A method for reconstructing a pore structure model of a carbon paper base paper

Abstract

The application discloses a pore structure model reconstruction method of carbon paper raw paper, and the two-point correlation function, the linear path function and the fractal control function of the statistical characteristic function are cited to statistically acquire the pore structure characteristics of the carbon paper raw paper binary image, and then the binary image is converted into an array and stored as a target value, the array meeting the target value is generated through the simulated annealing algorithm after optimization of parameters, and the transformation and reconstruction from two dimensions to three dimensions of the carbon paper raw paper are realized. The application has the advantages of simple steps, convenient operation, low cost, good accuracy and good reconstruction effect.

Description

Technical Field

[0001] This invention relates to the field of carbon paper base paper technology, and in particular to a method for reconstructing the pore structure model of carbon paper base paper. Background Technology

[0002] Carbon fiber paper (CFP) is currently the main product used as the base layer of the gas diffusion layer in proton exchange membrane fuel cells. It has a uniform porous thin-layer structure and excellent electrical conductivity, chemical stability and thermal stability.

[0003] Carbon paper is composed of carbon fibers with high tensile strength, which are firmly bonded together to make it durable. First, pretreated shredded carbon fibers are uniformly mixed with water, dispersants, and other additives, followed by a papermaking process to obtain the carbon fiber paper precursor. After impregnation, molding, carbonization, and graphitization, carbon paper is obtained. Modified phenolic resin is widely used as an adhesive in the impregnation process. Adding phenolic resin during molding and curing can produce carbon fiber-based paper with a certain degree of smoothness and strength. During carbonization, some of the adhesive undergoes volume decomposition and shrinkage, effectively reducing the density of the carbon fiber paper, increasing porosity, and decreasing resistivity. The graphitization process further improves the electrical conductivity of CFP.

[0004] In the study of three-dimensional structural reconstruction of porous materials, using computed tomography (CT) to obtain three-dimensional pore space images for reconstruction has the advantages of high speed, clear images, and non-destructive processing, but it requires expensive equipment and testing costs. Simulated annealing algorithms, as one of the earlier methods for establishing digital cores, can contain more information reflecting the spatial structural characteristics of porous materials, giving them irreplaceable advantages compared to other methods. Therefore, how to reconstruct the three-dimensional structural model of carbon paper base paper based on simulated annealing algorithms has become a technical problem that researchers urgently need to solve. Summary of the Invention

[0005] The purpose of this invention is to provide a method for reconstructing the pore structure model of carbon paper. This invention can realize the transformation and reconstruction of carbon paper from two-dimensional to three-dimensional, and has the advantages of simple steps, convenient operation, and low cost.

[0006] The technical solution of this invention: a method for reconstructing the pore structure model of carbon paper base paper, comprising the following steps:

[0007] Step 1: Pre-treat the carbon paper base paper to obtain the porosity. And obtain a binary image of the pores and fibers of the carbon paper base paper;

[0008] Step 2: Statistical analysis of pore features in the binarized image: Calculate the two-point correlation function, linear correlation function, and fractal control function of the binarized image, which serve as the objective function for reconstructing the model using the simulated annealing algorithm, denoted as... , and ;

[0009] Step 3, Initial Image Generation: Based on the porosity of the carbon paper base paper Set the size of the carbon paper base paper reconstruction model and generate it randomly. A number of pore volumetric elements are used as the initial solution for the model; coordinates are used. This represents the position of each pore voxel in the model, and the value of each pore voxel is expressed as follows: express;

[0010] Step 4: Initial Image Pore Feature Statistics: Calculate the two-point correlation function, linear correlation function, and fractal control function of the initial image under the initial solution, and statistically analyze the pore structure characteristics, denoted as... , and Then, the energy difference between the initial solution and the target solution is calculated using the energy difference formula of the simulated annealing algorithm. ;

[0011] Step 5: Simulated Annealing Algorithm Parameter Settings: Set the initial temperature for the simulated annealing algorithm. Number of iterations per temperature Temperature drop coefficient Termination temperature and minimum energy difference ;

[0012] Step 6: Generate a new structural model: Randomly swap the model pore voxels using a pixel selection method to generate a new structural model. The value of each voxel is determined by... The two-point correlation function, linear correlation function, and fractal control function of the new model are represented, and the new porosity characteristics are statistically analyzed and denoted as... , and Then, the energy difference between the new solution and the target solution is calculated using the energy difference formula of the simulated annealing algorithm. ;

[0013] Step 7, Simulated Annealing Algorithm Update Criteria: If > Then accept the new solution, replace the initial solution with the new solution, store the new solution as the optimal solution, and let... = , = , = , = , = Meanwhile, this solution is taken as the current solution, and let = , = , = , = Energy difference = Iterate in this way;

[0014] like < Then, the Metropololos criterion is used to determine whether to accept the new solution;

[0015] Step 8, Algorithm Cooling-Off Criteria: If the number of iterations reaches a set threshold... Then, according to the temperature drop coefficient , with temperature = This iterative process continues to generate new solutions;

[0016] Step 9, Algorithm Termination Criterion: During the iteration process, if the termination condition is met, the energy... < or < If so, exit the simulation;

[0017] Step 10: Output the final model: the obtained optimal solution. A 3D array can be imported into AVIZO software to visualize the reconstructed 3D model.

[0018] In the above-mentioned method for reconstructing the pore structure model of carbon paper, step 1, the preprocessing includes acquiring two-dimensional electron microscope (TEM) images of the carbon paper sample to obtain TEM images, and then performing image denoising processing on the TEM images to obtain a single-channel grayscale image of the carbon paper. The image denoising processing is performed using a median filtering algorithm. The median filtering algorithm is based on sorting statistics theory, constructing a filtering window containing an odd number of pixels, with a window size of 3×3 or 5×5. After obtaining the filtering window, all pixel values ​​within the range are arranged in descending order, and the median value of the pixel sorting is selected to replace the middle pixel of the filtering window. The window is then smoothly moved until the TEM image of the carbon paper is completely processed. The calculation of the median filtering is as follows:

[0019]

[0020] In the formula: The input sequence is the image signal of the electron microscope image. Represents pixel coordinates. The set of natural numbers; This represents the median filtering algorithm. The grayscale values ​​of the pixels output by the filtering window; .

