Dynamic prediction method for dye-resistant area of pure cotton dark-color fabric based on dye diffusion model

Abstract

The invention relates to the technical field of computer-aided engineering, in particular to a pure cotton dark-color fabric dye-resistant area dynamic prediction method based on a dye diffusion model. The method comprises the following steps: acquiring a parameter data set representing a fabric microstructure, dye properties and a printing process; on the basis, a multi-scale coupling mathematical model is constructed, the dye diffusion range is predicted, the diffusion process is decomposed into seepage diffusion between macroscopic yarns and diffusion in microcosmic fibers through the model, and the diffusion rate difference of the dye in the fabric direction is represented through anisotropic diffusion tensors; through finite element analysis of structure perception, running a model to calculate dye space-time concentration distribution, and generating geometric data for predicting a bleeding boundary according to a preset concentration threshold value; according to the data, printing process parameters and model parameters are adjusted in a self-adaptive mode, and dynamic prediction of the dye-resistant area is achieved; according to the method, computer simulation and finite element analysis technologies are utilized, and the accuracy of dynamic prediction of the dyeing-resistant area of the pure cotton dark-color fabric is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of computer-aided engineering, and in particular to a method for dynamically predicting the anti-dyeing area of ​​a pure cotton dark fabric based on a dye diffusion model. Background Art

[0002] Traditional dyeing processes rely primarily on empirical 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 for resist-dyeing areas. Furthermore, traditional technologies rarely incorporate optimization from the perspectives of computational modeling and dynamic prediction. 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 areas. However, existing technologies are unable to dynamically and accurately predict the boundary changes of anti-dyeing areas, and there are still deficiencies in real-time calculation optimization, making it difficult to meet the high precision and efficiency requirements of industrial production.

[0003] Therefore, a dynamic prediction method for the anti-dyeing area of ​​pure cotton dark fabrics based on the dye diffusion model was proposed. Summary of the Invention

[0004] The present invention aims to provide a method for dynamically predicting the anti-dyeing area of ​​pure cotton dark fabrics based on a dye diffusion model.

[0005] To achieve the above object, the present invention provides the following technical solutions: A dynamic prediction method for the anti-dyeing area of ​​pure cotton dark fabrics based on the dye diffusion model includes: Obtain parameter data sets for characterizing fabric microstructure, dye properties, and printing process, including fabric parameters, dye parameters, and printing process parameters; Based on the parameter data set, 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; and an anisotropic diffusion tensor is used to characterize the differences in dye diffusion rates along different directions of the fabric in the model; The multi-scale coupling mathematical model is run to calculate the spatiotemporal concentration distribution of the dye in the digital model based on structure-aware finite element analysis; based on the spatiotemporal concentration distribution calculated by simulation and according to a 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 multi-scale coupling mathematical model parameters are adaptively adjusted.

[0006] Furthermore, the fabric parameters include warp and weft yarn arrangement density, yarn diameter, fabric porosity, tortuosity and weaving structure; the dye parameters include dye quantity, viscosity, surface tension and concentration; the printing process parameters include color paste application amount, pressure and temperature.

[0007] Furthermore, the process of constructing a multi-scale coupled mathematical model includes: At the macroscale, the Richards equation is used to model the percolation and diffusion process between yarns driven by capillary action based on the porosity, tortuosity and weaving structure of the fabric. At the microscopic scale, Fick's second law is used to model the penetration and fixation of dyes into single fibers, where the boundary condition of dye concentration on the fiber surface is dynamically provided by the percolation-diffusion process at the macroscopic scale. Through a bidirectional 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 macroscopic sink term to mathematically couple macroscopic seepage and microscopic diffusion. The anisotropic diffusion tensor is introduced to characterize the differences in the diffusion rates of dyes along different directions of the fabric in the multi-scale coupled mathematical model.

[0008] Furthermore, the process of introducing the anisotropic diffusion tensor includes: A 3×3 anisotropic diffusion tensor is constructed, 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. determining an initial value of the anisotropic diffusion tensor based on fabric parameters in the parameter data set to predict a non-circular bleeding area formed by dye diffusion; The anisotropic diffusion tensor is embedded in a multi-scale coupled mathematical model and combined with structure-aware grid technology to perform finite element analysis and solution.

