Multi-objective calculation method for gradation optimization of solid waste aggregate slurry

Abstract

The application discloses a multi-objective calculation method for slurry grading optimization of solid waste aggregate, and relates to the technical field of data processing and analysis. The method comprises the following steps: arranging an electrical resistance tomography array, a high-speed linear array camera and a three-dimensional laser profilometer in a slurry conveying pipeline detection section and performing multi-modal synchronous acquisition to obtain conductivity distribution grayscale images, two-dimensional flow images and surface height point cloud data; pumping the slurry prepared according to a candidate grading scheme to the slurry conveying pipeline detection section, calculating a grayscale difference value based on the conductivity distribution grayscale images and calculating a grading deviation based on the two-dimensional flow images, and performing iterative subdivision on an equilateral triangle grading domain according to the grayscale difference value and the grading deviation to obtain a Pareto optimal solution set. The application can directly reflect the real flow state and particle distribution characteristics of the slurry, reduce the dependence on experience and static tests, and improve the pertinence and stability of the grading design.

Description

Technical Field

[0001] This invention relates to the field of data processing and analysis technology, and particularly to industrial cloud computing, specifically a multi-objective calculation method for optimizing the gradation of aggregate slurry containing solid waste. Background Technology

[0002] In engineering fields such as mine backfilling, solid waste resource utilization, building material preparation, and long-distance pumping construction, slurries containing solid waste aggregates are widely used for backfilling, pouring, and transportation operations. With the continuous increase in the comprehensive utilization rate of solid waste, using tailings, industrial by-products, and crushed construction solid waste as aggregate sources has become a common practice. These solid waste aggregates typically exhibit significant randomness in particle size distribution, particle morphology, surface roughness, and mud content. Compared with natural aggregates, their composition fluctuates more, directly affecting the slurry's flow properties, pumping stability, and structural uniformity. In practical engineering, a reasonable aggregate gradation is a key factor in ensuring the slurry's pumpability, anti-segregation properties, and final molding quality.

[0003] In current engineering practice, the gradation design of slurries containing solid waste aggregates typically relies on empirical formulas, static sieve tests, or pre-set target gradation curves. A common method is to first conduct sieve tests on the aggregates to obtain the particle size distribution, and then manually adjust it according to empirical gradation ranges or standard gradation curves. This method is applicable when raw material properties are stable and operating conditions vary little, but it often fails to reflect the true flow state in a timely manner when the solid waste aggregate source is complex and batch variations are significant. Especially during pumping, aggregate settling, segregation, and local enrichment exhibit obvious dynamic characteristics, and gradation design based solely on static sieve results cannot effectively predict the actual distribution within the pipeline. To improve the monitoring capability of the slurry pumping process, some projects have introduced pressure sensors, flow meters, or motor current monitoring methods to indirectly determine the slurry's flow resistance and pumping load. These methods can reflect changes in the overall pumping state, but their measurement results are the result of multiple factors acting together, making it difficult to distinguish between segregation problems caused by unreasonable aggregate gradation and load changes caused by variations in water-cement ratio, temperature, or equipment operating conditions. In addition, pressure and flow signals are not sensitive to local settlement or intra-section stratification, and often cannot be identified in time when segregation is in its early stages. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-objective calculation method for optimizing the gradation of aggregate slurry containing solid waste. This method can directly reflect the actual flow state and particle distribution characteristics of the slurry, reduce reliance on experience and static tests, and improve the pertinence and stability of gradation design.

[0005] To address the aforementioned technical problems, this invention provides a multi-objective calculation method for optimizing the gradation of slurry containing solid waste aggregate. The method includes: deploying a resistivity tomography array, a high-speed linear array camera, and a three-dimensional laser profilometer in the detection section of the slurry conveying pipeline and simultaneously acquiring multimodal data to obtain grayscale images of conductivity distribution, two-dimensional flow images, and surface height point cloud data; constructing an equilateral triangular gradation domain based on the mass percentages of fine, medium, and coarse aggregates and generating candidate gradation schemes corresponding to the grid vertices; preparing slurry for the candidate gradation schemes and pumping it to the detection section of the slurry conveying pipeline; calculating the grayscale difference based on the conductivity distribution grayscale image and the gradation deviation based on the two-dimensional flow image; performing iterative subdivision of the equilateral triangular gradation domain based on the grayscale difference and gradation deviation to obtain a Pareto optimal solution set; obtaining the apparent particle size distribution of the candidate gradation schemes corresponding to the Pareto optimal solution set based on the surface height point cloud data and comparing it with the target gradation curve to determine the optimal gradation scheme; and outputting the optimal gradation scheme to the slurry preparation control system.

[0006] Furthermore, the resistance tomography array consists of sixteen electrodes uniformly embedded along the circumference of the pipe wall of the slurry transport pipeline. The resistance tomography array acquires voltage data using an adjacent excitation and adjacent measurement mode. The adjacent excitation and adjacent measurement mode involves applying excitation current to two adjacent electrodes and acquiring the voltage between the remaining adjacent electrode pairs, rotating the excitation electrodes in turn until a frame of voltage data is acquired. The voltage data of the resistance tomography array is used to reconstruct the grayscale image of conductivity distribution by solving the inverse finite element problem. The inverse finite element problem solution includes establishing a finite element mesh of the pipeline cross section, establishing electrode boundary conditions, performing iterative inversion based on the sensitivity matrix, and performing smoothing and regularization processing on the mesh conductivity field after each iteration.

[0007] Furthermore, a high-speed linear array camera is installed above the transparent observation window of the slurry conveying pipeline inspection section. The high-speed linear array camera acquires line scan images at a scanning rate of no less than 8,000 lines per second. The two-dimensional flow image is formed by stitching the line scan images line by line according to the acquisition sequence. The row direction of the two-dimensional flow image corresponds to the flow direction, and the column direction of the two-dimensional flow image corresponds to the horizontal direction of the pipeline observation window.

[0008] Furthermore, a three-dimensional laser profilometer is set above the sampling platform. The three-dimensional laser profilometer scans the slurry sample laid flat on the sampling platform line by line to obtain surface height point cloud data. The surface height point cloud data includes the planar coordinates and height value of each scanning point. The height value is determined relative to the reference plane of the sampling platform.

[0009] Furthermore, the three vertices of the equilateral triangular gradation domain correspond to the following: fine aggregate mass percentage is 100% and medium aggregate mass percentage and coarse aggregate mass percentage are zero; medium aggregate mass percentage is 100% and fine aggregate mass percentage and coarse aggregate mass percentage are zero; coarse aggregate mass percentage is 100% and fine aggregate mass percentage and medium aggregate mass percentage are zero. Each side of the equilateral triangular gradation domain is evenly divided into six equal parts. The equilateral triangular gradation domain is divided into thirty-six congruent small equilateral triangular units by straight lines parallel to the three sides. The thirty-six congruent small equilateral triangular units contain twenty-eight grid vertices. Each grid vertex is uniquely determined by the centroid coordinates of the fine aggregate mass percentage, medium aggregate mass percentage, and coarse aggregate mass percentage and corresponds to a candidate gradation scheme.

[0010] Furthermore, the calculation of the grayscale difference includes: establishing a rectangular coordinate system in the conductivity distribution grayscale image with the center of the pipe circle as the origin; dividing the conductivity distribution grayscale image into an upper semicircle region and a lower semicircle region with the horizontal axis as the boundary; traversing all pixel grayscale values ​​in the upper semicircle region and calculating the arithmetic mean to obtain the average grayscale value of the upper semicircle; traversing all pixel grayscale values ​​in the lower semicircle region and calculating the arithmetic mean to obtain the average grayscale value of the lower semicircle; subtracting the average grayscale value of the upper semicircle from the average grayscale value of the lower semicircle to obtain the grayscale difference; and using the absolute value of the grayscale difference as the evaluation metric for the degree of segregation in the Pareto optimal solution set selection and iterative subdivision sorting.

[0011] Furthermore, the calculation of the gradation deviation includes: calculating the optimal segmentation threshold using Otsu's method for the two-dimensional flow image and performing binarization to obtain a binary image; applying the eight-neighbor connected component labeling algorithm to the binary image to assign a unique label to each connected component and calculating the total number of pixels in each connected component as the area of ​​the connected component; converting the area of ​​the connected components into the equivalent circle diameter using the equal area circle conversion formula; arranging all connected components in ascending order of equivalent circle diameter, using the proportion of each connected component area to the total area of ​​all connected components as the mass percentage, and accumulating them to obtain the cumulative mass percentage, the cumulative mass percentage changing with the equivalent circle diameter to form the measured gradation curve; reading the target gradation curve from the target gradation curve database, uniformly selecting ten comparison points on the equivalent circle diameter axis, reading the cumulative mass percentage values ​​of the measured gradation curve and the target gradation curve at the ten comparison points respectively, and adding the absolute values ​​of the difference between the cumulative mass percentage values ​​of the two curves at the ten comparison points to obtain the gradation deviation.

[0012] Further, the iterative subdivision includes: for each congruent small equilateral triangle unit, reading the absolute value of the grayscale difference and the gradation deviation of the candidate gradation schemes corresponding to the three vertices; calculating the arithmetic mean of the absolute values ​​of the grayscale differences of the three vertices to obtain the average segregation index; calculating the arithmetic mean of the gradation deviations of the three vertices to obtain the average deviation index; sorting all congruent small equilateral triangle units in ascending order of average segregation index to form a segregation sorting sequence; sorting all congruent small equilateral triangle units in ascending order of average deviation index to form a deviation sorting sequence; and calculating the sum of the ranking of the segregation sorting sequence and the ranking of the deviation sorting sequence for each congruent small equilateral triangle unit to obtain the comprehensive result. Ranking value; select the top six congruent small equilateral triangle units with the smallest comprehensive ranking value to form the dominant region unit set; for each congruent small equilateral triangle unit in the dominant region unit set, insert three new grid vertices at the midpoints of the three sides and subdivide them into four smaller equilateral triangle sub-units. The centroid coordinates of the three new grid vertices are obtained by taking the arithmetic mean of the centroid coordinates of the grid vertices at both ends of the corresponding sides; prepare slurry for the candidate gradation scheme corresponding to each new grid vertex and pump it to the slurry conveying pipeline detection section, and repeat the calculation of grayscale difference and gradation deviation; repeat the above dominant region unit set selection and subdivision operation until the subdivision level reaches four layers.

