A Dynamic Prediction Method for Anti-dyeing Zones in Dark-Colored Pure Cotton Fabrics Based on Dye Diffusion Model

Abstract

This invention relates to the field of computer-aided engineering technology, specifically a method for dynamically predicting the stain-resistant area of ​​dark-colored pure cotton fabric based on a dye diffusion model. The method acquires a parameter dataset characterizing the fabric's microstructure, dye properties, and printing process. Based on this, a multi-scale coupled mathematical model is constructed to predict the dye diffusion range. The model decomposes the diffusion process into macroscopic inter-yarn diffusion and microscopic intra-fiber diffusion, using anisotropic diffusion tensors to characterize the difference in dye diffusion rates along the fabric direction. Through structure-aware finite element analysis, the model calculates the spatiotemporal concentration distribution of the dye and generates geometric data for predicting the stain-resistant boundary based on a preset concentration threshold. Based on this data, the printing process parameters and model parameters are adaptively adjusted to achieve dynamic prediction of the stain-resistant area. This method utilizes computer simulation and finite element analysis techniques to improve the accuracy of dynamic prediction of the stain-resistant area on dark-colored pure cotton fabric.

Description

Technical Field

[0001] This invention relates to the field of computer-aided engineering technology, specifically to a method for dynamic prediction of anti-dyeing areas in dark-colored pure cotton fabrics based on a dye diffusion model. Background Technology

[0002] Traditional dyeing processes rely mainly on experience or static models, making it difficult to adapt in real time to complex fabric structures, changes in dye concentration, and the influence of environmental factors. This results in insufficient prediction accuracy of the resist zone. In addition, traditional technologies rarely optimize from the perspective of computational modeling and dynamic prediction.

[0003] In recent years, computer-aided engineering technology has gradually emerged in the textile field, especially in physics-based simulation and data-driven predictive modeling. By introducing mathematical models of dye diffusion and real-time calculation methods, theoretical support is provided for the accurate prediction of anti-dyeing zones. However, existing technologies cannot dynamically and accurately predict the boundary changes of anti-dyeing zones, and there are still shortcomings in real-time calculation optimization, making it difficult to meet the needs of high precision and efficiency in industrial production.

[0004] To address this, a dynamic prediction method for the anti-dyeing zone of dark-colored pure cotton fabric based on a dye diffusion model is proposed. Summary of the Invention

[0005] The purpose of this invention is to provide a method for dynamic prediction of anti-dyeing areas in dark-colored pure cotton fabrics based on a dye diffusion model.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for dynamic prediction of anti-dyeing zones in dark-colored pure cotton fabrics based on a dye diffusion model includes:

[0008] Obtain a parameter dataset for characterizing fabric microstructure, dye properties, and printing process, including: fabric parameters, dye parameters, and printing process parameters;

[0009] Based on the parameter dataset, a multi-scale coupled mathematical model is constructed for diffusion range prediction. The multi-scale coupled mathematical model mathematically decomposes the dye diffusion process into a macro-scale inter-yarn percolation diffusion process and a micro-scale intra-fiber diffusion process. An anisotropic diffusion tensor is used to characterize the difference in the diffusion rate of dye along different directions of the fabric in the model.

[0010] The multi-scale coupled mathematical model is run, and the spatiotemporal concentration distribution of dye in the digital model is calculated based on structure-aware finite element analysis. Based on the spatiotemporal concentration distribution calculated by simulation and according to the preset concentration threshold, the geometric data of the predicted bleeding boundary is determined. Based on the geometric data of the predicted bleeding boundary, the printing process parameters and the parameters of the multi-scale coupled mathematical model are adaptively adjusted.

[0011] Furthermore, the fabric parameters include the yarn arrangement density in the warp and weft directions, yarn diameter, fabric porosity, tortuosity, and weaving structure; the dye parameters include the amount, viscosity, surface tension, and concentration of the dye; and the printing process parameters include the amount of dye paste applied, pressure, and temperature.

[0012] Furthermore, the process of constructing a multi-scale coupled mathematical model includes:

[0013] At the macro scale, the Richards equation is used to model the capillary-driven percolation diffusion process between yarns based on the porosity, tortuosity and weave structure of the fabric.

[0014] At the microscale, Fick's second law is used to model the process of dye penetration and fixation into the interior of a single fiber, where the dye concentration boundary condition on the fiber surface is dynamically provided by the macroscale percolation diffusion process.

