Application of artificial intelligence in fabric performance prediction

In recent years, more and more researchers have begun to adopt data-driven prediction methods to establish prediction models based on the static attributes of woven fabrics (e.g., fiber type, yarn specification, fabric structure, etc.), and have achieved a certain degree of prediction accuracy.

Ahirwar M et al. [17] developed a machine learning-based neural network approach to predict the performance of fabric using fabric parameters as input and warp and weft tear strength as output. HOSSAIN MM et al. [18] used a correlation regression model to explain the effect of structural parameters on the tear and tensile strength of various base fabric designs to develop a neural network model for predicting tear and tensile strength. Ribeiro R et al. [19] successfully developed models with high prediction accuracy by applying machine learning techniques and analyzing multiple features of the textile production process. Xiao Q et al. [20] proposed an intelligent ball-starting prediction model based on the BP neural network and an optimization model based on a genetic algorithm to improve the training speed and accuracy of the ball-starting prediction. Tu Y F et al. [21] conducted a systematic review of AI-driven fabric performance and handle prediction technologies (focusing on model mechanisms, dataset diversity, and prediction accuracy). They identified research gaps and challenges in this field, providing practical references for improving AI prediction capabilities and guiding future innovations in textile technology. Sarkar J et al. [22] used Adaptive Neuro-Fuzzy Inference System (ANFIS) and Artificial Neural Network (ANN) methods to develop predictive models for textile substrate absorption properties, which can help in the scale-up of functional textiles. Doran EC et al. [23] proposed artificial neural network (ANN) and support vector machine (SVM) models to predict the quality characteristics of cotton/elastane fiber core yarns using fiber quality and spinning parameters.

Most of the existing research focuses on the prediction of finished product quality, while the real-time monitoring and prediction of the fabric experimental process itself is rarely involved. In addition, most of the existing monitoring techniques focus on data analysis under static conditions and lack a real-time response mechanism to dynamic changes in the experiment, which cannot meet the needs of the modern textile industry for efficient, accurate, and intelligent production processes.

Predictive applications of time series data

Since the data during the fabric performance experiments are all time-series data, the methods for time-series data prediction are broadly categorized into three types: statistical analysis, machine learning, and deep learning. Guo N et al. [24] created a hybrid prediction model by combining ARIMA (Autoregressive Integrated Moving Average) with SVR (Support Vector Regression) to more accurately predict electricity consumption data collected in an Internet of Things (IoT) environment. Xie Y et al. [25] proposed a hybrid model of ARIMA and triple exponential smoothing, which can accurately predict linear and nonlinear relationships in container resource loading sequences. However both ARIMA and exponential smoothing methods rely heavily on historical data, and they are not the right choice for forecasting long-term time series if there is a lot of variability in the data.

In recent years, deep learning has achieved excellent results in time series data prediction. BiLSTM is able to better capture the contextual information when dealing with sequential data: Guo Y et al. [26] proposed an MES combined load prediction method based on bi-directional long short-term memory (BiLSTM) multi-task learning and achieved good prediction results; Wu K et al. [27] proposed a hybrid prediction model based on wavelet threshold denoising (WTD), variational modal decomposition (VMD), and bi-directional long and short-term memory (BiLSTM) networks in order to reduce the short-term household load forecasting errors due to small load sizes and different residential electricity consumption behaviors, which provided more stable and accurate predictions under trend feature extraction, and improved the short-term household load forecasting accuracy. Transformer effectively captures long-term dependencies in time-series data, ensuring chronological accuracy, and its flexible model structure allows for adjustments to accommodate data of varying complexity, while the encoder-decoder architecture is particularly well suited for predicting future points in time [28]: Qu K et al. [29] applied the Transformer model in Natural Language Processing (NLP) to the field of wind power prediction, which not only can accurately extract different correlation levels between multiple wind farms but also can give accurate wind power prediction results; Reza, S. et al. [30] designed a multi-attention based transformer model for traffic flow prediction using five identical encoder and decoder layers and combined a comparative analysis between gated recurrent units and a long term memory based model with good performance in effectively predicting long term traffic flow patterns. Guo J et al. [31] proposed a hybrid method for bearing failure prediction: constructing health indicators through CEEMDAN and KPCA, extracting multi-domain features using dual-channel Transformer with CBAM, and realizing RUL probability prediction by combining the 3σ criterion and Wiener’s process, which verified the time-series modeling potential of Transformer. In recent years, temporal convolutional neural networks (TCNs) have emerged as a new approach for dealing with temporal problems, with significant advantages in weight sharing and convolutional local perception, and have achieved excellent performance in fusion prediction with other models: Lu P et al. [32] used TCN to extract the hidden temporal features in wind power data to establish the Informer wind power prediction model; Liu S et al. [33] and others proposed parallel structure TCN-LSTM wind power prediction model based on Savitzky-Golay filtering and TCN; Zhang G et al. [34] proposed a novel hybrid model based on adaptive quadratic decomposition method and robust time convolution network (RTCN) for wind speed prediction.