[0021] In the aforementioned method for reconstructing the pore structure model of carbon paper, step 1, the preprocessing includes image segmentation of the single-channel grayscale image to obtain a binarized image of the pores and fibers of the carbon paper. The image segmentation process first involves statistically analyzing the grayscale value of each pixel in the single-channel grayscale image of the carbon paper to obtain a grayscale distribution histogram of the image. Then, a threshold is set, and the grayscale value information of the grayscale image is output as 0 or 1 based on the threshold, as shown in the following formula:

[0022] ;

[0023] in, The selected threshold, Grayscale value Represents pixel coordinates. The set of natural numbers; This is the signal output from the grayscale image;

[0024] When the gray value of a pixel is greater than or equal to the selected threshold, the output signal value of that pixel is 1; when the gray value of a pixel is less than the selected threshold, the output signal value of that pixel is 0.

[0025] Repeat the above steps and compare the grayscale values ​​of the image with different thresholds to achieve the goal of completely separating the fibers and pores.

[0026] The aforementioned method for reconstructing the pore structure model of carbon paper base paper, wherein the threshold setting is based on the initial assumption that the threshold of the carbon paper base paper image is [value missing]. Let the pixels with gray values ​​of 0-T in the image be denoted as the set. The grayscale value is T-255, denoted as set. Statistical sets respectively and set The number of pixels is used to calculate the average gray value of the image.

[0027] ;

[0028] Compute set and sets Average grayscale value:

[0029] ; ;

[0030] Compute set and sets variance:

[0031] ; ;

[0032] Calculate the variance within and between sets:

[0033] ; ;

[0034] Finally, the threshold was determined:

[0035] ;

[0036] In the formula: This is the final threshold value obtained.

[0037] The grayscale value of the pixel in the grayscale image is greater than The pixel value is set to 1, representing the porosity of the carbon paper base. Pixels with grayscale values ​​less than 1 in the grayscale image are... The pixel value is set to 0, which indicates the fibers of the carbon paper base paper.

[0038] The aforementioned method for reconstructing the pore structure model of carbon paper base paper uses a two-point correlation function to statistically analyze the pore distribution characteristics in the carbon paper base paper. This two-point correlation function is defined by first digitizing the binary image, as follows:

[0039] ;

[0040] Then, two pixels are randomly selected from the digital image, and the probability that both points are located in the porous phase is calculated. This allows for the quantification of the microstructure of the carbon paper base in a probabilistic sense, and the extraction of the porous structure information of the carbon paper base. The probability calculation is as follows:

[0041] ;

[0042] In the formula: This represents the expectation operator.

[0043] The aforementioned method for reconstructing the pore structure model of carbon paper base paper uses a linear path function to statistically analyze the connectivity characteristics of the pore structure in the carbon paper base paper. The linear correlation function is defined as follows: Two pixels with a distance of i are randomly selected from the carbon paper base paper image. The probability that both pixels and the pixels between them are located in the pore phase is calculated. This is used to statistically analyze the pore connectivity information of the carbon paper base paper image. The formula is as follows:

[0044] ;

[0045] In the formula: This represents the expectation operator; Indicates unit distance.

[0046] The aforementioned method for reconstructing the pore structure model of carbon paper base paper involves the following steps for the fractal control function: first, selecting the box dimension, which is then used to cover the porous phase with square lattices of side length δ, to obtain the effective number of lattices covering the porous phase n(δ) and the corresponding total number of lattices N(δ); the formula for calculating the box dimension is as follows:

[0047] ;

[0048] In the formula: Represents the box dimension. Represents a two-dimensional image;

[0049] The formula for the fractal control function is as follows:

[0050] ;

[0051] In the formula: This represents the value of the fractal control function. Indicates the distance between two points;

[0052] This allows us to use fractal control functions to describe the irregular and discontinuous characteristics of the pore structure of carbon paper base paper.

[0053] In the aforementioned method for reconstructing the pore structure model of carbon paper, the energy term of the simulated annealing algorithm is the sum of squares of the characteristic statistical functions, and the energy difference formula is as follows: ;

[0054] In the formula: The maximum porosity voxel distance is a statistical function. The coefficients of the two-point correlation function. The coefficients of the linear correlation function, , and These are the objective function values ​​for the two-point correlation function, the linear correlation function, and the fractal control function, respectively. , and These are the pore characteristic function values ​​of the newly generated structural model.

[0055] The aforementioned method for reconstructing the pore structure model of carbon paper base paper, wherein the Metropololos criterion is based on... < Generate a random number e in the range [0,1) and calculate the probability. ,when When >e, the system accepts the new solution. Reject new solutions when <e;

[0056] At the same time, a memory function is added to the simulated annealing algorithm to store the current optimal solution in order to prevent the optimal solution from being lost.

[0057] In the aforementioned method for reconstructing the pore structure model of carbon paper base paper, step 6, the step of randomly exchanging model pore voxels using the pixel selection method, involves selecting a random voxel. If the number of pore voxels in all its neighborhoods whose values ​​are opposite to the value of the centrally selected pore voxel is greater than or equal to a threshold, then the selected voxel is determined to be an isolated point. The selected isolated point is then exchanged with the boundary point between the pores and fibers to eliminate the isolated point and form a new structural model.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] (1) This invention selects the commonly used two-dimensional electron microscope image for photographing carbon paper base paper. Compared with the use of computed tomography or X-ray CT in the market, it has the advantages of convenience and low cost. Then, this invention performs image noise reduction and image segmentation processing on the two-dimensional electron microscope image. Finally, the statistical feature function is used to statistically analyze the distribution characteristics of pores in carbon paper base paper and the connectivity characteristics of pore structure in carbon paper base paper. The fractal control function is used to describe the irregular and discontinuous characteristics of pore structure in carbon paper base paper. In this way, the pore feature information of carbon paper base paper is obtained simply and conveniently. It has the advantages of simple steps, convenient operation and low cost.

