Aggregate morphology quantification evaluation method and system based on frequency analysis

Abstract

This invention discloses a method for quantitatively evaluating the morphology of aggregates based on frequency analysis, comprising the following steps: performing three-dimensional laser scanning on aggregate particles and removing noise to obtain the boundary pixel coordinates of the aggregate particles; calculating the centroid coordinates and centered coordinates of the aggregate particles' outlines, and constructing a complex sequence of each pixel point in the aggregate particles based on the centered coordinates; performing a discrete Fourier transform on the complex sequence to calculate the Fourier coefficients and amplitude spectrum of the complex sequence; extracting feature values ​​of different morphological parameters according to a preset set of contribution frequencies, and constructing a morphological model of each morphological parameter based on the feature values; substituting the amplitude spectrum of the aggregate particles into the morphological model to quantify each morphological parameter of the aggregate particles. This invention also discloses a system for quantitatively evaluating the morphology of aggregates based on frequency analysis. This invention solves the technical problem of how to accurately and quickly determine the morphology of aggregate particles.

Description

Technical Field

[0001] This invention relates to the field of aggregate application technology, and in particular to a method and system for quantitative evaluation of aggregate performance based on frequency analysis. Background Technology

[0002] As a key component of pavement structure, aggregates directly influence the mechanical properties and functionality of pavement materials through their morphological characteristics. Within the pavement structure, aggregate particles form a stable internal skeletal network through direct contact and interlocking. This structure bears and transmits vehicle loads, fundamentally ensuring the pavement's load-bearing capacity. Simultaneously, the morphology and texture of the exposed portions of aggregates on the pavement surface constitute the macroscopic and microscopic structure of the road surface. These structural features directly affect the friction between tires and the pavement surface, determining the pavement's skid resistance and thus becoming a key factor influencing driving safety. Therefore, accurate, objective, and efficient quantitative evaluation of the apparent morphology of aggregate particles—primarily shape, angularity, and surface texture—is of paramount engineering significance for ensuring the scientific design of pavement materials, controlling construction quality, and predicting long-term performance.

[0003] However, current aggregate testing specifications and standards generally suffer from inefficiencies and high subjectivity in evaluation methods related to appearance morphology. For example, methods for determining the content of flat and elongated particles, assessing angularity based on the number of broken surfaces, or indirectly inferring the angularity of fine aggregates through loose porosity are not only cumbersome and time-consuming, but also highly dependent on the experience and subjective judgment of operators. This leads to poor comparability and repeatability of test results between different laboratories and even between different operators within the same laboratory, failing to meet the urgent needs of modern materials quality control for efficient, accurate, and standardized testing. While 2D image-based aggregate appearance morphology testing and evaluation methods can analyze aggregate appearance morphology relatively quickly and objectively, different systems exhibit significant differences in the calculation methods for various appearance morphology indicators. Furthermore, most analyses involved in these systems are conducted in the spatiotemporal domain, making it difficult to thoroughly distinguish different components of aggregate appearance morphology, such as shape, angularity, and surface texture. Moreover, limited by the dimensionality and resolution of two-dimensional images, these systems struggle to comprehensively and accurately collect aggregate surface structure information. Therefore, there is an urgent need to propose a quantitative evaluation method and system for aggregate performance based on frequency analysis to solve the technical problem of how to accurately and quickly determine the performance morphology of aggregate particles. Summary of the Invention

[0004] The main objective of this invention is to propose a quantitative evaluation method and system for aggregate morphology based on frequency analysis, aiming to solve the technical problem of how to accurately and quickly determine the morphology of aggregate particles.

[0005] To achieve the above objectives, the present invention provides a method for quantitative evaluation of aggregate behavior patterns based on frequency analysis, wherein the method includes the following steps:

[0006] S1. Perform three-dimensional laser scanning on the aggregate particles and remove noise to obtain the boundary pixel coordinates of the aggregate particles;

[0007] S2. Calculate the centroid coordinates and centered coordinates of the aggregate particles, and construct a complex sequence of each pixel in the aggregate particles based on the centered coordinates.

[0008] S3. Perform a discrete Fourier transform on the complex sequence to calculate the Fourier coefficients and amplitude spectrum of the complex sequence;

[0009] S4. Extract feature values ​​of different morphological parameters according to the preset contribution frequency set, and construct morphological models of each morphological parameter based on the feature values. Substitute the amplitude spectrum of the aggregate particles into the morphological model to quantify each morphological parameter of the aggregate particles.

