Modelling gas metal arc weld geometry usingartificial neural network technology

Canadian Metallur`ical Quarterly\ Vol[ 27\ No[ 0\ pp[ 32Ð40\ 0888Þ 0887 Canadian Institute of Mining and Metallurgy[ Published by Elsevier Science Ltd\ Pergamon Printed in Great Britain[ All rights reserved

9997Ð3322:88:, ! see front matter

PII] S9997Ð3322"87#99926Ð7

MODELLING GAS METAL ARC WELD GEOMETRYUSING ARTIFICIAL NEURAL NETWORK TECHNOLOGY

BILLY CHAN\$ JACK PACEY% and MALCOLM BIBBY&�$ MIL Systems\ 0049 Morrison Drive\ Ottawa\ Ont[\ Canada K1H 7S8

% Mech[ + Weld[ Technical Department\ Northern College\ Kirkland Lake\ Ont[\ Canada P1N 2L7& Faculty of Engineering\ Carleton University\ Ottawa\ Ont[\ Canada K0S 4B5

"Received 3 July 0887^ received in revised form 0 October 0887^ accepted 0 October 0887#

Abstract*A backpropagation network system for predicting gas metal arc "GMA# bead!on!plate weldgeometry from current\ voltage and wire travel speed is reported in this study[ Moreover\ workpiecethickness is a variable that is taken into consideration because its e}ect on weld shape is to this pointunknown in practice[ The database consists of some ninety six welds "cross!sectional weld shapes andcorresponding welding parameters#[ DCEP polarity\ C!14 shielding and electrode diameter and extensionof 9[8 and 08 mm respectively are assumed _xed for this study*consistent with the experimental databaseused to train and test the technology[ For the purposes of this investigation\ weld bead size and shape arede_ned by bead width\ bead height\ penetration and a new parameter\ bay length at 11[4>\ introduced tomodel the underbead recession that occurs in deeper penetration welds[ For pictorial representation\ theupper bead is modelled by _tting a parabola to the bead width and reinforcement height while a combinationof parabolas is suggested for the bead shape below the plate surface given the width\ penetration and baylength[ Deposit and plate fusion areas are also included[ Finally\ the reverse problem*predicting thewelding parameters "current\ voltage and travel speed# to achieve a given weld shape*is discussed in termsof the study[ Þ 0888 Canadian Institute of Mining and Metallurgy[ Published by Elsevier Science Ltd[ Allrights reserved[

Re�sume�*Dans cette e�tude\ on discute d|un syste�me de re�seau de propagation re�troactive pour la pre�dictionde la ge�ome�trie de la soudure du cordon de�pose� par soudage a� l|arc sous protection gazeuse avec _l!e�lectrode fusible\ a� partir du courant\ du voltage et de la vitesse de de�roulement du _l[ En plus\ l|e�paisseurde la pie�ce est une variable qui est prise en conside�ration parce que son e}et sur la forme de la soudure est\jusqu|a� ce point inconnu\ en pratique[ La base de donne�es consiste en quelque quatre!vingt seize soudures"coupes transversales de formes de soudure et parame�tres de soudage correspondants#[ Dans cette e�tude\on assume que les e�le�ments qui suivent sont _xes] polarite� DCEP "courant direct\ e�lectrode positive#\ gazprotecteur C!14\ diame�tre et extension de l|e�lectrode de 9[8 mm et 08 mm\ respectivement[ Ceci estconsistant avec la base de donne�es expe�rimentales utilise�e pour e�tablir et e�valuer la technique[ Pour les _nsde cette investigation\ la taille et la forme due cordon de soudure sont de�_nies par la largeur du cordon\par sa hauteur\ par la pe�ne�tration et par un nouveau parame�tre\ la longueur de baie a� 11[4>\ introduit pourmode�liser la re�cession sous le cordon qui se produit avec les soudures a� pe�ne�tration plus profonde[ Pourune repre�sentation picturale\ les cordon supe�rieur est mode�lise� en assujettissant une parabole a� la largeurdu cordon et a� la hauteur du renforcement alors qu|une combinaison de paraboles est sugge�re�e pur laforme due cordon sous la surface de la plaque\ e�tant donne� la largeur\ la pe�ne�tration et la longueur de baie[On inclut e�galement les zones de de�po¼t et de fusion de la plaque[ Finalement\ on discute\ dans le cadre decette e�tude\ du proble�me inverse*la pre�diction des parame�tres de soudage "courant\ voltage et vitesse dede�placement# pur l|obtention d|une forme donne�e de soudure[ Þ 0888 Canadian Institute of Mining andMetallurgy[ Published by Elsevier Science Ltd[ All rights reserved[

