A method for identifying solid waste screening behavior and modeling separation rates

Abstract

This invention relates to a method for identifying solid waste screening behavior and modeling separation rates, belonging to the field of particle segregation behavior prediction technology. It solves the problem of insufficient accuracy in segregation behavior prediction in existing technologies. The method involves acquiring multiple potential segregation starting points and / or potential segregation ending points during the rising process of each particle, filtering them, and then using the first remaining potential segregation starting point as the true segregation starting point and the last potential segregation ending point as the true segregation ending point. Based on the height difference and time difference between the true segregation ending point and the true segregation starting point for each particle, the statistical characteristics of the segregation rate of coarse particles and the particle temperature of fine particles in each segregation layer are calculated, and a training sample set is constructed to train the neural network model. The particle temperature of fine particles in the mixed particle bed is collected and input into the trained neural network model to predict the statistical characteristics of the segregation rate of coarse particles in each segregation layer. This achieves an accurate method for identifying solid waste screening behavior and modeling separation rates.

Description

Technical Field

[0001] This invention relates to the field of particle segregation behavior prediction technology, and in particular to a method for identifying solid waste screening behavior and modeling separation rates. Background Technology

[0002] Mining solid waste, especially coal-related byproducts (coal gangue, fly ash, gasification slag, etc.), contains metallic elements such as lithium, gallium, and rare earth elements. Sorting and enriching these metallic elements is crucial for ensuring energy security. Traditional sorting processes mainly include physical, chemical, and biological methods. The appropriate method must be determined based on the properties, recovery capacity, and value of the raw materials. Screening is a necessary preliminary step for most solid waste recycling because the content of metallic elements varies in raw materials of different particle sizes. Screening and grading can effectively enrich valuable metal carrier minerals, providing qualified raw materials for subsequent sorting.

[0003] The Discrete Element Method (DEM), based on the fundamental laws of classical mechanics, has proven to be an efficient numerical simulation process for simulating and analyzing the dynamics of bulk materials. Typically, the DEM analysis process consists of three main parts: preprocessing, simulation solving, and post-processing. Preprocessing primarily involves setting parameters such as material, geometry, and operation of particles and equipment. Post-processing involves statistical analysis based on the spatiotemporal properties of particles and equipment and their dynamic interactions, combined with Computer-Aided Design (CAD) technology to visualize the evolution of various property parameters and contact and adhesion relationships of bulk materials and geometric structures. Solver simulation is the core of the DEM process, mainly including setting the simulation time step based on the minimum particle size and dividing the simulation mesh. Based on this, the contact and adhesion between particles and equipment, as well as between particles, are determined within each mesh cell per unit time step. This allows for the calculation of the sum of forces and torques acting on each particle, ultimately achieving iterative updates of particle properties. Therefore, it has wide applications in research on the dynamic evolution of particle group structure on the screen during vibrating screening, the vibration energy transfer and distribution law of complex mixed particle beds, and the construction of particle segregation rate prediction models.

[0004] Despite significant attention being paid to predicting particle segregation behavior, few models maintain high accuracy across a wide parameter range, likely due to three main reasons. First, feature identification and extraction from oscillatory behavior data of large batches of particles present challenges. For example, methods for trend extraction and feature point determination of trajectory signals exhibiting both macroscopic non-monotonicity and significant local fluctuations require further development. Second, as particle beds evolve from single-particle to multi-particle sizes, their packing structures become increasingly disordered, making particle segregation behavior difficult to predict. Third, in equal-volume mixed particle beds, the spatial distribution of coarse particle segregation trajectories is sparse due to their limited number, resulting in insufficient data for observing the segregation rate distribution, thus limiting coarse particle segregation rate modeling based on vibration parameters. Existing particle segregation behavior prediction models mainly include segregation time (indirect) prediction models and segregation rate (direct) prediction models. The indirect prediction model analyzes the relative displacement between adhering particles and internal particles in a mixed particle bed. It assumes that the time it takes for the particle bed to complete its deceleration, upward throw, and free fall under moderate vibration conditions is one vibration cycle. Then, it uses a Taylor expansion of the reciprocal of the displacement to propose the segregation time and... Proportional, following Γ The assumptions mentioned above, which are subject to stringent conditions, are often not met and therefore cannot be applied to predicting segregation behavior over a wide range of parameters. Direct prediction models, on the other hand, construct prediction models of particle segregation rate and overall separation degree by piecewise fitting analysis of the correlation curves between vibration parameters and the degree of segregation in an equal-volume mixed particle group. However, these models cannot calculate the segregation rate of all particles or reflect the three-dimensional spatial evolution characteristics of their distribution. Therefore, existing particle segregation behavior prediction models cannot comprehensively and accurately predict segregation behavior. Summary of the Invention

[0005] Based on the above analysis, the embodiments of the present invention aim to provide a method for identifying solid waste screening behavior and modeling separation rate, in order to solve the problem that existing particle segregation behavior prediction models cannot comprehensively and accurately predict segregation behavior.