[0010] In one preferred embodiment, the centroid coordinates of the contour are:

[0011]

[0012]

[0013] in, For each pixel in the aggregate particles The average value of the coordinates This represents the total number of outline pixels. For the first 1 pixel Coordinate values For each pixel in the aggregate particles The average value of the coordinates For the first 1 pixel Coordinate values ;

[0014] The centralized coordinates are:

[0015]

[0016]

[0017] in, For the decentralized first 1 pixel Coordinate values For the decentralized first 1 pixel Coordinate values;

[0018] The complex sequence of each pixel in the aggregate particle is:

[0019]

[0020] in, For the first A complex sequence of pixels.

[0021] In one preferred embodiment, step S3 involves performing a discrete Fourier transform on the complex sequence and calculating the Fourier coefficients of the complex sequence, specifically as follows:

[0022]

[0023] in, For the first Fourier coefficients of a complex sequence of pixels. This represents the total number of outline pixels. For the first A complex sequence of pixels, , is the interval between two consecutive elements in a complex sequence.

[0024] In one preferred embodiment, step S3 involves performing a discrete Fourier transform on the complex sequence to calculate the amplitude spectrum of the complex sequence, specifically as follows:

[0025] S31. Substitute Euler's formula into the Fourier coefficients of the complex number sequence to obtain the Fourier coefficients in trigonometric form.

[0026] S32. Separate the real and imaginary parts of the Fourier coefficients in the form of the trigonometric function, and calculate the sum of the real and imaginary parts to synthesize the first Fourier coefficients;

[0027] S33. Based on the first Fourier coefficients, calculate the amplitude of the complex sequence, that is, the amplitude spectrum of each frequency component.

[0028] One preferred embodiment, step S31, specifically includes:

[0029] Substituting Euler's formula into the Fourier coefficients of the complex sequence, Euler's formula becomes:

[0030]

[0031] The Fourier coefficients in trigonometric form are obtained as follows:

[0032] .

[0033] One preferred embodiment, step S332, specifically includes:

[0034] Separate the real and imaginary parts of the Fourier coefficients in the trigonometric function form;

[0035] The real part is:

[0036]

[0037] The imaginary part is:

[0038]

[0039] Calculate the sum of the real and imaginary parts to synthesize the first Fourier coefficients; the first Fourier coefficients are:

[0040]

[0041] in, is the real part of the Fourier coefficients in trigonometric form. For the decentralized first 1 pixel Coordinate values For the decentralized first 1 pixel Coordinate values represents the imaginary part of the Fourier coefficients in trigonometric form. is the first Fourier coefficient.

[0042] In one preferred embodiment, the magnitude of the complex sequence is:

[0043]

[0044] in, denoted as the magnitude of the complex sequence.

[0045] In one preferred embodiment, step S4, extracting feature values ​​of different morphological parameters based on a preset set of contribution frequencies, includes:

[0046] The contribution frequencies of the angularity index UIAIA are -12 pixels / cycle, +8 pixels / cycle, +14 pixels / cycle, and +18 pixels / cycle;

[0047] The contribution frequencies of the aspect ratio ER are -5 pixels / cycle, -1 pixel / cycle, and +1 pixel / cycle;

[0048] The contribution frequencies of sphericity SP are -7 pixels / cycle, -5 pixels / cycle, -1 pixel / cycle, and +1 pixel / cycle;

[0049] The contribution frequencies of the average radius MR are -5 pixels / cycle, -3 pixels / cycle, -1 pixel / cycle, and +1 pixel / cycle;

[0050] The contribution frequencies of variance VR are -5 pixels / cycle, -3 pixels / cycle, -1 pixel / cycle, and +1 pixel / cycle.

[0051] One preferred embodiment is that constructing the morphological model for each morphological parameter based on the feature values ​​includes:

[0052] The morphological model of the angularity index UIAIA is as follows:

[0053]

[0054] The morphological model of the aspect ratio ER is as follows:

[0055]

[0056] The morphological model of sphericity SP is as follows:

[0057]

[0058] The morphological model of the average radius MR is:

[0059]

[0060] The morphological model of variance VR is:

[0061]

[0062] in, The morphological model of the angularity index UIAIA. The morphological model for the aspect ratio ER. The morphological model for sphericity SP. The morphological model is the average radius MR. This is the morphological model of variance VR.

[0063] A system including the aforementioned method for quantitative evaluation of aggregate morphology based on frequency analysis includes an image processing and boundary extraction module, a discrete Fourier transform analysis module, and a morphological parameter calculation module connected in sequence.