0[ INTRODUCTION

Weld bead size and shape are important considerations fordesign and manufacturing engineers in the fabrication industry[In fact\ weld geometry directly a}ects the complexity of weldschedules and thereby the construction and manufacturingcosts of steel structures and mechanical devices[ To a largeextent\ the size and shape of a weld bead can be controlled bythe welding parameters "e[g[\ arc current\ voltage\ travel speed\

� To whom correspondence should be addressed[ Tel[] ¦0!502!419!4632^ fax] ¦0!502!419!6370^ e!mail] malcombibbyÝcarleton[ca

32

electrode extension\ electrode diameter\ electrode polarity andplate thickness#[ It is apparent that determining optimal weldingconditions in a given situation is complex because of the numberof competing process variables involved[ In fact\ relativelyextensive _eld trials are often necessary to _x the process inmost cases[ An ability to predict and control weld beadgeometry would reduce the number of such trial runs and sim!plify the process of _xing weld schedules in practice[

Since the solution of a physics based mathematical modeldetailed enough to predict weld bead geometry is complex andthe variables involved are highly coupled\ some researchershave resorted to less comprehensive regression techniques basedon large experimental databases ð0\ 1Ł[ Mathematical relation!

B[ CHAN et al[] MODELLING GAS METAL ARC WELD GEOMETRY33

Fig[ 0[ Experimental weld bead shape trace with weld dimensionde_nitions

ships have been determined for bead width\ reinforcementheight and penetration[ In practice\ these have proven useful[Although regression relationships for predicting weld geometryare now available\ regression expressions for estimating thewelding parameters to obtain a given weld geometry\ i[e[\ thereverse problem\ are not available[ The backpropagation net!work "BPN# system is one of a family of arti_cial neural network"ANN# techniques used to solve physical problems such as thisone including both the forward and reverse situations[ Amongother things\ it is well established as a method for data mapping[In this investigation\ the welding parameters are mapped to theweld dimensions through the internal representation of BPNsand vice versa for the reverse problem[ Examples measuredfrom experiment are provided to a network at the learning stage\e[g[\ welding parameters and weld bead geometry dimensions[During network learning\ the network output is compared withthe desired output "provided from experiment# and the con!nector weights inside the network adjusted to minimize thedi}erence[ When the trained network is presented with newinput "beyond training#\ the network responds according to theknowledge it has acquired[

Weld size and shape are represented by bead width "BW#\bead height "BH# and penetration "Pene# as shown in Fig[ 0[ Inaddition\ two non!traditional weld bead geometry parameters\bay angle "u# and corresponding bay length "lu# are introducedin this study to quantify the internal bead shape[ They areessential for modelling the recession "bay# that occurs in deeperpenetration situations "see Fig[ 0#[ Moreover\ it is sometimesuseful in practice to deal with reinforcement area A0 and platefusion area A1 as shown in the _gure[ BPN technology is usedto predict all of these parameters and geometric shapes _ttedto them to provide a reasonable pictorial representation[

There are other systems similar to the one presented in thisreport for predicting weld geometry^ in particular the work ledby Jones et al[ ð2Ð4Ł[ However\ there is limited algorithm detailreported and thereby available to the research community\apparently because of commercial interests[ In this pres!entation\ the algorithm is well de_ned and su.cient exper!imental experience reported to provide a good basis for furtherdevelopment[

1[ EXPERIMENTAL

Ninety six bead!on!plate gas metal arc welds with C!14 "14)carbon dioxide and 64) argon# shielding were prepared for

Table 0[ Arc current\ voltage\ travel speed and plate thickness rangesused in the GMAW bead geometry investigation

Current Voltage Speed Thickness"amperes# "volts# "mm:s# "mm#

Minimum 059 19 2[28 5[24Maximum 219 31 00[90 04[76

this study ð5Ł[ They were sectioned metallographically to permitbead shape and size measurements[ Several critical parameterswere taken from the weld shape traces as shown in Fig[ 0] beadwidth "BW#\ bead height "BH#\ penetration "Pene#\ bay angle"u# and bay length "lu#[ The size of a weld was represented interms of the deposit and fusion areas\ A0 and A1 respectivelywhich were also measured and documented[ In addition\ thewelding parameters were recorded] arc current "I#\ voltage "V#and travel speed "S#[ Plate thickness "ht# was an independentparameter treated separately in the neural analysis[ Variableranges are listed in Table 0[