[0013] Furthermore, after the subdivision level reaches four levels, the Pareto optimal solution set consists of all grid vertices that simultaneously satisfy the following conditions: Condition 1 is that the absolute value of the gray-level difference of the grid vertex is less than or equal to the median of the absolute values ​​of the gray-level differences of all grid vertices in the same subdivision level; Condition 2 is that the grid vertex gradation deviation is less than or equal to the median of the gradation deviation of all grid vertices in the same subdivision level.

[0014] Furthermore, the process of obtaining the apparent particle size distribution based on surface height point cloud data and comparing it with the target gradation curve to determine the optimal gradation scheme includes: preparing slurry samples for each grid vertex corresponding to the candidate gradation scheme of the Pareto optimal solution set and spreading them on the sampling platform; acquiring surface height point cloud data using a 3D laser profilometer; projecting the surface height point cloud data onto a horizontal plane to obtain a planar projection point set; performing a density clustering algorithm based on Euclidean distance on the planar projection point set to obtain multiple independent point clusters, with the density clustering algorithm using the minimum number of points and the neighborhood radius as input and outputting point cluster labels; extracting the maximum and minimum heights of corresponding points in the surface height point cloud data for each point cluster and calculating the height range. The height range is used as the apparent particle size of the aggregate. The apparent particle sizes of all aggregate particles are counted and arranged from smallest to largest. The proportion of each cluster of points to the total number of all clusters is used as the mass percentage, and these proportions are accumulated to obtain the cumulative mass percentage. The cumulative mass percentage changes with the apparent particle size to form a three-dimensional measured gradation curve. Ten comparison points are evenly selected on the apparent particle size axis, and the cumulative mass percentage values ​​of the three-dimensional measured gradation curve and the target gradation curve are read at the ten comparison points. The absolute values ​​of the differences between the cumulative mass percentage values ​​of the two curves at the ten comparison points are added to obtain the three-dimensional gradation deviation. The candidate gradation scheme with the smallest three-dimensional gradation deviation is selected as the optimal gradation scheme.

[0015] The multi-objective calculation method for optimizing the gradation of aggregate slurry containing solid waste of the present invention has the following beneficial effects: By simultaneously introducing a resistivity tomography array, a high-speed linear array camera, and a three-dimensional laser profilometer into the detection section of the slurry conveying pipeline, the present invention achieves multi-angle and multi-scale acquisition of the slurry containing solid waste from the internal cross-sectional distribution of the pipeline, the two-dimensional projection characteristics during the flow process, and the three-dimensional geometric morphology after sampling. This allows the aggregate gradation evaluation to no longer be limited to static screening results or single sensor signals, but to be directly based on the actual flow and forming state. The conductivity distribution grayscale image obtained by the resistivity tomography array can reflect the spatial distribution differences of the slurry within the pipeline cross-section, thereby quantitatively characterizing aggregate settling and stratification phenomena. The two-dimensional flow image formed by the high-speed linear array camera can extract particle projection features under high temporal resolution conditions, construct the measured gradation curve, and thus evaluate the degree of deviation between the candidate gradation scheme and the target gradation curve. The surface height point cloud data obtained by the three-dimensional laser profilometer can perform three-dimensional verification of the apparent particle size distribution after sampling, avoiding the occlusion misjudgment that may be caused by relying solely on two-dimensional images. The aforementioned multi-source information is used collaboratively within the evaluation window of the same candidate gradation scheme, ensuring a consistent working condition across different evaluation dimensions and improving the reliability and repeatability of the gradation optimization results. This invention employs an equilateral triangular gradation domain to uniformly express the mass proportions of fine, medium, and coarse aggregates, ensuring all candidate gradation schemes naturally satisfy the mass conservation constraint. Furthermore, it uses an iterative subdivision method to concentrate trial mixes on areas with better performance, significantly reducing the time and material consumption caused by blind trial mixes. During the iteration process, grayscale difference and gradation deviation are simultaneously introduced as evaluation criteria, ensuring the optimization results consider both anti-segregation performance and the degree of matching with the target gradation, avoiding overall performance imbalance caused by pursuing only a single indicator. By verifying the Pareto optimal solution set with three-dimensional apparent particle size, this invention further improves the stability and adaptability of the final gradation scheme in practical engineering applications. Overall, this invention can achieve systematic optimization and reliable output of gradation schemes under conditions of complex solid waste aggregate sources and large property fluctuations. Attached Figure Description

[0016] Figure 1 The meshing structure of the finite element mesh for the pipe section provided in the embodiment of the present invention;

[0017] Figure 2 This is a schematic diagram illustrating the principle of grayscale image reconstruction based on conductivity distribution using a resistive tomography array.

[0018] Figure 3 A schematic diagram showing the arrangement and spatial relationship of 16 electrodes in the circumferential direction of the pipeline in the resistivity tomography array provided in an embodiment of the present invention;

[0019] Figure 4A schematic diagram of the three-dimensional spatial distribution characteristics of the surface height point cloud data of the slurry sample obtained by the three-dimensional laser profilometer provided in the embodiment of the present invention;

[0020] Figure 5 This is a schematic diagram illustrating the principle of screening the Pareto optimal solution set based on the dual objectives of the absolute value of grayscale difference and the degree of gradation deviation, and the distribution characteristics of candidate gradation schemes, as provided in this embodiment of the invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] A multi-objective calculation method for optimizing the gradation of slurry containing solid waste aggregate is proposed. The method includes: deploying a resistivity tomography array, a high-speed linear array camera, and a 3D laser profilometer in the detection section of the slurry conveying pipeline for multimodal synchronous acquisition, obtaining grayscale images of conductivity distribution, 2D flow images, and surface height point cloud data; constructing an equilateral triangular gradation domain based on the mass percentages of fine, medium, and coarse aggregates, and generating candidate gradation schemes corresponding to the grid vertices; preparing slurry for the candidate gradation schemes and pumping it to the detection section of the slurry conveying pipeline; calculating the grayscale difference based on the conductivity distribution grayscale image and the gradation deviation based on the 2D flow image; performing iterative subdivision of the equilateral triangular gradation domain based on the grayscale difference and gradation deviation to obtain a Pareto optimal solution set; obtaining the apparent particle size distribution of the candidate gradation schemes corresponding to the Pareto optimal solution set based on the surface height point cloud data and comparing it with the target gradation curve to determine the optimal gradation scheme; and outputting the optimal gradation scheme to the slurry preparation control system.

[0023] In one specific implementation scheme, when deploying the resistivity tomography array, high-speed linear array camera, and 3D laser profilometer in the slurry transport pipeline inspection section, a section with stable geometry, consistent inner wall material, and sufficient upstream and downstream straight pipe lengths is selected as the slurry transport pipeline inspection section. The purpose of the straight pipe section is to stabilize the flow field before it enters the inspection section, reducing secondary flow and vortices caused by bends and valves, thereby enhancing the repeatability of the conductivity distribution grayscale image and the 2D flow image under the same candidate gradation scheme. In practice, the slurry transport pipeline inspection section can use a circular pipe with an inner diameter of 100 mm, with a 300 mm long inspection section in the middle. To accommodate both electrode lead placement and transparent observation window installation, the inspection section can be formed by combining a metal pipe and a transparent observation window: the metal pipe provides structural strength and an electrode mounting base, while the transparent observation window provides the field of view for the high-speed linear array camera. The transparent observation window material can be a wear-resistant transparent material and flush with the inner wall of the pipe. The purpose of flushing is to avoid local deposition induced by the inner wall steps, which would cause the gray value difference to be biased due to the structure.

[0024] The resistance tomography (RTG) array is deployed along the circumference of the slurry transport pipeline's inspection section. The array consists of 16 electrodes evenly embedded along the circumference of the pipeline's inspection section. Each electrode can be a 316 stainless steel disc electrode with an 8mm diameter contact surface with the slurry. The electrode surface is flush with the inner wall of the pipeline, and the circumferential spacing between electrodes is 22.5 degrees. Electrode leads are led out through the pipe wall's sealed structure and connected to the acquisition circuit using shielded wires. The grounding of the shielded wires reduces crosstalk between the pump inverter and motor currents on weak voltage signals. The RTG array uses an adjacent excitation and adjacent measurement mode to acquire voltage data. This mode involves applying an excitation current to two adjacent electrodes and acquiring the voltage between the remaining adjacent electrode pairs, rotating the excitation electrodes sequentially until one frame of voltage data is acquired. The excitation current can be an AC excitation current with an amplitude of 5 ohms, and the excitation frequency can be 10 kHz. The benefit of AC excitation is to suppress DC drift caused by electrode polarization and reduce the impact of electrolytic reactions on the electrode surface, resulting in a more stable measurement baseline during long-term continuous operation. To ensure that usable signals can still be obtained for each frame of voltage data acquisition under pumping fluctuations, the acquisition circuit can be set to synchronously sample each voltage channel and then average the samples three times for the same electrode combination. This reduces random noise and does not introduce historical data dependence, because the average value comes only from instantaneous repeated sampling within the same frame.

