ISS 1746-7659, England, UK Journal of Informaton and Computng Scence Vol. 5, o. 4, 2010, pp. 271-278 LSSVM Model for Penetraton Depth Detecton n Underwater Arc Weldng Process WeMn Zhang 1, 2, GuoRong Wang 1, YongHua Sh 1 and BLang Zhong 1 1 South Chna Unversty of echnology, Guangzhou, 510640, PR Chna 2 Guangzhou Martme College, Guangzhou, 510725, PR Chna (Receved February 15, 2010, accepted September 9, 2010) Abstract. For underwater arc weldng, t s much more complexty and dffculty to detect penetraton depth than land arc weldng. Based on least squares support vector machnes (LSSVM), weldng current, arc voltage, travel speed, contact-tube-to-work dstance, and weld pool wdth are extracted as nput unts. Penetraton depth s predcted n underwater flux-cored arc weldng (FCAW). For mprovement predcton performance, the LSSVM parameters are adaptvely optmzed. he expermental results show that ths model can acheve hgher dentfcaton precson and s more sutable to detect the depth of underwater FCAW penetraton than back propagaton neural networks (BP). Keywords: underwater arc weldng, penetraton depth, least squares support vector machnes 1. Introducton he weld penetraton depth can manly represent the weld qualty n weld bead geometry (penetraton depth, bead heght, and weld pool wdth) [1]. If the defectve weld penetraton occurrences can be recognzed n tme, the weld qualty can be montored on-lne. For land arc weldng, some reports can be found on montorng weldng qualty through penetraton depth detectng. For underwater arc weldng, t s very hard to detect the depth of penetraton real-tme, ascrbed to the nvsblty of weldng process. Up to now, there s no research report on ths technque n underwater arc weldng, due to ts more complexty and dffculty than land arc weldng. evertheless, the underwater arc weldng technque plays a crtcal role n constructon and mantenance of shps, dockyards, port facltes, and ocean terrace etc [2]. As one of gas metal arc weldng, flux-cored arc weldng (FCAW) s sutable for underwater arc weldng. In ths paper, penetraton depth detectng n underwater FCAW s nvestgated n detal. In order to set up a gudelne for penetraton depth detecton from the mult-sensor data fuson model, the weldng process varables are systematcally and quanttatvely analyzed on ther nfluence on depth of penetraton and weld pool wdth through underwater FCAW experment. Because of hard envronment n underwater FCAW, t s dffcultes to get enough tranng sample sets for penetraton depth predcton. Suggested by Suykens [3-4], the least squares support vector machnes (LSSVM) s more sutable for non-lnearty functon predcton wth a reasonably small sze of tranng sample sets. Wth hgher performance of predcaton than back propagaton neural networks (BP), LSSVM has been very successfully appled n pattern recognton, non-lnear functon estmaton, and machne learnng domans, etc [3-6]. Hence, the LSSVM s ntroduced nto penetraton depth predcton modelng n underwater FCAW. In ths model, the radal bass functon (RBF) s selected as kernel functon and the LSSVM parameters are adaptvely optmzed to mprove predcton performance. 2. Methodology Underwater FCAW s a complex heat transfer process. he formaton of underwater weldng pool s nteracted by electrc feld, magnetc feld, and flow feld. he study showed that the depth of penetraton was manly affected by heat-transfer energy of workpece [7]. Moreover, the workpece thermal energy s manly affected by some underwater weldng process varables, such as weldng current, travel speed, arc Correspondng author. el.: +86-020-82384979. E-mal address: super208956@163.com. Publshed by World Academc Press, World Academc Unon
