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Quantitative analysis of wool and cashmere fiber mixtures using NIR spectroscopy

  • Jinni Chen , Yule Men EMAIL logo , Yunhong Li , Yaolin Zhu , Xin Chen , Gufeng Tian and Gang Zhang
Published/Copyright: November 5, 2024

Abstract

The quantitative determination of wool and cashmere mixed fiber is an indispensable quality control link in the textile industry, crucial for improving international trade status, ensuring product quality, and safeguarding consumer rights. Therefore, the goal of this study is to develop a reliable method for estimating fiber contents in wool–cashmere blends based on near-infrared (NIR) spectroscopy. A total of 210 mixed samples of 21 different proportions of cashmere and wool are prepared in the experiment, and data are collected in the NIR spectral band of 1,000–2,500 nm. Convolution Savitzky–Golay (S–G) combined with the second-order derivative is then used for spectral preprocessing. The variable iterative space shrinkage approach (VISSA) optimizes the characteristic wavelengths, and 339 wavelength points are selected. The prediction model of the least squares support vector machine (LSSVM) is established by particle swarm optimization (PSO), fast positioning, and analysis of key information related to the target in complex spectral data. Finally, the training set and the prediction set are divided according to the ratio of 8 : 2. Experiments show that in terms of modeling and prediction, the PSO-LSSVM model based on the wavelength selected by VISSA has a prediction determination coefficient R-squared of 0.9821, a prediction root mean square error of 1.1263, and an mean absolute error of 0.6527. The hybrid modeling method of VISSA, PSO, and LSSVM based on NIR spectroscopy (VISSA–PSO–LSSVM) can provide a more accurate and stable method for the non-destructive detection of cashmere and wool blended fiber content.

1 Introduction

Wool and cashmere are both natural protein fibers, which are very similar in chemical composition and tissue structure [1]. However, due to its excellent gloss, uniform fineness, good elasticity, and rarity, cashmere fiber has a higher value in textiles and is used to make high-end and luxury textiles. Due to limited production and supply difficulties, the economic value of cashmere far exceeds that of wool. In textile production, cashmere is often intentionally mixed with wool to reduce production costs. Therefore, how to test the blending ratio quickly, accurately, non-destructively, and green environmental protection has become a challenging task in the field of fiber testing [2].

The existing traditional methods mainly rely on microscopy, scanning electron microscopy, staining, quantitative analysis of stretching fluid, etc. [3]. In recent years, near-infrared (NIR) spectroscopy has utilized the characteristics of the interaction between the NIR light band and the material. By measuring the spectral information of the sample in this band, the non-destructive analysis of the composition, structure, and properties of the sample is realized [4]. Its advantages make it widely used in many fields such as chemistry [5], biology [6], food [7], and textile [8]. However, due to the high dimension, band overlap, and non-linearity of NIR spectral data [9], the established model may produce a large error in the process of data prediction [10]. In order to overcome these problems, the researchers preprocessed the spectrum and selected features before establishing the analysis model [11,12]. At the same time, the relationship between the spectral characteristics and the properties of the measured target was established by combining the chemometrics method to realize the quantitative analysis and the qualitative of the sample [13]. Deng et al. proposed a new VISSA based on model population analysis, which generates sub-models across variable subspaces by weighted binary matrix sampling (WBMS) and shows better prediction ability in NIR data correction [14]. Nawar et al. conducted the performance analysis of least squares regression, support vector regression, and multivariate adaptive regression splines on 102 soil samples to determine the best method for evaluating the effect of salt on soil organic matter and clay content [15]; Wu and Yong proposed a method combining principal component analysis (PCA) and support vector machines (SVM), which can identify and distinguish various cashmere varieties [16]. Anceschi et al. used NIR spectroscopy combined with chemometrics methods to analyze and discriminate the quantitative characteristics of raw cashmere fibers, regenerated cashmere fibers, and their mixtures [17]. Quispe et al. compared the accuracy of deep neural networks and SVM in machine learning for camel and goat fiber spectral classification [18].