[0025] refer to Figure 3In this embodiment, 16 electrodes are uniformly embedded along the circumference of the slurry conveying pipeline detection section, forming a complete electrode array. Each electrode is made of 316 stainless steel, which has good corrosion resistance and electrical conductivity. The electrode-slurry contact surface is designed as a circular disc with a diameter of [missing information]. The electrode surfaces are kept flush with the inner wall of the pipe to avoid the formation of steps or depressions that could cause local flow field disturbances. The circumferential positions of the 16 electrodes are determined using angular coordinates. Confirmed, among which Indicates the electrode number; the angular interval between two adjacent electrodes is constant. That is, the first The angular coordinates of each electrode are A polar coordinate system is established with the center of the pipeline as the origin, and all 16 electrodes are located at a radius of... On the circumference, the first The Cartesian coordinates of each electrode can be expressed as: , The electrode leads are led out through pre-drilled sealing holes in the pipe wall. Each sealing hole is waterproofed with epoxy resin or silicone to ensure that the slurry does not leak along the lead channel. The led-out electrode leads are connected to the data acquisition circuit board using shielded twisted-pair cables. The shielding layer is grounded to reduce the impact of external electromagnetic interference on weak voltage signals, which is especially important in pumping systems where the frequency converter and motor generate strong electromagnetic noise.

[0026] During voltage data acquisition, the resistivity tomography array adopts an adjacent excitation and adjacent measurement mode. Specifically, at any given time, two adjacent electrodes are selected as the excitation electrode pair, for example, electrode 1 and electrode 2. A positive excitation current is applied to electrode 1. Apply a negative polarity excitation current to electrode 2 The excitation current is frequency The purpose of using alternating current (AC) excitation is to suppress the polarization effect on the electrode surface and avoid electrolytic reactions and baseline drift caused by direct current excitation. Simultaneously with the application of the excitation current, voltage measurements are performed on adjacent electrode pairs among the remaining 14 electrodes; for example, the voltage between electrode 3 and electrode 4 is measured. Voltage between electrode 4 and electrode 5 Similarly, a total of 13 independent voltage measurements can be obtained. After completing a set of measurements, the excitation electrode pair is rotated clockwise by one position, that is, an excitation current is applied between electrode 2 and electrode 3, and the above measurement process is repeated. The excitation electrode pair is rotated in turn until it returns to the initial position, completing one frame of complete voltage data acquisition. One frame of data contains a total of 13 independent voltage measurements. indivual.

[0027] Voltage data from a resistivity tomography (RTG) array are used to reconstruct a grayscale image of conductivity distribution using a finite element inverse problem. The finite element inverse problem solution involves establishing a finite element mesh for the pipe cross-section, defining electrode boundary conditions, performing iterative inversion based on the sensitivity matrix, and smoothing and regularizing the mesh conductivity field after each iteration. When establishing the finite element mesh for the pipe cross-section, the circular cross-section can be divided into 2048 triangular elements. A denser mesh provides higher spatial resolution for the conductivity distribution grayscale image, but also increases computational complexity. With 2048 elements, single-frame reconstruction on an edge computing device can achieve a time consumption of less than 50 seconds, thus supporting near real-time visualization. The electrode boundary conditions include applying current boundary conditions to the excitation electrode, voltage observation conditions to the measurement electrode, and insulation boundary conditions to the remaining boundaries. The iterative inversion uses a least-squares framework, mapping the mesh conductivity field to the forward calculation of the electrode voltage as a constraint, and iteratively updating the calculated voltage to approximate the acquired voltage. To illustrate the implementation details, the single-step update idea can be expressed as follows: Let the conductivity vector be... The voltage vector is The forward model is Then there is The sensitivity matrix is ,in This represents the local rate of change of voltage with respect to conductivity. In each iteration, the linearized relationship is used... ,in This represents the conductivity vector of the current iteration, used to solve for the new conductivity vector. Smoothing regularization can be understood as constraining the spatial gradient of the grid conductivity field, preventing excessively drastic changes in conductivity between adjacent grid cells. This is because resistivity tomography array measurements are underdetermined; without smoothing constraints, the reconstruction results are prone to noise specks, making gray-level difference calculations sensitive to noise. Smoothing regularization does not force gray-level differences to converge to a fixed value, but rather makes the conductivity distribution gray-level image closer to the continuity of the slurry's physical distribution, improving the repeatability of subsequent gray-level differences.

[0028] refer to Figure 1 In this embodiment, to achieve accurate reconstruction of the conductivity distribution, a finite element mesh model of the circular cross-section of the slurry conveying pipeline needs to be established. This mesh model uses triangular elements as the basic discrete elements, and forms a complete computational domain through a combination of radial and circumferential partitioning. Specifically, a polar coordinate system is first established at the center of the pipeline cross-section, and multiple concentric circular layers are set in the radial direction. In this embodiment, the radial direction is divided into three layers, with corresponding normalized radii of... , and ,in This corresponds to the inner wall boundary of the pipe. The circumference is divided into 8 equal parts, with each sector corresponding to a central angle of... By combining radial rings and circumferential rays, quadrilateral regions are formed between two adjacent radial layers and two adjacent rays. Each quadrilateral region is further divided into two triangular units along the diagonal.

[0029] Using this partitioning method, when the radial number of layers is Fractions of a circle are: When the total number of triangular units is calculated using the formula... Calculation. In the complete implementation of this embodiment, to ensure that the spatial resolution of the reconstructed conductivity distribution meets engineering requirements, the actual mesh density used is significantly higher than the value shown in the figure. Specifically, the radial layer number can be increased to 16 layers, and the circumferential fraction can be increased to 16 parts, thereby increasing the total number of triangular elements to 2048, corresponding to a total of 1089 mesh nodes. The planar coordinates of the mesh nodes are obtained by converting polar coordinates to rectangular coordinates. Layer The coordinates of each node are , ,in Each triangular element carries the local distribution information of the conductivity field during the finite element solution process. The conductivity inside the element is represented by linear interpolation of the conductivity values ​​at the three vertices, and the interpolation function adopts a standard shape function. ,in Represents the three vertices of a triangle. and The coordinates within the element are the natural coordinates. The quality of the mesh generation directly affects the stability and convergence speed of the inverse problem solution. Therefore, in practical implementation, it is necessary to ensure that the aspect ratio of the triangular elements is controlled within a reasonable range to avoid numerical ill-conditioned results caused by excessively long and narrow elements. The radial-circular combined mesh generation method used in this embodiment can naturally ensure that the mesh density near the center of the circle is moderate, while the boundary resolution is improved near the pipe wall by increasing the circumferential fraction, thus meeting the accuracy requirements for applying electrode boundary conditions. After the mesh is generated, each element is assigned an initial conductivity value. This initial value can be set based on the estimated average conductivity of the slurry, for example, taking... During the iterative inversion process, the unit conductivity value will be continuously updated based on the residual between the measured voltage and the calculated voltage. The update formula is as follows: ,in From the sensitivity matrix and residual vector The solution is obtained.

[0030] See again Figure 2At the physical level, the circular cross-section of the slurry conveying pipeline inspection section is discretized into a series of non-overlapping micro-units. In this embodiment, the Delaunay triangulation algorithm is used to divide the circular cross-section into 2048 triangular finite element mesh elements. This discretization process transforms the continuous conductivity distribution field into a finite-dimensional conductivity vector solution problem. Figure 2 The sixteen surrounding rectangular blocks represent sixteen electrodes evenly embedded along the circumference of the pipe wall. These electrodes serve not only as input ports for current excitation but also as observation ports for voltage response. During data acquisition, the system executes an adjacent excitation adjacent measurement mode, that is, sequentially measuring the adjacent excitations in sequence. and the An amplitude of [value] is applied between the electrodes. The AC excitation current is applied, and the boundary voltage is measured between the remaining adjacent electrode pairs that do not carry the excitation current.

[0031] Figure 2 The underlying core calculation process involves solving the inverse problem of deducing the internal conductivity distribution from boundary voltage data. Let the conductivity distribution vector within the pipe cross-section be... The boundary measurement voltage vector is The two are connected through a forward physics model. Correlation, i.e., satisfying nonlinear equations Due to the nonlinear characteristics of the electric field distribution, this equation cannot be solved analytically directly. Instead, an iterative inversion algorithm based on the sensitivity matrix is ​​used. (Sensitivity matrix) Defined as the partial derivative matrix of the boundary voltage with respect to the change in internal conductivity, i.e. In each iteration, the algorithm utilizes a linearized approximation. To update the conductivity estimate, where Let be the conductivity vector of the current iteration step. This is the conductivity vector for the next step. Given the severe ill-conditioned and underdetermined nature of the inverse problem in resistivity tomography, a smoothing regularization constraint must be introduced during the iteration process to obtain a stable solution. Regularization adds a penalty term with respect to the spatial gradient of conductivity to the objective function, ensuring that the reconstructed conductivity distribution grayscale image remains spatially continuous and smooth, suppressing speckled artifacts caused by measurement noise. Figure 2 The pseudo-color or grayscale distribution displayed in the center represents the reconstructed conductivity field, where different grayscale values ​​map the local conductivity of different regions in the slurry. To eliminate the influence of measurement system gain drift and overall slurry conductivity variations, intra-frame normalization was performed on each frame before calculation, linearly mapping the grayscale values ​​to the range of 0 to 255.

