PREDICTION OF FABRIC PROPERTIES OF VISCOSE BLENDED KNITTED FABRICS BY FUZZY LOGIC METHODOLOGY

PREDICTION OF FABRIC PROPERTIES OF VISCOSE BLENDED KNITTED FABRICS BY FUZZY LOGIC

METHODOLOGY

Ismail Hossain, Altab Hossain, I. A. Choudhury, Abu Bakar

Department of Mechanical Engineering, Faculty of Engineering

University of Malaya (UM), 50603 Kuala Lumpur, Malaysia,

Hasib Uddin

Textile Research Laboratories APS, APS Group,

Gazipur, Bangladesh

ABSTRACT

The main purpose of this study is to develop a fuzzy model for the prediction of fabric GSM of viscose blended knitted fabrics as a function of yarn count and knitting stitch length. The most significant key factors yarn count and knitting stitch length affect the GSM of viscose knitted fabrics are very non-linear.

Hence, developing a prediction model by using mathematical or statistical approach is very difficult task. Conversely, artificial neural network and neural-fuzzy models are trained using vast amounts of experimental data which are also time consuming process. Fuzzy logic (FL) methodology on the other hand, is a promising modeling tool which performs extraordinarily very robust in a non-linear complex field with least trial data. The prediction model was found to be valid by correlation analysis. The mean relative error, correlation coefficient and goodness of fit from the predicted values were found to be 4.56%, 0.995 and 0.999 respectively.The results show very good performanc of the prediction model.

KEYWORDS— Fabrics GSM, Viscose, knitted fabrics, Prediction, FL

I. INTRODUCTION

Prediction of knitted fabrics properties is one of the most fascinating topics in the knit textile manufacturing due to the increasing demand of diversified product quality and costing. Recently, the demand of knitwear items especially viscose knitwear’s like T-shirts, shirts, sweaters, blouses, underwear, casual wear, active wear and sportswear etc. have increased rapidly due to lower price and exclusive quality characteristics such as elasticity, drape, wrinkle resistance, softness and high comfort compare to woven fabrics[1-4].

The Fabric GSM however, is one of the most important physical properties among all the qualities

of viscose knitted fabrics. Basically, GSM (gm/m²) is the weight per unit area of fabrics and GSM is directly related to the fabric weight. For readymade garments, costing of a garment depends on the fabrics weight or fabrics GSM. It has been seen in practically that garments price increase with the increase of fabrics GSM. The reason for that basic component of a garment is fabric. Moreover, buyers placed purchase order in the export oriented garments and textile industry on the basis of garments pieces for a specific fabrics GSM. In case of export quality garments, buyer will not accept any piece of garment out of that specified requirement. Further, the products with higher GSM than buyer’s requirement will increase the consumption of fabrics for target garments pieces.

Accordingly, garment cost will increase. Therefore, control of fabrics GSM for the knitted fabrics is an important issue in the knitting industry.

The present textile knitting industry is facing tremendous challenge, due to the short life cycle of product development, increasing product diversity, high demand of product quality as well as product costing in the global market. Moreover, the process automation in knitting industry is going slowly due to the complication of knitting process. Generally speaking, GSM of knitted fabrics depends on yarn properties, machine parameters and fabric density.

However, for viscose knitted fabrics, yarn count and knitting stitch length are the most important factors affecting the GSM of final fabrics. Since, relationship between yarn count, knitting stitch and fabrics GSM is very non-linear and has mutual interactions with each other that's why, it is very difficult to apply conventional models namely mathematical models or statistical models to predict the fabrics GSM before production [2- 4]. On the other hand, artificial neural network and neuro-fuzzy models involve with enormous amounts of experimental data for network training, which is challenging and time consuming process to collect from the knitting industry [2, 5].

In this context, fuzzy logic methodology is well- designed modeling tool rather than conventional, ANN and neuro-fuzzy models since fuzzy logic can execute extremely well and capable in linking multiple inputs to single out in a very non-linear complex domain with lowest amounts of experimental data [5-7]. Unlike statistical regression model, fuzzy logic needs no information or prior estimation of any mathematical models in advance [3, 5]. Moreover, unlike ANN and neuro-fuzzy models, fuzzy logic does not require huge amounts of input-output data [5-7]. Furthermore, fuzzy logic is used to resolve the problems in which descriptions of behavior and observations are imprecise, vague and indecisive [5].