272 WeMn Zhang, et al: LSSVM Model for Penetraton Depth Detecton n Underwater Arc Weldng Process voltage, and contact-tube-to-work dstance (CWD). Suppose the penetraton depth s P, weldng current s I, arc voltage s U, travel speed s S, and CWD s H. Based on mult-sensor data fuson model, P can be represented as P f ( I, U, S, H ) (1) In addton, there s a relatonshp between the penetraton depth and the weld pool wdth at certan tme and weldng condton. Combned wth the nformaton of weld pool wdth, the detected result of penetraton depth wll be more relable. hus, the depth of penetraton at certan tme can be predcted as P f ( I, U, S, H, W ) (2) where W s the weld pool wdth. In ths study, weldng current I, arc voltage U, and weld pool wdth W wll be acqured and analyzed from weldng current sensor system, arc voltage sensor system, and laser structured vson sensor system. Meanwhle, travel speed S and CWD H can be confrmed and nputted. Wth the hgher performance of predcaton than BP, LSSVM s selected as mult-sensor data fuson model [3-6]. 3. Experment and analyss 3.1. Experment he LSSVM predcton model of relatonshps between penetraton depth and weldng process varables must need to be establshed accurately. hus, the suffcent expermental data must be provded for predcton model tranng and verfyng [8]. Conducted the bead-on-plate weldng, the expermental materals were 140mm 40mm (6~10)mm A3 low-carbon steel plates. In ths study, the chosen weldng process varables were weldng current, arc voltage, travel speed, and CWD. he SQJ501 s used as the flux-cored wre wth a dameter of 1.6 mm. And the Dmenson of water tank s 15000 mm 600mm 500mm. Postoned n a plane 100mm deep water, the workpece weldng procedure s performed. Under the bounds of weldng process varables, the optmum weld geometry could be formed. ravel speed and CWD are confrmed for the same workpece durng underwater FCAW process. Meanwhle, weldng current, arc voltage, and weld pool wdth are detected and recorded n tme. For dfferent workpece, at least one of these parameters s varable. At one tme of underwater FCAW process, weldng current, travel speed, CWD, arc voltage and weld pool wdth are obtaned as nput data of tral model. o measure the penetraton depth, the bead secton was cut transversely from the mddle poston usng the wre cuttng machne. o assure the precson of the specmen dmenson, t was etched by HO 3 3% and H 2 O 97%. Hence, the actual penetraton depth at correspondng tme s measured after weldng and selected as output data of tral model. 3.2. Effects of the weldng current and arc voltage on penetraton depth and weld pool wdth (a) Penetraton depth curves (b) Weld pool wdth curves Fg. 1: Penetraton depth and weld pool wdth wth weldng current and arc voltage varable. JIC emal for contrbuton: edtor@c.org.uk
Journal of Informaton and Computng Scence, Vol. 5 (2010) o. 4, pp 271-278 273 (a) Penetraton depth curves (b) Weld pool wdth curves Fg. 2: Penetraton depth and weld pool wdth wth travel speed varable. Wth 240 mm mn-1 travel speed and 18 mm CWD, true penetraton depth and weld pool wdth curves for dfferent weldng currents at 25V and 30V arc voltage are shown n fg.1. Wth very sgnfcant effect, t s evdent that an ncrease n weldng current results n ncreased penetraton depth and weld pool wdth at all levels of arc voltage. hus, weldng current s the frst parameter to be consdered for decreasng penetraton depth and weld pool wdth. Wth less nfluence than weldng current, there s an ncrease n penetraton depth and weld pool wdth wth an ncrease n arc voltage. hs s due to the fact that, at hgher weldng current and arc voltage, the fuson rate becomes hgher wth hgher fludty of the molten wre and causng larger weld pool. herefore weldng current can assst n penetraton depth control. 