[0006] This invention provides a method for identifying solid waste screening behavior and modeling separation rates. ， include: Based on the migration trajectory of the segregated coarse particles, multiple potential segregation starting points and / or potential segregation ending points are obtained during the ascent of each coarse particle. After filtering out multiple potential segregation initiation points / potential segregation endpoints for each coarse particle, the first remaining potential segregation initiation point is taken as the true segregation initiation point, and the last potential segregation endpoint is taken as the true segregation endpoint. Based on the height difference and time difference between the actual segregation endpoint and the actual segregation start point of each coarse particle, the segregation rate of each coarse particle and the statistical characteristics of the segregation rate of coarse particles in each segregation layer are calculated. The instantaneous velocity of each fine particle is obtained, and then the particle temperature of the fine particles in each voxel is calculated. A training sample set was constructed based on the statistical characteristics of the particle temperature of fine particles in each voxel and the segregation rate of coarse particles in each segregation layer, and the neural network model was trained accordingly. The particle temperature of fine particles in each voxel in the mixed particle bed is collected and input into the trained neural network model to predict the statistical characteristics of the segregation rate of coarse particles in each segregation layer.

[0007] Furthermore, based on the migration trajectory of the segregated coarse particles, multiple potential segregation initiation points and / or potential segregation endpoints during the ascent of each coarse particle are obtained, including: Based on the migration trajectory of segregated coarse particles, obtain adjacent convex decrease-convex increase elbow point pairs and concave increase-concave decrease knee point pairs of smooth height curves that change over time; obtain the last local minimum point of each interval in the interval where the convex decrease-convex increase elbow point pairs are located, and obtain the first local maximum point of each interval in the interval where the concave increase-concave decrease knee point pairs are located, and determine whether the local minimum point and the local maximum point are local minimum points and local maximum points. The coarse particle segregation initiation point, the convex elbow point, and the local minimum point are all considered as potential segregation initiation points; the coarse particle segregation endpoint, the concave knee point, and the local maximum point are all considered as potential segregation endpoints.

[0008] Furthermore, determining whether the local minimum point, local maximum point is a local minimum point, or local maximum point includes: determining whether the local minimum point / local maximum point is an interior point; if it is an interior point, the derivative sign or instantaneous rate is used to determine whether the point is a local minimum point / local maximum point; if it is not an interior point, it is determined that the point is not a local minimum point / local maximum point.

[0009] Furthermore, it is determined whether the local minimum / local maximum point is an interior point. If it is an interior point, the derivative sign or instantaneous rate is used to determine whether the point is a local minimum / local maximum point, including: If the local minimum point / local maximum point is an interior point, the sign of the instantaneous velocity and instantaneous acceleration of the local minimum point / local maximum point, as well as the change in the sign of the instantaneous velocity within the range less than the first threshold of the local minimum point / local maximum point, are used to determine whether the point is a local minimum point / local maximum point.

[0010] Furthermore, filtering for potential segregation initiation points and potential segregation endpoints includes: The potential segregation start points and potential segregation end points are filtered based on the starting threshold height, the ending threshold height, the time interval between adjacent potential segregation start points / adjacent potential segregation end points, and the preset gradient threshold.

[0011] Furthermore, filtering is performed based on the starting threshold height and the ending threshold height, including: The potential segregation start points and potential segregation endpoints are obtained by filtering potential segregation start points that are higher than the starting threshold height and potential segregation endpoints that are lower than the ending threshold height.

[0012] Furthermore, filtering based on the time interval between adjacent potential segregation initiation points / adjacent potential segregation endpoints includes: If the time interval between adjacent potential separation initiation points after initial filtering is less than or equal to the first time threshold, then the latter potential separation initiation point is deleted to obtain the merged potential separation initiation points; if the time interval between adjacent potential separation endpoints after initial filtering is less than or equal to the first time threshold, then the former potential separation endpoint is deleted to obtain the merged potential separation endpoints.

[0013] Furthermore, potential segregation start points and potential segregation end points are filtered based on preset gradient thresholds, including: The first gradient of the potential separation endpoints after merging is calculated using the backward difference method. If the first gradient is lower than a preset gradient threshold, the next potential separation endpoint used in the calculation of the first gradient by the backward difference method is filtered out; if the first gradient is higher than the preset gradient threshold, the previous potential separation endpoint used in the calculation of the first gradient by the backward difference method is filtered out. The first-order gradient is calculated using the forward difference method for the merged potential separation starting points. If the first-order gradient is lower than a preset gradient threshold, the previous potential separation starting point used in the calculation of the first-order gradient by the forward difference method is filtered out; if the first-order gradient is higher than the preset gradient threshold, the next potential separation starting point used in the calculation of the first-order gradient by the forward difference method is filtered out.

[0014] Furthermore, a training sample set was constructed based on the statistical characteristics of the particle temperature of fine particles in each voxel and the segregation rate of coarse particles in each segregation layer, and the neural network model was trained, including: The particle temperature of the layer, row, column, and fine particles where each voxel is located is used as the four-dimensional input data of the neural network model. The average value and standard deviation of the segregation rate of coarse particles in each segregation layer are used as labels to form the first training sample set. The neural network model is trained based on the first training sample set.

[0015] Furthermore, the formula for calculating the particle temperature of fine particles in each voxel is as follows: , Where k is the voxel unit number, and j is the fine particle number within voxel unit k. This represents the number of fine particles contained in the voxel unit with serial number k. Let j be the instantaneous velocity vector of the fine particle numbered j in voxel unit k; Let be the average velocity vector of all fine particles in voxel unit k.

[0016] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: 1. This invention includes obtaining multiple potential segregation starting points and / or potential segregation ending points during the ascent of each coarse particle based on the migration trajectory of the coarse particles in the particle bed; filtering the multiple potential segregation starting points / potential segregation ending points of each coarse particle, and taking the first remaining potential segregation starting point as the true segregation starting point and the last potential segregation ending point as the true segregation ending point; calculating the segregation rate of each coarse particle and the statistical characteristics of the segregation rate of coarse particles in each segregation layer based on the height difference and time difference between the true segregation ending point and the true segregation starting point of each coarse particle; this invention proposes a particle segregation behavior feature recognition algorithm based on the potential starting and ending point identification algorithm and the true starting and ending point determination algorithm of the segregation process, realizing the noise reduction and reconstruction of the particle segregation trajectory and the accurate calculation of the particle segregation rate, and using the established deep spatiotemporal residual convolutional neural network to improve the prediction accuracy of the particle segregation rate at different layer heights.