[0064] The image processing and boundary extraction module is used to extract the boundary pixel coordinates from the two-dimensional image of the aggregate particles;

[0065] The discrete Fourier transform analysis module is used to calculate the Fourier transform and convert spatial domain coordinates into frequency domain features;

[0066] The morphological parameter calculation module is used to calculate the amplitude spectra of different contribution frequencies using different morphological models.

[0067] The above-described technical solution of the present invention provides a frequency-analysis-based quantitative evaluation method for aggregate morphology, comprising the following steps: performing three-dimensional laser scanning on aggregate particles and removing noise to obtain the boundary pixel coordinates of the aggregate particles; calculating the centroid coordinates and centered coordinates of the aggregate particles, and constructing a complex sequence of each pixel point in the aggregate particles based on the centered coordinates; performing a discrete Fourier transform on the complex sequence to calculate the Fourier coefficients and amplitude spectrum of the complex sequence; extracting feature values ​​of different morphological parameters according to a preset set of contribution frequencies, and constructing a morphological model of each morphological parameter based on the feature values; substituting the amplitude spectrum of the aggregate particles into the morphological model to quantify the morphological parameters of the aggregate particles. This invention solves the technical problem of how to accurately and quickly determine the morphology of aggregate particles. By optimizing the aggregate surface morphology analysis process through automation, it significantly reduces human subjectivity, time consumption, equipment costs, and data processing complexity, improves the analytical capabilities of laboratories, and makes aggregate morphology evaluation more standardized and scientific, providing strong technical support for aggregate quality control, mixture design, and pavement performance prediction. Attached Figure Description

[0068] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0069] Figure 1 This is a schematic diagram of a quantitative evaluation method for aggregate performance based on frequency analysis according to an embodiment of the present invention;

[0070] Figure 2 This is a schematic diagram of a certain aggregate particle according to an embodiment of the present invention.

[0071] The realization of the objective, functional characteristics and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0072] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0073] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature.

[0074] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0075] See Figures 1-2 According to one aspect of the present invention, the present invention provides a method for quantitative evaluation of aggregate behavior patterns based on frequency analysis, wherein the method for quantitative evaluation of aggregate behavior patterns based on frequency analysis includes the following steps:

[0076] S1. Perform three-dimensional laser scanning on the aggregate particles and remove noise to obtain the boundary pixel coordinates of the aggregate particles;

[0077] S2. Calculate the centroid coordinates and centered coordinates of the aggregate particles, and construct a complex sequence of each pixel in the aggregate particles based on the centered coordinates.

[0078] S3. Perform a discrete Fourier transform on the complex sequence to calculate the Fourier coefficients and amplitude spectrum of the complex sequence;

[0079] S4. Extract feature values ​​of different morphological parameters according to the preset contribution frequency set, and construct morphological models of each morphological parameter based on the feature values. Substitute the amplitude spectrum of the aggregate particles into the morphological model to quantify each morphological parameter of the aggregate particles.

[0080] Specifically, in this embodiment, the aggregate particles to be processed are selected, mainly including particles of different sizes, surface shapes, and angular shapes. A hardware system using three-dimensional laser technology to acquire high-precision aggregate morphology information scans the aggregate particles to obtain digital images, determines the pixel units of the scanned digital images, and uses accompanying analysis software to remove noise, resulting in a processed digital image. The hardware system using three-dimensional laser technology to acquire high-precision aggregate morphology information uses a line laser scanning system or similar equipment developed by the University of Texas at Austin, along with accompanying analysis software. The line laser scanning system can accurately capture the two-dimensional parameters of the aggregate particles, and the accompanying analysis software generates the coordinate points of the original pixels for subsequent Fourier transform analysis. The present invention does not impose specific limitations on the calculation of the amplitude spectrum, and the specific settings can be configured as needed. Each pixel can be searched using a pair of row and column numbers to obtain the boundary pixel coordinates of the aggregate particles. After obtaining the boundary pixel coordinates, the coordinates are located by subtracting the average of the x and y coordinates from the original coordinates of the boundary pixels. Then, the x-coordinate of each pixel is taken as the real part and the y-coordinate as the imaginary part to obtain a complex number sequence. These complex number sequences can be uniformly analyzed using Discrete Fourier Transform (DFT). The goal of performing DFT on the complex number sequences is to convert spatial domain (surface morphology) data into frequency domain data to analyze the surface performance at different frequencies. Specifically:

[0081]

[0082] in, For the first Fourier coefficients of a complex sequence of pixels. This represents the total number of outline pixels. For the first A complex sequence of pixels, , The interval between two consecutive elements in a complex sequence; These are the Fourier coefficients corresponding to frequency t=n, which can also be seen as the coefficients at frequency t=n. Description in the frequency domain;

[0083] According to Euler's formula:

[0084]

[0085] The Fourier coefficients in trigonometric form are:

[0086]

[0087] in,

[0088]

[0089] Combining the above formulas, we obtain the real and imaginary parts:

[0090] The real part is:

[0091]

[0092] The imaginary part is:

[0093]

[0094] Calculate the sum of the real and imaginary parts to synthesize the first Fourier coefficients; the first Fourier coefficients are:

[0095]

[0096] in, is the real part of the Fourier coefficients in trigonometric form. For the decentralized first 1 pixel Coordinate values For the decentralized first 1 pixel Coordinate values represents the imaginary part of the Fourier coefficients in trigonometric form. The first Fourier coefficient;

[0097] The step S4, which involves extracting feature values ​​of different morphological parameters based on a preset set of contribution frequencies, includes:

[0098] The contribution frequencies of the angularity index UIAIA are -12 pixels / cycle, +8 pixels / cycle, +14 pixels / cycle, and +18 pixels / cycle; the contribution frequencies of the aspect ratio ER are -5 pixels / cycle, -1 pixel / cycle, and +1 pixel / cycle; the contribution frequencies of the sphericity SP are -7 pixels / cycle, -5 pixels / cycle, -1 pixel / cycle, and +1 pixel / cycle; the contribution frequencies of the mean radius MR are -5 pixels / cycle, -3 pixels / cycle, -1 pixel / cycle, and +1 pixel / cycle; and the contribution frequencies of the variance VR are -5 pixels / cycle, -3 pixels / cycle, -1 pixel / cycle, and +1 pixel / cycle. The frequency unit is pixels / cycle. The sequence, frequency Corresponding Fourier transform index ,when When ≥0, = ,when When <0, = + Among them, the angularity index UIAIA is a dimensionless parameter that quantifies the sharpness of the aggregate particles' edges; the aspect ratio ER is a dimensionless parameter that describes the elongation of the aggregate particles; the sphericity SP is a dimensionless parameter that describes the degree to which the aggregate particles are close to a sphere; the mean radius MR is in pixels or actual size; and the variance VR is in pixels squared, representing the dispersion of the distance from each point on the aggregate profile to the centroid, describing whether the aggregate shape is regular.

[0099] The construction of the morphological model for each morphological parameter based on the feature values ​​includes:

[0100] The morphological model of the angularity index UIAIA is as follows:

[0101]

[0102] The morphological model of the aspect ratio ER is as follows:

[0103]

[0104] The morphological model of sphericity SP is as follows:

[0105]

[0106] The morphological model of the average radius MR is:

[0107]

[0108] The morphological model of variance VR is:

[0109]

[0110] in, The morphological model of the angularity index UIAIA. The morphological model for the aspect ratio ER. The morphological model for sphericity SP. The morphological model is the average radius MR. A morphological model for variance VR;

[0111] After performing complex sequence Fourier transform on the scanned aggregate particles, the frequency spectrum of each frequency component in the frequency domain is calculated. The calculated amplitude spectra of different contribution frequencies are then substituted into different morphological models. The results are used to comprehensively rate and judge the quality of the scanned aggregate particles based on the values ​​in Tables 1-5.

[0112] Table 1. Angularity Index (UIAIA) Segmentation and Aggregate Properties

[0113] UIAIA value range angularity level Description of aggregate properties Typical morphological characteristics 500-1000 Low angularity Smooth outline, rounded corners Almost no sharp corners, with rounded edges 1000-1500 Medium to low angularity A few corners are rounded, but the overall surface remains relatively smooth. A few obtuse angles, with gently undulating contours. 1500-2000 Medium angularity The corners are distinct, and the outline has a certain undulation, which is typical of crushed aggregates. Multiple corners, some of which are quite sharp 2000-2400 High angularity The corners are numerous and sharp, with significant variations in the outline. Sharp edges and distinct corners ＞2400 Extremely high angularity The corners are numerous and very sharp, with complex and varied outlines. Mostly freshly crushed aggregate with serrated edges.

