Using the FAST system to establish translation equations for the drape coefficient

Indi an Journal of Fibre & Textile Research Vol. 28, September 2003, pp. 270-274 Using the FAST system to establish translation equations for the drape coefficient Lai Sang-Song a Department of Apparel, National Pintung University of Science and Technology, Taiwan, Republic of Chi na Received I f March 2002: revised received and accepled 23 July 2002 The regression and neural network methods have been used to develop new translation equations for calculat ing the drape coefficient of fabric using three fabric mechani cal properties, namely bending rigidity, shear ri gidity and formabi lit y. by the FAST system. Fabri c mechani cal properties show significa nt correlations wi th drape coefficient. Both regression models and neural network models have hi gh correlation coefficients and low mean absolute values. It is observed that the neural network method has better ability of fitting than regression analysis. Keywords: Drape coefficient, FAST system. Neural network, Polyester fabric. Regression method 1 Introduction The KES and FAST are the two objective evalu ation systems to assess the fabrics often used as apparels. The drape coefficient of fabric is usually predicted by using th e fabric mechanical property of the KES system. For instance, Niwa and Morooka l used bending ri gidity, hysteresis of bending, shear rigidity and hysteresis (at 8 =0.5 ) of shearing; Yuk Fun g and Jinlian 2 used the linearity of load/extension curve, bending rigidity, hysteresis of bending, shear ri gidity, hysteresis (at 8 =0.5 ) of shearing, mean deviation of coefficient of friction, thickness and weight; and Matsudaira and Yang 3 and Furukawa el at 4. used bending rigidity, shear rigidity, hysteresis (at e =0.5 )of shearing and weight. They all used the regression models to establi sh the prediction of fabric drape coefficient equation. However, the high cost and complicated operation of the KES system cause some trouble. It is obvious to observe the strong relationship between fabric mechanical properties and drape 5. 6. Cieslinska et al. 7 predicted the fabric drape coefficient by using the fabric mechanical properties, such as bending rigidity, shear rigidity and formabi lity, by the FAST system. In the present work, the regression and neural network methods have been used to establish the translation equations for calculating drape coefficient o f fabric. 2 Materials and Methods 2.] Materia!s Sixty commercial polyester fabrics having the " Phone: 087703202; Fax:087704406; E-mail: ss l@mail.npust.edu.tw following specification were used: ends/inch, 68-120; pickslinch, 56-82; yarn linear density, 6.2-24.4 tex (warp) and 7.2 1-28.62 tex (weft); th ickness, 0.22-0.84 mm; and weight, 48.21-168.28 g/m 2. These samples are mainly used for fine women's wear, dresses and shirts. 2.2 Methods 2.2.1 Measurement of Drape Coellicient and Fabric Mechanical Properties T he three mechanical properties of the fabric, namely bending rigidity, shear rigidity and formability, were measured by FAST system and are shown in Table I. The following formulae of the FAST system were used to calculate the fabric properties: B=WxC 3 x9.8 1 x I 0. 6 G=1231EB5 F=(E20-E5)xBII4.7... ( I )... (2)... (3) where B is the bending rigidity; W, the weight; C, the bending length ; G, the shear stiffness; E20, the extensibility at a load of 20 gf/cm ; E5, the extensibility at a load of 5gflcm ; EB5, the extensibility at a load of 5 gf/cm of bi as directi on; and F, the formability. T he measurements were carried out at 20 C temperature and 65 % relative humidity. The size of the sample was taken according to the Cheng et at. 8. In the FAST system, the parameters Band W are relative, and the thickness and weight are exchangeable. Besides, the thickness of samples is very close in this study. Therefore, thi ckness and weight have been taken off fro m the translation equations.