[0009] 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: Generate structure-aware non-uniform finite element mesh based on the warp and weft information of the fabric; The macroscopic seepage equation and the microscopic diffusion equation in the multi-scale coupled mathematical model are converted into a discretized set of equations on a structure-aware grid by combining the anisotropic diffusion tensor; The discretized equations are calculated using a numerical solution method to obtain the spatiotemporal concentration distribution of the dye in the digital model.

[0010] Furthermore, based on the spatiotemporal concentration distribution calculated by simulation and according to a preset concentration threshold, the process of determining the geometric data of the predicted bleeding boundary includes: Extracting concentration distribution data of the dye varying with time and space from the finite element analysis results of the multi-scale coupled mathematical model, and defining a preset concentration threshold; Identifying all grid nodes whose concentration values ​​are equal to or greater than the concentration threshold, forming a boundary point set of the bleeding area; Perform geometric fitting on the boundary point set to generate a smooth predicted color bleeding boundary curve and output the corresponding geometric data.

[0011] Furthermore, the process of adaptively adjusting the printing process parameters and the multi-scale coupling mathematical model parameters based on the geometric data of the predicted bleeding boundary includes: generating a compensation vector field based on geometric data of the predicted bleeding boundary; generating an optimized compensation profile according to the compensation vector field for adjusting printing process parameters; The actual bleeding boundary is extracted through machine vision algorithms, compared with the predicted bleeding boundary, and the geometric error is calculated; Based on the geometric error, an inverse optimization algorithm is used to adjust the parameters of the multi-scale coupling mathematical model; The adjusted printing process parameters and model parameters are re-input into the multi-scale coupled mathematical model and run iteratively to optimize the next round of bleeding boundary prediction.

[0012] Compared with the prior art, the present invention has the following beneficial effects: 1. By integrating a multiscale coupling model and anisotropic diffusion tensors, comprehensive modeling from macroscopic yarn structure to microscopic fiber behavior is achieved, while also considering the impact of fabric directional differences on diffusion. This integrated modeling approach 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 predictions for anti-dyeing areas on dark cotton fabrics.

[0013] 2. By generating a structure-aware non-uniform finite element mesh based on the warp and weft information of the fabric, discretizing the macroscopic seepage equation and the microscopic diffusion equation, and numerically solving them using the anisotropic diffusion tensor, the spatiotemporal concentration distribution of the dye in the digital model can be efficiently calculated. This method fully utilizes the geometric characteristics of the fabric structure, improving the spatial resolution and computational efficiency of the simulation results. The extracted dynamic concentration data provides precise input for subsequent boundary prediction, enhancing the robustness and practicality of the entire simulation system, thereby improving the accuracy of dynamic prediction of the anti-dyeing area of ​​pure cotton dark fabrics.

[0014] 3. By generating a compensation vector field based on the predicted boundary geometry data, using machine vision algorithms to compare the actual and predicted boundaries, calculating geometric errors, and combining them with an inverse optimization algorithm to adjust the model and process parameters, the simulation model is iteratively optimized. This adaptive adjustment mechanism continuously improves the model's prediction accuracy, reducing the deviation between simulation and actual results, thereby enhancing the accuracy of dynamic prediction of anti-dyeing areas on dark cotton fabrics. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Schematic diagram of the process of the method for dynamically predicting the anti-dyeing area of ​​dark-colored cotton fabrics based on the dye diffusion model of the present invention; Figure 2 Schematic diagram of the structure of the multi-scale coupling mathematical model of the present invention; Figure 3 The figure is a schematic diagram of the process of adjusting the printing process parameters according to the present invention. DETAILED DESCRIPTION

[0016] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0017] See also Figures 1 to 3 The present invention provides a method for dynamically predicting the anti-dyeing area of ​​pure cotton dark fabrics based on a dye diffusion model. The technical solution is as follows:

[0018] Example 1: In order to achieve dynamic prediction of the anti-dyeing area of ​​pure cotton dark fabrics and improve product quality, a certain enterprise used the dynamic prediction method of the anti-dyeing area of ​​pure cotton dark fabrics based on the dye diffusion model proposed in this invention. The process of this method is shown in the following figure: Figure 1 As shown, the details are as follows: Obtain parameter data sets for characterizing fabric microstructure, dye properties, and printing process, including fabric parameters, dye parameters, and printing process parameters; Furthermore, fabric parameters and dye parameters are obtained by directly calling the internal process parameter library and dye formula library; printing process parameters are obtained through sensor collection; Furthermore, fabric parameters include warp and weft yarn density, yarn diameter, fabric porosity, tortuosity, and weaving structure; dye parameters include dye quantity, viscosity, surface tension, and concentration; and printing process parameters include color paste application amount, pressure, and temperature. Furthermore, the parameter data set is preprocessed, including denoising, normalization, and outlier detection. The denoising process is processed using median filtering. Min-Max normalization is used to linearly scale the denoised data to the range of [0, 1]. The normalized data is analyzed using the DBSCAN clustering algorithm to identify outliers. This operation can further improve the prediction accuracy of subsequent models.

