Carbon fiber dry-jet wet spinning data augmentation method guided by physical information

Abstract

This invention discloses a data enhancement method for carbon fiber dry-jet wet-spinning solidified filaments based on physical information guidance. The method first acquires experimental data of solidified filaments under different dry-jet wet-spinning process conditions, and then constructs a physical information neural network based on the dry-jet wet-spinning control equations to solve for the process field information distributed along the spinning path. Subsequently, the high-dimensional process field is encoded, and a conditional exponential family diffusion model is constructed using process parameters and the encoded low-dimensional process representation as conditions. Potential function constraint terms and physical constraint terms for performance indicators are introduced during training. Finally, the trained model is used to generate performance enhancement data for solidified filaments under the corresponding process conditions. This invention is applicable to dry-jet wet-spinning systems and can achieve performance indicator data enhancement with good extrapolation performance and strong physical interpretability under extremely small data sample conditions, overcoming the problems of existing methods where process physical information is difficult to effectively integrate into the performance data enhancement process and the reliability of the generated results is insufficient.

Description

Technical Field

[0001] This invention relates to the field of carbon fiber dry-jet wet spinning process modeling technology, specifically to a method for enhancing carbon fiber dry-jet wet spinning solidified yarn data based on physical information guidance. Background Technology

[0002] Carbon fiber possesses a series of excellent properties such as high strength, high modulus, high temperature resistance, and low density, and is widely used in high-end manufacturing fields such as aerospace, automotive, and electronics. Polyacrylonitrile-based carbon fiber dominates global carbon fiber production, accounting for approximately 90%. Precursor fiber, as its direct precursor, has a significant impact on the structure and properties of the final carbon fiber. Dry-jet wet spinning is one of the key processes in the preparation of polyacrylonitrile-based carbon fiber precursor fiber. During this process, the spinning solution undergoes complex physical changes through an air section and a coagulation bath to form solidified fiber. Different process conditions significantly affect the structural evolution and performance state of the solidified fiber, which in turn affects subsequent drawing, pre-oxidation, and carbonization processes, ultimately influencing the performance of the carbon fiber. Therefore, modeling and analyzing dry-jet wet-spun carbon fiber solidified fiber is of great significance for the preparation of high-performance carbon fibers.

[0003] Existing research on dry-jet wet-spun solidified carbon fibers mainly includes experimental studies and mechanistic analysis. For example, the experimental method in reference 1 (Pan Shilong, He Shuqian, Wang Huijie, et al. Characterization method of dry-jet wet-spun polyacrylonitrile solidified fibers [J]. Synthetic Fiber Industry, 2023.) usually relies on a large number of experimental tests to investigate the influence of different process parameters on the structure and properties of solidified fibers. This method is not only costly and time-consuming, but also has a limited amount of data available, making it difficult to support a reliable modeling of the process-performance relationship of solidified fibers on its own. Mechanism analysis attempts to describe the physical evolution of the dry-jet wet spinning process using a set of governing equations based on mass conservation, momentum conservation, and constitutive relations. However, existing studies mostly focus on local processes or involve significant simplifications. For example, reference 2 (Xu N, Ding Y, Schiesser WE, et al. Mathematical simulation of wet spinning coagulation process: Dynamic modeling and numerical results[J]. AIChE Journal, 2016.) constructed a coagulation bath wet spinning mechanism model, and reference 3 (Simon V. Analysis of fiber formation during air-gap wet spinning[J]. AIChE Journal, 1995.) constructed a simplified dry-jet wet spinning model. Furthermore, the solutions to the mechanism equations typically yield process variables such as velocity, stress, and geometric dimensions distributed along the spinning path, rather than the ultimately observable coagulated fiber performance indicators from experiments. Therefore, it is difficult to directly establish an effective correlation between the process and the final performance. Moreover, even under the same process conditions, the performance indicators of the coagulated fiber still exhibit significant fluctuations, demonstrating strong randomness. This indicates that the modeling problem in this process is not a simple deterministic mapping problem, but rather a modeling problem with obvious conditional distribution characteristics. Given the extremely limited sample size and significant performance dispersion, directly establishing a stable and reliable model relating process parameters and performance indicators remains quite challenging.

[0004] Given the small sample size and significant randomness in performance distribution, relying solely on limited experimental data often fails to adequately characterize the statistical distribution of solidified fiber performance under different process conditions, and also makes it difficult to provide stable data support for subsequent modeling of the relationship between process parameters and performance indicators. Therefore, compared to directly using limited samples for modeling, expanding the statistically representative solidified fiber performance data through data augmentation provides a feasible approach to alleviate the problem of sample scarcity and improve the reliability of subsequent modeling.