[0060] (2) This invention uses the two-point correlation function, linear path function and fractal control function of statistical characteristic functions to statistically analyze the pore structure characteristics of the binary image of carbon paper base paper, and then converts it into an array for storage as the target value. The simulated annealing algorithm with optimized parameters generates an array that meets the target value, thereby realizing the transformation and reconstruction of carbon paper base paper from two-dimensional to three-dimensional. It has the advantages of good accuracy and good reconstruction effect. Attached Figure Description

[0061] Figure 1 This is a flowchart illustrating the present invention;

[0062] Figure 2 This is a schematic diagram illustrating the principle of median filtering noise reduction;

[0063] Figure 3 It is a digitized two-dimensional image of carbon paper base paper;

[0064] Figure 4 This is a schematic diagram of the correlation function between two points;

[0065] Figure 5 This is a schematic diagram of a linear path function;

[0066] Figure 6 This is a schematic diagram of a square grid covering a porous phase;

[0067] Figure 7 This is a schematic diagram of the porosity voxel neighborhood;

[0068] Figure 8 This is a schematic diagram of the porous phase and the fibrous phase;

[0069] Figure 9 This is a schematic diagram of the exchange of pore volumetric elements;

[0070] Figure 10 These are before-and-after comparison images of isolated points being processed;

[0071] Figure 11 These are electron microscope images of the surfaces of six carbon paper samples, A1-A6.

[0072] Figure 12 These are binarized images of the surfaces of six carbon paper samples, A1-A6.

[0073] Figure 13 This is a schematic diagram of the correlation function values ​​between two points of six carbon paper samples (A1-A6).

[0074] Figure 14 This is a schematic diagram of the linear path function values ​​of six carbon paper samples (A1-A6).

[0075] Figure 15 This is a schematic diagram of the function values ​​of the fractal control function for six carbon paper samples (A1-A6).

[0076] Figure 16 This is a schematic diagram of the three-dimensional reconstruction model of three carbon paper samples, A1-A3;

[0077] Figure 17 This is a schematic diagram of the three-dimensional reconstruction model of three carbon paper samples, A4-A6. Detailed Implementation

[0078] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this should not be construed as limiting the present invention.

[0079] Example: A method for reconstructing the pore structure model of carbon paper base paper, such as... Figure 1 As shown, it includes the following steps:

[0080] Step 1: Pre-treat the carbon paper base paper to obtain a binary image of the pores and fibers of the carbon paper base paper, and obtain the porosity. ;

[0081] The porosity calculation is as follows:

[0082] The porosity of the carbon paper base paper was determined using a wet-dry method. The carbon paper base paper was dried at 80℃ for 24 h, and its mass was recorded as W1 using an electronic balance. Then, the carbon paper base paper was immersed in anhydrous ethanol for 1 min, and its mass was recorded as W2. The porosity of the carbon paper base paper was calculated using the following formula:

[0083] ;

[0084] In the formula: Porosity, % The density of anhydrous ethanol is g·cm³. -3 ; The average density of the carbon paper base paper is given in g·cm³. -3 .

[0085] Two-dimensional electron microscopy (SEM) images of the carbon paper sample were acquired. In this step, the carbon paper sample was photographed using a scanning electron microscope (SEM) to obtain two-dimensional electron micrographs. The electron micrographs are grayscale images; as the grayscale value increases, the color approaches white, and the brightness also increases; conversely, as the grayscale value decreases, the color approaches black, and the brightness also decreases. In the carbon paper sample, the grayscale value of the pores is 0, and the grayscale value of the fibers is 255.

[0086] Next, image denoising processing is performed on the electron microscope image to obtain a single-channel grayscale image of the carbon paper base. This step employs a median filtering algorithm for image denoising. Median filtering is one of the most commonly used image preprocessing techniques and is a non-linear filtering method. Compared to linear filtering, it can reduce noise while maintaining clear boundaries between phases and better preserving image details. It does not generate new pixel values ​​during denoising and is not affected by outliers. Furthermore, it is relatively simple to use and has low requirements for computer performance, making it suitable for denoising carbon paper base images.

[0087] The median filtering algorithm is based on sorting statistics theory. It constructs a filtering window containing an odd number of pixels, with a window size of 3×3 or 5×5. This step uses 3×3 as an example. Figure 2 As shown, after obtaining the filtering window, all pixel values ​​within that range are arranged in descending order. The median value of the pixel sorting is selected to replace the middle pixel of the filtering window, and the window is smoothly moved until the electron micrograph of the carbon paper is completely processed. The calculation of the median filtering is as follows:

[0088] ;

[0089] In the formula: The input sequence is the image signal of the electron microscope image. Represents pixel coordinates. The set of natural numbers; This represents the median filtering algorithm. The grayscale values ​​of the pixels output by the filtering window; .

[0090] The noise in the grayscale carbon paper electron microscope image was eliminated by median filtering, making the image clearer.

[0091] Finally, image segmentation processing is performed on the single-channel grayscale image of the carbon paper base, outputting a binary image of fibers and pores. Considering the computer's storage and processing of images, further image segmentation processing is required on the carbon paper base image to output a binary image of fibers and pores, reducing the amount of data stored in the computer and effectively improving the computational efficiency of image statistics and processing, accurately separating fibers and pores with different grayscale values.

[0092] The image segmentation process first involves statistically analyzing the grayscale value of each pixel in the single-channel grayscale image of the carbon paper base, obtaining the grayscale distribution histogram of the image, and then setting a threshold.

[0093] The grayscale value information of the grayscale image is output as 0 or 1 based on the threshold, as shown in the following formula:

[0094] ;

[0095] in, The selected threshold, Grayscale value Represents pixel coordinates. The set of natural numbers; This is the signal output from the grayscale image;

[0096] When the gray value of a pixel is greater than or equal to the selected threshold, the output signal value of that pixel is 1; when the gray value of a pixel is less than the selected threshold, the output signal value of that pixel is 0.