According to the above literature, in the application of NIR technology, the recognition of wool and cashmere has made important breakthroughs. However, it still faces severe challenges. The existing advanced methods mainly use PCA to reduce the dimension of data and extract a small number of principal component variables to explain most of the original variables. In terms of model selection, SVM is used to find the optimal hyperplane in the feature space to reduce the error of predicting or fitting continuous variables. Although PCA and SVM have shown potential in data dimensionality reduction and nonlinear data processing, they have their own limitations: PCA, as an unsupervised method, only analyzes the overall variable data, and each sample contributes equally to the model, ignoring the differences between samples; the parameter sensitivity of SVM requires tedious parameter optimization, which poses a challenge to the accuracy of quantitative analysis in the face of spectral similarity and overlap of cashmere and wool fibers.

In order to overcome these limitations, the VISSA is introduced. Compared with PCA, VISSA effectively reduces the complexity of the feature space by sorting features to identify the features that contribute most to data variability, especially in capturing nonlinear relationships. The least squares SVM model is combined with particle swarm optimization algorithm, the model parameters can be adaptively optimized, and the generalization ability and prediction accuracy of the model can be significantly improved. The main contributions and innovations of this article are summarized as follows:

  1. Self-built cashmere and wool mixed fiber spectral data set: Due to the lack of corresponding wool and cashmere mixed fiber spectral data sets, in this study, a data set was constructed based on the standard sample preparation method of NIR spectroscopy. The NIR spectrometer was used to scan the sample to obtain spectral data to meet the needs of mixed fiber detection and provide reliable data support for research.

  2. Feature band selection: VISSA is used to extract the feature bands, which can effectively capture the complex linear and nonlinear correlations in the spectral data. By calculating the correlation coefficient between the band and the cashmere fiber, the band characteristics with high correlation with the cashmere component content are retained, thus greatly reducing the dimension of the data.

  3. PSO-LSSVM model: The PSO algorithm is introduced to effectively search the optimal parameter combination of LSSVM. It has strong adaptability and generalization ability to deal with small sample high-dimensional data and nonlinear problems and provides a basis for improving the accuracy of quantitative analysis model.

2 Experimental

2.1 Sample preparation

In the experiment, the standard sample preparation KBr tableting method for NIR spectroscopy analysis of textile materials is used for sample preparation [19]. The KBr tableting method has multiple advantages, such as improving sample uniformity, enhancing absorption intensity, reducing scattering intensity, and eliminating hydrogen bonding in infrared spectrum preparation; it can provide a strong guarantee for the accuracy and reliability of NIR spectroscopy analysis. Therefore, the KBr tableting method is used for sample preparation in the experiment. The specific steps are as follows:

  1. The collected wool and cashmere fibers were weighed according to the mass fraction. The mass fraction of cashmere was from 0 to 100%, with an interval of 5%. Each sample weighed 0.1 g and was accurate to 0.001 g.

  2. Different proportions of mixed wool and cashmere fibers were cut into small pieces and then ground into small powder with agate mortar (the particle size was less than 1.5 mm after crushing treatment).

  3. Then, according to the ratio of sample: KBr = 1 : 20, 2 g KBr reagent was taken from each sample and uniformly mixed with it.

  4. The mixed sample powder was placed at the pressure film to obtain the potassium bromide tablet and finally placed on the NIR spectrometer for data measurement. The overall flow chart of the experiment is shown in Figure 1.

Figure 1 
                  The overall flow chart of the experiment.
Figure 1

The overall flow chart of the experiment.

2.2 Acquisition of spectral data sets

NIR spectral band data are collected using the RZNIR 7900 NIR spectrometer. The experimental environment temperature ranges from 10 to 30°C, and the infrared spectrometer is preheated for 30 min to ensure the stability and accuracy of the collected NIR spectral data. NIR spectral band data of samples are collected in diffuse reflection mode. The wavelength range is set from 1,000 to 2,500 nm with a sampling interval of 1 nm. Each sample is measured ten times, and the average values of positive and negative data sets are computed. After the measurement is completed, the average NIR spectral band data are exported and saved as a csv file. The original NIR spectra of some mixed samples with different proportions and wool-cashmere fiber spectra are shown in Figure 2.

