Regression model as well as ANN can be used for the prediction of finished width of the single jersey cotton knitted fabric from the input machine and knitting parameters, and prediction by ANN is more accurate than those obtained from multiple linear regression models, affirm Prasanta Kumar Panda and Dr Sumanta Bhattacharyya.
In cotton yarn knitted fabrics, change of dimension plays role in fabrics and garments at all segments of the production and processing and manufacturer to consumer. Change in width of the cotton knitted single jersey fabric is the dimensional change in fabric caused by an application of force or change in environment that either allows the goods to relax or force the fabric to move in a given direction. The cause of dimensional change is tension relaxation.
Knitting has remained an art therefore, because the basic laws of the knitted fabric, the relationships which will predict the fabric characteristics in terms of the constituent yarn properties and the knitted variables have not been discovered^{[1]}. Knitted structures have considerable advantages over woven structure, normally high elasticity, flexibility, easycare property, air permeability, etc. There is however a number of problems with knitted structures encountered at the stages of knitting makeup and of end use. The major problem is high rate of width shrinkage^{[2]}.
The success of knitted texturised polyester fabrics in replacing wovens for outer wear depends on the increased comfort imparted by the knitted fabric and texturised yarn, with good crease resistance and stability to relaxation treatments imparted by heat setting. With nonthermoplastic fibres such as cotton, thermosetting to reduce relaxation shrinkage is not possible and shrinkage must be controlled by mechanical means^{[3]}.
Articles knitted from synthetic thermoplastic fibres such as nylon and polyester can be heat set to a shape or dimensions, which are retained unless the setting conditions are exceeded during washing and wear. Fortunately it is now possible to achieve a shrink resist finish in wool yarns during spinning so that as with cotton yarns little yarn shrinkage will occur during washing and wearing^{[4]}. The properties of cotton are limited due to its natural origins; therefore, if the consumer continues to expect higher quality and dimensionally stable cotton garments, the actual construction of the fabric needs to be investigated^{[5]}.
Chemical free finishing is increasingly in demand in both the women's and men's and boy's outer wear sectors and through the under wear sectors too. This consumer behaviour imposes on the machine builder the requirement of designing machine in order to create dimensionally stable textiles from knitted fabric without the use of chemistry. So the garment manufacturers require a certain width with as low as possible shrinkage for the preparation of stable garment. This width can be achieved at the finishing stage by fixing suitable dependent parameters.
The 'starfish' project is a longterm program of applied research whose basic objective is to provide a set of working principles and a comprehensive database for finished cotton knits so that just such a simple, rational, reliable prediction system can gradually be erected. Still there is no better method compare to statistical method to predict the final dimensions of fabric before starting to knit^{[6]}. Neural networks are models for computational systems, either in hardware or software which intimate the behaviour of biological neurons in the human brain by using a large number of structural interconnected artificial neurons^{[7]}.
Artificial neural network is a powerful data modelling tool that is able to capture and represent complex input/output relationships. Aim of this study was to use the artificial neural network method to predict the finished width of knitted fabric from a set of manufacturing variables and compare the performance with statistical method.
Experimental
Methods
For this study 160 sets of data were collected from industrial source with specifications such as Fabric: Plain Jersey, Process: Jet Dye, Yarn: Singles, Combed, Ring spun. 160 sets of data randomised applying suitable 'c' programming and divided into two groups. One group consists of 130 sets of data used for the software learning and another group consists of 30 sets of data used for testing. Parameters for training and for testing are given in (Tables 1 and 2).
Artificial neural network
(Easy NN Plus) neural network software was used for the study. Software parameters such as learning rate, learning momentum, learning cycle and number of nodes in hidden layer were optimised one by one keeping other parameters fix to get the minimum root mean square (RMS) error.
Multiple regression analysis
'STATISTICA' & 'MATLAB' software was used to predict the same output parameter by multiple regression method. In this analysis independent variables were diameter, machine gauge, yarn count, stitch length, tightness factor, GSM and width shrinkage. Dependent variable was finished width.
Results and discussion
Optimisation of ANN software parameter
The software was trained with various combinations of learning rate and learning momentum [(0.1, 0), (0.2, 0.1), (0.3, 0.2), (0.4, 0.3), (0.5, 0.4), (0.6, 0.5), (0.7, 0.6)] keeping number of hidden layer 1, number of node in hidden layer 5 and learning cycle 1000. Root mean square error was calculated in each step. Minimum RMS error was observed in (0.6, 0.5) combination shown in (Figure 1). (0.6) was the fit learning rate for the least error. The optimised learning rate was taken forward for the Optimisation of learning momentum, and network was trained by increasing momentum from 0.5 to 0.9 (maximum).