[0005] However, in the scenario of dry-jet wet-spinning solidified carbon fiber, data augmentation not only needs to maintain the statistical rationality of the generated data, but also needs to reflect the physical constraints and evolution laws in the solidified fiber formation process under process changes. A series of physical information learning methods, represented by the physical information neural network proposed in Reference 4 (Raissi M, Perdikaris P, Karniadakis G E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[J]. Journal of Computational physics, 2019.), provide the technical foundation for this. However, the mechanistic equations usually represent high-dimensional continuous process information such as velocity field, stress field and geometric dimensions distributed along the spinning process, while the final performance indicators such as solidified fiber diameter, strength, modulus, tensile strength and elongation can be directly obtained in experiments. There are obvious differences between the two in physical stage and representation dimension, making it difficult to directly integrate process physical information into solidified fiber performance data augmentation. Therefore, how to effectively utilize the physical information of the dry-jet wet spinning process under small sample conditions to achieve data enhancement of carbon fiber dry-jet wet spinning solidified yarn performance indicators that take into account both statistical characteristics and physical rationality remains an urgent technical problem to be solved. Summary of the Invention

[0006] The purpose of this invention is to address the following problems in the existing modeling and data augmentation process of carbon fiber dry-jet wet-spinning solidified fibers: high experimental research costs and long cycles result in a limited number of available process conditions and sample sizes; even under the same process conditions, the performance indicators of solidified fibers still fluctuate significantly, making it difficult to establish a stable and reliable model of the relationship between process parameters and performance indicators based solely on limited experimental data; furthermore, the mechanistic equations typically characterize process information such as velocity, stress, and geometric dimensions distributed along the spinning path, which differs from the ultimately observable performance indicators of the solidified fibers in the experiment, making it difficult to directly integrate them into the data augmentation process. Therefore, this invention provides a data augmentation method for carbon fiber dry-jet wet-spinning solidified fibers based on physical information guidance, achieving solidified fiber performance data augmentation that balances statistical characteristics and physical plausibility under small sample conditions.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A data augmentation method for carbon fiber dry-jet wet-spun solidified fibers guided by physical information includes the following steps: Step S1: Obtain experimental data of carbon fiber dry-jet wet-spun solidified yarn under multiple process conditions. The experimental data includes process parameters and solidified yarn performance indicators corresponding to each process condition.

[0009] Step S2: Based on the control equations of the carbon fiber dry-jet wet spinning process, solve the process field information of the solidified filament distribution along the spinning path during the spinning process according to each process condition. The process field information is used to characterize the physical evolution state of the solidified filament during the dry-jet wet spinning process.

[0010] Step S3: Encode the process field information to obtain a low-dimensional process representation of the process field information under the corresponding process conditions, so as to realize the conversion of high-dimensional continuous process information distributed along the spinning process into compact condition information that can be used for generative modeling.

[0011] Step S4: Using the process parameters and the low-dimensional process characterization as conditional information, construct a conditional exponential family diffusion model to learn the conditional distribution of the solidified fiber performance indicators under the corresponding process conditions, wherein the conditional distribution satisfies:

[0012] in, Indicates the performance indicators of solidified fiber. Indicates process parameters, This represents a low-dimensional process characterization. To obtain sufficient statistical data, For natural parameters, It is a logarithmic partition function. It is a basic measure term.

[0013] Step S5: Train the conditional exponential family diffusion model using the experimental data, and introduce potential function constraint terms and physical performance index constraint terms based on the conditional distribution structure during the training process to enhance the statistical rationality and physical feasibility of the generated data.

[0014] Step S6: For the process conditions to be enhanced, first solve the corresponding process field information and obtain a low-dimensional process characterization, then input the process conditions and the low-dimensional process characterization into the trained conditional exponential family diffusion model to generate enhanced data of solidified filament performance indicators under the corresponding process conditions.

[0015] As a preferred technical solution: In step S2, the governing equations include the mass conservation equation, momentum conservation equation, and constitutive equation. The process field information includes at least the velocity field, stress field, and fiber geometry. The governing equations are solved using a physical information neural network, which includes an air segment network and a solidification bath network. The air segment network and the solidification bath network are coupled through interface continuity constraints to achieve continuous solution of the process field information within the air segment and the solidification bath. The physical information neural network is optimized by minimizing the residuals of the governing equations, initial conditions, interface continuity, and end-velocity constraints. Its optimization objective is... satisfy:

[0016] in, For the loss of air joke network, For the solidification bath network loss, For interface continuity constraint loss, For end-velocity constraint loss, , , and These are the corresponding weighting coefficients.

[0017] In step S3, a physical information encoder is used. The process field information is mapped to a low-dimensional process representation, and the mapping relationship is expressed as follows:

[0018] in, Represents process field information, This represents a low-dimensional process. Indicates the number of process variables. The number of discrete sampling points along the spinning direction is denoted as . The physical information encoder employs a dual-path feature extraction structure, extracting continuous evolution features and statistical features of the process field information respectively, and then fusing the extracted features to form the low-dimensional process representation. The physical encoder is pre-trained using a self-supervised method, and its pre-training loss is . Represented as:

[0019] in, To compare the losses, To reconstruct the loss, For gradient preservation loss, , , These are the corresponding weighting coefficients.