[0015] Through a two-way coupling mechanism, the macroscopic fluid saturation is used as the boundary condition at the microscopic scale, while the microscopic fiber absorption rate is used as the sink term at the macroscopic scale, thus achieving mathematical coupling between macroscopic seepage and microscopic diffusion.

[0016] An anisotropic diffusion tensor is introduced to characterize the differences in the diffusion rate of dye along different directions of the fabric in a multi-scale coupled mathematical model.

[0017] Furthermore, the process of introducing the anisotropic diffusion tensor includes:

[0018] Construct a 3×3 anisotropic diffusion tensor, where the main diagonal elements represent the diffusion coefficients along the warp, weft, and thickness directions of the fabric, respectively, and the off-diagonal elements represent the coupling effects between different directions;

[0019] Based on the fabric parameters in the parameter dataset, the initial value of the anisotropic diffusion tensor is determined to predict the non-circular bleeding regions formed by dye diffusion.

[0020] The anisotropic diffusion tensor is embedded into a multi-scale coupled mathematical model and combined with structure-aware grid technology for finite element analysis.

[0021] Furthermore, the process of running the multi-scale coupled mathematical model and calculating the spatiotemporal concentration distribution of the dye in the digital model based on structure-aware finite element analysis includes:

[0022] Based on the warp and weft direction information of the fabric, a structure-aware non-uniform finite element mesh is generated;

[0023] The macroscopic seepage equation and microscopic diffusion equation in the multi-scale coupled mathematical model are combined with the anisotropic diffusion tensor and transformed into a set of discretized equations on the structure-aware grid.

[0024] The discretized equations are calculated using numerical methods to obtain the spatiotemporal concentration distribution of the dye in the digital model.

[0025] Furthermore, the process of determining the geometric data of the predicted bleeding boundary based on the spatiotemporal concentration distribution calculated by simulation and according to a preset concentration threshold includes:

[0026] From the finite element analysis results of the multi-scale coupled mathematical model, the concentration distribution data of the dye with time and space variation are extracted, and a preset concentration threshold is defined.

[0027] Identify all grid nodes whose concentration values ​​are equal to or greater than the concentration threshold to form the boundary point set of the bleeding region;

[0028] Geometric fitting is performed on the boundary point set to generate a smooth predicted bleed boundary curve, and the corresponding geometric data is output.

[0029] Furthermore, based on the geometric data of the predicted bleeding boundary, the process of adaptively adjusting the printing process parameters and the parameters of the multi-scale coupled mathematical model includes:

[0030] A compensation vector field is generated based on the geometric data of the predicted bleeding boundary.

[0031] Based on the compensation vector field, an optimized compensation profile is generated to adjust the printing process parameters;

[0032] The actual bleeding boundary is extracted using machine vision algorithms, compared with the predicted bleeding boundary, and the geometric error is calculated.

[0033] Based on the aforementioned geometric error, a reverse optimization algorithm is used to adjust the parameters of the multi-scale coupled mathematical model.

[0034] The adjusted printing process parameters and model parameters are re-input into the multi-scale coupled mathematical model, and iteratively run to optimize the next round of bleeding boundary prediction.

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0036] 1. By integrating a multi-scale coupling model and anisotropic diffusion tensor, a comprehensive modeling of everything from macroscopic yarn structure to microscopic fiber behavior is achieved, while also considering the influence of fabric orientation differences on diffusion. This comprehensive modeling method not only improves the physical realism of the simulation results but also significantly enhances the model's adaptability to complex fabric systems, thereby improving the accuracy of dynamic prediction of anti-dyeing areas in dark cotton fabrics.

[0037] 2. By generating a structure-aware non-uniform finite element mesh based on the warp and weft information of the fabric, and discretizing the macroscopic seepage equation and the microscopic diffusion equation, and combining the anisotropic diffusion tensor for numerical solution, the spatiotemporal concentration distribution of dye in the digital model can be calculated efficiently. This method makes full use of the geometric characteristics of the fabric structure, improves the spatial resolution and computational efficiency of the simulation results, and the extracted dynamic concentration data provides accurate input for subsequent boundary prediction, enhances the robustness and practicality of the entire simulation system, and thus improves the accuracy of dynamic prediction of the anti-dyeing area of ​​pure cotton dark fabric.

