CN117524340A - Textile component quantitative characterization method based on multilayer one-dimensional CNN depth network - Google Patents

Abstract

The invention discloses a textile component quantitative characterization method based on a multilayer one-dimensional CNN depth network, which comprises the steps of selecting textile spectrum data formed by target components from near infrared spectrum sample data, and preprocessing the textile spectrum data; constructing a GAN model, and training the GAN model by using training set data and random noise samples; constructing a multi-pooling fusion one-dimensional convolution kernel neural network, generating pseudo sample data by using a trained generator, training the multi-pooling fusion one-dimensional convolution kernel neural network by using the pseudo sample data, and taking the trained multi-pooling fusion one-dimensional convolution kernel neural network as a classifier; quantitative characterization of the composition of the textile is performed using a classifier. The method utilizes a combination method of a multilayer one-dimensional CNN depth network, a GAN model and a multi-pooling fusion one-dimensional convolution kernel neural network to realize efficient, accurate and quantitative characterization of textile components, and has good application prospect.

Description

Textile component quantitative characterization method based on multilayer one-dimensional CNN depth network

Technical Field

The invention relates to a textile fabric component identification technology, in particular to a textile component quantitative characterization method based on a multilayer one-dimensional CNN depth network.

Background

Near infrared spectroscopy is widely used in the identification of textile fabric components. It is a nondestructive analysis method, and the spectral information of the sample is obtained by measuring the light absorption and reflection characteristics of the sample in the near infrared band (700-2500 nm).

Near infrared spectrum has the following characteristics: (1) full spectrum: the near infrared spectrum covers a wide wavelength range, can capture absorption peaks and absorption bands of substances under different wavelengths, and provides rich chemical information; (2) rapidity: the near infrared spectrum acquisition and analysis process is rapid, and the spectrum data of the sample can be acquired within a few seconds; (3) non-destructive: the near infrared spectrum collection process does not need to contact the sample, can not cause any damage to the sample, and is suitable for online or real-time detection.

In the identification of textile fabric components, the near infrared spectrum technology can realize the rapid and accurate identification of textile components according to the absorption characteristics of substances such as different celluloses, proteins, synthetic fibers and the like in the near infrared band. By collecting a series of sample spectra of known components and establishing a statistical model between the spectra and the components, the spectra of the unknown samples can be compared with the model, so that the components can be judged.

In order to improve the identification accuracy, the convolutional neural network (Convolutional Neural Network, CNN) is used for carrying out component identification on the near infrared spectrum data of the textile fabric, and the automatic, accurate and efficient component classification can be realized.

Common textile fabric component identification methods include visual observation, chemical testing and the like, and each method has certain defects. Visual observation is one of the simplest and most commonly used methods to initially determine the composition by observing the appearance characteristics of the textile fabric. However, due to the similarity of the fiber materials and the presence of blending, the components of the textile fabric often cannot be accurately determined by visual inspection alone. Chemical tests generally include combustion tests, dissolution tests, staining tests, and the like. The combustion test judges the components by observing the characteristics of the fibers in the combustion process, the dissolution test judges the dissolution condition of the fibers in a specific solvent, and the dyeing test identifies the components by utilizing the affinity difference between the dye and different fiber materials. These chemical testing methods can provide more accurate ingredient determinations, but require specialized experimental conditions and equipment, and destructive testing of the fibers.

Disclosure of Invention

The invention aims to: aiming at the problems, the invention aims to provide a textile component quantitative characterization method based on a multilayer one-dimensional CNN depth network.

The technical scheme is as follows: the invention relates to a textile component quantitative characterization method based on a multilayer one-dimensional CNN depth network, which comprises the following steps:

selecting textile spectrum data composed of target components from near infrared spectrum sample data, preprocessing the textile spectrum data, and dividing the preprocessed textile spectrum data into a training set and a testing set;

constructing a GAN model, and training the GAN model by using training set data and random noise samples; wherein the GAN model includes a generator and a arbiter;

constructing a multi-pooling fusion one-dimensional convolution kernel neural network, generating pseudo sample data by using a trained generator, training the multi-pooling fusion one-dimensional convolution kernel neural network by using the pseudo sample data, and taking the trained multi-pooling fusion one-dimensional convolution kernel neural network as a classifier; wherein the output of the classifier is the content of the target component;

evaluating the classifier by using the test set, and calculating the precision index;

quantitative characterization of the composition of the textile is performed using a classifier.

