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2 A S tu dy on Optim iz ation u s ing D e s ig n of E x perim ent s an d Gen etic A lg orithm s
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4 List of F igures List of T ables iii iv FMVSS i -
5 A b s tract ii -
6 Li s t of F ig ure s F ig, 1 Procedure of design of experim ent s 3 F ig. 2 F low chart of simple g enetic alg orithm s 11 F ig. 3 T he g eneral structure of g enetic alg orithm s 12 F ig. 4 S chem atic diagram for gas a ssist ed inj ection m olding 15 F ig. 5 Ga s assist ed injection m oldin g process 16 F ig. 6 Bum per sy st em 17 F ig. 7 One piece bum per dev elopm ent proces s 18 F ig. 8 Configur ation for pendulum t est 20 F ig. 9 F.E. m odel of reinforcem ent 21 F ig. 10 F in al deform ed shape 22 F ig. 11 F orce- deflection diagram 23 F ig. 12 T he procedure of GAIM an aly sis 25 F ig. 13 F.E. m odel for GAIM analy sis 26 F ig. 14 Sim plified m odel of g as ch ann el 26 F ig. 15 Definition of skin polym er fr action 27 F ig. 16 M ain effect 31 F ig. 17 M elt front adv ancem ent 33 F ig. 18 Skin polym er fraction 34 F ig. 19 Pres sure distribution 35 F ig. 20 Skin polym er fraction v s tim e 36 F ig. 21 Configur ation of sled test 37 F ig. 22 Sled t est u sin g g enetic alg orithm s 41 F ig. 23 Occupant behavior in sled test 47 F ig. 24 Best and av erag e v alues of each g eneration 48 F ig. 25 Comparison of acceleration 49 F ig. 26 Optim al result of g enetic alg orithm s 49 - iii -
7 Li s t of T ab le s T able 1 T erminology biology and genetic alg orithm s 6 T able 2 M ethod of scalin g 9 T able 3 P endulum t est con dition s 19 T able 4 M at erial properties 20 T able 5 Comparison of m as s an d pendulum intru sion 23 T able 6 F act or and lev el u sed in experim ent s 29 T able 7 Orthogonal array and th e result s 30 T able 8 M ain effect 31 T able 9 AN OVA t able 32 T able 10 Simulation param et er con dition 44 T able 11 Operation of gen etic algorithm s 46 - iv -
8 1..,,,,,..... (Design of Ex perim ent s ) ( ),,. (Genetic A lg orithm s ).,. (global optim um )
9 (D e s ig n of E x perim ent s ) 1),,,. 2) 1932 R. A. F ish er,.,,. 3). (1), ( ) (2), ( ) (3) ( ) - 2 -
10 4),, F ig. 1.. F ig. 1 Procedure of design of ex perim ent s (1). (2). (3).,
11 (4), (randomization ). (5). (6).,,. (7),. 5) (An aly sis of v arian ce), (sum of squares ),
12 2.2 (Gen etic A lg orithm ) 1), (gen eration ) (in dividu al) ( : population ) (fitn ess ), (cros sov er ) (m ut ation ). 2) 1975 (H olland ) A dapt ation in N atural and Artificial Sy st em ". (F og el) (ICGA ) ,. 3) (population size), (chrom osom e) (g en e). (locu s ), (allele). (phenotype), (g enotype). (epist asis ), (coding ) (decoding ). T able
13 T able 1 T erm in ology of biology an d g enetic alg orithm (chrom osom e) (strin g ) (gen e) (feature), (charact er ) (allele) (feature v alu e) (locu s ) (string position ) (gen otype) (ph enotype) (epistasis ) (stru cture) (param eter set ) (altern ativ e solution ) (decoded stru cture) (n onlinearity ) 4). (1) ( ), ( ). (2) ( ) ( ). (3)
14 5) (1) (genetic operat or ) (selection ), (crossov er ) (m ut ation ),. (selection ) (natural selection ). (fitn ess function ).. a. :,. i pse lect (1). pselect = f i n j = 1 f i (1) b... c. ( )