Figure 2 
                  (a) The original NIR spectra of some mixed samples with different proportions and (b) wool-cashmere fiber spectrum.
Figure 2

(a) The original NIR spectra of some mixed samples with different proportions and (b) wool-cashmere fiber spectrum.

All the algorithms are executed using MATLAB R2023a under the Windows 10 system.

2.3 Model evaluation index

The evaluation indexes used in this model are R-squared, mean absolute error (MAE), and root mean square error (RMSE) [20]. Among them, y i is the true value of cashmere fiber content, y ^ i is the predicted value of cashmere fiber content by the model, y ¯ i is the average value of cashmere fiber content predicted value, and n is the number of samples. The closer the R-squared value to 1, the better the accuracy of the model in predicting cashmere fiber content. RMSE is essentially a root number based on MAE, which can well reflect the degree of deviation between the predicted value and the true value of fiber content in the regression model. Therefore, the smaller the values of RMSE and MAE, the better. The calculation formula of the evaluation index mentioned above is as follows:

(1) R -squared = 1 i = 1 n ( y i y ^ i ) 2 i = 1 n ( y i y ¯ ) 2 ,

(2) MAE = 1 n i = 1 n y i y ^ i ,

(3) RMSE = 1 n i = 1 n ( y i y ^ i ) 2 .

2.4 Method

In this study, the convolution S–G filter is used to smooth the original spectral data, which effectively suppresses the noise and enhances the spectral characteristics through the second derivative. Subsequently, the VISSA algorithm is used to optimize the characteristic wavelength, and the efficiency and accuracy of the characteristic wavelength selection are improved by iteratively reducing the search space. Finally, the PSO algorithm is used to optimize the LSSVM model, and the rapid positioning and analysis of the key information related to the target are realized. The overall design flow chart of the algorithm is shown in Figure 3.

Figure 3 
                  Flow chart of the PSO-LSSVM model.
Figure 3

Flow chart of the PSO-LSSVM model.

In terms of feature selection, the core of VISSA is to construct a sub-model by WBMS, then extract the sub-model with the smallest prediction error, count the frequency of each variable, and assign variable weights to achieve variable space shrinkage. Among them, WBMS mainly allocates the number of variables in the sub-data set according to the current weight of the variable, ensuring that the variables with larger weights have a higher probability of being selected, so that each variable has a different sampling frequency. The weight formula of the variable is

(4) w i = f i / m best .

In the formula, f i is the frequency of the variable in the best sub-model, m best is the most the number of good models, and w i is the proportion of sub-models containing variables.

2.4.1 LSSVM prediction model

As an extension of SVM, LSSVM simplifies the solution of quadratic programming problem and reduces the computational complexity of the model and the selection of hyperplane parameters [21]. The inequality constraint of SVM is replaced by the linear least squares criterion of the loss function, which makes the optimization problem of LSSVM become a linear programming problem. Its robustness, generalization ability, and convergence speed are significantly improved, and it is more suitable for processing high latitude, nonlinear small sample data.

When using LSSVM for pattern recognition, based on the principle of structural risk minimization, the least square method is used to establish the objective function of LSSVM. The expression is

(5) min J ( w , e i ) = 1 2 w 2 + 1 2 C i = 1 n e i 2 ,

(6) s . t . y i = w T φ ( x i ) + b + e i .

In the formula, w 2 stands for the complexity of the control model, C is a regularization parameter, e i is the i relaxation variable, and φ ( x i ) is the feature vector of the input sample.

In order to better solve the optimization problem, the Lagrange multiplier is introduced into the above equation, and it can be obtained that

(7) L ( w , b , e i , a i ) = J ( w , e i ) i = 1 n a i ( w T φ ( x i ) + b + e i y i ) , i = 1 , 2 , , n .

In the formula, a i for the first Lagrange multiplier, according to the Kuhn–Tucker condition, the partial derivative operation is performed on the relevant parameters in the Lagrange function, and the result is equal to zero:

(8) L w = 0 w = i = 1 n a i φ ( x i ) L b = 0 i = 1 n a i = 0 L e i = 0 C e i = a i L a i = 0 w T φ ( x i ) + b + e i y i = 0 .

By eliminating w and e i , the linear equations are obtained as follows:

(9) 0 y = 0 Z T Z K + C 1 E b a .