[0097] Repeat the above steps and compare the grayscale values ​​of the image with different thresholds to achieve the goal of completely separating the fibers and pores.

[0098] In this step, the threshold setting involves selecting a large set of grayscale values ​​(0-255) from all pixels in the carbon paper image, dividing the large set into two smaller sets by selecting a segmentation point, calculating the within-set variance and between-set variance of each smaller set, comparing the within-set variance with the between-set variance, and selecting the segmentation point with the smallest ratio as the threshold. Specifically, the steps begin by assuming the threshold for the carbon paper image is... Let the pixels with gray values ​​of 0-T in the image be denoted as the set. The grayscale value is T-255, denoted as set. Statistical sets respectively and set The number of pixels is used to calculate the average gray value of the image.

[0099] ;

[0100] Compute set and sets Average grayscale value:

[0101] ; ;

[0102] Compute set and sets variance:

[0103] ; ;

[0104] Calculate the variance within and between sets:

[0105] ; ;

[0106] Finally, the threshold was determined:

[0107] ;

[0108] In the formula: This is the final threshold value obtained.

[0109] The grayscale value of the pixel in the grayscale image is greater than The pixel value is set to 1, representing the porosity of the carbon paper base. Pixels with grayscale values ​​less than 1 in the grayscale image are... The pixel value is set to 0, which indicates the fibers of the carbon paper base paper.

[0110] This step can select an appropriate threshold based on different grayscale value ranges of fibers and pores to divide the grayscale value set, thereby obtaining accurate fiber and pore regions. Simultaneously, regarding porosity... In this case, the proportion of pore pixels can be calculated using a binary image to obtain the value.

[0111] Step 2: Statistical analysis of pore features in the binarized image: Calculate the two-point correlation function, linear correlation function, and fractal control function of the binarized image, which serve as the objective function for reconstructing the model using the simulated annealing algorithm, denoted as... , and ;

[0112] To achieve the visualization reconstruction of carbon paper base material from two-dimensional electron micrographs to a three-dimensional model, it is necessary to statistically analyze the pore structure characteristics of the carbon paper base material based on the two-dimensional electron micrographs, and then use these characteristics as target values ​​to generate an array that satisfies the target values ​​through a reconstruction algorithm, thereby achieving a visualization representation from two-dimensional to three-dimensional. Statistically, a two-dimensional slice can reflect the main morphological information of the corresponding three-dimensional microstructure. In this invention, statistical characteristic functions and fractal control functions were used to statistically analyze the pore characteristics of the carbon paper base material.

[0113] Statistical characteristic functions are generally used to record the structural features of porous materials. It is crucial to use statistical characteristic functions to obtain more effective information about the pore structure of carbon paper base material and to accurately characterize the pore microstructure of carbon paper base material based on limited morphological information. Fractal control functions are used to describe the irregular and discontinuous features of the pore structure of carbon paper base material. This invention employs two-point correlation functions and linear correlation functions used for global image search, as well as fractal control functions from fractal theory, to reconstruct the three-dimensional model of carbon paper base material.

[0114] After binarizing the carbon paper image, the image consists of two phases: pores and fibers. The pores and fibers are represented by black and white, respectively. Figure 3 As shown. The statistical characteristic function includes a two-point correlation function, which is used to statistically analyze the porosity distribution characteristics in carbon paper base paper; the two-point correlation function is defined by first digitizing the binary image, as follows:

[0115] ;

[0116] Then, two pixels are randomly selected from the digital image, and the probability that both points are located in the porous phase is calculated. This allows for the quantification of the microstructure of the carbon paper base in a probabilistic sense, and the extraction of the pore structure information of the carbon paper base. Figure 4 As shown; the probability calculation is as follows:

[0117] ;

[0118] In the formula: This represents the expectation operator.

[0119] Since the two-point correlation function only calculates the values ​​of pixel pairs and does not consider the influence of pixels between pairs on the function, it cannot record the pore connectivity of the carbon paper base material structure and cannot be used alone to statistically analyze the micropore structure of carbon paper base material.

[0120] The linear path function is used to statistically analyze the connectivity characteristics of the pore structure in carbon paper base material; the linear correlation function is defined as randomly selecting two pixels with a distance of i on the carbon paper base material image, calculating the probability that both pixels and the pixels between them are located in the pore phase, and is used to statistically analyze the pore connectivity information of the carbon paper base material image, such as... Figure 5 As shown, the formula is as follows:

[0121] ;

[0122] In the formula: This represents the expectation operator; Indicates unit distance.

[0123] Linear path functions contain not only phase information of the selected pixels but also phase information of the pixels between the selected two points, thus characterizing the connectivity between the fibrous phase and the porous phase. Linear path functions between different phases exhibit non-linear dependence; therefore, compared to two-point correlation functions, linear path functions possess the ability to distinguish between different phases.

[0124] The two-point correlation function and the linear path function are integrated into the carbon paper base paper structure reconstruction algorithm. The two-point correlation function statistically analyzes the distribution characteristics of pores in the carbon paper base paper image, and the linear path function statistically analyzes the connectivity characteristics of the pore structure in the carbon paper base paper image.

[0125] Furthermore, the step of the fractal control function is to first select the box dimension, such as... Figure 6 As shown, this box dimension uses a square lattice with a side length of δ to cover the porous phase, obtaining the effective number of lattices n(δ) covering the porous phase and the corresponding total number of lattices N(δ); the formula for calculating the box dimension is as follows:

[0126] ;

[0127] In the formula: Represents the box dimension. Represents a two-dimensional image;

[0128] The fractal control function formula is as follows:

[0129] ;

[0130] In the formula: This represents the value of the fractal control function. Indicates the distance between two points;

[0131] This allows us to use fractal control functions to describe the irregular and discontinuous characteristics of the pore structure of carbon paper base paper.