[0032] Figure 2This further demonstrates a method for quantifying the degree of segregation based on image partitioning. A Cartesian coordinate system is established with the geometric center of the pipe cross-section as the origin, utilizing the horizontal axis... The reconstructed grayscale image of conductivity distribution is segmented into an upper and lower semicircular region. The upper semicircular region in the image represents the cross-section of the pipe. The lower semicircular area represents the part. The algorithm iterates through all pixels within the upper semicircle region and counts the number of pixels. The grayscale values ​​are then summed to calculate the average grayscale value of the upper semicircle. Its calculation formula is expressed as ,in The upper semicircular region Inner The algorithm calculates the grayscale value of each pixel. Similarly, it iterates through the lower semicircle region to calculate the average grayscale value of the lower semicircle. Its calculation formula is ,in The lower semicircular region Inner The grayscale value of each pixel is calculated. Finally, the grayscale difference is obtained by calculating the difference between the two values. ,Right now This parameter The physical significance lies in its direct reflection of the differences in medium distribution along the vertical direction of the pipe cross-section. In the transportation of solid waste aggregate slurry, if aggregate settling occurs, the solid concentration in the bottom region increases, leading to a change in the mixing conductivity of the lower semi-circular region (typically, for non-conductive aggregates, the conductivity decreases, and the grayscale value changes accordingly), thus... The value increases. Therefore, Figure 2 The computational scheme shown can compress complex tomographic imaging data into a single quantitative index, providing real-time feedback for subsequent gradation adjustments based on multi-objective optimization.

[0033] A high-speed linear array camera is installed above the transparent observation window of the slurry conveying pipeline inspection section. The camera acquires line scan images at a scanning rate of no less than 8000 lines per second. The two-dimensional flow image is formed by stitching the line scan images row by row according to the acquisition sequence. The row direction of the two-dimensional flow image corresponds to the flow direction, and the column direction corresponds to the transverse direction of the pipeline observation window. The high-speed linear array camera uses line scanning instead of area array because when the slurry flow velocity is high and particles quickly pass through the field of view, area array imaging is prone to motion blur. Line scanning, on the other hand, acquires images of a single row of pixels through extremely short exposures, and then stacks them along the time axis to form a two-dimensional flow image, significantly improving temporal resolution under the same illumination conditions. In practice, the exposure time can be set to 20 microseconds and illuminated by a bar light source. The bar light source can be a light-emitting diode line light source with a color temperature of 5000 Od. A polarizer is added in front of the camera lens to suppress specular reflections on the surface of the transparent observation window. To ensure that the column direction of a two-dimensional flow image corresponds to the actual lateral distance, pixel scale calibration is required: a calibration plate with known graduations is placed inside a transparent viewing window, a scan image of the calibration lines is acquired, and the pixel spacing between the graduations is calculated to obtain the pixel-to-length scaling factor. The scaling factor can be written as... ,in This represents the actual length corresponding to each pixel. This indicates the actual distance between adjacent graduations on the calibration plate. This represents the pixel spacing between adjacent ticks in the image. The benefit of doing this is that when converting the area of ​​the connected region to the equivalent circle diameter later, the equivalent circle diameter has a clear physical scale and does not depend on a subjective threshold.

[0034] A 3D laser profilometer is positioned above the sampling platform. It scans the slurry sample, laid flat on the platform after sampling, line by line to acquire surface height point cloud data. This data includes the planar coordinates and height value of each scan point, with the height value determined relative to the sampling platform's reference plane. Placing the 3D laser profilometer on the sampling platform, rather than directly measuring the flow inside the pipe, is chosen because the slurry surface is significantly affected by air bubbles, vibrations, and refraction through the transparent observation window; direct measurement would introduce uncontrollable errors. The slurry sample, laid flat after sampling, forms a relatively stable free surface under gravity, making the surface height point cloud data more suitable for particle segmentation and apparent particle size estimation. The laying thickness can be controlled between 10 and 15 mm. Too thin a thickness will result in an excessively high proportion of exposed coarse aggregate, leading to point cloud occlusion; too thick a thickness will cause fine aggregate to cover the surface of coarse aggregate, resulting in unclear particle boundaries. During line-by-line scanning, the line spacing can be set to 0.2 mm, and the single-line point spacing to 0.1 mm, allowing the surface height point cloud data to distinguish the convex morphology of typical solid waste aggregate particles. When surface height point cloud data is projected onto a horizontal plane to obtain a planar projection point set, the projection process retains the planar coordinates of each scanned point while ignoring the height value. This ensures that the neighborhood determination in the subsequent density clustering algorithm is based solely on planar distance, avoiding missegmentation caused by treating particle surface roughness as an additional dimension. To make the density clustering algorithm insensitive to splash points at the edge of the sampling platform, the planar coordinate range can be clipped before projection. The clipping region preferentially selects a rectangular area near the center of the sampling platform rather than an area near the edge. This is because edge areas are more prone to scratches and boundary gaps caused by scraping, while the surface height point cloud data in the central area better represents the natural distribution of particles. Clipping does not change the definition of apparent particle size, as apparent particle size comes from the height range of corresponding points in the point cluster. Clipping simply avoids introducing non-particle structures into the point cluster.

[0035] refer to Figure 4 In this embodiment, to obtain the apparent particle size distribution information of the slurry corresponding to the candidate gradation scheme, samples are taken from the detection section of the slurry conveying pipeline at the end of the evaluation window. The slurry sample is laid flat on the sampling platform and its surface is scanned using a three-dimensional laser profilometer. The sampling platform is made of a flat metal plate, and its surface has been precision ground to ensure that the flatness error is less than [value missing]. The slurry sample leveling process follows standardized procedures: first, approximately... The slurry is poured into the center area of ​​the sampling platform, and then leveled in one direction using a flat scraper, maintaining a fixed gap between the scraper and the sampling platform. The gap is controlled by positioning blocks at both ends of the scraper to ensure the consistency of sample thickness each time. The selection of the spreading thickness needs to balance sufficient exposure of coarse aggregate and moderate coverage of the surface by fine aggregate. Too thin a thickness will cause coarse aggregate to penetrate the surface and create excessive obstruction, while too thick a thickness will cause fine aggregate to completely cover the coarse aggregate, resulting in blurred particle boundaries. The three-dimensional laser profilometer works on the principle of laser triangulation. The device includes a line laser emitter and a CMOS image sensor. The line laser projects a laser line onto the sample surface. The laser line intersects the sample surface to form a contour line. The CMOS sensor observes the contour line from the side and calculates the surface height through trigonometric relationships.

[0036] During scanning, the 3D laser profilometer is fixedly mounted on a linear guide rail above the sampling platform and driven by a stepper motor along the rail. The laser moves line by line along the axis, completing one line scan with each step. Scanning parameters are set as follows: line spacing. Single-line inner point spacing The scanning area is The rectangular area was scanned at a speed of 20 lines per second to ensure the quality of the laser line imaging. After all scans were completed, the resulting surface height point cloud data was stored as a set of three-dimensional coordinate points, with each point containing planar coordinates. and the height value relative to the reference plane of the sampling platform ,in Point number, total number of points Approximately Point cloud data presents the true undulating morphology of the slurry surface in three-dimensional space. Aggregate particles form local protrusions on the surface, and the height and shape characteristics of the protrusions are related to the size and burial depth of the particles.

[0037] Multimodal synchronous acquisition is based on a unified time reference. When the resistivity tomography (RTG) array acquires voltage data, a timestamp is generated for each frame of voltage data acquired; the high-speed linear scan camera also generates a timestamp for each line scan image; when sampling occurs, the sampling start timestamp is recorded, and immediately after sampling, the 3D laser profilometer scan is started, simultaneously recording the scan start timestamp. Synchronization is limited to the evaluation window of the same candidate gradation scheme, which can be 5 seconds: the RTG array generates several frames of conductivity distribution grayscale images within 5 seconds, the high-speed linear scan camera generates two-dimensional flow images corresponding to the time period within 5 seconds, and sampling occurs at the end of the evaluation window, corresponding to the slurry state at the end of the evaluation window. The advantage of this arrangement is that the RTG array and the high-speed linear scan camera capture the real-time distribution within the tube, and the 3D laser profilometer captures the particle appearance information of the output slurry within the same evaluation window. These three types of data have a consistent operating condition background when used for multi-objective evaluation of the same candidate gradation scheme. To reduce clock drift between devices, a precise time protocol can be used to implement the time reference, achieving a time synchronization accuracy on the order of 1 microsecond. If network synchronization is not available, a hardware trigger line can be used to connect the row trigger signal of the high-speed linear scan camera and the acquisition start signal of the resistive tomography array to the same trigger source, aligning the two at the sampling start point.

[0038] The construction of the equilateral triangular gradation domain revolves around the fact that the sum of the mass proportions of fine aggregate, medium aggregate, and coarse aggregate is always equal to 100%. The mass proportions of fine aggregate, medium aggregate, and coarse aggregate correspond to the barycentric coordinate components within the equilateral triangular gradation domain. The direct benefit of this setup is that the proportion constraint is naturally embedded in the geometric space: any point falling within the equilateral triangular gradation domain naturally satisfies the requirement that the sum of the three proportions is 100%, without the need for additional normalization. To convert the barycentric coordinates into planar coordinates that are easier to calculate and mesh, the planar coordinates of the three vertices of the equilateral triangle can be selected: the vertex where the mass proportion of fine aggregate is 100% is taken as... The peak value where the proportion of medium aggregate is 100% is taken as The peak value where the coarse aggregate mass percentage is 100% is taken as Let the mass percentages of fine aggregate, medium aggregate, and coarse aggregate be respectively... , , ,in This represents the normalized value indicating the proportion of fine aggregate by mass. This represents the normalized value of the proportion of aggregate by weight. This represents the normalized value of the mass percentage of coarse aggregate, and satisfies... The corresponding planar coordinates can be written as... , ,in This represents the x-coordinate of a point within the equilateral triangle gradation domain. This represents the ordinate of a point within the equilateral triangle gradation domain. The advantage of this transformation is that the proportion of coarse aggregate mass only affects the ordinate, allowing changes along the longitudinal direction to directly reflect changes in the proportion of coarse aggregate mass; changes in the proportion of fine aggregate mass are more reflected in the lateral regression, making it easier to locate intuitively on the graphical interface or discrete grid.

