Yarn tenacity modeling using artificial neural networks and development of a decision support system based on genetic algorithms

Transcription

1 Journal of AI and Data Mnng Vol 2, No, 204, Yarn tenacty modelng usng artfcal neural networks and development of a decson support system based on genetc algorthms M Dasht, V Derham 2*, E Ekhtyar Textle Engneerng Department, Yazd Unversty 2 Electrcal and Computer Engneerng Department, Yazd Unversty Receved 25 Aprl 203; accepted 6 September 203 *Correspondng author: vderham@yazdacr (V Derham) Abstract Yarn tenacty s one of the most mportant propertes n yarn producton Ths paper focuses on modelng of the yarn tenacty as well as optmally determnng the amounts of effectve nputs to produce the desred yarn tenacty The artfcal neural network s used as a sutable structure for tenacty modelng of cotton yarn wth 30 Number Englsh The emprcal data was ntally collected for cotton yarns Then, the structure of the neural network was determned and ts parameters were adjusted by the back propagaton method The effcency and accuracy of the neural model was measured based on the error value and coeffcent determnaton The obtaned expermental results show that the neural model could predcate the tenacty wth less than 35% error Afterwards, utlzng genetc algorthms, a new method s proposed for optmal determnaton of nput values n the yarn producton to reach the desred tenacty We conducted several experments for dfferent ranges wth varous producton cost functons The proposed approach could fnd the best nput values to reach the desred tenacty consderng the producton costs Keywords: Artfcal neural network, Genetc algorthm, Yarn tenacty, Modelng, Cotton yarn Introducton The qualty and features of yarn determne possblty of usng t n producton of dfferent fabrcs In ths regard, tenacty s of specal mportance [] In fact, the yarn tenacty affects every next step n the processes of usng t Ths research was performed based on a request from Nakhchn and Nakheaftab factores, whch are two dstngushed textle producton factores located n Yazd, Iran Ths research ams at determnng the best nput values to produce 00% cotton yarn for a desred tenacty We are concerned wth two constrants: frst, although the effectve parameters n the yarn tenacty are almost known but t s not clearly determned how these parameters affect the fnal yarn tenancy In other words, there s no accurate mathematcal model for ths purpose Second, optmal determnaton of nput values to reach a desrable tenacty has not been nvestgated yet In fact, nonlnearty and complexty of the relaton gvng the yarn tenacty n terms of the effectve parameters, have led the textle engneers to determne the values of nput materals only by tral and error and ther former experences Investgatons show that although there s many research fndngs focused on modelng of tenacty but only a few of them proposed a practcal approach to optmal determnaton of values for effectve nputs Some usual methods for the yarn tenacty modelng are mechancal models, mathematcal models [2], statstcal (regresson) methods, fuzzy modelng [3], and artfcal neural network models [7] These prmary methods (mechancal, mathematcal and statstcal) requre hghly experenced personnel as well as numerous of test steps, therefore they could not gve accurate models wth reasonable computatonal costs [8] Artfcal Neural Network (ANN) whch s nspred from evoluton of bologcal neurons of bran s a powerful method for modelng of complex phenomena Some of ts characterstcs such as the ablty of learnng and generalzaton, robustness

2 Dasht et al/ Journal of AI and Data Mnng, Vol 2, No, 204 aganst dsturbances, and nformaton parallel processng have made ANN superor to other modelng approaches Nowadays, ANNs are wdely used for solvng many engneerng problems n modelng, controllng, and patternng recognton [5], [6] Already n an ANN based yarn tenacty predcton research, the fve parameters: spun fbers upper half mean length, package hardness, fneness, proportons of fber length unformty, and maturty of fbers content were used as neural network nput parameters [7] The accuracy of ths neural model was 2% In another study, 4 fber propertes have been used as neural network nputs to predct yarn tenacty [8] These nputs are values of mpurty, number of each package mpurty (amount of trash), upper half mean length, strength and length ncrease to the extent on whch the fber s torn (elongaton of break), fber fneness, brghtness, yellowness, fber maturty content, standard fber fneness (norm), length unformty, and