Further, constructing the multi-pooling fusion one-dimensional convolution kernel neural network comprises:

the input layer is respectively connected with the input end of a first convolution kernel, the output end of the first convolution kernel is sequentially connected with the first maximum pooling layer, the second convolution kernel, the second maximum pooling layer, the third convolution kernel and the third maximum pooling layer, the output end of the first convolution kernel is sequentially connected with the first average pooling layer, the fourth convolution kernel, the second average pooling layer, the fifth convolution kernel and the third average pooling layer, the output end of the third maximum pooling layer and the output end of the third average pooling layer are added, the input end of the full connection layer is connected after the addition, the output end of the full connection layer is connected with the activation function layer, and numerical values representing the content of target components in a sample are output through the activation function layer.

Further, training the GAN model using the training set data and the random noise samples includes the steps of:

step 21, defining a loss function and an optimizer; the loss function uses two kinds of cross entropy loss functions, the optimizer uses an Adam optimizer, and the generator and the discriminator are respectively provided with the optimizers;

step 22, training the discriminator:

step 221, for the input real data sample, calculating the output and loss of the real sample by the discriminator;

step 222, the generator generates the same number of dummy data samples as the real data samples, and calculates the output and loss of the dummy data samples by the discriminator;

step 223, adding the real sample loss and the pseudo data sample loss as the total loss of the discriminator, and carrying out back propagation and parameter updating;

training the discriminators in a mode of alternately training in the steps 221-223;

step 23, training generator:

step 231, the generator generates the same number of dummy data samples as the real data samples again, and calculates the output and loss of the dummy data samples by the discriminator;

step 232, setting the pseudo data loss as the loss of the real data, and then carrying out back propagation and parameter updating;

training of the discriminant model is achieved by means of alternating training of steps 231-232.

Further, training the multi-pooling fusion one-dimensional convolutional nuclear neural network using the pseudo-sample data comprises the steps of:

step 31, setting the number of samples used in each training as z, and changing the shape of the spectrum data of the pseudo textile fabric generated by the generator from z multiplied by 61 to z multiplied by 1 multiplied by 61; wherein z is an integer;

step 32, performing feature extraction by using 16 first convolution kernels with the size of 3×1 and the original z× 1×61 tensors, and outputting to obtain z× 16×59 tensors;

step 33, performing pooling operation on the output zx16x59 tensors by using a first maximum pooling layer and a first average pooling layer respectively, and outputting to obtain two zx16x19 tensors; wherein the first maximum pooling layer and the first average pooling layer are each 1 x 3 in size;

step 34, performing feature extraction on the two z×16×19 tensors respectively by using 64 convolution kernels with the size of 3×1, and outputting to obtain two z×64×17 tensors;

step 35, performing pooling operation on the two output z×64×17 tensors by using a second maximum pooling layer and a second average pooling layer respectively, and outputting to obtain two z×64×5 tensors; wherein the second maximum pooling layer and the second average pooling layer are each 1 x 3 in size;

step 36, performing feature extraction on the two z×64×5 tensors respectively by using 64 convolution kernels with the size of 3×1, and outputting to obtain two z×64×3 tensors;

step 37, performing pooling operation on the two output z64×3 tensors by using a third maximum pooling layer and a third average pooling layer respectively, obtaining and adding the two z64×1 tensors, and outputting one z64×1 tensor; wherein the third maximum pooling layer and the third average pooling layer are each 1 x 3 in size;

step 38, inputting the output tensor of z×64×1 into the fully connected layer, outputting the tensor with z×6 as the output result, inputting the output tensor into the softmax function layer, and mapping the tensor value output into the (0, 1) interval; wherein the number of neurons in the fully connected layer is 6.

Further, the target components comprise cotton, terylene, wool, viscose fiber, spandex and nylon, textile spectrum data composed of the six components are selected from near infrared spectrum sample data, and linear normalization processing is carried out on the data by using a linear function.

Further, evaluating the classifier using the test set, the calculating the precision index includes:

the selected evaluation indexes comprise a determination coefficient R-square, an average absolute error MAE and a root mean square error RMSE, and the calculation expressions are respectively as follows:

，

wherein,for the real content of textile fibers->For model predictive content of textile fibres, +.>Is the average value of the fiber content of the textile, and n is the number of samples.

