A multi-scale random reconstruction method and system for three-dimensional mesoscopic concrete aggregate

Abstract

The present invention discloses a multi-scale random reconstruction method and system for three-dimensional mesoscopic concrete aggregates. The method comprises the following steps: obtaining and performing three-dimensional reconstruction and segmentation on a scanned image of a concrete test block, extracting STL format files of multiple reference aggregates; selecting a reference aggregate with target morphological characteristics and performing a spherical harmonic expansion on it; then, by selecting a mode of the spherical harmonic expansion, fitting the discrete surface of the target reference aggregate into a continuous polar radius function; constructing a two-dimensional regular plane grid, using the polar radius function to perform radius sampling at each grid node in the two-dimensional regular plane grid, so that the target reference aggregate surface is converted into a regular reference radius field or reference radius fields of different scales; extracting statistical information of the reference radius field and performing random field reconstruction on it to generate multiple three-dimensional random aggregates. The present invention can reconstruct a large number of realistic three-dimensional random aggregates with multi-scale morphologies, effectively saving a large amount of costs associated with image scanning experiments and processing.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-scale modeling of concrete materials, and more specifically, relates to a multi-scale random reconstruction method and system for three-dimensional micro-concrete aggregates. Background Art

[0002] Mesoscale numerical simulation is an effective means of studying the physical and mechanical properties of concrete, facilitating the establishment of the mechanisms linking concrete's microstructure and macroscopic properties. At the mesoscale, a numerical model of concrete can be considered to consist of a cement matrix, aggregate, interfacial transition zones, and pores. Aggregate, representing 30% to 60% of the concrete volume, is a key parameter influencing concrete's macroscopic physical and mechanical properties. Aggregate, derived from natural gravel or crushed rock, is primarily formed through processes such as crushing, collision, and friction, resulting in a complex and random surface morphology. Aggregate surface morphology exhibits morphological features at different scales, such as coarse-scale overall shape, mesoscale local roundness, and fine-scale surface texture. These multiscale random aggregate morphologies lead to complex nonlinear mechanical phenomena in concrete, such as debonding at the mortar-aggregate interface, aggregate interlocking / bridging, and crack propagation orientation. This, in turn, significantly influences concrete's macroscopic physical and mechanical properties, such as compressive and tensile strength, carbonation, ion diffusivity, and thermal conductivity.

[0003] In order to improve the reliability of mesoscopic numerical simulations in the study of concrete physics, mechanical properties, and parameter optimization design, it is necessary to consider more realistic aggregate morphologies in the mesoscopic models. There are two main ways to consider aggregate morphologies in existing concrete mesoscopic models: one is a simplified aggregate morphology; the other is an aggregate surface morphology obtained based on different image scanning devices. Simplified aggregate morphologies such as spheres, ellipses, and polyhedrons cannot reflect the true aggregate morphology; obtaining the aggregate surface morphology through image scanning equipment requires a large number of expensive scanning experiments and tedious and time-consuming image processing. In addition, the obtained aggregate morphology cannot be controlled, making it difficult to find statistically representative samples. Summary of the Invention

[0004] In response to the shortcomings of the existing technology, the purpose of the present invention is to provide a multi-scale random reconstruction method and system for three-dimensional meso-concrete aggregates. Based on a small amount of real aggregates, a large number of real and multi-scale morphologically controllable three-dimensional random aggregates can be reconstructed, saving a lot of costs related to image scanning experiments and processing.

[0005] To achieve the above objectives, in a first aspect, the present invention provides a multi-scale random reconstruction method for three-dimensional meso-concrete aggregate, comprising the following steps:

[0006] (1) Obtaining a scanned image of a concrete test block, performing three-dimensional reconstruction and aggregate segmentation on the image, and extracting multiple STL format files of reference aggregates, wherein the STL format files contain vertex coordinates of discrete aggregate surfaces and their connection relationships;

[0007] (2) Select an STL file with target morphological characteristics from multiple STL files of reference aggregates, and perform spherical harmonic expansion of 15th order or above on it. Then, by selecting the mode of the spherical harmonic expansion, the discrete surface fitting of the target reference aggregate is converted into a continuous polar radius function;

[0008] (3) Constructing a two-dimensional regular plane grid, and then using the polar radius function to perform radius sampling on each grid node in the two-dimensional regular plane grid according to the selected mode of the spherical harmonic expansion, so that the target reference aggregate surface is converted into a regular reference radius field or reference radius fields of different scales;

[0009] (4) Extracting statistical information of the reference radius field, which includes mean, standard deviation and autocorrelation function, and then reconstructing the random field based on the statistical information to generate multiple three-dimensional random aggregates.

[0010] In one embodiment, in step (2), the modes of the spherical harmonic expansion include full modes and modes of different scales, and the modes of the spherical harmonic expansion are selected accordingly according to the scale morphology type of the three-dimensional random aggregate to be reconstructed.