[0132] Step 3, Initial Image Generation: Based on the porosity of the carbon paper base paper Set the size of the carbon paper base paper reconstruction model and generate it randomly. A number of pore volumetric elements are used as the initial solution for the model; coordinates are used. This represents the position of each pore voxel in the model, and the value of each pore voxel is expressed as follows: express;

[0133] Step 4: Initial Image Pore Feature Statistics: Calculate the two-point correlation function, linear correlation function, and fractal control function of the initial image under the initial solution, and statistically analyze the pore structure characteristics, denoted as... , and Then, the energy difference between the initial solution and the target solution is calculated using the energy difference formula of the simulated annealing algorithm. ;

[0134] The energy term of the simulated annealing algorithm is the sum of squares of the characteristic statistical functions, and the energy difference formula is as follows: ;

[0135] In the formula: The maximum porosity voxel distance is a statistical function. The coefficients of the two-point correlation function. The coefficients of the linear correlation function, , and These are the objective function values ​​for the two-point correlation function, the linear correlation function, and the fractal control function, respectively. , and These are the pore characteristic function values ​​of the newly generated structural model.

[0136] Step 5: Simulated Annealing Algorithm Parameter Settings: Set the initial temperature for the simulated annealing algorithm. Number of iterations per temperature Temperature drop coefficient Termination temperature and minimum energy difference In this embodiment, the optimal parameters are selected as follows:

[0137] Table 1

[0138] Step 6: Generate a new structural model: Randomly swap the model pore voxels using a pixel selection method to generate a new structural model. The value of each voxel is determined by... The two-point correlation function, linear correlation function, and fractal control function of the new model are represented, and the new porosity characteristics are statistically analyzed and denoted as... , and Then, the energy difference between the new solution and the target solution is calculated using the energy difference formula of the simulated annealing algorithm. ;

[0139] In the process of reconstructing the 3D carbon paper base structure model using the simulated annealing algorithm, a random selection method is used to exchange voxels (pixels) of pores and fibers to form a new structural model. However, as the system temperature decreases and the number of iterations increases, the morphology of the pore structure gradually forms, but the voxel distribution is relatively scattered, the connectivity of the pores is poor, and there are many isolated pore points or fiber points. Subsequent random exchange of fiber points and pore points to form a new structural model will destroy the already formed pore structure, trapping the pore structure in a vicious cycle of formation-destruction-reformation, increasing unnecessary computational load.

[0140] Therefore, this step involves exchanging pore points and fiber points to establish the carbon paper base paper structure model. The pixel selection method for randomly exchanging model pore voxels involves selecting a random voxel, such as... Figure 8 (A schematic diagram of the voxel neighborhood) shows that if the number of voxels in its neighborhood whose values ​​are opposite to the value of the selected central voxel is greater than or equal to a threshold, then the selected voxel is determined to be an isolated point. The selected isolated point is then exchanged with the boundary point between the pore and the fiber to eliminate the isolated point and form a new structural model. Figure 9 (Schematic diagram of porous phase and fibrous phase) As shown, if a central system is a pore point and its surrounding neighborhood is also a pore point, then the central voxel is a completely porous point, and its spatial position is set as (i, j, k). The voxel point in the positive z-axis direction of the center is (i, j, k+1), and the next voxel in the negative z-axis direction is (i, j, k-1); the voxel in the positive y-axis direction is (i, j+1, k), and the next voxel in the negative y-axis direction is (i, j-1, k); the previous voxel in the positive x-axis direction is (i+1, j, k), and the next voxel in the negative x-axis direction is (i-1, j, k). Traverse the central voxel in the six directions of x, y, and z. If the traversal result points from (i, j, k) to (i, j+n, k) are all pore points, and (i, j+n, k) is a fiber point, then (i, j+n, k) is the boundary point between the pore and the fiber.

[0141] The isolated points are exchanged with the boundary points between pores and fibers to form a new structural model, thus eliminating the isolated points. (See below.) Figure 9 As shown, with the fibrous phase region as the center point, if the number of values ​​in the surrounding 8 neighboring regions that are opposite to the center point value is greater than the threshold, it is selected as an isolated point, and this point is exchanged with the pore phase boundary point. Figure 10 This is a comparison image before and after eliminating isolated points during the 2D reconstruction process. Figure 10 In the diagram, 'a' represents the area before elimination, and 'b' represents the area after elimination. It is evident that the number of isolated points is reduced and pore connectivity is improved after treatment.

[0142] Step 7, Simulated Annealing Algorithm Update Criteria: If > Then accept the new solution, replace the initial solution with the new solution, store the new solution as the optimal solution, and let... = , = , = , = , = Meanwhile, this solution is taken as the current solution, and let = , = , = , = Energy difference = Iterate in this way;

[0143] like < Then, the Metropololos criterion is used to determine whether to accept the new solution;

[0144] Step 8, Algorithm Cooling-Off Criteria: If the number of iterations reaches a set threshold... Then, according to the temperature drop coefficient , with temperature = This iterative process continues to generate new solutions;

[0145] Step 9, Algorithm Termination Criterion: During the iteration process, if the termination condition is met, the energy... < or < If so, exit the simulation;

[0146] Step 10: Output the final model: the obtained optimal solution. A 3D array can be imported into AVIZO software to visualize the reconstructed 3D model.

[0147] To further illustrate this embodiment, six carbon paper base papers with different carbon fiber lengths, different carbon fiber / PVA fiber ratios, and different amounts of dispersant were selected for subsequent research. Table 2 below shows the papermaking parameters of the selected samples. Among them, the carbon fiber lengths of samples A1 and A3 are different in the papermaking process; the carbon fiber / PVA fiber ratios of samples A2 and A4 are different; and the amount of dispersant of samples A5 and A6 is different.

