Design Optimization Using Soft Computing Techniques For Extrusion Blow Molding Processes

Transcription

1 Desig Optimizatio Usig Soft Computig Techiques For Extrusio Blow Moldig Processes Desig Optimizatio Usig Soft Computig Techiques For Extrusio Blow Moldig Processes Jyh-Cheg Yu*, Tsug-Re Hug ad Jyh-Yeog Juag Departmet of Mechaical Egieerig Natioal Taiwa Uiversity of Sciece ad Techology Taipei 106, Taiwa Fracis Thibault Idustrial Materials Istitute Boucherville, Quebec, Caada Abstract The cotrol of thickess distributio i extrusio blow molded parts is critical to assure product quality ad reduce maufacturig cost. This study applies the soft computig strategy to determie the optimal die gap i the pariso programmig of extrusio blow moldig process. Two types of optimizatio problem are addressed i this study. The process optimizatio objective is obtaiig a uiform thickess of blow parts, ad the desig optimizatio objective is miimizig part weight subject to stress costraits. The fiite elemet software, BlowView, is used to simulate the pariso extrusio ad the blow moldig processes. However, the simulatios are time cosumig, ad miimizig the umber of simulatio becomes a importat issue. The proposed strategy, Fuzzy Neural-Taguchi ad Geetic Algorithm (FUNTGA), first establishes a back propagatio etwork usig Taguchi's experimetal array to predict the relatioship betwee the desig variables ad the respose. Geetic algorithm is the applied to search for the optimum desig of pariso programmig. As the umber of traiig samples is greatly reduced due to the use of orthogoal arrays, the predictio accuracy of the eural etwork model is closely related to the distace betwee samplig poits ad the evolved desigs. The Reliability Distace is proposed ad itroduced to the Geetic Algorithm usig fuzzy rules to modify the fitess fuctio ad thus improve search efficiecy. The desig of a HDPE bottle is used to illustrate the applicatio of the process optimizatio, ad the desig of a gas tak is used to illustrate the applicatio of performace. The desig optimizatio uses ANSYS to fid the stress distributio of blow parts uder loads. The compariso of results usig the optimizatio module of BlowView, Taguchi, ad FUNTGA demostrates the effectiveess of the proposed strategy. Keywords: Fuzzy logics, Neural Network, Geetic Algorithm, Taguchi, Multidiscipliary Desig Optimizatio 1 Itroductio Extrusio blow moldig is a low cost maufacturig process for complex hollow parts [1]. The process ivolves complex procedures such as pariso extrusio, clampig, blow up, ad coolig. First, the pariso extrusio produces a molte thermoplastic tube comig out from the die. Oce extrusio is fiished, the pariso is clamped ad high-pressure air is blow ito it to get the fial part. To cotrol the pariso thickess over time, there is a madrel that ca move i ad out to the die (Fig.1). Obviously, the pariso thickess determies the thickess of the iflated part. The fuctio of the pariso programmig is maipulatig the die gap opeigs to obtai the desired thickess distributio of blow parts. The programmig poits are specified by the extrusio time ad the die gap opeig of the pariso. As the example part show i Fig., we idetify the die gap opeigs at 7 discrete extrusio times as the desig variables: P(t 0 ), P(t 1 ), P(t ), P(t 3 ), P(t 4 ), P(t 5 ), ad P(t 6 ). These desig variables will be adjusted to obtai the desired thickess distributio of blow parts. Two types of optimizatio problem are ofte ecoutered i the desig of blow-molded parts by cotrollig the die gap programmig. The process optimizatio objective is targetig a uiform part 73

