o Fuz z l．Thep r ed i c t ed pa Ｇ y mode r ame t e r sby t h i s mode l we r et hencompa r ed wi t h t hos er e su l t i ngf r om p r a c t i c a lexpe r imen t s．Theob Ｇ t a i nedr e su l t sf o rwe l dbe adgeome t r r omt het e s t yf da t aandt her e su l t ed pe r c en t agee r r o rf r om e a ch r ed i c t i ona r eshowni n Tab l e８．Theave r agepe r Ｇ p , c en t agee r r o ro fdep t ho f pene t r a t i on we l d be ad wi d t handhe i tf r omt hede s i z la r e gh gnedFuz y mode , , ６ ０６％ ６ ４０％ and５ ８２％ r e spe c t i ve l y． F i ８ Be adwi d t hmemb e r s h i unc t i on s g pf
Tab l e５ I npu tandou t tv a r i ab l e swi t ht h e i rf u z z a l u e s pu yv Sys t em va r i ab l e
I npu t s
L i ngu i s t i c va r i ab l e
Cur r en t
L i ngu i s t i cva l ue Ve r ow yl
４２２ ０－４７８ ０
Hi gh
５２２ ０－５７８ ０
Med i um
I no r de rt oe s t ab l i shFuz z l e si nt hede s i yru gned Fuz z t em,t heknowl edgeob t a i nedf r om p r a c t i Ｇ ysys c a lexpe r imen t si sus ed．I nt o t a l,３８s e t so fda t a r e s en t edi n Tab l e４ a r echo s en r andoml r om p y,f wh i cht heFuz z l e sa r ee s t ab l i shed．The１２r e Ｇ yru ma i nedda t as e t sa r eus edt ot e s tt hep r opo s edmod Ｇ e l． Af t e r da t ac l a s s i f i c a t i on, s ome ou t t da t a pu i n t smaybel o c a t edi nt heove r l apr ange so fs e t s． po I tr e su l t si np r oduc i ngs omeru l e sf o ron l e to f yones da t a．Asar e su l t,t henumbe ro fru l e sp r oduc edf o r mode l i ngt hesubme r r cbe ad Ｇ on Ｇ l a t e we l d i ng geda p , i s１３３byus i ng３８s e t so fda t a．I nTab l e６ s omeo f t he s eru l e sa r edemons t r a t ed． I nt h i sr e s e a r ch,Mamdan i ′ si n f e r enc eeng i nei s , us ed．Af t e r en t e r i ng i n f e r enc e eng i ne t hei npu t Fuz z l ue sa r et u rnedi n t oFuz z t t sbyap Ｇ yva you pu l i ng Fuz z l e s． F i na l l z t t sa r e p y y ru y, Fuz y ou pu changedi n t onume r i c a lva l ue so fpene t r a t i ondep t h,
we l dbe ad wi d t handhe i tby me anso fCen t r o i d gh de f uz z i f i c a t i ont e chn i he va r i ous de Ｇ que．Among t f uz z i f i c a t i ont e chn i sava i l ab l ei nFuz z og i ct oo l Ｇ que yl box,t he Cen t r o i dde f uz z i f i c a t i ont e chn i e su l t s quer i n mi n imum ave r ageva l ueo fpe r c en t agee r r o rf o r r ed i c t i on ( Tab l e７)． p I no r de rt oob t a i nt hec apab i l i t fFuz z l yo y mode i np r ed i c t i on o f we l d be ad geome t r heave r age y,t r c en t agee r r o r wa sc a l cu l a t ed．To pe r f o rm t h i s, pe , t heva l ue so fcu r r en t vo l t ageandwe l d i ngspe edi n １２s e r i e so fda t a( r andoml s ent ot e s tt hemod Ｇ ycho
Spe ed
５７５ ０－６２５ ０
Low med i um
３０ ７－３３ ２
Hi i um ghmed Low
２９ ０－３１ ０
３２ ７－３５ ２
３５ ０－３７ ０
２７ ０－４５ ０
Med i um
４４ ０－４８ ０
Ve r r ow ( VVL) yve yl Ve r ow ( VL) yl
２ ７５－４ ２５
Hi gh
Low ( L)
Ou t t s Pene t r a t i on pu
４７２ ０－５２８ ０
Ve r i yh gh
Hi gh
F i ９ Be adh e i tmemb e r s h i unc t i on s g gh pf
３７５ ０－４２５ ０
Low
Low
Vo l t age
Fuz z n t e r va l yi
Low med i um ( LM) Med i um１ (M１)
Med i um２ (M２) Hi i um (HM) ghmed
４７ ０－５１ ０
２ ００－３ ２７
３ ７５－５ ２５
４ ７５－６ ００ ５ ７５－６ ２５