In the above formula, a = [ a 1 , a 2 , , a n ] T ; Z = [ 1 , 1 , , 1 ] T ; y = [ y 1 , y 2 , y n ] T ; unit matrix with E is n × n , K = k ( x i , x j ) .

In view of the good stability of the radial basis function, it is adopted as the kernel function of the LSSVM model, namely:

(10) k ( x i , x j ) = exp x i x j 2 2 σ 2 .

which x i x j 2 represents the square of Euclidean distance, 1 2 σ 2 is a hyperparameter of the Gaussian kernel function, which is used to control the distribution of samples in high-dimensional space.

The expression of the LSSVM prediction model is

(11) y i = i = 1 n a i k ( x i , x j ) + b .

2.4.2 The hyper-parameter selection of LSSVM optimized by PSO

PSO is a stochastic optimization algorithm, which is used to simulate the behavior of individuals in the population to find the optimal solution in the solution space and share information with other individuals in the group to find the global optimal solution [22]. In the PSO algorithm, each individual is represented as a particle, and each particle has its own position, speed, and corresponding fitness value by comparing with the adjacent particles and moving in the solution space to find the global optimal solution. The update process of the PSO algorithm can be described by the following formula:

(12) V i t + 1 = w V i t + c 1 r 1 ( p besti X i t ) + c 2 r 2 ( g besti X i t ) ,

(13) X i t + 1 = X i t + V i t + 1 .

In the formula, t is the number of iterations, V i t is the velocity of the particles at the t iteration, w is the inertia constant, c 1 is the local learning factor, c 2 is the global learning factor, and r 1 r 2 is a random number of [0, 1]. Represent the position of the particles at the t iteration.

Under the framework of PSO, the hyper-parameter selection of the LSSVM model is determined by two main components: the coding strategy of hyper-parameters and the formulation of the fitness function.

Hyperparameter coding involves transforming the hyperparameter set into the position representation of particles in the search space. For the LSSVM model, the key hyperparameters include kernel parameters and regularization factors. The particle swarm optimization algorithm uses particles to simulate the potential solutions in the search process, so each particle corresponds to a specific combination of hyperparameters [23]. In this article, we represent m hyperparameters as m-dimensional vectors, such as ν = ( γ , σ ) . Among them, the initial parameter setting of LSSVM optimized by PSO is shown in Table 1.

Table 1

PSO optimizes the initial parameter setting of LSSVM

Parameter variable Parameter value Parameter variable Parameter value
Learning factor c 1 0.5 Particle rate [ V min , V max ] [−0.25, 0.25]
Learning factor c 2 0.5 Particle value [ pop min , pop max ] [0.001, 200]
Population size 20 Inertia factor [ w min , w max ] [0.4, 0.6]
Evolution times 200

The fitness function is used to evaluate the pros and cons of particles in PSO. We define it as the generalization performance measure of the model; the calculation formula is as follows:

(14) fitness = 1 MRE ,

where the formulation of MRE can be seen in equation (14)

(15) MRE = 1 N i = 1 N y i y ^ i y i ,

where N is the number of the samples in the training set or test set, and y ^ i y i represent the predicted and actual fiber content, respectively.

3 Results and analysis

3.1 Spectral data preprocessing

From the original spectrum, it can be seen that the overall trend of the sample lines with different mixing ratios is basically similar, but there are differences in the absorption intensity at certain wavelengths (Figure 4). The establishment of the model requires reducing the fluctuation of spectral data and increasing the difference between classes. Therefore, it is necessary to preprocess the collected data, the standard normal variate (SNV) and S–G, one or more combinations of second-order derivatives are used for preprocessing, and then the PSO-LSSVM model is established for each processed full-band spectrum [24]. The results of Table 2 show that the determination coefficient R-squared of the model obtained by SG (window size is 9, polynomial fitting order is 7) and the second derivative combined with PSO-LSSVM is 0.8875 on the test set, and the model effect is more stable and accurate.