mcronare The accuracy of the later neural model was 8% Two other papers focused on fber propertes measured by Hgh Volume Instrument (HVI) and ncluded upper half mean length, length unformty, short fber content, strength, maturty rato, fneness, grayness, and yellowness used as neural network nput [9],[0] In ths research, we use neural networks n modelng of yarn tenacty of 00% cotton wth 30 Ne, where a new approach, whch s based on genetc algorthms, s used for optmal determnaton of values of nput materals The man advantages and nnovatons on ths research are: - Proposng an accurate neural model for predctng yarn tenacty of 00% cotton yarn Although there are some research works concernng neural modelng, but our model s a real case study wth dfferent nputs and condtons; hence, we use a dfferent structure of ANN 2- Proposng a new dea to fnd the optmal values of nputs to reach desred yarn tenacty by usng genetc algorthms To the best of our knowledge, ths research s the frst research of ts knd The structure of ths paper s as follows In the second secton, yarn tenacty and the parameters whch affect yarn tenacty are nvestgated and dscussed The thrd secton deals wth ntroducng neural networks; n the fourth secton, modelng of yarn tenacty of 00% cotton wth 30 NE (the most popular yarn) usng neural network s presented In the ffth secton, a method to fnd optmal values of nputs to reach a desrable tenacty s proposed Fnally, n the last secton, summary and conclusons are provded 2 Effectve parameters on yarn tenacty The resstance of yarn aganst tensle forces s called yarn tenacty It s the mnmum force whch s needed to tear out that yarn [] Several factors are nvolved n yarn tenancy, and the most mportant ones are the propertes of the fbers used to produce yarn (raw materals) such as: upper half mean length, length unformty, short fber content, fbers strength, maturty rato, yellowness, lnear densty, and fber length ncrease (whch s measured by HVI) Here, the nput varables have been chosen wth respect to the related research [7,8,0] The producton process was set fxed for the whole tme Ths means, fve adjustable parameters for textle machnes such as spn tube, breaker speed, rotor speed, were fxed Moreover, yarn twst and yarn counts were set constant as well In ths way, n our model, the seven mentoned parameters assocated wth fber property were consdered as effectve parameters on yarn tenacty 3 Artfcal neural networks Artfcal neural network s a structure nspred from the human bran It s very useful n modelng complex functons A neural network conssts of an nterconnected group of artfcal neurons where an artfcal neuron s a mathematcal functon representng an abstracton of bologcal neurons [4] Fgure shows the structure of a neuron Vector T x [ x,, x n ] s nput and the scalar y s the output of the neuron xn x w, w,n Fgure Model of a mult-nput neuron The nfluence of x on y s determned by w, Another nput s bas parameter that ts correspondng weght s The output of the neuron s computed by: f b y 74

3 Dasht et al/ Journal of AI and Data Mnng, Vol 2, No, 204 y f ( Wx b) () n (2) z xw, b Wx b [ w,,, w, n W ] (3) The actvaton functon f could be lnear or ether nonlnear Here, the desgner selects a sutable actvaton functon wth respect to the problem features Table shows some wdely used actvaton functons Table Some actvaton functons Functon Defnton Range Lnear Logstc Hyperbolc Threshold z (-,+), a s az e slope parameter z z e e z z e e 0 f z 0 f z 0 (0,+) (-,+) {0,+} In comparson wth sngle layer networks, multlayer neural networks have more capabltes Double layers feed forward neural networks (wth sgmod functons n frst layer and that of lnear n second layer) can estmate any contnuous functon wth arbtrary precson [4] In ths research, we employed a feed forward neural network wth two layers, where the frst layer s known as the hdden layer Fgure 2 shows the correspondng network structure Ths structure s presented as: n:nh:o where n s the number of nputs, nh s the number of hdden layer neurons, and o s the number of output layer neurons The output of network s computed by: y f ( o f ( o nh n j o w x j 2 w b), j b ),, nh (4) (5) where, y s the fnal output, f o s the actvaton 2 functon of output neuron, w s the weght of lnk between -th output neuron n the hdden layer and the fnal output, b s the bas of output neuron, o s the output of -th neuron n hdden layer, the weght of lnk between j-th nput and -th w, j s neuron n hdden layer, b s the bas of -th neuron n hdden layer, and f s the actvaton functon n -th neuron n hdden