3.3. Effect of the travel speed on penetraton depth and weld pool wdth Wth 210A weldng current, 30V arc voltage and 18 mm CWD, the true penetraton depth and weld pool wdth curves for varable travel speed are shown n fg.2. From fg. 2, t can be observed that there s a decrease n penetraton depth and weld pool wdth wth an ncrease n travel speed. But the effect s not very sgnfcant. hs may be due to the fact that, f the weldng speed s ncreased, the weld pool becomes smaller, penetraton depth and weld pool wdth decrease, but only to a certan lmt. 3.4. Effect of the CWD on penetraton depth and weld pool wdth (a) Penetraton depth curves (b) Weld pool wdth curves Fg. 3: Penetraton depth and weld pool wdth wth CWD varable. Fg.3 shows the true penetraton depth and weld pool wdth curves wth dfferent CWD at 210A weldng current, 30V arc voltage and 240 mm mn-1 travel speed weldng condton. hough the CWD does not have much nfluence on penetraton depth and weld pool wdth, compared to weldng current. It can be seen from fg.3 (a), f the CWD s ncreased, that at the begnnng of the drawng the depth of JIC emal for subscrpton: publshng@wau.org.uk
274 WeMn Zhang, et al: LSSVM Model for Penetraton Depth Detecton n Underwater Arc Weldng Process penetraton decreases a lttle and then sharply dmnshes. On the contrary, t can be seen from fg.3 (b) that the weld pool wdth frst ncreases a lttle and then ncreases more wth the further ncrease of CWD. Lower fuson rate may be attrbuted for ths decrease n penetraton depth and ncrease n weld pool wdth wth an ncrease n CWD. 4. he LSSVM model of adaptve optmzng parameters Introduced for nonlnear functon estmaton, LSSVM can be used to predct the depth of penetraton n underwater FCAW process [3-4]. Suppose we are gven a set of tranng data ponts n x, y, where x 1 R denotes the nput space of the sample and has a correspondng target value y R for 1,,. he non-lnear functon estmaton modellng takes the form as: y( x) w ( x) b (3) where (x) denotes the hgh dmensonal feature space whch s nonlnearly mapped from the nput space, w s the weght vector andb s the bas term. hen, n the framework of emprcal rsk mnmzaton the cost functon s formulated subect to the equalty constrans where 1 1 2 mn J ( w, e) w w e (4) 2 2 1 y ( x) w ( x ) b e, 1,, e s the random errors and s a regularzaton parameter n determnng the trade-off between mnmzng the tranng errors and mnmzng the model complexty. Important dfferences wth standard SVM are the equalty constrans and the squared error term, whch greatly smplfes the problem. For solvng ths optmzaton problem, he Lagrange functon s constructed 1 L( w, b, e, a) J ( w, e) a w ( x ) b e y (6) where a R are the Lagrange multplers. he condtons for optmalty soluton can be obtaned by partally dfferentatng wth respect to w,b, e and a L 0 w a ( x ) w 1 L 0 a 0 b 1 L 0 a re e L 0 w ( x ) b e a y 0 After elmnaton of e, w, the followng lnear equaton can be obtaned: y 1 0 1 where y y ; ;, 1 1; ; 1, Mercer condton has been appled 1 ( x ) ( x ) r I 1 a 1 a a ; ;, I s an (5) (7) b = (8) 0 a y dentty matrx, and the JIC emal for contrbuton: edtor@c.org.uk
Journal of Informaton and Computng Scence, Vol. 5 (2010) o. 4, pp 271-278 275 ( x ) ( x ) K( x, x ), where R, K x, x ) s defned as kernel functon. (, 1,, (9) Fnally, the parameters a, b are based on the soluton to (8). As seen n fg.4, LSSVM model regresson can be expressed as [3-4]: y( x) a K( x, x) b 1 where x [ x1, x2,, x l ] denotes the nput vector of ndependent varables, s the sze of data pont sets, y s the correspondng output, s the Lagrange multpler and b s the bas term. a In comparson wth some other feasble kernel functons, the radal bass functon (RBF) s selected as kernel functon due to ts good features [9]. We employ kernel functon wth the form 2 2 (10) K ( x, x) exp( x ) (11) x he wdth of kernel s a postve real constant. here are only two addtonal parameters to be tuned and, whch determne the trade-off between mnmzng the tranng errors and mnmzng the model complexty. If and parameters are selected as fnte canddate tunng sets, k -folds cross valdaton s a popular technque for certan optmzaton parameters (, ) [6]. However, the predcton error accuracy of ths tral may not be satsfed. For mprovng the generalzaton performance and predcton accuracy, an adaptve optmzng parameter method s proposed. he test predcton error of ths tral can be calculated by the followng equaton: 1 2 MSE [ y( ) f ( )] (12) 1 where MSE s the mean square error, y () and f () are the predcton and actual value respectvely, s the sze of the test subsets. Fg. 4: LSSVM model structure. l n Suppose averaged set of l tranng data ponts { x, y } 1 by k, where x R denotes the n dmenson nput space of the sample and has a correspondng target value y R for 1,2,,l. 0 s satsfacton MSE, mn s mnmum MSE for every certan (, ), L s the tranng steps, s the mum of, and s the mum of. he proposed adaptve parameter optmzaton procedure for LSSVM s descrbed as follows: l Step 1: Input { x, y } 1, 0, k,,, L, L 0. Step 2: L L 1. Step 3: Cross combnaton, ) ( JIC emal for subscrpton: publshng@wau.org.uk
276 WeMn Zhang, et al: LSSVM Model for Penetraton Depth Detecton n Underwater Arc Weldng Process ( 0.1 2 L L ) ( 0,, L); 0.01 ( Step 4: k - folds cross valdaton for certan parameters, ). ( L 2 Step 5: Go to step 3 untl t has mplemented ( L 1) ( L 1) generatons. L ) ( 0, L). Step 6: Calculate mn ( 1,,( L 1) ( L 1), reserve mn and correspondng (, ). mn Step 7: If mn 0 and L L, go to step 3. Step 8: Obtan certan optmzng parameters (, ). Fnally, the LSSVM model of adaptve optmzng parameters s set up for penetraton depth predcton n underwater FCAW. 5. Results and Verfcaton In the underwater FCAW experment, weldng current, arc voltage, travel speed, CWD, and weld pool wdth are selected as nput unts. Because of heat nerta, the currently and three-before tme weldng current, arc voltage and weld pool wdth are all obtaned as nputs [10]. Fnally, the total 14 nput unts are I( t), I( t 1), I( t 2), I( t 3), U ( t), U ( t 1), U ( t 2), U ( t 3), W ( t), W ( t 1), W ( t 2), W ( t 3), S (t) and H (t). Meanwhle, the one output s penetraton depth P (t). 2 able 1 Compare the predcton performance between BP and LSSVM. Predcton model MSE MaxAE MeanAE C (s) BP 0.010 0.34 0.07 2457.26 LSSVM 0.003 0.40 0.03 1125.70 In ths study, cross valdaton s averaged by four, L s 50,000, 0 of MSE s 0.004, s 1000, and s 100. Usng adaptve optmzng parameter method, the optmzaton parameters (, ) are obtaned. Gven the orgnal data pont sets, the LSSVM model s establshed. he test predcton error of valdaton data pont sets and modellng tme are lsted n table 1. he MaxAE (Maxmum Absolute Error) and the MeanAE (Mean Absolute Error) are calculated by followng equatons: MaxAE [ y( ) 1 f ( )] 1 MeanAE [ y( ) f ( )] (14) where y (), f () and are the same as (5). he C s the modellng tme. In addton, the BP model s ntroduced to compare the performance of ths LSSVM model. he non-lnear actvaton functon of BP s the sgmod functon 1 f ( x) 1 exp( x) (15) he optmzed BP structure s 14-12-1 three layers network. he BP algorthm wth momentum s chosen as algorthm of gradent method, and the tranng rate s 0.5, the momentum factor s 0.3 [10]. For the same orgnal data pont sets, cross valdaton s also averaged by four, and the tranng steps are 50,000 to confrm BP parameters. In order to compare the performance of predcton model, the test predcton error of valdaton data pont sets and modellng tme are also lsted n table 1. Moreover, the error curves of the predcton and actual value for valdaton data pont sets are shown n fg.5 to compare predcton precson between LSSVM and BP. (13) JIC emal for contrbuton: edtor@c.org.uk