６ ００－７ ２５
６ ７５－８ ２５ Hi ７ ７５－９ ２５ gh (H) Ve r i VH) ８ ７５－１０ ２５ yh gh ( Ve r r i VVH) ９ ７５－１１ ００ yve yh gh ( Ve r r r ow ( VVVL)８ ００－１２ ００ yve yve yl Ve r r ow ( VVL) yve yl ( Ve r ow VL) yl
Wi d t h
Low ( L) Low med i um ( LM) ( Med i um１ M１)
Med i um２ (M２) Hi i um (HM) ghmed
１１ ５０－１２ ５０
１２ ００－１３ ２５
１２ ７５－１４ ２５ １３ ７５－１５ ２５ １４ ７５－１６ ２５ １５ ７５－１７ ２５
１６ ７５－１８ ２５ Hi １７ ７５－１９ ２５ gh (H) Ve r i VH) １８ ７５－２０ ２５ yh gh ( Ve r r i VVH) １９ ５０－２２ ００ yve yh gh ( Ve r e r e r i VVVH)２０ ７５－２４ ７５ yv yv yh gh ( Ve r r ow ( VVL) yve yl ( Ve r l o w V L) y
He i t gh
Low ( L) Low med i um ( LM) Med i um (M)
Hi i um (HM) ghmed Hi gh (H)
Ve r i VH) yh gh ( Ve r r i VVH) yve yh gh (
１ ８０－２ ２０ ２ ００－２ ５０
２ ３０－２ ７０
２ ５０－３ ００ ２ ８０－３ ２０
３ ００－３ ５０
３ ３０－３ ７０ ３ ５０－４ ００
３ ８０－４ ２５
I s sue９ Mu l t i Ｇ ob e c t i veOp t imi z a t i ono fWe l d i ngPa r ame t e r si nSubme r c We l d i ngo fAPIX６５S t e e lP l a t e s j gedAr
８７５
Tab l e６ As amp l eo ff u z z u l e sp r odu c e dt omod e lt h ewe l d i ngp r o c e s so fp l a t e s yr Ru l eNo．
Ru l e s ( Cur r en ti sMed i um)( Vo l t agei sLow)( Spe edi sLow)t hen ( Pene t r a t i oni sM１)(Wi d t hi sVVH)(He i ti sVL) gh ( )( )( ) ( )( )( Cur r en ti sMed i um Vo l t agei sLow Spe edi sLow t hen Pene t r a t i oni sM１ Wi d t hi sVVH He i ti sL) gh
１ ２
( Cur r en ti sHi Vo l t agei sLow)( Spe edi sLow)t hen ( Pene t r a t i oni sMH)(Wi d t hi sVVH)(He i ti sH) gh)( gh ( )( )( ) ( )( )( Cur r en ti sVe r Ｇh i l t agei sLow Spe edi sLow t hen Pene t r a t i oni sH Wi d t hi sMH He i ti sML) y gh Vo gh ( )( )( ) ( )( )( Cur r en ti sLow Vo l t agei sLowＧmed i um Spe edi sLow t hen Pene t r a t i oni sM２ Wi d t hi sM２ He i ti sVL) gh
３
４
５
( Cur r en ti sLow)( Vo l t agei sLowＧmed i um)( Spe edi sLow)t hen ( Pene t r a t i oni sMH)(Wi d t hi sMH)(He i ti sVL) gh ( Cur r en ti sMed i um)( Vo l t agei sLowＧmed i um)( Spe edi sLow)t hen ( Pene t r a t i oni sML)(Wi d t hi sMH)(He i h t sVL) g i ( )( )( ) ( )( )( Cur r en ti sVe r Ｇ l o w V o l t a e i sH i h Ｇ m e d i u m S e e d i sL o w t h e n P e n e t r a t i o n i sL W i d t h i sM １ H e i h t i y g g p g sL)
６
７
８
( Cur r en ti sVe r Ｇh i Vo l t agei sHi Ｇmed i um)( Spe edi sLow)t hen ( Pene t r a t i oni sMH)(Wi d t hi sVVVH)(He i ti sVL) y gh)( gh gh ( )( )( ) ( )( )( ) Cur r en ti sVe r Ｇ l o w V o l t a e i sH i h S e e d i sL o w t h e n P e n e t r a t i o n i sML W i d t h i sM １ H e i h t i sL y g g p g
９
１０
Tab l e７ Pe r c en t a ee r r o ro fFu z z e lp r e d i c t i on g ymod wi t hd i f f e r en td e f u z z i f i c a t i onme t hod s No． １
De f uz z i f i c a t i on me t hod
Me anpe r c en t agee r r o r /％ o fFuz z l ymode
B i s e c t o r
１５ ５４
Lom
１８ ３３
Cen t r o i d
２ ３
６ ０９
Mom
４ ５
→
f ＝ [ f１( x), x),．．．, x)] ∈ F, f２( fm (
１６ ４９
Som
Me a sur edby /mm ope r a t o r
D
W
H
１３ ０６
Pr ed i c t edbyFuz z r c en t agee r r o r y Pe mode l o fp r ed i c t i on/％
D
W
H
D
W
H
２
５ ７５ １７ ７０ ２ ４０ ６ ２９ １８ ３０ ２ ３５ ９ ６９ ３ ３８ ２ ０８
１７
５ １０ １９ ００ ２ ５５ ５ ６２ １８ ００ ２ ４７ １０ １９ ５ ２６ ３ １３
１０ １８ ２３ ２７ ２９ ３１ ３５ ３９ ４３ ５０
→
