Modeling of cotton yarn hairiness using adaptive neuro-fuzzy inference system

Transcription

1 Indan Journal of Fbre & Textle Research Vol. 35, June 2010, pp Modelng of cotton yarn harness usng adaptve neuro-fuzzy nference system Abhjt Majumdar a Department of Textle Technology, Indan Insttute of Technology, Delh , Inda Receved 9 November 2009; revsed receved and accepted 3 December 2009 Ths paper reports the modelng of cotton yarn harness usng adaptve neuro-fuzzy nference system, combnng the advantages of both artfcal neural network and fuzzy logc. Three cotton fbre propertes, namely mean length, short fbre content and maturty, measured by the advanced fbre nformaton system and the yarn lnear densty (Englsh count, Ne) have been used as the nputs to the model. Two levels of membershp functon have been consdered for each of the four nputs and sxteen fuzzy rules are traned. The developed model predcts the cotton yarn harness wth average error of around 2% even n the unseen test samples. Traned fuzzy rules gve good understandng about the role of varous nput parameters on the cotton yarn harness. Yarn count and cotton fbre mean length are havng major role n determnng the yarn harness. Hgher cotton fbre maturty reduces the yarn harness. Keywords: Artfcal neural network, Cotton, Fuzzy logc, Harness, Membershp functon, Neuro-fuzzy system, Yarn 1 Introducton Harness, one of the most mportant propertes of spun yarn, s usually characterzed by the amount of fbres protrudng out of the compact yarn body. In a spun yarn, majorty of the fbre ends are embedded n the man structure, whereas some other ends may protrude out of the yarn body creatng harness. Yarn harness has great nfluence on the subsequent preparatory and fabrc manufacturng processes lke szng, weavng and knttng. Hgher harness ncreases the cost of szng as more sze chemcals are consumed to form coatng on the hary yarn body. Durng the sheddng operaton n weavng, the hary yarns often entangle wth each other and thus hnder the creaton of dstnct shed, whch s essental for the passage of the shuttle or projectle. In case of ar-jet weavng, the yarn harness ncreases the ar-drag exerted on the yarns. Hary yarns generate fly durng the knttng and obstruct the smooth functonng of the machne parts ncludng needles. Yarn harness s also detrmental for the fabrc appearance as peels are created durng use. However, certan harness n the yarn s also desred so that the fabrc possesses softer feel and warmer hand. Yarn harness s nfluenced by the fbre parameters as well as spnnng process parameters and therefore researchers have made efforts to relate the yarn harness wth the fbre propertes and process a E-mal: abhtextle@redffmal.com; majumdar@textle.td.ac.n parameters. Pllay 1 found that torsonal rgdty of cotton fbre s the most mportant parameter nfluencng the yarn harness. He reported that flexural rgdty and mean fbre length are the parameters n the order of nfluence after the torsonal rgdty. Neckar and Voborova 2 developed a mathematcal model to predct the number of hars of cotton yarns n the harness regon from the average cross-sectonal area of fbre and packng fracton of yarn. Chasmawala 3 derved a lnear regresson equaton for predctng the harness of ar-jet spun yarns. However, the predcton accuracy of mathematcal models, n general, s not very encouragng due to the dealzed assumptons nvolved. On the other hand, statstcal regresson equatons gve much better predcton accuracy. However, pror estmaton of the type of functonal relatonshp between nputs and output s necessary for developng regresson model. Besdes, lnear regresson models fal to capture the nonlnear relatonshps between nputs and output. In recent years, there has been growng use of artfcal neural network (ANN) to predct varous propertes of textle yarns 4-8. Rajamanckam et al. 9, Guha et al. 10 and Majumdar and Majumdar 11 have demonstrated that the predcton performance of ANN models s much better than that of classcal mechanstc or regresson models. Zhu and Ethrdge 12 forecasted the harness of rng- and rotor-spun yarns from the fbre propertes measured by HVI, AFIS and tradtonal