[0020] In step S4, the low-dimensional process characterization and process parameters are used together to modulate the natural parameters of the conditional exponential family diffusion model, so that the process field information enters the diffusion generation process through the energy structure of the conditional distribution, rather than being used as the direct input to the denoising network; the conditional distribution satisfies:

[0021] Based on the aforementioned conditional structural distribution, a potential function is defined as follows:

[0022] The potential function is used to constrain the denoising direction during the training process of the diffusion model, so as to guide the model to learn the distributed energy structure modulated by the process field information.

[0023] In step S5, the physical constraint term of the performance index is used to constrain the performance index of the generated solidified filament to meet the diameter requirement. powerful and intensity There is a pre-defined physical relationship between them, and the pre-defined physical relationship satisfies:

[0024] The physical information neural network and physical information encoder are pre-trained and their parameters are kept fixed during the training of the conditional exponential family diffusion model. The conditional exponential family diffusion model is optimized using a unified training objective. It is composed of a weighted average of the noise prediction loss of the diffusion model, the potential function constraint term, and the physical constraint term of the performance index, and its expression is:

[0025] in, For noise prediction loss in the diffusion model, For potential function constraint terms, For physical constraints of performance indicators, and These are the weighting coefficients.

[0026] In step S6, for the process conditions to be enhanced, the process conditions are first input into the physical information neural network to solve for the process field information of the distribution of the coagulated filament along the spinning path during dry-jet wet spinning under these process conditions. Then, the physical information encoder is used to encode the process field information to obtain the corresponding low-dimensional process representation. Finally, the process conditions and the low-dimensional process representation are jointly input into the trained conditional exponential family diffusion model to generate enhanced data for the coagulated filament performance indicators under the corresponding process conditions. The process conditions include extrusion speed, drafting speed, drafting ratio, and air section length. The coagulated filament performance indicators include diameter, strength, modulus, and elongation. The generated enhanced data for coagulated filament performance indicators is used to expand the original experimental dataset or for subsequent modeling of the relationship between process parameters and performance indicators.

[0027] Compared with the prior art, the present invention has the following beneficial effects: (1) In view of the problem that the experimental data of carbon fiber dry-jet wet spinning solidified yarn is limited in scale and the performance fluctuates significantly under the same process conditions, the present invention constructs a data augmentation framework based on physical information guidance. It can generate statistically representative and physically reasonable solidified yarn performance data under small sample conditions, and maintain good extrapolation ability under different process conditions, thereby effectively making up for the lack of experimental data and providing more reliable data support for subsequent modeling of the relationship between process parameters and performance indicators.

[0028] (2) The present invention constructs a physical information neural network solution framework for the dry-jet wet spinning process, which can solve the process information such as the speed, stress and geometric dimensions of the solidified filament distributed along the spinning process. It provides a feasible way to model the multi-physics field in the dry-jet wet spinning process. It can not only be used in the data enhancement process of the present invention, but also provide a reference for process modeling and physical information utilization of other dry-jet wet spinning systems.

[0029] (3) By constructing a conditional index family diffusion model, this invention realizes the effective connection between high-dimensional continuous process field information and final solidified yarn performance indicators in the dry-jet wet spinning process. This enables process physical information to participate in performance data generation through the modulation mechanism of the generation distribution, overcoming the problem that the mechanism analysis results in the prior art are difficult to be directly used for performance data enhancement, thereby improving the ability of enhanced data to characterize process changes and process evolution laws. Attached Figure Description

[0030] Figure 1 This is a general framework diagram of the data enhancement method for carbon fiber dry-jet wet-spinning solidified yarn based on physical information guided by the present invention. Figure 2 This is a schematic diagram of the dry-jet wet spinning process of carbon fiber solidified filament in an embodiment of the present invention; Figure 3The process field distribution along the spinning process under different technological conditions obtained by solving the physical information neural network in the embodiments of the present invention; Figure 4 This is a univariate distribution diagram of the solidified fiber performance index under a certain working condition in an embodiment of the present invention. Figure 5 This is a diagram showing the consistency between the generated strength and the theoretical strength under a certain working condition in an embodiment of the present invention. Figure 6 The graph shows the results of performance variation with process conditions under no observed process conditions in the embodiments of the present invention. Detailed Implementation

[0031] The present invention will be further described below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0032] Example 1: This embodiment proposes a data augmentation method for carbon fiber dry-jet wet-spinning solidified fibers based on physical information guidance. The overall framework diagram of this method is as follows: Figure 1 As shown, it includes the following steps: Step S1: Obtain experimental data of carbon fiber dry-jet wet-spun solidified filaments under multiple process conditions.

[0033] Experimental data include process parameters and solidified filament performance indicators corresponding to each process condition; process parameters include at least extrusion speed, drawing speed, drawing ratio, and air section length; solidified filament performance indicators include at least diameter, strength, modulus, and elongation.

[0034] Step S2: Solve the process field information of the dry-jet wet spinning process based on the various process conditions.