15 (cros sov er ). 2 (bit strin g ).. a. 1 (One - point cros sov er ),. A B b. (Multi- point crossov er ). A B (m ut ation ). (design space). (bit ).. (random search ),
16 (2) (F itn ess function ) (objectiv e function ),.., (scalin g ),,. T able 2 f, f ',.,. T able 2 M ethod of scaling S c alin g M ode l Lin ear scalin g Sigm a truncation P ow er law scalin g F un c tion f ' = a f + b f ' = f - (f - c ) f ' = f k - 9 -
17 (3) (binary string ).,., x i [ a i, b i ],. ( b i - a i ) 10 5., m i m i. 2 m i - 1 < ( b i - a i ) m i - 1 (2) x i. x i = a i + decim a l( ) ( b i - a i ) (2 m i - 1) (3),. decim a l ( )
18 (4) (simple g enetic alg orithm ) F ig. 2. F ig. 3. procedure S GA () initialize (P opulation ); ev aluat e (P opulation ); w hile n ot (t erm in al condition s atisfied) do M atingp ool = reprodu ce (P opulation ); Mut ationpool = crossov er (M atingp ool); P opulation = m utation (MutationPool); ev aluat e (P opulation ); end w hile en d procedure F ig. 2 F low chart of sim ple g en etic algorithm s
19 F ig. 3 T he g eneral structure of g en etic algorithm s
20 2.3.. (Inj ection m oldin g ). (Ga s - A ssist ed Injection M olding )., (sink m ark ), (w arpage ), (shrink age),,,..,.,,,,,,
21 2.4 F MV S S (F ederal M otor Vehicle S afety Standard) 208. (Sled test ), (, ),., (dum m y ), B - pillar,,. (Gen etic alg orithm )
22 (Ga s - A s s i s t e d Inj e ct i on M oldin g ),,. F ig. 4. F ig. 4 S chem atic diagram for Gas A s sisted Injection M oldin g
23 1),. (rib ) (boss ) (residu al stress ), (w arpage), (shrink age), (sink - m ark ). F ig. 5. F ig. 5 Gas assist ed injection m oldin g process
24 1.2 (B um per S y s t e m ) 1) (Conv entional bum per ) (F ascia ), (En ergy Ab sorbing F orm ) (Reinforcem ent Beam ) (F ig. 6a ).,., GMT (Glass F ib er ). 2) (One piece bum per ),, (F ig. 6b ).,..,. (a ) Conv entional bumper sy st em (b ) One piece bum per sy st em F ig. 6 Bumper sy st em
25 3) CAD,. F ig. 7., F MVS S 581,. P ro d u c t D e s i g n Cra s h A n a l y s i s (P A M - C RA S H ) St r u ct u r al st r engt h Cr a sh w or t h in es s GA IM A n a l y s i s ( C- GA S F L OW ) Design of exper im ent M old abilit y P r oces s con dit ion s P ra c t i c a l P ro d u c t D e s i g n M ol d D e s i g n F ig. 7 One piece bum per dev elopm ent process
26 1.3 (Cra s h A n aly s i s ), (F MV S S 581),. 1) (F MV S S 581) F MV S S 581 /. 1.5m ph, 2.5m ph 2.5m ph (fix ed b arrier ). (1) (lam ps sy stem ), (hood ), (trunk ), (door s ), (fuel and coolin g sy st em ), (ex hau st sy st em ), (propulsion ), (su spen sion ), (steerin g ), (braking ). (2) - Im pact ridge 34 AISI (3) T able 3 P en dulum t est condition s Im pa ct s pe e d T ri al F RT 2.5 mph 2 RR 2.5 mph 2 F RT CORNE R 1.5 mph 1 (20 inch) / 1 (16-20 inch) RR CORNER 1.5 mph 1 (20 inch) / 1 (16-20 inch)
27 2) F MV S S 581 (pendulum t est ). F ig. 8, 1/ 2. F ig , F ig. 9 (a ), F ig. 9 (b ) (P olypropylene : PP ). T able 4. F ig. 8 Con figu r a t ion for p en du lu m t e st T a b le 4 M a t e r i a l p r op e r t ie s Y oun g 's M odulu s Y i eld S t ren g t h M a s s D en s it y T hi ck n e s s F ascia / Rib 1, e- 09 ton/ 3.5 Reinforcem ent 200, e- 09 ton/
28 (a ) Con v e n t ion a l b u m p e r (s t e e l ) (b ) O n e p ie ce b u m p e r (P P ) F ig. 9 F.E. M odel of reinforcem ent