[0148] Sample number Carbon fiber length (mm) Carbon fiber specific gravity (%) Dispersant dosage (%) A1 8 85 0.12 A2 4 80 0.12 A3 2 85 0.12 A4 4 90 0.12 A5 4 85 0.16 A6 4 85 0.10

[0149] Table 2

[0150] Two-dimensional electron microscope (SEM) images of the carbon paper samples A1-A6 were obtained by scanning electron microscopy, as shown below. Figure 11 As shown, the two-dimensional electron microscope image is a fiber-pore binarized image obtained after grayscale processing, noise reduction processing, and image segmentation processing, as follows: Figure 12 As shown.

[0151] MATLAB software was used to statistically analyze the porosity characteristics of the binarized image of carbon paper base paper. Formulas were used to calculate the two-point correlation function, the linear correlation function graph, and the fractal control function. The results are shown below:

[0152] (1) Statistics of two-point correlation functions;

[0153] as follows Figure 13 As shown, Figure 13 In the figure, 'a' represents the two-point correlation function value of the carbon paper base paper of sample A1, which tends to stabilize after the distance between the two points is 40 pixels. Figure 13 In the figure, b represents the two-point correlation function value of the carbon paper base paper of sample A2, which tends to stabilize after the distance between the two points is 25 pixels. Figure 13 In the figure, c represents the two-point correlation function value of the carbon paper base paper of sample A3, which tends to stabilize after the distance between the two points is 40 pixels. Figure 13 In the figure, d represents the two-point correlation function value of the carbon paper base paper of sample A4, which tends to stabilize after the distance between the two points is 40 pixels. Figure 13 In the figure, e represents the two-point correlation function value of the carbon paper base paper of sample A5, which tends to stabilize after the distance between the two points is 25 pixels. Figure 13 In the figure, f represents the two-point correlation function value of the carbon paper base material of sample A6, which tends to stabilize after the distance between the two points is 25 pixels; this indicates that using the two-point correlation function to characterize image features is suitable for characterizing the structure of the carbon paper base material. Therefore, two-point correlation functions with a distance between the two points of less than 40 and 25 pixels were used to record the data. Figure 13 a, c, d and Figure 9 Two-dimensional structure of carbon paper base paper in the middle (b, e, f).

[0154] (2) Statistics of linear path functions;

[0155] as follows Figure 14 As shown, Figure 14 In the figure, 'a' represents the linear path function value of the carbon paper base paper of sample A1, which tends to 0 after the distance between the two points is 40 pixels. Figure 14 In the figure, b is the linear path function value of the carbon paper base paper of sample A2, which tends to 0 after the distance between the two points is 25 pixels. Figure 14 In the figure, c represents the linear path function value of the carbon paper base paper of sample A3, which tends to 0 after the distance between the two points is 25 pixels. Figure 14 In the figure, d represents the linear path function value of the carbon paper base paper of sample A4, which tends to 0 after the distance between the two points is 25 pixels. Figure 14 In the figure, e represents the linear path function value of the carbon paper base paper of sample A5, which tends to 0 after the distance between the two points is 25 pixels. Figure 14 In the figure, f represents the linear path function value of the carbon paper base material of sample A6, which tends to 0 after the distance between two points is 25 pixels; this indicates that using the linear path function to characterize image features is suitable for characterizing the structure of the carbon paper base material. Therefore, the two-point correlation function is used to record the data when the distance between the two points is less than 40 and 25 pixels, respectively. Figure 14 a and Figure 10 Two-dimensional structure of carbon paper base paper in the form of b, c, d, e, and f.

[0156] (3) Statistics of linear path functions;

[0157] as follows Figure 15 As shown in Figure af, the fractal control functions of samples A1-A6 are used to record the pore structure of the carbon paper base paper. As shown in the figure below, the box dimensions of samples A1-A6 are 3.42836, 3.44727, 3.42545, 3.47855, 3.33127, and 3.35418, respectively.

[0158] Based on the above parameter data and the parameters of the simulated annealing algorithm, a 3D model of the carbon paper base is created. The 3D array reconstructed in MATLAB is then imported into AVIZO software to visualize the reconstructed model. The specific steps are as follows:

[0159] (1) Import the reconstructed three-dimensional array in MATLAB into AVIZO software and use the Volume Rending module to visualize the three-dimensional model.

[0160] (2) The three-dimensional pore model is obtained by selecting the pore region in the model using the Interactive Thresholding algorithm.

[0161] (3) The three-dimensional fiber skeleton model is obtained by selecting the fiber region in the model using the Interactive Thresholding algorithm.

[0162] (4) The Volume Rending module is used to visualize the three-dimensional fiber model and the fiber skeleton model at the same time to obtain the overall three-dimensional model of the carbon paper base paper.

[0163] (5) Based on the three-dimensional pore model, the Axis Connectivity algorithm is used to obtain an effective connected pore structure model.

[0164] The three-dimensional reconstruction model of the carbon paper base obtained in AVIZO software is as follows. Figure 16 and Figure 17 As shown in the figures. Figures af correspond to samples A1-A6 respectively. Figure 1 shows the visualization of the pore structure, Figure 2 shows the fiber skeleton, and Figure 3 shows the visualization of the overall three-dimensional reconstruction structure of the carbon paper base paper.

[0165] To verify the accuracy of the 3D reconstruction model, two-point correlation functions, linear path functions, and fractal control functions were used to compare it with carbon paper samples. The results are as follows:

[0166] The two-point correlation function values ​​of the reconstructed model of sample A1 and the target image of A1 tend to stabilize after the distance between the two points is 40 pixels. The linear correlation function values ​​tend to 0 after the distance between the two points is 40 pixels. The two-point correlation function and the linear path function values ​​are in good agreement with the function values ​​of the target image, and the errors are all less than 10. -5 The box dimensions of the target image and the reconstruction model are 3.42836 and 3.42691, respectively, with a difference of 0.00145. The function values ​​of the fractal control function reconstruction model and the function values ​​of the target image are in good agreement.