This paper will extend the applicability of these models to a wider range of complex prediction tasks, including dynamic correlation and trend prediction of electrical power sequences and experimental processes for fabric tear performance testing.

Overall model design

The model developed in this paper predicts the trend of electric power parameters monitored during the experimental process of fabric tearing performance, and the overall work consists of the following three parts: data preprocessing part, data division part, and BLTT-FT part. The main flow is shown in Fig 1.

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Fig 1. Main flowchart of the overall model design.

Flow of electrical parameters prediction for the experimental process of fabric tearing performance based on BLTT-FT fusion model.

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The model first receives the raw data stored by the sensors in the database and composes the complete sample data by taking the electric power parameters in the order of the moments when the experiment is performed. Then the data is preprocessed, mainly for missing values, smoothing, and data leakage. Data partitioning presents an innovative integration of the principles of discrete-time state machines and the concept of dynamically tuned rolling windows, focusing on the prediction of multi-step states occurring after a single “change- tensile -reset” state. The model is trained on the divided data, and then gradually rolls forward. Whenever the “change- tensile-reset” state is completed once, the state window will roll to the next state point, and the BLTT-FT prediction model will be updated accordingly, forming a closed loop of continuous iteration and optimization. In this way, the real-time prediction environment is simulated and the output prediction results are obtained.

BLTT-FT system network construction

In this paper, the Transformer model is used as the basis, and a temporal convolutional network (TCN) is introduced to modify it so that it is more suitable for the prediction of time-series data in this paper. The Transformer model allows for parallel computing and good access to global information, however, the ability to capture global information is weak and not ideal for direct use as a predictor. TCN captures both high-level and low-level features with stable gradients and enables the model to process time series information in parallel, improving the prediction accuracy and training efficiency of the model. The improved Transformer model can fully utilize the advantages of Transformer and TCN to better predict the sequence data, and the improved model is called the “Trans-TCN” network structure.

However, the “Trans-TCN” network structure lacks sequential information, and although its position encoding uses sine and cosine to model positions, it is not sufficient for complete modeling and suffers from a certain lack of information. Therefore, the data will be processed using a bi-directional long and short-term memory network to capture the sequential dependencies before transferring them to the “Trans-TCN” polytope self-attention point. Due to the large sample size of the dataset, this paper will use the BiLSTM network model composed of improved LSTM to speed up the data learning speed, and the improved BiLSTM neural network model is called “Bi-LSTM” network architecture. Therefore, combining it with “Trans-TCN” can improve the prediction efficiency of the model.

In summary, after the input data is processed by the positional coding layer, the sequence features are captured by the “Bi-LSTM” and then input to the “Trans-TCN”. Specifically, it is first processed by the encoder of the Transformer, then the features are further extracted by the TCN layer, and finally, the full connectivity layer and activation function are utilized for dimensionality reduction. The main structure consists of a position coding layer, a Bi-LSTM layer, a Transformer encoder layer, a TCN layer, and a fully connected layer, and the overall network structure is called “BLTT-FT” as shown in Fig 2.

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Fig 2. BLTT-FT overall network structure.

The main structure consists of a position coding layer, a Bi-LSTM layer, a Transformer encoder layer, a TCN layer, and a fully connected layer.

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Trans-TCN network construction

This section describes in detail the improvement of TCN on the Transformer model, and the improved structure is called the “Trans-TCN” network structure. Although the Transformer model was originally designed for machine translation, it can still be applied to time series prediction by exploiting its architectural potential. Therefore, its encoder part is used as the basic model. The “Trans-TCN” network structure is shown in Fig 3.

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Fig 3. Trans-TCN network structure.

The left half of the Trans-TCN network structure is the Transformer encoder, and the right half is the TCN and fully connected layer.

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(1) The Transformer encoder consists of multiple encoder layers, each consisting of two sub-layer blocks. The first sublayer block includes a multi-head attention layer and a normalization layer connection; the second sublayer block includes a feed-forward layer and a normalization layer connection. The core part of the coding layer is the multi-head attention mechanism, and this part is the key part of the Trans-TCN network structure to realize accurate prediction.

