A method for calibrating parameters of discrete elements of non-spherical particles

Abstract

This invention relates to a method for calibrating discrete element parameters of non-spherical particles, comprising the following steps: Step 1, obtaining the basic physical and mechanical parameters of the non-spherical particles; Step 2, obtaining the contact characteristic parameters; Step 3, obtaining the DEM model of the non-spherical particle with the optimal number of facets and the basic model for simulation testing of the angle of repose; Step 4, obtaining the parameters that significantly affect the angle of repose, their optimal value ranges, and CCD experimental data; Step 5, obtaining the optimal combination of contact parameters and a high-precision discrete element simulation model of the non-spherical particles; Step 6, verifying the correctness of the discrete element parameter calibration. This invention calibrates discrete element parameters through a combination of experimental and discrete element simulation methods. The Plackett-Burman Design and the steepest climb test are used to screen parameters that affect the angle of repose and determine their optimal value ranges. Using the angle of repose as the response value, the central combinatorial design experiment and machine learning regression model algorithm are applied to optimize the significant parameters to obtain the optimal combination of significant parameters.

Description

Technical Field

[0001] This invention relates to the field of agricultural planting, and specifically to a method for calibrating discrete element parameters of non-spherical particles. Background Technology

[0002] Cassava is an upright shrub-like crop with woody stems reaching 2-5 meters in height. Its tuberous roots are rich in fiber and starch. Cassava is propagated by stem cuttings, where stems are cut into 13-17 cm long cuttings and planted horizontally or vertically after trenching. Cassava has advantages such as low planting costs and high yields. The tubers, stems, and leaves are all usable, not only for consumption but also for processing into starch, alcohol, and various organic chemicals, finding wide applications in the food and light industries. In 2024, my country's cassava planting area exceeded 667,000 hectares, with an annual fresh cassava production of over 20 million tons. Through the promotion of improved varieties and expansion of planting area, cassava production potential continues to increase. However, the low level of mechanization in precision planting and efficient harvesting hinders the industry's development. Currently, my country's cassava production cannot meet domestic demand, making it a major cassava importer. Therefore, developing the cassava industry is significant for ensuring national food security and alleviating the energy supply and demand imbalance. Precision planting is a crucial step in cassava production, but traditional research methods face significant challenges in elucidating the mechanisms of precision planting and seed stalk collision damage. Employing numerical simulation technology to conduct microscopic studies of the precision planting mechanism and seed stalk collision damage mechanism in cassava can provide a theoretical basis for optimizing the key structures and operating parameters of cassava planters.

[0003] The Discrete Element Method (DEM) is a computer simulation method based on the assumption of discontinuity. It is also an important tool for analyzing particle fracture phenomena, capable of simulating the fracture process of particles of different materials and scales in working equipment. It is widely used in research on straw, fertilizer, and cottonseed. Li Yanjie et al. simplified corn straw into a fractureable flexible fiber model composed of multiple segments of spherical cylindrical units connected by nodal spheres, and calibrated the model's elasticity ratio, plasticity ratio, bending limit angle, and failure ratio using the steepest slope test design method. Du Zhe et al., using tea stems as the object, proposed a three-layer DEM model based on the bonding reinforcement method, and constructed tensile and puncture models using calibrated parameters to conduct corresponding simulation experiments. Analysis shows that the contact parameters of different materials differ significantly, and there are still few reports on the collision damage mechanism of cassava seed stems based on the DEM. Furthermore, research on agricultural material fracture mainly uses bonding contact models, whose sub-particles are usually spherical particle aggregates, which differ significantly from the actual material morphology. In contrast, the Tavares model, as a particle replacement model, is widely used in the field of particle collision damage. When simulating particle collision damage, its sub-particles are polyhedral in shape, which can more accurately represent particle damage behavior and is widely used in the study of the motion mechanism of multi-scale cohesive particle models. Given the advantages of the Tavares model in representing the collision damage of non-spherical particles, it is also suitable for simulating the damage phenomenon of non-spherical seed stalks during operation, providing a more effective tool for analyzing the collision damage mechanism of agricultural materials. To ensure the accuracy of discrete element parameter calibration, establishing an accurate material discrete element model is crucial. Current material discrete element modeling typically simplifies real particles into simple geometries, obtaining particle outlines through 3D scanning technology and then filling in the particles to complete the modeling. Seed stalks are non-spherical with a complex structure (composed of phloem, epidermis, xylem, and pith), and the buds are randomly distributed, resulting in complex shapes that are difficult to simplify into simple geometries. Using a particle-filling method to construct the model leads to excessively long simulation times. Considering the shape of the seed stalk, treating it as a model with protruding buds allows for a more accurate representation of its morphology. Because non-spherical particle models differ significantly in geometry from traditional particle aggregation models, it is necessary to recalibrate the contact parameters between seed and stem in discrete element simulations. In the calibration of discrete element parameters for materials such as straw and fertilizer, response surface methodology (RSM) is commonly used to optimize significant parameters. Furthermore, machine learning (ML), as an emerging nonlinear regression modeling method, demonstrates excellent predictive performance in data prediction and optimization.The BP neural network model optimized by the genetic algorithm (GA-BP) can avoid the drawback of response surface methodology being prone to getting trapped in local optima, and is more conducive to achieving the goal of globally optimal parameter combination design, thus obtaining higher fitting accuracy. However, this method has not yet been reported in the study of parameter calibration for discrete element simulation of cassava seed stems. Summary of the Invention