Table 2

Effects of different pretreatments on the PSO-LSSVM model

Pretreatment method R-squared
S–G 0.8565
SNV 0.8616
SNV + S–G 0.8636
SNV + second derivative 0.8824
S–G + second derivative 0.8875
Original data 0.8527
Figure 4 
                  The original NIR spectra of 210 samples: (a) after treatment with S–G and (b) after treatment with S–G + D2.
Figure 4

The original NIR spectra of 210 samples: (a) after treatment with S–G and (b) after treatment with S–G + D2.

3.2 Characteristic wavelength extraction

In the analysis of spectral data, based on the spectral data preprocessed by SG and second derivative combination, different algorithms were used to set parameters, and dimension reduction experiments were carried out. Specifically, the competitive adaptive reweighted sampling (CARS) algorithm used in this experiment carried out 50 Monte Carlo samplings, and the number of latent variable factors was set to 5 [25]; the optimal number of characteristic variables for successive projection algorithm (SPA) characteristic wavelength analysis was set to 2–18 [26]. The WBMS of the VISSA algorithm is set to 100 samples. All experiments used a fivefold cross-validation, the number of iterations was 10, and the median of the respective experimental results was used as the criterion.

By observing Figures 57, we found that the CARS algorithm obtained the minimum root mean square error of cross validation (RMSECV) of 0.0793 after 12 Monte Carlo samplings and screened 282 wavelength points. The characteristic variables selected in the SPA algorithm tended to be stable after 17. Therefore, 17 wavelength points were finally selected, and the minimum RMSECV of the model was 0.2639. The VISSA algorithm selected 339 wavelength points, and the minimum RMSECV of the model was 0.0685 (Table 4). It should be noted that the sampling methods and the determination methods of the optimal variable characteristics used by these three algorithms are different, and they are based on the sub-model of random sampling, so there is no direct correlation between the algorithms [27].

Figure 5 
                  CARS selects characteristic variables.
Figure 5

CARS selects characteristic variables.

Figure 6 
                  The change of RMSECV in SPA.
Figure 6

The change of RMSECV in SPA.

Figure 7 
                  VIASSA feature extraction: (a) screening the distribution of characteristic variables on the spectral curve and (b) RMSECV changes with the number of characteristic variables.
Figure 7

VIASSA feature extraction: (a) screening the distribution of characteristic variables on the spectral curve and (b) RMSECV changes with the number of characteristic variables.

The spectral absorption intensity of wool and cashmere is very similar, but the absorption intensity of wool is usually higher than that of cashmere. Therefore, we can distinguish these two fibers by selecting wavelengths with significant spectral differences and use them to evaluate their mixing ratio in the mixture. When selecting characteristic wavelengths, we found that there was a high correlation between the wavelengths corresponding to C–H, N–H, and C═O chemical bonds and cashmere content. However, by analyzing the visualization results of wavelength selection in Figure 8 and the corresponding chemical bonds in Table 3, it can be found that the number of wavelengths selected by CARS and SPA methods is small, and some key information variables may be missed. In contrast, the characteristic wavelengths selected by the VISSA algorithm not only cover the wavelength of the C–H bond at 1700 nm but also include other non-main absorption peaks. This shows that the VISSA algorithm can capture and contain more relevant information variables more comprehensively, thereby improving the stability and accuracy of the model.

Figure 8 
                  Comparison of wavelength selection of different algorithms.
Figure 8

Comparison of wavelength selection of different algorithms.

Table 3

Wavelengths and corresponding chemical bonds of wool and cashmere

Absorption compartment Main absorption peaks of wool and cashmere Functional group
Single bond region 1,178, 1,500, 1,700, 1,942, 2,052, 2,180, 2,280 nm C–H, N–H, S–H
Stretching vibration
CH2 bending vibration
Double bond region 1,500, 1,942, 2,052 nm C═O stretching vibration
Table 4

Modeling results of different characteristic wavelength selection methods

Pretreatment Feature extraction Model R-square RMSE MAE
SG_d2 CARS PSO-LSSVM 0.9284 1.0793 0.5490
SPA 0.9591 1.2639 0.6595
VISSA 0.9821 1.1263 0.6527