[0017] 2. This invention obtains the instantaneous velocity of each fine particle and then calculates the particle temperature of the fine particles in each voxel; based on the particle temperature of the fine particles in each voxel and the statistical characteristics of the segregation rate of coarse particles in each segregation layer, a training sample set is constructed, and a neural network model is trained; the particle temperature of the fine particles in each voxel of the mixed particle bed is collected and input into the trained neural network model to predict the statistical characteristics of the segregation rate of coarse particles in each segregation layer. This quantifies the response of the coarse particle segregation rate to the particle temperature of fine particles on a macroscopic scale, significantly reducing the number of parameters required for model training.

[0018] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0019] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0020] Figure 1 is a schematic flowchart of a solid waste screening behavior identification and separation rate modeling method according to an embodiment of the present invention. Figure 2 This is the core flowchart of the potential start and end point identification method for the separation process in this embodiment of the invention; Figure 3This is a schematic diagram of the convex decrease-convex increase elbow point pair and concave increase-concave decrease knee point pair on the height curve changing with time according to an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the combined effect of potential segregation initiation points and potential segregation endpoints in an embodiment of the present invention. Figure 5 This is a schematic diagram illustrating the initial conditions and preliminary filtering effect of an embodiment of the present invention. Figure 6 This is a schematic diagram illustrating the effect of deleting two adjacent segregation initiation points or segregation endpoints in an embodiment of the present invention. Figure 7 This is a schematic diagram of the true starting point and true ending point of the separation process extracted based on gradient threshold in an embodiment of the present invention; Figure 8 This is an architectural design diagram of the Deep Spatiotemporal Residual Convolutional Neural Network (DSTRes-CNNs) according to an embodiment of the present invention; Figure 9 This is a schematic diagram of the data structure of the particle temperature dataset and the segregation rate dataset in an embodiment of the present invention. Detailed Implementation

[0021] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0022] A specific embodiment of the present invention discloses a method for identifying solid waste screening behavior and modeling separation rates, such as... Figure 1 As shown. Specifically, it includes steps S1-S5.

[0023] S1. Based on the migration trajectory of the segregated coarse particles, obtain multiple potential segregation starting points and / or potential segregation ending points during the ascent process of each coarse particle.

[0024] The adjacent convex decrease-convex increase elbow point pairs and concave increase-concave decrease knee point pairs are obtained from the smooth height curve that changes over time based on the migration trajectory of segregated coarse particles.

[0025] Specifically, convex decreasing: a convex curve that is monotonically decreasing; convex increasing: a convex curve that is monotonically increasing; concave increasing: a concave curve that is monotonically increasing; concave decreasing: a concave curve that is monotonically decreasing. Convex decreasing-convex increasing elbow pair: the elbow points of convex decreasing and convex increasing are matched to form a pair; concave increasing-concave decreasing knee pair: the knee points of concave increasing and concave decreasing are matched to form a pair. Convex: the shape of the line connecting any two points on a curve that is higher than the curve between those two points; concave: the shape of the line connecting any two points on a curve that is lower than the curve between those two points.

[0026] The Lowe's algorithm is used to extract the temporal evolution trend of the segregated particle migration trajectory. In this technical solution, the smoothing fraction (frac) and the number of iterations (it) are set to 0.1 and 5, respectively. The smoothing fraction refers to the proportion of data required for each estimated value (smoothed value), and the number of iterations refers to the number of times the weighted average is recalculated based on the residuals. A smoothing fraction that is too large will cause distortion (underfitting: deviating from the trend of the true data), while a smoothing fraction that is too small will lead to instability (overfitting: noise is not effectively filtered out, and the trend is not reflected). Therefore, this embodiment uses 0.1 as the smoothing fraction. The resulting curve shows the change of smoothed height data over time (i.e., the smoothed height curve).

[0027] Considering that extreme points on a smooth height curve may become the starting / ending points of a dissociation, a pair of elbow / knee points with the same concavity / convexity will inevitably appear on the left and right sides of the extreme point due to the change in curvature. Therefore, this embodiment uses a matching algorithm to search for adjacent elbow / knee point pairs: convex decreasing-convex increasing (potential starting point of dissociation) and concave increasing-concave decreasing (potential ending point of dissociation). Compared with traditional graph theory matching problems, stable matching considers the preferences of both parties in the matching process. This makes the algorithm design rely more on the preference order rather than the simple graph structure, thus ensuring that no pair abandons the current matching result to obtain a better choice (one-sided local optimum) (two-sided global optimum).

[0028] This embodiment is an improvement upon the GS matching algorithm (delayed acceptance algorithm). Specifically, it adds the constraint that the convex decreasing elbow point precedes the convex increasing elbow point and the concave increasing knee point precedes the concave decreasing knee point, and filters out inferior sets in the pairing results. Inferior sets refer to a group of elbow / knee point pairs that are forced to pair due to perfect matching; these are specifically those pairings with long time intervals and containing at least one other elbow / knee point pair within that interval.