[0004] In summary, to overcome the shortcomings of existing technologies, the technical problem this invention aims to solve is to provide a method for calibrating discrete element method (DEM) parameters for non-spherical particles. Addressing the limitation of DEM simulation in studies of cassava precision planting mechanisms and seed stem collision damage mechanisms due to the lack of accurate parameters, this invention uses the seed stem of 'Gui Re 7' cassava as the research object and calibrates the DEM parameters through a combination of physical experiments and DEM simulation. Using 3D scanning technology combined with SolidWorks 2023 modeling capabilities, a seed stem model is constructed in EDEM software to investigate the impact of the number of facets on simulation accuracy. The experiment measured the average angle of repose of the seed stalks (30.28°±1.09°), as well as parameters such as the seed-stalk collision recovery coefficient, the seed-steel plate collision recovery coefficient, and the seed-steel plate static friction coefficient. Plackett-Burman Design experiments were used to screen parameters affecting the angle of repose, and their optimal value range was determined through steepest slope tests. Using the angle of repose as the response value, a central composite design experimental method combined with a machine learning regression model algorithm was applied to optimize the influencing parameters and compare model performance. The study shows that the GA-BP algorithm has better predictive ability than Support Vector Machine (SVR) and Backpropagation Neural Network (BP neural network). The genetic algorithm (GA) was used to optimize and obtain a seed-steel plate static friction coefficient of 0.488, a seed-stalk static friction coefficient of 0.489, and a seed-stalk rolling friction coefficient of 0.131. The simulated angle of repose was 30.73°, with a relative error of 1.47% compared to the actual angle of repose. The optimization effect of the GA-BP-GA method is better than that of the central composite design experimental method, verifying the accuracy of the seed-stalk contact parameter calibration. The parameters of the Tavares model were calibrated through physical experiments on the seed stems, and the calibration was performed using collision damage force and collision damage energy as indicators. The results showed that the relative errors of both collision damage force and collision damage energy were less than 3%, which is within the allowable error range, confirming the correctness of the discrete element parameter calibration of the seed stems.

[0005] The technical solution of this invention to solve the above-mentioned technical problems is as follows: A method for calibrating discrete element parameters of non-spherical particles, comprising the following steps:

[0006] Step 1: By measuring the intrinsic parameters of the non-spherical granular seed stem, the basic physical and mechanical parameters of the non-spherical granular seed stem are obtained;

[0007] Step 2: Conduct physical experiments based on the same batch of non-spherical granular seed stem samples used in Step 1, measure the angle of accumulation, and simultaneously determine the contact characteristic parameters required for discrete element simulation.

[0008] Step 3: Based on the intrinsic parameters and contact parameters obtained in Steps 1 and 2, construct a generalized discrete element model of non-spherical granular seed stems, and at the same time build a simulation test model of the angle of repose.