2 122 INDIAN J. FIBRE TEXT. RES., JUNE 2010 testng nstruments usng back-propagaton ANN. They found that the HVI model s the best predctor of rng and rotor yarn harness. However, the major drawback of ANN model s that t acts lke a black box wthout revealng any nformaton about the ntrcaces of the process. It s very good n decson makng but does not explan how t arrves at a partcular decson. Fuzzy modelng technque can help ANN n a great way by dscoverng the lngustc rules whch relate the nputs (antecedent part) and outputs (consequent part). Therefore, amalgamaton of neural network and fuzzy logc would gve the advantages of both the ntellgent systems. Neuro-fuzzy systems have already been used by Fan et al. 13, Huang and Chen 14, Huang and Yu 15 and Ucar and Ertuguel 16 for fabrc drape modelng, fabrc defect dentfcaton, dyeng defect dentfcaton and knttng machne parameter predcton respectvely. Hybrd neuro-fuzzy system has also been employed to predct the tenacty, elongaton and unevenness of spun yarns They found that the predcton accuracy of the neuro-fuzzy model s hgher than that of lnear regresson and ANN models. However, there has been no publshed lterature, whch focuses on the modelng of cotton yarn harness usng neuro-fuzzy system. The present study s therefore undertaken to develop a model to predct cotton yarn harness usng adaptve neuro-fuzzy nference system, combnng the advantage of both artfcal neural network and fuzzy logc. 2 Materals and Methods 2.1 Data Collecton and Analyss Cotton crop study results of 1997 by the Internatonal Textle Centre, Texas Tech Unversty, USA 20 have been used n ths study. Bales of Upland and Pma were tested for fbre propertes (mean length, short fbre content, maturty, neps, seed coat neps and trash) usng Zellweger Uster AFIS (N). Carded rng-spun yarns of 16s, 22s and 30s were produced usng Saco Lowell SF-3H rng spnnng frame wth a spndle speed of 10,000 rpm. Yarn harness was measured by Uster Tester III usng optcal prncple. The nstrument calculates the harness ndex, whch s the cumulatve length of all protrudng fbres outsde the yarn body per unt length of yarn. The database was havng 54 data sets of fbre and yarn propertes for rng-spun yarns. Thrty-sx data sets were randomly chosen for the tranng or model development. The remanng 18 datasets were used to valdate the models. The summary statstcs of fbre propertes and yarn count s shown n Table Fuzzy Set Theory and Fuzzy Logc A fuzzy set s an extenson of a classcal crsp set 21. A fuzzy set contans elements wth only partal membershp rangng from 0 to 1 to defne uncertanty for classes that do not have clearly defned boundares 22. If X s the unverse of dscourse and ts elements are denoted by x, then a fuzzy set A n X s defned as a set of ordered pars as A = { x, µ ( x) x X} A where µ A (x) s the membershp functon of x n A. Once the fuzzy sets are chosen, a membershp functon for each set s created. A membershp functon s a typcal curve that converts the nput between 0 and 1, ndcatng the belongngness of the nput to a fuzzy set. Ths step s known as fuzzfcaton. Membershp functon can have varous forms, such as trangle, trapezod, sgmod and Gaussan. Trangular membershp functon s the smplest one and t s a collecton of three ponts formng a trangle as shown below: x L, for L < x < m m L R x µ ( ), for m x R A x = < < R m 0, otherwse where m s the most promsng value; and L and R, the left and rght spread (the smallest and largest value that x can take). The trapezodal membershp curve has a flat top and t s just a truncated trangle producng µ A (x) = 1 over a large regon of unverse of dscourse. The trapezodal curve s a functon of a vector x and depends on four scalar parameters namely a, b, c, and d, as shown below: 0, for x a or x d x a for a x b b a µ A( x) = 1, for b x c d x, for c x d d c Table 1 Summary statstcs of fbre propertes and yarn count Fbre/yarn propertes Mnmum Maxmum Mean Mean length, nch Short fbre content, % Maturty rato Yarn count, Ne