SANG-SONG: TRANSLATION EQUATIONS FOR DRAPE COEFFICIENT 27 1 Property Table I- Mechanical properties and drape coefficients o f fabrics studied Minimum Max imum Mean Standard deviation Bending ri gidity (8). /1 Nm 2.41 Shear rigidity (G). N/m 10.30 Formability (n. mm 0.15 Drape coefficient (Dc) 0.23 The fabric drape was measured by Cusick's drape tester (GT-25 type) according to linlian test method 9. In Cusick's modified formula, the drape coefficient (Dc) is defined as the ratio of paper weight from the drape shadow (W 2 ) to the paper weight of the full specimen (WI) as shown below '0.2:... (4) 2.2.2 Establishment of Translation Equations 2.2.2.1 Regression Model To find a good equation for describing the relationship between fabric drape coefficient and mechanical properties, the following seven regression equations 2 were considered: Dc=bo+ b,b+ b 2 G+ b 3 F (5) Dc= bo+ b, log B+ b 2 10g G+ b 3 10g F (6) Dc= bo+ b, log B+ b 2 10g G+ b 3 F (7) Dc= bo+ b, T (8) Dc= bo+ b, T+ b 2 r (9) Dc=e (bo+ bit)... (10) Dc= boxb, T... (11) where bo, b l, b 2 and b 3 are the coefficients; B, G and F, the mechanical properties as described in Table 1; T, the transformation variable (log B+log G+F); and Dc, the drape coefficient of the fabric. Eqs (5)-(9) are linear regression models and Eqs (10) and (11) are quadratic model and growth model respectively. 2.2.2.2 Neural Network Model The multi-layer perceptron (MLP) artificial neural network applied in this study is a kind of supervised learning network. A statistical package in the Neural Connection (version 2.0) was used to establish an evaluation method for the drape coefficient. Structure of MLP can be divided into three layers, namely input layer, hidden layer and output layer. The neural network models (A, B, C and D) are reflecting to the Eqs (5)-(8). According to the input variance, the models are divided into four. In this study of non-linear transformation function, the dual bending function f (x) = _1 whose value I+e., 18.88 10.96 5.86 68.0 43.65 17.89 0.51 0.29 0.09 0.66 0.43 0.11 Input layer Table 2- Hidden layer Output layer Weights Learning rule Training stages Stop when Parameters of artificial neural network Item Normalization Transfer function Normal ization Parameter Standard Model A: 3 Model B: 3 Model C: 3 Model D: I Sigmoid 5 Standard Distribution Range Uniform 0. 1-1 Algorithm Steepest descent Learning coefficient 0.5 Momentum coefficient 0.3 Max. record 105 Max. updates 10000 RMS - Training - Validation 0.001 0.001 lies in the range of 0-1 was used. However, for the computation of weighted value variation between the hidden layer and the output layer, the generalized delta learning rules were employed. The learning network reduced the margin between the target value and the prediction output. The quality of learning network was expressed by the energy function. To minimize the results of the energy function, the gradient steepest descend entry method [ E =..!. I (Tj - Yj Y] was used, where E is the 2 energy function; 0, the target value of output layer; and Y j, the prediction output of output layer. The optimal data convergence after network training was obtained under these conditions (Table 2). The degree of convergence can be expressed using the following formula: RMSE=[..!.I(Tj-Y}('... (12) n

272 INDIAN J. FIBR E TEXT. RES.. SEPTEMBER 2003 where RMSE is the root-mean-square error; 11, the number of units processed by output layer; O' the target value of number j output unit; and Y j, the predicti on output of number j output unit. The value of RMSE lies in th e range of 0-1.0. If RMSE converges to less than 0.0 I, a very good convergence effect is obtained and the network learn ing resul t is satisfactory. 2.2.3 Model Test Ten fabric pieces without models processll1g previously were used for measuring the drape coeffi cient. All the model test samples of polyester, including new si lky (3 pieces), new worsted (S pieces), and peach face (2 pi eces), were within the required mechani cal property ranges as shown in Table I. The procedural steps involved: (i) use o f the FAST system to identi fy the three mechani cal properties of th e fabrics pri or to inputting the regression models and neural network to calcul ate th e drape coefficient; th e fin al drape coeffi cient is the predicted value, (i i) use of drape tester to measure ten samples; the fin al drape coefficient is the target value, and (iii) assessment of the applied efficiency by th e correlation coeffi cient between the predicted value and th e target value, mean absolute value, and a pai red-samples T-test analysis. 3 Results and Discussion 3. 