29 3) F MV S S 581. F ig. 10,.,. (a ) Conv ention al bum per (b ) On e- piece bum per F ig. 10 F inal deform ed shape
30 T able 5., 35%. F ig T able 5 Com parison of m ass an d pendulum intru sion M a s s P e n d u l u m In t ru s i o n Con v en t ion a l b u m p e r On e- p ie ce b u m p er R a t io F ig. 11 F orce- deflection diagram
31 1.4 (Ga s - A s s i s t e d Inj e ct ion M ol din g A n aly s i s ),.,.,. (gas penetration ),,, (delay tim e ), /,.,,. F ig. 12 CAE
32 F E M o de lin g Runn er - Gate Gas Channel F illin g A n aly si s F l ow B al an c e R un n e r - Gat e B al an c e GA IM A n aly s i s D e s i g n of E x perim ent Process Condition Gas ch ann el L/ O F ig. 12 T he procedure of GAIM An aly sis
33 1) F ig , F ig. 14 (part runn er elem ent ). 3206, 25m m. F ig. 13 F.E. m odel for GAIM analy sis F ig. 14 Sim plified m odel of gas channel
34 2),,, (delay tim e) (packing tim e).... (1) (g as fing erin g ),., (sink m ark ). (2) skin polym er fraction. skin polym er fraction F ig. 15, 1, 0. F ig. 15 Definition of skin polym er fr action
35 skin - polym er fraction 0 1, 1,. (4). = - 10 log [1 n n i = 1 1 y 2 i ] (4), SN (sign al- t o- n oise ratio), n, y i. y i skin - polym er fraction (5). y i = 1 l l a (5), l, l 0, a Skin - polym er fraction, 1, 2.,
36 (3) (g as pen etration ),,,, /,. T able 6. (control fact or ),,,, (n oise fact or )., 3. T able 6 F actor and level u sed in experiment s F a ct or le v el 1 l ev el 2 lev el 3 A : Gas Injection P ress. [MPa] B : M elt T em perature [ ] C : Delay T im e [sec] D : Rib T hickn ess [mm] E : Gas Ch ann el Dia. [mm]
37 T able 7 (trial). y i Skin polym er fraction (5), SN (4). T able 7 Orthog on al A rray an d the result s A B C D E 1 E 2 E 3 S N
38 (4) (V arian ce of An aly sis ) T able 7, T able 8, 9 M ain effect t able ANOVA t able., M ain effect (lev el) (fact or ). A NOVA t able (significance ). T able 8 M ain effect F ac t or L ev e l 1 L ev e l 2 L ev e l 3 A B C D F ig. 16 M ain effect
39 T able 9 ANOVA table F act ors dof S V F - ratio A * B (2) (0.0527) - - C * D Error T otal * At least 90% confiden ce AN OVA t able B (m elt t em perature) (poolin g ) F -., A (Gas injection pressure) C (Delay tim e ) 90%. A C, SN A 2 B 1 C 3 D 3. B (m elt temperature), (ga s fin gering )
40 (5) F ig. 17.,.,. F ig. 18, 19 ANOVA t able A 2 B 1 C 3 D 3 E 1, E 2, E 3,. E 3 (dia.=13.5m m ). F ig. 20 Skin polym er fraction. Skin polym er fraction, 0 1, 1, 1. F ig. 17 M elt front adv an cem ent
41 (a ) Ga s channel dia. = 10.5 m m ( E 1 ) (b ) Ga s channel dia. = 12.0 m m ( E 2 ) (a ) Ga s channel dia. = 13.5 m m ( E 3 ) F ig. 18 Skin polym er fraction
42 (a ) Ga s channel dia. = 10.5 m m ( E 1 ) (b ) Ga s channel dia. = 12.0 m m ( E 2 ) (a ) Ga s channel dia. = 13.5 m m ( E 3 ) F ig. 19 Pres sure distribution
43 F ig. 20 Skin polym er fraction v s tim e
44 2. (Oc c upan t B e h av ior A n aly s is u s in g Gen e tic A lg orithm ) 2.1 (S l e d T e s t ) (sled t est )...,. F ig. 21. F ig. 21 Configur ation of sled t est
45 2.2 F M V S S 208 (F ron t al c ra s h of v eh i cle ) 1) (dum m y ) 30m ph,. 2) (1) (HIC ; H ead Injury Criterion ) HIC 36 m sec (6). H IC = [ ( t 2 - t 1 ) t a dt t 2 ] ( t 2 - t 1 ) < 1000 (6) (2) (CSI ; Ch est S ev erity In dex ) 3 m sec 60G. (3) (Chest compression ) 3 in ch, 2 inch. (4) (F L ; F em ur Load ) 2250 lbf(10000 N )