3 MAJUMDAR: MODELING OF COTTON YARN HAIRINESS 123 The Gaussan membershp functon depends on two parameters, namely standard devaton (σ) and mean (µ) and t s represented as shown below: 2 ( x ) 2 2σ µ µ A( x ) = e After determnng the nput and output fuzzy sets, the lngustc terms are then used to establsh fuzzy rules. Fuzzy rules provde quanttatve reasonng that relates nput fuzzy sets wth output fuzzy sets. A fuzzy rule base conssts of a number of fuzzy f-then rules. For example, n the case of two-nput and sngle-output fuzzy system, t could be expressed as follows: If x s A and y s B then z s C where x, y and z are the varables representng two nputs and one output; and A, B and C, the lngustc values of x, y and z respectvely. The output of each rule s also a fuzzy set. Output fuzzy sets are then aggregated nto a sngle fuzzy set. Ths step s known as aggregaton. Fnally, the resultng set s resolved to a sngle output number by defuzzfcaton. 2.3 Neuro-fuzzy Modelng System Neuro-fuzzy system combnes the fuzzfcaton technque of fuzzy logc wth the learnng capablty of ANN. Therefore, t possesses the merts of both the approaches and can ft the tranng data more accurately. Artfcal neural network technque ads the fuzzy modelng procedure to learn the nformaton about the data set and computes the membershp functon parameters that allow the assocated fuzzy nference system (FIS) to track the gven nput-output data. ANFIS (adaptve network based fuzzy nference system) s a class of adaptve network that s functonally equvalent to FIS 23. Usng a gven nput-output data, ANFIS constructs a FIS whose membershp functon parameters are adjusted usng ether a back-propagaton algorthm or a hybrd learnng algorthm (a combnaton of backpropagaton and least squares method). Fgure 1 llustrates the archtecture of ANFIS havng fve layers assumng that there are two nputs x and y and only one output z. A common rule set wth two fuzzy f-then rules s shown below. Rule 1: f x s A 1 and y s B 1 then f1 = p1x + q1 y + r1 Rule 2: f x s A 2 and y s B 2 then f = p x + q y + r Layer 1: Every node n ths layer s an adaptve node wth a node functon as shown below: O1, = µ A ( x) for = 1,2 or O1, = µ B ( y) for =3,4. 2 where x and y are the nputs to node ; and A and B, the lngustc level (fuzzy sets such as long or short) for nputs x and y respectvely, assocated wth ths node. O 1 s the membershp grade of a fuzzy set A (=A1, A2) or B (=B 1, B 2 ) Layer 2: Every node n ths layer s a fxed node labelled Π, whose output s the product of all the ncomng sgnals, as shown by the followng relatonshp: O2, = µ A ( x) µ B ( y) = w, =1, 2. Each node output represents the frng strength of a rule. In general, any other T-norm operators that perform fuzzy AND can be used as the node functon n ths layer. Layer 3: Every node n ths layer s a fxed node labelled N. The th node calculates the rato of the th rule s frng strength to the sum of all rules frng strengths. The output of ths layer s called normalzed frng strength. The expresson s shown below: O 3, w w + w = = 1 2 Fg. 1 ANFIS archtecture w (1) Layer 4: Every node n ths layer s an adaptve node wth the node functon, as shown below: O = w f = w ( p x + q y + r ) (2) 4, where w s the normalzed frng strength from layer 3; and {p, q, r }, the parameter set of ths node. Parameters n ths layer are referred to as consequent parameters. Layer 5: The sngle node n ths layer s a fxed node labelled, whch computes the overall output as