2 00 NRC-NSC Caada-Taiwa Joit Workshop o Advaced Maufacturig Techologies, Lodo, Caada thickess distributio of blow parts, ad the desig optimizatio objective is miimizig part weight subject to stress costraits. P(t 6 ) 0% ope Die 100% ope P(t 5 ) P(t 4 ) P(t 3 ) Madre l P(t ) P(t 1 ) Pariso programmig % die ope i fuctio of time P(t 0 ) Figure 1. The cotrol of the pariso thickess usig the pariso programmig Figure. Programmig poits of pariso extrusio Lee et al. [4] used a fiite elemet model of thi film to simulate blow moldig processes, ad applied the feasible directio method to miimize the pariso volume at the costraits of part thickess. Diraddo et al. [] established a eural etwork to predict the distributio of pariso thickess ad applied Newto-Raphso method to obtai the fial blow molded part specificatios [3]. However, the ivestigatio of the relatioship betwee desig variables ad the wall thickess distributio of blow parts requires expesive experimets ad time-cosumig simulatios. To reduce the umber of experimets ad simulatios, a efficiet strategy of data aalysis is essetial. I this study, we apply a optimizatio strategy based o Taguchi s experimetal desig [5] ad soft computig techiques [6] to the optimizatio of pariso programmig to obtai the required thickess distributio. The proposed strategy establishes a local eural etwork based o Taguchi s orthogoal array experimets ad assumes the fuzzy iferece to geetic algorithm to search for the optimal operatig coditios. The fiite elemet software, BlowSim [8], is used to simulate the pariso extrusio ad the blow moldig processes. The desig of a gas tak targetig a uiform part thickess distributio illustrates the applicatio of the proposed method to the process optimizatio. For the blow parts subjected to exteral ad iteral loadig, a adequate part thickess profile has to be determied to satisfy the part mechaical performace. The aim is the to fid the optimal die gap programmig that will miimize the part weight ad satisfy the part mechaical performace as well. Optimizatio Strategy Taguchi s method has prove its efficiecy ad simplicity i parameter desig. The proposed optimizatio strategy, FUzzy Neural-Taguchi with Geetic Algorithm (FUNTGA) [10], applies Taguchi s experimetal desig to the traiig ad testig of a eural etwork model. The traied etwork becomes the fuctio geerator of the desig fitess i the Geetic Algorithm. The optimum search usig GA ehaces the possibility for a better desig tha the covetioal aalysis of meas (ANOM). A fuzzy iferece of egieerig kowledge is itroduced to ehace the searchig efficiecy of GA. The flowchart of the optimizatio strategy is illustrated i Fig.3..1 Taguchi s Method Ispired from statistical factorial experimets, Taguchi s method features orthogoal arrays ad aalysis of mea (ANOM) to aalyze the effects of desig variables. Each variable is assumed to have fiite levels (set poits), such as two or three levels, withi the ivestigatig rage. The orthogoal array is a type of fractioal factorial experimets. The applicatio of orthogoal arrays reduces the umber of experimets, which is particular effective for desig optimizatio ivolvig expesive experimets or time-cosumig simulatios. For istace, istead of 7 experimets for three 3-level full factorial experimets, the L9 orthogoal array selects oly ie treatmets. ANOM study of experimet results reveals the effects of desig parameters that are used to determie the optimal 74

3 Desig Optimizatio Usig Soft Computig Techiques For Extrusio Blow Moldig Processes level of each parameter. Kowig that Taguchi s result is ot a global optimum, however iteratios of Taguchi s method ca provide a solutio ear to the optimum desig. Taguchi s approach utilizes ANOM of fractioal factorial experimets to predict the optimal desig of the full factorial experimets. However, the predictio of the optimal desig is sesitive to the selectio of factorial levels ad iteractio effects. Also, the restrictio of parameter values to factorial levels reduces the possibility of havig better desigs betwee preset levels. Samplig Iitial Desig Orthogoal Array Verificatio Experimet Traiig Testig Simulatio Model Neural Network Fuzzy Iferece Samples Distace Fuzzy Reliability Objective Geetic Algorithm Costraits Predict Optimum Verificatio Experimet No Covergece Yes Ed Figure 3 The Optimizatio flowchart of FUNTGA (1,3,3) (3,3,3) (1,3,3) (,,3) (1,3,1) (1,,) (3,1,3) (3,3,) (1,1,1) (3,1,1) (3,3,1) (1,1,1) (,1,) (,3,1) (3,,1) (a) Full factorial exp. (b) Fractioal factorial exp. Figure 4 Full factorial ad fractioal factorial experimets for three variables. Neural-Taguchi etwork Neural etwork techologies are effective i process cotrol. The etwork is used to set up a simulatio model for a complex oliear system. The back propagatio etwork (BPN) is a type of supervised learig etworks. Samplig data are divided ito learig ad testig samples. Learig samples are used to determie the weightig matrices, W ij ad W jo, amog euros ad testig samples to determie the accuracy ad the geerality of the etwork. 75

