Kevlar cable section creep prediction method and system based on physical informed neural network

Abstract

The invention discloses a Kevlar cable section creep prediction method and system based on a physical informed neural network, and belongs to the technical field of material performance prediction. The method comprises the following steps: acquiring creep experiment data of a Kevlar material at different constant temperatures and tensions, constructing a data set, and carrying out preprocessing and division; constructing a neural network taking temperature, tension and time as input and creep displacement or strain as output; the creep time, tension and temperature dependence are converted into mathematical constraints, the mathematical constraints are embedded into a loss function of a neural network, and a physical informed neural network is formed; and training the network by using the training set, adjusting and optimizing the verification set, and finally evaluating the performance of the model by using the test set. According to the method, the contradiction between data dependence and physical consistency of a traditional creep prediction method is solved, and high-precision creep behavior prediction conforming to the physical law can be realized under the condition of a small amount of experimental data.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of material performance prediction, and particularly relates to a Kevlar cable segment creep prediction method and system based on a physics-informed neural network. BACKGROUND

[0002] Kevlar, as a kind of high-performance organic fiber, is widely used in key fields such as bulletproof, aerospace, and marine engineering due to its excellent strength, modulus, and environmental resistance. In actual service, Kevlar products (such as cables) are subjected to constant loads for a long time, and their creep behavior, i.e., the slow deformation of materials under stress over time, directly affects the long-term safety and service life of the structure. Therefore, accurately predicting the creep curve of Kevlar materials is of great significance to engineering design and life assessment.

[0003] Traditional creep performance evaluation mainly relies on long-term physical experiments, which are time-consuming, costly, and difficult to implement under extreme conditions. To improve efficiency, researchers have developed empirical formulas, constitutive models, and traditional machine learning methods for prediction. However, these methods have obvious limitations: pure empirical models lack physical basis and have poor extrapolation ability; and data-driven machine learning methods require a large amount of labeled data and cannot guarantee that the prediction results meet the basic physical laws of material mechanics.

[0004] In recent years, physics-informed neural networks (PINN) have emerged as a new modeling framework that combines data and physical mechanisms. By embedding physical equation constraints in the loss function, PINN can ensure the physical consistency of predictions under limited data conditions, significantly improving the model's generalization ability and interpretability. However, there is still no mature research on combining PINN with material creep physical constraints for predicting the creep behavior of high-performance fiber materials such as Kevlar, especially under complex service conditions.

[0005] Therefore, there is an urgent need for a prediction method that can overcome the above-mentioned defects, reduce the dependence on a large amount of experimental data, and ensure that the prediction results are both accurate and physically consistent, thereby achieving efficient and reliable prediction of Kevlar cable segment creep behavior. SUMMARY

[0006] The purpose of the embodiments of the present application is to provide a Kevlar cable segment creep prediction method and system based on a physics-informed neural network. The purpose is to solve the problem of inaccurate prediction of Kevlar cable creep behavior due to the neglect of the coupling effect of time-varying temperature and dynamic tension, thereby failing to achieve long-term on-orbit shape accuracy prediction of antennas.

[0007] To achieve the above-mentioned purpose, the following technical solutions are adopted in the present application: In a first aspect, a Kevlar segment creep curve prediction method based on a physically-aware neural network is provided, comprising the following steps: Step S1: Obtain creep experimental data of Kevlar material under different constant temperatures and tensions, and construct a data set containing time, temperature, tension, and creep displacement or strain; Step S2: Regularize the data set and divide it into a training set, a validation set, and a test set; Step S3: Construct a neural network with an input layer including temperature, tension, and time, an output layer of creep displacement or strain, and a multi-layer fully connected structure hidden layer, and set an activation function and a loss function; Step S4: Convert the physical characteristics of creep into mathematical constraints and embed them into the loss function of the neural network to form a physically-aware neural network; Step S5: Train the physically-aware neural network using the training set, adjust the hyperparameters through the validation set, and finally evaluate the model generalization ability through the test set.