[0035] The process parameters from step S1 are input into the dry-jet wet spinning process solution module. Based on the control equations of the dry-jet wet spinning process, the process field information of the solidified filament distributed along the spinning path is solved to obtain the process field results under the corresponding process conditions. The process field information includes at least the velocity field, stress field, and fiber geometry. Preferably, the process solution module is implemented using a physical information neural network, which includes an air segment sub-network and a solidification bath sub-network, and the two sub-networks are coupled through interface continuity constraints.

[0036] The governing equations for the carbon fiber dry-jet wet spinning process in step S2 describe the evolution of the velocity field, stress field, and fiber geometry in the air section and coagulation bath under steady-state, axisymmetric, and isothermal assumptions. These equations include the mass conservation equation, momentum conservation equation, and constitutive equation. The meanings of the variables involved in the equations are shown in Table 1.

[0037] Table 1. Consistencies and their meanings in the control equations for dry-jet wet spinning.

[0038] Regarding mass conservation, the mass flow rate remains constant during fiber stretching. In the coagulation bath, due to the coexistence of solid and liquid phases, the mass conservation equation is:

[0039] Since solidification has not yet occurred in the air section, the mass conservation equation degenerates into:

[0040] Regarding the conservation of momentum, neglecting inertia, gravity, and surface tension, the equation for the conservation of axial momentum in the solidification bath simplifies to:

[0041] The momentum conservation equation in the air section is:

[0042] Regarding constitutive relations, the liquid phase adopts the Phan-Thien-Tanner constitutive model, and the solid phase is approximated as a rubber-like nonlinear elastic body, with the following set of stress evolution equations:

[0043] Where the nonlinear coefficient satisfy .

[0044] Table 2 Dimensionless variables and their definitions in the control equations for dry-jet wet spinning.

[0045] Table 3 Dimensionless control parameters and their definitions in the control equations for dry-jet wet spinning.

[0046] To reduce the difficulty of solving the problem and improve numerical stability, the above governing equations are dimensionless. The meanings of the dimensionless variables and dimensionless control parameters involved are shown in Tables 2 and 3. Therefore, the dimensionless mass conservation equation in the solidification bath is:

[0047] in This represents the solid-liquid density ratio, which degenerates into [value] in the air section. .

[0048] The dimensionless momentum conservation equation in the solidification bath is:

[0049] The air section contains:

[0050] The dimensionless constitutive equation for the liquid phase is:

[0051] in .

[0052] The solid phase is:

[0053] in This represents the solid-liquid modulus ratio. The above dimensionless governing equations are used together to describe the evolution of the velocity field, stress field, and geometric quantities of the solidified filament along the spinning direction.

[0054] The governing equations are solved using a physical information neural network. This network comprises an air segment sub-network and a condensation bath sub-network, with each sub-network defined by dimensionless axial coordinates. It serves as the input and is coupled through interface continuity constraints.

[0055] For the air segment network, the input is The output is The physical information loss function of this subnetwork is defined as:

[0056] in These are the parameters of the air segment network, and the residual loss term in the governing equation. residuals from the constitutive equation of liquid phase PTT , With momentum conservation residual Composition, its set of sampling points in the air segment The above is defined in the form of mean square error:

[0057] Initial condition loss Used to restrain the area below the spinneret. Velocity and stress state:

[0058] For the solidification bath network, the input is... Its output is The corresponding loss function is:

[0059] in These are the parameters of the coagulation bath segment network. The residual loss term of the governing equation for the coagulation bath, which includes the residuals of the momentum conservation equation and the constitutive equations of the liquid and solid phases, is defined on the set of sampling points in the coagulation bath as follows:

[0060] This is the initial condition loss term for the coagulation bath, used in... The output at the end of the inherited air section, and constrained by the initial solid stress and liquid volume fraction, are defined as:

[0061] Furthermore, considering the difficulty in directly measuring the initial stress state during the experiment, an end-effector velocity constraint is introduced during the training process, and the dimensionless parameter is... As trainable variables, they are optimized together with network parameters. The overall optimization objective of the physical information neural network is:

[0062] in For interface continuity constraint loss, For end-velocity constraint loss, , , , These are their respective weighting coefficients.

[0063] To improve solution stability, preferably, denser sampling points are arranged near the spinneret, in the initial region of the air section, and near the interface between the air section and the solidification bath, while relatively uniform sampling is used in other regions. Simultaneously, a smoothing mechanism that varies with the axial coordinate is introduced into the exponential term of the liquid-phase PTT constitutive equation. Let the smoothing factor be... The smoothed exponential term is

[0064] The above settings can suppress the numerical rigidity of the initial region of the spinning process and improve the robustness of the physical information neural network in solving the problem.

[0065] By following the steps above, the process field information distributed along the spinning process under the given process conditions can be obtained, providing input for the process field coding in the subsequent step S3.

[0066] Step 3: Encode the process field information to obtain a low-dimensional process representation.