９ １５ ２０ ３０ ３ ７０ ８ ２８ ２１ ２０ ３ ３０ ９ ５０ ４ ４３ １０ ８１ ６ ８０ １９ ６０ ３ ２５ ６ ３２ ２１ ００ ２ ７９ ７ ０５ ７ １４ １４ １５ ５ ６０ １３ ９０ ２ ３０ ５ ４１ １１ ３０ ２ １７ ３ ３９ １８ ７０ ５ ６５ ４ ５５ １２ ３０ ２ ４０ ４ ７１ １２ ００ ２ ３７ ３ ５１ ２ ４３ １ ２５ ６ ００ １２ ３０ ２ ２０ ６ １１ １４ ２０ ２ ４０ １ ８３ １５ ４４ ９ ０９ ５ ０５ １０ ８０ ２ ２０ ４ ３８ １０ ９０ ２ ２８ １３ ２６ ０ ９２ ３ ６３ ７ ３０ １３ ７５ ２ ４５ ７ ０９ １４ ９０ ２ ４７ ２ ８７ ８ ３６ ０ ８１ ６ ５０ １４ ３０ ２ ５０ ７ ０１ １４ ６０ ２ ４７ ７ ８４ ２ ０９ １ ２０ ６ ６０ １６ ００ ２ ８０ ６ ６０ １６ ４０ ２ ８２ ０ ００ ２ ５０ ０ ７１
８ ２０ １８ ５５ ３ ３０ ７ ９２ １７ ４０ ２ ７３ ３ ４１ ６ １９ １７ ２７
３ Mu l t i Ｇ ob e c t i v eOp t imi z a t i on j Thec onc ep to f mu l t i Ｇ ob e c t i veop t imi z a t i oni s j ba s edont hef a c tt ha tmanyr e a l Ｇwo r l dop t imi z a t i on r ob l emsi nvo l ves imu l t aneousop t imi z a t i ono fmu l Ｇ p t i l eo b e c t i v e sw h i c ha r eo f t e n i nc o n f l i c tw i t he a c h p j o t he r．I n mu l t i Ｇ ob e c t i veop t imi z a t i onc a s e s,t he r e j mayno tbeones o l u t i on wh i chi sop t ima lwi t hr e Ｇ , spe c tt oa l lob e c t i v e s r a t h e r t h e r e a r e a s e t o f s o l u Ｇ j t i onswi t ha l t e rna t i vet r ade Ｇ o f f swhena l lob e c t i ve s j a r econs i de r ed．The s es e to fs o l u t i onsa r eknowna s [ １３] Pa r e t o Ｇ op t ima ls o l u t i ons ． De f i n i t i on １ (Mu l t i Ｇ ob e c t i ve op t imi z a t i on): j Thema i ngoa lo fmu l t i Ｇ ob e c t i veop t imi z a t i oni st o j → ∗ ∗ ∗ ∗ x２ ,．．．, xn ] t o f i ndve c t o rx ＝ [ x１ ,
( １)
st heob e c t i v ev e c t o r;Er xi st hed e c i s i onv e c t o r;fi e Ｇ j ; e no t e s r e s e n t sc on s t r a i n t si np r ob l em and X andF d p [ １４] d e c i s i ons a c eandob e c t i v es a c e,r e s e c t i v e l p j p p y ． De f i n i t i on２ ( Pa r e t oDomi nanc e):Fo ranytwo → → → , , ti ss a i dt ha tu domi Ｇ ob e c t i veve c t o r s uandv i j → → → na t e sv ( fandon l f u＜v)i yi , , ∀j ∈ { １,． ． ． ． ． m} : uj ≤vj ∧ ∃j ∈ { １,． m} : ( uj ＜vj ２) Ac co rd i ngt o Pa r e t o domi nanc e,t he de c i s i on →
Tab l e８ Re s u l t so fwe l db e adg e ome t r r e d i c t i on s yp byFu z z e lf o rt e s tda t a ymod P l a t e No．
mi nf( x)＝ { f１( x), x),．．．, x)} f２( fm ( wi t hr e spe c tt o E( x)＝ {e１( x), e２( x),．．．, ek( x)} ≤０ → , , , , whe r e x ＝ [ x１ x２ ．．．xn ] ∈ X,
→
→
→ → ve c t o radomi na t e sde c i s i onve c t o rb ( a＜b)i fand →
→
→
on l ff ( a)＜f ( b)． yi De f i n i t i on３ (Pa r e t o op t ima l i t c i s i on y): A de ve c t o rx∈Xi ss a i dt ha ti snon Ｇ domi na t edr ega rd i ng fandon l f t oas e tS⊆Xi yi ( The r edoe sno tex i s t s∈S:s≺x． ３) , , snon Ｇ domi n a t e dr e a r d i ngt oX i ti s Al s oi fxi g s a i dt ha txi sPa r e t o Ｇ op t ima l．Mo r e ov e r,as e to fd e c i Ｇ s i onv e c t o r st ha ti snon Ｇ domi n a t e dr e a r d i ngt o X,i s g , knowna sPa r e t o Ｇ op t ima ls e t andt hec o r r e s i ngob Ｇ pond →
e c t i v ev e c t o r sa r eknowna sPa r e t o Ｇ op t ima lFr on t． j Toso l ve mu l t i Ｇ ob e c t i veop t imi z a t i onpr ob l ems j (MOPs),manyevo l u t i ona r l r i t hmsp r opos edi n ya go [ １５ Ｇ １６] t hel i t e r a t ur e sr e c en t l ．Howeve r,i nt h i spa Ｇ y r,t heNon Ｇ domi na t edSo r t i ngGene t i cAl r i t hmＧ pe go [ ] I I( NSGAＧ I I)pr opos edbyDeb１７ i sus edf o ri t sr o Ｇ [ ] bus t ne s sandpopu l a r i t nso l v i ng MOPs１８ ． yi