layer x xn w,n w, w nh,n w nh, w 2 nh w 2 Fgure 2 The feed forward neural network 2 The weghts ( w, w, b, ) are f b f nh b nh b, j adjustable parameters that need to be tuned by tranng In fact, the objectve of network tranng s adjustng these parameters n such a way that the network generates desred output for dfferent nputs 4 Modelng Snce neural networks fnd and learn patterns n the tranng data, n the frst step of modelng, we need some tranng data The cotton yarn wth 30 NE (Number Englsh) s produced n tenacty range of 3 to 6 Some experments have already been conducted on cotton fbers and the yarn 30 NE produced from them n order to collect requred nput data n the mentoned range As stated n Secton 2, seven propertes (see Table 2) of cotton fber are consdered as effectve parameters on yarn tenacty and they are selected as nputs of our model The network output would be the yarn tenacty The actvaton functon for the neurons n the hdden layer s sgmod and t s lnear for the output neuron Here, we use the obtaned data from 33 cotton samples for rng carded spun yarns for nput-output data The tranng data must cover the whole nput range and need to have a sutable dsperson Generally, f we use more tranng data, we would often be more accurate n predcton In the prmary experments of ths research, we used 00 data samples The obtaned result for ths data was poor Therefore, we had to obtan and use more data Here, we encountered some practcal constrants For example, n measurng yarn tenacty for each sample, frst we had to produce the yarn wth those nput materals Fnally, we totally prepared 990 expermental data for tunng our neural network Durng frst experments, we observed that the major problem n tranng our neural model was f o b y 75

4 Dasht et al/ Journal of AI and Data Mnng, Vol 2, No, 204 over fttng In fact, we could see an error whch was gettng smaller and smaller n the course of tranng (for the tranng data) but the magntude of the error for the test data was not acceptable Ths phenomenon was due to the fact that durng tranng phase, the network parameters are adjusted to reduce the error for the tranng data; hence, the network s ftted for the tranng data and ths s why the property of generalzaton of the neural network degrades consderably As a result, network s error n the output of the network was too hgh for any data other than the tranng data Provdng a soluton for the problem, we used some vald data, whch are not used for tranng, but they are only used to stop the tranng properly to avod over fttng After each tranng epoch, network s error was calculated for vald data and f the tranng procedure was gong n a way that the error was ncreasng the tranng would be stopped Therefore, we dvded our data nto three parts: Tranng data, vald data, and test data They ncluded 800, 90, and 00 samples, respectvely The test data was used n the fnal to assess our neural model The statstcal features of the mentoned data shown n Table 2 4 Neural network structure Prevous studes focused on modelng have shown that feed forward networks are sutable for modelng We used a two layer feed forward neural network for modelng It conssts of seven nputs and one output The number of neurons n hdden layer s dfferent for these networks Actvaton functon for neurons n hdden layer s logstc and for the last layer s lnear These networks have been traned usng tranng data regardng the vald data The tranng method was the error back propagaton algorthm Results of the experments on dfferent structures are shown n Table 3 Fbers Characterstcs Fber Tenacty )CN/Tex( Table 2 Statstcal summary of data for fber propertes Fber %50 length Mcronare Elongaton Length Average unformty Reflecton Degree Yellowness Maxmum Mnmum Average Standard Devaton Table 3 Results of tranng on dfferent structures of neural networks Network Structure 7:9: 7:0: 7:: 7:2: 7:3: 7:4: Error Percentage for Tranng Data 33% 3% 08% 35% 2% % Error Percentage for Test Data 2% 35% 04% 04% 64% 6% R2 for Test Data The frst row n the table shows structure of the neural network The error rate for tranng data has been gven n the second row The thrd row shows the error percent for test data, and the determnaton coeffcent [4] has been gven n the last row As Table 3 shows, the best results have been obtaned from the neural network model consstng of 0 neurons n the hdden layer The tranng stopped after 06 epochs The percentage error for ths structure n the tranng phase s 3% and 35% for the test data Comparng the smlar results from [2, 5] ths error s acceptable Therefore, the ANN