[0029] After filtering out the inferior set in the pairing results, the last local minimum point of each interval is obtained in the interval where the convex decrease-convex increase elbow point pair is located, and the first local maximum point of each interval is obtained in the interval where the concave increase-concave decrease knee point pair is located. Then, it is determined whether the local minimum point and the local maximum point are local minimum points and local maximum points.

[0030] Specifically, based on the kneele algorithm provided in KneeLocator, local extrema of curvature in the smooth height curve are searched, and categorized into four types according to the curve's monotonicity and concavity: convex increasing elbows, convex decreasing elbows, concave decreasing elbows, and concave increasing elbows. Convex increasing elbows and concave increasing elbows are respectively potential segregation start points and potential segregation end points. For example... Figure 3 As shown, adjacent convex decrease-convex increase elbow point pairs and concave increase-concave decrease knee point pairs are obtained based on the Gale-Shapley stable matching algorithm. Smooth height curves are then extracted according to the occurrence times of these point pairs, and the resulting segments are denoted as follows: and .exist P Within each sub-segment, find the last local minimum point within the current segment; these local minimum points form a point set. ;exist Q Within each sub-segment, find the first local maximum point within the current segment; these local maximum points form a point set. .

[0031] Use boundary conditions to traverse and judge the above U , V If each point in the point set is an interior point, the sign of the derivative is used to verify whether it is an extremum (the derivative sign is determined by the first derivative being 0, and the second derivative being non-zero, indicating an extremum bag point). Otherwise, the derivative sign determination fails, and the point is judged based on whether the instantaneous velocity at that point is non-zero. Specifically, a local extremum is a necessary condition for an extremum. If a local extremum is satisfied, the sign of the second derivative (instantaneous acceleration) is verified. If the instantaneous acceleration is greater than zero, the point is a minimum; if the instantaneous acceleration is less than zero, the point is a maximum. If the instantaneous acceleration sign verification fails (second derivative is 0), the first derivative (instantaneous velocity) sign verification is used. If the instantaneous velocity sign changes from positive to negative, the point is a maximum; if the instantaneous velocity sign changes from negative to positive, the point is a minimum. If the sign verification of the instantaneous acceleration at an interior point fails (second derivative is 0), or the instantaneous velocity at a boundary point is non-zero (first derivative is not 0), then the local extremum point does not meet the requirements for an extreme point, and therefore returns None (i.e., null value), meaning there is no extreme point, and no potential segregation start point or segregation end point. Figure 4 As shown, the starting point, the convex elbow point, and the local minimum point are merged and duplicate values ​​are removed to form the set of "potential segregation starting points"; the ending point, the concave knee point, and the local maximum point are merged and duplicate values ​​are removed to form the set of "potential segregation ending points".

[0032] Determining whether the local minimum point, local maximum point, or local maximum point is a local minimum point or a local maximum point includes: determining whether the local minimum point / local maximum point is an interior point; if it is an interior point, the derivative sign or instantaneous rate is used to determine whether the point is a local minimum point / local maximum point; if it is not an interior point, it is determined that the point is not a local minimum point / local maximum point.

[0033] Determine whether the local minimum / local maximum point is an interior point. If it is an interior point, use the derivative sign or instantaneous rate to determine whether the point is a local minimum / local maximum point, including: If the local minimum point / local maximum point is an interior point, the sign of the instantaneous velocity and instantaneous acceleration of the local minimum point / local maximum point, as well as the change in the sign of the instantaneous velocity within the range less than the first threshold of the local minimum point / local maximum point, are used to determine whether the point is a local minimum point / local maximum point.

[0034] Specifically, the central difference method is used to calculate the first derivative (instantaneous segregation rate) and the second derivative (instantaneous segregation acceleration) of the smoothed height data, which are then used to determine whether the extreme points are potential segregation start / end points based on the sign of the derivatives.

[0035] The formula for calculating the instantaneous segregation rate is shown in formula (1): (1) in, For the first The particle height at any given moment; For the first The time corresponding to a given moment.

[0036] The formula for calculating instantaneous segregation acceleration is shown in formula (2): (2) in, For the first The particle height at any given moment.

[0037] Determine whether the local minimum / local maximum point is an interior point. If it is an interior point, use the derivative sign or instantaneous rate to determine whether the point is a local minimum / local maximum point, including: If the local minimum / local maximum point is an interior point, then the point is a local minimum point if the derivative of its instantaneous velocity is 0 and the derivative of its instantaneous acceleration is greater than 0; if the derivative of its instantaneous velocity is 0 and the derivative of its instantaneous acceleration is less than 0, then the point is a local maximum point; if both the derivatives of its instantaneous velocity and instantaneous acceleration are 0, the point is determined to be a maximum / minimum point based on the change in the sign of its instantaneous velocity within a range less than a first threshold; if the derivative of its instantaneous acceleration is 0 and the derivative of its instantaneous velocity is not 0, the point is determined not to be a local minimum or a local maximum point.

[0038] The coarse particle segregation initiation point, the convex elbow point, and the local minimum point are all considered as potential segregation initiation points; the coarse particle segregation endpoint, the concave knee point, and the local maximum point are all considered as potential segregation endpoints.

[0039] Specifically, the starting and ending points of coarse particle segregation are the two endpoints of a smooth height curve that changes over time, obtained from the migration trajectory of the coarse particles.

[0040] S2. After filtering the multiple potential segregation initiation points / potential segregation endpoints of each coarse particle, the first remaining potential segregation initiation point is taken as the true segregation initiation point, and the last potential segregation endpoint is taken as the true segregation endpoint.