A multiple attention strength mechanism consists of multiple heads with self-attention. The self-attention process in the multi-head attention mechanism can be described as a process solved by a query vector and a set of key-value vector matrices. Where the query vector (Q), key vector (K), and weight vector (V) are transformed from the previous set of outputs.In the actual operation, the model simultaneously computes the attention functions on a set of query vectors packs them into a matrix Q, and packs the key vectors and value vectors into matrices K and V. The output of the query vector is actually determined by the hidden vectors encoded in the previous layer, and the matrices K and V are assigned the same value as Q in the self-concern. The result of the output calculation is the weighted value, which is derived from the compatibility operation between the query vector and the key vector. is the input to the multi-head self-attentive module. The key vectors, weight vectors, and query vectors are calculated as shown in Eq (1):

(1)

where is the trainable projection matrix. The derived results are utilized and the Billet dot product attention calculation is performed as shown in Eq (2):

(2)

In order to jointly focus on the information from different representation subspaces at different locations, further optimization is required by using H parallel attention computations, in the case of the multi-head attention mechanism computation process shown in Eq (3):

(3)

The functional realization of the coding layer also passes through the feedforward layer The feedforward network consists of two linear transformations connected in the middle by a ReLU activation function, which is applied separately and with the same status for each time step. The linear transformation formulas are shown in Eq (4):

(4)

where W^T is the weight matrix and b is the bias vector.

(2) The TCN consists of multiple layers of residual blocks (RBs), and each RB is mainly composed of two layers: the dilated causal convolution (DCC), the weight initialization layer, and the ReLU. As shown in Fig 4A, the output of the Transformer encoder module is used as the input of the first layer of the TCN RB. Fig 4B shows the structure of DCC.

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Fig 4. TCN network structure.

A:Structure of TCN residual block. B:Structure of TCN expansion causal convolution.

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Among them, the weight initialization layer and the Droupt layer are mainly used to suppress the network noise and optimize the network training effect, and then in order to ensure that the input and output dimensions are the same, a 1x1 convolution module is introduced, and finally the deep TCN can be constructed by continuously stacking the RBs. The combination of DCC and RB network structure can effectively improve the robustness and feature learning ability of TCN models.

Here is a brief introduction to DCC. Recurrent neural networks rely on historical data to process information and are unable to achieve massively parallel computation like CNNs, TCNs are an improved CNN that compensates for the shortcomings of traditional CNNs in dealing with long-term data dependency by introducing DCC, which ensures that the model utilizes only historical data to make predictions and thus avoids interference from future data. The input sequence undergoes DCC to obtain the output sequence , and d is the number of expansions. Together, these elements improve the generalization ability of the model, accelerate the training process, and effectively prevent the overfitting problem, and the calculation of DCC is shown in Eq (5):

(5)

where ⋅ is the convolutional computation, d is the number of expansions, s is the neuron, k is the convolutional kernel, f(i) is the ith data in the convolutional kernel,and denotes the result of convolving the past data.

In summary, the parts of TCN that improve on the Transformer model are shown in the following:

1. Deleted “Input Embedding”, which is a module for vectorization of language and text, is required for machine language translation and does not need to be vectorized for power.

2. Replace the transformer decoder with a TCN layer, a fully connected layer (FC-Linear), and an activation function Tanh (activation function).

3. The other inputs to the decoder are removed, leaving the output of the encoder as the only input to the decoder.

Bi-LSTM network construction

The BiLSTM neural network model is constituted by two independent LSTM networks, where the sequence information is fed into the network separately by means of forward and reverse order, making forward and backward information available to each LSTM unit.

(1) Recurrent Neural Networks (RNN) are deep neural networks used to predict time series, however, RNNs suffer from the problem of gradient vanishing, which is solved by the emergence of LSTM. The LSTM has three special gates, i.e., the forgetting gate f_t, the input gate i_t, and the output gate o_t, as well as the hidden unit , which is used to regulate the information flow in the network. where C_t−1 is the output of the previously hidden cell, C_t is the output of this hidden cell, h_t−1 is the output of the previous cell, h_t is the output of this cell, x_t is the input at this moment, σ is the sigmoid function, and tanh is the hyperbolic tangent function.

Due to the large sample size of the dataset, the traditional LSTM, although performing well, leads to a large number of parameters that need to be learned for each gate, which results in a long-running time for the LSTM, so an improved LSTM network is proposed to speed up the data learning. The structure of the LSTM network is shown in Fig 5, and the structure of the improved LSTM network is shown in Fig 6.