[0039] The generation of candidate gradation schemes corresponding to grid vertices starts from the uniform partitioning of the equilateral triangular gradation domain. Dividing each side of the equilateral triangular gradation domain into 6 equal parts is essentially equivalent to restricting the proportions of fine aggregate, medium aggregate, and coarse aggregate to a discrete set with a step size of 1 / 6. This discreteness can be represented by integers: Let... , , are non-negative integers and satisfy ,in This indicates the percentage of fine aggregate by weight relative to the total weight. This indicates the percentage of medium aggregate by weight relative to the total weight. This indicates the percentage of coarse aggregate by mass out of the total mass. The corresponding percentages for fine aggregate, medium aggregate, and coarse aggregate are respectively... , , .exist Under the constraints, all combinations form a total of 28 grid vertices, and the geometric relationship between the 28 grid vertices and the 36 congruent small equilateral triangle elements is automatically established. The reason for using 6 equal parts is that the number of candidate gradation schemes is moderate, the workload of a single round of full-coverage trial gradation is controllable, and the resolution is sufficient to cover the main variation range of fine aggregate mass ratio, medium aggregate mass ratio, and coarse aggregate mass ratio. If a finer search granularity is desired, the 6 equal parts can be replaced with 8 or 10 equal parts, and the number of grid vertices will increase accordingly, which is suitable for use when automated batching equipment and online detection conditions are relatively mature.

[0040] When implementing candidate gradation schemes to trial mix design, the mass percentages of fine aggregate, medium aggregate, and coarse aggregate are converted into actual weighed masses. Let the total mass of the target solid waste aggregate be... ,in Let represent the total mass of the three types of solid waste aggregates: fine aggregate, medium aggregate, and coarse aggregate. Then, the mass of fine aggregate is: The quality of medium aggregate is The quality of coarse aggregate is ,in Indicates the quality of fine aggregate. Indicates the quality of medium aggregate. This represents the mass of coarse aggregate. For example, when the total mass of solid waste aggregate is 50, a certain grid vertex corresponds to... , , At that time, the mass of fine aggregate was 16.666, the mass of medium aggregate was 25.000, and the mass of coarse aggregate was 8.333. Actual weighing was performed with an accuracy of 0.1, allowing for minor deviations due to weighing resolution. Subsequently, the three types of solid waste aggregates were mixed with water and cementitious materials to prepare a slurry, which was then pumped to the slurry delivery pipeline testing section. To ensure comparability between candidate gradation schemes, the amounts of water and cementitious materials were kept constant during the evaluation of the same batch of candidate gradation schemes, and the stirring time was also kept constant; for example, the stirring time was set to 120, and the settling and defoaming time to 30. Thus, the difference between the grayscale conductivity distribution image and the two-dimensional flow image mainly came from changes in the mass proportions of fine, medium, and coarse aggregates, rather than fluctuations in the preparation process.

[0041] In optional implementations, the resistivity tomography array can replace 16 electrodes with 32 electrodes to improve the spatial resolution of the conductivity distribution grayscale image. With 32 electrodes, the alternation sequence of adjacent excitation and adjacent measurement modes is longer, but it is more sensitive to grayscale changes in the lower semicircular region caused by subtle sedimentation. The high-speed linear scan camera can be increased from 8000 lines per second to 12000 lines per second to maintain a similar spatial sampling density at higher flow rates. The three-dimensional laser profilometer can select different line spacings, such as 0.1, to improve the apparent particle size segmentation accuracy. The mesh of the equilateral triangular gradation domain can also be changed from 6 equal parts per side to 8 equal parts per side, making the deviation length of the candidate gradation scheme smaller, thereby improving the matching accuracy when the target gradation curve database resolution is high. The above optional methods keep the representations of fine aggregate mass ratio, medium aggregate mass ratio, coarse aggregate mass ratio, equilateral triangle gradation domain, grid vertices, candidate gradation schemes, conductivity distribution grayscale image, two-dimensional flow image, and surface height point cloud data unchanged, only changing the specific values ​​and sampling density, which is convenient for direct implementation and transplantation under different engineering conditions.

[0042] When preparing slurries for candidate gradation schemes and pumping them to the slurry delivery pipeline testing section, to ensure the comparability of grayscale differences and gradation deviations among different candidate gradation schemes, the preparation process should first be fixed to the same set of repeatable process conditions. A directly implementable approach is as follows: each candidate gradation scheme corresponds to one independent preparation. The weighing mass of fine, medium, and coarse aggregates is determined by the mass percentages of fine, medium, and coarse aggregates in the candidate gradation scheme, with the total mass of fine, medium, and coarse aggregates set at 50%. The amounts of water and cementitious materials remain constant within the same round of iteration and subdivision. The mixing process uses a combination of low-speed premixing (60%) and high-speed dispersion (90%). After mixing, the slurry is allowed to stand for 20 seconds to release entrained air bubbles before being connected to the pumping loop. The advantage of fixing the water and cementitious material conditions is that the grayscale image of conductivity distribution and the two-dimensional flow image primarily reflect the influence of the mass percentages of fine, medium, and coarse aggregates, rather than the interference caused by consistency drift during mixing.

[0043] When pumping to the slurry delivery pipeline inspection section, the pumping system first enters the stabilization section, and then enters the evaluation section to collect data. The purpose of the stabilization section is to allow the flow state inside the pipe to transition from the transient state at pump start-up to a quasi-steady state, preventing pressure fluctuations at pump start-up from pulling the conductivity distribution grayscale image out of the representative range. The stabilization section can be set to 10, and the evaluation section can be set to 5. During the evaluation section, the pumping flow rate is maintained at the same set value, for example, 30 m³ / min. Sampling is performed at the end of the evaluation section to allow the 3D laser profilometer to acquire surface height point cloud data. Simultaneously, the conductivity distribution grayscale image and the 2D flow image are acquired during the evaluation section: the resistivity tomography array outputs the conductivity distribution grayscale image at a frame rate of 20, and the high-speed linear scan camera outputs line scan images at no less than 8000 lines per second, which are then stitched together to form a 2D flow image. To avoid inconsistencies in the evaluation window for the same candidate gradation scheme due to sampling time deviations between different devices, the resistivity tomography array and the high-speed linear scan camera are simultaneously activated by the same trigger signal at the beginning of the evaluation section and simultaneously stopped at the end of the evaluation section.

[0044] The calculation of grayscale difference uses a grayscale image of conductivity distribution as input. This grayscale image is typically obtained by mapping the reconstructed conductivity distribution to 8-bit grayscale, with grayscale values ​​ranging from 0 to 255. To ensure that the grayscale difference is unaffected by changes in the absolute dimensions of conductivity, each frame of the conductivity distribution grayscale image undergoes intra-frame normalization: the minimum grayscale value of all pixels in the frame is mapped to 0, the maximum grayscale value is mapped to 255, and the remaining pixels are mapped linearly. The practical benefit of this processing is that when the overall conductivity of the slurry shifts due to temperature or ion concentration, the grayscale difference is still primarily determined by the relative distribution differences between the upper and lower semicircular regions, rather than by the overall shift.

[0045] When establishing a Cartesian coordinate system in the conductivity distribution grayscale image with the pipe center as the origin, the position of the center pixel and the radius pixel length are first determined using the geometric information of the pipe cross-section corresponding to the resistivity tomography array. The center pixel position can be directly obtained from the reconstructed mesh mapping relationship. When dividing the conductivity distribution grayscale image into an upper and lower semicircular region with the horizontal axis as the boundary, the upper semicircular region contains pixels that satisfy the condition that the ordinate is greater than or equal to 0 and are located inside the circle, and the lower semicircular region contains pixels that satisfy the condition that the ordinate is less than 0 and are located inside the circle. The average grayscale value of the upper semicircular region is obtained by traversing all pixel grayscale values ​​in the upper semicircular region and calculating the arithmetic mean. The average grayscale value of the lower semicircular region is obtained by traversing all pixel grayscale values ​​in the lower semicircular region and calculating the arithmetic mean. To write the above calculation in a directly reproducible form, we can use... ,in This represents the average gray value of the upper semicircle. This indicates the number of pixels in the upper semicircular region. This represents the grayscale value of each pixel in the upper semicircular region; This represents the average gray value of the lower semicircle. This indicates the number of pixels in the lower semicircle region. This represents the grayscale value of each pixel in the lower semicircular region. The grayscale difference is determined by... Received, among which This represents the grayscale difference. The absolute value of the grayscale difference is used as the evaluation metric for the degree of separation in Pareto optimal solution set selection and iterative subdivision sorting because the sign of the grayscale difference only reflects whether the high grayscale is concentrated in the upper or lower semicircle area, while the degree of separation is concerned with the strength of the deviation. The larger the absolute value, the more obvious the difference between the upper and lower areas.

[0046] The resistivity tomography (RTG) array within the evaluation segment will generate multiple frames of grayscale images showing the conductivity distribution. To improve noise robustness without introducing historical data across candidate gradation schemes, the grayscale differences can be summarized within each frame of the evaluation segment. For example, the arithmetic mean of the absolute values ​​of the grayscale differences across all frames within the evaluation segment can be used as the absolute value of the grayscale difference for that candidate gradation scheme. The arithmetic mean is chosen because inter-frame noise in RTG arrays typically exhibits zero-mean random perturbations; averaging reduces noise variance without amplifying short-term anomalies to dominate the results. Alternatively, the median of the absolute values ​​of the grayscale differences within the evaluation segment can be used to suppress occasional spikes, which is more stable when the pumping system experiences intermittent pulsations.