A few application of fuzzy logic approach related to this research has been discussed as follows:

Majumder and Ghosh developed fuzzy logic expert system for yarn strength modeling [5]. Jahmeerbacusa et al. applied fuzzy method for controlling pH in exhaust dyeing [8]. Hung and Yu discovered fuzzy controller for controlling dye bath concentration, pH and temperature in cotton fabric dyeing [9]. Nasri and Berlic presented evolutionary fuzzy logic approach for modeling polyester dyeing process [10]. Tavanai et al. proposed fuzzy regression approach to model the color yield in polyester dyeing as a function of dye concentration, time and temperature [11]. Therefore, the main objective of this work is to develop a fuzzy logic model based on mamdani approach for the prediction of fabric GSM of viscose blended knitted fabrics where yarn count and knitting stitch length are input variables, which has not so far been reported in the published literature. Moreover, this fuzzy prediction model can be applied as a decision making support tool for knitting engineer to select and adjust knitting process parameters to achieve desired fabric GSM before knitting.

II. METHODLOGY

In this research investigation, 25 viscose fabrics blended samples were knitted with 20 denier elastane yarn and according to (Table I) knitting process parameters on FUKUHARA single jersey circular knitting machine (Model FXC-3S), having 30 inches diameter, 24 gauges (needles/inch) and 90 yarn feeders. After knitting then, all fabrics samples were subjected to proper heat setting, dyeing and finishing processes. After production, all the fabrics samples were conditioned firstly on a flat surface for at 24 hours prior to testing under standard atmospheric conditions at relative humidity (65 ± 2 %) and temperature (20 ± 2 °C). Then, the fabric GSM (gm/m²) of each sample was tested according to ASTM D-3776 test standard.

TABLE I. RANGE OF KNITTED FABRIC VARIABLES

Process Parameters Values

Yarn count (Ne) 20 24 30 34 40 Knitting Stitch length

(mm)

2.6 2.8 3.0 3.2 3.4

III. FUZZY PREDICTION MODEL DEVELOPMENT

(a) Structure of Fuzzy logic System

The artificial intelligence fuzzy logic is the most successful methodology in various research investigation in the world which is a branch of mathematics developed by Zadeh at the University of California in 1965 [12, 14].

Figure 1 Basic configuration of fuzzy logic system [13-14].

Fig.1 shows the basic configuration of a fuzzy logic system which comprises four principal components [9, 13-14]. The four principal components are as follows:

i) Fuzzification interfaces- The selection of input and output variables is the first task in fuzzification interfaces. After selection, numeric variables have to define in linguistic terms such as low, medium, high.

Next, membership functions for all input and output variables have to be created. The central concept of fuzzy set theory is membership functions, which represent numerically to what degree an element belongs to a set. The triangle membership function is the simplest and most often used among all. [5, 7, 9, 13-14].

(ii) Knowledge base –It consists of a data base and a rule base. In the fuzzy knowledge base system, knowledge is represented by if-then rules [5, 7, 9 and 14]. Fuzzy rules are the heart of fuzzy logic system which determines the correlation between input- output of the model. For instance, in the case of two inputs P and Q and one output Z, which have the linguistic variables of low and medium for P and Q

respectively and medium for Z, then development of fuzzy inference rules can be demonstrated as follows:

Fuzzy rule: If P is low, and Q is medium, then Z is medium.

(iii) Decision making logic – It plays a central role in a fuzzy logic model due to its ability to create human decision making and deduce fuzzy control actions as per the information provided by the fuzzification module by applying knowledge about how to control best the process. Most commonly, Mamdani max-min fuzzy inference mechanism is used because it assures a linear interpolation of the output between the rules [5, 7, 9, and 13]. For instance, in case of two-inputs and single-output fuzzy system, it can be shown as Fig.2

Figure 2 Fuzzy inference mechanisms (iv) Defuzzification interface –The defuzzification interface combines the conclusions reached by the decision making logic and converts the fuzzy output into precise crisp numeric value as control actions. Most commonly, center of gravity (centroid) defuzzification method is used, since this operator assures a linear interpolation of the output between the rules. In this stage, output membership values are multiplied by their corresponding singleton values and then are divided by sum of the membership values to calculate Output ^crisp as follows:

 

 



 i i ibi i crisp

Output





(1)

where b_i is the position of the singleton in the i^th universe, and μ(i) is equal to the firing strength of truth values of rule i [5,7,13-14].