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Fig 5. LSTM network structure.

The LSTM has three special gates.

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Fig 6. Improved LSTM network structure.

The improved LSTM structure retains only 1 gate.

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The improved LSTM structure retains only 1 gate, which can effectively reduce the number of parameters while extracting the hidden timing information to ensure the accuracy of the model. The specific formula is shown in Eq (6):

(6)

where: X_t is the input; H_t−1 is the upper moment output; , , W_xg, W_hg and P_cg represent the corresponding weight matrices, respectively; and b_g represent the bias vectors; and g_t is the output gate.

(2) The BiLSTM model is constituted by the above improved LSTM, which is a network in which the output vectors (i.e., extracted feature vectors) of the forward LSTM and the backward LSTM are spliced to form a vector as the final output. The final output vector is calculated as shown in Eq (7):

(7)

where the output of the forward LSTM is and the output of the backward LSTM is .

BiLSTM is modeled so that the feature data obtained at moment t has information from the previous and subsequent moments, which results in better feature extraction efficiency and performance compared to a single LSTM structure. The model structure is shown in Fig 7, where M_t is the weight matrix and Z_t is the output vector. The BiLSTM model using the improved LSTM composition is called “Bi-LSTM” in this paper.

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Fig 7. Bi-LSTM network structure.

Bi-LSTM network structure composed of improved LSTMs.

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Dataset construction

Experimental sampling for fabric tearing performance testing.

This paper is based on the international standard “ISO 139372-2000 Textile fabrics-Tear properties-Part 2: Determination of tear strength of trouser specimens (single seam)” to carry out the test experiment of tear properties of trouser specimens. For each laboratory fabric samples should be cut 2 groups of specimens, a group of radial and a group of weft, specimens for the rectangular selection of samples, each group of samples should be 5 pieces of specimens, and every two pieces of specimens can’ t contain the same length or width of the direction of the yarn, should be avoided at the crease, the edge of the fabric and the fabric on the unrepresentative area, can’t be taken in the distance from the edge of the fabric within 150mm sample from the lab samples to be cut from the sample is shown in Fig 8A for example. Trouser shaped specimens were (200±2) mm long and (50±1) mm wide. Each specimen should be cut from the middle of the width direction with a split of (100±1) mm long parallel to the length direction, and the end point of tearing was marked at (25±1) mm from the uncut end in the middle distance of the specimen as shown in Fig 8B. The denser yarns are the warp yarns and the less dense yarns are the weft yarns, as shown in Fig 8C. The experimental principle of trouser specimen tearing performance testing is to clamp the two legs of the trouser specimen, so that the specimen notch line between the upper and lower fixtures into a straight line, to set the length of the spacing of the fabric tear tester to 100 mm, the tensile rate is set to 100 mm/min. open the instrument will be tensile force is applied in the direction of the notch, as shown in Fig 8D. All samples were cut from the middle of wrinkle-free and undamaged fabric bolts, avoiding areas within 150 mm of the fabric edges as well as defective regions such as yarn joints and stains. For samples taken from the same fabric, the warp/weft direction samples do not contain overlapping yarns to ensure the independence of each sample. After sampling, the samples were pre-treated in a constant temperature and humidity chamber (20±2 ^°c, 65±4% RH) for 24 hours to eliminate the impact of environmental factors on the physical properties of the fabrics.

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Fig 8. Sampling diagram for fabric tearing test.

A: Example of a specimen cut from a laboratory sample. B: Standardized specimen charts. C: Detail of warp and weft yarns. D: Schematic diagram of tearing.

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Data acquisition.

The fabric tearing performance test experiment adopts CRE isokinetic elongation tester to carry out the trouser specimen tearing performance test experiment. The CRE isokinetic elongation tester used was an Instron 5967 double-column bench-top tester.

For fabric tearing performance testing experiments, real-time monitoring of the power usage of the fabric tear tester, including current, voltage, and power parameters, was carried out, and one experiment was composed of five sets of radial and five sets of weft tearing experiments for each fabric. During the data perception of a single tearing experiment the CRE isokinetic elongation tester can obtain the time course of the four device states: The first is the equipment standby state, waiting for the experiment to be carried out, low-power mode; followed by the equipment sample change state, the installation of the specimen, low-power mode; followed by the equipment tensile state, subject to the different characteristics of different fabrics consume different power; and finally, the equipment reset state, the deformation of different fabrics is different, so that the device’s pneumatic jig reset consumes a larger amount of power, specifically as shown in Table 1:

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Table 1. Working status of CRE isokinetic elongation tester equipment.