[0011] In one embodiment, in step (2), the step of performing a spherical harmonic expansion of order 15 or above, and then converting the discrete surface fitting of the target reference aggregate into a continuous polar radius function by selecting the mode of the spherical harmonic expansion, is specifically as follows:

[0012] (2.1) The coordinates of the target reference aggregate surface vertices are converted into local polar coordinates. The conversion formula is:

[0013]

[0014] Where (x, y, z) represents the coordinates of the vertex on the surface of the target reference aggregate; (x0, y0, z0) represents the coordinates of the geometric center of the target reference aggregate; represents the local polar coordinates of the vertex on the target reference aggregate surface;

[0015] (2.2) The discrete surface of the target reference aggregate is expanded with 15th order or above spherical harmonics. When the selected spherical harmonic expansion mode is the full mode, the formula for converting the discrete surface fitting of the target reference aggregate into a continuous polar radius function is:

[0016]

[0017] Where, is the spherical harmonic coefficient, and the local polar coordinates of the target reference aggregate surface vertex are obtained from step (2.1) Substituted into the expansion formula, calculated by least squares fitting; is the 1st degree mth order spherical harmonic basis, and its expression is: i is the imaginary unit; P l m (x) represents the Legendre function of degree 1 and order m, which is expressed as:

[0018] When the selected spherical harmonic expansion modes are modes of different scales, the formula for converting the discrete surface fitting of the target reference aggregate into a continuous polar radius function is:

[0019]

[0020] Where, f0 and f1 correspond to the initial sphere representing the spherical harmonic expansion; The corresponding representations are the overall shape of the target reference aggregate at the coarse scale, the local roundness at the mesoscale, and the surface roughness at the fine scale.

[0021] In one embodiment, step (3) is specifically:

[0022] (3.1) In θ∈[0,π], Construct a two-dimensional plane regular grid D within the range, and the expression is:

[0023]

[0024] Where, Δθ=π / N, N represents θ and The number of mesh nodes in the direction, θ and Corresponding to the elevation and azimuth in the polar coordinate system; x ij represents the polar coordinates corresponding to the grid nodes in the plane regular grid D;

[0025] (3.2) When the mode of the spherical harmonic expansion is selected as the full mode, the polar coordinates of each grid node in the two-dimensional plane regular grid D are substituted into the polar radius function, and the radius of the target reference aggregate corresponding to each grid vertex coordinate direction is calculated, thereby decomposing the target reference aggregate surface into a regular plane reference radius field; when the mode of the spherical harmonic expansion is selected as the mode of different scales, the polar coordinates of each grid node in the two-dimensional plane regular grid D are substituted into the polar radius function, and the function terms of different scales in the polar radius function are used to calculate the radius values ​​of the target reference aggregate of different scales corresponding to each grid vertex coordinate direction, thereby converting the target reference aggregate surface into a reference radius field of different scales.

[0026] In one embodiment, step (4) is specifically:

[0027] (4.1) When the mode of the spherical harmonic expansion is a full mode, the statistical information of the reference radius field is extracted, and based on this statistical information, a random reconstruction algorithm is used to reconstruct multiple reconstructed random fields. When the mode of the spherical harmonic expansion is a mode of different scales, the statistical information of the reference radius field of different scales is extracted, and based on this statistical information, a random reconstruction algorithm is used to reconstruct a plane random field of the corresponding scale, which is then superimposed to generate multiple reconstructed random fields. The statistical information includes the mean, standard deviation, and autocorrelation function.

[0028] (4.2) Each reconstructed planar random field is folded into a three-dimensional closed surface to generate multiple three-dimensional random aggregates.

[0029] In one embodiment, in step (4.1), the formula of the random reconstruction algorithm is:

[0030]

[0031] Where μ represents the mean value obtained from the reference radius field; S X (ω) represents the Gaussian power spectral density function, which is obtained by Fourier transforming the autocorrelation function of the reference radius field; α represents a random phase angle between 0 and 2π; N1 and N2 represent the two-dimensional regular plane grids θ and The number of grid nodes in the direction; ω represents a random sample, and I(x,ω) represents the reconstructed planar random field.

[0032] In one embodiment, in step (4.2), the step of folding each reconstructed planar random field into a three-dimensional closed surface is specifically:

[0033] (a) Take the average of all radii in the first row of the reconstructed planar random field I(x,ω) and replace all radii in the first row with the average;

[0034] (b) average all the radii in the last row of the reconstructed plane random field I(x,ω) and replace all the radius values ​​in the last row with the average;

[0035] (c) average the corresponding radii in the first and last columns of the reconstructed plane random field I(x,ω), and then replace the corresponding values ​​in the first and last columns with the average;

[0036] (d) Performing spherical harmonic expansion on the reconstructed planar random field transformed in steps (a) to (c) to remove local rough areas on its surface and obtain a three-dimensional closed surface.

[0037] In one embodiment, in step (1), the concrete test block is scanned using an XCT device to obtain an XCT scan image.

[0038] In one embodiment, in step (2), the step of selecting an STL format file having target morphological features from a plurality of STL format files of reference aggregates is specifically as follows:

[0039] According to the vertex coordinates of each reference aggregate surface, the four morphological parameters of each reference aggregate, namely sphericity, convexity, roundness and roughness, are calculated accordingly;

[0040] According to the morphological parameters of each reference aggregate, an STL format file with target morphological characteristics is selected.