[0019] 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 the dynamic prediction of the anti-dyeing area of ​​pure cotton dark fabrics.

[0020] Based on the parameter data set, a multi-scale coupled mathematical model was constructed to predict the diffusion range. The multi-scale coupled mathematical model mathematically decomposes the dye diffusion process into the macro-scale inter-yarn percolation diffusion process and the micro-scale intra-fiber diffusion process. The anisotropic diffusion tensor was used to characterize the differences in the dye diffusion rate along different directions of the fabric in the model. Furthermore, the structure of the multi-scale coupling mathematical model is as follows Figure 2 As shown, the construction process includes: At the macroscale, the Richards equation is used to model the percolation and diffusion process between yarns driven by capillary action based on the porosity, tortuosity and weaving structure of the fabric. At the microscopic scale, Fick's second law is used to model the penetration and fixation of dyes into single fibers, where the boundary condition of dye concentration on the fiber surface is dynamically provided by the percolation-diffusion process at the macroscopic scale. Through a bidirectional 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 macroscopic sink term to mathematically couple macroscopic seepage and microscopic diffusion. The anisotropic diffusion tensor is introduced to characterize the difference in the diffusion rate of dye along different directions of fabric in the multi-scale coupled mathematical model. Furthermore, the Richards equation is used to describe the unsaturated flow of color paste in the spaces between yarns, driven by capillary action. The left side of the Richards equation represents the rate of change of color paste saturation over time, while the right side consists of the anisotropic hydraulic conductivity tensor, the gradients of the capillary force and gravity, and the sink term. The anisotropic hydraulic conductivity tensor reflects the fabric's ability to transport liquid in different directions, that is, it characterizes the differences in liquid diffusion rates along different directions of the fabric. Therefore, the anisotropic hydraulic conductivity tensor is represented by the anisotropic diffusion tensor. Furthermore, Fick's second law is used to describe the process by which a dye penetrates into a single fiber and chemically bonds with it. The left side of Fick's second law represents the rate of change of the dye concentration inside the fiber over time, while the right side represents the divergence of the dye concentration gradient and the diffusion coefficient. By constructing a multi-scale coupled mathematical model, dye diffusion is decomposed into macro-scale inter-yarn seepage and micro-scale intra-fiber diffusion, and the Richards equation and Fick's second law are used to model them separately. Combined with the bidirectional coupling mechanism and the anisotropic diffusion tensor, an accurate description of the 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 simulation ability of non-uniform diffusion processes and providing high-precision theoretical support for predicting dye diffusion boundaries.

[0021] Furthermore, the process of introducing the anisotropic diffusion tensor includes: A 3×3 anisotropic diffusion tensor is constructed, 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. According to the fabric parameters in the parameter data set, the initial value of the anisotropic diffusion tensor is determined to predict the non-circular bleeding area formed by dye diffusion; The anisotropic diffusion tensor is embedded into a multi-scale coupled mathematical model and combined with structure-aware grid technology to perform finite element analysis. Furthermore, the diffusion coefficients in the warp, weft, and thickness directions are proportional to the corresponding porosity and inversely proportional to the corresponding tortuosity; the off-diagonal element is related to the fabric type and is initially set to zero or close to zero for plain weave fabrics; for non-plain weave fabrics, it is composed of the coupling coefficient, the sine of the yarn interlacing angle, and the square root of the product of the diffusion coefficients in the warp and weft directions; Furthermore, the diffusion coefficient of the anisotropic diffusion tensor in the thickness direction is ensured to be smaller than that in the warp and weft directions, while maintaining symmetry and positive definiteness. Furthermore, the fabrics actually produced have microstructural uncertainties, such as random pore distribution and uneven yarn thickness. Therefore, a random field model is additionally introduced in the mathematical modeling process. Specifically, the diffusion coefficients in the warp, weft, and thickness directions related to structural parameters such as porosity and tortuosity are defined as Gaussian random fields; the Gaussian random field is processed using the Karhunen-Loève expansion method to generate random samples of multiple anisotropic diffusion tensors; the random field samples are embedded in a multi-scale coupling model for subsequent processing to provide uncertainty quantification of boundary predictions, thereby generating a more realistic color bleeding boundary distribution.