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According to the working condition of the CRE isotropic elongation tester, the collection of electrical parameters needs to be carried out throughout the whole experimental process, especially the current power consumption in the electrical parameters is the largest when the equipment is working for stretching and it is mentioned in the international standard that for the isotropic elongation tester, if the strong force and elongation records are obtained through the data collection chip and software, then the frequency of data collection should be at least 8Hz. According to the Nyquist sampling theorem, to recover the original signal from the sampled signal without distortion, the sampling frequency should be greater than two times the highest frequency of the signal, so the design of power parameters should be collected at a frequency of not less than 16Hz, which can reflect the changes in the power load of the monitoring equipment in real-time. In the predictions of this paper, only the electric power is used as the prediction data because the electric power most clearly demonstrates the complete process of the entire fabric tearing performance testing experiment.

Environmental temperature and humidity will affect the physical properties of the fabric, in the high-temperature environment, the strength and toughness of the fabric will be reduced; in the humid environment, the softness and elasticity of the fabric will be reduced, and the fabric tearing performance testing requires a specific temperature and humidity conditions for testing. The international standard ISO 139-1973 Textiles-Standard atmospheres for conditioning and testing stipulates that the atmospheric temperature is 20.0^°C with a tolerance of ±2.0% for temperature and 65.0% for relative humidity with a tolerance of ±4.0% for relative humidity. The electric power data of the experimental process of different fabric material samples were collected in a temperature and humidity range that ensures that it is a suitable temperature and humidity for doing the experiments, and the predictive analysis will be performed based on each individual experimental unit in order to improve the representativeness and generalization of the dataset.

Preprocessing

Data description

In the process of fabric tearing performance testing experiments, the equipment used is the Instron 5967 double-column bench-top tester, and in the whole experiment, the working state of the equipment can be divided into four states, which are: standby state, sample change state, tensile state, and reset state, as shown in Table 1 of “Research methods”. Because the standby state has little correlation with the fabric tearing experiment, only the remaining three states are predicted in this paper.

The power visualization time series plot of the fabric tearing performance testing experiment is shown in Fig 9 below, where the shaded portion indicates the different states in the fabric tearing performance testing experiment. Fig 9A shows the changeover state, Fig 9B shows the stretching state, and Fig 9C shows the reset state.

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Fig 9. Sequence diagram of power visualization.

A:Sample change state. B:Tensile state. C:Reset state.

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On the time-series data in this paper, the principle of discrete-time state machines and the concept of dynamically adjusted rolling windows are integrated, focusing on predicting the multi-step state that occurs after a “change- tensile -reset” state. Set the “change- tensile -reset” state as a whole state, every time the “change- tensile -reset” state is completed, the state window will scroll to the next state point, and the model will be updated accordingly, forming a closed loop of continuous iteration and optimization.

Electrical power data were collected from the same fabric warp and weft tear performance testing experiments at a frequency of 20 Hz. Each prediction will focus on the results of the next “change- tensile -reset” operation. As shown in Fig 10, x₁ represents a “change- tensile -reset” operation, which generates sequence of temporal features as input to the model.

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Fig 10. Scrolling time window.

x₁ represents a “change- tensile -reset” operation, which generates sequence of temporal features as input to the model.

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Based on the power of the experimental process of tearing fabrics with three different categories of high, medium, and low elasticity, the data sets were divided into three categories, as shown in Table 2 below:

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Table 2. Three types of data sets.

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Model training and parameter setting

In this study, the experimental system is running on Windows 11 operating system with Intel(R) Core(TM) i5-8250U CPU @ 1.60GHz processor, 16.0GB of system memory, Python version 3.9 installed in the experimental environment, and Pytorch version 1.13.1.

The BLTT-FT model proposed in this paper is first trained offline. The datasets used are datasets 1, 2 and 3 described in Table 2, taking dataset 1 as an example: the whole dataset collects the electric power acquisition signals of the experimental process of testing the tearing performance of fabrics with fabric properties of high elasticity, in chronological order. There are five warp direction specimens and five weft direction specimens for one fabric, in order to increase the generalization of the experiments, there are 150, 170 and 160 types of fabrics with high, medium and low elasticity, respectively, and a total of ten experiments are done for each type of doing warp and weft, which basically includes most of the fabric fabrics and ensures the diversity of the fabric types to achieve wider applicability. The long data segment is composed of the electric power signals collected during the experimental process of 10 specimens, the medium data segment is composed of the electric power signals collected during the experimental process of the longitudinal and latitudinal specimens, respectively, and the short data segment is composed of the electric power signals collected during the experimental process of the first group of radial and the first group of latitudinal specimens. From the above, it can be seen that each dataset has been categorized into long, medium, and short data segments, and each dataset is fed in parallel to the BLTT-FT model for offline training. In the online application, when the first set of electric power data of the experimental process is obtained, every time the “change- tensile -reset” operation is completed, the state window will scroll to the next state point, and the model will be updated accordingly, and the incremental learning will be repeated, updating the database to form a continuous iteration and optimization of the closed loop. It is used to predict the next electric power data. The specific flow is shown in Fig 11.

