International Journal of Chemical Engineering

Volume 2019, Article ID 8256817, 8 pages

https://doi.org/10.1155/2019/8256817

## Simultaneous Determination of Several Fiber Contents in Blended Fabrics by Near-Infrared Spectroscopy and Multivariate Calibration

^{1}Key Lab of Process Analysis and Control of Sichuan Universities, Yibin University, Yibin, Sichuan 644000, China^{2}Hospital, Yibin University, Yibin, Sichuan 644000, China^{3}The First Affiliated Hospital, Chongqing Medical University, Chongqing 400016, China

Correspondence should be addressed to Chao Tan; moc.361@2111natoahc

Received 12 November 2018; Accepted 18 December 2018; Published 3 January 2019

Academic Editor: Bhaskar Kulkarni

Copyright © 2019 Hui Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The qualitative and quantitative determination of the components of textile fibers takes an important position in quality control. A fast and nondestructive method of simultaneously analyzing four fiber components in blended fabrics was studied by near-infrared (NIR) spectroscopy combined with multivariate calibration. Two sample sets including 39 and 25 samples were designed by simplex mixture lattice design methods and used for experiment. Four components include wool, polyester, polyacrylonitrile, and nylon and their mixture is one of the most popular formulas of textiles. Uninformative variable elimination-partial least squares (UVEPLS) and the full-spectrum partial least squares (PLS) were used as the tool. On the test set, the mean standard error of prediction (SEP) and the mean ratio of the standard deviation of the response variable and SEP (RPD) of the full-spectrum PLS model and UVEPLS model were 0.38, 0.32 and 7.6, 8.3, respectively. This result reveals that the UVEPLS can construct local models with acceptable and better performance than the full-spectrum PLS. It indicates that this method is valuable for nondestructive analysis in the field of wool content detection since it can avoid time-consuming, costly, and laborious wet chemical analysis.

#### 1. Introduction

To blend fibers of different types is a common practice to obtain expected characteristics in the textile industry. According to the national standard of China, textile products have to be marked with fabric type and composition on the label. Also, this quantitative composition is mandatory information [1]. Thus, determining the composition of the textile blend is a key issue in the textile industry. Current standard methods are mainly based on physical, chemical, or microscopic techniques and are time-consuming, costly, and often require the use of some undesirable chemicals to dissolve fibers [2, 3]. Some alternatives to these methods including various spectroscopic techniques have shown considerable potential in recent years [4–6].

Especially, near-infrared (NIR) spectroscopy has shown great potential and gained wide acceptance in food industry [7–9], drug industry [10–12], cigarette manufacturing [13], fuel processing [14], wood industry [15], etc. It is also a green method for multicomponent analysis of complex samples. Compared to conventional analytical methods, NIR spectroscopic technique is based on multivariate models by which the spectral data are correlated with the index of interest, thus providing several outstanding advantages such as being fast, nondestructive, and a potentially multicomponent method. Also, it is inexpensive and environment-friendly as it needs no solvents/reagents, thus avoiding a major expense. The NIR spectrum records signal on overtones and combinations of the fundamental molecular vibrations [16]. NIR spectral information is thus hardly selective, but quantitative analysis can be carried out with the aid of chemometrics. The main advantage of simultaneous multicomponent analysis is to quantify several components in mixtures without a prior separation, which is generally necessary owing to the overlapped signals.

In NIR-based quantitative applications, a reliable calibration model is of great importance and its predictive performance even directly determines its availability [17]. It is well known that partial least squares (PLS) is the most commonly used calibration algorithm since it is a full-spectrum method and can utilize information from the whole spectrum to construct a predictive model. Even so, both theoretical and experimental evidences have been shown that an efficient variable selection can significantly improve the performance of PLS and greatly reduce its complexity [18, 19]. Uninformative variable elimination (UVE) [20] is a good variable selection method capable of eliminating variables which are not more informative for modeling than noise. When combined with PLS, it provides a way of constructing a simpler calibration model but without the loss of predictive ability. UVE is also widely used in NIR spectroscopy and have shown great advantage at eliminating of uninformative spectral variables [21].

