U sing drape form to establish discriminant models of fabric characteristics

Transcription

1 Indian Journal of Fibre & Textile Research Vo l. 29, June 2004, pp U sing drape form to establish discriminant models of fabric characteristics Lai Sang-Song a Department of Apparel, Natio nal Pintung Uni versity of Science and Technology, T aiwan, Republic of China Received 21 October 2002; accepted 24 Jun e 2003 T hi s paper foc uses on the approaches to di scriminate between the fabrics with di fferent characteri zed generic drape fo rms. Four fabric groups, woven fro m cotton, linen, wool and sil k, were used. Di scriminant analysis was used to characteri ze and discriminate between the differe nt fa bric groups. T he parameters for analysis were from drape fo rms based on the Cusic k fabric drape instrument. It is observed that the 14 drape fo rms are able to classify the four groups of fa brics wi th a 98.3% classification accuracy rate. Also, by using the fac tor analysis, the distri bution of characteristics dime nsion for the fo ur kinds of fabrics can be understood. Keywords: Cotton, Drape form, Di scriminant analysis, Line n, Si lk, Wool IPC Code: Int. C I 7 D06J 1/00; GO IN 33/36 1 Introduction Natural fibres possess characteri stics of nature, elegance and comfort. Today, the manufacturers aim to make synthetic fibres, including imitations of cotton, linen, wool and silk, that can keep the hand, appearance and drape of natural fibres 1. However, there is no criterion fo r evalu ati ng the generic of different fabric types. It is di ffic ult to apply the generic of one fabric to another fabric during manufacturing. In other words, it is hard to say that to whi ch natural fibres fa bric, a newly developed or processed syntheti c fibres fa bric has sim ilarity. Whil e difficu lties in eval u ating the characteri stics of synthetic fibres fab ri cs have constantly troubled texti le workers, it is necessary to establish an objective discri minant model for fabric characteristics of natural fibres. Kawabata, Lai and Fan appl ied mechani cal properties measured by KES-FB syste m to establish a discriminant model for fabric characteristics 2-4. They found that the characteristics of colton, linen, wool and silk can use the di scriminant analysis and neural network to categori ze. However. the hi gh cost and complicated operation of the KES system cause some troub le. Fabric drape for m is significantly correlated with th e fabric characteri stics and appearance S. 6. T he identificati on of a generic fabric drape with characteristi c parameters and discrimi nating fabrics with different generi c drapes is needed. In the present work, the discrimi- "Phone: ; Fax: ; 5sl@mail. npust. edu.tw nant analysis was used to characteri ze the four groups of fabrics, namely cotton, linen, wool and silk, and the factor analysis was used to understand the distribution of characteri sti cs dimension for the four groups of fabrics. 2 Materials and Methods 2.1 Materials Si xty pieces (15 pieces each fabric group) of fabri cs wove n from four different natural fibres, namely cotton, linen, silk, and wool, were used as fo ur fabric groups. Each fabric group was woven from a single natural fibre. The basic properties of each fabric group are shown in Table I. 2.2 Drape ;. 'm T est T he C u ~..;k fabri c drape instrument was used fo r drape form test. Firstly, the flat transparent surface was used to project the drape form of the fabric onto the flat surface. T hen, a digital camera was used to capture the image (Fig. 1)7 of the drape form using photoshop and solidwork s software. Fi nally, the drape Table I- Fabric properties Fibre Yarn con- Sample Thickness Weight struc tion size mm mg /em 2 Calion Spun Linen Spun Wool Spun Silk Filament

2 144 INDIAN J. FrBRE TEXT. RES., JUNE 2004 form was calculated. Drape form definition is given in Table 2 and drape form wave diagram is shown Fig Discriminant Analysis Discriminant analysis was used to characterize the four groups of fabrics. The generic for each fabric group was characterized using the Fisher linear di s criminant (FLD)7 function. Assuming Y parameters (X) in the sample characteristic function, the equation of function for the different generic fabrics is given as follows: where A is the function coefficient; subscript n, the number of sample characteristic functions; and subscript i, the sample size for each fabric group. In this study, n is from 1 to 4 for the four fabric groups. The (1) sample characteristic functions were assessed usll1g the classification accuracy rate. In order to know the discriminant space for effective sample discrimination of the follr fabrics, the Canonical discriminant analysis method was applied 8. The discriminant functions of the four fabric groups were presented lising the Canonical di scriminant function (CDF) 8. Y parameters (X) in the sample discriminant functions were used in the same manner as in the characteristic function as shown below:... (2) where B is the function coefficient; and subscript m, the number of sample di scriminant functions. In this study, m is from 1 to 3 for the four fabric groups. The Wave trough Wave arc Wave crest Fig. l--collectiol1 of drape wave form of fabric (A- digital camera, B- projection disk, C- fabric, D-- projection screen, E- lamp light, and F-- computer) Fig. 2-Drape wave form diagram \ -Sl' Ice angie of wave Table 2- Definition of drape form Symbols WN MC MT MA SA DA DC RCT MSA VC VT VA VS VCT Item Wave number Mean wave crest, em Mean wave trough, cm Mean wave arc, cm Mean area of single wave, cm 2 Drape area, cm 2 Drape coefficient Ratio of mean wave arc and crest Mean slice angle of wave (0) CV of wave crest CV of wave trough CV of wave arc CV of single wave area (0) CV of ratio of mean wave crest and trough Explanation Sum of single wave number Sum wave crest! wave number Sum wave trough/ wave number Sum wave arc/ wave number Single wave areal wave number Sum of single wave drape area Drape area /circular paper mold area (Wave arc / wave crest)/ wave number S lice angle of wave/ wave number Standard deviation/mean of wave crest Standard deviation/mean of wave trough Standard deviation/mean of wave arc Standard deviation/mean of single wave area Standard deviation/mean of rati o of mean wave crest and trough CV- Coefficient of variation