[0114] Table 2. Aspect Ratio ER Zoning and Appearance Morphology Judgment Criteria

[0115] ER range Apparent morphology determination Typical geometric features Engineering significance ER≤1.5 Near-equiaxed Approximately circular or cube Good stability and high shear resistance 1.5<ER≤2.0 Slightly longer Slightly oval The skeletal structure is still stable. 2.0<ER≤2.5 Slender Obvious ellipse Enhanced contact anisotropy ER>2.5 needle-like Noticeably slender or flat Fragile, mechanically unfavorable

[0116] Table 3 Sphericity SP Zone and Apparent Morphology Judgment Criteria

[0117] SP range sphericity Contour features Engineering meaning SP≥0.80 High sphericity Smooth and uniform Stable contact and uniform stress distribution 0.65≤SP<0.80 medium Slightly elliptical Acceptable engineering forms 0.50≤SP<0.65 Low sphericity Obviously deviates from a circle Concentrated contact reduces crack resistance SP<0.50 Extremely low Strong non-rules Unfavorable to skeletal structure

[0118] Table 4. Average Radius MR Zones and Apparent Morphology Judgment Criteria

[0119] MR range (relative) Geometric Scale illustrate MR is small Fine aggregate or small particles Limited influence of morphology MR Medium Conventional coarse aggregate Morphological control area MR is relatively large Large-diameter particles The magnification effect of morphological defects is obvious.

[0120] Table 5. Variance VR partitioning and apparent morphology determination criteria

[0121] VR level Boundary features Morphological determination Frequency domain correspondence VR Low The radius changes gradually Uniform contour Low frequency dominance VR and other medium Fluctuations exist Obvious non-circularity Low-mid frequency VR is relatively high. Dramatic changes irregular shapes Low frequency plus mid frequency enhancement VR Extremely High Sharp serrations Brutallite, rough High frequency enhancement

[0122] Specifically, in this embodiment, according to Figure 2 The aggregate particles were scanned to obtain 128 aggregate coordinates, and the specific coordinates are shown in Table 6.

[0123] Table 6. Aggregate coordinates of a certain aggregate particle

[0124] N X Y N X Y N X Y N X Y 0 42 0 34 -40.751 -11.417 68 61.955 6.004 102 -29.305 8.347 1 41.821 1.544 35 -40.455 -11.707 69 62.406 4.613 103 -30.888 9.363 2 41.285 3.06 36 -39.773 -11.801 70 62.497 3.129 104 -32.202 10.219 3 40.398 4.522 37 -38.707 -11.697 71 62.231 1.574 105 -33.247 10.9 4 39.17 5.906 38 -37.262 -11.395 72 61.612 0 106 -34.027 11.395 5 37.612 7.188 39 -35.446 -10.9 73 60.647 -1.574 107 -34.549 11.697 6 35.739 8.347 40 -33.27 -10.219 74 59.346 -3.129 108 -34.821 11.801 7 33.566 9.363 41 -30.75 -9.363 75 57.719 -4.613 109 -34.855 11.707 8 31.113 10.219 42 -27.903 -8.347 76 55.781 -6.004 110 -34.662 11.417 9 28.4 10.9 43 -24.751 -7.188 77 53.546 -7.283 111 -34.255 10.936 10 25.451 11.395 44 -21.316 -5.906 78 51.031 -8.431 112 -33.648 10.271 11 22.291 11.697 45 -17.623 -4.522 79 48.256 -9.432 113 -32.858 9.432 12 18.949 11.801 46 -13.699 -3.06 80 45.242 -10.271 114 -31.901 8.431 13 15.453 11.707 47 -9.575 -1.544 81 42.01 -10.936 115 -30.797 7.283 14 11.833 11.417 48 -5.285 0 82 38.584 -11.417 116 -29.564 6.004 15 8.119 10.936 49 -0.866 1.544 83 34.989 -11.707 117 -28.222 4.613 16 4.342 10.271 50 3.646 3.06 84 31.252 -11.801 118 -26.792 3.129 17 0.531 9.432 51 8.213 4.522 85 27.401 -11.697 119 -25.294 1.574 18 -3.281 8.431 52 12.799 5.906 86 23.463 -11.395 120 -23.748 0 19 -7.064 7.283 53 17.366 7.188 87 19.468 -10.9 121 -22.175 -1.574 20 -10.787 6.004 54 21.875 8.347 88 15.444 -10.219 122 -20.593 -3.129 21 -14.419 4.613 55 26.288 9.363 89 11.42 -9.363 123 -19.023 -4.613 22 -17.928 3.129 56 30.569 10.219 90 7.426 -8.347 124 -17.484 -6.004 23 -21.284 1.574 57 34.684 10.9 91 3.491 -7.188 125 -15.994 -7.283 24 -24.456 0 58 38.603 11.395 92 -0.359 -5.906 126 -14.571 -8.431 25 -27.417 -1.574 59 42.296 11.697 93 -4.099 -4.522 127 -13.232 -9.432 26 -30.139 -3.129 60 45.738 11.801 94 -7.704 -3.06 27 -32.597 -4.613 61 48.904 11.707 95 -11.153 -1.544 28 -34.768 -6.004 62 51.773 11.417 96 -14.422 0 29 -36.631 -7.283 63 54.328 10.936 97 -17.492 1.544 30 -38.168 -8.431 64 56.553 10.271 98 -20.345 3.06 31 -39.361 -9.432 65 58.436 9.432 99 -22.964 4.522 32 -40.197 -10.271 66 59.968 8.431 100 -25.337 5.906 33 -40.663 -10.936 67 61.142 7.283 101 -27.453 7.188

