Abstract
The textile bleaching process that involves hot hydrogen peroxide (H2O2) solution is commonly practised in cotton fabric manufacture. The purpose of the bleaching process is to remove color from the cotton, achieving a permanent white before proceeding to dyeing or shape matching. Normally, the visual ratings of whiteness on the cotton are measured based on whiteness index (WI). However, it is found that there is little research on chemical predictive modelling of the cotton fabric’s WI compared to experimental study. Analytics using predictive modelling can forecast the outcomes, leading to better-informed cotton quality assurance and control decisions. Up to date, there is limited study applying least square support vector regression (LSSVR) model in the textile domain. Hence, the present study aims to develop a multi-output LSSVR (MLSSVR) model using bleaching process variables and results obtained from two different case studies to predict the WI of cotton. The predictive accuracy of the MLSSVR model was measured by root mean square error (RMSE), mean absolute error (MAE), and the coefficient of determination (R2). The obtained results were compared with other regression models including partial least square regression, predictive fuzzy model, locally weighted partial least square regression, and locally weighted kernel partial least square regression. Our findings indicate that the proposed MLSSVR model performed better than other models in predicting the WI as it showed significantly lower values of RMSE and MAE. Furthermore, it provided the highest R2 values which are up to 0.9999.
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Abbreviations
- A:
-
A matrix consisting Lagrange multipliers
- \(b\) :
-
A threshold value
- bk :
-
Kernel parameter for locally weighted kernel partial least square
- CIE:
-
Commission on Illumination
- CPU:
-
Central processing unit (CPU)
- H, P, Q, K, \(\Omega\), \(0\),\(S\) :
-
A definite matrix
- H2O2 :
-
Hydroxide peroxide
- LSSVR:
-
Least squares support vector regression
- LOO:
-
Leave-one-out
- LW-KPLSR:
-
Locally weighted Kernel partial least square regression
- LW-PLSR:
-
Locally weighted partial least square regression
- LV:
-
Latent variable
- MAE:
-
Mean absolute error
- p:
-
A positive hyperparameter of radial basis function kernel function
- PE:
-
Prediction error
- PLSR:
-
Partial least square regression
- MLSSVR:
-
Multi-output least square support vector regression
- NT :
-
Total number of data sets
- N1 :
-
Number of training data sets
- N2 :
-
Number of testing data sets
- R2 :
-
R-squared or the coefficient of determination
- RBF:
-
Radial basis function
- RMSE:
-
Root mean square error
- SVM:
-
Support vector machine
- T:
-
Temperature of bleaching process
- t:
-
Time of bleaching process
- \(V\),\(v_{i}\) :
-
A vector in multi-output least square support vector regression
- WI:
-
Whiteness index
- W:
-
Weighed value vector
- \(x_{i}\), \(x\) :
-
Input vector
- \(x_{c}\) and \(y_{c}\) :
-
Chromaticity coordinates of the bleached cotton fabric samples
- \(x_{n}\) and \(y_{n}\) :
-
Chromaticity coordinates of the illuminant
- \(y^{i}\),\(y\), \(Y\) :
-
Output vector
- \(Y_{L}\) :
-
Lightness
- Z:
-
A mapping to some high or even unlimited/infinite dimensional Hilbert space or feature space via the nonlinear mapping function \(\phi\) with \(n_{h}\) dimensions
- \(\gamma\),\(\lambda\) :
-
Two positive real regularised parameters in the multi-output least square support vector regression
- \(\phi (x)\) :
-
A nonlinear mapping function
- \(\xi\) :
-
A vector containing slack variables
- \(\Xi\) :
-
A matrix consisting of slack variables with an order of \(l \times m\)
- \(\alpha\) :
-
A vector consisting of Lagrange multipliers
- \(\ell\) :
-
The Lagrangian function
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The authors would like to thank Curtin University Malaysia and Universiti Teknologi Malaysia for providing the support for this paper.
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Yeo, W.S., Lau, W.J. Predicting the whiteness index of cotton fabric with a least squares model. Cellulose 28, 8841–8854 (2021). https://doi.org/10.1007/s10570-021-04096-y
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DOI: https://doi.org/10.1007/s10570-021-04096-y