[0041] In a second aspect, the present invention provides a multi-scale random reconstruction system for three-dimensional meso-concrete aggregates, comprising:

[0042] An acquisition module is used to acquire a scanned image of a concrete test block, perform three-dimensional reconstruction and aggregate segmentation on the image, and extract multiple STL format files of reference aggregates, wherein the STL format files contain vertex coordinates of discrete surfaces of the aggregates and their connection relationships;

[0043] The fitting conversion module is used to select an STL file with target morphological characteristics from multiple STL files of reference aggregates, perform spherical harmonic expansion of 15th order or above on it, and then convert the discrete surface fitting of the target reference aggregate into a continuous polar radius function by selecting the mode of the spherical harmonic expansion;

[0044] The radius sampling module is used to construct a two-dimensional regular plane grid, and then use the polar radius function to perform radius sampling on each grid node in the two-dimensional regular plane grid according to the selected mode of the spherical harmonic expansion, so as to convert the target reference aggregate surface into a regular reference radius field or reference radius fields of different scales;

[0045] The reconstruction module is used to extract statistical information of the reference radius field, which includes the mean, standard deviation and autocorrelation function, and then reconstruct the random field according to the statistical information to generate multiple three-dimensional random aggregates.

[0046] The multi-scale random reconstruction method and system of three-dimensional micro-scale concrete aggregate provided by the present invention have the following effects: (1) the statistical information extracted from the real aggregate surface is used during random reconstruction, which can avoid the unreliability introduced by the use of assumed statistical information; and compared with the simplified random aggregates used in the previous concrete micro-model, such as spheres, ellipsoids and polyhedrons, the aggregate morphology generated by the multi-scale random reconstruction method provided by the present invention is more diverse, realistic and reliable; (2) the present invention provides a rigorous basis for decomposing, reconstructing and superimposing the morphological characteristics of aggregates of different scales, and spherical harmonic modes corresponding to the morphology of aggregates of different scales are selected for spherical reconstruction. Harmonic expansion and random reconstruction can control the surface morphology of the reconstructed aggregate, providing good controllability and flexibility for the three-dimensional random reconstruction of the aggregate surface morphology; (3) based on a small amount of real aggregate, a large number of real and diverse random aggregates can be reconstructed, avoiding the need to carry out a large number of expensive, tedious and time-consuming image scanning experiments and related image processing to obtain aggregates with different surface morphologies, saving a lot of costs related to image scanning experiments and processing; (4) since the morphology of aggregates has an important influence on the physical and mechanical properties of concrete, the random aggregates generated by the present invention are used to perform concrete micro-numerical simulations, and the simulation results can be more reliable and representative. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a flow chart of a multi-scale random reconstruction method of three-dimensional meso-concrete aggregate provided by one embodiment of the present invention;

[0048] Figure 2 are 635 reference aggregates segmented and extracted from the concrete XCT image in Example 1 of the present invention;

[0049] Figure 3 is a randomly selected target reference aggregate shape (a) and its aggregate shape after 15th-order spherical harmonic expansion (b) in Example 1 of the present invention;

[0050] Figure 4 In the first embodiment of the present invention, θ∈[0,π], Construct a regular plane grid within the range;

[0051] Figure 5 are the plane reference radius field (a) and the reconstructed three plane random fields (b) in Example 1 of the present invention;

[0052] Figure 6 These are the three full-modal three-dimensional reconstructed aggregates finally generated in Example 1 of the present invention;

[0053] Figure 7 The morphologies of the coarse, medium and fine scales and their superposition are obtained by performing spherical harmonic expansion of the target reference aggregate at different scales in Example 2 of the present invention;

[0054] Figure 8 The plane reference radius fields corresponding to the three scale forms of coarse, medium and fine in Example 2 of the present invention and their superposition properties;

[0055] Figure 9 These are the three multi-scale reconstructed aggregates finally generated in Example 2 of the present invention. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0057] In order to solve the problems of oversimplification of aggregate morphology used in existing concrete mesoscopic simulations and the expensive and time-consuming process of obtaining the true aggregate morphology through image scanning equipment, the present invention provides a multi-scale random reconstruction method for three-dimensional mesoscopic concrete aggregates, such as Figure 1 As shown, the multi-scale random reconstruction method includes steps S10 to S40, which are described in detail as follows:

[0058] S10, acquiring an image obtained by scanning the concrete test block, and performing 3D reconstruction and aggregate segmentation extraction on the image to obtain multiple STL format files of reference aggregates, wherein the STL format files contain vertex coordinates (i.e., global Cartesian coordinates) of discrete surfaces of aggregates and their connection relationships.

[0059] In step S10, to ensure the authenticity and reliability of the acquired aggregate image, the concrete test block may be scanned using XCT equipment to obtain an XCT scan image. This XCT scan image is then subjected to three-dimensional reconstruction and aggregate segmentation to extract multiple STL files of reference aggregates. Specifically, the three-dimensional reconstruction and aggregate segmentation mentioned in this embodiment can utilize common three-dimensional reconstruction and image segmentation techniques in the art to obtain an STL file containing the coordinates of the discrete surface vertices of the aggregates, which is not limited in this embodiment.

[0060] S20, selecting an STL format file of a target reference aggregate from the STL format files of the multiple reference aggregates, then performing a 15th-order or higher spherical harmonic expansion on the STL format file of the target reference aggregate, and converting the discrete surface fitting of the target reference aggregate into a continuous polar radius function by selecting a mode of the spherical harmonic expansion.

[0061] In step S20, an STL file of a target reference aggregate can be selected from multiple STL files of reference aggregates based on the desired aggregate morphological characteristics, such as sphericity, convexity, roundness, and roughness, to ensure that the selected reference aggregate has the desired morphological characteristics. Sphericity and convexity are used to characterize the coarse-scale aggregate morphology, roundness is used to describe the mesoscale aggregate morphology, and roughness is used to describe the fine-scale aggregate morphology.