wth structure of 7:0: s selected as a neural model to predct yarn tenacty 5 Optmal nput values for desred tenacty After fndng the sutable neural model, we turn our attenton to the determnaton of nput parameters to reach the desred tenacty usng Genetc Algorthms (GA) Ths s, n fact, a mult-goal problem From one sde, the producton cost should be mnmzed and from other sde the tenacty of produced yarn should be equal to or hgher than the desred tenacty If the cost reduces but the tenacty s less than the desred value, t would not be acceptable From the other sde, f the tenacty mproves but the cost goes too hgh, t would not be acceptable too In order to overcome ths dlemma, we frst convert t nto an optmzaton problem and then propose an approach to solve t by GA In Secton 2, we ntroduced the seven 76

5 Dasht et al/ Journal of AI and Data Mnng, Vol 2, No, 204 varables whch are effectve n yarn tenacty The cost producton functon C(x) would be: (6) C ( x) v x 7 Where, v s the assgned weght for the -th varable x Weghts show how effectve each parameter s n the cost functon In other words, more expensve varables are expressed by hgher weghts The evaluaton crteron n GA s the ftness functon Here, the algorthm looks for the responses n such a way that the ftness functon decreases to a mnmum value The space of the problem s defned by all combnatons of the values of varables x where they fall n the ranges mentoned n Table 2 Our objectve s to reach the desred tenacty whle the cost functon (Eq 6) s mnmzed The most mportant challenge n usng GA s defnng the sutable ftness functon Here, the ftness functon s defned as: Ft F K * f ( e) C( x) e T T (x) T actual desred actual ( x) Output of NeuralModel of Tenacty e f ( e) 0 e 0 Otherwse (7) ) (8) (9) In the above ftness formula, the frst term s the error functon The error s equal to the dfference between the desred tenacty and the actual tenacty (T actual(x)) The actual tenacty s the tenacty of produced yarn wth x s (the amounts of nput materals) We use the neural model obtaned n Secton 4, to predct the actual tenacty for each x and fnally to compute f(e) n Eq (9) In the frst relaton, K serves as a weght parameter Each ntermedate soluton for a problem n GA s called a chromosome A chromosome conssts of genes, correspondng to a seres of values gven to the problem varables (n our case x s) The number of genes s equal to the number of varables; therefore n our case, each chromosome wll have seven genes Usng values of genes n chromosome as the neural model nput, we can get the tenacty of the yarn as well as the producton cost usng Eq6 In ths way, the ftness functon can be computed for each chromosome If the predcted tenacty (output of neural model) s less than the desred tenacty, then the frst term n ftness functon would be postve and ts amount s error proporton In a stuaton where the predcated tenacty s equal or greater than desred tenacty, the frst term n ftness functon would be zero The second term stands for the producton cost functon As the cost ncreases, the ftness functon wll ncrease, too Regardng the amount of K n Eq 7, snce the man objectve s to reach the desred tenacty, K has to be determned n such a way that GA fnds answers havng frst term equal to zero Snce the maxmum of cost functon s 000, we set K to 000 as well Ths value for K lets one thousandth of error from the desred tenacty be equal to one unt n the second term (cost functon) Ths wll gude our GA model to fnd the solutons wth values n frst term equal to zero In general, a GA s nspred from evaluaton theory It looks for a chromosome that mnmzes the ftness functon The algorthm begns wth a random populaton (some chromosomes), then t uses present populaton to generate new populaton based on the followng steps n each teraton []: The value of ftness functon s computed for each chromosome n the current populaton 2 The algorthm selects some chromosomes based on ther ftness values These chromosomes are called parents and used to generate next generaton Some well known approaches for selecton of parents are: Roulette-wheel selecton, rank selecton, and eltst selecton 3 The algorthm generates chldren wth applyng crossover operaton on selected parents 4 Mutaton on a chld s changng one or more of ts propertes randomly Mutatonal chldren are produced n ths step 5 The obtaned chldren are added to the populaton The algorthm contnues untl t fnds a chld who fts the desred crtera 6 Expermental results To assess the proposed approach, we performed a number of experments wth dfferent desred tenactes and dfferent weghts (v s) as cost functon The objectve was fndng the nput parameters for yarn producton such that the obtaned tenacty becomes greater than the desred tenacty and as a result, the producton cost s mnmzed In the experments, we used one-pont crossover, and mutaton rate of 0; based on the prmary results, the populaton sze was set to 40 77