[0167] The two-point correlation function values ​​of the reconstructed model of sample A2 and the target image of A2 tend to stabilize after the distance between the two points is 25 pixels. The linear correlation function values ​​tend to 0 after the distance between the two points is 25 pixels. The two-point correlation function and the linear path function values ​​are in good agreement with the function values ​​of the target image, and the errors are all less than 10. -5 The box dimensions of the target image and the reconstruction model are 3.44727 and 3.44655, respectively, with a difference of 0.00072. The function values ​​of the fractal control function reconstruction model and the function values ​​of the target image are in good agreement.

[0168] The two-point correlation function values ​​of the reconstructed model of sample A3 and the target image of A3 tend to stabilize after the distance between the two points is 40 pixels. The linear correlation function values ​​tend to 0 after the distance between the two points is 25 pixels. The two-point correlation function and linear path function values ​​are in good agreement with the function values ​​of the target image, and the errors are all less than 10. -5 The box dimensions of the target image and the reconstruction model are 3.42545 and 3.42000, respectively, with a difference of 0.00545. The function values ​​of the fractal control function reconstruction model and the function values ​​of the target image are in good agreement.

[0169] The two-point correlation function values ​​of the reconstructed model of sample A4 and the target image of A4 tend to stabilize after the distance between the two points is 40 pixels. The linear correlation function values ​​tend to 0 after the distance between the two points is 25 pixels. The two-point correlation function and linear path function values ​​are in good agreement with the function values ​​of the target image, and the errors are all less than 10. -5 The box dimensions of the target image and the reconstruction model are 3.47855 and 3.47782, respectively, with a difference of 0.00073. The function values ​​of the fractal control function reconstruction model and the function values ​​of the target image are in good agreement.

[0170] The two-point correlation function values ​​of the reconstructed model of sample A5 and the target image of A5 tend to stabilize after the distance between the two points is 25 pixels. The linear correlation function values ​​tend to 0 after the distance between the two points is 25 pixels. The two-point correlation function and linear path function values ​​are in good agreement with the function values ​​of the target image, and the errors are all less than 10. -5The box dimensions of the target image and the reconstruction model are 3.33127 and 3.33055, respectively, with a difference of 0.00072. The function values ​​of the fractal control function reconstruction model and the function values ​​of the target image are in good agreement.

[0171] The two-point correlation function values ​​of the reconstructed model of sample A6 and the target image of A6 tend to stabilize after the distance between the two points is 25 pixels. The linear correlation function values ​​tend to 0 after the distance between the two points is 25 pixels. The two-point correlation function and linear path function values ​​are in good agreement with the function values ​​of the target image, and the errors are all less than 10. -5 The two fitted lines almost overlap. The box dimensions of the target image and the reconstruction model are 3.35418 and 3.35636, respectively, with a difference of 0.00218. The function values ​​of the fractal control function reconstruction model and the function values ​​of the target image are in good agreement.

[0172] The above results show that the reconstructed model of the sample has almost identical fractal characteristics to the pore structure of the target image, proving the effectiveness of the method of reconstructing the three-dimensional pore structure of carbon paper base paper using simulated annealing algorithm.

[0173] In summary, this invention utilizes statistical characteristic functions to statistically analyze the distribution and connectivity of pores in carbon paper base material, and employs fractal control functions to represent the irregular and discontinuous characteristics of the pore structure. This simple and convenient method achieves the acquisition of pore feature information from carbon paper base material, offering advantages such as simple steps, easy operation, and low cost. This invention uses two-point correlation functions, linear path functions, and fractal control functions of statistical characteristic functions to statistically analyze the pore structure features of binary images of carbon paper base material. These features are then converted into arrays and stored as target values. An optimized simulated annealing algorithm generates arrays that match the target values, achieving the transformation and reconstruction of carbon paper base material from two-dimensional to three-dimensional, offering advantages of high accuracy and good reconstruction results. Based on the reconstructed three-dimensional structural model of carbon paper base material, this invention extracts an equivalent three-dimensional pore network model, enabling quantitative and visual analysis of the pore structure parameters of carbon paper base material samples. This helps to analyze the influence of different pore structures corresponding to different papermaking process parameters on porosity from a microscopic pore perspective.

Claims

1. A method for reconstructing a pore structure model of a carbon paper base paper, characterized by: Includes the following steps: Step 1, pretreatment of carbon paper base paper, obtain porosity and get the binaryzation of carbon paper base paper porosity and fiber; Step 2, binarized image pore feature statistics: calculate the two-point correlation function, linear correlation function and fractal control function of the binarized image as the objective function of the simulated annealing algorithm to reconstruct the model, denoted as , and ; Step 3, initial image generation: according to the porosity of the carbon paper base paper , set the size of the carbon paper base paper reconstruction model, and randomly generate pore voxels as the initial solution of the model; using coordinates representing the position of each pore voxel in the model, the value of each pore voxel is represented by ; Step 4, initial image pore feature statistics: calculate the two-point correlation function, linear correlation function and fractal control function of the initial image under the initial solution, and count the pore structure features, denoted as , and ; According to the energy difference formula of the simulated annealing algorithm, the energy difference between the initial solution and the target solution is calculated ; Step 5, Simulated Annealing Algorithm Parameter Settings: Set the initial temperature of the simulated annealing algorithm , number of iterations at each temperature , temperature drop coefficient , termination temperature and minimum energy difference ; Step 6, generating new structure model: using pixel selection method to generate new structure model by random exchange of model pore voxel, the value of each pore voxel is represented by , and the two-point correlation function, linear correlation function and fractal control function of new model are calculated, and the new pore characteristics are calculated, recorded as , and ; According to the energy difference formula of the simulated annealing algorithm, the energy difference between the new solution and the target solution is calculated as ; Step 7, Simulated Annealing Algorithm Update Criteria: If > Then accept the new solution, replace the initial solution with the new solution, store the new solution as the optimal solution, and let... = , = , = , = , = Meanwhile, this solution is taken as the current solution, and let = , = , = , = Energy difference = Iterate in this way; like < Then, the Metropololos criterion is used to determine whether to accept the new solution; Step 8, Algorithm Cooling-Off Criteria: If the number of iterations reaches a set threshold... Then, according to the temperature drop coefficient , with temperature = This iterative process continues to generate new solutions; Step 9, Algorithm Termination Criterion: During the iteration process, if the termination condition is met, the energy... < or < If so, exit the simulation; Step 10: Output the final model: the obtained optimal solution. A three-dimensional array is used to import the results of a three-dimensional array into AVIZO software to visualize the reconstructed three-dimensional model. The two-point correlation function is used to statistically analyze the porosity distribution characteristics in carbon paper base paper; the two-point correlation function is defined by first digitizing the binary image, as follows: ； Then, two pixels are randomly selected from the digital image, and the probability that both points are located in the porous phase is calculated, so as to quantify the microstructure of the carbon paper base paper in a probabilistic sense and extract the pore structure information of the carbon paper base paper. The probability is calculated as follows: ； In the formula: This represents the expectation operator; The linear path function is used to statistically analyze the connectivity characteristics of the pore structure in carbon paper base material; the linear correlation function is defined as follows: Two pixels with a distance of i are randomly selected on the carbon paper base material image, and the probability that both pixels and the pixels between them are located in the pore phase is calculated. This is used to statistically analyze the pore connectivity information of the carbon paper base material image. The formula is as follows: ； In the formula: This represents the expectation operator; Indicates unit distance; In step 6, the random exchange step of the model pore voxels by the pixel selection method is to select a random voxel. If the number of pore voxels in all its neighborhoods whose values ​​are opposite to the value of the central selected pore voxel is greater than or equal to a threshold, then the selected voxel is determined to be an isolated point. The selected isolated point is exchanged with the boundary point of the pore and fiber to eliminate the isolated point and form a new structural model.