[0022] By introducing the anisotropic diffusion tensor and combining it with fabric parameter initialization, the differences in dye diffusion rates in the warp, weft and thickness directions of the fabric, as well as the coupling effects between directions, can be characterized. Embedding the tensor into a multi-scale model and combining it with structure-aware grid technology further improves the computational accuracy and efficiency of finite element analysis, providing key technical support for accurately predicting dye diffusion boundaries.

[0023] Run a multi-scale coupled mathematical model and calculate the spatiotemporal concentration distribution of the dye in the digital model based on structure-aware finite element analysis; Furthermore, the multi-scale coupled mathematical model is run, and the process of calculating the spatiotemporal concentration distribution of the dye in the digital model based on structure-aware finite element analysis includes the following: Generate structure-aware non-uniform finite element mesh based on the warp and weft information of the fabric; The macroscopic seepage equation and microscopic diffusion equation in the multi-scale coupled mathematical model are transformed into a discretized set of equations on a structure-aware grid by combining the anisotropic diffusion tensor. The numerical solution method is used to calculate the discretized equations and obtain the spatiotemporal concentration distribution of the dye in the digital model. Furthermore, the process of generating a structure-aware non-uniform finite element mesh includes: importing a 3D geometric model of the fabric area to be analyzed from CAD software and defining the fabric's material orientation, namely the principal axes of the warp and weft directions; defining an anisotropic size field to divide the mesh cells into different groups based on diffusion rate differences, where 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 front advancing method, to output a non-uniform finite element mesh. Furthermore, the finite element method is used in conjunction with a time-stepping algorithm to solve the discretized system of equations. An iterative solver is then used to accelerate the convergence of the nonlinear system of equations. The iterative solver can apply a conjugate gradient method or a multigrid method. Regularization techniques are then introduced into the iterative solution process to prevent numerical instabilities. Furthermore, since the generated non-uniform grid remains static throughout the entire simulation process, it cannot adapt to the dynamic characteristics of concentration gradients or boundary changes during the dye diffusion process; therefore, adaptive grid optimization and dynamic re-division technology are used in the finite element analysis process to dynamically adjust the grid density. The process includes: using the posterior error estimation method to evaluate the calculation error of the concentration distribution, and marking high-error areas with large concentration gradients; then, using the adaptive grid re-division algorithm to dynamically adjust the density of the grid, and using the frontier advancing method to regenerate the non-uniform grid, so that the grid can adapt to the real-time dynamic diffusion process and improve the subsequent boundary prediction accuracy.

[0024] By generating a structure-aware non-uniform finite element mesh based on the warp and weft information of the fabric, discretizing the macroscopic seepage equation and the microscopic diffusion equation, and numerically solving them using the anisotropic diffusion tensor, the spatiotemporal concentration distribution of the dye in the digital model can be efficiently calculated. This method fully utilizes 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 predictions.

[0025] 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 coupling mathematical model are adaptively adjusted.

[0026] Furthermore, based on the spatiotemporal concentration distribution calculated by simulation and according to a preset concentration threshold, the process of determining the geometric data of the predicted bleeding boundary includes: Extract the concentration distribution data of the dye over time and space from the finite element analysis results of the multi-scale coupled mathematical model, and define a preset concentration threshold; Identify all grid nodes whose concentration values ​​are equal to or greater than the concentration threshold, forming a set of boundary points of the bleeding area; Perform geometric fitting on the boundary point set to generate a smooth predicted color bleeding boundary curve and output the corresponding geometric data; 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 data set of concentration distribution is constructed based on it, including time, space coordinates and corresponding concentration values; Furthermore, a 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 characteristics of the fabric, and experience. This concentration threshold is then calibrated using standard color difference analysis to ensure consistency with human eye perception. Furthermore, a Bezier curve is used to smoothly interpolate the boundary point set of the bleeding area to generate a continuous boundary curve. Then, a grid topology analysis is performed on the fitted boundary curve to detect discontinuous points and topological defects in the boundary curve. Finally, a Laplace smoothing algorithm is used to adjust the position of the boundary points in the boundary curve to reduce curvature fluctuations.