[0038] 3. By generating a compensation vector field based on the predicted boundary geometric data and using machine vision algorithms to compare the actual and predicted boundaries to calculate the geometric error, combined with a back-optimization algorithm to adjust the model and process parameters, iterative optimization of the simulation model was achieved. This adaptive adjustment mechanism can continuously improve the model's prediction accuracy, reduce the deviation between simulation and actual results, and thus improve the accuracy of dynamic prediction of the anti-dyeing area of ​​dark cotton fabric. Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating the dynamic prediction method for anti-dyeing areas of dark-colored pure cotton fabric based on a dye diffusion model according to the present invention.

[0040] Figure 2 This is a schematic diagram of the structure of the multi-scale coupled mathematical model of the present invention;

[0041] Figure 3 This is a flowchart illustrating the process of adjusting printing parameters according to the present invention. Detailed Implementation

[0042] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0043] Please see Figures 1 to 3 This invention provides a method for dynamic prediction of anti-dyeing areas in dark-colored pure cotton fabrics based on a dye diffusion model. The technical solution is as follows:

[0044] Example 1:

[0045] To improve product quality, a company used the proposed method for dynamic prediction of stain-resistant areas on dark-colored pure cotton fabrics based on a dye diffusion model. The flowchart of this method is shown below. Figure 1 As shown, the details are as follows:

[0046] Obtain a parameter dataset for characterizing fabric microstructure, dye properties, and printing process, including: fabric parameters, dye parameters, and printing process parameters;

[0047] Furthermore, the fabric parameters and dye parameters are obtained by directly calling the internal process parameter library and dye formula library; the printing process parameters are obtained by sensor data acquisition.

[0048] Furthermore, fabric parameters include warp and weft yarn arrangement density, yarn diameter, fabric porosity, tortuosity, and weave structure; dye parameters include dye amount, viscosity, surface tension, and concentration; printing process parameters include pigment application amount, pressure, and temperature.

[0049] Furthermore, the parameter dataset is preprocessed, including denoising, normalization, and outlier detection. The denoising process uses median filtering. Min-Max normalization is used to linearly scale the denoised data to the range [0, 1]. The DBSCAN clustering algorithm is used to analyze the normalized data and identify outliers. This operation can further improve the prediction accuracy of subsequent models.

[0050] By using fabric parameters, dye parameters, and printing process parameters, comprehensive and accurate input data is provided for the multi-scale coupled mathematical model. These parameters cover multiple dimensions of fabric microstructure, dye physical properties, and process conditions, ensuring that the model can accurately reflect the physical characteristics of the actual dye diffusion process, thereby improving the accuracy of dynamic prediction of anti-dyeing areas on dark cotton fabrics.

[0051] Based on the parameter dataset, a multi-scale coupled mathematical model is constructed for diffusion range prediction. The multi-scale coupled mathematical model mathematically decomposes the dye diffusion process into a macro-scale inter-yarn percolation diffusion process and a micro-scale intra-fiber diffusion process. An anisotropic diffusion tensor is used to characterize the difference in the diffusion rate of dye along different directions of the fabric in the model.

[0052] Furthermore, the structure of the multi-scale coupled mathematical model is as follows: Figure 2 As shown, its construction process includes:

[0053] At the macro scale, the Richards equation is used to model the capillary-driven percolation diffusion process between yarns based on the porosity, tortuosity and weave structure of the fabric.

[0054] At the microscale, Fick's second law is used to model the process of dye penetration and fixation into the interior of a single fiber, where the dye concentration boundary condition on the fiber surface is dynamically provided by the macroscale percolation diffusion process.

[0055] Through a two-way coupling mechanism, the macroscopic fluid saturation is used as the boundary condition at the microscopic scale, while the microscopic fiber absorption rate is used as the sink term at the macroscopic scale, thus achieving mathematical coupling between macroscopic seepage and microscopic diffusion.

[0056] An anisotropic diffusion tensor is introduced to characterize the differences in the diffusion rate of dye along different directions of the fabric in a multi-scale coupled mathematical model.

[0057] Furthermore, the Richards equation is used to describe the unsaturated flow process of pigment in the gaps between yarns driven by capillary action. The left side of the Richards equation is the rate of change of pigment saturation over time, and the right side consists of the anisotropic conductivity tensor, the gradient of capillary force and gravity, and the sink term. Among them, the anisotropic conductivity tensor reflects the fabric's ability to transport liquid in different directions, that is, it characterizes the difference in the diffusion rate of liquid along different directions of the fabric. Therefore, the anisotropic conductivity tensor is represented by the anisotropic diffusion tensor.