The consumable electrode ER69S!5 was used in all cases[Electrode extension\ electrode diameter and electrode polaritywere constant throughout this particular study] 08 mm\ 9[8 mmand DCEP "DC reverse# polarity\ respectively[ The shielding gas~ow rate was set at 24 cubic feet per hour "cfh#[ All workpiecesmeasured 041 mm "5 in# by 395 mm "05 in#[ Of considerablesigni_cance is the fact that the welding conditions covered thethree heat ~ow ranges "1!D\ 1[4!D and 2!D# determined fromthe conventional heat ~ow models of Adams et al[ ð6Ł[ By sodoing\ heat ~ow morphology was incorporated implicitly intothe BPN method[ In general\ there is considerable uncertaintywith respect to heat ~ow regimes in conventional weld processanalyses[ The fact that it can be incorporated without unduedi.culty in a BPN study is one of the merits of the ANNapproach to this problem[

2[ BACKPROPAGATION NETWORK

CONFIGURATION

In general\ a backpropagation network ð7\ 8Ł is a series ofunidirectional inter!connected nodes organized in layers\ asshown in Fig[ 1[ For the basic arrangement\ there are threelayers] input\ hidden and output[ A weight\ Whi or Wij\ is associ!ated with every connection[ The nodes are also called processingunits because the incoming signals are gathered "eqn 0#\ pro!cessed and relayed "eqn 1# to other nodes]

Sum � sfor all i

Wij = Xi "0#

F"Sum# �0

0¦e−Sum"1#

where xi is the incoming signal and F"Sum# is the transferfunction or the nodal output[ For the purposes of this study\ asigmoidal transfer function "eqn 1# is used[ It is very importantto include a bias node in every layer "except for the output layer#

B[ CHAN et al[] MODELLING GAS METAL ARC WELD GEOMETRY 34

Fig[ 1[ A backpropagation network[

for stabilizing the network[ The bias node is always assigned avalue of one and is not connected to the previous layer[

Network prediction is accomplished by signals moving inthe forward sense\ i[e[\ input parameters are submitted to thenetwork through the input layer\ adjusted by the weightedconnections\ and relayed to nodes in the next layer until theyreach the output[ Because the values of the output are limitedto a range between zero and one "9 ¾ yn

j ¾ 0# by the sigmoidaltransfer function\ it is logical to normalize all input and outputparameters accordingly[ In this study\ they were linearly nor!malized between 9[0 and 9[8 since the output will equal zero orone only when F"Sum# is 2�[

Network learning is composed of forward motion signalsand error back!propagation[ The forward motion signals areidentical to the network prediction[ However\ the network com!puted results\ yn

j \ are compared to the desired results\ ydj "pro!

vided in advance from experimental measurements# and theerrors\ Ej\ are backpropagated through the network for weightadjustment[ The forward and backpropagation activities repeatuntil the overall network error\ i[e[\ the root mean squared error"RMS error# is less than a pre!de_ned tolerance level and thelearning is said to be successful[ The RMS error is computedas follows]

RMS error �csp

a�0

st

b�0

"ydab −yna

b #1

p = t"2#

where p is the number of patterns in the training set and t is thenumber of output parameters[ In this study\ a tolerance levelof 9[94 was used[ A tighter tolerance ensures a more accuratesystem but the learning time "and thereby the computerdemands# may increase dramatically[

The weight adjustments are based on the least mean squaresmethod\ otherwise known as the generalized delta rule ð7\ 8Ł asfollows]

Ej �01"yd

j −ynj #1 "3#

The weights of the connectors between the hidden and outputlayers are adjusted by]

Wtij � Wt−0

ij ¦DWtij¦aDWt−0

ij "4#

DWij � nIidJj "5#

dJj � F"Sumj#ð0−F"Sumj#Łðyd

j −ynj Ł "6#

where n is the learning rate\ a is the momentum coe.cient and"t−0# signi_es the previous pass[ The learning time is controlledby the learning rate[ Values between zero and one are rec!ommended for the learning rate[ The network may learn fasterwith a large learning rate\ e[g[\ 9[8[ However\ a large rate tendsto destabilize the learning process[ The momentum term\aDWt−0\ reduces the learning time by recalling a fraction of thelast adjustment[ A typical value of 9[14 is used for a in thisstudy[