The beneficial effects are that: compared with the prior art, the invention has the remarkable advantages that:

1. high efficiency and accuracy: according to the invention, by adopting a multilayer one-dimensional CNN depth network and combining with the pretreatment of textile spectrum data, the textile spectrum data formed by target components can be effectively selected from near infrared spectrum sample data, thereby being beneficial to improving the accuracy and efficiency of quantitative characterization;

2. data enhancement: according to the invention, the training set data and the random noise samples are utilized to train the generator by using the generated countermeasure network GAN model, so that the pseudo sample data can be generated, the number of original training sets is expanded, and the diversity and the richness of the samples for training are increased;

3. a multi-pooling fusion one-dimensional convolution kernel neural network: the invention constructs a multi-pooling fusion one-dimensional convolution kernel neural network as a classifier, and the network combines the characteristics of various pooling modes and convolution kernels, so that the characteristics in the textile spectrum data can be better extracted, and the quantitative characterization of textile components can be realized;

4. the manual intervention is reduced: the whole process is automatically processed based on the deep learning model, so that the dependence on manual experts is reduced, the time and the cost are saved, and the reproducibility and the stability of the method are improved.

Drawings

FIG. 1 is a flow chart of a method for quantitatively characterizing textile components based on a multi-layer one-dimensional CNN depth network in an embodiment;

in the embodiment of fig. 2, the GAN model and the multi-layer one-dimensional CNN network are structured schematically;

FIG. 3 is a schematic diagram of the structure of the maximum pooling layer and the average pooling layer in the embodiment;

FIG. 4 is a comparison of the decision coefficient errors of the embodiment and the CNN model that is not optimized using the GAN network;

FIG. 5 is a comparison of the mean absolute error of an embodiment with a CNN model that is not optimized using a GAN network;

FIG. 6 is a root mean square error comparison of an embodiment with a CNN model that is not optimized using a GAN network;

FIG. 7 is a graph showing the predicted component content of six samples in a test set according to an embodiment;

FIG. 8 is the true component content of the corresponding sample in the test set of the example.

Detailed Description

In order to make the objects, technical solutions and advantages of the present application more apparent, the present application will be further described in detail with reference to the accompanying drawings and examples.

Fig. 1 is a flowchart of a method for quantitatively characterizing textile components based on a multi-layer one-dimensional CNN depth network according to the embodiment, which specifically includes the following steps:

and 1, selecting textile spectrum data formed by target components from near infrared spectrum sample data, preprocessing the textile spectrum data, and dividing the preprocessed textile spectrum data into a training set and a testing set.

In one example, textile spectrum data composed of six components are selected from near infrared spectrum sample data aiming at cotton C, terylene T, wool W, viscose fiber V, spandex P and nylon N which need to be identified as target components, linear normalization processing is carried out on the data by utilizing a linear function, and data division is carried out on 1400 sample data after pretreatment, wherein 700 samples are used as training sets, and 700 samples are used as test sets.

Step 2, constructing a GAN model, and training the GAN model by using training set data and random noise samples; wherein the GAN model includes a generator and a arbiter.

In one example, a bifurcated arbiter is constructed for discriminating whether the input data is real data or spurious data generated by the generator. Defining the shape of input spectrum data as 61, wherein the discriminator comprises 3 fully connected layers, the output size of the 1 st fully connected layer is 128, and the ReLU is used as an activation function; the output size of the 2 nd fully connected layer is 64, again using the ReLU activation function; the output size of the last 1 fully connected layer is 1, a sigmoid activation function is used, and the output result represents the probability that the input data is real spectrum data.

In one example, a generator is constructed for generating dummy data, the generator comprising 3 fully connected layers, the 1 st fully connected layer having an input size of 61 and an output size of 128, the activation function using a ReLU; the output size of the 2 nd fully connected layer is 256, again using the ReLU activation function; the output size of the last 1 full-connection layer is required to be the same as the types of the components of the textile fabric, and is set to be 6, and the output result is between 0 and 1 by using a sigmoid activation function.

The generator and the discriminant are combined together to construct a GAN model for joint training, and the input parameters are the generator and the discriminant models defined previously.