[0058] Furthermore, Fick's second law equation is used to describe the process by which dye penetrates into the interior of a single fiber and forms a chemical bond with it; the left side of Fick's second law equation is the rate of change of dye concentration inside the fiber with time, and the right side is represented by the divergence between the dye concentration gradient and the diffusion coefficient.

[0059] By constructing a multi-scale coupled mathematical model, dye diffusion is decomposed into macro-scale inter-yarn percolation and micro-scale intra-fiber diffusion. The Richards equation and Fick's second law are used to model these processes respectively. By combining a two-way coupling mechanism and anisotropic diffusion tensor, an accurate description of dye diffusion behavior in complex fabric systems is achieved. This multi-scale modeling method can comprehensively consider the cross-scale interaction between fabric structure and dye behavior, significantly improving the model's ability to simulate non-uniform diffusion processes and providing high-precision theoretical support for predicting dye diffusion boundaries.

[0060] Furthermore, the process of introducing the anisotropic diffusion tensor includes:

[0061] Construct a 3×3 anisotropic diffusion tensor, where the main diagonal elements represent the diffusion coefficients along the warp, weft, and thickness directions of the fabric, respectively, and the off-diagonal elements represent the coupling effects between different directions;

[0062] Based on the fabric parameters in the parameter dataset, the initial value of the anisotropic diffusion tensor is determined to predict the non-circular bleeding regions formed by dye diffusion.

[0063] Anisotropic diffusion tensors are embedded into multi-scale coupled mathematical models and combined with structure-aware grid technology for finite element analysis and solution.

[0064] Furthermore, the diffusion coefficients in the warp, weft, and thickness directions are directly proportional to the corresponding porosity and inversely proportional to the corresponding tortuosity; the off-diagonal elements are related to the fabric type. For plain weave fabrics, they are initially set to zero or close to zero; for non-plain weave fabrics, they are composed of the coupling coefficient, the sine of the yarn interlacing angle, and the square root of the product of the warp and weft diffusion coefficients.

[0065] Furthermore, ensure that the diffusion coefficient in the thickness direction of the anisotropic diffusion tensor is less than the diffusion coefficients in the meridional and latitudinal directions, while maintaining symmetry and positive definiteness.

[0066] Furthermore, the fabrics produced in actual production have uncertainties in their microstructure, such as random pore distribution and uneven yarn thickness. Therefore, a random field model is introduced in the mathematical modeling process. Specifically, the diffusion coefficients in the warp, weft, and thickness directions, which are related to structural parameters such as porosity and tortuosity, are defined as Gaussian random fields. The Karhunen-Loève expansion method is used to process the Gaussian random fields to generate multiple random samples of anisotropic diffusion tensors. The random field samples are then embedded into a multi-scale coupled model for subsequent processing to provide uncertainty quantification for boundary prediction, thereby generating a more realistic dye penetration boundary distribution.

[0067] By introducing anisotropic diffusion tensors and combining them with fabric parameter initialization, the differences in dye diffusion rates and interdirectional coupling effects in the warp, weft, and thickness directions of the fabric can be characterized. Embedding the tensors into a multi-scale model and combining them with structure-aware mesh technology further improves the computational accuracy and efficiency of finite element analysis, providing key technical support for accurately predicting dye diffusion boundaries.

[0068] Run a multi-scale coupled mathematical model and calculate the spatiotemporal concentration distribution of dye in the digital model based on structure-aware finite element analysis;

[0069] Furthermore, the process of running a multi-scale coupled mathematical model and calculating the spatiotemporal concentration distribution of dye in the digital model based on structure-aware finite element analysis includes:

[0070] Based on the warp and weft direction information of the fabric, a structure-aware non-uniform finite element mesh is generated;

[0071] The macroscopic seepage equation and microscopic diffusion equation in the multi-scale coupled mathematical model are combined with the anisotropic diffusion tensor and transformed into a set of discretized equations on the structure-sensing grid.

[0072] Numerical solution methods were used to calculate the discretized equation set and obtain the spatiotemporal concentration distribution of the dye in the digital model.

[0073] Furthermore, the generation process of the structure-aware non-uniform finite element mesh includes: importing the three-dimensional geometric model of the fabric region to be analyzed from CAD software and defining the material orientation of the fabric, namely the principal axis directions of the warp and weft directions; defining an anisotropic size field to divide different mesh elements according to the difference in diffusion rate, wherein the anisotropic size field is the inverse mapping of the anisotropic diffusion tensor; and using a mesh generation algorithm that supports anisotropic metric fields, such as the leading edge method, to output a non-uniform finite element mesh.