The weights of the connectors between the input and hiddenlayers are adjusted by back!propagating the network erros\ Ej]

Wthi � Wt−0

hi ¦DWthi¦aDWt−0

hi "7#

DWhi � nHhdi "8#

dIi � F"Sumi#ð0−F"Sumi#Ł s

t

a�0

"dJaWia# "09#

However\ the learning may become saturated when Sumapproaches 2� and d approaches zero[ This leads to a valueof DW � 9 and the learning stops[ To avoid saturated learning\eqns 6 and 09 are modi_ed as follows]

dJj � "9[0¦F"Sumj#ð0−F"Sumj#Ł#ðyd

j −ynj Ł "00#

dIi � "9[0¦F"Sumi#ðl−F"Sumi#Ł# s

t

a�0

"dJaWia# "01#

as suggested by Fahlman et al[ ð09Ł[ This modi_cation is nowcommonly called the Fahlman derivative[ The value 9[0 is arbi!trary but it is a pragmatic assignment to keep the networklearning[

Instead of using a _xed learning rate\ it can be adjustedaccording to the RMS error as initially proposed by Jacobsð00Ł[ This is termed dynamic learning[ The authors of this studyhave suggested a further modi_cation to the original dynamiclearning algorithm and call it step!declining learning ð01Ł[ Inthe step!declining method\ the rate is reduced by 0) wheneverthe RMS error increases[ In addition\ it is limited to a value of9[994 to avoid a zero learning rate[ By employing the step!declining method\ a large initial learning rate\ e[g[\ 9[4\ can beapplied and the stability of the network is not jeopardized[

In this study\ BPN was used to determine bead width andheight\ penetration and bay length as the critical shape par!ameters[ In addition\ the deposit and fusion areas were deter!mined to provide an independent estimate of weld size[Similarly\ a BPN solution to the reverse problem\ i[e[\ predictingthe welding parameters necessary to achieve a given weld sizeand shape\ which was presented at a recent conference ð02Ł isincluded in the discussion[

3[ WELD SHAPE REPRESENTATION

3[0[ Bay an`le

By measuring bay angles from the mid point of the beadwidth and plate surface "see Fig[ 2# for the 85 bead!on!plate


Fig[ 2[ Frequency diagram of the bay angle of C!14 shielding weld beadshape[

welds "081 measurements#\ the median\ mean and standarddeviation were found to be 11[4>\ 11[3> and 7[1> respectively[The consistency of the results was surprising but at the sametime useful for representing an approximate pictorial shape[ Inview of these results\ a value of p:7 "11[4># is assumed to bethe nominal bay angle for shape representation purposes[ Thisassumption is fortunate since it reduces the number of variablesnecessary to model the bay region[ Therefore the critical welddimensions for de_ning the weld shape in this study are beadwidth\ bead height\ penetration and bay length at 11[4> fromthe weld centreline at the plate surface[

3[1[ Pictorial representation

The upper weld bead shape "Fig[ 0# may be approximatedpictorially from the shape parameters by _tting either a semi!ellipse or parabola to the bead width and bead height[ Notsurprisingly\ neither representation truly matches the shape ofthe reinforcement[ Nonetheless\ either representation providesa reasonable approximation to the deposit area as shown inFig[ 3[ However\ it seems that the ellipse tends to overestimatethe deposit area somewhat while the parabola tends to under!estimate it slightly[ A comparison of the experimental and pic!torial deposit areas is shown in Fig[ 3 and Table 1[ From theseresults\ it seems that the upper!bead shape is best representedby a parabola in general and this is suggested by these authors[

Having _xed the bay angle\ the lower!bead shape can berepresented by two parabolas one rotated 89> and intersectingthe other at l11[4 ð01Ł\ as shown in Fig[ 0[ The use of a double!parabola to represent the lower!bead shape is more accuratethan using alternatives such as a cosine representation\ as shownin Table 1[

4[ NETWORK EXPERIMENTATION

Thirty out of the original ninety six data sets were selectedfor network learning "training data set# and the remainder usedfor _nal network evaluation and veri_cation[ The training dataset was selected randomly from the experimental data set but