(b) Application of Fuzzy Logic System

In this study, two knitting process parameters, namely yarn count (YC) and stitch length (SL) were used as input parameters and fabric GSM (FG) of the knitted fabrics as the output parameter. For fuzzification, the input variable YC and SL were given five possible linguistic variables namely very low (VL), low (L), medium (M), high (H) and very high (VH). In this

study, five membership functions for YC and SL have been selected based on system knowledge, expert’s appraisals, and experimental conditions and arbitrary choice. Nine linguistic variables namely, very very low (VVL), very low (VL), low (L) low medium (LM), medium (M), high medium (HM), high (H), very high (VH) and very very high (VVH) were used for the output variable FG, so that the expert system could map small changes in fabric GSM with changes in the input variables. In present research investigation, triangular shaped membership functions have been used for both input and output variables due to their accuracy [7]. The units for the input and output variables are: YC (Ne), SL (mm) and FG (gm/m²). For the input and output parameters, a fuzzy associated memory was created as regulation rules based on expert knowledge and previous experience.

A total of 25 rules have been formed. Some of the rules are shown in Table II as follows:

TABLE II. Fuzzy rules Rules Input variables Output

variables

YC SL FG

Rule 1 VL VL VVH

……… ………… …………. ………

Rule 12 L M H

……… ………… …………. ………

Rule 25 VH VH VVL

There is a level of membership for each linguistic word that applies to that input variable. Fuzzifications of the used factors are made by aid follows functions.

 





  

 otherwise

i i i

YC 0;

40 20

; ₁

1 1

(2)

 





  

 otherwise

i i i

SL 0;

4 . 3 6

. 2

; ₂

2

2

(3)

 





  

 otherwise

o o o

FG 0;

370 140

; ₁

1 1

(4)

Where i_1, is first input (YC) and i₂ is second input (SL) and o₁ is output variable (FG) showing in Eq. (2)-(4).

Prototype triangular fuzzy sets for the fuzzy variables, namely yarn count (YC) and knitting stitch length (SL) and fabric GSM (FG) are set up using MATLAB FUZZY Toolbox. The membership values obtained from the above formula are shown in Figs. 2-4

Figure 3 Membership functions of input variable SL

Figure 4 Membership functions of input variable YC

Figure 5 Membership functions of output variable FG

To demonstrate fuzzification process, linguistic expressions and membership functions of yarn count (YC) and stitch length (SL) obtained from the developed rules and above formula (Eq. 2-4) are presented as follows:

 

































 





 





35

; 0

35 30 30;

35 35

30 25 25;

30 25

1 1 1

1 1

i i i

i i

M YC



(5)

  YC  0/25.....1/30......0/35

M

 

































 





 





2 . 3

; 0

2 . 3 0 . 3 0;

. 3 2 . 3

2 . 3

0 . 3 8 . 2 8;

. 2 0 . 3

8 . 2

2 2 2

2 2

i i i

i i

M SL



(6)

  SL  0/2.8...1/3.0.....0/3.2

M

In defuzzification stage, truth degrees (μ) of the rules are calculated for each rule by aid of the min and then by taking max between working rules. To comprehend fuzzification, an example is considered. For crisp input YC=30 Ne and SL=3.0 mm the rules 13 is fired. The firing strength (truth values) α of the one rule 13 is obtained as follows:

   

 



^,



^min

   

^{1,1 1}

13min _M YC _M SL  



Consequently, the membership function for rule 13 is obtained as follows.

 

^FG



^_L

 

^FG



13 min1,

Rajasekaran and Vijayalakshmi [15] have mentioned that in many circumstances for a system whose output is fuzzy, it can be simpler to obtain a crisp decision if output is represented as a single scalar quantity. Using Eq. (1) with Fig. 5 the crisp output of FG is obtained as 190.