3.3 Establishment and comparison of models

The spectral data optimized by the VISSA feature is used as input to ensure the consistency of the spectral data before being put into the model. The prediction model of wool and cashmere blended fiber content was constructed by BP, KNN, LSSVM, and PSO-LSSVM. The modeling results are shown in Table 5. It can be seen that the R-square of the PSO-LSSVM model prediction set is 0.9821, RMSE is 1.1263, and MAE is 0.6527. It is better than BP, KNN, and LSSVM models. The BP model uses the gradient descent algorithm to adjust the weight and deviation in the network, but it is easy to fall into the local optimal solution. The KNN model relies on the characteristics of the surrounding K neighbors to predict and is sensitive to outliers; the LSSVM model fits the data by optimizing the distance between the smoothing curve and the data points, but it needs to carefully select the kernel function and adjust the parameters; according to the sub-model established by PSO-LSSVM, the VISSA characteristic wavelength input by modeling is selected. Therefore, the total variation of the dependent variable is explained by the independent variable (characteristic wavelength) through the regression relationship, that is, the coefficient of determination and the RMSE are optimal. The model is more stable and accurate.

Table 5

Prediction results of cashmere fiber content based on different modeling methods

Modeling method Prediction set
R-square RMSE MAE
BP 0.8963 1.8236 0.8429
KNN 0.9224 2.3763 1.2571
LSSVM 0.9582 1.6452 0.7385
VISSA-PSO-LSSVM 0.9821 1.1263 0.6527

Figure 9 shows the comparison of the model effects of different modeling methods, in which the straight line represents the fitting curve with a slope of 1. The closer the data points are to the fitting curve, the smaller the prediction deviation is. It can be seen that the predicted value of the cashmere content in the mixed fiber by the model constructed by the PSO-LSSVM method is basically evenly distributed near the fitting curve, and the effect is obviously better than that of BP, KNN, and LSSVM models, indicating that the model constructed by the PSO-LSSVM method has better performance.

Figure 9 
                  Comparison of model effects of different modeling methods: (a) BP, (b) KNN, (c) LSSVM, and (d) PSO-LSSVM.
Figure 9

Comparison of model effects of different modeling methods: (a) BP, (b) KNN, (c) LSSVM, and (d) PSO-LSSVM.

4 Conclusions

In this study, a prediction model for cashmere content in a mixed sample set of wool and cashmere was constructed using the combination of VISSA and PSO-LSSVM. The effectiveness of this model was compared with models constructed using BP, KNN, and LSSVM methods. The analysis of model evaluation parameters shows that S–G combined with the second derivative is used to process the original spectral data, and the characteristic bands extracted by VISSA are used to make the constructed PSO-LSSVM model perform better in prediction accuracy. However, its quantitative analysis model based on NIRS is only based on wool and cashmere samples. Therefore, its applicability to the prediction of cashmere content in other types of wool and cashmere mixed samples remains to be further explored. Future research will focus on collecting a wider range of fiber samples, preparing more fine sample ratios, enhancing the practical value of the model in related fields, and establishing a more comprehensive, accurate, and universally applicable quantitative analysis tool for mixed fibers, providing reliable support for quality control in the textile industry and related fields.

  1. Funding information: This work is supported by the National Natural Science Foundation of China (62203344), Shaanxi Science and Technology Plan Day (2022GY-053), Key Project of Natural Science Basic Research in Shaanxi Province (2022JZ-35), Key Research Project of Shaanxi Provincial Department of Education Industrial Textiles Collaborative Innovation Center (20JY026), Shaanxi Provincial Department of Education Research Project (23JC031), Xi‘an Science and Technology Project (23DCYJSGG0008-2023), and Yulin City Science and Technology Plan Project (CXY-2020-052) funding.

  2. Author contributions: Yule Men: Methodology, Writing, Editing. Jinni Chen: Conceptualization, Review. Yunhong Li, Yaolin Zhu, Xin Chen: Funding acquisition. Gufeng Tian: Software. Gang Zhang: Investigation.

  3. Conflict of interest: The authors declare no conflicts of interest.

  4. Ethical approval: The conducted research is not related to either human or animals use.

  5. Data availability statement: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Received: 2024-07-22
Revised: 2024-10-06
Accepted: 2024-10-07
Published Online: 2024-11-05

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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