Journal of Informaton and Computng Scence, Vol. 5 (2010) o. 4, pp 271-278 277 Fg. 5: Predcton error results of penetraton depth. Except MaxAE for LSSVM model n table 1, the other results of test predcton error are all better and the modellng tme s less than BP model. Also, predcton error of LSSVM s usually less than BP n fg.5. Because of strong non-lnear characterstcs, a lot of tranng data samples must be requred to establsh BP model n underwater FCAW. Fewer tranng data wll cause neutral network learnng not enough. But the LSSVM algorthm s sutable for small data samples learnng. Further more, the predcton error accuracy s assured and the complexty of computaton s reduced by the proposed adaptve optmzng parameter method. Compared wth BP, the dentfcaton precson and modellng effcency are all mproved. 6. Concluson Represented by weld penetraton depth, the weld qualty s successfully detected wth LSSVM model n underwater FCAW. In order to evaluate the penetraton depth, the effects of underwater weldng process varables on penetraton depth and weld pool wdth are analyzed. he parameters and of LSSVM are adaptvely optmzed to avodng the unsatsfed predcton error accuracy. As a result, the depth of penetraton can be detected effectvely. Expermental analyss proves that ths model can obtan hgher predcton performance and s more sutable for penetraton depth detecton than BP n underwater FCAW. 7. Acknowledgements hs work was supported by the atonal ature Scence Foundaton of Chna (o. 50705030) and the Guangdong Provncal Hgh School ature Scence Research Important Proect of Chna (o.06z028). 8. References [1] B. S. Sung, I. S. Km, Y. Xue, et al. Fuzzy regresson model to predct the bead geometry n the robotc weldng process. Acta Metallurgca Snca(Englsh Letters). 2007, 20(6):391-397. [2] A. P. Mchale. Underwater wet weldng became a vable opton. Weldng & Fabrcaton. 1998, 66(6): 12-14. [3] J. A. K. Suykens, J. Vandewalle. Least squares support vector machnes classfers. eural Processng Letters. 1999, 9(3):293-300. [4] J. A. K. Suykens, J. Vandewalle. Recurrent least squares support vector machnes. IEEE rans. Crcuts Systems-I. 2000, 47(7): 1109-1114. [5] J. A. K. Suykens, J. De Barbanter, and L. Lukas, et al. Weghted least squares support vector machnes: robustness and sparse approxmaton. eurocomputng. 2002, 48(1-4): 85-105. [6] D. F. Sh,.. Gndy. ool wear predctve model based on least squares support vector machnes. Mechancal Systems and Sgnal Processng. 2007, 21: 1799-1814. [7] M. A. Wahab, M. J. Panter, and M. H. he predcton of the temperature dstrbuton and weld pool geometry n the gas metal arc weldng process. Journal of Materals processng technology. 1998, 77: 233-239. [8] C. S. Wu, J. Q. Gao, and Y. H. Zhao. A neural network for weld penetraton control n gas tungsten arc weldng. Acta Metallurgca Snca(Englsh Letters). 2006, 19(1): 27-33. JIC emal for subscrpton: publshng@wau.org.uk
278 WeMn Zhang, et al: LSSVM Model for Penetraton Depth Detecton n Underwater Arc Weldng Process [9] J. C. Patra, A. V. D. Bos. Modelng of an ntellgent pressure sensor usng functonal lnk artfcal neural networks. ISA ransactons. 2000, 39: 15-27. [10] S. B. Chen, Y. Zhang, and. Qu, et al. Robotc weldng systems wth vson-sensng and self-learnng neuron control of arc weldng dynamc process. Journal of Intellgent and Robotc Systems. 2003, 36: 191-208. JIC emal for contrbuton: edtor@c.org.uk