4 00 NRC-NSC Caada-Taiwa Joit Workshop o Advaced Maufacturig Techologies, Lodo, Caada Traiig samples are essetial to the predictio quality of etwork models. This study employs Taguchi s experimetal desig to select traiig samples to reduce the umber of experimets ad to maitai a good sample represetatio [7][9]. The steepest gradiet method is assumed to trai the weightig matrices. The verificatio experimet of the optimal desig from the ANOM study will serve as a testig sample. The traied etwork ca accurately predict resposes for the parameter desigs betwee factorial levels. Sigificat iteractios ofte itroduce complexity to experimetal desig ad lead to erroeous predictio of optimal factorial levels. The etwork model ca resolve iteractio effects amog variables. These features eable the etwork to explore a better desig as compared with Taguchi s additive model [5]..3 The search for the optimum of the Neural-Taguchi etwork The traied Neural-Taguchi etwork ca predict resposes for the parameter combiatios i the ivestigatig rage. Geeric Algorithm is thus applied to search for the optimum. If the verificatio result of the predicted optimum is ot satisfactory, the desig will be used as a iitial desig ad aother set of orthogoal array experimets will be coducted. The results will be served as additioal testig data for the etwork. The iteratio process stops whe the predicted optimum obtaied from GA ad the etwork coverges. The Neural-Taguchi etwork replaces Taguchi s additive model to predict desig outputs. The search for the optimum i the ivestigatig rage usig GA will explore the possibility of better desigs other tha factorial poits. However, the applicatio of orthogoal arrays sigificatly reduces the umber of traiig samples as compared with covetioal radom samplig. Owig to that better predictio accuracy will exist aroud samplig poits, our approach itroduces a fuzzy iferece to steer the search directio of GA..3.1 Normalizatio of desig parameters To facilitate the calculatio of the distace amog desigs, the values of the set poits of cotiuous variable x k are ormalized to z k usig the followig trasformatio ( max( x ) mi( x )) k + k xkl = z (1) kl ( max( x ) mi( x )) k k where max(x k ) represets the maximum ad mi(x k ) represets the miimum values of the factorial variable x k. Thus the ormalized factorial values of a equal spaced three-level cotiuous variable, x 1, will become (z 11, z 1, z 13 ) = (-1, 0, 1). For discrete variables, the factorial values are equally assiged betwee -1 ad The Reliability Distace The mea Euclid distaces betwee predictive desigs, D i, ad the sample data S j are defied as follows r ij = ( Dik S jk ) () k = 1 where represets the umber of variables. Sice predictios aroud the samplig poits of the traied etwork will have higher accuracy, we proposed to use the Reliability Distace of a predictive desig as the miimum factorial distace betwee the predictio ad samplig data. RD i = mi( r ij ) (3) Smaller RD results i higher predictio accuracy. Also, the distace of a iterpolatig desig is assumed egative ad the distace of a extrapolatig desig is assumed positive. For istace, the Reliability Distace of D 1 i Fig.5 is egative ad the Reliability Distace of D is positive. 76