4 124 INDIAN J. FIBRE TEXT. RES., JUNE 2010 the summaton of all ncomng sgnals, as shown below: w f Overall output = O5, = w f = (3) w 2.4 Optmzaton of ANFIS Parameters For neuro-fuzzy modelng, selectng the proper combnaton of nputs and determnng the number of membershp functons for each nput are very mportant snce they determne the number of rules to be traned. If α s the number of membershp functon for each nput and β s the number of nputs, then there are α β rules to be traned. As there were only 36 data sets for tranng, the number of rules was kept at such a level that they could be adequately traned. An nput selecton scheme was employed to elct the best combnaton of nputs usng MATLAB programmng command. It was found that the combnaton of mean length, short fbre content, maturty and yarn count (Ne) was optmum for the neuro-fuzzy modelng. Trangular, trapezodal, sgmod and Gaussan type membershp functons were tred and t was found that the Gaussan form wth two membershp functons for each nput s gvng the best predcton accuracy. Therefore, the total number of fuzzy rules nvolved n ths modelng was 2 4 = 16. As the Gaussan membershp functon s defned by two parameters (mean and standard devaton), the total number of non-lnear parameters was 16 (2 membershp functons 4 nputs 2 non-lnear parameters). The output membershp functons for the consequent part were constant type. So, the total number of lnear parameters was 16. The antecedent parts of the fuzzy rules were connected wth fuzzy AND functon, as shown below: { } Fuzzy and = prod µ ( x), µ ( x) = µ ( x). µ ( x) A B A B For the defuzzfcaton, weghted average method was used. For neuro-fuzzy modelng, the fuzzy logc toolbox of MATLAB software (verson 7.3) was used. 3 Results and Dscusson 3.1 Predcton Performance of Neuro-fuzzy Model Table 2 shows the overall predcton performance of neuro-fuzzy model n the tranng and testng data set. The mean absolute error of predcton n the tranng and testng data sets s qute low.e. 1.91% and 2.07% respectvely. The scatter plot of actual and predcted harness of all the tranng and testng samples s shown n Fgs 2 and 3 respectvely. The coeffcents of determnaton of the tranng and testng data set are and respectvely. The comparatve error of predcton and coeffcent of determnaton n the tranng and testng data sets sgnfy good generalzaton of the neuro-fuzzy model. Ths s because f the tranng s contnued for too long then the error of predcton wll be very low for the tranng data set, whereas the error of predcton wll be very hgh for the testng data set. Ths s called over-tranng. Durng the tranng of neuro-fuzzy model, t s observed that as the tranng epoch ncreases the r.m.s. error n the tranng data shows concomtant reducton. However, the r.m.s. error n the testng data frst reduces up to the 4 th epoch and then ncreases as shown n Fg. 4. To prevent the Table 2 Summary of predcton results n tranng data Statstcal parameter Tranng data Testng data Correlaton coeffcent (R) Mean absolute error, % Maxmum absolute error, % r.m.s. error Fg. 2 Actual and predcted harness n the tranng data set Fg. 3 Actual and predcted harness n the testng data set

5 MAJUMDAR: MODELING OF COTTON YARN HAIRINESS 125 over-tranng of the model, tranng was ceased as soon as the 4 th epoch was reached and mnmum r.m.s. error n the testng set was attaned. 