３ １ Non Ｇ domi na t e ds o r t i ngg ene t i ca l o r i t hmＧ I I g ３ １ １ Non Ｇdomi na t eds o r t i ng Tocompa r et heso l u t i onsa c co rd i ngt ot hedomＧ i nanc econc ep t,e a chso l u t i oni scompa r ed wi t ha l l , o t he rso l u t i ons．Then t hes e to fso l u t i onsno tdomＧ i na t edbyanyso l u t i oni sdeno t eda st heso l u t i onso f
８７６
J ou r na lo fI r onandS t e e lRe s e a r ch,I n t e r na t i ona l Vo l ２２
t hef i r s tPa r e t oFr on t( r ank＝１)．Thes amep r oc e Ｇ dur ei sapp l i edt ot her e s to fs o l u t i onst ode t e rmi ne t hes e c ondPa r e t oFr on t( r ank＝２)．Th i sp r o c edur e con t i nuedt i l la l ls o l u t i onst obec l a s s i f i edt ot hePF１ t oPFP Pa r e t oFr on t s,andt henumbe ro ft hePa r e t o Fr on tt ha ti sa s s i n e dt oas o l u t i o nd e t e r m i n e st h e g Pa r e t o domi nanc er ank o ft ha ts o l u t i on．F i １０ g showsanexemp l a rs e to fs o l u t i onsi ntwod imen Ｇ ( s i ona l ob e c t i ve spa c e c l a s s i f i ed i n t o ３ Pa r e t o j Fr on t sPF１ ,PF２ andPF３)．
F i １０ Pa r e t oFr on t sf o rane x emp l a rs e to fs o l u t i on s g
３ １ ２ Cr owdi ngdi s t anc efac t o r Thec r owd i ngd i s t anc ei sadens i t s t ima t i ono f ye so l u t i ons su r r ound i ng a pa r t i cu l a rs o l u t i on． The c r owd i ngd i s t anc e( f o rapa r t i cu l a rs o l u t i oni nanon Ｇ domi na t eds e t)i sde t e rmi ned byt heave r ages i de l eng t ho facubo i d( who s eve r t i c e sa r et head a c en t j so l u t i onso ft ha tpa r t i cu l a rs o l u t i on wi t hr e spe c tt o e a ch ob e c t i ve f unc t i on)． F i １１ shows cubo i d j g wh i chi sf o rmedbyad a c en to fs o l u t i oni．Thepe r Ｇ j ime t e ro ft h i scubo i di sp r opo r t i ona lt oc r owd i ng d i s t anc eo fs o l u t i oni．I ti swo r t hno t i ngt ha tani n Ｇ f i n i t eva l uea st hec r owd i ngd i s t anc eva l uea s s i o gnst t heex t r emes o l u t i ons ( t hes o l u t i on wi t hh i s t ghe va l ueandt hes o l u t i onwi t hsma l l e s tva l uer ega rd i ng t oe a chob e c t i vef unc t i on)i nanon Ｇ domi na t eds e t． j
F i １１ Cr owd i nge s t ima t i onf o rt h es o l u t i oni g
３ １ ３ Impl emen t a t i onof NSGAＧ II Thef i r s ts t ep o f NSGAＧ I Iimp l emen t a t i oni s i n i t i a l i z a t i on．I nt h i ss t ep,ar andom pa r en tpopu l a Ｇ
t i onP０i sc r e a t ed．Fo rt h i sr e a son,r andom va l ue s c i s i onve c t o r st opa r en tt he a r ea s s i ot heN de gnedt nex tgene r a t i on．Co r r e spond i ngob e c t i veva l ue sa r e j ( c a l cu l a t edandt he popu l a t i oni sso r t ed ba s ed on non Ｇ domi na t edso r t i ngandc r owd i ngd i s t anc eva l ue f o re a chnon Ｇ domi na t eds e t)． ( １) Ma i nl oopo fNSGAＧ I I Thema i nl oopo fNSGAＧ I Is t a r t swi t ht heva r i Ｇ a t i oni nt hepopu l a t i on．Theb i na r ournamen ts e Ｇ yt l e c t i oni sus edt os e l e c tpa r en t sf r om Pt．