46 2.3 (Head Injury Crit erion ; HIC) (Chest S ev erity In dex : CSI), (F em ur Load ). (7), (8) Combin ed Probability (CP ). CP = ( P 1 + P 2 - P 1 P 2) (7) P 1 = 1 / ( 1 + E X P ( H IC ) P 2 = 1 / ( 1 + E X P ( CSI) (8), HIC (H ead Injury (Chest S ev erity In dex ). Criterion ), CSI
47 2.4.. (v ent hole size) (seat belt elong ation ).,. S GI W ork station IRIX 6.2, PAM - CRA SH. P AM - CRA SH,, PAM - CRA SH. F ig. 22., (random num ber generat or ) (initial population ), (indiv idual), (fitness ). (gen etic operator ),
48 F ig. 22 Sled test u sing g en etic algorithm s
49 1) (F itness fun ction )., (HIC) (CSI) CP (Com bined Probability ). (v ent h ole size) (seat belt elong ation ), CP.. F (x 1, x 2 ) = CP ( m in im ize prob lem ) (9), x 1, x 2, x x , x x ) (bin ary string ),.., x 1, x 2 ( b i - a i ) m i - 1 < ( b i - a i ) m i - 1, m i
50 x 1 x 2. 2 m m 2-1 < ( ) m 1-1 ; m 1 = 9 < ( ) m 2-1 ; m 2 = 14 x 1 x , 1 23., v i 9 x 1, 14 x 2. v i : ( ) x 1 x 2, x 1,. x 2 x i = a i + decim a l( ) ( b i - a i ) ( 2 m i - 1), decim a l( )., x i [ a i, b i ]., x 1, x 2 [ 0.03, 0.07 ], [ 0.6, 2.0 ]. x 1 = decim a l( ) x 2 = decim a l( ) = , =
51 3) (fitn ess function ), (binary strin g )..,, 1 (population size), (P _cross ), (P_m utat e), (chrom osom e length ), (g eneration ) (fitnes s function ) (T able 10). T able 10 Sim ulation param et er condition P opulation size 8 P_cros s 0.5 P_m utat e 0.01 Chrom osom e length 23 Generation 9 F itn ess function F (x 1, x 2 ) = C P (m in im ize)
52 . (in dividu al) (initial population ). v i ( I=1,,pop_size) ev al( v i ).. F = pop siz e i = 1 ev al ( v i ) v i ( I=1,,pop_size) p i. p i = ev al ( v i ) / F v i ( I=1,,pop_size) q i. q i = i p j j = 1. [ 0, 1] r. r < q 1, ( v 1 ), q i - 1 < r q i i v i ( 2 i pop_size ).,. [ 0, 1] r. r < p c,. [ 1, m - 1] pos (m ). pos.. [ 0, 1] r. r < p m,
53 T able 11 (CP ), CP. T able 11 Operation of g enetic alg orithm. G B in ary S t rin g V / H B/ E CP
54 F ig. 23. (a ) at 0 m sec (b ) at 120 m sec F ig. 23 Occupant beh avior in sled t est
55 F ig %, 15.68% CP 9.823%. F ig. 24 Best and av erag e v alu es of each generation
56 4) F ig. 25. (a ) (HIC), (b ) (CSI).. F ig (a ) H ead acceleration (b ) Chest acceleration F ig. 25 Com parison of acceleration (a ) H ead acceleration (b ) Chest acceleration F ig. 26 Optim al result of g enetic alg orithm
57 1.. 1.,. 2..,. 3.,
58 2., %, 55.3mm, (CP ) 9.823% 11.4 % 1.2%. 3. 4,. 4. S GI W ork st ation 1 40,
59 [1] K.K. H o, C.S. Chen an d Y.C. Chen, "Application of C- GA SF LOW S oftw are An aly sis on the 15- inch Ga s - assist ed Injection M olding M onit or Cabin et ", CMUG, No. 13, [2] S.C. Chen, K.S. H su, N.T. Ch eng. an d W.R. Jong, "Characteristics of Ga s P en etration in Gas - A ssist ed Injection M olding ", CMUG, No.15, [3] S.C. Chen, J.G. Dong, an d W.R. Jong, "Effect of g as channel design on m oldin g w indow an d part m ech anical properties of Gas - A s sist ed Injection M olding ", pp ANT E K, [4] H. H ay ashi, Y. F ujioka, M. Im ai, an d Y. Kan, "Dev elopm ent of Gas Injection M olding for Aut om otiv e bum per s", JSAE, [5] S.H. Paik, "Gas A s sisted Injection M olding Bumper - Perform ance and Proces sing ", CMUG, N o [6] P.M. Glance and G. Daroczy, "Com puter - Aided Design, Analy sis, & T