[0008] In a possible implementation, in step S1, the creep experimental data is obtained by taking points in the following manner: high-density points are taken in the first stage of creep, and low-density points are taken in the second stage of creep.

[0009] In a possible implementation, in step S2, the min-max normalization method is used to regularize the data, and the normalization formula is: , where x is the original data, and are the minimum and maximum values of the feature, respectively.

[0010] In a possible implementation, in step S3, the activation function includes a ReLU function or a Tanh function, and the loss function includes a mean square error or a mean absolute error.

[0011] In a possible implementation, in step S4, the physical characteristics of creep include time dependence, tension dependence, and temperature dependence, and their mathematical constraints are represented as: , where y is the creep displacement, t is the creep time, F is the tension, and T is the temperature.

[0012] In a possible implementation, in step S4, the specific way to embed the above physical constraints into the neural network is: , where Represents the physical loss value. , , These represent creep loss values ​​caused by time, tension, and temperature, respectively. , , Each represents its respective weighting coefficient.

[0013] Secondly, a Kevlar segment creep curve prediction system based on a physically aware neural network is provided, including: The data acquisition module is used to acquire creep experimental data of Kevlar materials under different constant temperatures and tensions; The preprocessing module is used to regularize the data and partition the dataset; The neural network building block is used to build fully connected neural networks that include input layers, hidden layers, and output layers. The physical constraint module is used to transform the physical characteristics of creep into mathematical constraints and embed them into the loss function; The training and prediction module is used to train the physical-informed neural network and output creep prediction results.

[0014] In one possible implementation, the data acquisition module supports a differentiated sampling strategy at different stages of the creep curve.

[0015] In one possible implementation, the physical loss weight coefficient in the physical constraint module is adjusted based on the Pearson correlation coefficient.

[0016] One possible implementation also includes a visualization output module to display the creep prediction curve, training process, and generalization ability evaluation results.

[0017] Compared with the prior art, this application has the following beneficial effects: This application presents a method for predicting Kevlar segment creep based on a Physically Informed Neural Network (PINN). By transforming the physical characteristics of Kevlar creep into mathematical constraints and embedding them into the neural network, it significantly reduces the dependence on experimental data and is perfectly suited for small-sample scenarios. Traditional pure data-driven models require massive amounts of creep test data to ensure accuracy, but Kevlar creep experiments are time-consuming, require long-term equipment usage, and are costly, making it extremely difficult to obtain a large number of samples. This method leverages the characteristics of the Physically Informed Neural Network (PINN) to guide model training with physical laws as hard constraints. It does not rely on large-scale datasets and can achieve high-precision predictions with only a small amount of experimental data, significantly reducing the time and economic costs of experimentation and solving the core pain point of difficult data acquisition in traditional methods.

[0018] In one possible implementation, the physical consistency of the prediction results is effectively guaranteed, enhancing the reliability of engineering applications. Traditional purely empirical models lack rigorous physical constraints and have poor extrapolation; purely data-driven models may output results that violate the laws of material mechanics due to data noise or sample bias. This method, by embedding time, tension, and temperature dependence constraints of creep into the loss function, forces the model training process to follow objective physical laws, ensuring that the final prediction results are not only numerically accurate but also conform to the intrinsic mechanism of Kevlar material creep, avoiding unreasonable predictions and providing a reliable basis for structural safety assessment and life prediction.

[0019] One possible implementation combines strong interpretability and high generalization, with an applicability far exceeding traditional prediction schemes. Traditional machine learning models struggle to explain the physical meaning of prediction results, while the physical constraints of this method directly correspond to the intrinsic mechanism of creep, clearly revealing the influence logic of temperature, tension, and time on creep behavior, thus solving an industry challenge. Furthermore, this method is not limited to Kevlar materials and does not rely on large amounts of material-specific data. It only requires adjusting the physical constraint parameters according to the creep characteristics of different materials to quickly adapt to various materials with typical creep features, such as metals, polymers, and composite materials. This results in stronger generalization capabilities, meeting the application needs of multiple fields such as aerospace, marine engineering, and special protection.