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Fig 11. Offline training-online application flowchart.

Flowchart of BLTT-FT model for offline training and online application.

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The parameters for experimental training are as follows: epoch = 100, batch size is set to 32, the initial learning rate of Adam is set to 0.00001, the ReLU activation function is adopted, the loss function is the MSE function, and predictions are made for the ranges of 1, 4, and 9 steps respectively. The cross-validation parameters are consistent with the above, with only the data division method adjusted: the training set and test set of each fold strictly follow the hierarchical 3-fold rules, and the model parameters of each fold are initialized independently to avoid cross-fold information leakage. The parameters of the proposed model are shown in Table 3.

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Table 3. Parameter settings for the BLTT-FT model.

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In the offline training phase, the BLTT-FT model completes 100 epoch training based on Windows 10 system (Intel i5-8250U CPU, 16GB RAM) with a total time of 8 hours, and the test set loss curves are highly fitted to the training set, as shown in Fig 12, indicating that the model is not overfitted. The loss curve of BLTT-FT not only decreases considerably, but also has a shorter fitting time, and the loss curve of the test set is closer to the training set, with excellent training results.

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Fig 12. BLTT-FT’s loss curve.

The loss function curve shows the trend of the loss value of the model during the training process, which helps to determine whether the model is overfitting or underfitting in order to adjust the model structure and training strategy.

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In online application, whenever the “change - tensile - reset” operation is completed, the model realizes incremental learning by scrolling through the state window, and a single update takes about 200 ms, and the prediction error after the update is reduced by 3.2% on average compared with that before the update, which demonstrates the fast adaptability to real-time data. The performance data of the two modes are shown in Table 4.

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Table 4. Performance data in two modes.

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Indicators for model evaluation

Mean Absolute Error (MAE), Mean Square Error (MSE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE) were used as the evaluation criteria for the method, and these error evaluation metrics were calculated as shown in Eq (8):

(8)

In the above equation, is the predicted value, y_t is the actual value, is the mean value, and n is the number of samples. Generally speaking, the smaller the values of MAE, MSE, RMSE, MAPE, and the closer R² is to 1, the smaller the error between predicted and actual power is, indicating the better prediction performance of the model.

Comparative experiments

In order to verify the effectiveness of the BLTT-FT model in monitoring the power changes during the fabric tearing performance monitoring experiments, five common prediction models were selected for comparative analysis, which include LSTM model, BiLSTM model, Transformer model, TCN model, and Transformer-LSTM model for comparison of prediction performance. The parameters of each comparison model are shown in Table 5. And the power of the experimental process of tearing performance of fabrics with three different categories of high elasticity, medium elasticity, and low elasticity was collected within the range of atmospheric temperature of 20.0-22.0^°C and relative humidity of 61.0-69.0% and was divided into three types of datasets, in which the electrical power data of the experimental process was predicted for the warp and weft fabrics of the same category of fabrics. Considering that the sample data is relatively limited, the ratio of 9:1 is used to divide the training set and test set to ensure that the model can be adequately trained.

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Table 5. Different model parameter settings.

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The sequence data of each data segment in the dataset were input into the model for training, and the loss function descent curves of the training and test sets during the training of the five models were obtained as shown in Fig 13.

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Fig 13. Changes in loss curves during the fitting of the 5 models.

A: LSTM’s loss curve. B: BiLSTM’s loss curve. C: Transformer’s loss curve. D: TCN’s loss curve. E: Transformer-LSTM’s loss curve.

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As seen in Fig 13, in LSTM, BiLSTM, Transformer, and TCN models, the training set loss curves still tend to decrease slightly in the late iterations, while the loss curves of the test set slightly increasing, which may lead to overfitting phenomenon if the number of iterations increases. However, the Transformer-LSTM model’s loss curve does not have this phenomenon, and the validation set loss function decreases more than the LSTM, BiLSTM, Transformer, and TCN models, but the fitting time is relatively long. From Fig 12, it can be seen that the loss curve of BLTT-FT not only decreases more, but also has a shorter fitting time, and the test set loss curve is closer to the training set, which is a better training result.