[0009] Step 4: Based on the simulation test model of non-spherical particle packing angle obtained in Step 3, and combined with the intrinsic parameters and contact parameter value ranges in Steps 1 and 2, parameter screening and optimal range determination are completed through generalized experiments, while CCD test data are obtained.

[0010] Step 5: Based on the CCD test data obtained in Step 4, using the packing angle as the response value, perform generalized machine learning modeling and genetic algorithm optimization, determine the optimal method after comparison, obtain the optimal combination of contact parameters, and construct a high-precision discrete element simulation model for non-spherical particles.

[0011] Step 6: Based on the high-precision discrete element simulation model of non-spherical particles obtained in Step 5, and combined with the Tavares model, conduct generalized collision damage parameter calibration and dual verification experiments to fully verify the correctness of the overall parameter calibration.

[0012] In some possible implementations, step 1 specifically involves:

[0013] Step 1.1: Select the target non-spherical particle test material, process it into test samples that are free from pests and diseases and have uniform specifications, and measure the basic physical properties of the samples;

[0014] Step 1.2: The particle density is determined using the water displacement method. This is done by placing the test sample and weights together in a graduated cylinder and then using the formula... The density range was obtained through repeated experiments, among which For the quality of the test samples, The total volume of the sample, weights, and water. The volume of the weight;

[0015] Step 1.3: Perform a compression test using a multi-functional texture analyzer, and first calculate Poisson's ratio using the formula. Where ε1 is the strain perpendicular to the load direction, ε2 is the strain in the direction of applied load, L1 is the transverse dimension before compression, L2 is the transverse dimension after compression, and H1 is the axial dimension before compression; then, using the formula... Calculate the shear modulus, where F is the maximum force that the test sample can withstand during the elastic deformation stage, L is the initial length of the test sample, S is the cross-sectional area of ​​the test sample, and ΔL is the length difference of the sample before and after compression.

[0016] In some possible implementations, step 2 specifically involves:

[0017] Step 2.1, Angle of repose determination: Using the sidewall collapse method, the quantitative test sample is placed into a steel plate measuring device. After the baffle is removed, the angle of repose is measured by image processing. The average value is obtained by repeating the test multiple times.

[0018] Step 2.2, Static Friction Coefficient Determination: Using an inclined plane apparatus, the static friction coefficient is determined using the formula... The static friction coefficients between particles and the contact medium, and between particles, were measured respectively, where f s α is the static friction coefficient, and α is the critical angle for the static friction coefficient; the range of the coefficient was obtained through repeated experiments.

[0019] Step 2.3, Rolling Friction Coefficient Determination: Based on the force analysis of the inclined plane apparatus, the rolling friction coefficients between particles and the contact medium, and between particles, are determined using the following set of formulas:

[0020] ,

[0021] ,

[0022] ,

[0023] ;

[0024] in For rolling friction torque, The coefficient of rolling friction is To provide support for the seed stem at an angle, For the weight of the seed stem, The critical angle of rolling friction of the seed stem. The radius of the seed stem; the range of coefficients was obtained through repeated experiments;

[0025] Step 2.4, Collision Recovery Coefficient Determination: By observing the free fall of the material and capturing the rebound trajectory using high-speed video recording, the velocity before the collision is first obtained using the free fall formula. Then, through two tests with different receiving tray heights, the horizontal component velocity was derived. and vertical component velocity Ultimately, it is determined by the formula. The collision recovery coefficients between particles and between particles and the contact medium were determined. The collision recovery coefficient is... The normal separation velocity after the collision. The normal velocity before the collision, The angle of inclination of the collision plate; the coefficient range was obtained through repeated experiments.

[0026] In some possible implementations, step 3 specifically involves:

[0027] Step 3.1, Construction of non-spherical particle model: Obtain target particle point cloud data through 3D scanning, process it and import it into SolidWorks for mesh modeling;

[0028] Step 3.2, Optimal facet number selection: Set multiple gradient facet numbers, explore the impact of facet number on volume relative error and simulation time, and finally select the optimal facet number model that balances simulation accuracy and efficiency, and export the STL format file to EDEM software;

[0029] Step 3.3, Building the Angle of Accumulation Simulation Model: Construct an angle of accumulation measuring device in EDEM that is consistent with the physical test size in Step 2, statically generate quantitative test samples, simulate the accumulation process after the baffle is removed, and extract the simulated angle of accumulation using the same image processing method as the physical test to obtain a basic model for angle of accumulation simulation test that can be used for subsequent parameter tests.

