**1. Introduction**

172 Genetic Programming – New Approaches and Successful Applications

of Discontinuity. Math Finance. 11: 347-355.

[46] Grandits P, Schachinger W (2001) Leland's Approach to Option Pricing: The Evolution

Advanced fabric production demands developing strategies with regard to new fabric constructions in which sample-production is reduced to a minimum. It is clear that a new fabric construction should have the desired end-usage properties pre-specified as project demands. Achieving such a demand is a complex task based on our knowledge of the relations between the fabric constructional parameters and the predetermined fabric endusage properties that fit the desired quality. Individual fabric properties are difficult to predict when confronting the various construction parameters, which can be separated into the following categories: raw materials, fabric structure, design, and manufacturing parameters.

Many attempts have been made to develop predictive models for fabric properties with different modelling tools. There are essentially two types of modelling tools: deterministic (mathematical models, empirical models, computer simulation models) and nondeterministic (models based on genetic methods, neural network models, models based on chaos theory and theory of soft logic), and each of them has its advantages and disadvantages [1].

Deterministic modelling 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 relations between constructional parameters and predetermined fabric property, but due some simplifying assumptions large prediction errors occur. Empirical models based on statistical techniques show a much better agreement with the real values but the problems with samples preparing, process repeatability, measurements errors and extrapolation occur. They usually refer to the one type of testing method of particular fabric property. The advantage of computer simulation models is their ability to capture the randomness inherent in fabric structure so the predicted values are very near the

© 2012 Dubrovski and Brezočnik, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Dubrovski and Brezočnik, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

real ones, but on the other hand they require numerous fabric samples data. The problem with extrapolation still remains. In general, when deterministic modelling is used, the obtained models are the results of strict mathematical rules and/or the models are set in advance. In this case the goal is to discover merely a set of numerical coefficients for a model whose form has been pre-specified. However, nowadays more and more processes and systems are modelled and optimized by the use of non-deterministic approaches. This is due to the high degree of complexity of the systems, and consequently, inability to study them successfully by the use of conventional methods only. In non-deterministic modelling of systems, no precise and strict mathematical rules are used [2, 3, 4, 5, 6, 7]. For example, in genetic programming, no assumptions about the form, size, and complexity of models are made in advance. They are left to the stochastic, self-organized, intelligent, and noncentralized evolutionary processes [1, 8].

The Usage of Genetic Methods for Prediction of Fabric Porosity 175

(1)

*VV V v s* (2)

(4)

(5)

(3)

Fabrics protect users against micro-organisms, pesticides, chemicals, hazardous particles and radiations (radioactive particles, micro-meteorites, X-rays, micro-waves, UV radiation, etc.). They act very important role also by environmental protection as filters for air and water filtrations, sound absorption and isolation materials against noise pollution, adsorption materials for hazardous gas pollution, etc. [10, 12, 13]. By all mentioned applications dedicated to absorption, desorption, filtration, drainage, vapours transmission, etc., the essential constructional parameter that influences fabric efficiency to protect human or environment is porosity. The fabric in a dry state is a two-phase media which consists of the fibrous material – solid component and void spaces containing air – gas (void) component. The porosity of a material is one of the physical properties of the material and describes the fraction of void space in the material. The porosity (or void volume fraction) is expressed as coefficient ranging between 0 and 1 or as percentage ranging between 0% and 100% (by multiplying the coefficient by 100). Mathematically, the porosity is defined as the

ratio of the total void space volume to the total (or bulk) body volume [14, 15]:

the volumes of the solid and void components as follows:

from the Equation 2, the Equation 1 can be further written as follows:

the Equation 3 could be further written in the form of Equation 6:

*Vv V* 

where, ε is the porosity expressed as coefficient, Vv is the volume of the total void space in cm3, and V is the total or bulk body volume in cm3. The total volume of the body consists of

where, V is the total volume of the body in cm3, Vv is the volume of void component in cm3, and VS is the volume of solid component in cm3. If the volume of void component is exposed

> 1 1 *V VV V v ss VV V*

> > *Vs V*

where, β is the fulfilment (or solid volume fraction) which describes the fraction of solid component volume in the material expressed as coefficient ranging between 0 and 1 or as percentage. If we take into account the common equation for material density (Equation 5), and assume that the mass of the material is actually the mass of solid component (ms=mb),

> *m V*

11 1 *s sb b*

 *V m V m*

*sb s*

(6)

Fabrics are porous materials having different porous structures as the consequence of different manufacturing techniques needed to interlace the fundamental structural elements, e.g. fibres, yarns or layers, into fibrous assembly. Fabric porosity strongly determines important physical, mechanical, sorptive, chemical, and thermal properties of the fabrics such as mechanical strength, thermal resistance, permeability (windproofness, breathability), absorption and adsorption properties (wicking, wetting), translucence, soiling propensity, UV light penetration, sound absorption ability, etc. [9, 10]. Knowledge about the fabric's porous structure is, therefore, an important step when characterising fabrics, in order to predict their behaviour under different end-usage conditions regarding a product. Hence, if porosity is estimated or predicted then when developing a new product the desired porosity parameters can be set in advance on the basis of selecting those fabric constructional factors that have an effect on porosity and, in this way sample production trials could be reduced.

This chapter gives some basic information about the porosity, porosity parameters of woven and nonwoven fabrics, and the results of the studies dealing with the prediction of porosity parameters of two types of fabrics, e.g. woven fabrics made from the 100% cotton staple yarns and needle-punched nonwovens made from the mixture of viscose/polyester fibres, using nondeterministic modelling tools, e.g. genetic programming (GP) and genetic algorithms (GA), respectively.