[0067] The process field information obtained in step S2 is input into the physical information encoder to perform feature extraction and compressed representation on the process field information, thereby obtaining a low-dimensional process characterization under the corresponding process conditions, which serves as one of the conditional information for subsequent model generation. Preferably, the physical information encoder adopts a dual-path feature extraction structure to extract the continuous evolution features and statistical features of the process field information respectively, and then fuses the extraction results.

[0068] In step S3, the process field data corresponding to each process condition is first read and organized into a process field matrix: ,in Indicates the number of process variables. This indicates the number of sampling points along the spinning direction; preferably, Then, the process field matrix of all process conditions is standardized according to the variable channels.

[0069] Furthermore, a physical information encoder is employed. Encoding the standardized process field matrix yields a low-dimensional process representation. The mapping relationship is as follows:

[0070] in To represent the dimension of a low-dimensional process, preferably, .

[0071] The physical information encoder employs a dual-path structure, including a structural coding branch and a statistical coding branch. The structural coding branch uses a one-dimensional convolutional network to extract the continuous evolution features of the process field along the spinning direction, obtaining a structural feature vector. The statistical coding branch extracts six statistics for each process variable: mean, standard deviation, minimum, maximum, first-order gradient mean, and first-order gradient standard deviation. These are then linearly mapped to obtain a statistical feature vector. .Will and By splicing and normalizing, the final low-dimensional process representation is obtained. .

[0072] The physical information encoder is pre-trained using a self-supervised approach. Two enhanced views are generated for the process field matrix corresponding to the same process conditions, and these views are input into the physical information encoder to obtain two low-dimensional representations. and Preferably, the enhancement methods include at least one of random scaling, random noise perturbation, local random occlusion, and smoothing. Further, a decoding head is set after the physical information encoder to reconstruct the process field matrix based on the low-dimensional process representation. The pre-training loss function of the physical information encoder is:

[0073] in, To compare the losses, To reconstruct the loss, For gradient preservation loss, , , These are the corresponding weighting coefficients.

[0074] After pre-training is completed, the physical information encoder parameters are fixed, and the process field matrix obtained in step S2 is input into the trained physical information encoder to obtain a low-dimensional process representation under the corresponding process conditions. This is used for condition generation modeling in the subsequent step S4.

[0075] Step 4: Construct a conditional exponential family diffusion model.

[0076] Using the process parameters in step S1 and the low-dimensional process characterization in step S3 as conditional information, a conditional exponential family diffusion model is constructed to learn the conditional distribution of solidified filament performance indicators under corresponding process conditions. The low-dimensional process characterization and process parameters are used together to modulate the natural parameters of the conditional distribution, so that the process field information enters the diffusion generation process through the energy structure of the conditional distribution.

[0077] In step S4, the process parameters from step S1 and the low-dimensional process characterization from step S3 are used. To provide conditional information, a conditional exponential family diffusion model is constructed. Let the process parameters be expressed as... The performance indicators of the solidified fiber are: Conditional exponential family diffusion models are used to characterize... exist and The conditional distribution under the combined effect is expressed as follows:

[0078] in To obtain sufficient statistical data, For natural parameters, It is a logarithmic partition function. As a basic measure term. Characterization of low-dimensional processes. With process parameters Together used to modulate natural parameters . Obtained from natural parameter networks, Both are parameterized using statistical networks. In practice, both are implemented using lightweight neural networks to improve the flexibility of learning the shape of conditional distributions.

[0079] Potential functions are used to characterize the energy structure of conditional distributions. Low-dimensional processes are characterized through potential functions. The process field information carried is not used as a direct input to the denoising network, but rather modulates the energy form of the conditional distribution through natural parameters, and further affects the diffusion generation process.

[0080] Preferably, a denoised diffusion probability model is used as the basis for generative modeling. This applies to noisy samples during the diffusion process. The denoising network predicts noise, and its standard diffusion loss function is expressed as:

[0081] in This represents a denoising network. Indicates the diffusion time step. This represents real noise.

[0082] The potential function constraint loss term is: ,in This indicates the diffusion process at time step The corresponding noise scale. The potential function constraint term is used to constrain the denoising direction during the diffusion model training process, so that it reflects the conditional distribution structure jointly determined by process parameters and low-dimensional process representation.

[0083] Step 5: Train the conditional exponential family diffusion model.

[0084] The conditional exponential family diffusion model constructed in step S4 is trained using the experimental data from step S1. During training, a potential function constraint term based on the conditional distribution structure and a performance index physical constraint term based on the preset physical relationships between solidified filament performance indicators are introduced. The performance index physical constraint term is used to constrain the generated diameter, strength, and intensity to meet the preset physical relationships. Preferably, the physical information neural network and physical information encoder are pre-trained and their parameters are kept fixed during the training of the conditional exponential family diffusion model.