[0074] Furthermore, the finite element method is used in conjunction with a time-stepping algorithm to solve the discretized equation system. Then, an iterative solver is used to accelerate the convergence of the nonlinear equation system. The iterative solver can apply the conjugate gradient method or the multigrid method. Next, regularization techniques are introduced during the iterative solution process to prevent numerical instability.

[0075] Furthermore, since the generated non-uniform mesh remains static throughout the simulation, it cannot adapt to the dynamic characteristics of concentration gradient or boundary changes during dye diffusion. Therefore, adaptive mesh optimization and dynamic re-meshing techniques are used in the finite element analysis to dynamically adjust the mesh density. The process includes: using the posterior error estimation method to evaluate the calculation error of the concentration distribution and marking high-error regions with large concentration gradients; then, using the adaptive mesh re-meshing algorithm to dynamically adjust the mesh density and using the leading edge method to regenerate the non-uniform mesh. This enables the mesh to adapt to the real-time dynamic diffusion process and improves the accuracy of subsequent boundary prediction.

[0076] By generating a structure-aware non-uniform finite element mesh based on the warp and weft information of the fabric, and discretizing the macroscopic seepage equation and the microscopic diffusion equation, and combining the anisotropic diffusion tensor for numerical solution, the spatiotemporal concentration distribution of dye in the digital model can be calculated efficiently. This method makes full use of the geometric characteristics of the fabric structure, improves the spatial resolution and computational efficiency of the simulation results, and the extracted dynamic concentration data provides accurate input for subsequent boundary prediction.

[0077] Based on the spatiotemporal concentration distribution calculated by simulation and according to the preset concentration threshold, the geometric data of the predicted bleeding boundary are determined; based on the geometric data of the predicted bleeding boundary, the printing process parameters and the parameters of the multi-scale coupled mathematical model are adaptively adjusted.

[0078] Furthermore, the process of determining the geometric data of the predicted bleeding boundary based on the spatiotemporal concentration distribution calculated by simulation and according to a preset concentration threshold includes:

[0079] From the finite element analysis results of the multi-scale coupled mathematical model, the concentration distribution data of the dye with time and space variation are extracted, and a preset concentration threshold is defined.

[0080] Identify all grid nodes with concentration values ​​equal to or greater than the concentration threshold to form the boundary point set of the infiltration region;

[0081] Geometric fitting is performed on the boundary point set to generate a smooth predicted bleeding boundary curve and output the corresponding geometric data.

[0082] Furthermore, the dye concentration value of each grid node at a preset time step is obtained from the finite element analysis results, and a three-dimensional dataset of concentration distribution is constructed based on it, including time, spatial coordinates and corresponding concentration values;

[0083] Furthermore, the preset concentration threshold represents the minimum concentration at which the dye produces visible color on the fabric surface. This threshold is determined based on the chemical properties of the dye, the optical properties of the fabric, and experience. Then, the concentration threshold is calibrated using standard color difference analysis to ensure that it is consistent with human visual perception.

[0084] Furthermore, Bézier curves are used to smooth the boundary point set of the bleeding area to generate a continuous boundary curve. Then, mesh topology analysis is performed on the fitted boundary curve to detect discontinuous points and topological defects in the boundary curve. Next, the Laplace smoothing algorithm is used to adjust the position of the boundary points in the boundary curve to reduce curvature fluctuations.

[0085] By extracting concentration distribution data from finite element analysis results, identifying boundary point sets based on preset concentration thresholds, and performing geometric fitting to generate smooth predicted dye diffusion boundary curves, the geometric characteristics of dye diffusion boundaries can be accurately described. The two-dimensional boundary contour mapped onto the fabric plane provides intuitive and operable output results for subsequent process verification. This method improves the accuracy of dynamic prediction of anti-dyeing areas in dark cotton fabrics.

[0086] Furthermore, based on the geometric data of the predicted bleeding boundary, the process of adaptively adjusting the printing process parameters and the parameters of the multi-scale coupled mathematical model includes:

[0087] A compensation vector field is generated based on the geometric data of the predicted bleeding boundary.

[0088] Based on the compensation vector field, an optimized compensation profile is generated to adjust the printing process parameters;

[0089] The actual bleeding boundary is extracted using machine vision algorithms, compared with the predicted bleeding boundary, and the geometric error is calculated.