Root mean square error shown in (Figure 2) was calculated in each step for different combinations [(0.6, 0.5), (0.6, 0.6), (0.6, 0.7), (0.6, 0.8), (0.6, 0.9)]. From the observation (0.6, 0.8) was the optimised combination of learning rate and learning momentum. Then optimised combination of learning rate and learning momentum (0.6, 0.8) was taken forward for the Optimisation of number of nodes in the hidden layer. The network was trained for different number of nodes (5, 6, 7, 8, 9, 10) in the hidden layer keeping learning rate and learning momentum combination (0.6, 0.8) fix.
Root mean square error shown in (Figure 3) was calculated at each step. From the observation 8 numbers of nodes were suitable for getting least error.Then optimised learning rate, momentum, and number of nodes in the hidden layer were taken forward for the Optimisation of number of learning cycles. Keeping learning rate 0.6, learning momentum 0.8 and number of nodes in the hidden layer 8 constant, network was trained for different numbers of (1000, 2000, 4000, 6000, 8000, 10000, 12000, 14000, 16000, 18000, 20000, 22000, 24000, 26000, 28000) learning cycles.
In each step RMS error was calculated and shown in (Figure 4). Early stoppage hinders the network to learn the relationship between fabric and knitting properties whereas late stoppage induces the network to loss the generalisation property. From the observation 20000 learning cycle was the optimised learning cycle for the prediction with least error.
Regression model
130 data sets were taken into the regression analysis to form the regression equation. From the analysis tvalue of the variables was high and 'p – level' is below (.05) at 95% confidence interval. Again beta coefficient of variable number 4 (stitch length) was insignificant means there was no contribution of this variable to the model. To get the model, which is fit to the data the equation was reduced removing the variable number 4 by the backward stepwise multiple regression. The regression summary of the reduced model is given in (Table 3).
From the model multiple regression equation was Finished width = (9.71967698 + 1.149659821 x Diameter + 1.452910561 x Gauge  0.436112342 x Yarn count – 1.982628888 x Tightness factor + 0.082948985 x GSM  0.716183983 x Width shrinkage). The 't' and 'p' value gives a rough indication of the impact of each predictor variable. A big absolute 't' value and small 'p' value suggests that a predictor variable having a large impact on the criterion variable.
Analysis of variance of the dependent variable (finished width) given in (Table 4). Analysis of variance assesses the overall significance of our model. As plevel was less than .05 our model was significant and Fvalue was satisfying the null hypothesis. So the formed equation was fit to the data. The comparative results of prediction performance of artificial neural network and regression model for testing data shown in Table 5 and plot of actual value and predicted value shown in (Figures 5 & 6). From the values it was clear that the prediction performance of ANN was much better than that of regression model considering testing and training sets of data separately.
From the performance point of view artificial neural network was better way for prediction. Performance summary of both the methods are given in (Table 6).
The ranking of knitting and finishing variables was done using the difference in test performance values. Accordingly, the order of input parameters for Width was: Machine gauge, Diameter of machine, width shrinkage, GSM, tightness factor, counts of yarn and stitch length.
Conclusion
Regression model as well as ANN can be used for the prediction of finished width of the single jersey cotton knitted fabric from the input machine and knitting parameters. Prediction error in case of back propagation neural network is less than the prediction error in case of regression model. In this study stitch length has no contribution for the prediction in regression model, but stitch length has impact on the prediction in neural network.
In actual case stitch length has impact on the finished width. Gauge of the machine is more important for the prediction of the finished width according to the impact test of the input parameters. For the prediction of width optimised neural network parameters are learning rate 0.6, momentum 0.8, hidden layer 1, number of nodes in hidden layer 8 and learning cycles 20,000.
All the manufacturers of the knitted products should use this method to know the finished width of the fabric before knitting, which will be suitable to achieve the required width by adjusting the parameters. This process will be helpful for avoiding wastage of material money and time and also will be helpful for knitter to knit the fabric according to the order of the garment manufacturers.
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Prasanta Kumar Panda Indian Institute of Technology Department of Textile Technology New Delhi16. Email: pkp.gd.pp@gmail.com.
Dr Sumanta Bhattacharyya Government College of Engineering & Textile Technology, Serampore Hoogly, West Bengal.