[0085] In step S5, the conditional exponential family diffusion model constructed in step S4 is trained using the experimental data from step S1, and additional physical constraint terms for performance indicators are introduced during the training process. Physical constraint terms for performance indicators are constructed based on the physical relationships between the performance indicators of the solidified fiber. For fiber diameter... powerful and intensity Satisfying the relationship Define the physical constraints of the performance index as follows:

[0086] Furthermore, by weighting and combining the above losses, a unified training objective for the conditional exponential family diffusion model is obtained:

[0087] in and These are the weighting coefficients. The physical information neural network in step S2 and the physical information encoder in step S3 are pre-trained and their parameters are kept fixed when training the conditional exponential family diffusion model.

[0088] Step 6: Generate augmented data.

[0089] For the process conditions to be enhanced, the process conditions are first input into the process solving module in step S2 to obtain the corresponding process field information; then, the process field information is input into the physical information encoder in step S3 to obtain the corresponding low-dimensional process representation; finally, the process conditions and the low-dimensional process representation are jointly input into the trained conditional exponential family diffusion model to generate enhanced data for the solidified filament performance indicators under the corresponding process conditions. This enhanced data is used to expand the original experimental dataset or for subsequent modeling of the relationship between process parameters and performance indicators.

[0090] In step S6, for the process conditions to be enhanced, the process conditions are first input into the process solving module in step S2 to obtain the corresponding process field information; then the process field information is input into the physical information encoder in step S3 to obtain the corresponding low-dimensional process characterization. Then, the process conditions to be enhanced and The conditional exponential family diffusion model trained in step S5 is used as a common input to generate enhanced data for the solidified fiber performance indicators under the corresponding process conditions. The process conditions to be reinforced include at least extrusion speed, drawing speed, drawing ratio, and air section length; the resulting solidified filament performance enhancement data includes at least diameter, strength, modulus, and elongation. The diffusion sampling process can be repeated for the same process conditions to generate multiple sets of solidified filament performance enhancement data, which are used to characterize the statistical distribution of solidified filament performance indicators under that process condition.

[0091] Example 2: Based on Example 1, but with a difference, this example uses data of dry-jet wet-spinning solidified carbon fiber collected in the laboratory to illustrate the execution process of the method of the present invention, but the present invention is not limited to the following specific parameter settings.

[0092] In this embodiment, experimental data on carbon fiber dry-jet wet-spinning solidified fibers under different process conditions were first collected. A schematic diagram of the dry-jet wet-spinning process is shown below. Figure 2As shown. Experimental data were organized according to process conditions, including 29 independent operating conditions. Data on solidified filament samples under corresponding process conditions were obtained by adjusting extrusion speed, drawing speed, drawing ratio, and air section length. Twenty solidified filament samples were collected under steady-state operation for each process condition to characterize the natural fluctuations in performance indicators under the same condition. Recorded performance indicators included diameter, strength, modulus, and elongation. Strength, strength, modulus, and elongation were measured as single-filament values, and the diameter was the average diameter of all filaments under the same condition as the geometric representation of that condition.

[0093] Subsequently, a set of control equations for the dry-jet wet spinning process is constructed and solved based on each set of process conditions to obtain the process field information distributed along the spinning direction. In this embodiment, the process field solution is implemented using a physical information neural network, which includes an air segment network and a coagulation bath network. The air segment network takes dimensionless axial coordinates as input and outputs the air segment velocity. Axial stress in the liquid phase Radial stress in the liquid phase and dimensionless radius The coagulation bath subnet takes dimensionless axial coordinates as input and outputs the coagulation bath velocity. Axial stress in the liquid phase Radial stress in the liquid phase Axial stress in solid phase Radial stress of solid phase Liquid core radius ratio and dimensionless radius In this embodiment, 3000 calibrated points are configured in the air section, 5000 calibrated points are configured in the coagulation bath section, and 150 initial condition points are set at the spinneret nozzle. Strip-based dense sampling is used near the interface. During joint training, the end-velocity constraint is used as one of the optimization objectives, and the parameters are... The trainable parameters are set to be updated synchronously with the network parameters. The optimizer is Adam, and the initial learning rate is set to 0.001.

[0094] The process fields obtained for each working condition are organized into a process field matrix of uniform length and input into a physical information encoder to obtain a low-dimensional process characterization. In this embodiment, the process field for each working condition is uniformly discretized into 1000 sampling points along the spinning process. The selected process variables include velocity, diameter, core diameter, axial stress of the liquid phase in the air section, radial stress of the liquid phase in the air section, axial stress of the liquid phase in the coagulation bath, radial stress of the liquid phase in the coagulation bath, axial stress of the solid phase in the coagulation bath, radial stress of the solid phase in the coagulation bath, liquid phase fraction, solid phase fraction, and draft ratio, totaling 12 channels. The physical information encoder employs a dual-path structure: the first is a one-dimensional convolutional branch, consisting of three convolutional layers, each with a kernel size of 9 and channel numbers of 64, 128, and 128 respectively, followed by an adaptive average pooling layer to compress the sequence length to 32, and then outputting structural features via flattening and linear layers; the second is a statistical branch, extracting six statistical measures for each process variable: mean, standard deviation, minimum, maximum, first-order gradient mean, and first-order gradient standard deviation, and mapping these to obtain statistical features via linear layers; the features from both branches are concatenated and normalized to obtain the final process representation. Preferably, the process representation dimension is set to 128. During encoder pre-training, the number of training epochs is set to 300, the batch size to 16, and the encoder learning rate to [missing information]. .