[0047] The calculation of gradation deviation uses a two-dimensional flow image as input. The two-dimensional flow image is formed by stitching together line-scan images row by row according to the acquisition sequence. The row direction of the two-dimensional flow image corresponds to the flow direction, and the column direction corresponds to the lateral direction of the pipe observation window. In the two-dimensional flow image, aggregate particles typically exhibit local patches of higher or lower brightness under illumination. Binarization is used to separate particle boundaries from the background texture. The advantage of using Otsu's method to calculate the optimal segmentation threshold is that it does not require manual threshold setting; the threshold is adaptively determined by the maximum inter-class variance criterion of the image histogram. Even when different candidate gradation schemes cause changes in brightness distribution, the segmentation remains relatively consistent.

[0048] After binarization to obtain a binary image, an eight-neighbor connected component labeling algorithm is applied to assign a unique label to each connected component. This algorithm considers pixels connected vertically, horizontally, and diagonally as the same connected component, making it more suitable for situations where particles exhibit oblique connections under motion blur or lighting / shadow conditions, reducing the need to split the same particle into multiple small connected components. When calculating the total number of pixels in each connected component as its area, the total number of pixels needs to be converted to an actual area to ensure a consistent scale for the subsequent equivalent circle diameter. If the pixel-to-length ratio is... ,in Let represent the actual length corresponding to each pixel, in millimeters per pixel. Then the actual area of ​​the connected component is... ,in This represents the actual area of ​​the connected component, in square millimeters. This represents the total number of pixels in the connected component. The equivalent circle diameter is calculated using the formula for converting to a circle with equal area, which can be written as: ,in This indicates the equivalent circle diameter, in millimeters. This represents the constant value of pi. This conversion maps connected domains of arbitrary shapes to a diameter value, making it easier to summarize multiple connected domains into a measured gradation curve, while avoiding the introduction of directional deviations by directly using length, width, or perimeter.

[0049] After arranging all connected components in ascending order of their equivalent circle diameter, the mass percentage is calculated by summing the proportions of each connected component's area to the total area of ​​all connected components. The cumulative mass percentage then varies with the equivalent circle diameter to form a measured gradation curve. This approach is based on the fact that the area of ​​connected components in a two-dimensional flow image is statistically related to the projected area of ​​the particles in the field of view, and the projected area is positively correlated with the particle size. Constructing the mass percentage using area proportions allows for a repeatable relative distribution without disassembling and weighing the particles. To express this process in an explicit and calculable form, the total area can be defined as... ,in This represents the total area of ​​all connected components. Indicates the first The area of ​​the nth connected region; define the nth... The quality percentage of each connected component is: ,in This represents the percentage of mass; after arranging the equivalent circle diameters from smallest to largest, the cumulative percentage of mass is... ,in Indicates as of the date The cumulative mass percentage of each equivalent circle diameter. Here This indicates the sorting sequence number. Cumulative frequencies are used instead of binning frequencies to make the curve less sensitive to a small number of anomalous connected components, while also facilitating point comparison with the target gradation curve.

[0050] When retrieving the target gradation curve from the target gradation curve database, the target gradation curve can be stored in tabular form, with each row containing a diameter and its corresponding cumulative mass percentage. The selection of comparison points, uniformly choosing 10 points along the equivalent circle diameter axis, is a trade-off between accuracy and computational cost: too few comparison points will mask local differences in the curve, while too many comparison points will increase the evaluation time for individual candidate gradation schemes and make them more sensitive to noise. The advantage of uniform point selection is that it covers the entire diameter range, avoiding bias towards fine or coarse aggregate intervals. When retrieving the cumulative mass percentage values ​​at each comparison point from the measured and target gradation curves, if the diameter of the comparison point does not coincide with the nodes in the curve table, linear interpolation can be used. The gradation deviation is obtained by summing the absolute differences, and can be written as... ,in Indicates the degree of deviation in gradation. Indicates the comparison point number. This indicates that the measured gradation curve is in the th... Cumulative mass percentage at each comparison point Indicates the target gradation curve at the th The cumulative quality percentage at each comparison point. The reason for using the sum of absolute differences instead of the sum of squared differences is that the absolute difference is less likely to amplify local outliers and is more suitable for situations where connected components occasionally stick together in on-site image segmentation.

[0051] When performing iterative subdivision of the equilateral triangular gradation domain based on grayscale difference and gradation deviation, a full-coverage evaluation is first performed on the initial grid vertices of the equilateral triangular gradation domain to obtain the absolute value of the grayscale difference and the gradation deviation of the candidate gradation scheme for each grid vertex. Subsequently, for each congruent small equilateral triangular cell, the absolute value of the grayscale difference and the gradation deviation of the three vertices are read. The arithmetic mean of the absolute values ​​of the grayscale differences of the three vertices is calculated to obtain the average segregation index, and the arithmetic mean of the gradation deviations of the three vertices is calculated to obtain the average deviation index. The vertex arithmetic mean is used instead of additional sampling inside the triangle because candidate gradation schemes require actual preparation and pumping, and internal sampling would significantly increase the number of trial runs; vertex averaging provides a low-cost local area estimation, allowing the subdivision process to concentrate trial run resources on more promising areas.

[0052] All congruent small equilateral triangle units are sorted in ascending order of average segregation index to form a segregation sorting sequence, and all congruent small equilateral triangle units are sorted in ascending order of average deviation index to form a deviation sorting sequence. For each congruent small equilateral triangle unit, the ranking of the segregation sorting sequence and the ranking of the deviation sorting sequence are calculated to obtain a comprehensive ranking value. Using ranking summation instead of directly weighting and summing the average segregation index and average deviation index avoids bias caused by different dimensions or numerical ranges, and eliminates the need for manually setting weighting coefficients, reducing subjectivity. Selecting the top 6 congruent small equilateral triangle units with the smallest comprehensive ranking value to form the dominant region unit set is to limit the computational burden and number of trial runs of iterative subdivision within a controllable range. For example, each subdivision adds 3 grid vertices per unit, so 6 units add 18 grid vertices. Combined with the initial 28 grid vertices, the total number of trial runs can be completed in a laboratory or pilot production line. Alternatively, if the batching and pumping automation is higher, the top 6 can be adjusted to the top 8 to more broadly cover the potential optimal region.

[0053] When inserting three new grid vertices at the midpoints of the three sides of each congruent small equilateral triangle element in the dominant region unit set and subdividing it into four smaller equilateral triangle sub-elements, the centroid coordinates of the new grid vertices are obtained by taking the arithmetic mean of the centroid coordinates of the grid vertices at the two ends of the corresponding sides. The effect of taking the arithmetic mean of each component is that the new grid vertex still satisfies the condition that the sum of the mass percentages of fine aggregate, medium aggregate, and coarse aggregate is always equal to 100%, and it falls at the midpoint of the original boundary, ensuring that the geometric subdivision and gradation constraints are completely consistent. For each new grid vertex corresponding to the candidate gradation scheme, the preparation, pumping, grayscale difference calculation, and gradation deviation calculation are repeatedly performed to form the vertex evaluation data for the next layer of subdivision. The above dominant region unit set selection and subdivision operation is repeated until the subdivision level reaches 4 layers. The setting of 4 layers takes into account both local search accuracy and total number of trial mixes, and can usually improve the effective resolution of the mass percentages of fine aggregate, medium aggregate, and coarse aggregate to the initial step size. The horizontal level allows for finer positioning of the optimal area. In optional methods, if the target gradation curve database has a coarse resolution or the number of trial mixes allowed on-site is limited, the subdivision level can be set to 3 levels to shorten the iteration cycle.

[0054] After reaching four subdivision levels, the Pareto optimal solution set is constructed using a median selection rule. For all grid vertices at the same subdivision level, the median of the absolute value of the gray-level difference and the median of the gradation deviation are calculated respectively. The median is used to divide the evaluation index into relatively good and relatively bad halves, and has the characteristic of being insensitive to outliers; when a candidate gradation scheme exhibits an extreme value in a certain index due to occasional bubbles or image adhesion, the median will not be dragged down by the extreme value. The Pareto optimal solution set consists of grid vertices that simultaneously satisfy the condition that the absolute value of the gray-level difference is less than or equal to the median of the absolute value of the gray-level difference of all grid vertices at the same subdivision level and the gradation deviation is less than or equal to the median of the gradation deviation of all grid vertices at the same subdivision level. This selection method ensures that the selected candidate gradation schemes are in the relatively good range of the same level in terms of both the degree of segregation evaluation and the gradation deviation, thereby avoiding the situation where they only perform well in one index while being significantly poor in another.

[0055] When determining the optimal gradation scheme by obtaining the apparent particle size distribution of the candidate gradation schemes corresponding to the Pareto optimal solution set based on surface height point cloud data and comparing it with the target gradation curve, the process begins by preparing slurry samples for each grid vertex of the Pareto optimal solution set corresponding to the candidate gradation scheme and spreading them evenly on a sampling platform. Surface height point cloud data is then acquired using a 3D laser profilometer. The spreading process can be performed by using a scraper to form the sample in one continuous motion in a single direction, maintaining a fixed gap (e.g., 1 / 2) between the scraper and the sampling platform to ensure consistent sample thickness and prevent systematic shifts in the apparent particle size distribution caused by thickness variations. The scanning area of ​​the 3D laser profilometer can be 100x100 mm, with the scanning time controlled within 3 seconds. Point cloud processing is performed immediately after scanning to minimize the impact of slurry surface flow on the point cloud morphology.