[0062] In this embodiment, sphericity is defined as the surface S of a sphere of equal volume of aggregate. eq The product is divided by the surface area S of the aggregate and is calculated as Where V is the volume of the aggregate. Convexity is defined as the volume of the aggregate divided by the volume of its minimum convex hull, calculated as CI = V / V conv , where V conv is the volume of the minimum convex hull of the aggregate. The formula for calculating roundness is Among them, r i is the unit vector connecting the geometric center of the aggregate and the center of the i-th triangle unit on its surface, u i and ΔS i are the unit normal vector and area of ​​the i-th triangle element, respectively, and m is the total number of discrete triangle elements on the aggregate surface. The calculation formula for roughness is where η(x,y,z) is the distance between the vertex (x,y,z) on the aggregate surface and the average surface of the aggregate.

[0063] Then, based on the STL file of the target reference aggregate, a spherical harmonic expansion is performed on the discrete surface of the target reference aggregate, and the discrete surface of the target reference aggregate is fitted and converted into a continuous polar radius function. During the spherical harmonic expansion, the order of the spherical harmonic expansion affects the accuracy of the polar radius function, so the order of the spherical harmonic expansion can be selected to be 15 or above. The modes of the spherical harmonic expansion affect the type of scale morphology of the subsequently reconstructed 3D random aggregate, so the modes of the spherical harmonic expansion can be selected accordingly based on the type of scale morphology of the 3D random aggregate to be reconstructed. For example, when the 3D random aggregate to be reconstructed needs to have more diverse morphological characteristics, the modes of the spherical harmonic expansion can be selected to be full modes. However, in this case, the morphology of the reconstructed aggregate is more volatile than that of the reference aggregate. When the 3D random aggregate to be reconstructed needs to retain the morphological characteristics of certain scales of the reference aggregate, such as the coarse-scale morphology, the modes of the spherical harmonic expansion can be selected to be modes of different scales, leaving the spherical harmonic expansion modes corresponding to the coarse-scale morphology unchanged while reconstructing the morphologies of the other two scales.

[0064] Specifically, in step S20, the implementation method of converting the discrete surface fitting of the target reference aggregate into a continuous polar radius function includes the following steps:

[0065] S21, convert the global Cartesian coordinates of the target reference aggregate surface vertices into local polar coordinates. The conversion formula is:

[0066]

[0067] Where (x, y, z) represents the global Cartesian coordinates of the vertex on the surface of the target reference aggregate; (x0, y0, z0) represents the geometric center coordinates of the target reference aggregate; Represents the local polar coordinates of the vertex on the target reference aggregate surface.

[0068] S22, perform spherical harmonic expansion of 15 orders and above on the discrete surface of the target reference aggregate. When the selected spherical harmonic expansion mode is the full mode, the formula for converting the discrete surface fitting of the target reference aggregate into a continuous polar radius function is:

[0069]

[0070] Where, is the spherical harmonic coefficient, and the local polar coordinates of the target reference aggregate surface vertex are obtained by step S21 Substituted into the above formula and calculated by least squares fitting; is the 1st degree mth order spherical harmonic basis, and its expression is: i is the imaginary unit; P l m (x) represents the Legendre function of degree 1 and order m, which is expressed as:

[0071] When the selected spherical harmonic expansion modes are modes of different scales, the formula for converting the discrete surface fitting of the target reference aggregate into a continuous polar radius function is:

[0072]

[0073] Where, f0 and f1 correspond to the initial sphere representing the spherical harmonic expansion; The corresponding representations are the overall shape of the target reference aggregate at the coarse scale, the local roundness at the mesoscale, and the surface roughness at the fine scale.

[0074] S30, constructing a two-dimensional regular plane grid as a radius field, and then using a polar radius function to perform radius sampling on each grid node in the two-dimensional regular plane grid according to the selected mode of the spherical harmonic expansion, so that the target reference aggregate surface is converted into a regular reference radius field or reference radius fields of different scales.

[0075] In step S30, when the mode of the spherical harmonic expansion is a full mode, the polar radius function is used to perform radius sampling on each grid node in the two-dimensional regular plane grid, so that the target reference aggregate surface is converted into a regular reference radius field; when the mode of the spherical harmonic expansion is selected as a mode of different scales, the function items of different scales in the polar radius function are used to perform radius sampling on the vertex coordinates of each grid in the two-dimensional regular plane grid, so that the target reference aggregate surface is converted into a reference radius field of different scales.

[0076] Specifically, the specific implementation of step S30 in this embodiment may include the following steps:

[0077] Step S31, at θ∈[0,π], Construct a regular plane grid D within the range as follows:

[0078]

[0079] Where, Δθ=π / N, N represents θ and The number of mesh nodes in the direction, θ and Corresponding to the elevation and azimuth in the polar coordinate system; x ij Represents the polar coordinates corresponding to the grid nodes in the plane regular grid D.

[0080] Step S32: when the mode of the spherical harmonic expansion is selected as the full mode, the polar coordinates x of each grid node in the two-dimensional plane regular grid D are ij Substituting these values ​​into the polar radius function in step S20, the radius value corresponding to the target reference aggregate in each grid vertex coordinate direction can be obtained, thereby converting the discrete surface of the target reference aggregate into a regular radius field. Since the polar radius function in step S20 is related to the mode of the spherical harmonic expansion, the target reference aggregate surface can be converted into reference radius fields of different scales by controlling the mode of the spherical harmonic expansion. That is, the mode of the spherical harmonic expansion is selected as a mode of different scales, the polar coordinates of each grid node in the two-dimensional plane regular grid D are substituted into the polar radius function, and the function terms of different scales in the polar radius function are used to calculate the radius value of the target reference aggregate of different scales corresponding to each grid vertex coordinate direction, thereby converting the target reference aggregate surface into a reference radius field of different scales.