3.2 Fuzzy Lngustc Rules Fgure 5 shows the sxteen fuzzy rules, whch are relatng the four nput parameters and yarn harness n the form of fuzzy nference system. All the nputs are havng two membershp functons (low and hgh) of Gaussan form. The output parameter or yarn harness s havng sxteen membershp functons (constant type), one each for every fuzzy rule. Rule 1 nterprets that f the fbre length s low, the short fbre content s low, maturty s low and the yarn count s Fg. 4 Tranng and testng errors coarse (low value of Ne) then the yarn harness s From rules 1 and 2, t could be nferred that as the yarn count becomes fner (hgher value of Ne) keepng all other nput varables at the same level, yarn harness reduces to Comparng rules 1 and 9, t could be nferred that the ncrease n cotton fbre mean length from low to hgh reduces the yarn harness from 5.79 to Ths dfference s neglgble from practcal pont of vew. It s observed from Fg. 5 that when the values of mean fbre length, short fbre content, maturty and yarn count are 0.82 nch, 8.4%, 0.85 and 15.8 Ne respectvely, fuzzy rules 1 and 3 are actve wth certan strength whch s ndcated by the heght of the black pllars. Fnally, the weghted average of these two fuzzy outputs (5.79 and 6.68) s calculated to obtan the yarn harness of Influence of Input Parameters on Yarn Harness Fgure 6 shows the surface plots of yarn harness when two nput parameters are vared wthn the expermental range keepng the thrd and fourth nput varables fxed at ther md value. Fgure 6 (a) shows the effect of cotton fbre length and short fbre content on the yarn harness when cotton fbre maturty and yarn count were kept constant at 0.85 and respectvely. It s evdent from Fg. 6 (a) that the nfluence of cotton fbre mean length on yarn Fg. 5 Sxteen fuzzy rules relatng the nputs and yarn harness

6 126 INDIAN J. FIBRE TEXT. RES., JUNE 2010 Fg. 6 Influence of (a) mean length and short fbre content; (b) mean length and maturty; (c) mean length and yarn count; (d) maturty and short fbre content; (e) yarn count and short fbre content; and (f) maturty and yarn count, on yarn harness harness s more domnant than that of short fbre content. As the fbre length ncreases the possblty of a fbre to be embedded n the yarn body from the spnnng trangle ncreases and therefore yarn harness reduces. The maxmum yarn harness s obtaned when mean cotton fbre length s mnmum and short fbre content s maxmum. Ths s harmonous wth the establshed percepton of the spnnng process. Fg. 6 (b) depcts the smultaneous nfluence of cotton fbre mean length and maturty on the yarn harness. Hgher cotton fbre maturty gves lower yarn harness and ths effect s more promnent at hgher fbre length. At lower cotton fbre length the effect of maturty on yarn harness s almost nsgnfcant. Matured cotton fbres are less prone to damage durng the mechancal processes of spnnng due to ther hgher strength and therefore there are less chances of fbre breakage. Broken fbres ultmately reduce the mean cotton fbre length. The mnmum yarn harness s attaned wth the combnaton of maxmum cotton fbre length and maxmum maturty. Ths fndng s agan n agreement wth the knowledge of spnnng process. Fgure 6 (c) shows that as the yarn count becomes coarser (lower value of Ne) the yarn harness ncreases contnuously. Ths s due to the fact that as the yarn count becomes coarser, the number of fbres n the yarn cross-secton ncreases and therefore the

7 MAJUMDAR: MODELING OF COTTON YARN HAIRINESS 127 probablty of a fbre to protrude out of the yarn body also ncreases, resultng n more harness. Fgure 6 (d) shows the smultaneous effect of cotton fbre maturty and short fbre content on yarn harness. The maxmum harness s observed wth the maxmum level of short fbre content and mnmum level of cotton fbre maturty. However, at hgher fbre maturty level, yarn harness s reducng wth the ncrease n short fbre content, whch s rather nexplcable. Fgure 6 (e) shows that yarn count has much more domnant role n nfluencng yarn harness than the short fbre content. At coarser yarn counts, hgher short fbre content ncreases the yarn harness further, as short fbres are havng lower number of contact ponts wth the neghbourng fbres and therefore they are more prone to protrude out of the yarn body causng harness. Fgure 6 (f) depcts the smultaneous nfluence of yarn count and cotton fbre maturty on yarn harness. Coarser yarn counts and lower cotton fbre maturty produce hgher yarn harness. However, the role of yarn count s more pronounced as compared to that of maturty n nfluencng yarn harness. 