As can be seen in Tables 6, 7, 8, in datasets 1, 2, and 3: the average RMSE for 1-step prediction is 0.0691, the average MAE is 0.0467, the average MAPE is as low as 2.31%, and the average R² was as high as 0.9865; the average RMSE for the 4-step prediction is 0.0911, the average MAE is 0.0632, the average MAPE is as low as 3.12%, and the average R² is as high as 0.9600; the average RMSE for the 9-step prediction is 0.1040, the average MAE is 0.0729, the average MAPE is as low as 3.74%, and the average R² is as high as 0.9252. In these three datasets, the proposed prediction method achieved high prediction accuracy for the prediction of electric power parameters during the experimental process of fabric tearing performance testing for different elasticity levels. As the prediction time step increases, the accuracy of the BLTT-FT based method will decrease but still maintain a high prediction accuracy. Moreover, the proposed method uses only the previous 1-step electric power data to achieve high-precision prediction for the next 9 steps. These results show that the BLTT-FT-based method has excellent performance and strong generalization ability in the prediction of electric power parameters during fabric tearing experiments with different elasticity levels.

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Table 6. Evaluation metrics for dataset 1 in different models with multi-step prediction.

https://doi.org/10.1371/journal.pone.0336501.t006

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Table 7. Evaluation metrics for dataset 2 in different models with multi-step prediction.

https://doi.org/10.1371/journal.pone.0336501.t007

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Table 8. Evaluation metrics for dataset 3 in different models with multi-step prediction.

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The multi-step prediction errors of BLTT-FT in in Tables 6, 7, 8 above are visualized as shown in Fig 14A, 14B, 14C.The smaller the values of MAE, MSE, RMSE, MAPE, and the closer the R² is to 1, the smaller the error between the predicted power and the actual power is, which indicates that the prediction performance of the model is better. It can be seen that the BLTT-FT model in this paper has excellent prediction effect in the three datasets and stable prediction effect in different datasets.

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Fig 14. Multi-step prediction error visualization plots for datasets (1–3).

A: Multi-step error visualization plot for dataset 1. B: Multi-step error visualization plot for dataset 2. C: Multi-step error visualization plot for dataset 3.

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In datasets 1, 2, and 3, the comparison of the prediction curves of the BLTT-FT based method with the actual curves are shown in Figs 15, 16, 17, demonstrating the comparison of the prediction results of different models with different prediction ranges. Figs 15A, 15B, 16A, 16B, 17A, 17B show the prediction of longitude and latitude fabrics at 1 step, Figs 15C, 15D, 16C, 16D, 17C, 17D show the prediction of longitude and latitude fabrics at 4 steps, and Figs 15E, 16E, 17E show the prediction of a whole set of fabrics at 9 steps. In these datasets, from 1 step prediction to 9 steps prediction, the error between the predicted curve and the actual curve increases as the prediction range increases, because the larger the prediction range, the greater the amount of missing information and the lower the prediction accuracy. However, the proposed BLTT-FT based method still has a high fit between the actual and predicted curves in steps 1, 4, and 9.

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Fig 15. Comparison of prediction results for different model comparisons with different prediction ranges for dataset 1.

A: Longitudinal direction at step 1. B: Latitudinal direction at step 1. C: Longitudinal direction at step 4. D: Latitudinal direction at step 4. E: Overall at step 9.

https://doi.org/10.1371/journal.pone.0336501.g015

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Fig 16. Comparison of prediction results for different model comparisons with different prediction ranges for dataset 2.

A: Longitudinal direction at step 1. B: Latitudinal direction at step 1. C: Longitudinal direction at step 4. D: Latitudinal direction at step 4. E:Overall at step 9.

https://doi.org/10.1371/journal.pone.0336501.g016

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Fig 17. Comparison of prediction results for different model comparisons with different prediction ranges for dataset 3.

A: Longitudinal direction at step 1. B: Latitudinal direction at step 1. C:Longitudinal direction at step 4. D: Latitudinal direction at step 4. E: Overall at step 9.

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Based on the above analysis, the proposed model shows excellent performance in terms of prediction accuracy and stability, especially in the long-term prediction task.

As shown by the prediction graphs and evaluation indexes with prediction ranges of 1, 4, and 9 steps, the BLTT-FT prediction model proposed in this paper is excellent, and it can realize the conception of doing only the first group of tearing experiments in fabric tearing experiments to predict the fabric tearing experiments of the following groups, simplify the experimental process, and improve the efficiency and accuracy of the experiments.