5 Desig Optimizatio Usig Soft Computig Techiques For Extrusio Blow Moldig Processes D z r r 1 S 1 (-1, 1) S (1, 1) D 1 S 5 (0, 0) r 15 z 1 S 3 (-1, -1) S 4, (1, -1) Figure 5 The factorial distaces of predicted desigs.3.3 The fuzzy rules of predictio accuracy The Reliability Distace of a predictive desig determies the Predictio Reliability (PR) of the desig. The reliability of the predicted desig decreases whe the absolute value of RD icreases. Also, the reliability of extrapolatig desigs is ofte much worse tha the iterpolatig desigs. Based o the above characteristics of eural etwork, we propose to use fuzzy rules of the desig reliability as follows R1: If RD is PB the predictio reliability is Bad R: If RD is PM the predictio reliability is Poor R3: If RD is PS the predictio reliability is Fair R4: If RD is ZE the predictio reliability is Excellet R5: If RD is NS the predictio reliability is Good R6: If RD is NM the predictio reliability is Fair R7: If RD is NB the predictio reliability is Poor Seve levels are defied to describe the coditio variables: PB(Positive Big), PM(Positive Medium), PS(Positive Small), ZE(Zero), NS(Negative Small), Negative Medium (NM), ad NB(Negative Big). Five levels are defied to describe the assessmet results: Excellet, Good, Fair, Poor, ad Bad. Stadard membership fuctios associated with these statemets are illustrated i Fig.6 ad Fig.7. Fig.8 is the reliability cotour plot for the two dimesioal case usig the fuzzy iferece. The solid dots represet the traiig samples. μ NB NM NS ZE PS PM PB Bad Poor Fair Good Excellet Iterpolatio RD Extrapolatio Reliability Figure 6 Membership fuctios of coditio variables Figure 7 Membership fuctios of assessmet variables.3.4 Geetic Algorithm FUNTGA uses the Geetic Algorithm to search the optimum of the Neural-Taguchi etwork. However, the accuracy of the etwork is limited due to the reduced umber of traiig samples. The desig fitess obtaied from the etwork is thus modified to reflect the characteristics of predictio accuracy. The search of the local optimum will the be restricted to the surroudigs of the traiig samples to prevet the possible erroeous predictio. Fitesset PR, if Fitesset > 0 Fitess = (4) GA Fitesset / PR, if Fitesset < 0 77

6 00 NRC-NSC Caada-Taiwa Joit Workshop o Advaced Maufacturig Techologies, Lodo, Caada Figure 8 Reliability cotour plot for two variables 3 Optimizatio of Blow Moldig Parameters for Process Desig This work uses the proposed optimizatio strategy to get the optimal parameter desig of extrusio blow moldig process for the gas tak case of the Kautex Textro Compay. The gas tak is made of High Desity Polyethylee (HDPE). The desig objective is to target a uiform part thickess of 5 mm. The blow molded part thickess distributio is estimated by usig the BlowSim software. Fig.9 shows that the die gap opeigs at 13 discrete extrusio times are selected as the cotrol variables: P(t 1 ), P(t ), P(t 1 ), ad P(t 13 ). Figure 9 The cotrol poits of the gas tak example 3.1 The Objective Fuctio A quality blow moldig part requires o-target ad uiformly distributed part thickess. To reach this goal, we propose to defie a objective fuctio as the average quality loss due to the deviatio of thickess, Avg _ loss i= = 1 ( t T ) i (5) where t i stads for the thickess of ode i, T for the target thickess, ad for the total umber of odes of the simulatio model. Ay deviatio from the target thickess will cause quality loss. The average quality loss ca be divided ito two parts: the mea deviatio from the target thickess ad the thickess variatio aroud mea as the followig 78

7 Desig Optimizatio Usig Soft Computig Techiques For Extrusio Blow Moldig Processes i= 1 i i= 1 ( t T) + ( t T) + s ( t T ) ( t t ) i = (6) where t is the mea stress ad s is the samplig variace. Reducig the quality loss leads to a thickess distributio of a smaller variace ad a mea thickess closer to the target. 3. Taguchi s parameter desig 3..1 Experimetal Desig The die gap opeigs at 13 discrete extrusio times are selected as the cotrol factors. The desig optimizatio maipulates the die gap opeigs of programmig poits to obtai a uiform thickess distributio. The iitial desig adopts a uiform die gap opeig of 10% for first four cotrol poits ad 0% for the rest. The L36 orthogoal array is selected as the experimetal desig (Table 1). For each opeig, we assume a three-levels variatio aroud the iitial desig located i the middle of the desig space. The rage betwee upper ad lower levels represets the desig space. Table 1. L36 orthogoal array L36 Ru Ppt1 Ppt Ppt3 Ppt4 Ppt5 Ppt6 Ppt7 Ppt8 Ppt9 Ppt10 Ppt11 Ppt1 Ppt13 Loss Iitial Parameter desig Taguchi s method applies the aalysis of meas (ANOM) to estimate parameter sesitivities. Fig.10 represets the factor effects for each die opeig o objective. The additive model estimates the optimum treatmet combiatio to be A 1 B 3 C 3 D E F 1 G 1 H 1 I 1 J 1 K 1 L 1 M 3. The BlowSim simulatio of Taguchi s optimum shows the loss of 6.44, which is ot the best desig i Table 1. The failure of Taguchi s approach might due to iteractios amog desig variables ad strog system o-liearity. 79