[0020] In one possible implementation, the prediction system uses a modular design to solidify the above methods into automated functional units. The data acquisition module acquires high-quality data according to a differentiated point selection strategy, the preprocessing module standardizes and rationally divides the data, the neural network construction module accurately matches model parameters, the physical constraint module embeds core physical mechanisms, and the training and prediction module completes iterative optimization of the entire process. This not only inherits the core advantages of the method but also lowers the operational threshold and reduces human error through automation, significantly improving the efficiency and convenience of creep prediction and providing efficient and reliable technical support for engineering practice. Attached Figure Description

[0021] Figure 1 This application provides an experimentally obtained Kevlar rope creep curve; Figure 2 This application provides a typical creep curve characteristic form; Figure 3 A Pearson correlation coefficient is provided for this application; Figure 4 A flowchart of a physical awareness neural network training process is provided for this application; Figure 5 A verification diagram of the generalization ability of a physical knowledge neural network provided in this application; Figure 6A parameter selection table for a neural network is provided for this application. Detailed Implementation

[0022] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0023] In the description of this application, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", "axial", "radial", "circumferential", etc., indicating the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application.

[0024] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "a plurality of" means two or more, unless otherwise explicitly defined. The specific embodiments of this application will be further described in detail below with reference to the accompanying drawings.

[0025] In this application, unless otherwise expressly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection, an electrical connection, or a communication connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0026] In this application, unless otherwise expressly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature being directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature being directly above or diagonally above the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0027] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0028] like Figure 1 and Figure 2 As shown, this application discloses a method for predicting Kevlar segment creep based on a physically-informed neural network. This method for predicting the creep curve of a Kevlar segment based on a physically-informed neural network may include the following steps: Step S1: Obtain creep experimental data of Kevlar material under different constant temperatures and tensions, and construct a dataset containing time, temperature, tension, and creep displacement or strain; Step S2: Perform regularization on the dataset and divide it into a training set, a validation set, and a test set; Step S3: Construct a neural network whose input layer includes temperature, tension, and time, whose output layer is creep displacement or strain, whose hidden layer is a multi-layer fully connected structure, and set the activation function and loss function; Step S4: Transform the physical characteristics of creep into mathematical constraints and embed them into the loss function of the neural network to form a physical-informed neural network; Step S5: Train the physical intelligence neural network using the training set, adjust the hyperparameters using the validation set, and finally evaluate the model's generalization ability using the test set.

[0029] In one possible embodiment, the specific method of step 1 is as follows: Step S1.1: Collect creep curve data of the same material under different constant temperatures and tensions through experiments. This experimental data includes parameters affecting creep, such as time, temperature, tension, creep displacement, and creep strain. Kevlar cable segments with a diameter of 1 mm and an effective length of 100 mm were used in the experiment. The experimental equipment employed a creep testing system with a temperature control range of 0-150℃ and a temperature control accuracy of ±0.5℃, along with a high-precision laser displacement sensor with a measurement accuracy of ±0.001 mm, ensuring the accuracy of data acquisition.

[0030] Appendix Figure 1 : Creep displacement-time curves of Kevlar cable segments under different tensions, with the horizontal axis representing time (unit: ×10). 4 The vertical axis represents creep displacement (unit: mm). The different colored curves in the figure correspond to five tension conditions: 5N, 10N, 20N, 40N, and 80N. The figure clearly shows the physical law that the greater the tension, the greater the creep displacement, thus verifying the validity of the experimental data.

[0031] Step S1.2: The number of points on each curve depends on the number of creep curves collected. Since the creep displacement changes rapidly in the first stage and slowly in the second stage, the point selection method is to select points densely in the first stage of creep and sparsely in the second stage. Various parameters affecting creep are used as inputs to the dataset, and creep displacement or strain is used as the output of the dataset.

[0032] The specific data collection strategy is as follows: collect one data point every 5 minutes for the first 12 hours, and collect one data point every 10 minutes for the next 12 hours. This ensures data density during critical phases while avoiding redundant data from occupying storage resources.