4 Conclusons The harness of cotton spun yarns has been successfully modeled usng adaptve neuro-fuzzy nference system. Three cotton fbre propertes and yarn lnear densty have been used as the nputs to the model. The predcton accuracy of the neuro-fuzzy model s found to be very hgh. The mean absolute error of predcton s around 2%. The developed fuzzy rules explaned the role of varous nput parameters on the cotton yarn harness. The nfluence of cotton fbre length and yarn count s found to be domnant on yarn harness. Yarn harness reduces as the cotton fbre mean length ncreases and yarn becomes fner. Hgher cotton fbre maturty also reduces the yarn harness. The nfluence of short fbre content on yarn harness s not very pronounced. Hgher short fbre content ncreases the yarn harness when mean fbre length s low and yarn count s coarser. References 1 Neckar B & Voborova J, Yarn harness: A new theory and expermental method, paper presented at the 7 th Asan Textle Conference, New Delh, 1-3 December, Pllay K P R, A Study on the harness of cotton yarns, Part 1: Effect of fbre and yarn factors, Text Res J, 34 (1964) Chasmawala R J, Hansen S M & Jayaraman S, Structure and propertes of ar-jet spun yarn, Text Res J, 60 (1990) Cheng L & Adams D L, Yarn strength predcton usng neural networks, Text Res J, 65 (1995) Ramesh M C, Rajamanckam R & Jayaraman S, Predcton of yarn tensle propertes usng artfcal neural networks, J Text Inst, 86 (1995) Ethrdge D & Zhu R, Predcton of rotor spun cotton yarn qualty: A comparson of neural network and regresson algorthm, paper presented at the Beltwde Cotton Conference, 6-9 January Zhu R & Ethrdge D, The predcton of cotton yarn rregularty based on the AFIS measurement, J Text Inst, 87 (1996) Pynckels F, Kekens P, Sette S, Langenhove L V & Impe K, The use of neural nets to smulate the spnnng process, J Text Inst, 88 (1997) Rajamanckam R, Hansen S M & Jayaraman S, Analyss of modellng methodologes for predctng the strength of ar-jet spun yarns, Text Res J, 67 (1997) Guha A, Chattopadhyay R & Jayadeva, Predctng yarn tenacty: a comparson of mechanstc, statstcal and neural network models J Text Inst, 92 (2001) Majumdar P K & Majumdar A, Predcton of rng spun cotton yarn elongaton usng mathematcal, statstcal and artfcal neural network models, Text Res J, 74 (2004) Zhu R & Ethrdge D, Predctng harness for rng and rotor spun yarns and analysng the mpact of fbre propertes, Text Res J, 67 (1997) Fan J, Newton E & Au R, Predctng garment drape wth a fuzzy-neural network, Text Res J, 71 (2001) Huang C C & Chen I, Neural-fuzzy classfcaton of fabrc defects, Text Res J, 71 (2001) Huang C C & Yu W H, Fuzzy neural network approach to classfyng dyeng defects, Text Res J, 71 (2001) Ucar N & Ertuguel S, Predctng crcular knttng machne parameters for cotton plan fabrcs usng conventonal and neuro-fuzzy methods, Text Res J, 72 (2002) Majumdar A, Majumdar P K & Sarkar B, Applcaton of an adaptve neuro-fuzzy system for the predcton of cotton yarn strength from HVI fbre propertes, J Text Inst, 96 (2005) Majumdar A, Majumdar P K & Sarkar B, Applcaton of lnear regresson, artfcal neural network and neuro-fuzzy algorthms to predct the breakng elongaton of rotor-spun yarns, Indan J Fbre Text Res, 30 (2005) Majumdar, A., Cocou, M., & Blaga, M., Modellng of rng yarn unevenness by soft computng approach, Fbers Polym, 9 (2) (2008) Zadeh L A, Fuzzy sets, Informaton Control, 8 (1965) Zmmerman H J, Fuzzy set theory and ts applcatons, 2 nd edn (Alled Publshers Lmted, New Delh), 1996, Jang J S R, ANFIS: Adaptve network based fuzzy nference system, IEEE Transactons on Systems, Man and Cybernetcs, 23 (1993)