8 00 NRC-NSC Caada-Taiwa Joit Workshop o Advaced Maufacturig Techologies, Lodo, Caada Objective A1 A A3 B1 B B3 C1 C C3 D1 D D3 E1 E E3 F1 F F3 G1 G G3 H1 H H3 I1 I I3 J1 J J3 K1 K K3 L1 L L3 M1 M M3 Figure 10 Factor effects plot of cotrol variables 3.3 Desig optimizatio usig FUNTGA The establishmet of the eural etwork FUNTGA provides a more efficiet ad accurate optimum search usig the same experimetal data of Taguchi s experimets. The L36 orthogoal experimets are divided ito two smaller orthogoal arrays as differetiated by the shade i Table experimets are used as traiig samples ad the other 18 experimets are used as testig samples. There are 15 euros i the hidde layer. The iitial learig rate is set to 1.0 ad the iitial mometum term is set to Optimum search usig GA The fuzzy rules for predictio accuracy are applied to GA to improve the searchig efficiecy. The fitess fuctio is defied as follows, Fitess GA = Avg _ loss / PR (7) The traied etwork will the be used as the fuctio geerator for each chromosome combiatio. The parameters of Geetic Algorithm used i this study are listed i Table. Populatio size Table Geetic Algorithm parameters Pool selectio style Scale style Cross Over rate Mutatio rate Max iteratio 37 Paret ad offsprig Liear scale The search result of GA will the be added to the traiig samples of the eural model to further improve the etwork accuracy. The optimizatio process iterates util the results coverge. The iteratio history of FUNTGA is show i Fig.11. Avg_Loss Iteratio Figure 11 The iteratio history of the gas tak example usig FUNTGA 80

9 Desig Optimizatio Usig Soft Computig Techiques For Extrusio Blow Moldig Processes 3.4 Compariso of results Fig.1 ad Table 3 preset the die gap opeigs of the pariso programmig ad the optimizatio results obtaied from Taguchi s method, BlowOp, ad FUNTGA. BlowOp is a BlowSim optimizatio module that uses a gradiet-based algorithm to cotrol the die gap opeigs of the pariso programmig poits. Although BlowOp optimum provides a mea thickess closer to the target of 5 mm, FUNTGA s optimum exhibits a more uiform distributio ad the lowest quality loss. Opeig(%) 60 BlowOp 50 Iitial Taguchi 40 FUNTGA_ Extrusio Time(Sec) Table 3 The compariso of various optima of replicate sixth experimet Iteratio Iitial Desig Taguchi s BlowOp FUNTGA s Mea Stadard Deviatio Average Loss Figure 1 The optimal desigs from various methods 4 Optimizatio of Blow Moldig Parameters for Performace Desig This work applies the proposed optimizatio strategy to get the optimal parameter desig of extrusio blow moldig process for the HDPE bottle of the Lear Corporatio. Two types of loadig will be ivestigated: a iteral pressurizatio at 110 (psi) ad a top displacemet of 5 (mm) durig 5 secods as illustrated i Fig.13. The maximum allowable stress, correspodig to the ultimate tesile stregth of the material, is set to 33 MPa. For this material, the Youg s modulus is 879 MPa ad we assume that the thickess part shrikage is 3%. From a part thickess distributio obtaied from BlowSim, ANSYS software is used to make the structural aalysis for the specified loadig [11]. T P Objective Loss value Performace Output Yield Stress Pealty value mea Stress, σ Figure 13 The mechaical loadig of the HDPE bottle: the iteral pressurizatio ad the top displacemet Figure 14 The illustratio of the desig objective for performace optimizatio 4.1 The Objective Fuctio The iitial formulatio for this optimizatio ca be represeted as follows, Miimize: Part_Weight[P(t j )] Desig Variable: P(t j ) Costraits: s i [P(t j ), P, T] σ a 81