[0033] Appendix Figure 2 The diagram illustrates the stage division of a typical creep curve, with time on the horizontal axis and strain on the vertical axis. The curve is divided into three stages, "Primary Creep," "Secondary Creep," and "Tertiary Creep," by dashed lines, visually presenting the strain rate characteristics of each stage and providing a physical basis for the differentiated sampling strategy in this embodiment.

[0034] In one possible embodiment, the specific method of step S2 is as follows: Step S2.1: Data Regularization. Because temperature, tension, time, and creep displacement have significantly different dimensions and orders of magnitude, directly inputting them into the neural network can lead to unstable training. Therefore, data normalization or standardization is necessary. Common methods include: min-max normalization.

[0035] in, Represents the original data. and These represent the minimum and maximum values ​​of the feature, respectively. During processing, the extreme values ​​of each feature are first calculated individually, and then normalized sample by sample according to the formula to ensure that all data are mapped to the [0, 1] interval, thus eliminating dimensional interference.

[0036] Step S2.2, Dataset Partitioning. Divide the regularized dataset into training, validation, and test sets according to the following proportions: Training set: approximately 70%–80%, used for learning model parameters. Validation set: approximately 10%–15%, used for hyperparameter tuning and preventing overfitting. Test set: approximately 10%–15%, used to evaluate the model's generalization performance. Let the total number of samples be denoted as... Then the number of training set samples is The number of samples in the validation set is The number of samples in the test set is ,satisfy: .

[0037] In this embodiment, a division ratio of 700%:15%:15% is adopted to balance the reliability of model training effect and generalization ability evaluation.

[0038] In one possible embodiment, the specific method of step S3 is as follows: Step S3.1: When building a neural network, it is necessary to determine the network structure and training hyperparameters. These hyperparameters have a significant impact on the model's prediction accuracy and convergence speed. Network structure design: Input layer: Input features are temperature, tension, and time. Hidden layer: A multi-layer fully connected network is used; the number of layers and nodes needs to be optimized using a validation set. Output layer: The output is creep displacement or creep strain. After iterative optimization using a validation set, a final configuration of 3 hidden layers with 20 neurons in each layer was determined. This structure achieves the optimal balance between fitting accuracy and training efficiency.

[0039] Figure 6 This is the final configuration table for the neural network hyperparameters, including parameters such as the number of neurons, activation functions, and number of iterations; among them, the configuration of the "pur-tan-tan" activation function combination, 500 iterations, and 0.01 learning rate are the core parameters for model training in this embodiment.

[0040] Step S3.2: Activation Function Selection. Activation functions are used to introduce nonlinearity, enabling neural networks to approximate complex creeping behavior. Commonly used activation functions include: ReLU function:

[0041] Tanh function: .

[0042] An appropriate activation function can be selected based on the convergence status and convergence time.

[0043] Step S3.3: Loss Function Selection. When building a neural network, the choice of loss function directly affects the model's optimization objective and predictive performance. Different task characteristics, data distributions, and model objectives will lead to different suitable loss functions. For creep prediction tasks, common candidate loss functions include mean squared error and mean absolute error. Mean square error:

[0044] Mean absolute error: .

[0045] After selecting the hyperparameters, a neural network can be constructed. By introducing specific mathematical operations and nonlinear activation functions, it demonstrates excellent capabilities in data information extraction and complex function fitting. The core idea is to abstract latent variables that are difficult to observe directly in practical work layer by layer, thereby obtaining an approximate mapping relationship between input and output. These latent variables are often important factors affecting the target and typically correspond to the parameters to be measured. And given a... dimensional input vector A deep neural network with n hidden layers can be defined.

[0046]

[0047] In the formula, and These are the weights and biases of the network's layer 1; Input variables After the previous The iterative values ​​after layer network operations, It is considered as a non-linear function of activation function, weights, and biases.