[0090] Based on geometric errors, a reverse optimization algorithm is used to adjust the parameters of the multi-scale coupled mathematical model;

[0091] The adjusted printing process parameters and model parameters are re-input into the multi-scale coupled mathematical model and iteratively run to optimize the next round of bleeding boundary prediction.

[0092] Furthermore, the process of generating the compensation vector field includes: comparing the geometric data of the predicted diffusion boundary with the original design pattern data to calculate the diffusion offset of the boundary points; combining the principal direction of the anisotropic diffusion tensor to determine the compensation vector and applying Gaussian smoothing to it to generate the compensation vector field; and storing the compensation vector field as vector mesh data for subsequent boundary profile optimization.

[0093] Furthermore, the process of adjusting the printing process parameters is as follows: Figure 3 As shown, the process includes: obtaining the boundary point set of the original design pattern and applying a compensation vector field to it for non-uniform displacement to generate a new boundary point set; using the NURBS algorithm to smoothly fit the new boundary point set to generate an optimized compensation contour curve; determining the maximum shrinkage distance based on the shrinkage distance distribution of the compensation contour relative to the original design boundary; and adjusting the printing process parameters by weighting based on the maximum shrinkage distance.

[0094] Furthermore, the surface images of the printed finished products actually acquired by the industrial camera are preprocessed, including grayscale conversion, Gaussian filtering, and adaptive contrast enhancement; then, edge detection and contour extraction algorithms are applied to the preprocessed images to extract the two-dimensional contours of the actual bleeding boundary, which are used for the calculation of geometric errors.

[0095] Furthermore, based on geometric errors, the process of adjusting the parameters of the multi-scale coupled mathematical model using a reverse optimization algorithm is as follows: An optimization objective function is constructed, including the sum of squared geometric errors and a regularization term; the regularization term calculates the L1 norm of the difference between the model parameters and the initialization parameters to prevent the parameters from deviating from the physical range; the parameters are iterated using gradient descent to minimize the objective function, and physical constraints are applied during the iteration process, including the physical range of fabric porosity, the range of fiber saturation absorption rate, and the range of the main diagonal elements of the anisotropic diffusion tensor;

[0096] Furthermore, in the process of using the NURBS algorithm for compensating contour fitting, only the information of boundary points is considered, ignoring the visual impact caused by texture loss. Therefore, a convolutional neural network is used to extract the texture features of the original design pattern and the pattern after shrinking, generating their respective multi-scale features. Based on the multi-scale features, the visual bias loss is calculated to predict the visual impact of shrinking on texture features. Then, the gradient descent method is used to balance the visual bias loss and the maximum shrinking distance, and the NURBS control points are adjusted to optimize the compensating contour while preserving texture details and improving product quality.

[0097] By generating a compensation vector field based on the geometric data of the predicted dye diffusion boundary, and using machine vision algorithms to compare the actual and predicted boundaries to calculate the geometric error, combined with the inverse optimization algorithm to adjust the model and process parameters, the simulation model is iteratively optimized. This adaptive adjustment mechanism can continuously improve the prediction accuracy of the model, reduce the deviation between simulation and actual results, thereby improving the reliability and process adaptability of dye diffusion boundary prediction, and providing a dynamic optimization technical guarantee for high-precision printing process design.

[0098] Example 2:

[0099] This embodiment takes the optimization of the printing process for producing dark-colored pure cotton T-shirts by a textile company as an example. The specific process is as follows:

[0100] Obtain a parameter dataset for characterizing the fabric microstructure, dye properties, and printing process, including: fabric parameters, dye parameters, and printing process parameters.

[0101] To optimize the anti-dyeing area of ​​the floral pattern on the chest of T-shirts, the company first collected data from its internal process parameter library, dye formula library, and real-time sensors to obtain a parameter dataset that characterizes the fabric microstructure, dye properties, and printing process.

[0102] The reference fabric parameters are as follows: yarn diameter 0.2mm, porosity 0.35, tortuosity 1.15, and standard plain weave structure; the reference dye parameters are as follows: dosage 50g / m², surface tension 0.03N / m, and initial concentration 0.1mol / L; the reference printing process parameters are as follows: pigment application amount 80g / m², printing pressure 0.3MPa, and temperature 60℃.

[0103] Based on the parameter dataset, a multi-scale coupled mathematical model is constructed for diffusion range prediction. This model mathematically decomposes the dye diffusion process into a macroscopic inter-yarn percolation diffusion process and a microscopic intra-fiber diffusion process. An anisotropic diffusion tensor is used to characterize the differences in dye diffusion rates along different directions of the fabric in the model.