Byapp l Ｇ y i ng mu t a t i onandc r os sove rope r a t o r st ot hos epa r Ｇ , r ec r e a t ed． en t so f f spr i ngpopu l a t i onQ０ o fs i z eN a Bycomb i n i ngPt wi t hQt,t hepopu l a t i ons i z ewi l lbe ti sne c e s s a r ochoos e N so l u t i onsf r om２N ２N ．I yt ( so l u t i ont of o rm t henex tpopu l a t i on Pt＋１ )．Fo r t h i sr e a son,non Ｇ domi na t edso r t i ng app l i e st ot he cur r en t popu l a t i on,andso l u t i onsen t e ri nt ot he nex tpopu l a t i onba s edont he i ro rde ro fPa r e t odomi Ｇ nanc er ank．I ft heen t r anc eo fas e to fso l u t i onswi t h oexc e edN ,t r t i cu l a rr ankl e adsPt＋１t heso l u t i ons pa ( o ft ha ts e t wi t hh i rc r owd i ngd i s t anc eva l ue)i s ghe chos ent o bet he membe ro f Pt＋１ andt her e s to f t hema r er emoved．Thema i nl oopo fNSGAＧ I Icon Ｇ t i nue sun t i las t opp i ngc r i t e r i oni sme t．Th i spr oc e Ｇ [ ] dur ei sshowni nF i １２１８ ． g
F i １２ Imp l emen t a t i ono fNSGAＧ I I g
( ２)B i na r ournamen ts e l e c t i on yt Theb i n a r ou r n ame n ts e l e c t i oni su t i l i z e dbyNS Ｇ yt GAＧ I Ia st hes e l e c t i onf o rv a r i a t i ons t a e ． F o r t h i sr e a Ｇ g s on,twos o l u t i on sa r ep i c ke dr andoml r om c u r r e n t yf o u l a t i o n ．T h es o l u t i o nw i t hb e t t e rP a r e t od o m i n a n c e pp r anki ss e l e c t e d．I ft hetwos o l u t i on ss ha r et hes amePa Ｇ r e t or ank,s o l u t i onwi t hh i rc r owd i ngd i s t an c ev a l u e ghe i ss e l e c t e d．I fbo t hs o l u t i on ss ha r et hes ame Pa r e t o domi n an c er ankandt hes amec r owd i ngd i s t an c ev a l u e, on eo ft hemi ss e l e c t e dr andoml y．
３ ２ Mu l t i Ｇ ob e c t i v eop t imi z a t i ono fwe l d i ngpr o c e s s j r ame t e r s pa I nt h i spape r,t he NSGAＧ I Ia l r i t hmi sus ed go
I s sue９ Mu l t i Ｇ ob e c t i veOp t imi z a t i ono fWe l d i ngPa r ame t e r si nSubme r c We l d i ngo fAPIX６５S t e e lP l a t e s j gedAr
f o rt he mu l t i Ｇ ob e c t i veop t imi z a t i ono ft hep r o c e s s． j Thec onvex i t ndex ( he i tt o wi d t hr a t i oo fwe l d yi gh be ad)and pene t r a t i oni ndex ( t r a t i ondep t ht o pene we l dbe ad wi d t hr a t i o)a r ec ons i de r eda sob e c t i ve j f unc t i ons．Thewe l d i ngcu r r en t,vo l t ageandspe ed a r ec on s i d e r e da sd e c i s i onv a r i a b l e s．Fo rt h eph a s eo f i n i t i a l i z a t i oni nNSGAＧ I Ia l r i t hm, t h ec u r r e n t,v o l t a e go g andwe l d i ngs e e da r ec ho s e nr a ndoml nt h er a ng eo f p yi [ ３７５,６２５],[ ２９,３７]a nd [ ２７,５１],r e s e c t i v e l p y．The a s s i e dnumb e rt opopu l a t i oni nd i v i du a l sa ndnumb e r gn o fi t e r a t i on sa r e５０a nd１００,r e s e c t i v e l ec r o s s ov e r p y．Th andt h e mu t a t i onr a t e sa r ec on s i d e r e dt ob e０ ７and ０ ３,r e s e c t i v e l i sl e a d st o７０％ o ft h ec h i l d r e n p y．Th r odu c e dbyc r o s s o v e rop e r a t o ra nd３０％ o ft h em p r o Ｇ p du c e dbymu t a t i onop e r a t o r．