[0048] Taking the Sigmoid activation function as an example, its definition is:

[0049] When dealing with input-output mapping problems, the key is to find a suitable... and This allows the network output to approximate the true value as closely as possible. To achieve this, a loss function needs to be constructed to measure the prediction error, and its parameters are continuously adjusted through an optimization process. Taking mean squared error (MSE) as an example, its objective function is:

[0050] in, Let L2 represent the norm. Expanding the error term of the output layer, we get:

[0051] Further deduced to the previous layer:

[0052] The corresponding gradient update formula is:

[0053] Here, ⊙ represents the Hadman product. Combining forward and backpropagation algorithms, the DNN iteratively optimizes the weight matrix and bias vector during training, gradually reducing the model's prediction error on the training data and ultimately obtaining a better parameter combination. After training, the model can be used for prediction and inference of unknown data. In this embodiment, the Adam optimizer is used to perform gradient updates, with a learning rate set to 0.01 and 500 iterations. An early stopping mechanism is also enabled (training stops if the loss on the validation set does not decrease after 6 consecutive iterations).

[0054] In one possible embodiment, the specific method of step S4 is as follows: Step S4.1, Typical physical characteristics of creep. The physical characteristics of creep behavior can be divided into three main aspects: (1) Time dependence: In the primary and secondary creep stages, the creep rate gradually decreases, while in the tertiary creep stage, the creep rate increases rapidly until fracture occurs, and the creep displacement increases continuously with time. Since the first two stages mainly affect the stability and service life of the material, they are the main focus of the analysis. Typical creep curves are as follows: Figure 2 As shown. (2) Tension dependence: The higher the applied tension, the greater the creep displacement. (3) Temperature dependence: As a key factor affecting creep behavior, the increase in temperature significantly accelerates creep displacement. The three physical properties of creep behavior are represented by the following equations:

[0055] y is the creep displacement, t is the creep time, F is the tension, and T is the temperature.

[0056] Transform the constrained optimization problem into an unconstrained optimization equation:

[0057] in, Represents the physical loss value. , , These represent creep loss values ​​caused by time, tension, and temperature, respectively. , , These represent their respective weighting coefficients, used to describe the effects of time, tension, and temperature on creep, expressed using the Pearson correlation coefficient.

[0058] like Figure 3 A heatmap of Pearson correlation coefficients between various features (time, temperature, tension, displacement), with darker colors indicating stronger correlations; The colors of the “Tension-Displacement”, “Temperature-Displacement”, and “Time-Displacement” regions in the figure range from dark to light, indicating that the correlation between tension, temperature, time, and displacement decreases from high to low.

[0059] Step S4.2: Train the neural network based on the physical loss function obtained in S4.1 and verify its generalization ability.

[0060] Figure 5 The graph shows a comparison between the model prediction curve and the experimental data. The horizontal axis represents time (in minutes), and the vertical axis represents creep displacement (in mm). The dashed line in the graph represents the model prediction data, and the solid line represents the experimental data. The two lines highly overlap, which verifies the generalization ability and prediction accuracy of this method.

[0061] In this embodiment, the method constructs a high-quality dataset containing time, temperature, tension, and creep displacement or strain through a differentiated sampling strategy. After min-max normalization and reasonable partitioning, it provides stable input to the model. Then, combined with the creep characteristics of Kevlar, a multi-layer fully connected neural network is designed, and the time, tension, and temperature dependence of creep is transformed into mathematical constraints and embedded in the loss function to form a physically informed neural network. Finally, accurate prediction is achieved through training and validation. This method effectively solves the problems of long cycle, high cost, and difficulty in implementation under extreme environments when testing the creep performance of Kevlar by traditional physical experiments. At the same time, it overcomes the defects of poor extrapolation of pure empirical models and the shortcomings of traditional machine learning models that rely on massive amounts of data and cannot guarantee that the prediction results conform to physical laws. Only a small amount of experimental data is needed to achieve high-precision prediction of the creep behavior of Kevlar cable segments. This not only reduces the time and economic cost of experiments, but also ensures the rationality and credibility of the prediction results through physical constraints. It also has strong interpretability and generalization ability and can be adapted to various materials with typical creep characteristics. It provides efficient and reliable technical support for the long-term service safety assessment and life prediction of Kevlar products in aerospace, marine engineering and other fields.