[0104] Based on the fabric porosity, tortuosity, and plain weave structure, the Richards equation is used to simulate the inter-yarn percolation diffusion driven by capillary action, and Fick's second law is used to simulate the penetration and fixation of dye into the fiber interior. The macroscopic pigment saturation is used as the microscopic boundary condition, and the microscopic fiber absorption rate is used as the macroscopic sum term to achieve the mathematical coupling between the macroscopic and microscopic.

[0105] Construct a 3×3 anisotropic diffusion tensor, where the main diagonal elements represent the diffusion coefficients in the longitudinal, latitudinal, and thickness directions, respectively, with initial values ​​of 0.0012 m² / s, 0.0010 m² / s, and 0.0005 m² / s, respectively, and the off-diagonal elements are set to zero.

[0106] A multi-scale coupled mathematical model is run, and based on structure-aware finite element analysis, the spatiotemporal concentration distribution of dye in the digital model is calculated. Based on the simulated spatiotemporal concentration distribution and according to a preset concentration threshold, the geometric data of the predicted bleeding boundary are determined. Based on the geometric data of the predicted bleeding boundary, the printing process parameters and the parameters of the multi-scale coupled mathematical model are adaptively adjusted.

[0107] Import the 3D geometric model of the T-shirt fabric area into CAD software and define the principal axes of the warp and weft directions; based on the inverse mapping of the anisotropic diffusion tensor, generate a non-uniform finite element mesh, reduce the mesh size to 0.05mm at the pattern boundary, and 0.1mm in the high diffusion region.

[0108] The Richards equations and Fick's second law are combined with the diffusion tensor to transform the system into a discrete set of equations on a grid, which is then solved using the conjugate gradient method. Regularization techniques are also introduced to ensure numerical stability.

[0109] Regions with large concentration gradients were marked using the posterior error estimation method, and the mesh was dynamically re-divided using the leading edge method to adapt to the dynamic changes in dye diffusion. The analysis results showed that the concentration gradient at the edge of the floral pattern was high, indicating a risk of dye bleeding.

[0110] Concentration distribution is extracted from finite element results, and a concentration threshold of 0.02 mol / L is set. Grid nodes with concentrations greater than or equal to 0.02 mol / L are identified to form a boundary point set. The boundary point set is smoothed by interpolation using Bézier curves to generate a continuous boundary curve. The curvature is then optimized using a Laplace smoothing algorithm to output a two-dimensional boundary profile. The predicted characteristics of the bleed boundary are as follows: the shape is non-circular, with a longitudinal diffusion of 2.5 mm, a latitudinal diffusion of 2.0 mm, and a thickness diffusion of 0.8 mm.

[0111] The NURBS algorithm is used to apply a 1.5mm inward displacement to the boundary point set of the original pattern to generate an optimized compensation profile. Based on the inward distance distribution of the optimized compensation profile relative to the original design boundary, the printing process parameters are adjusted as follows: the amount of pigment is reduced to 70g / m², the pressure is reduced to 0.25MPa, and the temperature is maintained at 60℃.

[0112] Images of printed products are acquired using an industrial camera. The actual boundaries are extracted through grayscale conversion, Gaussian filtering, and edge detection, and compared with the predicted boundaries. The average geometric error is calculated to be 0.3 mm. An objective function is constructed, and the model parameters are adjusted using the gradient descent method. The adjusted parameters are then re-inputted into the model. After five iterations, the prediction error is reduced to within 0.1 mm.