Th eimp l eme n t a t i ono ft he c r o s s o v e ra ndmu t a t i onop e r a t o r sc a nb es umma r i z e da s twon e x ts ub s e c t i on s． ３ ２ １ Cr o s s ove r Theus edc r o s s ove rope r a t o rf o rt h i sp r ob l em c anbeexp r e s s eda s: → → ( C１ ＝ ( α)P１ ＋ ( １－α) ４) → → ( ) ( ) ( C２ ＝ １－α P１ ＋ α ５) → → ep r e s en tde c i s i onve c t o ro fpa r Ｇ whe r e,P１ andP２ r → → en t s;C１ and C２ r ep r e s en tde c i s i on ve c t o ro fch i l Ｇ d r en;andαi sar andomva l uei n( ０,１)． ３ ２ ２ Mu t a t i on Th eu s e dmu t a t i onop e r a t o rc a nb es umma r i z e da s: ( ) １ Cho o s eon ee l eme n to fv a r i a b l ev e c t o ro fp a r Ｇ e n tr a ndoml i t ht h ep r ob a b i l i t f１/d,wh e r edi s yw yo t henumb e ro fv a r i a b l e s( d＝３i nt h i sp r ob l em)． ( ２)As s i andomva l uef o rs e l e c t ede l emen t gnar ([ , i napp r opr i a t er angef o rt ha te l emen t ３７５ ６２５] ,[ , ] , f o rcu r r en t ２９ ３７ f o rvo l t age and [ ２７,５１]f o r we l d i ngspe ed)．
４ Re s u l t sandDi s c u s s i on
As men t i oned above,t he ave r age pe r c en t age e r r o ro f pene t r a t i on dep t h, we l d be ad wi d t h and he i tf r omt hede s i z la r e６ ０６％ , gh gnedFuz y mode ６ ４０％ and ５ ８２％ , r e spe c t i ve l ． T h i s d emon Ｇ y s t r a t e st ha tt he pr opo s ed Fuz z li sr e l i ab l e． y mode Mo r eove r,t heimp l emen t a t i ono ft he NSGAＧ I Iap Ｇ oa cht os o l vet h i sop t imi z a t i on p r ob l em p r e s en t s pr t hePa r e t o Ｇ op t ima ls e tshowni nF i １３a st heso l u Ｇ g t i ons e tf o rt h i s pa r t i cu l a rp r ob l em．Th i ss e ti n Ｇ c l ude s５０po i n t swi t hd i f f e r en tva l ue so fwe l d i ngi n Ｇ tpa r ame t e r s (wi t h i ns e l e c t ed expe r imen t a ldo Ｇ pu ma i n),r e su l t i ngi nd i f f e r en tva l ue so fc onvex i t yand t r a t i oni ndexe sr ang i ng f r om ０ １０６ t o０ １６８ pene and０ ３５４t o０ ５６１r e spe c t i ve l ． T a b l e９s h o w st he y va l ue so fpr o c e s sva r i ab l e sr e l a t edt oe a ch Pa r e t o Ｇ op t ima landt he i rc o r r e spond i ng va l ue so fpene t r a Ｇ t i onandc onvex i t ndexe s．Cons i de r i ngt hede s i r ed yi
８７７
va l ue so fconvex i t t r a t i oni ndexe sandi n yand pene t urn,t hewe l dbe adgeome t r equ i r ed,anyve c t o r yr o ft hep r oc e s spa r ame t e r sshowni nTab l e９cou l dbe Tab l e９ SAW p r o c e s spa r ame t e r sandc o r r e s i ng pond c onv e x i t F１)andp en e t r a t i on ( F２)i nd e x e s y( a ch i e v e dbyNSGAＧ I Ia l o r i t hm g
No．
F１
F２
１
０ １０６
０ ３５４
３
０ １０８
０ ３５８
２ ４ ５ ６ ７ ８ ９
１０ １１ １２ １３ １４ １５ １６ １７ １８ １９ ２０ ２１ ２２ ２３ ２４ ２５ ２６ ２７ ２８ ２９ ３０ ３１ ３２ ３３ ３４ ３５ ３６ ３７ ３８ ３９ ４０ ４１ ４２ ４３ ４４ ４５ ４６ ４７ ４８ ４９ ５０
０ １０７ ０ １０８ ０ １０９ ０ １１０ ０ １１１ ０ １１１ ０ １１２
０ １１３ ０ １１３ ０ １１４ ０ １１５ ０ １１６ ０ １１７ ０ １１８ ０ １１９ ０ １２０ ０ １２１ ０ １２２ ０ １２２ ０ １２３ ０ １２５ ０ １２６ ０ １２８ ０ １３０ ０ １３２ ０ １３４ ０ １３５ ０ １３８ ０ １４０ ０ １４１ ０ １４３ ０ １４５ ０ １４６ ０ １４７ ０ １４８ ０ １４９ ０ １５１ ０ １５２ ０ １５３ ０ １５５ ０ １５６ ０ １５９ ０ １６１ ０ １６３ ０ １６４ ０ １６６ ０ １６７ ０ １６８
０ ３５７ ０ ３６２ ０ ３６６ ０ ３６８ ０ ３７１ ０ ３７７ ０ ３８０
０ ３８６ ０ ３８８ ０ ３９２ ０ ３９５ ０ ３９６ ０ ３９９ ０ ４０３ ０ ４０８ ０ ４１１ ０ ４１６ ０ ４１７ ０ ４１９ ０ ４２３ ０ ４２５ ０ ４２８ ０ ４３０ ０ ４３４ ０ ４３５ ０ ４３６ ０ ４３７ ０ ４４２ ０ ４４４ ０ ４５４ ０ ４６３ ０ ４７７ ０ ４８３ ０ ４８６ ０ ４８９ ０ ４９１ ０ ４９３ ０ ５０５ ０ ５０６ ０ ５１７ ０ ５１９ ０ ５３０ ０ ５３４ ０ ５４４ ０ ５４８ ０ ５５６ ０ ５５９ ０ ５６１
/A Vo /V Cur r en t l t age ６０７ ３
３３ ７
５９９ ３
３３ ７
６０７ ３ ５８９ ９ ５８３ ２ ５７９ ７ ５７３ ４ ５６９ ２ ５６７ ４