[0041] Filtering for potential segregation initiation points and potential segregation endpoints includes: The potential segregation start points and potential segregation end points are filtered based on the starting threshold height, the ending threshold height, the time interval between adjacent potential segregation start points / adjacent potential segregation end points, and the preset gradient threshold.

[0042] Filtering is performed based on the starting threshold height and the ending threshold height, including: The potential segregation start points and potential segregation endpoints are obtained by filtering potential segregation start points that are higher than the starting threshold height and potential segregation endpoints that are lower than the ending threshold height.

[0043] Filtering based on the time interval between adjacent potential segregation initiation points / adjacent potential segregation endpoints includes: If the time interval between adjacent potential separation initiation points after initial filtering is less than or equal to the first time threshold, then the latter potential separation initiation point is deleted to obtain the merged potential separation initiation points; if the time interval between adjacent potential separation endpoints after initial filtering is less than or equal to the first time threshold, then the former potential separation endpoint is deleted to obtain the merged potential separation endpoints.

[0044] The potential segregation start point and potential segregation end point are filtered according to a preset gradient threshold, including: The first gradient of the potential separation endpoints after merging is calculated using the backward difference method. If the first gradient is lower than a preset gradient threshold, the next potential separation endpoint used in the calculation of the first gradient by the backward difference method is filtered out; if the first gradient is higher than the preset gradient threshold, the previous potential separation endpoint used in the calculation of the first gradient by the backward difference method is filtered out. The first-order gradient is calculated using the forward difference method for the merged potential separation starting points. If the first-order gradient is lower than a preset gradient threshold, the previous potential separation starting point used in the calculation of the first-order gradient by the forward difference method is filtered out; if the first-order gradient is higher than the preset gradient threshold, the next potential separation starting point used in the calculation of the first-order gradient by the forward difference method is filtered out.

[0045] Specifically, the algorithm for determining the true start and end points of the separation process consists of the following steps: Step 1, Initial Condition Setting: Set the initial conditions for the potential segregation start and end points, including a bed height of 200 mm, an start threshold of 125 mm, and an end threshold of 175 mm. The unit for height data in this technical solution is... d s =3 mm, meaning the bed height, starting threshold, and ending threshold are 66.67 mm. d s 41.67 d s and 58.33 d s ; The second step is preliminary filtering: filtering out potential segregation start points above the start threshold and potential segregation end points below the end threshold. Additionally, filtering is performed based on temporal logic order, removing end points that appear before the first potential segregation start point and start points that appear after the first potential segregation end point. The diagram illustrates the initial conditions and preliminary filtering effect. Figure 5 As shown.

[0046] The third step is clustering: The time interval between adjacent potential segregation initiation points is calculated. If the interval is ≤0.5 s, the latter initiation point is deleted to merge pairs of segregation initiation points that are too close together. Similarly, the time interval between adjacent potential segregation endpoints is calculated. If the interval is ≤0.5 s, the former endpoint is deleted to merge pairs of segregation endpoints that are too close together. A schematic diagram illustrating the effect after deleting two adjacent segregation initiation points or segregation endpoints in this embodiment is shown below. Figure 6 As shown.

[0047] Step 4, Gradient Analysis and Threshold Verification: For potential separation endpoints, calculate the first-order gradient using backward differencing and compare it with a preset gradient threshold. Filter out separation endpoints with gradients below the threshold (because they are not rising and are considered to be approaching the endpoint, the next potential separation endpoint used in calculating the first-order gradient is deleted). For potential separation starting points, calculate the first-order gradient using forward differencing and filter out potential separation starting points with gradients below the threshold (calculate the gradient between two adjacent potential separation starting points, and delete the previous potential separation starting point used in calculating the first-order gradient). The last point after the waiting area can be retained as the starting point, excluding oscillation points.

[0048] Step 5: Determine the true start and end points of the separation process: After gradient threshold filtering, the first potential separation start point is taken as the true separation start point, and the last potential separation end point that meets the conditions is taken as the true separation end point. A schematic diagram of the true start and end points of the separation process extracted based on gradient thresholding in this embodiment of the invention is shown below. Figure 7 As shown.

[0049] This technical solution uses an experiment with an amplitude of 1.96875 mm and a frequency of 20 Hz as an example. Table 1 lists the time steps and heights corresponding to the start and end times of the rising process of some segregated particles. Figure 7 This displays the original migration trajectory of the separated particles, the smoothed trajectory trend curve, and the characteristic points at the beginning and end of the separation process. Thus, the identification of the separation behavior characteristics is achieved.

[0050] Table 1. Start and end times of the segregation particle ascent process and particle height at corresponding positions.

[0051] S3. Based on the height difference and time difference between the actual segregation endpoint and the actual segregation start point of each coarse particle, calculate the segregation rate of each coarse particle and the statistical characteristics of the segregation rate of coarse particles in each segregation layer.

[0052] Specifically, statistical characteristics refer to standardizing the average segregation rate of coarse particles in each segregation layer, and standardizing the standard deviation of the segregation rate of coarse particles in each segregation layer.

[0053] The segregation velocity of tracer coarse particles is defined as the ratio of their ascent height to the time taken, and the calculation formula is as follows: (3) in, h stop,i and t stop,i They represent the numbers respectively. i The height and time step at the end of the particle's ascent, and h start,i and t start,i This indicates the initial height and time step of the same particle's ascent.