In one example, training the GAN model using training set data and random noise samples includes the steps of:

step 21, defining a loss function and an optimizer; the loss function uses two kinds of cross entropy loss functions, the optimizer uses an Adam optimizer, and the generator and the discriminator are respectively provided with the optimizers;

step 22, training the discriminator:

step 221, for the input real data sample, calculating the output and loss of the real sample by the discriminator;

step 222, the generator generates the same number of dummy data samples as the real data samples, and calculates the output and loss of the dummy data samples by the discriminator;

step 223, adding the real sample loss and the pseudo data sample loss as the total loss of the discriminator, and carrying out back propagation and parameter updating;

training the discriminators in a mode of alternately training in the steps 221-223;

step 23, training generator:

step 231, the generator generates the same number of dummy data samples as the real data samples again, and calculates the output and loss of the dummy data samples by the discriminator;

step 232, the goal of the generator is to make the arbiter unable to distinguish between real data and dummy data, so the dummy data loss is set as the loss of the real data, and then the back propagation and parameter update are performed;

training of the discriminant model is achieved by means of alternating training of steps 231-232.

The GAN model takes the generator and the discriminator as opponents to conduct countermeasure training, and the purpose of generating vivid data is achieved by competing the manner of the countermeasure training between the generator and the discriminator. The generator is responsible for generating false data samples and the arbiter is responsible for distinguishing between real data and data samples generated by the generator. Along with the progress of training, the generator and the discriminator are continuously game with each other, the progress of the other side is promoted, and finally, dynamic balance is achieved, and the generator can generate a vivid data sample, so that the discriminator cannot accurately distinguish real data from false data.

Step 3, constructing a multi-pooling fusion one-dimensional convolution kernel neural network, generating pseudo sample data by using a trained generator, training the multi-pooling fusion one-dimensional convolution kernel neural network by using the pseudo sample data, and taking the trained multi-pooling fusion one-dimensional convolution kernel neural network as a classifier; wherein the output of the classifier is the content of the target component.

As shown in fig. 2, constructing the multi-pooling fusion one-dimensional convolution kernel neural network includes:

the input layer is respectively connected with the input end of a first convolution kernel, the output end of the first convolution kernel is sequentially connected with the first maximum pooling layer, the second convolution kernel, the second maximum pooling layer, the third convolution kernel and the third maximum pooling layer, the output end of the first convolution kernel is sequentially connected with the first average pooling layer, the fourth convolution kernel, the second average pooling layer, the fifth convolution kernel and the third average pooling layer, the output end of the third maximum pooling layer and the output end of the third average pooling layer are added, the input end of the full connection layer is connected after the addition, the output end of the full connection layer is connected with the activation function layer, and numerical values representing the content of target components in a sample are output through the activation function layer.

In the multi-pooling fusion one-dimensional convolution kernel neural network, the convolution kernel is used for extracting local features of spectrum data, the pooling layer is used for reducing dimensionality and extracting the most obvious features, the pooling layer comprises a maximum pooling layer and an average pooling layer, and the full connection layer is used for final classification. Fig. 3 is a schematic diagram of the structure of the maximum and average pooling layers.

Specifically, training the multi-pooling fusion one-dimensional convolution kernel neural network by using the pseudo-sample data comprises the following steps:

step 31, setting the number of samples used in each training as z, and changing the shape of the spectrum data of the pseudo textile fabric generated by the generator from z multiplied by 61 to z multiplied by 1 multiplied by 61; where z is an integer, e.g., 256;

step 32, performing feature extraction by using 16 first convolution kernels with the size of 3×1 and the original z× 1×61 tensors, and outputting to obtain z× 16×59 tensors;

step 33, performing pooling operation on the output zx16x59 tensors by using a first maximum pooling layer and a first average pooling layer respectively, and outputting to obtain two zx16x19 tensors; wherein the first maximum pooling layer and the first average pooling layer are each 1 x 3 in size;

step 34, performing feature extraction on the two z×16×19 tensors respectively by using 64 convolution kernels with the size of 3×1, and outputting to obtain two z×64×17 tensors;

step 35, performing pooling operation on the two output z×64×17 tensors by using a second maximum pooling layer and a second average pooling layer respectively, and outputting to obtain two z×64×5 tensors; wherein the second maximum pooling layer and the second average pooling layer are each 1 x 3 in size;

step 36, performing feature extraction on the two z×64×5 tensors respectively by using 64 convolution kernels with the size of 3×1, and outputting to obtain two z×64×3 tensors;

step 37, performing pooling operation on the two output z64×3 tensors by using a third maximum pooling layer and a third average pooling layer respectively, obtaining and adding the two z64×1 tensors, and outputting one z64×1 tensor; wherein the third maximum pooling layer and the third average pooling layer are each 1 x 3 in size;

step 38, inputting the output tensor of z×64×1 into the fully connected layer, outputting the tensor with z×6 as the output result, inputting the output tensor into the softmax function layer, and mapping the tensor value output into the (0, 1) interval; each number represents the percentage of six components contained in the sample and is calculated as:

，

wherein,represents the i-th value in tensor, < ->Representing the first in tensorsjA value.

And 4, evaluating the classifier by using the test set, and calculating the precision index.

In one example, evaluating the classifier using the test set, calculating the precision index includes:

the selected evaluation indexes comprise a determination coefficient R-square, an average absolute error MAE and a root mean square error RMSE, and the calculation expressions are respectively as follows:

,

wherein,for the real content of textile fibers->For model predictive content of textile fibres, +.>Is the average value of the fiber content of the textile, and n is the number of samples.

In one example, the trained classifier is evaluated using a test set, the accuracy index is calculated, fig. 4, fig. 5 and fig. 6 are the accuracy comparison of the method with a one-dimensional CNN model using only one pooling mode, and fig. 7 and fig. 8 are the predicted component content and the real component content of six kinds of samples in a part of the test set. In fig. 4-6, the inventive decision coefficients, the mean absolute error and the root mean square error in the test data are respectively [2.90,0.94,6.34], the decision coefficients, the mean absolute error and the root mean square error of the network using only the maximum pooling are respectively [4.47,0.92,7.60], and the decision coefficients, the mean absolute error and the root mean square error of the network using only the average pooling are respectively [4.93,0.88,9.16]. The specific calculation steps are as follows:

step 401: the test set is input into a classifier, and then a decision coefficient (R-Squared) of the predicted component content and the true component content is calculated, wherein,for the real content of textile fibers->For model predictive content of textile fibres, +.>Is the average value of the fiber content of the textile, and n is the number of samples. The closer the R-Squared value is to 1, the better the fitting effect of the model is, and the calculation expression is:

，

step 402, after inputting the test set into the classifier, calculating the Mean Absolute Error (MAE) between the predicted component content and the true component content, where the calculation expression is:

，

step 403, after inputting the test set into the classifier, calculating a Root Mean Square Error (RMSE) of the predicted component content and the true component content, wherein the RMSE amplifies a sample with a larger error in the model predicted fiber content compared with the MAE, so that the smaller the value of the RMSE, the more meaningful, and the calculation expression is:

and 5, quantitatively characterizing the components of the textile by using a classifier.

And inputting the near infrared spectrum data of the textile after pretreatment (such as spectrum smoothing, normalization and the like) into a classifier to obtain the percentages of six target components in the textile.

Claims (6)

1. The quantitative characterization method of the textile components based on the multilayer one-dimensional CNN depth network is characterized by comprising the following steps:

selecting textile spectrum data composed of target components from near infrared spectrum sample data, preprocessing the textile spectrum data, and dividing the preprocessed textile spectrum data into a training set and a testing set;

constructing a GAN model, and training the GAN model by using training set data and random noise samples; wherein the GAN model includes a generator and a arbiter;

constructing a multi-pooling fusion one-dimensional convolution kernel neural network, generating pseudo sample data by using a trained generator, training the multi-pooling fusion one-dimensional convolution kernel neural network by using the pseudo sample data, and taking the trained multi-pooling fusion one-dimensional convolution kernel neural network as a classifier; wherein the output of the classifier is the content of the target component;

evaluating the classifier by using the test set, and calculating the precision index;

quantitative characterization of the composition of the textile is performed using a classifier.

2. The method for quantitatively characterizing textile components based on a multilayer one-dimensional CNN depth network according to claim 1, wherein constructing a multi-pooling fusion one-dimensional convolutional kernel neural network comprises:

the input layer is respectively connected with the input end of a first convolution kernel, the output end of the first convolution kernel is sequentially connected with the first maximum pooling layer, the second convolution kernel, the second maximum pooling layer, the third convolution kernel and the third maximum pooling layer, the output end of the first convolution kernel is sequentially connected with the first average pooling layer, the fourth convolution kernel, the second average pooling layer, the fifth convolution kernel and the third average pooling layer, the output end of the third maximum pooling layer and the output end of the third average pooling layer are added, the input end of the full connection layer is connected after the addition, the output end of the full connection layer is connected with the activation function layer, and numerical values representing the content of target components in a sample are output through the activation function layer.