[0027] 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 a smooth predicted bleeding boundary curve, the geometric characteristics of the dye diffusion boundary can be accurately described. The two-dimensional boundary contour mapped to the fabric plane provides intuitive and actionable output results for subsequent process verification. This method improves the accuracy of dynamic prediction of anti-dyeing areas in pure cotton dark fabrics.

[0028] Furthermore, the process of adaptively adjusting the printing process parameters and the multi-scale coupling mathematical model parameters based on the geometric data of the predicted bleeding boundary includes: generating a compensation vector field based on geometric data of the predicted bleeding boundary; Generate an optimized compensation profile based on the compensation vector field to adjust printing process parameters; The actual bleeding boundary is extracted through machine vision algorithms, compared with the predicted bleeding boundary, and the geometric error is calculated; Based on the geometric error, the inverse optimization algorithm is used to adjust the parameters of the multi-scale coupling mathematical model; The adjusted printing process parameters and model parameters are re-input into the multi-scale coupling mathematical model and run iteratively to optimize the next round of bleeding boundary prediction; Furthermore, the compensation vector field generation process includes: comparing the geometric data of the predicted bleed boundary with the original design pattern data to calculate the diffusion offset of the boundary point; combining the main direction of the anisotropic diffusion tensor to determine the compensation vector and apply Gaussian smoothing to it to generate the compensation vector field; storing the compensation vector field as vector grid data for subsequent use in boundary contour optimization; Further, the process of adjusting the printing process parameters is as follows Figure 3 As shown, the method includes: obtaining the boundary point set of the original design pattern and applying the compensation vector field to perform non-uniform displacement to generate a new boundary point set; using the NURBS algorithm to perform smooth fitting on the new boundary point set to generate an optimized compensation contour curve; determining the maximum indentation distance based on the distribution of the indentation distance of the compensation contour relative to the original design boundary; and performing weighted adjustment on the printing process parameters based on the maximum indentation distance; Furthermore, the surface images of the finished printed product, captured by the industrial camera, were preprocessed using grayscale conversion, Gaussian filtering, and adaptive contrast enhancement. Edge detection and contour extraction algorithms were then applied to the preprocessed images to extract the two-dimensional contours of the actual bleed boundary for use in geometric error calculation. Furthermore, based on the geometric error, an inverse optimization algorithm is used to adjust the parameters of the multi-scale coupling mathematical model 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 the gradient descent method to minimize the objective function, and physical constraints are imposed 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; Furthermore, in the process of using the NURBS algorithm to fit the compensating contour, only the information of the boundary points is paid attention to, and the visual impact caused by the lack of texture is ignored; therefore, a convolutional neural network is used to extract the texture features of the original design pattern and the indented pattern, and generate their respective multi-scale features; and based on the multi-scale features, the visual deviation loss is calculated to predict the visual impact of indentation on the texture features; then, the gradient descent method is used to balance the visual deviation loss and the maximum indentation distance, and the NURBS control points are adjusted to optimize the compensating contour while retaining the texture details, thereby improving product quality.

[0029] By generating a compensation vector field based on the geometric data of the predicted bleeding boundary, using a machine vision algorithm to compare the actual and predicted boundaries, calculating the geometric error, and combining the inverse optimization algorithm to adjust the model and process parameters, iterative optimization of the simulation model is achieved. This adaptive adjustment mechanism can continuously improve the prediction accuracy of the model and reduce the deviation between the simulation and actual results, thereby improving the reliability of the dye diffusion boundary prediction and process adaptability, providing a dynamic optimization technical guarantee for the design of high-precision printing processes.

[0030] Example 2: This embodiment takes the printing process optimization of a pure cotton dark T-shirt produced by a textile enterprise as an example, and the specific process is as follows: Obtain parameter data sets for characterizing fabric microstructure, dye properties, and printing process, including fabric parameters, dye parameters, and printing process parameters: To optimize the anti-dyeing area of ​​the floral pattern on the chest of the T-shirt, the company first collected data from the internal process parameter library, dye formula library and real-time sensors to obtain a parameter data set that characterizes the fabric microstructure, dye properties and printing process.