3 SANG-SONG: DISCRIMINANT MODELS OF FAB RIC CHARACTERI STICS 145 sample grouping is based on the Bayes theorem criterion. The classificati on accuracy rate was used to assess the sample discriminant functions. 2.4 Factor Analysis The factor analysis was carried out to summarize multiple parameters into few groups of new factors, a kind of multiple analysis, and can be represented by fo llowing vectors and matrices 9 : Z=Af+... (3) where Z=(ZI, Z~,... Zp) is a (px I) observable random vector; A=[(ri)], a (pxq) unknown matrix of factor loading where rij is th e unknown parameter to represent the loading of the ith variable on the /' factor; f=(f1, f2,... fq), a (qx I) unobservable error or socalled common factor; and =( 1, 2,... p), a (px I) unobservable error or so-cal led specific factor. It is found after many tests that principal component method provides a better reduction effect on the dimension of variance-covariance matrix and, therefore, is used to estimate the model parameters. 3 Results and Discussion 3.1 Descriptive Statistics The descriptive statistics values of each fabric group are shown in Table 3, where the predicted scope of the di scrimination model is provided. 3.2 Discriminate Model Establishment Fabric drape forms measured by the Cusick fabric drape instrument were used to establish a di scriminant function for the characteri stics of cotton, linen, wool and silk. Fourteen drape forms were analyzed through the test of equali ty of four group means. The Wilks' Lambda statistical values of each drape forms are shown in Table 4. The P-value of each drape form has a significant difference (P<0.05). It affirms that the characteristics of cotton, linen, wool and silk can use the drape forms to categori ze. Classification accuracy rate of discriminant functions obtained from discriminant analysis are shown in Table 5. Classification accuracy rate of model was 98.3 % when only one piece of linen was wrongly discriminated as cotton. Therefore, it is feasible to use fabric drape form to establi sh discriminant functions for the characteristics of cotton, linen, wool and si lk. T he Fisher linear discriminant function for the four fabric groups was establi shed under a 98.3 % classification accuracy rate [Eq. (I)]. The coefficients of sample characteristic functions are given in Table 6. The sample Canonical discriminant functions with the 14 drape forms mentioned above are presented as in Eq. (2). The coefficients of the functions are shown in Table 7. The eigen value and variance for the Canonical discriminant fu nctions are given in Table 8. In the significance test results for the Canonical discriminant functions CDF 1 and CDF 2, the eigen values are found to be and 0.61, and Canonical Table 3--Drape forms of four fabric groups Para- Cotton Linen Wool Si lk meter Min. Max. Mean S.D. Min. Max. Mea n S.D. Min. Max. Mean S.D. Min. Max. Mean S.D. WN MC MT MA SA DA DC RCT MSA VC 0.Q VT VA VS VCT

4 146 INDIAN J. FIBRE TEXT. RES., JUNE 2004 Table 4--Test of equality of group means Table 7--Coefficients of the CDF Parameter Wilks' F-value P-vall.le X Lambda CDFI CDF 2 CDF3 Bo Constant WN IOE-20 BI WE MC E-13 B 2 MC MT E-24 B3 MT MA B4 MA SA E-13 DA E-1 7 B5 SA DC E-J3 B6 DA RCT B7 DC MSA E-21 B8 RTC VC B9 MSA VT E- 14 BIO VC VA E-09 BII VT VS E-25 B 12 VA VCT E-13 B I3 VS Table 5--Classification results B 14 VCT Group Predicted fabric grou12s Table 8-- Eigen value and cumulative variance percentage Cotton Linen Wool Silk ofcdf Cotton Function Eigen Variance Cumulative Canonical Linen I value % variance, % correlation Wool Silk Classification accuracy rate = 98.3% CDFI CDF ' COF Table 6--The coefficients of the FLO correlation coefficients are 0.98 and 0.62 respectively. X Cotton Linen Wool Silk Their cumulative variance percentages are> 98 %. (n=l ) (n=2) (n=3) (n=4) Therefore, it only needs to find the two functions CDF, and CDF 2 to possess good interpretation ability. Ao Constant Also, finding the two functions will help in visual AI WE observation where a two-dimensional scatter diagram A2 MC can be used to indicate fabric characteristics. Fig. 3 is A3 MT the discriminant space of CDF, and CDF 2 For CDF" A4 MA the coordinates of centurions for the characteristics of As SA linen, cotton, silk and wool are (1. 9 1, 0.72), (7.68, - A6 DA ), (-2.02, 0.786) and (-7.57, -0.77) respectively. A7 DC For both CDF, and CDF 2, the centurions for the char- As RTC acteristics of four fabrics can be classified in different A'l MSA quadrants of a two-dimensional plane. A IO VC Ali VT AI 2 VA Au VS AI4 VCT Factor Analysis It indicates that the four fabric groups possess their own characteristics when they have been correctly discriminated in accordance with their drape forms in the previous section. In order to know the characteri-