3. The method for quantitatively characterizing textile components based on a multi-layer one-dimensional CNN depth network according to claim 2, wherein training the GAN model using training set data and random noise samples comprises:

step 21, defining a loss function and an optimizer; the loss function uses two kinds of cross entropy loss functions, the optimizer uses an Adam optimizer, and the generator and the discriminator are respectively provided with the optimizers;

step 22, training the discriminator:

step 221, for the input real data sample, calculating the output and loss of the real sample by the discriminator;

step 222, the generator generates the same number of dummy data samples as the real data samples, and calculates the output and loss of the dummy data samples by the discriminator;

step 223, adding the real sample loss and the pseudo data sample loss as the total loss of the discriminator, and carrying out back propagation and parameter updating;

training the discriminators in a mode of alternately training in the steps 221-223;

step 23, training generator:

step 231, the generator generates the same number of dummy data samples as the real data samples again, and calculates the output and loss of the dummy data samples by the discriminator;

step 232, setting the pseudo data loss as the loss of the real data, and then carrying out back propagation and parameter updating;

training of the discriminant model is achieved by means of alternating training of steps 231-232.

4. A method for quantitatively characterizing textile components based on a multi-layer one-dimensional CNN depth network according to claim 3, wherein training a multi-pooling fusion one-dimensional convolutional nuclear neural network using pseudo-sample data comprises the steps of:

step 31, setting the number of samples used in each training as z, and changing the shape of the spectrum data of the pseudo textile fabric generated by the generator from z multiplied by 61 to z multiplied by 1 multiplied by 61; wherein z is an integer;

step 32, performing feature extraction by using 16 first convolution kernels with the size of 3×1 and the original z× 1×61 tensors, and outputting to obtain z× 16×59 tensors;

step 33, performing pooling operation on the output zx16x59 tensors by using a first maximum pooling layer and a first average pooling layer respectively, and outputting to obtain two zx16x19 tensors; wherein the first maximum pooling layer and the first average pooling layer are each 1 x 3 in size;

step 34, performing feature extraction on the two z×16×19 tensors respectively by using 64 convolution kernels with the size of 3×1, and outputting to obtain two z×64×17 tensors;

step 35, performing pooling operation on the two output z×64×17 tensors by using a second maximum pooling layer and a second average pooling layer respectively, and outputting to obtain two z×64×5 tensors; wherein the second maximum pooling layer and the second average pooling layer are each 1 x 3 in size;

step 36, performing feature extraction on the two z×64×5 tensors respectively by using 64 convolution kernels with the size of 3×1, and outputting to obtain two z×64×3 tensors;

step 37, performing pooling operation on the two output z64×3 tensors by using a third maximum pooling layer and a third average pooling layer respectively, obtaining and adding the two z64×1 tensors, and outputting one z64×1 tensor; wherein the third maximum pooling layer and the third average pooling layer are each 1 x 3 in size;

step 38, inputting the output tensor of z×64×1 into the fully connected layer, outputting the tensor with z×6 as the output result, inputting the output tensor into the softmax function layer, and mapping the tensor value output into the (0, 1) interval; wherein the number of neurons in the fully connected layer is 6.

5. The quantitative characterization method of textile components based on the multilayer one-dimensional CNN depth network according to claim 1, wherein the target components comprise cotton, terylene, wool, viscose fiber, spandex and nylon, the textile spectrum data composed of the six components are selected from the near infrared spectrum sample data, and the data are subjected to linear normalization processing by using a linear function.

6. The method for quantitatively characterizing textile components based on a multi-layer one-dimensional CNN depth network according to claim 1, wherein evaluating the classifier using a test set, calculating the precision index comprises:

the selected evaluation indexes comprise a determination coefficient R-square, an average absolute error MAE and a root mean square error RMSE, and the calculation expressions are respectively as follows:

，

wherein,for the real content of textile fibers->For model predictive content of textile fibres, +.>Is the average value of the fiber content of the textile, and n is the number of samples.