[0095] To illustrate the changes in process field information under different technological conditions, the velocity and diameter distributions of the solidified filament along the spinning path under representative technological conditions are presented, as shown in the appendix. Figure 3 As shown. By Figure 3 It is evident that under different process conditions, the velocity and diameter evolution of the coagulated filament along the spinning path exhibit significant differences, and these differences remain continuous at the interface between the air section and the coagulation bath. These results demonstrate that the process field obtained in this embodiment can characterize the differences in physical states during the coagulated filament formation process under different process conditions, and can serve as input for subsequent physical information encoders to extract low-dimensional process representations.

[0096] Based on this, a conditional exponential family diffusion model is constructed and trained using experimental data. In this embodiment, the denoising network of the diffusion model adopts a conditional UNet structure, including a temporal embedding layer, a conditional projection layer, an input projection layer, two encoder layers, one intermediate bottleneck layer, and two decoder layers; the hidden dimension is set to 128, the temporal embedding dimension is set to 64, and the diffusion steps are set to 1000. The encoder's first layer output dimension is 128, the second layer output dimension is 256, and the intermediate layer dimension is 256. In the decoding stage, features from the encoding stage are concatenated through skip connections to recover the noise prediction result step by step, ultimately outputting a noise prediction result consistent with the performance index dimension. The natural parameter network adopts a multilayer perceptron structure, with inputs including process parameters, process representations, and temporal step embeddings, and a hidden dimension set to 256; the sufficient statistics network adopts a two-layer perceptron structure, with an output dimension consistent with the natural parameter dimension. During training, the batch size is set to 32, the number of training epochs is set to 1200, and the learning rate of the main denoising network is set to... The learning rates for the Natural Parameter Network and the Sufficient Statistics Network are set to... The weight of the potential function constraint term is set to 0.3, and the weight of the physical constraint term of the performance index is set to 0.1.

[0097] In this embodiment, training and validation are divided according to process conditions, and samples under the same process conditions are processed as a group. After the model training is completed, for the process conditions to be enhanced, the corresponding process field is first obtained according to the above process and encoded into a low-dimensional process representation. Then, the process parameters and the low-dimensional process representation are input into the trained conditional exponential family diffusion model for sampling to generate enhanced data of solidified filament performance indicators under that process condition.

[0098] The method described in the above embodiments is used to enhance the data of carbon fiber dry-jet wet-spun solidified yarn performance indicators. To verify the effectiveness of the method of the present invention, the generated results are evaluated from three aspects: overall distribution, univariate statistical characteristics, and physical relationships. Specifically, the overall distribution is evaluated using energy distance ED, maximum mean difference MMD, Fréchet distance FID, precision, coverage, and pairwise distance shift PWShift; the univariate statistical aspects are evaluated using KS distance, Wasserstein-1 distance W1, and log-normal distribution parameter deviation (…). ) and coefficient of variation error ( The evaluation is performed using the mean error (RMSE) for the diameter; at the physical relationship level, the root mean square error (RMSE) between the generated strength and the theoretical strength calculated based on the diameter and force is used. ) and relative error ( The method was evaluated. TabDDPM, ForestDiffusion, TabDiff, and STaSy were selected as comparative methods and compared under the same data partitioning and evaluation criteria to demonstrate the effectiveness of the method (PIHD) of this invention.

[0099] The results show that the solidified filament performance data generated by the method of this invention have a high degree of consistency with the real experimental data in terms of overall distribution. The quantitative results in Table 4 show that the method of this invention outperforms the comparative methods in terms of ED, MMD, FID, and PWShift, while maintaining high precision and coverage. This indicates that the generated data is closer to the real data in the multidimensional performance index space and can better cover the distribution support range of the real samples.

[0100] Table 4 Evaluation Results of Overall Distribution of Generated Data

[0101] At the univariate statistical level, Figure 4 As shown in Table 5, the method of the present invention can reproduce the central trend and distribution width of real data well in terms of performance indicators such as diameter, strength, elongation, and modulus. In particular, for performance indicators with strong fluctuations such as elongation, the generated results still maintain low mean deviation and standard deviation, indicating that the method of the present invention can stably characterize the random fluctuation characteristics of solidified filament performance indicators under the same process conditions.

[0102] Table 5. Results of Univariate Statistical Evaluation of Generated Data

[0103] At the level of physical relationships, the quantitative results in Table 6 show that the intensity error and relative error of the samples generated by the method of the present invention are both lower than those of the comparative method. Figure 5 The 45° consistency result further indicates that the generated samples are more concentrated near the reference line corresponding to the theoretical relationship, which shows that the data generated by the method of the present invention can better satisfy the preset physical relationship between diameter, strength and intensity, and has good physical rationality.

