Yarn Strength Prediction using Hybrid Genetic Algorithm - Fuzzy Approach

Subhasis Das, Anindya Ghosh

Government College of Engineering and Textile Technology, Berhampore, India-742 101

*Corresponding Author E-mail:

INTRODUCTION:

Yarn strength modelling and prediction has remained as the cynosure of research for the textile engineers although the investigation in this domain was first reported around one century ago [1,2]. In recent years fuzzy logic has evolved as a very popular prediction technique in textile industry. In the domain of textile technology there are plentiful examples of imprecise variables. For an example, a spinner often uses the terms like ‘fine’ and ‘coarse’ to assess the fibre and yarn count, although these terms do not constitute a well defined boundary. Although fuzzy logic is a powerful tool for dealing with imprecision and uncertainty, however, it has its inherent limitation. This limitation may be minimized by combining it with genetic algorithm (GA) which is a potential tool for global optimization. In this work an effort has been made to improve the prediction performance of fuzzy modelling of cotton yarn strength by developing a hybrid genetic algorithm- fuzzy logic model. This paper deals with modelling of GA- fuzzy model for more accurate prediction of ring spun cotton yarn strength.

GENETIC ALGORITHM IN BRIEF:

GA is a heuristic search algorithm that can be applied when the dimension of the data space is too large for an exhaustive search [3]. GA proceeds first by randomly generating an initial population of individuals, which should ideally cover the domain to explore. Each individual is represented by a binary coded string or chromosome encoding a possible solution in the data space. At every iteration step or generation, the individuals in the current population are tested according to the fitness function. To form a new population (the next generation), good individuals are selected according to their fitness, which is termed as reproduction. Selection alone cannot introduce new individuals into the population, which is necessary in order to make the solution as independent of the initial population as possible. New individuals in the search space are thus generated by two operations: crossover and mutation. Crossover concerns two selected individuals (parents) that exchange parts of their chromosome to form two new individuals (offsprings). The crossover operation is not always applied to all selected chromosomes. The application of crossover is governed by a crossover probability, denoted by p_c. If p_c is too large, then the structure of a high quality solution could be prematurely destroyed, on the contrary, a too small p_c reduces the searching efficiency. Generally, p_c is chosen between 0.5 and 0.8. The mutation operation is used as a means to achieve a local change around the current solution. Thus, if a solution gets stuck at the local minimum, mutation may help it to come out of this situation and consequently, it may jump to global basin. The mutation consists in flipping bits of individual’s strings at random and with some small probability, termed as mutation probability (p_m). If p_m is too small, then new gene segment could not be induced, whereas if p_m is too big, then the genetic evolution degenerates into a random local search. Generally, p_m is chosen between 0.001 and 0.1.

HYBRID GA-FUZZY MODEL FORMULATION:

The data of 36 types of cotton fibres and corresponding yarns of 20s count are collected from the textile industry. Four parameters of cotton fibres namely fibre strength (FS), fibre length (UHML), fibre fineness (FF) i.e. fibre weight in µg per one inch and short fibre content (SFC) have been used as the input parameters to the fuzzy expert system. These fibre parameters have been exclusively selected since they influence the yarn strength significantly [4]. Three linguistic fuzzy sets namely low, medium and high were chosen for each of the input parameters in such a way that they are equally spaced and cover the whole input spaces. The triangular membership functions were used for inputs and output. The triangular membership curves were considered for FS, UHML, FF and SFC, which are the inputs to fuzzy model. Nine output fuzzy sets (level 1 to 9) were considered for yarn strength, so that the expert system can map the small changes in yarn strength with the changes in input variables. Figure 1 shows the triangular membership curve for yarn strength. Theoretically there could be 3⁴ = 81 fuzzy rules, as there are four input variables and each one of them are having three linguistic levels. However, to simplify the expert system only 36 fuzzy rules were developed [5].

Figure 1: Membership function for yarn strength of fuzzy model

GA is used to improve the performance of fuzzy model by tuning the membership function distributions of the input and output variables with the help of 30 and 6 randomly partitioned data sets for training and testing, respectively. The same linguistic fuzzy sets and rule base as used in hybrid model.