[0054] Specifically, the segregation (rise) rate of all segregated particles is calculated in batches based on the ratio of the height difference to the time difference between the endpoints. Then, stratified statistics are performed on the particle bed to calculate the average (avg) and standard deviation (std) of the segregation rate at each layer. Specifically, the stratification scheme in this technical solution uses a layer height of 4.5 d. s (d) s The sample was taken as 3 mm, and it was divided into 7 layers (Layer 0 to 6). The results showed that only layers 0-4 were segregated layers, while layers 5 and 6 did not separate out coarse particles.

[0055] S4. Obtain the instantaneous velocity of each fine particle and then calculate the particle temperature of the fine particles in each voxel. A training sample set was constructed based on the statistical characteristics of the particle temperature of fine particles in each voxel and the segregation rate of coarse particles in each segregation layer, and the neural network model was trained accordingly.

[0056] The formula for calculating the particle temperature of fine particles in each voxel is: , Where k is the voxel unit number and j is the voxel unit. k The fine particles in the numbering, For the serial number k The number of fine particles contained in a voxel unit; For voxel units k The Chinese number is j The instantaneous velocity vector of fine particles; For voxel units k The average velocity vector of all fine particles in the mixture.

[0057] The particle temperature of local fine particles is defined as the mean variance of the velocity components of the fine particle group in each orthogonal direction (X, Y, and Z axes of the spatial Cartesian coordinate system).

[0058] In one specific embodiment of the present invention, a particle tracer is used to measure the instantaneous velocity of fine particles. The particle tracer is installed on the side wall along the length of the particle bed. The width of the particle bed is limited; otherwise, some fine particles would be obscured. In this embodiment, the diameter of the coarse particles is three times that of the fine particles. The system in this embodiment uses an equal-volume particle bed, meaning that the volume occupied by all coarse particles is equal to the volume occupied by all fine particles.

[0059] In another specific embodiment of the present invention, after preprocessing the separation particle motion data in steps S1-S2, the instantaneous velocity of the fine particles can also be calculated using the method in step S3. However, the calculation is based on the influence of the instantaneous velocity of the fine particles moving downward on the coarse particles moving upward.

[0060] A dataset of fine-particle temperature data and coarse-particle segregation rate statistics is constructed and then fed into a deep spatiotemporal residual convolutional neural network for parameter training.

[0061] Specifically, particle temperature reflects the oscillation consistency of a particle swarm within a local area, thus determining the packing structure and density of the particle swarm, and ultimately significantly affecting the ascent rate of coarse segregated particles. Since calculating particle temperature requires grid partitioning, the spatial distribution of particle temperature data is relatively sparse. Upsampling the particle temperature data using interpolation algorithms does not effectively increase the information entropy of particle cluster behavior; instead, it causes an exponential explosion in the number of parameters, leading to poor subsequent training results. Therefore, this embodiment aims to quantify the response of coarse particle segregation rate to fine particle temperature on a macroscopic scale, significantly reducing the number of parameters required for model training.

[0062] Binary mixed particle beds undergo continuous structural reorganization during particle size segregation, resulting in a significant dynamic interaction between particle temperature and segregation rate across time and space. To improve the accuracy of the established prediction model, this technical solution uses the C3D operator to precisely quantify the impact of the spatiotemporal evolution of particle temperature distribution within each bed layer on the statistical characteristics of segregation rates in different bed layers. Figure 9 This demonstrates the data structure using a fine-grained temperature dataset as model input and a coarse-grained segregation rate dataset as model output. This embodiment employs a multi-task loss function to simultaneously train the classification task. Figure 9 (obj in the middle) and regression task ( Figure 9 The values ​​of avg and std in the equation are used to determine the presence of coarse segregated particles in the bed, and if present, to predict the segregation rate of these particles. Where L... temp This indicates the number of layers in the particle bed along the vertical direction, while L seg This indicates the layer number (layers 0 to 4, 5 layers in total) of interest in the particle segregation behavior analysis. T represents the number of time step blocks, and H and W are the number of voxel grids along the X and Y axes of the container, respectively. obj determines the presence of coarse segregated particles within the bed, while avg and std represent the average and standard deviation of the coarse particle segregation rate, respectively. CNNs3D is the segregation kinetic correlation model established in this embodiment. Furthermore, to accelerate the training and convergence process of the loss function, this embodiment designs a standardized preprocessing procedure for the statistics of the coarse particle segregation rate data, the calculation formula of which is as follows: (4) in, This represents the average segregation rate of the original coarse particles. This represents the standard deviation of the initial coarse particle segregation rate. and Each layer represents a different layer. The mean and standard deviation, and Each layer represents a different layer. The mean and standard deviation, 、 The distribution is then calculated as the standardized value (Z-score) of the ratio of the average original coarse particle segregation rate to the standard deviation of the original coarse particle segregation rate for each layer, representing the number of standard deviation units of the data point deviating from the mean. The standardized average coarse particle segregation rate / standard deviation is used as the label.

[0063] A training sample set was constructed based on the statistical characteristics of the particle temperature of fine particles in each voxel and the segregation rate of coarse particles in each segregation layer, and the neural network model was trained accordingly, including: The particle temperature of the layer, row, column, and fine particles where each voxel is located is used as the four-dimensional input data of the neural network model. The average value and standard deviation of the segregation rate of coarse particles in each segregation layer are used as labels to form the first training sample set. The neural network model is trained based on the first training sample set.