[0081] S40, extracting statistical information of the reference radius field, the statistical information including mean, standard deviation and autocorrelation function, and then performing random field reconstruction based on the statistical information to generate a plurality of three-dimensional random aggregates.

[0082] Specifically, the implementation of step S40 includes the following steps:

[0083] S41: When the mode of the spherical harmonic expansion is a full mode, statistical information of the reference radius field is extracted, and a random reconstruction algorithm is used to reconstruct multiple reconstructed random fields based on the statistical information. When the mode of the spherical harmonic expansion is a mode of different scales, statistical information of the reference radius field of different scales is extracted, and a random reconstruction algorithm is used to reconstruct planar random fields of corresponding scales based on the statistical information, and then the planar random fields are correspondingly superimposed to generate multiple reconstructed random fields. The statistical information includes a mean, a standard deviation, and an autocorrelation function.

[0084] S42, then folding each reconstructed planar random field into a three-dimensional closed surface to generate a plurality of three-dimensional random aggregates.

[0085] Among them, in step S41, the formula of the random reconstruction algorithm is:

[0086]

[0087] Where μ represents the mean value obtained from the reference radius field; S X (ω) represents the Gaussian power spectral density function, which is obtained by Fourier transforming the autocorrelation function of the reference radius field; α represents a random phase angle between 0 and 2π; N1 and N2 represent the two-dimensional regular plane grids θ and The number of grid nodes in the direction; ω represents a random sample, and I(x,ω) represents the reconstructed planar random field.

[0088] In step S42, each reconstructed plane random field is folded into a three-dimensional closed surface to generate multiple three-dimensional random aggregates. Specifically, the steps can be: averaging all the radii in the first row of the reconstructed plane random field I(x, ω), and replacing all the radii in the first row with the average value; averaging all the radii in the last row of the reconstructed plane random field I(x, ω), and replacing all the radius values ​​in the last row with the average value; averaging the corresponding radii in the first column and the last column of the reconstructed plane random field I(x, ω), and replacing the corresponding values ​​in the first column and the last column with the average value; and then performing spherical harmonic expansion on the reconstructed plane random field after the above transformation to remove the locally rough areas on its surface to obtain a three-dimensional closed surface.

[0089] The multi-scale random reconstruction method for three-dimensional micro-scale concrete aggregates provided in this embodiment has the following effects: (1) the statistical information extracted from the real aggregate surface is used in random reconstruction, which can avoid the unreliability introduced by the use of assumed statistical information; and compared with the simplified random aggregates used in previous concrete micro-scale models, such as spheres, ellipsoids and polyhedrons, the aggregate morphology generated by the multi-scale random reconstruction method provided in this embodiment is more diverse, realistic and reliable; (2) this embodiment provides a rigorous basis for decomposing, reconstructing and superimposing the morphological features of aggregates of different scales, by selecting the spherical harmonic modes corresponding to the morphologies of aggregates of different scales for spherical reconstruction. Harmonic expansion and random reconstruction can control the surface morphology of the reconstructed aggregate, providing good controllability and flexibility for the three-dimensional random reconstruction of the aggregate surface morphology; (3) based on a small amount of real aggregate, a large number of real and diverse random aggregates can be reconstructed, avoiding the need to carry out a large number of expensive, tedious and time-consuming image scanning experiments and related image processing to obtain aggregates with different surface morphologies, saving a lot of costs related to image scanning experiments and processing; (4) since the morphology of aggregates has an important influence on the physical and mechanical properties of concrete, the random aggregates generated by this embodiment are used to perform concrete micro-numerical simulations, and the simulation results can be more reliable and representative.

[0090] Based on the same inventive concept, the present invention also provides a multi-scale random reconstruction system for three-dimensional meso-concrete aggregate, including an acquisition module, a fitting conversion module, a radius sampling module and a reconstruction module.

[0091] Among them, the acquisition module is used to obtain the scanning image of the concrete test block, perform three-dimensional reconstruction and aggregate segmentation on it, and extract STL format files of multiple reference aggregates. The STL format files contain the vertex coordinates of the discrete surface of the aggregate and their connection relationships.

[0092] The fitting conversion module is used to select an STL format file with target morphological characteristics from multiple STL format files of reference aggregates, and perform spherical harmonic expansion of 15th order or above on it. Then, by selecting the mode of the spherical harmonic expansion, the discrete surface fitting of the target reference aggregate is converted into a continuous polar radius function.

[0093] The radius sampling module is used to construct a two-dimensional regular plane grid, and then use the polar radius function to perform radius sampling on each grid node in the two-dimensional regular plane grid according to the selected mode of the spherical harmonic expansion, so that the target reference aggregate surface is converted into a regular reference radius field or reference radius fields of different scales.

[0094] The reconstruction module is used to extract statistical information of the reference radius field, which includes the mean, standard deviation and autocorrelation function, and then reconstruct the random field according to the statistical information to generate multiple three-dimensional random aggregates.