In the present work, a fast and nondestructive method of simultaneously analyzing four components in blended fabrics was studied by near-infrared (NIR) spectroscopy combined with multivariate calibration. Two sample sets including 39 and 25 samples were designed by simplex mixture lattice design methods and used as the training set and the independent test set, respectively. Four components include wool, polyester, polyacrylonitrile, and nylon and represent one of the most popular formulas of textiles. Uninformative variable elimination-partial least squares (UVEPLS) and the full-spectrum partial least squares (PLS) were used as the tool of variable selection and multivariate calibration. This result reveals that the UVEPLS can construct local models with acceptable and better performance than the full-spectrum PLS. It indicates that this method can serve as a tool of fast and nondestructive analysis of fiber contents since it can avoid time-consuming, costly, and laborious wet chemical analysis.

#### 2. Theory and Methods

##### 2.1. Partial Least Squares (PLS)

Partial least squares (PLS) [22, 23], one of the most widely used methods in multivariate calibration, aims at predicting a dependent variable, , from a matrix of independent variables/predictors, , by projecting and to the latent variable (LV) subspaces maximizing their covariance. It is different from principal component regression (PCR), which consists of a two-step process, and the projection stage is separated and independent from the regression one. PLS actively uses the information in for defining the latent variable subspaces. Indeed, PLS looks for components which compromise between explaining the variation in and predicting the responses in . This corresponds to a bilinear model as follows:where is a score matrix, and are matrices of coefficients that relate to the independent variables and dependent variables, respectively, and and represent the corresponding residual matrices. PLS is a sequential algorithm: The latent variables are computed so that the first component is the direction of maximum covariance with the dependent variable, the second component is orthogonal to the first and has maximal residual covariance, and so on. The estimation of can be obtained by the NIPALS algorithm as follows:where is a matrix of weights of size . It is possible to obtain the general equation for prediction of :where is the matrix of estimated regression coefficients. If only a dependent variable is considered, and will be vectors. The differences of many algorithms are the ways of calculating . Many algorithms are available for obtaining a satisfactory .

##### 2.2. Uninformative Variable Elimination-Partial Least Squares (UVEPLS)

Uninformative variable elimination (UVE) is a classic method of variable selection by analyzing the stability of the regression coefficient [24, 25]. UVE aims at eliminating variables which are not more informative for modeling than noise. One can construct a better PLS model based on the remaining variables from UVE. The combination of UVE and PLS is named as UVEPLS. Taking the case of a single response as an example, the main steps of UVEPLS is summarized as follows:(1)First PLS regression is made on instrumental signal matrix () and reference values () of an interest property on the calibration/training set, and the optimal number of PLS factors is determined.(2)Then a noise matrix with an approximate size is generated and its elements are random numbers in the interval of 0-1. And the elements are multiplied by a small constant so as to make their influence on the model negligible. Such a noise matrix is appended to the original signal matrix to form an extended matrix.(3)PLS models are constructed on the extended matrix () and based on leave-one-out cross-validation. This leads to a matrix of regression coefficients with as many rows as samples and one column for each variable, including both original and random.(4)The reliability of each variable is quantitatively measured by the stability value, which is defined as the mean of the corresponding column divided by the standard deviation of that column in the matrix of regression coefficients.(5)Based on the fact that any variable with less stability than a random variable is uninformative and should be eliminated, a cutoff value is calculated as the maximum of the stability values among the random variables. Every original variable with lower stability values than the cutoff value is assumed to contain nothing but noise and is therefore eliminated.(6)Based on the remaining variables, a final PLS model can be constructed and optimized.

#### 3. Experimental

##### 3.1. Sample Design

This work used the simplex lattice design for preparing the four-component mixture samples. For an four-component system, the regular simplex is a tetrahedron where each vertex represents a straight component, an edge represents a binary system, and a face represents a ternary one. Points inside the tetrahedron correspond to quaternary systems. The basis of designing experiments of this kind is a uniform scatter of experimental points on the so-called simplex lattice. Points, or design points, form a [*q*, *n*] lattice in a (*q* − 1) simplex, where *q* is the number of components in a composition and *n* is the degree of a polynomial. The design was done by MINITAB software. The degree of lattice was set as 4 and 3 for generating the training and test sets, respectively. Also, each design was also augmented with the center point and the axial point. Thus, a total of 39 and 25 mixtures were obtained for the training and test sets, respectively. Table 1 shows the composition of each mixture from simplex lattice design for both the training and test sets, among which A, B, C, and D denote wool, polyester, polyacrylonitrile, and nylon, respectively. Each time, all fibers were first weighed separately based on a given blend ratio and were then mixed. Textiles made up of these components are industrially existent and popular in the market of China, and each content is ranging from 0 to 1 (w/w, the weight percentage).