[0064] like Figure 8 As shown, a specific embodiment of the present invention employs a deep spatiotemporal residual convolutional neural network (CBR3D) as the neural network model. This CBR3D is a discrete operator that combines local receptive fields, shared weights, and spatiotemporal downsampling, effectively ensuring the stability of the spatiotemporal distribution features of the image under translation, scaling, and deformation conditions, thereby significantly improving the accuracy of the prediction model. Specifically, the three-dimensional convolutional neural network (CBR3D), as a high-performance convolution operator, can extract the spatiotemporal distribution features and targets of the input data with a simple and compact structure. CBR3D includes: Conv3d convolutional kernel, BN3D, and ReLU. The Conv3d convolutional kernel slides across three dimensions, performing convolution operations on fine particle temperature in the layer, row, and column dimensions. The Conv3d convolution results are normalized to mean and standard deviation using BN3D, and then the ReLU activation function is used to extract key data features from the normalized BN3D results. After repeating this process twice using CBR3D, three identical feature extraction combination units are input, including CBR3D, Bottleneck3D, Dropout, and Bottleneck3D. Bottleneck3D is used for detail stacking, and Dropout randomly resets the trained weight parameters to zero to avoid overfitting. After another CBR3D, the data is input into SPP3D for dimensionality reduction and concatenation. SPP3D is a feature pyramid pooling layer, whose core function is to resample feature maps of different sizes and then merge them together to continue subsequent steps. This is equivalent to considering multiple scales simultaneously, thus improving the ability to identify the spatiotemporal distribution characteristics of fine particle temperature data. The SPP3D output is connected through fully connected layers and then outputs the final result through classification and regression tasks. The classification task determines whether coarse segregated particles exist in the bed (this requires calculating two probabilities: the probability of presence and the probability of absence. If the number of segregated coarse particles is less than a certain value (40 particles in this example), the probability is considered 0; the sum of the probability of presence and the probability of absence equals 1, which is a constraint). In the regression task, avg and std represent the average and standard deviation of the predicted coarse particle segregation rate, respectively. 5×2 indicates a total of 5 segregation layers. The 2 in the classification task represents the presence and absence of particles; the 2 in the regression task represents the standardized results of the average and standard deviation of each layer.

[0065] S5. Collect the particle temperature of fine particles in each voxel in the mixed particle bed and input it into the trained neural network model to predict the statistical characteristics of the segregation rate of coarse particles in each segregation layer.

[0066] like Figure 8 As shown, this technical solution introduces a bottleneck-shaped residual block structure and sets all convolutional layer operators to 3×3×3 convolutional kernels to improve the model's ability to extract the nonlinear correlation between fine particle temperature and coarse particle segregation rate. To prevent overfitting while enhancing the model's ability to identify the spatiotemporal distribution characteristics of particle temperature data, this solution incorporates a Dropout module between the residual block structures and embeds a Spatial Pyramid Pooling (SPP) module before the detection head (predictor) at the tail of the model.

[0067] Since the spatiotemporal data of particle temperature is significantly downsampled during the three-dimensional mesh generation process, there is no need for feature fusion, context enhancement, and multi-scale perception. The deep spatiotemporal residual convolutional neural network (DSTRes-CNNs) established in this technical solution abandons the deep neck structure and only uses the convolution operators in the backbone network to extract spatiotemporal features.

[0068] Furthermore, considering the differences in the convergence process between the classification and regression tasks during training, this technical solution sets the ratio of the penalty coefficients for classification bias and regression bias in the loss function to 1:2.

[0069] Compared with existing technologies, the solid waste screening behavior identification and separation rate modeling method provided in this embodiment obtains multiple potential segregation starting points and / or potential segregation ending points during the ascent process of each coarse particle based on the transport trajectory of coarse particles in the particle bed. After filtering the multiple potential segregation starting points / potential segregation ending points of each coarse particle, the first remaining potential segregation starting point is taken as the true segregation starting point, and the last potential segregation ending point is taken as the true segregation ending point. Based on the height difference and time difference between the true segregation ending point and the true segregation starting point of each coarse particle, the segregation rate of each coarse particle and the statistical characteristics of the segregation rate of coarse particles in each segregation layer are calculated. This invention proposes a particle segregation behavior feature identification algorithm based on the potential starting and ending point identification algorithm and the true starting and ending point determination algorithm of the segregation process, realizing the noise reduction and reconstruction of the particle segregation trajectory and the accurate calculation of the particle segregation rate. Furthermore, the constructed deep spatiotemporal residual convolutional neural network improves the prediction accuracy of the particle segregation rate at different layer heights. This embodiment obtains the instantaneous velocity of each fine particle and then calculates the particle temperature of the fine particles in each voxel. A training sample set is constructed based on the particle temperature of the fine particles in each voxel and the statistical characteristics of the segregation rate of coarse particles in each segregation layer, and the neural network model is trained accordingly. The particle temperature of the fine particles in each voxel of the mixed particle bed is collected and input into the trained neural network model to predict the statistical characteristics of the segregation rate of coarse particles in each segregation layer. This quantifies the response of the coarse particle segregation rate to the particle temperature of fine particles on a macroscopic scale, significantly reducing the number of parameters required for model training.

[0070] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0071] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for solid waste screening behavior identification and separation rate modeling, characterized in that, include: Based on the migration trajectory of the segregated coarse particles, multiple potential segregation starting points and / or potential segregation ending points are obtained during the ascent of each coarse particle. After filtering out multiple potential segregation initiation points and / or potential segregation endpoints for each coarse particle, the first remaining potential segregation initiation point is taken as the true segregation initiation point, and the last potential segregation endpoint is taken as the true segregation endpoint. Based on the height difference and time difference between the actual segregation endpoint and the actual segregation start point of each coarse particle, the segregation rate of each coarse particle and the statistical characteristics of the segregation rate of coarse particles in each segregation layer are calculated. The instantaneous velocity of each fine particle is obtained, and then the particle temperature of the fine particles in each voxel is calculated. A training sample set was constructed based on the statistical characteristics of the particle temperature of fine particles in each voxel and the segregation rate of coarse particles in each segregation layer, and the neural network model was trained accordingly. The particle temperature of fine particles in each voxel in the mixed particle bed is collected and input into the trained neural network model to predict the statistical characteristics of the segregation rate of coarse particles in each segregation layer.