Fig[ 3[ Comparison of the actual and pictorial approximated "semi!ellipse and parabola# deposit areas[

covered the entire problem domain\ including extreme cases[The initial connector weights of the networks were set randomlybetween −9[4 and 9[4[ All networks were initially trained with10 out of the 29 training data sets[ The number of trainingpatterns was then increased until the desired accuracy wasachieved[ Various network structures were examined\ e[g[\ onehidden layer with 3 nodes\ one hidden layer with 4 nodes\ twohidden layers with 3 and 2 nodes\ two hidden layers with 4 and2 nodes\ two hidden layers with 5 and 3 nodes and two hiddenlayers with 7 and 5 nodes[

Set "process parameters# to set "bead geometry parameters#mapping is not good BPN practice when the input vector "I\ V\ Sand ht# is smaller than the output vector "BW\ BH\ Pene\ l11[4\ A0and A1# which is analogous to solving a non!trivial problem inmathematical terms[ Therefore\ set "process parameters# to one"one of the weld bead dimensions# mapping was necessary forthis study[ As a result\ four independent networks were used topredict the weld dimensions] bead width "BW#\ bead height"BH#\ penetration "Pene#\ bay length at 11[4> from plate surface"l11[4#[ Each network was used to predict one and only onedimension[ The accuracy of the solution was increased andnetwork training times were reduced by limiting the problemdomain in this way[ Furthermore\ two separate networks wereconstructed to predict deposit area "A0# and plate fusion area"A1# given the welding parameters as described previously[ Aschematic representation of one of the networks is shown inFig[ 4[ The hidden network structure contains one or morehidden layers\ and a bias node[

5[ RESULTS

Three independent statistical parameters are reported toevaluate the results[ The correlation coe.cient is used to mea!sure the relationship between the measured and predicted


Table 1[ Comparison of upper!bead and lower!bead areas with valves from representative algorithms

Absolute di}erenceCorrelation

Area Algorithm coe.cient ) S[D[ "mm1#

Deposit area Semi!ellipse 9[83 01 1[02Parabola 9[83 6 0[33

Fusion area Cosine curve 9[64 14 1[75Double!parabola 9[82 8 0[61

Fig[ 4[ A schematic diagram of the BPN used for predicting the weld bead dimensions[

values[ However\ a high correlation is not necessarily equivalentto accurate predictions since the slope of the measured vs pre!dicted plot is not re~ected "Figs 5Ð8# by this parameter[ There!fore\ absolute percentage di}erence and standard deviation"S[D[# of the absolute di}erence are also included to measurethe spread of the prediction error[

Fig[ 5[ Comparison of BPN predicted bead widths with experimentalvalues[

The most accurate network con_gurations for predictingcritical weld dimensions "BW\ BH\ P and l11[4# and both deposit"A0# and fusion "A1# areas are summerized in Table 2[ Theoptimum number of hidden layers seems to be one or two[ Theadditional complexity of more hidden layers may reduce theaccuracy of the prediction[ Similarly\ the optimum number of

Fig[ 6[ Comparison of BPN predicted bead heights with experimentalvalues[


Fig[ 7[ Comparison of BPN predicted penetrations with experimentalvalues[

Fig[ 8[ Comparison of BPN predicted bay lengths with experimentalvalues[

Table 2[ Summary of results of weld dimensions predictions using BPN technology

Absolute di}erenceWeld No[ of training No[ of hidden No[ of hidden Correlationdimension patterns layers nodes coe.cient ) S[D[ "mm#

BW 10 0 4 9[89 4 9[44BH 17 0 4 9[62 6 9[12Pene 10 1 7:5 9[73 01 9[33l11[4 10 1 3:2 9[73 6 9[19A0 14 0 3 9[79 01 2[12 "mm1#A1 10 1 4:2 9[89 01 6[97 "mm1#

Fig[ 09[ Experimental and predicted weld shapes*plate thickness 8[4mm[ The dotted box is the measured weld size[

training patterns seems to be between 19Ð29[ Additional pat!terns increase training time\ adds little to the accuracy of theoutput\ and can in some cases even reduce the accuracy of theprediction[ Plots of measured vs predicted bead width\ beadheight\ penetration and bay length are shown in Figs 5\ 6\ 7and 8\ respectively[ For visual comparison purposes\ typicalexperimental and predicted weld shapes are included in Figs 09and 00[