An initial population of the binary coded GA is created at random. Starting from the left most bit position; eight bits are assigned to indicate each of the b values (i.e. b₁, b₂, b₃, b₄ and b₅) and the next 36 bits represents the rule base of the hybrid model. The 1 and 0 of the last 36 bits of a GA string denote whether the particular rule from the rule base will be fired or not. The b₁, b₂, b₃, b₄ and b₅ values represent the distribution parameters of the triangular membership functions for the input variables viz. FS, UHML, FF, SFC and the output variable viz. yarn strength, respectively. In fuzzy model, these b values are manually designed based on the experience which may not be optimal in any sense. In hybrid model, these b values are optimised to get better suited membership functions that increase the prediction accuracy of the system. In this work, the mean absolute deviation of predicted yarn strength from the actual training data has been considered as the objective function which is minimized using the binary coded GA for obtaining the optimum b values. The optimum solution of GA is obtained with the values of 0.7 and 0.001 for p_c and p_m, respectively. Roulette wheel selection scheme is applied for reproduction operation and uniform cross-over method has been applied.

RESULTS:

A MATLAB 7.11 based coding was used to execute both models of yarn strength. Figures 10-13 show the optimized membership functions for four input parameters and Figure 2 depicts the 9 levels of membership function for yarn strength obtained by GFES model.

Figure 2: Optimized membership function for yarn strength of GA-Fuzzy hybrid model

The prediction accuracies of the fuzzy and hybrid models were evaluated by calculating coefficient of determination (R²) and mean absolute error (%) from the actual and predicted yarn strength values. Table 1 shows the prediction error of testing data set obtained by both the models. The hybrid model is showing lower mean error (4.6 %) as compared to that of the fuzzy model (8.9 %). The prediction results are also depicted in Figure 3. It is observed from the Figure 3 that R²is 0.81 for the GA-Fuzzy hybrid model which means that it can explain up to 81% of the total variability of yarn strength. Therefore, hybrid model of yarn strength demonstrates a reasonably good degree of prediction consistency. Whereas, a low value of R²for fuzzy model (0.36) signifies a poor prediction consistency.

Table 1: Prediction of yarn strength (cN/tex) by FES and GFES models

Actual yarn strength	FES model		GFES model
Actual yarn strength	Predicted strength	Absolute error (%)	Predicted strength	Absolute error (%)
14.01	15.41	10	14.45	3.14
14.18	14.82	4.51	14.85	4.72
13.35	15.12	13.26	14.10	5.62
14.28	15.29	7.07	15.27	6.93
14.75	16.01	8.54	15.22	3.19
13.96	15.35	9.96	14.52	4.01
Mean absolute error (%)		8.9	4.6

Figure 3: Actual vs. predicted yarn strength with fuzzy model and hybrid model on the testing data

CONCLUSIONS:

A GA-Fuzzy hybrid model has been developed to model the strength of cotton yarns by tuning the membership functions of the fuzzy with binary coded GA. The prediction accuracy of the hybrid model is reasonably good as the mean error (%) of prediction is significantly less than that of the fuzzy model. In addition, a higher coefficient of determination obtained with the hybrid model shows it has much better prediction consistency as compared to the fuzzy model.

REFERENCES:

1. Zadeh, L. A., (1965), Fuzzy Sets, Information and Control, 8, 338-353.

2. Zimmerman, H. J., (1996), ‘Fuzzy Set Theory and Its Applications’, 2nd Edition, Allied Publishers Limited, New Delhi.

3. J. H. Holland, “Adaptation in Natural and Artificial Systems”, University of Michigan Press, Ann Arbor, 1975.

4. Sette, S., Boullart, L., and Langenhove, L. V., (2000), Building a Rule Set for the Fibre-to-Yarn Production Process by Means of Soft Computing Techniques, Text. Res. J., 70, 375-386.

5. Majumdar, A., and Ghosh, A., (2008), Yarn Strength Modelling Using Fuzzy Expert System, J. Eng. Fibers and Fabrics, 3, 61-68.

Received on 22.01.2014 Accepted on 02.02.2014

Int. J. Tech. 4(1): Jan.-June. 2014; Page 109-111