[0125] Feature values ​​are extracted based on a preset set of contribution frequencies. The contribution frequencies of the angularity index UIAIA are -12 pixels / cycle, +8 pixels / cycle, +14 pixels / cycle, and +18 pixels / cycle; the contribution frequencies of the aspect ratio ER are -5 pixels / cycle, -1 pixel / cycle, and +1 pixel / cycle; the contribution frequencies of the sphericity SP are -7 pixels / cycle, -5 pixels / cycle, -1 pixel / cycle, and +1 pixel / cycle; the contribution frequencies of the mean radius MR are -5 pixels / cycle, -3 pixels / cycle, -1 pixel / cycle, and +1 pixel / cycle; and the contribution frequencies of the variance VR are -5 pixels / cycle, -3 pixels / cycle, -1 pixel / cycle, and +1 pixel / cycle.

[0126] Calculate the centroid coordinates of the profile, whereby the centroid coordinates are:

[0127]

[0128]

[0129] The centralized coordinates are Taking the coordinates (41.821, 1.544) when = 1 as an example, the centered coordinates are:

[0130]

[0131]

[0132] The complex sequence of each pixel in the aggregate particle is:

[0133]

[0134]

[0135] Repeat the above steps for each of the 128 coordinates. The transformed coordinates are shown in Table 7.

[0136] Table 7. Coordinates of aggregate particles after decentering

[0137] N X Y N X Y N X Y N X Y 0 38.54809 -1.09588 33 -44.1149 -12.0319 65 54.98409 8.336117 97 -20.9439 0.448117 1 38.36909 0.448117 34 -44.2029 -12.5129 66 56.51609 7.335117 98 -23.7969 1.964117 2 37.83309 1.964117 35 -43.9069 -12.8029 67 57.69009 6.187117 99 -26.4159 3.426117 3 36.94609 3.426117 36 -43.2249 -12.8969 68 58.50309 4.908117 100 -28.7889 4.810117 4 35.71809 4.810117 37 -42.1589 -12.7929 69 58.95409 3.517117 101 -30.9049 6.092117 5 34.16009 6.092117 38 -40.7139 -12.4909 70 59.04509 2.033117 102 -32.7569 7.251117 6 32.28709 7.251117 39 -38.8979 -11.9959 71 58.77909 0.478117 103 -34.3399 8.267117 7 30.11409 8.267117 40 -36.7219 -11.3149 72 58.16009 -1.09588 104 -35.6539 9.123117 8 27.66109 9.123117 41 -34.2019 -10.4589 73 57.19509 -2.66988 105 -36.6989 9.804117 9 24.94809 9.804117 42 -31.3549 -9.44288 74 55.89409 -4.22488 106 -37.4789 10.29912 10 21.99909 10.29912 43 -28.2029 -8.28388 75 54.26709 -5.70888 107 -38.0009 10.60112 11 18.83909 10.60112 44 -24.7679 -7.00188 76 52.32909 -7.09988 108 -38.2729 10.70512 12 15.49709 10.70512 45 -21.0749 -5.61788 77 50.09409 -8.37888 109 -38.3069 10.61112 13 12.00109 10.61112 46 -17.1509 -4.15588 78 47.57909 -9.52688 110 -38.1139 10.32112 14 8.381094 10.32112 47 -13.0269 -2.63988 79 44.80409 -10.5279 111 -37.7069 9.840117 15 4.667094 9.840117 48 -8.73691 -1.09588 80 41.79009 -11.3669 112 -37.0999 9.175117 16 0.890094 9.175117 49 -4.31791 0.448117 81 38.55809 -12.0319 113 -36.3099 8.336117 17 -2.92091 8.336117 50 0.194094 1.964117 82 35.13209 -12.5129 114 -35.3529 7.335117 18 -6.73291 7.335117 51 4.761094 3.426117 83 31.53709 -12.8029 115 -34.2489 6.187117 19 -10.5159 6.187117 52 9.347094 4.810117 84 27.80009 -12.8969 116 -33.0159 4.908117 20 -14.2389 4.908117 53 13.91409 6.092117 85 23.94909 -12.7929 117 -31.6739 3.517117 21 -17.8709 3.517117 54 18.42309 7.251117 86 20.01109 -12.4909 118 -30.2439 2.033117 22 -21.3799 2.033117 55 22.83609 8.267117 87 16.01609 -11.9959 119 -28.7459 0.478117 23 -24.7359 0.478117 56 27.11709 9.123117 88 11.99209 -11.3149 120 -27.1999 -1.09588 24 -27.9079 -1.09588 57 31.23209 9.804117 89 7.968094 -10.4589 121 -25.6269 -2.66988 25 -30.8689 -2.66988 58 35.15109 10.29912 90 3.974094 -9.44288 122 -24.0449 -4.22488 26 -33.5909 -4.22488 59 38.84409 10.60112 91 0.039094 -8.28388 123 -22.4749 -5.70888 27 -36.0489 -5.70888 60 42.28609 10.70512 92 -3.81091 -7.00188 124 -20.9359 -7.09988 28 -38.2199 -7.09988 61 45.45209 10.61112 93 -7.55091 -5.61788 125 -19.4459 -8.37888 29 -40.0829 -8.37888 62 48.32109 10.32112 94 -11.1559 -4.15588 126 -18.0229 -9.52688 30 -41.6199 -9.52688 63 50.87609 9.840117 95 -14.6049 -2.63988 127 -16.6839 -10.5279 31 -42.8129 -10.5279 64 53.10109 9.175117 96 -17.8739 -1.09588