[0056] refer to Figure 5 In this embodiment, after iterative subdivision to the 4th layer, all candidate gradation schemes corresponding to the generated mesh vertices need to be screened using multi-objective optimization criteria to obtain a Pareto optimal solution set that performs well in both segregation degree and gradation deviation. The horizontal axis in the figure represents the absolute value of the grayscale difference. This parameter quantifies the average grayscale difference between the upper and lower semicircular regions in the conductivity distribution grayscale image, reflecting the degree of segregation of the slurry within the pipe cross-section. A larger value indicates more pronounced stratification. The vertical axis represents the degree of gradation deviation. This parameter is calculated by comparing the sum of the absolute values ​​of the cumulative mass percentage differences between the measured gradation curve and the target gradation curve at 10 comparison points. The larger the value, the more serious the deviation between the actual particle distribution and the target requirement.

[0057] Each scatter point in the graph represents a candidate gradation scheme, and the planar coordinates of the scatter point are the coordinates of that scheme. Value and To visually distinguish between Pareto optimal solutions and dominated solutions, different symbols are used: hollow circles represent solutions not selected for the Pareto optimal solution set, and solid squares represent solutions selected for the Pareto optimal solution set. The selection of Pareto optimal solutions is based on a two-condition criterion: condition one requires the absolute value of the grayscale difference between candidate gradation solutions. Less than or equal to the median of the absolute values ​​of the grayscale differences of all grid vertices at the same subdivision level ,Right now Condition two requires the gradation deviation of the candidate gradation scheme. Less than or equal to the median of the vertex gradation deviation of all meshes at the same subdivision level ,Right now Only candidate gradations that simultaneously satisfy conditions one and two are included in the Pareto optimal solution set. The figure shows two median dividing lines, with the vertical dashed line corresponding to... Horizontal dotted line corresponds to Two dividing lines divide the entire evaluation plane into four quadrants. The candidate gradation schemes located in the lower left quadrant are the Pareto optimal solutions. The median is used as the screening threshold instead of the average value because the median is insensitive to outliers. When an evaluation metric for a candidate gradation scheme becomes extreme due to unforeseen factors (such as air bubbles during sampling or image segmentation adhesion), the median will not be significantly affected by this extreme value, ensuring the robustness of the screening results. The lower left quadrant in the figure is marked with a light gray shading, representing the Pareto optimal region. Candidate gradation schemes in this region are relatively advantageous in both segregation control and gradation matching, avoiding situations where a scheme performs well in one objective but poorly in another. The scatter plot distribution in the figure shows that the candidate gradation schemes generated in the initial level are relatively dispersed. As the iterative subdivision deepens, the newly generated candidate gradation schemes gradually concentrate in the Pareto front region, indicating that the iterative subdivision strategy effectively guides the search direction.

[0058] When projecting surface height point cloud data onto a horizontal plane to obtain a planar projection point set, the planar coordinates of each scanned point are retained. These planar coordinates can be written as... ,in Represents the horizontal coordinate of the plane. Represents the longitudinal coordinate of the plane, with the height value denoted as... ,in This represents the height value relative to the reference plane of the sampling platform. The projection process only uses... Clustering is performed because of the surface height of the same particle. There will be natural undulations at the edges and center of the particles. Directly using neighborhood distance will split the same particle into multiple point clusters. When performing a density clustering algorithm based on Euclidean distance on a planar projected point set to obtain multiple independent point clusters, the Euclidean distance-based density clustering algorithm uses the minimum number of points and the neighborhood radius as input and outputs point cluster labels. Using millimeters as the unit of neighborhood radius is more convenient for engineering settings; for example, a neighborhood radius of 1.0 and a minimum number of points of 20. A neighborhood radius that is too small will split a particle into multiple point clusters, while a neighborhood radius that is too large will merge adjacent particles into the same cluster. Therefore, the neighborhood radius is generally chosen to be slightly larger than the point cloud plane sampling interval by 5 to 15 times, allowing points on the same particle surface to be interconnected while still maintaining gaps between adjacent particles. The minimum number of points is used to filter out splash points and noise points; a minimum number of points of 20 ensures that sporadic noise does not form point clusters while not affecting normal particle point clusters. In the optional mode, when the scan line spacing is smaller and the dot density is higher, the minimum number of dots can be increased to 50 to enhance noise resistance; when the scan area has fewer particles and the dot density is lower, the minimum number of dots can be reduced to 10 to avoid missing small particles.

[0059] For each point cluster, extract the maximum and minimum heights of corresponding points in the surface height point cloud data and calculate the height range. Use this height range as the apparent particle size of the aggregate. The height range can be written as... ,in This indicates the height range, in millimeters. This represents the maximum height value of the corresponding point in the point cluster. This represents the minimum height value of the point corresponding to the cluster. The consideration for using the height range as the apparent particle size is that: in a flat-lay sample, particles form protrusions on the surface, and the height of these protrusions is correlated with the exposed particle size, especially when the slurry coverage thickness is uniform; coarse aggregates typically form higher protrusions, while smaller particles form lower protrusions. Using the height range avoids the problem of particle projection profiles being affected by slurry smearing and surface reflection, making the three-dimensional measurement between different candidate gradation schemes more stable. Alternatively, the area of ​​the cluster projected onto the plane can be converted into the equivalent circle diameter, and then used in conjunction with the height range. For example, the equivalent circle diameter and height range can be calculated simultaneously for each cluster, and the height range can be used as the primary factor, with the equivalent circle diameter as a secondary factor, to eliminate pseudo-clusters caused by slender scratches.

[0060] The apparent particle size of all aggregate particles was statistically analyzed and arranged from smallest to largest. The proportion of each cluster's points to the total number of cluster points was used as the mass percentage, and these proportions were accumulated to obtain the cumulative mass percentage. The cumulative mass percentage, as it varied with the apparent particle size, formed a three-dimensional measured gradation curve. The cluster point ratio was used as the mass percentage because the sampling point density of the three-dimensional laser profilometer is approximately constant within the scanning area. The number of cluster points is positively correlated with the cluster coverage area, and further positively correlated with the exposed surface area of ​​the particles. Under the condition of uniform paving thickness, the exposed surface area is statistically related to the particle volume, and the point ratio can construct a stable relative distribution. For ease of reproduction, the total number of cluster points can be defined as... ,in This represents the total number of points in all point clusters. Indicates the first Number of points in the nth point cluster; define the nth point cluster. The quality percentage of each point cluster is: ,in This represents the percentage of mass; after arranging the apparent particle sizes from smallest to largest, the cumulative percentage of mass is... ,in Indicates as of the date Cumulative mass percentage of each apparent particle size.

[0061] Ten comparison points were evenly selected along the apparent particle size axis. The cumulative mass percentage values ​​of the measured three-dimensional gradation curve and the target gradation curve were recorded at each of the ten comparison points. The absolute values ​​of the differences between the cumulative mass percentage values ​​of the two curves at the ten comparison points were added together to obtain the three-dimensional gradation deviation. The three-dimensional gradation deviation can be written as... ,in Indicates the deviation of the three-dimensional gradation. The three-dimensional measured gradation curve represents the 3D measured gradation curve at the 3rd... Cumulative mass percentage at each comparison point Indicates the target gradation curve at the th The cumulative mass percentage at each comparison point. The candidate gradation scheme with the smallest three-dimensional gradation deviation is selected as the optimal gradation scheme. This ensures that the final output not only meets the requirements for grayscale difference and gradation deviation under the in-pipe flow state, but also further verifies the apparent particle size distribution through the sampled three-dimensional geometric information, thereby reducing the probability of misjudgment caused by two-dimensional projection obstruction or reflection from the transparent observation window. In optional methods, when the Pareto optimal solution set contains a large number of candidate gradation schemes, the top 5 can be selected first according to the absolute value of grayscale difference from smallest to largest, and then scanned with a three-dimensional laser profilometer to shorten the total three-dimensional scanning time, while still maintaining the final decision determined by the three-dimensional gradation deviation.

[0062] When the optimal gradation scheme is output to the slurry preparation control system, the output content remains consistent with the candidate gradation scheme, directly outputting the mass percentages of fine aggregate, medium aggregate, and coarse aggregate. After receiving the mass percentages of fine aggregate, medium aggregate, and coarse aggregate, the slurry preparation control system converts them into the weighing setpoints for each type of aggregate and drives the weighing and feeding operations. If the total mass of solid waste aggregate is set to... ,in If the total mass of solid waste aggregates (fine aggregate, medium aggregate, and coarse aggregate) is represented, then the set value for the fine aggregate weighing is [value missing]. The set value for medium aggregate weighing is The coarse aggregate weighing setting value is ,in This represents the normalized value indicating the proportion of fine aggregate by mass. This represents the normalized value of the proportion of aggregate by weight. This represents the normalized value indicating the percentage of coarse aggregate by mass. This indicates the weighed mass of fine aggregate. This indicates the weighing mass of medium aggregate. This indicates the weighing mass of coarse aggregate. In actual operation, the weighing setpoint can be sent to the weighing controller, and after weighing is completed, the mixing and pumping process begins, thus enabling the optimal gradation scheme to be continuously reproduced on site.

[0063] In optional implementations, in addition to the arithmetic mean of the upper and lower semicircular regions, the calculation of grayscale difference can also include the calculation of the variance of pixel grayscale values ​​in the upper and lower semicircular regions. This is used to identify grayscale patch enhancement caused by local clustering. However, the grayscale difference is still used as an evaluation metric for the degree of segregation in the average segregation index and median screening rules. In the calculation of gradation deviation, uniformly selecting 10 comparison points on the equivalent circle diameter axis can be replaced with uniformly selecting 12 comparison points to improve the curve comparison resolution. The top 6 congruent small equilateral triangle units with the smallest comprehensive ranking value in iterative subdivision can be replaced with the top 4 to reduce the number of trial matchings, or replaced with the top 8 to expand the search coverage. The neighborhood radius of the density clustering algorithm based on Euclidean distance can be adaptively set according to the scanning point spacing. For example, the neighborhood radius can be taken as 10 times the scanning point spacing to maintain consistent point cluster connectivity under different scanning resolutions. These optional methods maintain complete consistency in the representation of conductivity distribution grayscale images, two-dimensional flow images, surface height point cloud data, grayscale difference, gradation deviation, iterative subdivision, Pareto optimal solution set, apparent particle size distribution, target gradation curve, and optimal gradation scheme, facilitating direct implementation and verification under different equipment configurations and different field cycle times.