[0030] In some possible implementations, step 4 specifically involves:

[0031] Step 4.1, Plackett-Burman Design Experiment: Using particle density (X1), Poisson's ratio (X2), and shear modulus (X3) as factors, and the angle of repose as the response value, an experiment was designed using Design-Expert software. Through analysis of variance and factor effect t-tests, parameters with significant influence on the angle of repose were selected, and a first-order fitting model was obtained.

[0032]

[0033] Where X4 is the collision recovery coefficient between seed stalks, X5 is the minimum collision recovery coefficient between seed stalk and steel plate, X6 is the static friction coefficient between seed stalk and steel plate, X7 is the static friction coefficient between seed stalks, X8 is the rolling friction coefficient between seed stalk and steel plate, and X9 is the rolling friction coefficient between seed stalks.

[0034] Step 4.2, Steepest Slope Test: Divide the range of values ​​for the selected significant parameters into equal parts, and take the middle level for the non-significant parameters, using the relative error between the simulation and the measured angle of repose in Step 2. To achieve this goal, simulation experiments were conducted on the basic simulation test model in step 3 to determine the optimal range of parameter values. This is a relative error. To determine the angle of accumulation of seed stems, To simulate and determine the angle of accumulation of seed stems;

[0035] Step 4.3, CCD Experiment: Using the optimal value range determined by the steepest slope test as the upper and lower limits, CCD experimental design is carried out for significant parameters. Full-scale simulation experiments are conducted in the simulation test basic model of Step 3. The parameter combination and corresponding repose angle simulation results of each group of experiments are recorded to obtain CCD experimental data. At the same time, the experimental data are analyzed using Design-Expert software to obtain a quadratic regression model. After eliminating insignificant factors, the model is optimized to determine the interaction law of significant parameters.

[0036] In some possible implementations, step 5 specifically involves:

[0037] Step 5.1, Construction of three types of machine learning models: In MATLAB, using the significant parameters selected in Step 4 as the input layer and the stacking angle as the output layer, support vector machine (SVR), backpropagation (BP) neural network, and GA-BP neural network models are constructed based on the CCD experimental data from Step 4.

[0038] Support Vector Machine (SVR): Set to epsilon-SVR regression, loss function 0.05, gamma function value 0.2, and fit CCD experimental data through hyperplane fitting;

[0039] Backpropagation Neural Network: The number of hidden layer nodes is determined through trial and error. Confirmed, among which and The number of neurons in the input and output layers. The constant is 1 to 11. The value range is 3~13; the transfer function is a sigmoid function and a linear function; the training target error is 0.0001; the learning rate is 0.005; and the model training is completed based on CCD experimental data.

[0040] GA-BP Neural Network: First, optimize the initial weights of the BP neural network using GA. / and threshold / The evolutionary iterations were performed 200 times, the population size was 150, the crossover coefficient was 0.9, and the mutation coefficient was 0.1. The optimized weights / thresholds were then assigned to the backpropagation algorithm for training, and the training was completed based on experimental data designed with the center combination.

[0041] Step 5.2, Model Performance Comparison: Using the coefficient of determination The mean square error (MSE) and mean absolute deviation (AAD) were used to evaluate the fitting and prediction capabilities of the three types of models for CCD experimental data, and the GA-BP model with the best performance was determined.

[0042] Step 5.3, GA-BP-GA optimization: The training objective error between the predicted and actual stacking angle values ​​obtained from the best-performing GA-BP model is used as the fitness function of GA. The measured stacking angle in Step 2 is used as the optimization objective. Global optimization is performed on the significant parameters selected in Step 4. The evolutionary iteration is 150 times, the population size is 200, the crossover coefficient is 0.9, and the mutation coefficient is 0.1 to obtain the optimal combination of contact parameters.