1 Correlation Analysis Before applying the regression models as discussed earl ier, we obtained correlation coefficients between the dependent variance Dc and th e independent vari ables 8, G. F, log 8, log G and T were obtained. The correlati on coefficients were used to assess the relati onships among the above six parameters and Dc. Table 3 shows th at all the six parameters exhibit a good positi ve correlati on. The signi ficant correlati on is at 0.00 1 level. The increase in 8 value indicates th at th e fa bri c is sti ff and shon of limpness, ancl therefore the Dc va lue increases too. As th e G value increases, the Dc value also increases. This increases the low bias ex tension of fa bric and short of extension. Because the correlation of F and 8 is positive, the correlati on of F and Dc is also posi ti ve. The reason is increase fo r Dc, as 8 and G turn into logarithm function. In addi tion, a hi gh relationship is obtained between T and Dc. Therefore, the fitting ability of th e model is increased as a resul t of variance exchange, or provides another ty pe of mode l. 3.2 Regression Model According to the seven models suggested earlier, a regression method in SPSS (a tatistical package) was selected to find out the combinati on of closely related parameters that best predicts th e fabri c drape coeffi cient. The analysis of vari ance with respect to the regression models is shown in Table 4. These regression models have a hig h level of signi ficance (Sig. F<O. OOOO), refl ecting a rather hi gh fit capabil ity. Table S shows the coeffi cients and mul tipl e R of seven regression models. The hi ghest multiple R is the result of the combinati on of parameters in Eq (7). T herefore, the non-linear regression analysis was executed by using th e T variance. It shows good fitting abilities, as multiple R of t;lese models is hi gher than 0.8S. It was sure to establi sh the predi ction mode of fabric drape coeffi cient through 8, G and F values. Both linear regression models and non-linear regression models have excellent fitting ability. 3.3 Neural Network Model To execute th e network training, the independent vari ables of Eqs (S)-(8) were taken as input values and Dc as target values. It is found that the RMSE value decreases rapidly when the number of training Dc Table 3---Correlati on coefficients of parameters Dc B G F 10g B log G T B 0.711 ** G 0.587*** 0.324* I F 0.524*** 0.539*** -0.073 log B 0.72 1*** 0.978*** 0.3 17* 0.547*** logg 0.607*** 0.369** 0.964*** -0. 149 0.31 6* T 0.854*** 0.895*** 0.670*** 0.455** * 0.904*** 0.698*** * P<0.05. ** P<O.OI. and ***P<O.oOI.

SANG-SONG: TRANSLATION EQUATIONS FOR DRAPE COEFFICIENT 273 Table 4- Analysis of variance Equation Variance SS OF MS F Sig. F No. 5 Regression 0.549 3 0.183 54.387 1.31 E-16 Residuals 0.188 56 0.003 6 Regression 0.555 3 0.185 57.006 4.92E-17 Residuals 0.182 56 0.003 7 Regression 0.580 3 0.193 69.203 7.67E-19 Residuals 0.157 56 0.003 8 Regression 0.538 3 0.538 156.723 1.36E-17 Residuals 0.199 56 0.003 9 Regression 0.549 2 0.275 83.487 0.0000 Residuals 0. 188 57 0.003 10 Regression 3.418 I 3.418 173.794 0.0000 Residuals 1.141 58 0.019 I I Regression 3.419 3.412 173.794 0.0000 Residuals 1.140 58 0.019 SS- Sum of squares, OF- Degrees of freedom, MS- Mean of square, F- F-ratio, and Sig. F- Significant level for the regression model Table 5- Coefficients and mu ltiple R of seven regression models Equation b n b l b 2 b J Multiple R No. 5 0.093 0.006 0.003 0.426 0.863 6 0.106 0.088 0.272 0.342 0.868 7-0.236 0.092 0.262 0.554 0.887 8-0.117 0.193 0.854 9 0.315-0.139 0.06 1 0.863 10-2.260 0.486 0.866 II 0.104 1.627 0.866 Dependent variable- Drape coefficient b o. b" b 2 and b,-the coefficients Table 6- Correlation coefficients between target drape coefficient and predicted drape coefficient Neural Correlation Mean absolute model coefficient value Model A 0.956* 0.027 Model B 0.946* 0.Q28 Model C 0.960* 0.028 Model D 0.863* 0.045 *P<O.OOI Mean absolute = [Target drape coefficient - Predicted drape coefficient] Total number of samples (60) 05 0.4 IJJ 0.3 CIl ~ 0.2 0.1 ~ModelA -o-model B -;:,-Model C ~ Model D o L- -L ~ ~ ~ -J o 100 300 400 500 Training cycles Fig.l-Convergence of RMSE with four neural network models runs is increased (Fig. 1 ). When the number of training runs increases to 100 cycles, the RMSE decreases below 0.06. When the number of training runs increases to 500 cycles, the RMSE converges to 0.04, showing a good result. There is an obvious correlation between the target values and predicted values (Table 6). The correlation coefficients in four models are higher than 0.86. Both of the drape coefficients nearly fit together. The correlation coefficient and the mean absolute values of models A, Band C are close to each other and show the feature of high correlation coefficient and low mean absolute value. The fitting ability of models A, B and C is superior to that of model D. 3.4 Model Test The capacity of regression models and neural network models was tested for predicting the drape