[0138] The 128 transformed complex sequences were sequentially subjected to Discrete Fourier Transform, and the frequency contributions were recorded. Each cycle Taking the coordinates of time as an example:

[0139]

[0140]

[0141] By analogy, the real and imaginary parts of the 128 coordinates are calculated:

[0142]

[0143]

[0144]

[0145]

[0146] The contribution frequency is calculated using the above steps to obtain the amplitude of the complex sequence, as follows:

[0147]

[0148]

[0149] Substituting the magnitude of the complex sequence into the morphological model, we get:

[0150]

[0151]

[0152]

[0153]

[0154]

[0155] According to Tables 1-5, the aggregate particles can be determined to be typical needle-like and flaky aggregates. The angularity index (UIAIA) of the aggregate particles analyzed in this invention is 531.302, indicating low angularity, almost no sharp corners, and rounded edges; ER is 2.651, indicating that the aggregate particles are obviously slender and have typical needle-like and flaky shapes; SP is 0.551, indicating that the sphericity of the aggregate particles is low and deviates significantly from a circle; MR is 12.689, indicating that the aggregate particles are of medium size, with a high VR, and the radius of the aggregate particles varies greatly and the outline is uneven.

[0156] According to another aspect of the present invention, the present invention provides a quantitative evaluation system for aggregate performance morphology based on frequency analysis, wherein the quantitative evaluation system for aggregate performance morphology based on frequency analysis includes an image processing and boundary extraction module, a discrete Fourier transform analysis module, and a morphological parameter calculation module connected in sequence.

[0157] The image processing and boundary extraction module is used to extract the boundary pixel coordinates from the two-dimensional image of the aggregate particles;

[0158] The discrete Fourier transform analysis module is used to calculate the Fourier transform and convert spatial domain coordinates into frequency domain features;

[0159] The morphological parameter calculation module is used to calculate the amplitude spectra of different contribution frequencies using different morphological models.

[0160] The above are merely preferred embodiments of the present invention and do not limit the patent scope of the present invention. All equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A quantitative evaluation method for aggregate behavior patterns based on frequency analysis, characterized in that, Includes the following steps: S1. Perform three-dimensional laser scanning on the aggregate particles and remove noise to obtain the boundary pixel coordinates of the aggregate particles; S2. Calculate the centroid coordinates and centered coordinates of the aggregate particles, and construct a complex sequence of each pixel in the aggregate particles based on the centered coordinates. S3. Perform a discrete Fourier transform on the complex sequence to calculate the Fourier coefficients and amplitude spectrum of the complex sequence; S4. Extract feature values ​​of different morphological parameters according to the preset contribution frequency set, and construct morphological models of each morphological parameter based on the feature values. Substitute the amplitude spectrum of the aggregate particles into the morphological model to quantify each morphological parameter of the aggregate particles.

2. The method for quantitative evaluation of aggregate performance based on frequency analysis according to claim 1, characterized in that, The centroid coordinates of the profile are: in, For each pixel in the aggregate particles The average value of the coordinates This represents the total number of outline pixels. For the first 1 pixel Coordinate values For each pixel in the aggregate particles The average value of the coordinates For the first 1 pixel Coordinate values ; The centralized coordinates are: in, For the decentralized first 1 pixel Coordinate values For the decentralized first 1 pixel Coordinate values; The complex sequence of each pixel in the aggregate particle is: in, For the first A complex sequence of pixels.