[0095] Specifically, the functions of each module provided in this embodiment can be found in the detailed description of the aforementioned method embodiment, and will not be repeated in this embodiment.

[0096] To more clearly illustrate this solution, the multi-scale random reconstruction method of three-dimensional meso-concrete aggregate provided by the present invention is described below in conjunction with specific embodiments:

[0097] Example 1

[0098] In this embodiment, after performing spherical harmonic expansion on the reference aggregate, all modes are selected for random weighting to illustrate the implementation process of the method proposed in the present invention, which includes the following steps:

[0099] Step 1: Scan the concrete test block using XCT equipment, perform 3D reconstruction and aggregate segmentation extraction on the XCT scan image, and obtain 635 reference aggregates, such as Figure 2 shown.

[0100] Step 2: Select a target reference aggregate such as Figure 3 As shown in part (a), the global Cartesian coordinates of the surface vertices are converted to local polar coordinates. The conversion formula is as follows:

[0101]

[0102] Where (x, y, z) represents the global Cartesian coordinates of the vertex on the surface of the target reference aggregate; (x0, y0, z0) represents the geometric center coordinates of the target reference aggregate; Represents the local polar coordinates of the vertex on the target reference aggregate surface.

[0103] Perform a 15th-order spherical harmonic expansion on the target reference aggregate, and convert the discrete point fitting on the target reference aggregate surface into a continuous polar radius function as follows:

[0104]

[0105] Where, are the spherical harmonic coefficients; is the 1st degree mth order spherical harmonic basis, and its expression is: Where i is the imaginary unit, P l m (x) represents the Legendre function of degree 1 and order m, which is expressed as:

[0106] Set the local polar coordinates of the target reference aggregate Substituting the above polar radius function, the spherical harmonic coefficients can be calculated by least squares fitting The aggregate shape after spherical harmonic expansion of the 15th order mode is as follows Figure 3 As shown in part (b).

[0107] Step 3: Construct a two-dimensional regular plane grid as the radius field and random field, and use the continuous polar radius function in step 2 to perform radius sampling on each grid node, thereby converting the reference aggregate surface into a regular plane reference radius field.

[0108] First, in θ∈[0,π], A plane regular grid D is constructed within the range as the radius field and random field, such as Figure 4 As shown, its expression is as follows:

[0109]

[0110] Where, Δθ=π / N, N represents θ and The number of grid nodes in the direction; in this embodiment, N=100.

[0111] Secondly, the polar coordinates of each grid node in the plane regular grid D are substituted into the polar radius function in step 2, and the radius value of the reference aggregate corresponding to each grid vertex coordinate can be obtained, thereby converting the target reference aggregate surface into a regular reference radius field, such as Figure 5 As shown in part (a).

[0112] Step 4: Calculate the mean, standard deviation and autocorrelation function of the above-mentioned rule reference radius field, and use the following formula to reconstruct the random field. The three reconstructed random fields generated are as follows: Figure 5 As shown in part (b).

[0113]

[0114] Where μ represents the mean value obtained from the reference radius field; S X (ω) represents the Gaussian power spectral density function, which is obtained by Fourier transforming the autocorrelation function of the reference radius field; α represents a random phase angle between 0 and 2π; N1 and N2 represent the two-dimensional regular plane grids θ and The number of grid nodes in the direction; ω represents a random sample, and I(x,ω) represents the reconstructed planar random field.

[0115] Step 5: Fold the planar random field reconstructed in step 4 into a closed three-dimensional surface to generate a three-dimensional random aggregate that inherits the surface statistical information and morphological characteristics of the reference aggregate.

[0116] First, all radius values ​​in the first row of the random field I(x,ω) are averaged and replaced with the mean.

[0117] Second, all radius values ​​in the last row of the random field I(x,ω) are averaged and replaced with the mean.

[0118] Furthermore, the corresponding values ​​in the first and last columns of the random field I(x,ω) are averaged, and then the corresponding values ​​in the first and last columns are replaced with the average.

[0119] Finally, the transformed random field is subjected to a 15th-order spherical harmonic expansion using the spherical harmonic expansion method in step 2 to remove the locally rough areas on its surface.

[0120] Using the above folding method, the three reconstructed random fields generated in step 4 are folded into three three-dimensional reconstructed aggregates as follows: Figure 6 shown.

[0121] Example 2

[0122] In this example, modes of different scales are randomly reconstructed after spherical harmonic expansion of the target reference aggregate, which shows that the method proposed in the present invention can perform multi-scale reconstruction of the reference aggregate to control the morphology of the reconstructed aggregate.

[0123] Step 1: Same as in Example 1, and will not be described in detail in this example.

[0124] Step 2: Same as Example 1, the polar radius function obtained by performing a 15th-order spherical harmonic expansion of the discrete points on the reference aggregate surface is divided into three scales, and the expression is as follows:

[0125]

[0126] The first two terms on the right side of the equation correspond to the initial sphere of the spherical harmonic expansion, and the third, fourth, and fifth terms characterize the overall shape of the reference aggregate at the coarse scale, the local roundness at the mesoscale, and the surface roughness at the fine scale, respectively. Figure 7 shown.

[0127] Step 3: Construct a two-dimensional regular plane grid as the radius field and random field, and use the polar radius function terms of different scales in step 2 to perform radius sampling on each grid node, thereby converting the reference aggregate surface into a plane reference radius field of different scales.