2. The method for reconstructing the pore structure model of carbon paper base paper according to claim 1, characterized in that: In step 1, the preprocessing includes acquiring two-dimensional electron micrographs of the carbon paper sample, obtaining electron micrographs, and then performing image denoising on the electron micrographs to obtain a single-channel grayscale image of the carbon paper. The image denoising is performed using a median filtering algorithm. The median filtering algorithm is based on sorting statistics theory, constructing a filtering window containing an odd number of pixels, with a window size of 3×3 or 5×5. After obtaining the filtering window, all pixel values ​​within the range are arranged in descending order, and the median value of the pixel sorting is selected to replace the middle pixel of the filtering window. The window is then smoothly moved until the electron micrograph of the carbon paper is completely processed. The calculation of the median filtering is as follows: In the formula: The input sequence is the image signal of the electron microscope image. Represents pixel coordinates. The set of natural numbers; This represents the median filtering algorithm. The grayscale values ​​of the pixels output by the filtering window; .

3. The method for reconstructing the pore structure model of carbon paper base paper according to claim 2, characterized in that: In step 1, the preprocessing includes image segmentation of the single-channel grayscale image to obtain a binarized image of the pores and fibers of the carbon paper base paper. The image segmentation process first involves statistically analyzing the grayscale value of each pixel in the single-channel grayscale image of the carbon paper base paper to obtain a grayscale distribution histogram of the image. Then, a threshold is set, and the grayscale value information of the grayscale image is output as 0 or 1 according to the threshold, as shown in the following formula: ； in, The selected threshold, Grayscale value Represents pixel coordinates. The set of natural numbers; This is the signal output from the grayscale image; When the gray value of a pixel is greater than or equal to the selected threshold, the output signal value of that pixel is 1; when the gray value of a pixel is less than the selected threshold, the output signal value of that pixel is 0. Repeat the above steps and compare the grayscale values ​​of the image with different thresholds to achieve the goal of completely separating the fibers and pores.

4. The method for reconstructing the pore structure model of carbon paper base paper according to claim 3, characterized in that: The threshold setting is based on the initial assumption that the threshold for the carbon paper base image is... Let the pixels with gray values ​​of 0-T in the image be denoted as the set. The grayscale value is T-255, denoted as set. Statistical sets respectively and set The number of pixels is used to calculate the average gray value of the image. ； Compute set and sets Average grayscale value: ； ； Compute set and sets variance: ； ； Calculate the variance within and between sets: ； ； Finally, the threshold was determined: ； In the formula: This is the final threshold value obtained. The grayscale value of the pixel in the grayscale image is greater than The pixel value is set to 1, representing the porosity of the carbon paper base. Pixels with grayscale values ​​less than 1 in the grayscale image are... The pixel value is set to 0, which indicates the fibers of the carbon paper base paper.

5. The method for reconstructing the pore structure model of carbon paper base paper according to claim 1, characterized in that: The steps of the fractal control function are as follows: first, select the box dimension, which uses square grids with a side length of δ to cover the porous phase, and obtain the effective number of grids n(δ) covering the porous phase and the corresponding total number of grids N(δ); The formula for calculating the box dimension is as follows: ； In the formula: Represents the box dimension. Represents a two-dimensional image; The formula for the fractal control function is as follows: ； In the formula: This represents the value of the fractal control function. Indicates the distance between two points; This allows us to use fractal control functions to describe the irregular and discontinuous characteristics of the pore structure of carbon paper base paper.

6. The method for reconstructing the pore structure model of carbon paper base paper according to claim 1, characterized in that: The energy term of the simulated annealing algorithm is the sum of squares of the characteristic statistical functions, and the energy difference formula is as follows: ； In the formula: The maximum porosity voxel distance is a statistical function. The coefficients of the two-point correlation function. The coefficients of the linear correlation function, , and These are the objective function values ​​for the two-point correlation function, the linear correlation function, and the fractal control function, respectively. , and These are the pore characteristic function values ​​of the newly generated structural model.

7. The method for reconstructing the pore structure model of carbon paper base paper according to claim 1, characterized in that: The Metropololos criterion. < Generate a random number e in the range [0,1) and calculate the probability. ,when When >e, the system accepts the new solution. Reject new solutions when <e; At the same time, a memory function is added to the simulated annealing algorithm to store the current optimal solution in order to prevent the optimal solution from being lost.

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