Significance test analysis

In the performance assessment of prediction models, it is difficult to determine whether the differences between different datasets are statistically significant by only comparing the numerical magnitude of the prediction error metrics. In order to scientifically assess the performance of the model on different datasets, this study analyzes the significance test of MAE, RMSE and MAPE metrics for three datasets under one-step, four-step and nine-step prediction. The prediction error metrics of different datasets under each prediction step are visualized by box-and-line diagrams to visually present the data distribution characteristics. Figs 18, 19 and 20 show the distributions of MAE, RMSE and MAPE for different datasets under each prediction step, respectively.

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Fig 18. Comparison of MAE at prediction step for different datasets.

The figure shows the distribution of MAE at steps 1, 4 and 9 for the three datasets.

https://doi.org/10.1371/journal.pone.0336501.g018

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Fig 19. Comparison of RMSE at prediction step for different datasets.

The figure shows the distribution of RMSE at steps 1, 4 and 9 for the three datasets.

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Fig 20. Comparison of MAPE at prediction step for different datasets.

The figure shows the distribution of MAPE at steps 1, 4 and 9 for the three datasets.

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From Fig 18, it can be seen that the median MAE of dataset 2 is relatively low in one-step prediction; in four-step prediction, dataset 2 still shows a low median MAE; and in nine-step prediction, the median MAE of dataset 2 is also at a low level. This indicates that the prediction error of dataset 2 is relatively small and the prediction result is more accurate in terms of MAE. At the same time, the degree of data dispersion (box height and whisker length) varies among datasets at different prediction steps, reflecting the differences in the stability of prediction errors. For example, dataset 3 has a larger box height at nine prediction steps, which indicates that it has a high degree of data dispersion and poorer stability of prediction error.

Observing Fig 19, the median RMSE of dataset 3 is the lowest in one-step prediction, and the median RMSE of dataset 3 is relatively low in four-step prediction. In nine-step prediction, the median RMSEs of dataset 1, dataset 2, and dataset 3 are relatively close to each other, but there are high outliers in dataset 2 and low outliers in dataset 3. This indicates that dataset 3 has some advantages in RMSE indicators, especially in one-step prediction, and the prediction error is relatively small, but in nine-step prediction, the performance difference of each dataset is not obvious and there are outliers.

As shown in Fig 20, the median MAPE of dataset 2 is mostly the lowest under each prediction step. For one-step prediction, the median MAPE of dataset 2 is significantly lower than that of other datasets; for four- and nine-step prediction, dataset 2 also maintains a low median MAPE. This indicates that the prediction error of dataset 2 is relatively small under the MAPE indicator, and the model’s prediction accuracy of the data is better in this indicator dimension.

One-way analysis of variance (ANOVA) was used to test the significance of the MAE, RMSE and MAPE indicators for different datasets at each prediction step, and the test results are summarized in Table 9.

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Table 9. Display of significance test results.

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The ANOVA results show that there are significant differences (p-value less than 0.05) between different datasets at each prediction step (1, 4, and 9 steps) under the three indicators of MAE, RMSE, and MAPE. This indicates that statistically speaking, the prediction errors of different datasets at each prediction step are not caused by random factors, but there are real and significant differences, and the F-value reflects the ratio of the between-group variance to the within-group variance, the larger the F-value is, the larger the degree of difference between the different datasets is compared with the degree of difference within the datasets, which further supports the conclusion that the datasets have significant differences in the corresponding indexes and the prediction steps. The

A one-way ANOVA was conducted to test the MAE, RMSE and MAPE indicators of different samples under each prediction step, and the results showed that there were extremely significant differences among different samples under all indicators and prediction steps.

The significance of MAE, RMSE and MAPE indicators of the three datasets under 1, 4 and 9 steps of prediction is tested by ANOVA, and the results show that there are extremely significant differences in all indicators and prediction steps, indicating that the differences between different datasets are not random. From the box plot visualization results, the corresponding dataset of this algorithm has outstanding performance in the error indicators, such as the MAE value is significantly lower than other datasets under most prediction steps. Combined with the significant results of ANOVA, it strongly proves that the present algorithm is significantly different from other methods in terms of prediction accuracy, and more superior in terms of statistical significance. At the same time, the information of box location and degree of dispersion of the corresponding dataset boxes of this algorithm in the box-line diagram further aids in arguing its superiority in prediction accuracy and stability from the perspective of intuitive error distribution, which provides a solid data and statistical basis for the validity and reliability of this algorithm in practical applications.