[0128] First, in θ∈[0,π], A plane regular grid D is constructed within the range as the radius field and random field, such as Figure 4 As shown, its expression is as follows:

[0129]

[0130] Where, Δθ=π / N, N is θ and The number of grid nodes in the direction, in this embodiment, N=100.

[0131] Secondly, the polar coordinates of each grid node in the two-dimensional plane regular grid D are substituted into the polar radius function in step 2. The radius value of the target reference aggregate of different scales corresponding to each grid vertex coordinate can be obtained by using the function terms of different scales, thereby converting the target reference aggregate surface into a reference radius field of different scales, such as Figure 8 shown.

[0132] Step 4: The random field reconstruction method is the same as Example 1, but only the medium and fine scale reference radius fields are randomly reconstructed, and the coarse scale reference radius field is fixed unchanged. Finally, the coarse scale reference radius field and the medium and fine scale reconstructed random fields are superimposed to generate the final random field.

[0133] Step 5: The random field folding method is the same as in Example 1. The random field finally obtained in step 4 is folded into a three-dimensional reconstructed aggregate. The three random aggregate samples generated are as follows: Figure 9 The three random aggregates generated have morphological characteristics at different scales, among which they have the same overall morphology at the coarse scale as the reference aggregate, but different local roundness at the mesoscale and surface roughness at the fine scale.

[0134] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-scale random reconstruction method for three-dimensional meso-concrete aggregate, characterized by: The steps include: (1) Obtaining a scanned image of a concrete specimen, performing three-dimensional reconstruction and aggregate segmentation on the image, and extracting multiple STL format files of reference aggregates, wherein the STL format files contain vertex coordinates of discrete aggregate surfaces and their connection relationships; (2) Select an aggregate STL file with target morphological characteristics from multiple reference aggregate STL files, perform 15th-order or higher spherical harmonic expansion on it, and then convert the discrete surface fitting of the target reference aggregate into a continuous polar radius function by selecting the mode of the spherical harmonic expansion; (3) Construct a two-dimensional regular plane grid, and then use the polar radius function to perform radius sampling on each grid node in the two-dimensional regular plane grid according to the selected mode of the spherical harmonic expansion, so that the target reference aggregate surface is converted into a regular reference radius field or a reference radius field of different scales; (4) Extracting statistical information of the reference radius field, which includes mean, standard deviation and autocorrelation function, and then reconstructing the random field based on the statistical information to generate multiple three-dimensional random aggregates; step (4) is specifically as follows: (4.1) When the mode of the spherical harmonic expansion is a full mode, the statistical information of the reference radius field is extracted, and a random reconstruction algorithm is used to reconstruct multiple reconstructed random fields based on the statistical information; when the mode of the spherical harmonic expansion is a mode of different scales, the statistical information of the reference radius field of different scales is extracted, and a random reconstruction algorithm is used to reconstruct a plane random field of the corresponding scale based on the statistical information, and then the two are superimposed to generate multiple reconstructed random fields; wherein the statistical information includes the mean, standard deviation and autocorrelation function; in step (4.1), the formula of the random reconstruction algorithm is: Where, μ represents the mean value obtained from the reference radius field; S X ( ω ) represents the Gaussian power spectral density function, which is obtained by Fourier transforming the autocorrelation function of the reference radius field; α represents a random phase angle between 0 and 2𝜋; N 1 and N 2 represents the two-dimensional regular plane grid θ and φ The number of mesh nodes in the direction; ω represents a random sample, I(x, ω ) represents the reconstructed planar random field; (4.2) Each reconstructed planar random field is folded into a three-dimensional closed surface to generate multiple three-dimensional random aggregates.

2. The multi-scale random reconstruction method of three-dimensional meso-concrete aggregate according to claim 1, characterized in that: In step (2), the modes of the spherical harmonic expansion include full modes and modes of different scales, and the modes of the spherical harmonic expansion are selected accordingly according to the scale morphology type of the three-dimensional random aggregate to be reconstructed.

3. The multi-scale random reconstruction method of three-dimensional meso-concrete aggregate according to claim 2, characterized in that: In step (2), the step of performing a spherical harmonic expansion of order 15 or above, and then converting the discrete surface fitting of the target reference aggregate into a continuous polar radius function by selecting the mode of the spherical harmonic expansion is specifically as follows: (2.1) The coordinates of the target reference aggregate surface vertices are converted into local polar coordinates. The conversion formula is: Where, ( x , y , z ) represents the coordinates of the vertex of the target reference aggregate surface; ( x 0, y 0, z 0) represents the geometric center coordinates of the target reference aggregate; ( r , θ , φ ) represents the local polar coordinates of the vertex on the target reference aggregate surface; (2.2) The discrete surface of the target reference aggregate is expanded with spherical harmonics of order 15 or above. When the selected spherical harmonic expansion mode is the full mode, the formula for converting the discrete surface fitting of the target reference aggregate into a continuous polar radius function is: Where, ( l = 1 ~ n, m = ‒ l ~ l ) are spherical harmonic coefficients, and the local polar coordinates of the target reference aggregate surface vertices are obtained from step (2.1) ( r , θ , φ ) is substituted into the formula of the polar radius function and calculated by least squares fitting; ( θ , φ )yes l Spend m The order spherical harmonic basis is expressed as: ; i is an imaginary unit; ( x )express l Spend m The Legendre function of order is expressed as: ； When the selected spherical harmonic expansion modes are modes of different scales, the formula for converting the discrete surface fitting of the target reference aggregate into a continuous polar radius function is: Where, ; f 0. f 1 corresponds to the initial sphere of the spherical harmonic expansion; ( i ∈ [2, 4]), ( j ∈ [5, 8]), ( k ∈ [9, 15]) corresponds to the overall shape of the target reference aggregate at the coarse scale, the local roundness at the mesoscale, and the surface roughness at the fine scale.