(c) Statistical methods for comparison

The prediction ability of accuracy the developed system has been investigated according to mathematical and statistical methods. In order to establish the relative error (ε) of formation, the following equation is used:

n y

y y

n

i i

i

i 100%

1

 

 



 (7)

In addition, goodness of fit (η) of the predicted system is calculated as follows:

 

 

 



 



 











n i

i n

i i i

y y

y y

1

2 1

2

 1 (8)

Where n is the number of observations, y_i is the measured value,



y

i is the predicted value, and

y

is the mean of measured (actual) value. The relative

error provides the difference between the predicted and measured values and it is necessary to attain zero.

The goodness of fit also provides the ability of the developed system and its highest value is 1.

IV. RESULTS AND DISCUSSION (a) Operation of fuzzy prediction model

The graphical operation of the fuzzy logic model has been shown in Fig. 6. For instance, if YC is 30 Ne and SL is 3.0 mm, then all twenty five fuzzy rules are evaluated parallel to find the fuzzy output fabric GSM, which is190 g/m². Using MATLAB the fuzzy control surfaces was developed as demonstrated in Fig.7. It can serve as a visual depiction of how the fuzzy logic expert system operates dynamically over time. The figure shows the mesh plot for the above example case, showing the relationship between yarn counts (YC) and knitting stitch length (SL) on the input side and fabric GSM (FG) on the output side.

The surface plots illustrated in Fig.7 depict the impact of yarn count and knitting stitch length on fabric GSM. Fig.7 and Fig.8 show the fabric GSM decreases with increases of yarn count and knitting stitch length and vice versa. It is observed that fabric GSM increases with the decreasing of stitch length because of increasing number of loops per unit area. A similar phenomenon has been observed for yarn count on fabric GSM as shown in Fig 7 and 8. Figures show that fabric GSM increases with the decreasing of yarn count due to the increase of yarn linear density which indicates the coarseness of yarn. From this investigation, it can be obviously seen that yarn count and stitch length have the significant effect on fabrics GSM in the knitting process. As GSM increases further than an optimum level, fabric become stiffer and less extensible, hence resulting in fabrics hole.

Therefore, is very important to maintain optimum level of knitting parameter in the knitting process to get required GSM with good quality fabrics.

(b) Validation of the prediction model

The prediction model has been validated by comparing and analyzing the actual and predicted values of fabric GSM. The correlation between the measured (actual) and predicted (FLES) values of fabric GSM have been depicted in Fig. 9. The correlation coefficient (R) from the actual and predicted values of fabric GSM was found to be 0.995 (R²=0.990). Therefore, it can be concluded that the developed fuzzy prediction model can explain up to 99.0% of the total variability of fabric GSM. The mean relative error between the actual values and the predicted values of fabric GSM was found to be 4.56% which less than the acceptable limits of 5%.

The relative error gives the deviation between the predicted and experimental (actual) values and it is required to reach towards zero. The goodness of fit was found to be 0.999 which was found to be close to 1.0. The goodness of fit gives the ability of the developed system. The results indicate very strong prediction accuracy of the developed model.

Figure 6. Graphical operation of the fuzzy prediction model

Figure 7 Control surfaces of the fuzzy inferring system

Figure 8 Effect of yarn count and stitch length on fabric GSM

Figure 9 Correlation between actual and predicted values of fabric GSM.

V. CONCLUSION

In the present study, a fuzzy model has been developed based on the yarn count and knitting stitch length as input variables and fabrics GSM as output variable for the prediction of fabric properties of viscose knitted fabrics. The Model validation is assessed by means of different statistical error criteria.

The correlation coefficient was found to be 0.995, the mean relative error was found to be 4.56 % and the goodness of fit was found to be 0.999 from the actual and predicted values of fabrics GSM. The results indicate a very strong ability and accuracy of the fuzzy prediction model. Therefore, it can be positively acknowledged that fuzzy prediction model can be applied as an efficient tool to predict the fabrics properties of viscose knitted fabrics satisfactorily.

ACKNOWLEDGEMENT

The authors are grateful to the University of Malaya for providing the support for this project under the grant PG048-2013A. The authors are also thankful to the Management of Textile research laboratory APS, APS Group, Gazipur, Bangladesh for providing the laboratory facilities for this research work.

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