[0031] Among them, the reference fabric parameters are as follows: yarn diameter 0.2mm, porosity 0.35, tortuosity 1.15, weaving structure is standard plain weave, etc.; the reference dye parameters are as follows: dosage 50g / m², surface tension 0.03N / m, initial concentration 0.1mol / L, etc.; the reference printing process parameters are as follows: color paste application amount 80g / m², printing pressure 0.3MPa, temperature 60℃, etc.

[0032] Based on the parameter data set, a multi-scale coupled mathematical model was constructed to predict the diffusion range. The multi-scale coupled mathematical model mathematically decomposes the dye diffusion process into the macro-scale inter-yarn percolation diffusion process and the micro-scale intra-fiber diffusion process. The anisotropic diffusion tensor was used to characterize the differences in the diffusion rate of the dye along different directions of the fabric in the model: According to the porosity, tortuosity and plain weave structure of the fabric, the Richards equation is used to simulate the inter-yarn seepage and diffusion driven by capillary action, and Fick's second law is used to simulate the penetration and fixation of dyes into the fiber. The macroscopic color paste saturation is used as the microscopic boundary condition, and the microscopic fiber absorption rate is used as the macroscopic sink term to achieve mathematical coupling between the macro and micro.

[0033] A 3×3 anisotropic diffusion tensor is constructed. The main diagonal elements represent the diffusion coefficients in the longitudinal, latitudinal, and thickness directions, with initial values ​​of 0.0012 m² / s, 0.0010 m² / s, and 0.0005 m² / s, respectively. The off-diagonal elements are set to zero.

[0034] A multi-scale coupled mathematical model is run, and based on structure-aware finite element analysis, the spatiotemporal concentration distribution of the dye in the digital model is calculated. Based on the spatiotemporal concentration distribution calculated by simulation and a preset concentration threshold, the geometric data for predicting the bleeding boundary is determined. Based on the geometric data for the predicted bleeding boundary, the printing process parameters and the parameters of the multi-scale coupled mathematical model are adaptively adjusted: A 3D geometric model of the T-shirt fabric area was imported from CAD software, and the principal axes in the warp and weft directions were defined. A non-uniform finite element mesh was generated based on the inverse mapping of the anisotropic diffusion tensor. The mesh size was reduced to 0.05 mm at the pattern boundary and 0.1 mm in the high diffusion area.

[0035] The Richards equation and Fick's second law are combined with the diffusion tensor and transformed into a set of discrete equations on the grid. The conjugate gradient method is used to solve them, and regularization techniques are introduced to ensure numerical stability.

[0036] The areas with large concentration gradients are marked by the posterior error estimation method, and the frontier advancing method is used to dynamically re-divide the grid to adapt to the dynamic changes of dye diffusion; the operational analysis results show that the concentration gradient at the edge of the floral pattern is high, and there is a risk of color bleeding.

[0037] The concentration distribution was extracted from the finite element results, and the concentration threshold was set at 0.02 mol / L. Mesh nodes with concentrations greater than or equal to 0.02 mol / L were identified to form a boundary point set. The boundary point set was smoothly interpolated using Bezier curves to generate a continuous boundary curve. The curvature was then optimized using the Laplace smoothing algorithm to output a two-dimensional boundary contour. The relevant features of the predicted bleeding boundary were as follows: a non-circular shape, a longitudinal diffusion of 2.5 mm, a latitudinal diffusion of 2.0 mm, and a thickness diffusion of 0.8 mm.

[0038] A NURBS algorithm was used to apply a 1.5mm inward displacement to the boundary point set of the original pattern to generate an optimized compensation contour. Based on the distribution of the inward displacement of the optimized compensation contour relative to the original design boundary, the printing process parameters were adjusted as follows: the color paste volume was reduced to 70g / m², the pressure was reduced to 0.25MPa, and the temperature was maintained at 60°C.

[0039] The finished printed product image is captured by an industrial camera, and the actual boundary is extracted through grayscale conversion, Gaussian filtering and edge detection. The actual boundary is compared with the predicted boundary, and the average geometric error is calculated to be 0.3mm. The objective function is constructed, and the model parameters are adjusted using the gradient descent method. The adjusted parameters are re-entered into the model. After 5 iterations, the prediction error is reduced to within 0.1mm.