10 00 NRC-NSC Caada-Taiwa Joit Workshop o Advaced Maufacturig Techologies, Lodo, Caada Where P(t j ) are the gap opeigs of the cotrollig poits, s i are the stresses of ode i, σ a is the allowable stress of the material, P is the iteral pressure, ad T is the top displacemet. The objective fuctio is modified to obtai a wall thickess distributio of miimal weight subject to stress costraits. The reductio of a elemet thickess results i the icrease of its stress level. Cosequetly, the desig objective ca be replaced by a miimizatio of the stress variace aroud the stress mea close to the stress costrait. The smaller variace of the stress distributio, the closer the mea ca be moved to the allowable material stregth, that leads to thier elemets, ad thus miimal part weight. However, ay elemet stress exceedig the allowable stregth might result i part failure. I this work the costraied optimizatio is replaced by a ucostraied miimizatio of the variace of stress distributio aroud the allowable stress level usig the exteral pealty method as illustrated i Fig.14. The objective fuctio (Eq. [8]) cotais two portios: the quality loss due to variatio of stress distributio ad the pealty loss due to costrait violatio MOBJ = i= 1 ( s σ ) i a + i= 1 < s i σ > a (8) where is the total umber of odes of the simulatio model. The quality loss due to variatio of stress distributio is estimated by the mea squared deviatio of the elemet stress from the allowable stress level that is similar to the objective used i the previous process optimizatio. The average quality loss ca be divided ito two parts: the deviatio of the mea stress from the allowable stregth ad the variatio of the stress aroud mea. The secod portio of the modified objective fuctio, the pealty loss, is estimated usig a secod order sigularity fuctio. This portio accouts for the pealty of elemets violatig the stress costrait. 0, if si σ a < si σ a > = (9) ( si σ a), if si > σ a The search for the desig of miimum objective fuctio will provide a thickess of miimum part weight while satisfyig the stress requiremet. 4. Taguchi s parameter desig 4..1 Experimetal Desig The die gap opeigs at 7 discrete extrusio times are selected as the cotrol factors: P i (t 0 ), P i (t 1 ), P i (t ), P i (t 3 ), P i (t 4 ), P i (t 5 ), ad P i (t 6 ). The iitial desig adopts a uiform die gap opeig of 75%. The L18 orthogoal array is selected as the experimetal desig. For each opeig, we assume a three-levels variatio aroud the iitial desig located i the middle of the desig space. The rage betwee upper ad lower levels represets the desig space. We assume 40% variatio rage. S / N _ ratio = 10 log( MOBJ ) (10) 4.. Parameter desig Taguchi s method applies the aalysis of meas (ANOM) to estimate parameter sesitivities. Fig.15 represets the factor effects for each die opeig o the S/N ratio. A desig with higher S/N ratio has a smaller value of the objective fuctio. Taguchi s additive model estimates the optimum treatmet combiatio to be A 1 B 3 C 1 D 1 E 1 F 1 G 3. The BlowSim simulatio result of Taguchi s optimum shows a S/N ratio of 7.45 that is worse tha the S/N of the iitial desig of 5.6. The failure of Taguchi s approach might due to iteractios amog desig variables ad strog system o-liearity. 8

11 Desig Optimizatio Usig Soft Computig Techiques For Extrusio Blow Moldig Processes -7 S/N ratio A1 A3 A B3 C1 B D1 E1 F1 D C E D3 E3 C3 F G1 F3 G3 G B Desig optimizatio usig FUNTGA Figure 15 The factor effects plot of the bottle case Establishmet of eural etwork FUNTGA uses L18 orthogoal experimets as learig samples for the Back Propagatio Network (BPN) of the extrusio blow moldig process. The iitial desig ad Taguchi s optimum desig are used as testig samples for the traied etwork. There are 14 euros i the first hidde layer ad 6 euros i the secod hidde layer. The iitial learig rate is set to 1.4 ad the iitial mometum term is set to 0.5. The RMS error reduces to after epochs Optimum search usig GA The fuzzy rules for predictio accuracy are applied to GA to improve the searchig efficiecy. The fitess fuctio is defied as follows, Fitess GA = ( S / N _ ratio) / PR (11) The traied etwork will the be used as the fuctio geerator for each chromosome combiatio. The parameters of Geetic Algorithm used i this study are listed i Table 4. Table 4 Geetic Algorithm parameters Populatio size Pool selectio style 0 Paret ad offsprig Scale style Liear scale Cross Over rate Mutatio rate Max iteratio Compariso of the results Fig.16 shows the profiles of optimal die gap opeigs of pariso programmig ad Table 5 compares the stress distributios of the iitial desig ad the optimal oe obtaied from Taguchi s method ad FUNTGA strategy. Taguchi s ANOM approach is disturbed by parameter iteractios ad system o-liearity. Taguchi s optimum provides a mea stress closer to the allowable stregth 33 MPa. However, the large variace of the stress distributio results i stroger violatio of stress costraits tha the iitial desig. FUNTGA s optimum exhibits a mea thickess close to the allowable ad the smallest deviatio i three desigs, which leads to a desig of smaller weight while satisfyig the stress costraits. Fig.17 presets the stress distributios of three desigs. 5 Coclusios This study presets how to apply soft computig techology to determie the optimum die gap opeigs of pariso programmig of extrusio blow moldig process. Taguchi s method is cost effective to obtai a improved desig i a few experimets. However, possible iteractios amog parameters ad system o-liearity could complicate parameter desig. Istead of usig ANOM of Taguchi s experimetal desig, FUNTGA establishes a back propagatio etwork usig Taguchi s experimetal data. Heuristic kowledge of predictio accuracy is 83