５７０ ９ ５６８ ０ ５６８ ６ ５５７ ３ ５７０ ５ ５６８ １ ５６８ １ ５７３ ４ ５６７ ７ ５７９ ４ ５８８ ７ ５７２ ２ ５７９ ３ ５７５ ３ ５７５ ４ ５７８ ７ ５７４ ５ ５７２ ５ ５９９ ８ ６００ ４ ６００ １ ６０３ ０ ６０５ ２ ６０６ ９ ６０８ １ ６０９ ０ ６０８ ３ ６０２ ０ ６０２ ９ ６０５ １ ６０３ ７ ６０２ ５ ６０２ ７ ６０２ ７ ５９０ ２ ６０２ ６ ６０２ ８ ５８８ ３ ６０２ ７ ６０２ ０ ６０９ ０
３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７
３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３３ ７ ３０ ４ ３０ ２ ３０ ３ ３０ ４ ３０ ４ ３０ ７ ３０ ２ ３０ ２ ３０ ２ ３０ １ ３０ ５ ３０ ２ ３０ ３ ３０ １ ３０ １ ２９ ６ ３０ ３ ３０ ３ ３０ ３ ３０ ８ ３０ １ ３０ ２ ３０ ２
Spe ed/ ( cm∙mi n－１) ３５ ０ ３５ １ ３５ ９ ３５ ８ ３６ ３ ３５ ０ ３５ ０ ３６ ３ ３５ ９
３６ ６ ３６ ６ ３６ ７ ３５ ０ ３６ ８ ３６ ８ ３６ ９ ３７ １ ３７ ０ ３７ ２ ３７ ４ ３７ ３ ３７ ４ ３７ ５ ３７ ５ ３７ ６ ３７ ６ ３７ ７ ３８ ０ ３８ ０ ３７ ７ ３７ ９ ３７ ９ ３７ ７ ３７ ７ ３７ ３ ３８ ０ ３８ １ ３８ １ ３８ １ ３８ １ ３８ １ ３８ １ ３８ １ ３８ １ ３８ １ ３８ １ ３８ ２ ４４ ５ ３８ ２ ３８ ２
J ou r na lo fI r onandS t e e lRe s e a r ch,I n t e r na t i ona l Vo l ２２
８７８
F i １３ Re s u l to fNSGAＧ I Iimp l emen t a t i on g
r ame t e r so f we l d be ad geome t r t r a t i on pa y (pene dep t h,be ad wi d t h and he i t)i n op t imi z a t i on gh r oc e s sgavet hede s i r edva l ue sf o rt he s epa r ame t e r s p s imu l t aneous l s i r edwe l d i ngpa r ame t e r sc an y．Thede r educ et hecos t sf r om l ow qua l i t l d i ngp r oc e s Ｇ y we ( s e s．Thee f f e c t so fon l t h r e em a i nv a r i a b l e s v o l t Ｇ y age,cur r en tand we l d i ngspe ed)we r econs i de r ed． Ont h i sba s i s,t heop t imi z a t i on wa sconduc t edf o r t hef i xedi n i t i a lcond i t i onssuch a sspe c i f i ed ba s e me t a lwi t hknownchemi c a lcompos i t i onandt ens i l e r ope r t i e s,f i xed e l e c t r ode and powde r (we l d i ng p consumab l e s)．I fanyo ft he s epa r ame t e r schanged, t heou t t so fwe l d i ngp r oc e s swou l dno tne c e s s a r i l pu y r ema i nt hes ame．
i n t r oduc eda st her e su l to fop t imi z a t i on．S i nc et he max imumo fpene t r a t i oni ndexandmi n imumo fcon Ｇ , vex i t i n d e xa r et h ed e s i r e dv a l u e s t h ev e c t o rt h a t y c aus e st he h i s t va l ue o f pene t r a t i on i ndexe s ghe ( wh i chi st hede s i r edva l ueo ft h i si ndex)c anno tbe t hef avo r ab l eone,be c aus ei tb r i ngsabou tt heh i ghＧ ( e s tva l uef o rc onvex i t ndex wh i chi sno tde s i r a Ｇ yi b l e)and v i c eve r s a．Thus,ba s ed ont he de s i r ed shapeo ft hewe l dbe adgeome t r ft he s eve c Ｇ y,oneo t o r sc anbeus ed．
Thes uppl l i nes t e e landt he yof APIX６５pipe he lpon we ldi ng expe r imen t sby Sadid Pipeand Equ ipmen tCompany ( I ran)andt hehe lponimpl e Ｇ men t i ng t he mu l t i Ｇ o b e c t i ve opt imi za t i on by Mr． j Hamo onNi ko oar egr ea t l knowl edged． yac
Anewapp r oa ch,ba s edonFuz z og i candNS Ｇ yl GAＧ I Ia l r i t hmf o rwe l dbe adgeome t r r ed i c t i on go yp andf o rp r o c e s spa r ame t e r sop t imi z a t i on,wa sp r e s Ｇ en t ed． Re a l expe r imen t a l da t a we r e ga t he r ed t hr ought hesubme r r cbe ad Ｇ on Ｇ l a t ewe l d i ngo f geda p f i f t t e e lp l a t e s．The me t a l l u r i c a lf e a Ｇ y API X６５s g t ur e sandme chan i c a lp r ope r t i e so fwe l deds t ruc t ur e s a r eaf unc t i ono ft hewe l dbe adgeome t r Ｇ y．