4. The multi-scale random reconstruction method of three-dimensional meso-concrete aggregate according to claim 2, characterized in that: Step (3) is as follows: (3.1) θ ∈ [0, 𝜋], φ Construct a two-dimensional regular plane grid within the range of ∈ [0, 2𝜋] D , the expression is: Where, ∆ θ = 𝜋 ∕ N ,∆ φ =2𝜋 ∕ N ; N express θ and φ The number of mesh nodes in the direction, θ and φ Corresponding to the elevation and azimuth in the polar coordinate system; x ij Represents a regular grid on a plane D Polar coordinates corresponding to the grid nodes; (3.2) When the mode of the spherical harmonic expansion is selected as the full mode, the two-dimensional regular plane grid D Substitute the polar coordinates of each grid node into the polar radius function to calculate the radius of the target reference aggregate in the coordinate direction of each grid vertex, thereby decomposing the target reference aggregate surface into a regular plane reference radius field; When the modes of the spherical harmonic expansion are selected as modes of different scales, the two-dimensional regular plane grid D The polar coordinates of each grid node are substituted into the polar radius function, and the function terms of different scales in the polar radius function are used to calculate the radius values ​​of the target reference aggregate of different scales corresponding to the coordinate direction of each grid vertex, thereby converting the target reference aggregate surface into a reference radius field of different scales.

5. The multi-scale random reconstruction method of three-dimensional meso-concrete aggregate according to claim 1, characterized in that: In step (4.2), the step of folding each reconstructed planar random field into a three-dimensional closed surface is specifically as follows: (a) Reconstruct the plane random field I(x, ω ) and replace all radii in the first row with the average value; (b) Reconstruct the plane random field I(x, ω ) and replace all radius values ​​in the last row with the average value; (c) Reconstruct the plane random field I(x, ω ) and then replace the corresponding values ​​in the first and last columns with the average value; (d) Performing spherical harmonic expansion on the reconstructed planar random field transformed in steps (a) to (c) to remove the locally rough areas on its surface and obtain a three-dimensional closed surface.

6. The multi-scale random reconstruction method of three-dimensional meso-concrete aggregate according to claim 1, characterized in that: In step (1), the concrete test block is scanned using an XCT device to obtain an XCT scan image.

7. The multi-scale random reconstruction method of three-dimensional meso-concrete aggregate according to claim 1, characterized in that: In step (2), the step of selecting an aggregate STL format file having target morphological characteristics from a plurality of reference aggregate STL format files is specifically as follows: According to the vertex coordinates of each reference aggregate surface, the four morphological parameters of each reference aggregate, namely sphericity, convexity, roundness and roughness, are calculated accordingly; According to the morphological parameters of each reference aggregate, an STL format file with target morphological characteristics is selected.

8. A multi-scale random reconstruction system for three-dimensional meso-concrete aggregates, characterized by: include: An acquisition module is used to acquire a scanned image of a concrete test block, perform three-dimensional reconstruction and aggregate segmentation on the image, and extract multiple STL format files of reference aggregates, wherein the STL format files contain vertex coordinates of discrete surfaces of the aggregates and their connection relationships; The fitting conversion module is used to select an STL file with target morphological characteristics from multiple STL files of reference aggregates, perform spherical harmonic expansion of 15th order or above on it, and then convert the discrete surface fitting of the target reference aggregate into a continuous polar radius function by selecting the mode of the spherical harmonic expansion; The radius sampling module is used to construct a two-dimensional regular plane grid, and then use the polar radius function to perform radius sampling on each grid node in the two-dimensional regular plane grid according to the selected mode of the spherical harmonic expansion, so as to convert the target reference aggregate surface into a regular reference radius field or reference radius fields of different scales; The reconstruction module is used to extract statistical information of the reference radius field, including the mean, standard deviation, and autocorrelation function, and then reconstruct the random field based on the statistical information to generate multiple three-dimensional random aggregates; specifically: The first unit is used to extract statistical information of the reference radius field when the mode of the spherical harmonic expansion is a full mode, and reconstruct multiple reconstructed random fields using a random reconstruction algorithm based on the statistical information; when the mode of the spherical harmonic expansion is a mode of different scales, extract statistical information of the reference radius field of different scales, and reconstruct planar random fields of corresponding scales using a random reconstruction algorithm based on the statistical information, and then superimpose them accordingly to generate multiple reconstructed random fields; wherein the statistical information includes a mean, a standard deviation, and an autocorrelation function; in the first unit, the formula of the random reconstruction algorithm is: Where, μ represents the mean value obtained from the reference radius field; S X ( ω ) represents the Gaussian power spectral density function, which is obtained by Fourier transforming the autocorrelation function of the reference radius field; α represents a random phase angle between 0 and 2𝜋; N 1 and N 2 represents the two-dimensional regular plane grid θ and φ The number of mesh nodes in the direction; ω represents a random sample, I(x, ω ) represents the reconstructed planar random field; The second unit is used for folding each reconstructed plane random field into a three-dimensional closed surface to generate a plurality of three-dimensional random aggregates.

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