6 Dasht et al/ Journal of AI and Data Mnng, Vol 2, No, 204 The fnal expermental results are shown n Table 4 The frst column s the desred tenacty, the second column s the obtaned tenacty of the produced yarn, the thrd column s the fnal value of the ftness functon at the termnaton of the search process n GA, and the last column s the value of V for each experment For effcency mprovement of our algorthm, all nput values, x, were normalzed to be n the range of [0, ] Table 4 The results of the experments Tobtaned FtF V Tdesred [ ] [ ] [ ] [ ] [ ] [ ] Table 4 shows that the proposed approach was capable to fnd values for the nput parameters n a way that the obtaned tenacty s satsfactory; the amount of frst term of the ftness functon s equal to zero and the values of the ftness functon are equal to the producton cost Meanwhle, the obtaned values for nputs depend on the amounts of v s For example, the values n the fourth row, (T desred=6, V=[ ]), s: x=[ ] and for the last row wth the same desred tenacty and V=[ ] s: x=[ ] Comparng the two results ndcates that the second case, whch s the weght of frst nput varable n the cost functon, has been decreased (changed from 4 to ), the value of ths nput has been ncreased In opposte, the value of forth nput varable has been reduced due to ts weght ncrease 6 Concluson In ths research, a neural network model of yarn tenacty for 00% yarn cotton 30 NE usng emprcal data s presented The output of neural model for test data confrmed the accuracy of the proposed model Based on the obtaned results n modelng secton, feed forward neural network wth 0 neurons n hdden layers was a sutable structure for modelng of tenacty We also used GA for optmal determnaton of values of nputs n yarn manufacturng The results of the experment showed that GA wth the defned ftness functon can fnd the best values for nputs such that produced yarn wth the obtaned values of nputs satsfy the desred tenacty whle the producton cost becomes mnmal The proposed method can be used to fnd the best-nput values for any knd of yarn producton wth a desred tenacty For usng the proposed method, a user determnes the desred tenacty of yarn and then he/she assgns weghts of nput materals based on ther prces Afterwards, our proposed method presents the amounts of nput materals for yarn producton so that the produced yarn has the desred tenacty, and above all, the producton cost has been mnmzed References [] Taher, A, (990) General Technology of Cotton Textle Industry, (n Persan) Aghabk [2] Majumdar, P K, and Majumdar, A, (2004) Predctng the Breakng Elongaton of Rng Spun Cotton Yarns Usng Mathematcal, Statstcal, and Artfcal Neural Network Models", Textle Research Journal, Vol74, No7, pp [3] Shams Nater, A (2005) Usng Neuro-Fuzzy For Predcton Rng Spun Yarn Strength From Cotton Fbers Propertes", 3rd Internatonal Industral Smulaton Conference, June 9- [4] M Menhaj, (2002) Fundamental of Neural Networks, Amkabr Unversty publcaton, (n Persan) [5] Gharehaghaj, AA, Palhang, M, and Shanbeh, M, (2006) Usng Artfcal Neural Network Algorthm to Predct Tensle Propertes of Cotton-covered Nylon Core Yarns", Esteghlal, Vol 24, No2 [6] Jackowska-Strumllo, L, Ackowsk, T, Cynak, D, Czekalsk, J, (2004) Neural Model of the Spnnng Process for Predctng Selected Propertes of Flax/Cotton Yarn Blends", Abres & Textles In Eastem Europe, Vol 2, No 4, pp 7-2 [7] Sette, S, Boulart, L, Van Langenhove, L Kekens, P, (997) Optmzng the Fber to Yarn Producton Process wth a Combned Neural Network/Genetc Algorthm Approach", Textle Research Journal, Vol 67, No 2, pp [8] Cheng, L, Adams, D L, (995) Yarn Strength Predcton Usng Neural Networks, Part : Fber Propertes and Yarn Strength Relatonshp", Textle Research Journal, Vol 65, No 9, pp [9] Majumdar, A, Majumdar, P K, Sarkar, B, (2004) Selectng Cotton Bales By Spnnng Consstency Index And Mcronare Usng Artfcal Neural Networks", AUTEX Research Journal, Vol 4, No, pp-8 [0] Pynckels, F, Sette, S, Van Langenhove, L, Kekens, P, and Impe K (995) Use of Neural Nets for Detemnng the Spnnablty of Fbres ; Journal of the Textle Insttute; October Vol 86, No 395, pp [] Back, T (996) Evolutonary Algorthms n Theory and Practce, Oxford Unversty Press, New York 78