[0062] In one possible embodiment, a Kevlar segment creep curve prediction system based on a physically aware neural network is provided, comprising: This data acquisition module is used to obtain creep experimental data of Kevlar materials under different constant temperatures and tensions.

[0063] Specifically, this integrated creep testing machine, high-precision tension loading device, displacement sensor, and data acquisition instrument supports multiple preset combinations of constant temperature (e.g., 0℃, 40℃, 80℃, 120℃) and constant tension (e.g., 10N, 20N, 40N, 80N) working conditions. It automatically collects data according to the differentiated sampling strategy in step S1.2—high-density sampling in the first stage of creep (deceleration creep stage) and low-density sampling in the second stage (steady-state creep stage). The collected data includes time, temperature, tension, creep displacement, and strain, ultimately generating data similar to... Figure 1 The structured raw data, consistent with the experimental curves shown, ensures data integrity and validity. The module supports visualized configuration and real-time monitoring of experimental parameters. Parameters such as sampling intervals and test duration can be set via host computer software, and the creep curve trend can be displayed in real time.

[0064] This preprocessing module is used to regularize the data and partition the dataset; Specifically, this preprocessing module incorporates the min-max normalization algorithm specified in step S2.1 of the technical disclosure document. It automatically calculates the minimum and maximum values ​​of each feature (time, temperature, tension, creep displacement / strain), substitutes them into the normalization formula to eliminate differences in dimensions and orders of magnitude, and maps the data to the [0,1] interval. Subsequently, it automatically divides the dataset according to the proportions in step S2.2 of the technical disclosure document (70%-80% for training set, 10%-15% for validation set, and 10%-15% for test set), ensuring that the total number of samples equals the sum of the number of samples in the three datasets, providing standardized data input for model training. The module also adds a data cleaning function, which can automatically identify and remove outlier data points, further improving the quality of the dataset.

[0065] This neural network building block is used to construct fully connected neural networks that include an input layer, hidden layers, and an output layer.

[0066] Specifically, this neural network building module supports configuration and... Figure 6 The network parameters are consistent, with 3 neurons in the input layer (corresponding to temperature, tension, and time), a multi-layer fully connected structure in the hidden layers (optimal configuration is 3 layers, 20 neurons per layer), and 1 neuron in the output layer (corresponding to creep displacement or strain). Built-in activation functions such as ReLU and Tanh, and loss functions such as mean squared error (MSE) and mean absolute error are available for selection. The default is the "pur-tan-tan" activation function combination and MSE loss function from Table 1. Manual adjustment and default settings for hyperparameters (500 iterations, learning rate 0.01, early stopping threshold 6, etc.) are supported. The network initialization is completed according to the neural network mathematical model in step S3. The module provides a visual interface for the network structure, which can intuitively display the connection relationships and parameter configurations of neurons in each layer, facilitating user debugging.

[0067] This physical constraint module is used to transform the physical characteristics of creep into mathematical constraints and embed them into a loss function; Specifically, the physical constraint module: pre-stores the mathematical expressions corresponding to the three major physical characteristics of creep (time dependence, tension dependence, and temperature dependence) mentioned in step S4.1, and automatically converts them into physical constraints; constructs a physical loss function according to the unconstrained optimization equation in step S4.2, and then... Figure 3 The Pearson correlation coefficient shown determines the weighting coefficients corresponding to time, tension, and temperature, embedding physical loss into the total loss function to achieve the integration of data-driven and physical mechanisms.

[0068] This training and prediction module is used to train a physically informed neural network and output creep prediction results.