2. The method for identifying solid waste screening behavior and modeling separation rates according to claim 1, characterized in that, Based on the migration trajectory of the segregated coarse particles, multiple potential segregation initiation points and / or potential segregation endpoints during the ascent of each coarse particle are obtained, including: Based on the migration trajectory of segregated coarse particles, obtain adjacent convex decrease-convex increase elbow point pairs and concave increase-concave decrease knee point pairs of smooth height curves that change over time; obtain the last local minimum point of each interval in the interval where the convex decrease-convex increase elbow point pairs are located, and obtain the first local maximum point of each interval in the interval where the concave increase-concave decrease knee point pairs are located, and determine whether the local minimum point and the local maximum point are local minimum points and local maximum points. The coarse particle segregation initiation point, the convex elbow point, and the local minimum point are all considered as potential segregation initiation points; the coarse particle segregation endpoint, the concave knee point, and the local maximum point are all considered as potential segregation endpoints.

3. The method for identifying solid waste screening behavior and modeling separation rate according to claim 2, characterized in that, Determining whether the local minimum point, local maximum point, or local maximum point is a local minimum point or a local maximum point includes: determining whether the local minimum point / local maximum point is an interior point; if it is an interior point, the derivative sign or instantaneous rate is used to determine whether the point is a local minimum point / local maximum point; if it is not an interior point, it is determined that the point is not a local minimum point / local maximum point.

4. The method for identifying solid waste screening behavior and modeling separation rate according to claim 3, characterized in that, Determine whether the local minimum / local maximum point is an interior point. If it is an interior point, use the derivative sign or instantaneous rate to determine whether the point is a local minimum / local maximum point, including: If the local minimum point / local maximum point is an interior point, the sign of the instantaneous velocity and instantaneous acceleration of the local minimum point / local maximum point, as well as the change in the sign of the instantaneous velocity within the range less than the first threshold of the local minimum point / local maximum point, are used to determine whether the point is a local minimum point / local maximum point.

5. The method for identifying solid waste screening behavior and modeling separation rates according to claim 2, characterized in that, Filtering for potential segregation initiation points and potential segregation endpoints includes: The potential segregation start points and potential segregation end points are filtered based on the starting threshold height, the ending threshold height, the time interval between adjacent potential segregation start points / adjacent potential segregation end points, and the preset gradient threshold.

6. The method for identifying solid waste screening behavior and modeling separation rate according to claim 5, characterized in that, Filtering is performed based on the starting threshold height and the ending threshold height, including: The potential segregation start points and potential segregation endpoints are obtained by filtering potential segregation start points that are higher than the starting threshold height and potential segregation endpoints that are lower than the ending threshold height.

7. The method for identifying solid waste screening behavior and modeling separation rates according to claim 6, characterized in that, Filtering based on the time interval between adjacent potential segregation initiation points / adjacent potential segregation endpoints includes: If the time interval between adjacent potential separation initiation points after initial filtering is less than or equal to the first time threshold, then the latter potential separation initiation point is deleted to obtain the merged potential separation initiation points; if the time interval between adjacent potential separation endpoints after initial filtering is less than or equal to the first time threshold, then the former potential separation endpoint is deleted to obtain the merged potential separation endpoints.

8. The method for identifying solid waste screening behavior and modeling separation rate according to claim 7, characterized in that, The potential segregation start point and potential segregation end point are filtered according to a preset gradient threshold, including: The first gradient of the potential separation endpoints after merging is calculated using the backward difference method. If the first gradient is lower than a preset gradient threshold, the next potential separation endpoint used in the calculation of the first gradient by the backward difference method is filtered out; if the first gradient is higher than the preset gradient threshold, the previous potential separation endpoint used in the calculation of the first gradient by the backward difference method is filtered out. The first-order gradient is calculated using the forward difference method for the merged potential separation starting points. If the first-order gradient is lower than a preset gradient threshold, the previous potential separation starting point used in the calculation of the first-order gradient by the forward difference method is filtered out; if the first-order gradient is higher than the preset gradient threshold, the next potential separation starting point used in the calculation of the first-order gradient by the forward difference method is filtered out.

9. The method for identifying solid waste screening behavior and modeling separation rate according to claim 1, characterized in that, A training sample set was constructed based on the statistical characteristics of the particle temperature of fine particles in each voxel and the segregation rate of coarse particles in each segregation layer, and the neural network model was trained accordingly, including: The particle temperature of the layer, row, column, and fine particles where each voxel is located is used as the four-dimensional input data of the neural network model. The average value and standard deviation of the segregation rate of coarse particles in each segregation layer are used as labels to form the first training sample set. The neural network model is trained based on the first training sample set.

10. The method for identifying solid waste screening behavior and modeling separation rates according to claim 1, characterized in that, The formula for calculating the particle temperature of fine particles in each voxel is: ， Where k is the voxel unit number, and j is the fine particle number within voxel unit k. This represents the number of fine particles contained in the voxel unit with serial number k. Let j be the instantaneous velocity vector of the fine particle numbered j in voxel unit k; Let be the average velocity vector of all fine particles in voxel unit k.

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