[0064] The present invention has been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of the invention. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and core ideas of the present invention. It should be noted that those skilled in the art can make various improvements and modifications to the present invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A multi-objective calculation method for optimizing the gradation of aggregate slurry containing solid waste, characterized in that, The method includes: deploying a resistivity tomography array, a high-speed linear array camera, and a three-dimensional laser profilometer in the inspection section of the slurry conveying pipeline and performing multimodal synchronous acquisition to obtain grayscale images of conductivity distribution, two-dimensional flow images, and surface height point cloud data; constructing an equilateral triangular gradation domain based on the mass proportions of fine aggregate, medium aggregate, and coarse aggregate, and generating candidate gradation schemes corresponding to the grid vertices; preparing slurry for the candidate gradation schemes and pumping it to the inspection section of the slurry conveying pipeline; calculating the grayscale difference based on the grayscale image of conductivity distribution and calculating the gradation deviation based on the two-dimensional flow image; performing iterative subdivision of the equilateral triangular gradation domain based on the grayscale difference and gradation deviation to obtain a Pareto optimal solution set; obtaining the apparent particle size distribution of the candidate gradation schemes corresponding to the Pareto optimal solution set based on the surface height point cloud data and comparing it with the target gradation curve to determine the optimal gradation scheme; and outputting the optimal gradation scheme to the slurry preparation control system.

2. The method according to claim 1, characterized in that, The resistivity tomography array consists of sixteen electrodes uniformly embedded along the circumference of the pipe wall of the slurry transport pipeline. The resistivity tomography array acquires voltage data using an adjacent excitation and adjacent measurement mode. The adjacent excitation and adjacent measurement mode involves applying excitation current to two adjacent electrodes and acquiring the voltage between the remaining adjacent electrode pairs, and sequentially rotating the excitation electrodes until a frame of voltage data is acquired. The voltage data of the resistivity tomography array is used to reconstruct a grayscale image of conductivity distribution by solving the inverse finite element problem. The inverse finite element problem solution includes establishing a finite element mesh of the pipeline cross section, establishing electrode boundary conditions, performing iterative inversion based on the sensitivity matrix, and performing smoothing and regularization processing on the mesh conductivity field after each iteration.

3. The method according to claim 2, characterized in that, A high-speed linear array camera is installed above the transparent observation window of the slurry conveying pipeline inspection section. The high-speed linear array camera acquires line scan images at a scanning rate of no less than 8,000 lines per second. The two-dimensional flow image is formed by stitching the line scan images line by line according to the acquisition sequence. The row direction of the two-dimensional flow image corresponds to the flow direction, and the column direction of the two-dimensional flow image corresponds to the horizontal direction of the pipeline observation window.

4. The method according to claim 3, characterized in that, The three-dimensional laser profilometer is set above the sampling platform. The three-dimensional laser profilometer scans the slurry sample laid flat on the sampling platform line by line to obtain surface height point cloud data. The surface height point cloud data includes the planar coordinates and height value of each scanning point. The height value is determined relative to the reference plane of the sampling platform.

5. The method according to claim 4, characterized in that, The three vertices of the equilateral triangular gradation domain correspond to the following: fine aggregate mass percentage is 100% and medium aggregate mass percentage and coarse aggregate mass percentage are zero; medium aggregate mass percentage is 100% and fine aggregate mass percentage and coarse aggregate mass percentage are zero; coarse aggregate mass percentage is 100% and fine aggregate mass percentage and medium aggregate mass percentage are zero. Each side of the equilateral triangular gradation domain is evenly divided into six equal parts. The equilateral triangular gradation domain is divided into thirty-six congruent small equilateral triangular units by straight lines parallel to the three sides. The thirty-six congruent small equilateral triangular units contain twenty-eight grid vertices. Each grid vertex is uniquely determined by the centroid coordinates of the fine aggregate mass percentage, medium aggregate mass percentage, and coarse aggregate mass percentage and corresponds to a candidate gradation scheme.

6. The method according to claim 5, characterized in that, The calculation of grayscale difference includes: establishing a rectangular coordinate system on the conductivity distribution grayscale image with the center of the pipe circle as the origin; dividing the conductivity distribution grayscale image into an upper semicircle region and a lower semicircle region with the horizontal axis as the boundary; traversing all pixel grayscale values ​​in the upper semicircle region and calculating the arithmetic mean to obtain the average grayscale value of the upper semicircle; traversing all pixel grayscale values ​​in the lower semicircle region and calculating the arithmetic mean to obtain the average grayscale value of the lower semicircle; subtracting the average grayscale value of the upper semicircle from the average grayscale value of the lower semicircle to obtain the grayscale difference; using the absolute value of the grayscale difference as the evaluation metric for the degree of segregation in the Pareto optimal solution set selection and iterative subdivision sorting.

7. The method according to claim 6, characterized in that, The calculation of gradation deviation includes: calculating the optimal segmentation threshold using Otsu's method for the two-dimensional flow image and performing binarization to obtain a binary image; applying the eight-neighbor connected component labeling algorithm to the binary image to assign a unique label to each connected component and calculating the total number of pixels in each connected component as the area of ​​the connected component; converting the area of ​​the connected components into the equivalent circle diameter using the equal area circle conversion formula; arranging all connected components in ascending order of equivalent circle diameter, using the proportion of each connected component area to the total area of ​​all connected components as the mass percentage, and accumulating them to obtain the cumulative mass percentage, which changes with the equivalent circle diameter to form the measured gradation curve; reading the target gradation curve from the target gradation curve database, uniformly selecting ten comparison points on the equivalent circle diameter axis, reading the cumulative mass percentage values ​​of the measured gradation curve and the target gradation curve at the ten comparison points respectively, and adding the absolute values ​​of the differences between the cumulative mass percentage values ​​of the two curves at the ten comparison points to obtain the gradation deviation.

8. The method according to claim 7, characterized in that, Iterative subdivision includes: for each congruent small equilateral triangle unit, reading the absolute value of the grayscale difference and the gradation deviation of the candidate gradation schemes corresponding to the three vertices; calculating the arithmetic mean of the absolute values ​​of the grayscale differences of the three vertices to obtain the average segregation index; calculating the arithmetic mean of the gradation deviations of the three vertices to obtain the average deviation index; sorting all congruent small equilateral triangle units in ascending order of average segregation index to form a segregation sorting sequence; sorting all congruent small equilateral triangle units in ascending order of average deviation index to form a deviation sorting sequence; and calculating the sum of the ranking of the segregation sorting sequence and the ranking of the deviation sorting sequence for each congruent small equilateral triangle unit to obtain the comprehensive ranking value. The top six congruent small equilateral triangle units with the smallest comprehensive ranking value are selected to form a set of dominant region units. For each congruent small equilateral triangle unit in the set of dominant region units, three new grid vertices are inserted at the midpoints of the three sides and subdivided into four smaller equilateral triangle sub-units. The centroid coordinates of the three new grid vertices are obtained by taking the arithmetic mean of the centroid coordinates of the grid vertices at both ends of the corresponding sides. For each new grid vertex, the candidate gradation scheme is used to prepare slurry and pump it to the slurry conveying pipeline detection section. The calculation of grayscale difference and gradation deviation is repeated. The above selection and subdivision operation of the dominant region unit set is repeated until the subdivision level reaches four layers.

9. The method according to claim 8, characterized in that, After the subdivision level reaches four levels, the Pareto optimal solution set consists of all grid vertices that simultaneously satisfy the following conditions: Condition 1 is that the absolute value of the gray-level difference of the grid vertex is less than or equal to the median of the absolute values ​​of the gray-level differences of all grid vertices in the same subdivision level; Condition 2 is that the grid vertex gradation deviation is less than or equal to the median of the gradation deviation of all grid vertices in the same subdivision level.

10. The method according to claim 9, characterized in that, Obtaining the apparent particle size distribution based on surface height point cloud data and comparing it with the target gradation curve to determine the optimal gradation scheme includes: preparing slurry samples for each grid vertex corresponding to the candidate gradation scheme of the Pareto optimal solution set and spreading them on a sampling platform; acquiring surface height point cloud data using a 3D laser profilometer; projecting the surface height point cloud data onto a horizontal plane to obtain a planar projection point set; performing a density clustering algorithm based on Euclidean distance on the planar projection point set to obtain multiple independent point clusters, with the density clustering algorithm using the minimum number of points and the neighborhood radius as input and outputting point cluster labels; extracting the maximum and minimum heights of corresponding points in the surface height point cloud data for each point cluster and calculating the height range, and then... The apparent particle size of the aggregate particles is taken as the range of apparent particle size. The apparent particle size of all aggregate particles is counted and arranged from smallest to largest. The proportion of the number of points in each cluster to the total number of points in all clusters is taken as the mass percentage and accumulated to obtain the cumulative mass percentage. The cumulative mass percentage changes with the apparent particle size to form a three-dimensional measured gradation curve. Ten comparison points are evenly selected on the apparent particle size axis. The cumulative mass percentage values ​​of the three-dimensional measured gradation curve and the target gradation curve at the ten comparison points are read. The absolute values ​​of the difference between the cumulative mass percentage values ​​of the two curves at the ten comparison points are added to obtain the three-dimensional gradation deviation. The candidate gradation scheme with the smallest three-dimensional gradation deviation is selected as the optimal gradation scheme.

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