3. A quantitative evaluation method for aggregate performance based on frequency analysis according to any one of claims 1-2, characterized in that, In step S3, the complex sequence is subjected to a discrete Fourier transform, and the Fourier coefficients of the complex sequence are calculated, specifically as follows: in, For the first Fourier coefficients of a complex sequence of pixels. This represents the total number of outline pixels. For the first A complex sequence of pixels, , is the interval between two consecutive elements in a complex sequence.

4. The method for quantitative evaluation of aggregate performance based on frequency analysis according to claim 3, characterized in that, In step S3, the complex sequence is subjected to a discrete Fourier transform to calculate the amplitude spectrum of the complex sequence, specifically as follows: S31. Substitute Euler's formula into the Fourier coefficients of the complex number sequence to obtain the Fourier coefficients in trigonometric form. S32. Separate the real and imaginary parts of the Fourier coefficients in the form of the trigonometric function, and calculate the sum of the real and imaginary parts to synthesize the first Fourier coefficients; S33. Based on the first Fourier coefficients, calculate the amplitude of the complex sequence, that is, the amplitude spectrum of each frequency component.

5. The method for quantitative evaluation of aggregate performance based on frequency analysis according to claim 4, characterized in that, Step S31 specifically includes: Substituting Euler's formula into the Fourier coefficients of the complex sequence, Euler's formula becomes: The Fourier coefficients in trigonometric form are obtained as follows: 。 6. The method for quantitative evaluation of aggregate performance based on frequency analysis according to claim 5, characterized in that, Step S332 specifically includes: Separate the real and imaginary parts of the Fourier coefficients in the trigonometric function form; The real part is: The imaginary part is: Calculate the sum of the real and imaginary parts to synthesize the first Fourier coefficients; the first Fourier coefficients are: in, is the real part of the Fourier coefficients in trigonometric form. For the decentralized first 1 pixel Coordinate values For the decentralized first 1 pixel Coordinate values represents the imaginary part of the Fourier coefficients in trigonometric form. is the first Fourier coefficient.

7. The method for quantitative evaluation of aggregate performance based on frequency analysis according to claim 6, characterized in that, The magnitude of the complex sequence is: in, denoted as the magnitude of the complex sequence.

8. A method for quantitative evaluation of aggregate performance based on frequency analysis according to any one of claims 1-2, characterized in that, The step S4, which involves extracting feature values ​​of different morphological parameters based on a preset set of contribution frequencies, includes: The contribution frequencies of the angularity index UIAIA are -12 pixels / cycle, +8 pixels / cycle, +14 pixels / cycle, and +18 pixels / cycle; The contribution frequencies of the aspect ratio ER are -5 pixels / cycle, -1 pixel / cycle, and +1 pixel / cycle; The contribution frequencies of sphericity SP are -7 pixels / cycle, -5 pixels / cycle, -1 pixel / cycle, and +1 pixel / cycle; The contribution frequencies of the average radius MR are -5 pixels / cycle, -3 pixels / cycle, -1 pixel / cycle, and +1 pixel / cycle; The contribution frequencies of variance VR are -5 pixels / cycle, -3 pixels / cycle, -1 pixel / cycle, and +1 pixel / cycle.

9. The method for quantitative evaluation of aggregate performance based on frequency analysis according to claim 8, characterized in that, The construction of the morphological model for each morphological parameter based on the feature values ​​includes: The morphological model of the angularity index UIAIA is as follows: The morphological model of the aspect ratio ER is as follows: The morphological model of sphericity SP is as follows: The morphological model of the average radius MR is: The morphological model of variance VR is: in, The morphological model of the angularity index UIAIA. The morphological model for the aspect ratio ER. The morphological model for sphericity SP. The morphological model is the average radius MR. This is the morphological model of variance VR.

10. A system comprising the method for quantitative evaluation of aggregate performance based on frequency analysis as described in any one of claims 1-9, characterized in that, It includes an image processing and boundary extraction module, a discrete Fourier transform analysis module, and a morphological parameter calculation module connected in sequence; The image processing and boundary extraction module is used to extract the boundary pixel coordinates from the two-dimensional image of the aggregate particles; The discrete Fourier transform analysis module is used to calculate the Fourier transform and convert spatial domain coordinates into frequency domain features; The morphological parameter calculation module is used to calculate the amplitude spectra of different contribution frequencies using different morphological models.

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