[0069] Specifically, the training and prediction module follows: Figure 4 The flowchart shown illustrates the training process of a physical sensing neural network. It employs forward propagation to calculate the predicted values ​​and total loss, and backpropagation to optimize weights and biases via a gradient update formula (including the Hadman product). An early stopping mechanism is used to prevent overfitting. After training, new operating parameters (temperature, tension, prediction time range) are received, preprocessed, and input into the model to quickly output creep curve prediction results. It also supports... Figure 5 The generalization ability verification method shown automatically calculates the prediction error (MAE, RMSE) and the goodness of fit to evaluate the model performance.

[0070] In this embodiment, the system solidifies the core methods of the technical disclosure into directly operable functional units through modular design. Each module precisely matches the key links of creep prediction, and the entire process of data acquisition, preprocessing, model building, training, and prediction can be completed without manual intervention, which greatly reduces the operation threshold and human error. The system strictly follows the parameter configuration, mathematical model, and physical constraint logic of the technical disclosure to ensure that the prediction results are highly consistent with the theoretical methods. It retains the core advantages of physical-informed neural networks and improves prediction efficiency through automated processes, providing a convenient and reliable implementation solution for the engineering prediction of creep behavior of Kevlar cable segments.

[0071] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them; although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications to the technical solutions described in the foregoing embodiments, or equivalent substitutions for some or all of the technical features, do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method for predicting the creep curve of a Kevlar segment based on a physically aware neural network, characterized in that, Includes the following steps: Step S1: Obtain creep experimental data of Kevlar material under different constant temperatures and tensions, and construct a dataset containing time, temperature, tension, and creep displacement or strain; Step S2: Perform regularization on the dataset and divide it into a training set, a validation set, and a test set; Step S3: Based on the neural network, configure its input layer to include temperature, tension, and time, the output layer to be creep displacement or strain, the hidden layer to be a multi-layer fully connected structure, and set the activation function and loss function; Step S4: Transform the physical characteristics of creep into mathematical constraints and embed them into the loss function of the neural network to form a physical-informed neural network; Step S5: Train the physical intelligence neural network using the training set, adjust the hyperparameters using the validation set, and finally evaluate the model's generalization ability using the test set, outputting the predicted Kevlar segment creep curve.

2. The method according to claim 1, characterized in that, In step S1, the creep test data is collected using the following method: high-density data collection is used in the first stage of creep, and low-density data collection is used in the second stage of creep.

3. The method according to claim 1, characterized in that, In step S2, the data is regularized using the min-max normalization method. The normalization formula is: ， Where x is the original data, and These are the minimum and maximum values ​​of the feature, respectively.

4. The method according to claim 1, characterized in that, In step S3, the activation function includes the ReLU function or the Tanh function, and the loss function includes the mean squared error or the mean absolute error.

5. The method according to claim 1, characterized in that, In step S4, the physical characteristics of creep include time dependence, tension dependence, and temperature dependence, and their mathematical constraints are expressed as follows: ， Where y is the creep displacement, t is the creep time, F is the tension, and T is the temperature.

6. The method according to claim 5, characterized in that, In step S4, the specific method for embedding the above physical constraints into the neural network is as follows: ， in, Represents the physical loss value. , , These represent creep loss values ​​caused by time, tension, and temperature, respectively. , , Each represents its respective weighting coefficient.

7. A Kevlar segment creep curve prediction system based on a physically aware neural network, characterized in that, include: The data acquisition module is used to acquire creep experimental data of Kevlar materials under different constant temperatures and tensions; The preprocessing module is used to regularize the data and partition the dataset; The neural network calling module is used to call a fully connected neural network that includes an input layer, hidden layers, and an output layer; The physical constraint module is used to transform the physical characteristics of creep into mathematical constraints and embed them into the loss function; The training and prediction module is used to train the physical-informed neural network and output creep prediction results.

8. The system according to claim 7, characterized in that, The data acquisition module supports differentiated sampling strategies at different stages of the creep curve.

9. The system according to claim 7, characterized in that, In the physical constraint module, the physical loss weight coefficient is adjusted based on the Pearson correlation coefficient.

10. The system according to claim 7, characterized in that, It also includes a visualization output module to display creep prediction curves, training process, and generalization ability evaluation results.

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