6[ DISCUSSION

The use of the BPN technique for modelling the weld beadgeometry problem is attractive in practice[ In the _rst place\ itis not yet possible to provide a physical based solution to theproblem[ In the end\ such a solution would provide a fun!damental understanding of all the factors that control the weld!ing process and this would be preferable[ In the absence ofsuch a solution\ mathematical relationships based on regressionanalyses have been established by Chandel et al[ ð0\ 03Ł andothers ð1Ł that are used by welding and manufacturing engineersin practice[

While the regression technique has provided several useful


Fig[ 00[ Experimental and predicted weld shapes*plate thickness 04[8mm[ The dotted box is the measured weld size[

relationships\ the mathematical form has to be established"guessed# before the analysis and there is little guidance for thepractitioner in this regard[ With the BPN process\ the relation!ship is implicit in the network weights once the learning processis complete[ Moreover\ in principle\ it is relatively easy to add{learning data| to the system "retraining# as experimental experi!ence expands and therefore\ BPN should be convenient in prac!tice[ While this is true in principle\ these authors caution thatin practice it seems to require a judicious selection of trainingdata and considerable operator judgement to ensure reliableoutput[ In other words\ retraining a BPN system is not anexacting process but rather it requires skill and experience[ Thiscan be somewhat unsettling to those who are accustomed tothe precision of a physics based model or even the stability ofregression relationships[ Nonetheless\ a BPN system for antici!pating weld geometry is ~exible and potentially quite useful indesign and manufacturing practice[

There are some di.culties with the presentation of the pic!torial representation[ For example\ the discontinuities associ!ated with the parabola upper!bead "plate surface# and double!parabola lower!bead "bay situation# approximations "see Figs09 and 00#\ are unrealistic[ While this does not make a greatdeal of di}erence to the shape\ discontinuities at the junctionsare not right in principle and criticism on this basis is justi_ed[Extra e}ort would be required to smooth the shape[ However\the extra complexity may not be justi_ed because exacting shapedetail is usually not necessary in practice[ Furthermore\ dis!continuities between upper! and lower!beads can be justi_ed inpractice to some extent because most of the experimental weldshapes examined show relatively sharp corners at these inter!sections[

Instead of _xing the bay angle at a nominal value of 11[4>\another network could be employed to determine the bay anglefor each set of experimental data used for training[ In this way\the predicted weld shape accuracy might be further re_ned[However\ it was found that variations in the bay angle are

surprisingly small and the assumption of p:7 seems su.cientfor approximating the weld bead shape where there is under!bead recession[ It is the judgement of these authors that theadded complexity of a network to determine bay angle is notjusti_ed\ at least in this case\ although it might be necessary inother weld modelling situations[

In general\ the networks used in this investigation predict thelower!bead features "BW\ Pene\ l11[4 and A1# more accuratelythan those of the upper!bead "BH and A0#[ It seems reasonableto suppose that the upper!bead features are subject to morevariation because of environmental conditions "surface tension\slag metal interactions\ etc[# and therefore this is not unex!pected[

An attempt was made to construct a single multi!input andmulti!output system to predict all weld dimensions with onenetwork[ However\ this is not good modelling practice becausethe input vector is smaller than the output vector and in additionaccuracy is sacri_ced by enlarging the problem domain[ None!theless\ a single network was used to estimate welding par!ameters "I\ V\ S# for a given set of weld dimensions"BW\ BH\ Pene and l11[4#\ i[e[\ the reverse problem\ because thisdoes not violate the modelling principle[ Moreover\ it is believedthat the welding parameters and weld dimensions are inter!related in such a way that the solution should always be con!sidered as a set[ Therefore\ solving all three parameters "I\ Vand S# with one network is a more logical approach in this case[However\ because of the increased complexity of the network\the accuracy is not expected to be as high for the reverse prob!lem as it is in the forward case[

Results of the experimentation with the reverse problem\i[e[\ estimating the welding parameters to achieve a given weldshape\ were presented at a recent conference ð02Ł[ The networksuggested to achieve this is shown in Fig[ 01[ A summary of theresults based on experimentation with this system is given inTable 3 to provide a basis for discussion[

Indeed\ the reverse problem is best handled with set to setmapping as supposed\ i[e[\ given the weld bead dimensions"BW\ BH\ Pene\ l11[4 and ht#\ there is a corresponding set ofwelding parameters "I\ V and S#[ Moreover\ the accuracy of thepredicted results is not as high for the reverse problem as it isfor the forward problem "compare the results of Table 2 tothose in Table 3[# as mentioned above\ this is not unexpected\since the reverse problem is more complex[ Although the accu!racy for the reverse problem is lower than that for the weld