274 INDIAN 1. FIBRE TEXT. RES.. SEfYfEMBER 2003 Table 7---Results of the model test Model Correlati on Mean T- value coefficient absolute value Equation 5 0.918* 0.040 0.555 Equation 6 0.919* 0.048 0.565 Equation 7 0.927* 0.043 0.425 Eq uation 8 0.928* 0.045 1.088 Eq uation 9 0.931 * 0.041 1.013 Eq uation 10 0.933* 0.042 1.271 Equation II 0.930* 0.041 1.056 Neural model A 0.978* 0.024 0.565 Neural model B 0.977* 0.019-0.776 Neural model C 0.978* 0.028-0.649 Neural model D 0.937* 0.038-0.841 *P<O.OO I ; T value- Paired-samples T-test value; and Si g. T- Si gnificant level for the paired-samples T-test Fig.2-0.8 E dl u 0.6 e g u 8. 0.4 «:I... "0 ~ u 0.2 ]... 0.. o n=lo o Equation 6 Model A o 0.2 0.4 0.6 Target drape coefficient Sig. T 0.592 0.586 0.681 0.305 0.338 0.236 0.319 0.586 0.457 0.533 0.422 0.8 Scaller plot of the predicted and target drape coefficients coefficient. If a model has high correlation coefficient, low mean absolute and no significant difference between predicted and target drape coefficients, it provides a good fit. The results of models test are shown in Table 7. The four predictive models show correlation coefficient of above 0.9 and the mea.n absolute value within the range 0.019-0.048. The difference between the predicted and the target drape coefficients was approximately 0.04. Both regression models and neural models have the feature of high correlation coefficient and low mean absolute value. Besides, there is no significant difference between predicted and target values as observed through the paired-samples T-test. Neural network method has the characteristics of high correlation coefficient and low mean absolute value and shows apparently better ability of fitting than regression method. The fitting ability of the models A, Band C is superior to that of model D. For example, using the Eq (6) and model A, the corresponding predicted and target drape coefficient values are described in Fig. 2. The closer dots reach to diagonal, showing better fitting ability. The dots separate in Eq (6) and converge on the diagonal of model A. Also, the slope values (between predicted and target values) for model A and Eq (6) are 0.76 and 0.93 respectively. This proves again that the fi tting ability of model A is superior to that of Eq (6). The predicted and target values of the other nine models have excellent linear property. 4 Conclusion The regression and neural network methods have been used to establish the translation equations for predicting the drape coefficient of fabric. The fabric mechanical properties that have significant correlations with the drape coefficient are bending rigidity (8), shear stiffness (G), formabil ity (F), log B, log G and the transformation variable (T). Through models test, both regression models and neural network models have the features of high correlation coefficient and low mean absolute value. This is, therefore, a good approach to establish effective translation equations for the drape coefficient from the regression analysis and neural network methods. Neural network method has better ability of fitting than the regression analysis. References Niwa M & Moraoka H. Relation between drape coefficients and mechanical properties of fabrics. 1 Text Mach Soc lpn, 22(3) (1976) 67. 2 Yuk-Fung C & linlian H. Effect of fabric mechanical properties on drape, Text Res l, 68(1) (1998) 57. 3 Matsudaira M & Yang M. 1 Textlnst. 91(4) (2000) 600. 4 Furukawa S, Mitsui Takatera M & Shimizu Y. Drape formation based on geometric constraints and its application to skirt modeling, In! 1 Clothing Sci Techllol. 13(1) (2001) 23. 5 Bricis A M, Ascough 1 & Bez H E, A simple finite element model for cloth drape simulation, In! 1 Clothing Sci Tee/mol. 8(3) (1996) 59. 6 Collier 1 B, Measurement of fabric drape and it's relation to fabric mechanical properties and subjective evaluation, Clothing Text Res l, 10(1) (1991) 46. 7 Cieslinska A, Frydrych I & Dziwarska G, Mechanical fabric properties influencing drape and handle, lnt 1 Clothillg Sci Technol. 12(3) (2000) 171. 8 Cheng S Kp, How Y L & Yick K L. Objective measurement in shirt manufacture, In! J Clothing Sci Technol. 8(4) (1996) 44. 9 Siuping C & linlian H. Drape behaviour of woven fabrics with seams. Text Res l, 68( 12) (1998) 913. EO Cusick G E, The measurement of fabric drape, 1 Text Inst, 59(6) (1968) 253.