[0040] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A dynamic prediction method for the anti-dyeing area of ​​pure cotton dark fabrics based on a dye diffusion model, characterized in that: include: Obtain parameter data sets for characterizing fabric microstructure, dye properties, and printing process, including fabric parameters, dye parameters, and printing process parameters; Based on the parameter data set, 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; and an anisotropic diffusion tensor is used to characterize the differences in dye diffusion rates along different directions of the fabric in the model; The multi-scale coupling mathematical model is run to calculate the spatiotemporal concentration distribution of the dye in the digital model based on structure-aware finite element analysis; based on the spatiotemporal concentration distribution calculated by simulation and according to a 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 multi-scale coupling mathematical model parameters are adaptively adjusted.

2. The method for dynamically predicting the anti-dyeing area of ​​dark-colored cotton fabrics based on the 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 weaving structure; the dye parameters include dye quantity, viscosity, surface tension and concentration; the printing process parameters include color paste application amount, pressure and temperature.

3. The method for dynamically predicting the anti-dyeing area of ​​dark-colored cotton fabrics based on the dye diffusion model according to claim 1, characterized in that: The process of building a multi-scale coupled mathematical model includes: At the macroscale, the Richards equation is used to model the percolation and diffusion process between yarns driven by capillary action based on the porosity, tortuosity and weaving structure of the fabric. At the microscopic scale, Fick's second law is used to model the penetration and fixation of dyes into single fibers, where the boundary condition of dye concentration on the fiber surface is dynamically provided by the percolation-diffusion process at the macroscopic scale. Through a bidirectional 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 macroscopic sink term to mathematically couple macroscopic seepage and microscopic diffusion. The anisotropic diffusion tensor is introduced to characterize the differences in the diffusion rates of dyes along different directions of the fabric in the multi-scale coupled mathematical model.

4. The method for dynamically predicting the anti-dyeing area of ​​dark-colored cotton fabrics based on the dye diffusion model according to claim 3, characterized in that: The process of introducing the anisotropic diffusion tensor includes: A 3×3 anisotropic diffusion tensor is constructed, 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. determining an initial value of the anisotropic diffusion tensor based on fabric parameters in the parameter data set to predict a non-circular bleeding area formed by dye diffusion; The anisotropic diffusion tensor is embedded in a multi-scale coupled mathematical model and combined with structure-aware grid technology to perform finite element analysis and solution.

5. The method for dynamically predicting the anti-dyeing area of ​​dark-colored cotton fabrics based on the dye diffusion model according to claim 1, characterized in that: 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: Generate structure-aware non-uniform finite element mesh based on the warp and weft information of the fabric; The macroscopic seepage equation and the microscopic diffusion equation in the multi-scale coupled mathematical model are converted into a discretized set of equations on a structure-aware grid by combining the anisotropic diffusion tensor; The discretized equations are calculated using a numerical solution method to obtain the spatiotemporal concentration distribution of the dye in the digital model.

6. The method for dynamically predicting the anti-dyeing area of ​​dark-colored cotton fabrics based on the dye diffusion model according to claim 1, characterized in that: The process of determining the geometric data of the predicted bleed boundary based on the spatiotemporal concentration distribution calculated by simulation and a preset concentration threshold includes: Extracting concentration distribution data of the dye varying with time and space from the finite element analysis results of the multi-scale coupled mathematical model, and defining a preset concentration threshold; Identifying all grid nodes whose concentration values ​​are equal to or greater than the concentration threshold, forming a boundary point set of the bleeding area; Perform geometric fitting on the boundary point set to generate a smooth predicted color bleeding boundary curve and output the corresponding geometric data.

7. The method for dynamically predicting the anti-dyeing area of ​​dark-colored cotton fabrics based on the dye diffusion model according to claim 1, characterized in that: The process of adaptively adjusting the printing process parameters and the multi-scale coupling mathematical model parameters based on the geometric data of the predicted bleeding boundary includes: generating a compensation vector field based on geometric data of the predicted bleeding boundary; generating an optimized compensation profile according to the compensation vector field for adjusting printing process parameters; The actual bleeding boundary is extracted through machine vision algorithms, compared with the predicted bleeding boundary, and the geometric error is calculated; Based on the geometric error, an inverse optimization algorithm is used to adjust the parameters of the multi-scale coupling mathematical model; The adjusted printing process parameters and model parameters are re-input into the multi-scale coupled mathematical model and run iteratively to optimize the next round of bleeding boundary prediction.

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