Fig[ 01[ A schematic diagram of the BPN used for predicting the weldingparameters[


Table 3[ Summary of welding parameter estimates using BPN� tech!nology ð02Ł

Absolute di}erenceWelding Correlationparameter coe.cient ) S[D[

Current "l# 9[73 8 19[20 "Amps#Voltage "V# 9[75 6 0[86 "Volts#Travel Speed "S# 9[66 01 9[57 "mm:s#

� The BPN is a 1!hidden layer with 5 and 3 hidden nodes networktrained with 10 training patterns[

geometry prediction\ practitioners only need approximate out!put process parameters* such is the nature of the weldingprocess[

Three networks were constructed to test the performance ofthe step!declining learning algorithms[ The networks containedfour input parameters "I\ V\ S and ht# and three output par!ameters "BW\ BH and Pene# with two hidden layers and 6 and4 hidden nodes in each hidden layer[ The numbers of learningiterations required for successful training were recorded for"a# the basic network ð7Ł^ "b# the basic network with dynamiclearning ð00Ł^ and "c# the basic network with step!declininglearning ð01Ł[ The results obtained were 1252\ 1372 and 1079epoches respectively[ These results were based on the averageof three trial runs for each network[ Although the numbers ofepoches for successful training were not greatly di}erent\ severalunsuccessful training runs were experienced with the basic net!work and the original dynamic learning network[ On the otherhand\ the step!declining learning method consistently recordedsuccessful training on the _rst trial or at most after only oneunsuccessful attempt[ Although the step!declining learning net!work does not lead to outstanding performance\ it seems tostabilize the training process[

Designing a backpropagation network is sometimes said tobe more art than science because there are few rules governingthe appropriate numbers of nodes or training patterns to beused[ The complexity of the network structure depends on theinput!output relationship to be determined[ However\ the sim!plest network and the minimum number of training patternsfor the desired accuracy is considered to be the best[ Therefore\a network design always starts with the least nodes and trainingpatterns possible[ Nodes are added as training fails to generatethe accuracy required[ The main disadvantage of the BPN tech!nique is the absence of reasoning[ Therefore\ BPN can be usedas a regression analysis alternative for predicting weld beadgeometry but it is not a replacement for a fundamental physicalsolution for such a problem[

In general\ it is assumed that alloying materials in low alloysteels have minimal e}ect on the weld bead geometry ð03Ł andtherefore the results of this investigation should apply to all lowalloy structural steels in principle[ However\ these authors notethat such an assumption is not always justi_ed although it isconvenient at this point in the absence of more re_ned exper!imental input[ Re_nements to BPN weld bead models will bepossible when alloying e}ects are better understood or whenmore data is available for further BPN processing[ However\

weld bead geometry depends on the fusion temperature\ surfacetension and thermal conductivity which in most cases are rela!tively independent of alloying and the model presented in thisinvestigation is thought to be generally applicable to a widerange of steels[

7[ CONCLUSIONS AND CONTRIBUTIONS

"0# The weld bead geometry problem can be accurately mod!elled by using the backpropagation network technique forDECP polarity gas metal arc welds with C!14 shielding[ Theprinciples and experiences submitted in this investigationsuggest that this technology can be easily extended to otherwelding processes and situation[

"1# A new weld shape parameter\ l11[4 "length from the originto periphery at 11[4> from the workpiece surface# has beende_ned to model the bay shape of deeper penetration welds[Weld shape "pictorial# is best represented by _tting thepredicted weld dimensions to a parabola for the upperreinforcement bead and a double!parabola for the lowerplate fusion zone shape[

"2# The reverse problem\ i[e[\ predicting the welding parametersgiven the bead shape dimensions\ has been discussed andcompared with the forward model[ Set!to!set data mappingrather that set!to!one mapping is recommended in this casebecause of the relative inputÐoutput vector size and thecoupled nature of the problem[

"3# A method termed step!declining learning has been intro!duced in this work to enhance the BPN training stability[

Acknowled`ements*The authors would like to acknowledge the sup!port of the National Science and Engineering Research council\ grantNSERC A3590[ The valuable comments on the application of thebackpropagation network technique by Dr H[M[ Hafez\ Department ofSystem and Computer Engineering\ Carleton University\ were greatlyappreciated[

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