12 00 NRC-NSC Caada-Taiwa Joit Workshop o Advaced Maufacturig Techologies, Lodo, Caada applied to GA usig fuzzy rules to steer the search directio. The proposed strategy works well with both the process optimizatio ad the performace optimizatio examples. Extra iteratios usig FUNTGA s approach are possible if further improvemet is desired. The compariso of results demostrates the effectiveess of the proposed strategy. Iitial Taguchi s FUNTGA s 100 Ope (%) Iitial Taguchi's FUNTGA's Extrusio Time (Sec) Figure 16 The optimal desigs from various methods (Mpa) Figure 17 The compariso of the stress distributio Table 5 The compariso of various optima Mea Std.Dev. Pealty Objective Quality Loss Stress Stress Loss Fuctio Iitial Taguchi s FUNTGA s Ackowledgmets The authors would like to thak the Natioal Sciece Coucil of the Republic of Chia for fiacially supportig this research uder Cotract No. NSC90-1-E Refereces [1]. D. Rosato ad D. Rosato, Blow Moldig Hadbook, Haser Publisher, Muich, []. R. W. Diraddo ad A. Garcia-Rejo, O-Lie Predictio of Fial Part Dimesios i Blow Moldig: A Neural Network Computig Approach, Polymer Egieerig ad Sciece, MID-JUNE, v33, 11 (1993) ,. [3]. R. W. Diraddo ad A. Garcia-Rejo, Profile Optimizatio for The Predictio of Iitial Pariso Dimesios From Fial Blow Moulded Part Specificatios, Computers Chem. Egg, v17 8 (1993) [4]. D. K. Lee ad S. K. Soh, "Predictio of Optimal Preform Thickess Distributio i Blow Moldig", Polymer egieerig ad sciece, v36 11 (1996). [5]. G. Taguchi, Performace Aalysis Desig. It. Joural of Productio Research, 16 (1978) [6]. J. S. Jag, C. T. Su ad E. Mizutai, Neuro-Fuzzy ad Soft Computig: a computatioal approach to learig ad machie itelligece, Pretice-Hall, (1997). [7]. C. T. Su, C. C. Chiu ad H. H. C, Parameter Desig Optimizatio via Neural Network Ad Geetic Algorithm, It. Joural Of Idustrial Egieerig, 7(3) (000) 4-31 [8]. BlowSim, 6.0, Idustrial Materials Istitute, Natioal Research Coucil Caada [9]. G. J. Wag, J. C. Tsai, P. C. Tseg ad T. C. Che, Neural-Taguchi Method for Robust Desig Aalysis, Joural of the Chiese Society of Mech. Eg., v19 (1998) 3-30 [10]. J. Yu, X. Che, ad T.R. Hug (001) Optimizatio of Extrusio Blow Moldig Usig Soft Computig ad Taguchi Method, Proceedigs of the Sixth Iteratioal Coferece o Computer Supported Cooperative Work i Desig, July 1-15, 001, Lodo, Otario, Caada. [11]. J. Yu, T.R Hug, ad F. Thibault (00) Performace Optimizatio of Extrusio Blow Molded Parts Usig Fuzzy Neural- Taguchi Method ad Geetic Algorithm, ASME Desig Automatio Coferece 00, Sept., 00, Motreal, Caada. 84