Thede s i r edwe l dbe adgeome t r nt u rnc anbea ch i evedby yi , r oc e s spa r ame t e r sop t imi z a t i on wh i ch gua r an t e e s p t hea c c ep t ab l e we l d i ngqua l i t i s t i ngp r ob Ｇ y．Theex l emsi ns i ng l e Ｇ ob e c t i veop t imi z a t i ono fe f f e c t i vepa Ｇ j r ame t e r so fwe l d i ngp r o c e s sl e adt ot heus eo fmu l t i Ｇ ob e c t i veop t imi z a t i ont e chn i ndo i ngs o,Fuz z j que．I y l og i c wa sus edf o r mode l i ngt heSAW p r o c e s s．I n , o rde rt oa ch i evede s i r ed we l dbe ad geome t r Ｇ y NS GAＧ I Ia l r i t hm wa st henus edf o r mu l t i Ｇ ob e c t i ve go j op t imi z a t i ono fe f f e c t i vepa r ame t e r si nt he we l d i ng , r oc e s s．Vo l t age cu r r en tand we l d i ngspe ed we r e p cons i de r eda st hep r o c e s spa r ame t e r sandt heop t imi Ｇ z a t i onpr o c e s swa spe r f o rmedi no r de rt oa ch i evet he r ope rva l ue sf o rbo t ho fc onvex i t t r a t i on p yandpene i ndexe ss imu l t aneous l t e rmi n i nganapp r op r i Ｇ ybyde a t eve c t o ro fwe l d i ngp r o c e s sva r i ab l e s．Thr e ema i n
[ ４] D． S． Na e s h,G． L． Da t t a,App l．So f tCompu t．１ ０( ２ ０ １ ０)８ ９ ７ Ｇ ９ ０ ７． g [ ] , , ５ P． Sa t h i Y． J a l e e l Advanc ei nPr oduc t i onEng i ne e r i ng & ya M．
５ Conc l u s i on s
Re f e r enc e s: [ １] N．Mur ugan, V．Guna r a t e r．Pr o c e s s．Te chno l．１６８ j,J．Ma ( ２００５)４７８ Ｇ ４８７．
[ ２] Y． S． T a r ng,W．H． Ya ng,I n t． J． Adv．Ma nu f． T e c hno l． １４ ( １９９８) ５４９ Ｇ ５５４． [ ３] F． Ko l ahan,M． He i da r i,Eng i ne e r i ngandTe chno l ogy５９ ( ２００９) No． １１,１３８ Ｇ １４１．
Managemen t５ ( ２０１０)No． １１,２２５ Ｇ ２３４． [ ６] R． Sudhaka r an,V．Mur ugan,K．M．Kuma r,R． J aya r am,A． Pushpa r a Pr ave en,N． Pr abhu,Eur ope anJ our na lo fSc i en Ｇ j,C．
t i f i cRe s e a r ch６２ ( ２０１１)No． １,７６ Ｇ ９４． [ ７] P． Sa t h i Panne e r s e l vam,M．Y．J a l e e l, Ma t e r．De s．３６ ya,K． ( ２０１２) ４９０ Ｇ ４９８．
[ ８] A． P． Pa i va,S． C． Co s t a,E． J． Pa i va,P． P． Ba l e s t r a s s i,J． R． Fe r Ｇ r e i r a, I n t． J． Adv．Manu． Te chno l．５０ ( ２０１０)１１３ Ｇ １２５．
[ ９] L．M． Tr ev i no,F．A．Va l de s,V． Lope z,R．Al e o,Expe r tSys Ｇ j t emswi t hApp l i c a t i ons３８ ( ２０１１)８０４５ Ｇ ８０５３．
[ １０] M． Sa t he e sh,J． R． Dha s,I JST Tr ans a c t i onso fMe chan i c a lEn Ｇ i ne e r i ng３７ ( ２０１３)１７５ Ｇ １８７． g [ １１] S． Da t t a,S． S．Mah a a t r a,Th eJ ou r n a lo fEng i n e e r i ngRe s e a r c h７ p ( ２０１０)No． １,４２ Ｇ ５２．
[ １２] A． Zadeh,I n f o rma t i onSc i enc e s８ ( １９７５)１９９ Ｇ ２４９． [ １３] N． Sr i n i va s,K． Deb,Evo l u t i ona r t a t i on２ ( １９９４)２２１ Ｇ yCompu ２４８． [ １４] E． Z i t z l e r,Evo l u t i ona r r i t hmsf o rMu l t i ob e c t i veOp t imi Ｇ yAl go j z a t i on:Me t hodsandApp l i c a t i ons,ETH Zur i ch,１９９９．
[ o l u t i on a r t a t i on３ ( １９９５) １５] C．M． Fon s e c a,P． J． F l emi ng,Ev yCompu No． １,１ Ｇ １６． [ １６] R． T．Ma r l e r,J． S．Ar o r a,S t r uc t．Mu l t i d i s c． Op t im． ２６ ( ２００４) ３６９ Ｇ ３９５． [ １７] K．Deb,A． Pr a t ap,S．Ag r awa l,T．Meya r i van,Evo l u t i ona r y Compu t a t i on６ ( ２００２)１８２ Ｇ １９７．
[ １８] K．Deb,Pr o c．Gene t i cand Evo l u t i ona r t a t i on Con f． y Compu At l an t a( ２００８)６３３ Ｇ ６４０．