[0113] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for dynamic prediction of anti-dyeing areas in dark-colored pure cotton fabric based on a dye diffusion model, characterized in that, include: Obtain a parameter dataset for characterizing fabric microstructure, dye properties, and printing process, including: fabric parameters, dye parameters, and printing process parameters; Based on the parameter dataset, a multi-scale coupled mathematical model is constructed for diffusion range prediction. The multi-scale coupled mathematical model mathematically decomposes the dye diffusion process into a macro-scale inter-yarn percolation diffusion process and a micro-scale intra-fiber diffusion process. An anisotropic diffusion tensor is used to characterize the difference in the diffusion rate of dye along different directions of the fabric in the model. The process of constructing a multi-scale coupled mathematical model includes: At the macro scale, the Richards equation is used to model the capillary-driven percolation diffusion process between yarns based on the porosity, tortuosity and weave structure of the fabric. At the microscale, Fick's second law is used to model the process of dye penetration and fixation into the interior of a single fiber, where the dye concentration boundary condition on the fiber surface is dynamically provided by the macroscale percolation diffusion process. Through a two-way coupling mechanism, the macroscopic fluid saturation is used as the boundary condition at the microscopic scale, while the microscopic fiber absorption rate is used as the sink term at the macroscopic scale, thus achieving mathematical coupling between macroscopic seepage and microscopic diffusion. An anisotropic diffusion tensor is introduced to characterize the differences in the diffusion rate of dye along different directions of the fabric in a multi-scale coupled mathematical model. A multi-scale coupled mathematical model is run, and the spatiotemporal concentration distribution of dye in the digital model is calculated based on structure-aware finite element analysis. Based on the spatiotemporal concentration distribution calculated by simulation and according to the preset concentration threshold, the geometric data of the predicted bleeding boundary is determined. Based on the geometric data of the predicted bleeding boundary, the printing process parameters and the parameters of the multi-scale coupled mathematical model are adaptively adjusted.

2. The method for dynamic prediction of anti-dyeing areas in dark-colored pure cotton fabric based on a dye diffusion model according to claim 1, characterized in that, The fabric parameters include warp and weft yarn arrangement density, yarn diameter, fabric porosity, tortuosity, and weave structure; the dye parameters include dye amount, viscosity, surface tension, and concentration; and the printing process parameters include pigment application amount, pressure, and temperature.

3. The method for dynamic prediction of anti-dyeing areas in dark-colored pure cotton fabric based on a dye diffusion model according to claim 1, characterized in that, The process of introducing the anisotropic diffusion tensor includes: Construct a 3×3 anisotropic diffusion tensor, where the main diagonal elements represent the diffusion coefficients along the warp, weft, and thickness directions of the fabric, respectively, and the off-diagonal elements represent the coupling effects between different directions; Based on the fabric parameters in the parameter dataset, the initial value of the anisotropic diffusion tensor is determined to predict the non-circular bleeding regions formed by dye diffusion. The anisotropic diffusion tensor is embedded into a multi-scale coupled mathematical model and combined with structure-aware grid technology for finite element analysis.

4. The method for dynamic prediction of anti-dyeing areas in dark-colored pure cotton fabric based on a dye diffusion model according to claim 1, characterized in that, Running the multi-scale coupled mathematical model, the process of calculating the spatiotemporal concentration distribution of the dye in the digital model based on structure-aware finite element analysis includes: Based on the warp and weft direction information of the fabric, a structure-aware non-uniform finite element mesh is generated; The macroscopic seepage equation and microscopic diffusion equation in the multi-scale coupled mathematical model are combined with the anisotropic diffusion tensor and transformed into a set of discretized equations on the structure-aware grid. The discretized equations are calculated using numerical methods to obtain the spatiotemporal concentration distribution of the dye in the digital model.

5. The method for dynamic prediction of anti-dyeing areas in dark-colored pure cotton fabric based on a dye diffusion model according to claim 1, characterized in that, The process of determining the geometric data of the predicted bleeding boundary based on the spatiotemporal concentration distribution calculated by simulation and according to the preset concentration threshold includes: From the finite element analysis results of the multi-scale coupled mathematical model, the concentration distribution data of the dye with time and space variation are extracted, and a preset concentration threshold is defined. Identify all grid nodes whose concentration values ​​are equal to or greater than the concentration threshold to form the boundary point set of the bleeding region; Geometric fitting is performed on the boundary point set to generate a smooth predicted bleed boundary curve, and the corresponding geometric data is output.

6. The method for dynamic prediction of anti-dyeing areas in dark-colored pure cotton fabric based on a dye diffusion model according to claim 1, characterized in that, The process of adaptively adjusting the printing process parameters and the parameters of the multi-scale coupled mathematical model based on the geometric data of the predicted bleeding boundary includes: A compensation vector field is generated based on the geometric data of the predicted bleeding boundary. Based on the compensation vector field, an optimized compensation profile is generated to adjust the printing process parameters; The actual bleeding boundary is extracted using machine vision algorithms, compared with the predicted bleeding boundary, and the geometric error is calculated. Based on the aforementioned geometric error, a reverse optimization algorithm is used to adjust the parameters of the multi-scale coupled mathematical model. The adjusted printing process parameters and model parameters are re-input into the multi-scale coupled mathematical model, and iteratively run to optimize the next round of bleeding boundary prediction.

Images