Using Genetic Programming to

Predict the of Woven Cotton Fabrics

POLONA DOBNIK DUBROVSKI

AND

Macroporosity

MIRAN BREZOCNIK

Faculty of Mechanical Engineering, University of Maribor, Maribor,

Slovenia

ABSTRACT This paper reports the effect of woven fabric construction on macroporosity properties. The area of a macropore’s cross section, equivalent, maximum, and minimum pore diameters, pore density, and open porosity are observed in this research involving woven fabric construction parameters—yarn linear density, fabric tightness, weave type, and denting. Predictive models, determined by genetic programming, are derived to describe the influence of fabric construction. The results show very good agreement between the experimental and predicted values. This work provides guidelines for engineering stapleyarn cotton fabrics in a grey state in terms of macroporosity properties.

If

fabrics are to be engineered to fit desired with minimum production costs, then the relaqualities between their construction parameters and their tionships properties must first be quantitatively established. Individual fabric properties are difficult to predict when confronting the various construction parameters, which can be separated into the following categories: raw materials (e.g., fiber density, fineness, shape, length, etc.), threads (linear density, packing factor, yarn flexibility, volume coefficient, mechanical properties, etc.), fabric structure (warp and weft density, weave type, design features), and manufacturing parameters (weaving con-

advantage of computer simulation models is their ability

woven

ditions, finishing type). Many attempts have been made

to

fabric structures, so the predicted values are very close to real ones. On the other hand, they require extensive woven sample data, so the problem with extrapolation still remains. In general, when deterministic modeling is used. the models obtained are the result of strict mathematical rules or they are set in advance. In that case, the goal is merely to discover a set of numerical coefficients for a model whose form has been prespecified. However. nowadays more and more processes and systems are modeled and optimized using nondeterministic approaches. This is due to the high degree of complexity of the systems, and consequently, the inability to study them successfully with conventional methods only. In nondeterministic modeling of systems, there are no precise, strict mathematical rules. For example, in genetic programming, no assumptions about the form. size, and complexity of models are made in advance. They are left to stochastic, self-organized, intelligent, and noncentralized evolutionary processes 13, 5]. To predict the macroporosity properties of woven fabrics, we first developed empirical models based on a statistical technique (a three-factor analysis), which shows much better agreement with real values according to ideal mathematical models that include some simplifying assumptions [6]. While woven fabrics made from staple yarns have much more heterogeneity of macropore size, shape, and orientation compared to fabrics made from mono- or multifilament yarns [7], the results were not good enough. The next stage of our research was to use another modeling tool to predict macroporosity properties precisely enough. to

develop predictive

models for fabric properties using different modeling tools, of which there are essentially two kinds: deterministic (mathematical models, empirical models, computer simulation models) and nondeterministic (models based on genetic methods, neural network models, models based on chaos theory and soft logic theory), and each has its advantages and disadvantages [3]. Deterministic modeling tools present the heart of conventional science and have their basis in first principles, statistical techniques, or computer simulations. Mathematical models offer a deep understanding of relationships between constructional parameters and predetermined fabric properties, but because of some simplifying

assumptions, large prediction errors occur. Empirical models based on statistical techniques show much better agreement with real values, but there are problems with sample preparation, process repeatability, measurement errors, and extrapolation. These models usually refer to one testing method of a particular fabric property. The

187

capture the randomness inherent in

woven

188

this study, we investigate the effects of yarn linear density, weave value, fabric tightness, and denting on a woven fabric’s macroporosity properties. We then use genetic programming to develop models to predict the following macroporosity properties: the area of a pore’ss cross section, equivalent, minimum, and maximum pore diameters, pore density, and open porosity. In

Experimental

minimum and maximum pore diameters actually present the minimum and maximum widths of a pore with a geometrically irregular cross-sectional shape. From these measurements, we could calculate two more macroporosity properties, open porosity Po (%) and equivalent diameter d, (jum) according to Equations I and 2 [11]. The equivalent pore diameter determines the diameter of a circle with the same area as the pore with the geometrically irregular cross-sectional shape:

MATERIALS Our experiments involved twenty-seven woven fabrics made from staple yarns with two restrictions: first, only fabrics made from 100% cotton yarns (made by a combing and carding procedure on a ring spinning machine) were used in this research; second, fabrics were measured in the grey state because the influence of finishing processes could not be properly quantified. We believe that it is very hard, perhaps even impossible, to include all woven fabric types to predict individual macroporosity properties precisely enough, so we focused our research on unfinished staple yarn cotton fabrics. We would like to show that genetic programming can be used to establish the many relationships between woven fabric construction parameters and particular fabric properties, and that the results are more useful for fabric engineering than ideal theoretical models. The cotton fabrics varied according to yam structure, weave type (weave value), fabric tightness, and denting (see Appendix). They were woven on a Picanol weaving machine under the same technological conditions. The weave values of plain (0.904), twill ( 1.188), and satin (1.379) fabrics, as well as fabric tightness, were determined according to Kienbaum’s setting theory [8]. MACROPOROSITY MEASUREMENTS

optical method to measure the macroporosity properties of woven fabrics, since it is the most accurate technique for macropores with diameters of more than 10 tLm. For each fabric specimen, we observed between 50 and 100 macropores using a Nikon SMZ-2T computer-aided stereomicroscope with special We used

an

software. It is clear that a macropore as a three-dimensional form has a nonpermanent cross section over all its length. While our research treated the macropore as a twodimensional formation, we considered only that pore cross section where the hydraulic diameter of the pore has its minimum. We measured the following macroporosity properties: area of the pore cross section, pore density, and minimum and maximum (Feret’s) pore diameters. Since the area of a pore’s cross section is far from circular, the

and An (mm 2) stand for pore of the and area pore’s cross section. Our results density of measured and calculated characteristics of woven fabric macroporosity are presented in Figure 3 (experimental values).

Here,

Np (pores/mm 2

’

PREDICTIVE MODELING

predictive models of macroporosity propusing genetic programming. The theory of genetic programming can be found in many books and articles that deal with evolutionary computation [ 1, 2, 3, 4, 9, 10]. In our research, the independent input variables (the We created

erties

set of

yam fineness T (tex), weave value V, fabric tightness t (%), and denting D (ends/dent in the reed). The set of terminals also included random floating-point numbers between -10 and + 10. Variegated reed denting was treated as an average value of treads, dented in the individual reed dent. The dependent output variables were area of pore cross section A p ( 10-3 3 mm2), maximum pore diameter dmaX (AM), minimum pore diameter dmi. (jum), and pore density Np (pores/cm2). For all modeling, the initial set of functions includes the basic calculating operations of addition, subtraction, multiplication, and division. In the case of modeling pore density, the initial set of functions also includes a power function, whereas the set of functions for modeling minimum and maximum pore diameters and the pore cross section includes an exponential function. We then used the genetic programming system to evolve appropriate models consisting of the above-mentioned sets of terminals and functions.

terminals)

were

Results and Discussion EFFECT OF FABRIC CONSTRUCTION PROPERTIES

Effect of Fabric Construction

on

ON

MACROPOROSITY

Area

of a

Pore’s

Cross Section

Obviously, fabrics made bigger pore cross-sectional

from thick yams will have areas. Thick yarns take up

189 space, so the warp/weft density of fabrics made from them is lower, which means that the distance between yarns is bigger and consequently also the pore size. This relationship is not linear, since in the case of staple yarns, the phenomenon of latticed pores appears. The influence of yarn hairiness on pore size is greater for thin yarns where the pores are smaller and latticing is more apparent. The influence of fabric tightness is similar-higher fabric tightness means a smaller pore size and the phenomenon of the latticed pore is more obvious. Weave type is another important factor that greatly influences the area of the pore’s cross section. From Figure 1, which represents the distribution diagrams of fabrics with the same tightness and yarn fineness but different weave type, we see that the area of the pore’s

more

section is much more affected by the satin than the plain weave. This is the consequence of structural weave modules [6, 12). A plain weave consists only of one weave structural module, so pores have very good dimensional stability and homogeneity compared to satin

cross

weave, which consists of weave structural modules 2 and

3. Pores of twill fabrics have better dimensional stability and homogeneity than satin fabrics but less than plain fabrics, possessing a weave structural module 2. The left side of Figure 2 shows grey images of plain, twill, and satin fabrics at 60x magnification, while the right side of Figure 2 refers to the area, shape, and density of visible macropores at 20x magnification, respectively. From this figure, the influence of denting on the area of the pore’s cross section can be seen. Yarns that are within a reed dent tend to group together, so the area of the pore’s cross section is reduced. With satin fabrics, where yarn densities are higher, the pores are mostly visible only in the place where the warps threads are separated by a reed wire.