5 SANG-SONG: DISCRIMINANT MODELS OF FABRIC CHARACTERISTICS I! o 0 u Wool I Cotton Table 9-- Eigen value and cumulative variance Parameter Factor I Factor 2 Eigen val ue Variance, % Cumulative variance, % Silk -5 o CDFI linen 5 10 Fig Centurions of cotton, linen, wool and silk fabrics 1 linen 0.5 l- Cotton Wool -0.5 t- -1 Silk o 1 2 Factor 1 Fig. 4--Distributi on of fabric average factor scores in the characteristic spaces stic combinations of the fou r fabrics, the principal component method of factor analysis was applied. Under the condition that e igen value> 1, fourteen drape forms were transformed into two new factors: Factor 1- consisting of YS, YT, DC, MT, MC, MSA, WE, YCT, RTC, and DA. Since area properties has a high communality, Factor 1 is defined as "area variation"; and Factor 2-consisting of MA, SA, Y A, and yc. Since wave arc properties has a hig h communality, Factor 2 is defined as "wave arc". The cumulative. variance percentages of the factors I and 2 are 42.66% and % respectively (Table 9). New combinations of the 14 drape forms are shown in Table 10. Table IO--Component matrix Parameter Factor I Factor 2 VS VT DC MT MC MSA WE VCT RTC DA MA SA VA VC By transforming large number of parameters that can affect discrimination of fabric characteristics into small number of factors, it helps in evaluating the characteristics of the four fabrics groups. Fig. 4 shows the distribution for the average factor scores of cotton, linen, wool and si lk samples in the two factor spaces. From the characteristic space formed by Factor 1 and Factor 2, the following observations can be made: cotton tends to have medium area variation and wave arc, linen tends to have extremely high area variation and medium wave arc, wool tends to have medium area variation and wave arc and silk tends to have low area variation and medium wave arc. In the new factor space, the characteristics of the four fabrics groups will not overlap. rn other words, each of cotton, linen, wool and si lk has its own unique characteristics. 4 Conclusions By applying discriminant analysis, 14 fabric drape forms measured by the Cusick fabric drape instrument have been successfully used to establish discriminant models for characteristics of cotton, linen, wool and silk. Four fabric groups were discriminated with a 98.3% classification accuracy rate, regardless of either

6 148 INDIAN J. FIBRE TEXT. RES., JUNE 2004 the Fisher linear discriminant function or the Canonical discriminant function has a high classification accuracy rate. Using the Canonical discriminant functions, the characteristics of the four fabrics can be classified in different quadrants of a two-dimensional plane. The results show that the characteristics and discrimination of different generic drape fabrics can be assessed using discriminant analysis. Using the factor analysis, the distribution of the characteristics dimension for the four kinds of fabrics can be understood. References Chang B L, Jou C H & Wang T P, Research model for fabric handle categorizing recognition, J China Text Illst, 5 (1995) Kawabata S, The standardization and analysis of hand evaluation, Text Mach Soc Japan, (1980) Lai S S, Shyr T W & Lin J Y, Comparison between KES-FB and FAST in di scrimination of fabric characteristics, J Text Eng, 48 (2002) Fan K C & Wang Y K, Fabric classification based on recognition usi ng a neural network and dimensionality reduction, Text Res J, 68 (1998) Cusick G E, The dependence of fabric drape on bending and shear stiffness, J Textlnst, 56 (1965) Moore C L, Effects of fabric skewness on the drape of fourgore ski rts, Clothing Text Res J, 13 (1995) Morrison D F, Multivariate Statistical Methods (McGrew Hill Publishing Co., New York), 1990, Hair J F, Anderson R E, Tatham R L & Black W C, Multivariate Data Analysis (Prentice-Hall International, Inc., New Jersey), 1998, Zhang J B, Application of Multivariate Analysis (Wen Fu Publishing Co., Taiwan), 1993, 77.