estin g of Aut om otiv e Bumper ", SAE, [7] T.H. Han, J.H. Lim, an d J.H. Hw ang, "A Stu dy of Optimization of Coolin g F in U sin g Design of Ex perim ent s", KSME, pp , [8], " ",, pp , [9],,,,, 1998 [10] J. Krottm aier, "Optim izing En gineerin g Design s", M cgraw - HILL, pp , [11] T.C. Kim, H.Y. Kim, J.J. Kim, "A Study on the Design of Ga s - A ssist ed Injection M olded Bum per U sing Design of Ex perim ent s", T he Korea - Japan P lastics Processin g Joint S em in ar, pp.25-31, [12] "CM OLD u ser ' s m anual", V95 [13] David E. Goldberg, "Genetic A lg orithm s in S earch, Optim ization & M achine Learnin g ", A ddison - W esley [14] Zbigniew Mich alew icz, "Gen etic Algorithm s + Dat a Stru ctures = Ev olution Program s", Sprin ger - V erlag [15] "Practical H an dbook of GENET IC ALGORIT HM S ", Lan ce
60 Ch am ber s [16] M it su o GEN, Run w ei CHENG, "Genetic A lg orithm s and Engin eerin g Design ", W iley Int er scien ce [17] P eter J. An gelin e, Kenneth E. Kinn ear, Jr. "A dv an ces in Gen etic P rogram m ing " [18] J. Krottm aier, " Optimizin g En gineering Design s", M cgraw - HILL [19],,,, 1996 [20],,,, 1997 [21],,, [22],,,
61 A St udy on Opt i mi zat i on Usi ng Desi gn of Exper i ment s and Genet i c Al gor i t hms Ki m, Tae Che o l D ep a r tm ent of M e chan ica l E ng ine e r ing Gra d ua t e S cho ol, K ang w on N a t iona l Un iv e rs ity Summar y T his study is con cerned w ith optim al design u sin g design of experim ents and genetic algorithm s. Recently developm ents of a com puter are able t o solv e complex engin eerin g problem s an d optim ized alg orithm s are b een dev elopin g an d applyin g for m any en gineering problem s t o obtain optim al solution s. One of these optim ized algorithm s is design of experim ent s and gen etic algorithm s. Design of ex perim ent s is applied t o obt ain optim al process con dition s in th e ga s as sisted inj ection m oldin g of on e piece bum per. T he process con dition s of gas assisted injection m oldin g are m ore difficult t o setup than the cas e of injection m oldin g becau se inert ga s is inj ect ed int o the m olt en polym er. It is v ery difficult t o predict the g as behavior an d the proces s param et er s are coupled w ith each other. T his study predict s the g as beh avior and present s th e optim al process condition s u sing design of experim ent s. Genetic algorithm s is applied to minimize occupant injury by optimizing the design parameter s for occupant restraint sy stem in sled test. T he design parameter s to optimize using genetic algorithm s are selected vent
62 hole size of airbag and elongation of seat belt. T he criterion to judge Occupant injury are expressed as the combined probability (CP ) of head injury criteria (HIC) and chest sev erity in dex (CSI). T herefore, the goals of sled test are to obtain the minimum combined probability value and to determine the optimal values of design parameter s. T his study present s the optimal values of design parameter s to minimize combined probability u sing genetic algorithm s. K ey W ords : Design of Experiment s, Genetic Algorithm s, Optimization, Gas Assisted Injection Molding, Sled T est
63 , 2.,,.,.,,,,,.,,,,,,,,,....,,.,.,,,,,.,,,
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