PtGURE 2. Grey and binary microscopic images of plain, twill, and satin fabrics (magnification of binary images. 20x ).

.

Effect of Fabric FIGURE 1. Pore cross-sectional same yam fineness and fabric

distribution of fabrics with the tightness but different weave type.

area

Construction

on

Pore

Densih·

It is clear that pore density due to higher fabric tightyarns, higher weave values, higher denting,

ness, finer

190 and the phenomenon of latticed pores is reduced. The number of &dquo;lost&dquo; pores increases from plain to twill to satin fabrics, as can be seen from the binary images of Figure 2 or the pore density values of Figure 3. Theoretically, pore density is equal to the product of warp and weft densities. Experimental results from Figure 3 show that in most cases, pore density is lower than the theoretical value. Remember that due to the phenomenon of latticing, the spaces between two warp and weft yarns actually have a very random pore size distribution, similar to nonwovens. Such a space is treated as one pore with a reduced area.

for fabrics with the same weave but different yarn finenesses. For example, plain fabric specimens with the same tightness also have the same theoretical values of open porosity (31.1 %) for yarns with fineness values of 14, 25, and 36 tex. But experimental values show a difference between the yarns. For the above-mentioned fabric specimens, the values of open porosity are 10.2, 11.6, and 22.4%, respectively. This means that lower values of yam fineness reduce the area of a pore’s cross section and its density more than higher values of yarn fineness. In other words, the influence of latticed pores is greater for small pores than for bigger pores.

Effect of Fabric

Effect of Fabric

Construction

on

Open Porosity

Open porosity is calculated from Equation 1. A comparison of experimental and theoretical values shows a large average difference of 52.5% if the area of the pore’s cross section is a rectangle and 39.6% if it is an ellipse. As we stated above, the experimental values sections as well as lowei is pore density, open porosity also reduced. fabric While specimens are comparable in tightness, we would expect that the open area would be the same show lower

areas so

of pore

cross

Construction

on

Pore Diameters

The pores of fabrics made from staple yarns have irregularly shaped cross sections due to the phenomenon of latticed pores, changing positions of threads according to the longitudinal or transversal fabric axis, thread spacing irregularity, and yarn flattening. During fabric engineering, the pore cross section is usually treated as a circle, but the equivalent diameter actually represents the pore width and can be calculated according to Equation 2. When engineering woven fabric filters, the minimum

FIGURE 3. Theoretical, experimental, and predicted values of macroporosity properties.

191 and maximum pore widths are very important features. The influences of fabric tightness, weave value, and denting on the maximum and minimum pore diameters (Figure 3) is negative, while the influence of yarn linear density is positive. PREDICTIVE MODELS

OF

MACROPOROSITY PROPERTIES

Equations 3, 4, 5, and 6 present predictive models of area of a pore’s cross section A in 10-3 MM2, pore maximum in pore diameter dmax’ density Np poreS/CM2, and minimum pore diameter dm&dquo;, in Am, respectively. Here V is the weave factor, T is yarn linear density in tex, t is fabric tightness in %, and D is denting in ends per reed dent. While the model of the area of a pore’s cross section is very complicated, the functions II ’ f2, ,/10 are written in the appendix. When calculating the values of models presented in this paper, the following, rules have to be taken into account: The protected division the

...

,

function returns to 1 if the denominator is 0; otherwise, it returns to the normal quotient. The protected power function raises the absolute value of the first argument to the power specified by its second argument.

,

Figure 3 presents a comparison of the theoretical, experimental, and predicted values of some macroporosity properties of woven fabrics. Predictive values of open porosity are calculated using Equation 3, Equation 4, and

192 then Equation 1. Predictive values of equivalent pore diameter are determined using Equation 3 and then Equation 2. The results of macroporosity properties determined with models based on genetic programming show very good agreement with experimental values. The experimental values deviate from predicted ones on average by 1.6% for the area of the pore cross section, 2.0% for the pore density, 3.2% for open porosity, 0.8% for equivalent pore diameter, 1.6% for minimum pore diameter, and 3.1 % for maximum pore diameter. PRACTICAL VALUE OF PREDICTIVE MODELS MACROPOROSITY PROPERTIES

OF .