[0104] Table 6 Evaluation Results of Physical Relationships of Data Generation Performance Indicators

[0105] Furthermore, under process conditions without training, Figure 6The extrapolation results show that as the distance between the test process conditions and the training process conditions increases, the distribution error of each method increases. However, the growth rate of the corresponding index of the method of the present invention is lower, indicating that the method of the present invention can still maintain a relatively stable data generation capability under unseen process conditions and has a good generalization ability for operating conditions.

[0106] In summary, the method of this invention can enhance the performance index data of carbon fiber dry-jet wet-spinning solidified yarn under small sample conditions, taking into account both statistical distribution characteristics and physical rationality, and can provide reliable data support for subsequent modeling and optimization of process parameters-performance index relationships.

[0107] The above specific embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Those skilled in the art should understand that the above embodiments do not limit the present invention in any way, and all similar technical solutions obtained by equivalent substitution or equivalent transformation are within the protection scope of the present invention.

Claims

1. A data augmentation method for carbon fiber dry-jet wet-spun coagulation filament based on physical information guided, characterized in that, Includes the following steps: Step 1: Obtain experimental data of carbon fiber dry-jet wet-spinning solidified fibers under multiple process conditions. The experimental data includes the process parameters corresponding to each process condition. and solidified fiber performance indicators ; Step 2: Based on the governing equations of the carbon fiber dry-jet wet spinning process, solve for the process field information of the solidified fiber distribution along the spinning path during the spinning process according to various process conditions. ; Step 3: Process field information Encode the data to obtain a low-dimensional representation of the process field information under the corresponding technological conditions. ; Step 4: Using the aforementioned process parameters and low-dimensional representation Using conditional information, a conditional exponential family diffusion model is constructed to learn the performance indicators of solidified filaments. Model the condition distribution under the corresponding process conditions, wherein the condition distribution satisfies: in, To obtain sufficient statistical data, For natural parameters, It is a logarithmic partition function. Basic measure term; Step 5: Train the conditional exponential family diffusion model using the experimental data, and introduce potential function constraint terms and physical constraint terms of performance index based on the conditional distribution structure during the training process. Step 6: Input the process conditions to be enhanced into the trained conditional index family diffusion model to generate enhanced data of solidified filament performance indicators under the corresponding process conditions.

2. The data enhancement method for carbon fiber dry-jet wet-spinning solidified filament based on physical information guidance according to claim 1, characterized in that, The governing equations in step 2 include the mass conservation equation, the momentum conservation equation, and the constitutive equation; the process field information It includes at least the velocity field, stress field, and fiber geometry; The governing equations are solved using a physical information neural network, which includes an air segment sub-network and a solidification bath sub-network. The air segment network and the solidification bath sub-network are coupled through interface continuity constraints to achieve continuous solution of process field information within the air segment and the solidification bath.

3. The method for data enhancement of carbon fiber dry-jet wet-spinned solidified filament based on physical information guidance according to claim 1, characterized in that, In step 3, a physical information encoder is used to transmit the process field information. Mapping to low-dimensional process representation The mapping relationship is expressed as follows: in, Represents the physical information encoder. Indicates the number of process variables. This represents the number of discrete sampling points along the spinning direction; The physical information encoder adopts a dual-path feature extraction structure to extract the continuous evolution features and statistical features of the process field information, respectively, and fuses the extracted features to form the low-dimensional process representation.

4. The method for data enhancement of carbon fiber dry-jet wet-spinned solidified fibers based on physical information guidance according to claim 1, characterized in that, Characterization of the low-dimensional process described in step 4 With process parameters Together they are used to modulate the natural parameters of the conditional exponential family diffusion model. This allows process field information to enter the diffusion generation process through the energy structure of the conditional distribution, rather than being used as direct input to the denoising network; a potential function is defined based on the conditional exponential family distribution structure: The superscript T indicates transpose; The potential function is used to constrain the denoising direction during the training process of the diffusion model, so as to guide the model to learn the distributed energy structure modulated by the process field information.

5. The method for data enhancement of carbon fiber dry-jet wet-spun solidified fibers based on physical information guidance according to claim 1, characterized in that, In step 5, the physical constraint term of the performance index is used to constrain the performance index of the generated solidified filament to meet the diameter requirement. powerful and intensity The preset physical relationship between them satisfies: The physical constraint term of the performance index is used to constrain the deviation between the generated strength and the theoretical strength calculated based on the generated diameter and the generated strength.

6. The method for data enhancement of carbon fiber dry-jet wet-spun solidified filament based on physical information guidance according to claim 1, characterized in that, The physical information neural network and physical information encoder described in step 5 are pre-trained and their parameters are kept fixed when training the conditional exponential family diffusion model; The conditional exponential family diffusion model is optimized using a unified training objective, which is a weighted sum of the diffusion model noise prediction loss, the potential function constraint term, and the performance index physical constraint term. Its expression is: in, For noise prediction loss in the diffusion model, For potential function constraint terms, For physical constraints of performance indicators, and These are the weighting coefficients.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1-6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-6.

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