To confirm the practical value of our predictive models of macroporosity properties, we have chosen some random combed and carded cotton fabrics in a grey state, which were not used to derive the equations. We measured the macroporosity properties using the same experimental (optical) method (see Table l, experimental values). From the construction data of the individual woven specimens, we calculated the predicted values, which are collected in Table I, according to our models. From these results, we can draw the following conclusions : The average deviations from the predicted

follows: 4.9% for the area of the pore cross section, 9.4% for the pore density, 10.5% for the open porosity, to. Ilk for the equivalent pore diameter, 21.5% for the minimum pore diameter, and 21.49c for the maximum pore diameter. The average deviations for the minimum and maximum pore diameters are a bit higher still, and this confirms the fact that the irregular shape of the pore cross section is very random. Knowing that the average differences between the experimental and theoretical values of individual macroporosity properties are much bigger-for instance, for the area of a pore cross section of 45.1 cIc (from 8.lclc to 81.9~Ic), pore density is 16.0% (from 0.0% to 79.8%), open porosity is 52.2% (from 16.6% to 95.0ilk). and equivalent pore diameter is 28.89c (from 6.2% to 59.5%) [6J-we believe the predictive values

models

are as

are more

trustworthy. Conclusions

fabric’s construction has a great influence on macroporosity properties. While there is a big difference between pores of fabrics made from staple yarns, mono-, or multifilament yarns, it is almost impossible to observe all fabric types to predict macroporosity properA

woven

its

TABLE I. The results of macroporosity

properties

of

testing

fabrics.

193 ties. Thus we have focused our investigation on cotton fabrics made from staple yams. Despite the fact that such fabrics have pores with very different shapes, sizes, and densities, as a result of varying yam linear densities, weave types, fabric tightness values, denting, and the phenomenon of latticed pores, we were able to create predictive models very precisely. We show that genetic programming is a successful modeling tool for predicting fabric properties in the case where the testing population is limited but still very different. The proposed models provide guidelines for engineering woven cotton fabrics to fit desired macroporosity properties.

Appendix

Functions of

Equation

3:

_

194

Forming Efficiency Using Genetic Programming, J. Mater. Process. Technol. 109 (1-2), 20-29 (2001). 5. Brezocnik, M., and Balic, J., A Genetic-based Approach to Simulation of Self-Organizing Assembly, Robot. Comput.

(1-2), 113-120 (2001). Integrat. Manufact. 17 6. Dobnik

Dubrovski, P., The Influence of Woven Fabric

Geometry on Porosity of Biaxial Fabrics, Doctoral thesis, University of Maribor, Faculty of Mechanical Engineering,

Literature Cited 1.

Banzhaf, W., Nordin, P., Keller, R. E., and Francone, F. D.,

"Genetic Programming—An Introduction: On the Automatic Evolution of Computer Programs and Its Applications," Morgan Kaufman Publisher, USA, 1998. 2. Bäck, T., Fogel, D. B., and Michalewicz, Z., Eds., "Handbook of Evolutionary Computation," Institute of Physics Publishing and Oxford University Press, U.K., 1997. 3. Brezocnik, M., "The Use of Genetic Programming in Intelligent Manufacturing Systems," University of Maribor Press, Faculty of Mechanical Engineering, 2000. 4. Brezocnik, M., Balic, J., and Kampus, Z., Modelling of

1999. 7. Dimitrovski, K., A New Method for Determination of Porosity in Textiles, Doctoral thesis, University of Ljubljana, 1996. 8. Kienbaum, M., Gewebegeometrie und Produktenwicklung, Melliand Textilber. 71, 737-742 (1990). 9. Kinnear, K. E., Jr., "Advances in Genetic Programming," The MIT Press, Cambridge, MA, 1994. 10. Koza, J. R., "Genetic Programming: On the Programming of Computers by Means of Natural Selection," MIT Press, Cambridge, MA, 1992. 11. Russ, J. C., "The Image Processing Handbook," CRS Press, FL, 1995. 12. Szosland, J., Modelling of the Inner-thread Spaces in Woven Fabrics, in "Conference Proc., Novelties in Weaving Research and Technology," University of Maribor, Faculty of Mechanical Engineering, Slovenija, 1999. Manuscript received C7ctober 27. 20lX): accepted June 29,

2001,