[0043] Step 5.4, Method Comparison and High-Precision Model Construction: The GA-BP-GA method is compared with the CCD response surface method to verify that the GA-BP-GA method has a better optimization effect; the optimal combination of contact parameters is substituted into the discrete element model in step 3 to obtain a high-precision discrete element simulation model for non-spherical particles.

[0044] In some possible implementations, step 6 specifically involves:

[0045] Step 6.1, Angle of Accumulation Verification: Directly use the angle of accumulation simulation results of the high-precision discrete element simulation model in Step 5, and compare the simulation with the measured angle of accumulation values ​​and sample accumulation contours in Step 2 to verify the accuracy of the contact parameters;

[0046] Step 6.2, Tavares model parameter derivation: Based on the particle collision damage principle, determine:

[0047] Relationship between impact damage energy and normal / tangential energy: ;in , For normal energy and tangential energy, The tangential energy coefficient;

[0048] Collision damage energy distribution formula: , ;in Let be the error function. This represents the median collision damage energy. The standard deviation of collision damage energy. This is the upper limit cutoff value of the distribution;

[0049] Damage energy median formula: ;in The limiting impact damage energy at the maximum particle size. This represents the median particle size. The parameters that can be fitted to the collision damage are... For particle size, For particle stiffness, It is the collision stiffness;

[0050] Step 6.3, Tavares model parameter calibration: Select multiple groups of target particle test samples with different particle sizes / specifications. For each group, quantitatively select samples with intact surfaces. Conduct compression tests using a universal testing machine to obtain pressure-displacement curves. Then, use the formula... Calculate the specific energy of the collision damage, where For the impact damage force of the seed stem, The depth of the seed stem damage. The depth of the severely damaged point on the seed stem. To determine the seed stem quality, the median damage energy for each sample size was obtained through fitting. and standard deviation Substitute the damage parameters obtained from the physical experiment into the Tavares model framework in step 6.3, and combine and adapt them with the high-precision discrete element simulation model in step 5 to complete the full parameter calibration of the Tavares model.

[0051] Step 6.4, Collision Damage Verification: Using collision damage force and collision damage energy as the core indicators, conduct collision damage simulation experiments in the Tavares model after parameter calibration and integration with the high-precision model. Compare the simulated values ​​with the measured values ​​from physical experiments to verify whether the error is within the allowable range. At the same time, plot the curve of collision damage force as a function of damage depth to verify the consistency between the simulation and experimental patterns.

[0052] The beneficial effects of this invention are as follows: Discrete element parameters are calibrated through a combination of experiments and discrete element simulations. Plackett-Burman Design and steepest climb tests are used to screen parameters influencing the angle of repose and determine their optimal value range. Using the angle of repose as the response value, central combinatorial design experiments and machine learning regression model algorithms (Support Vector Machine (SVR), Backpropagation Neural Network (BP) and GA-BP algorithm) are applied to optimize the significance parameters, obtaining the optimal combination of significance parameters. Furthermore, based on the optimal combination of significance parameters and the Tavares model, seedling simulation experiments are conducted, and the experimental and simulated values ​​of seedling collision damage force and collision damage energy are compared to verify the correctness of the calibrated parameters. Attached Figure Description

[0053] Figure 1 A force analysis diagram of cassava seed stalks on a rolling friction coefficient measuring device;

[0054] Figure 2 Schematic diagram of the principle of measuring the collision recovery coefficient of cassava seed stems;

[0055] Figure 3 This is a schematic diagram of the Tavares model.

[0056] Figure 4 Models of cassava seed stems with different fractal surface numbers;

[0057] Figure 5 The relative volume error and simulation time of cassava seed stem models with different fractal surface numbers;

[0058] Figure 6 The process of simulating the angle of packing of cassava seed stems;

[0059] Figure 7 Pareto chart;

[0060] Figure 8 The influence of interactive factors on the angle of packing;

[0061] Figure 9 The topology of the GA-BP model;

[0062] Figure 10 For performance curves;

[0063] Figure 11 The results are from the regression analysis;

[0064] Figure 12 The predicted and measured values ​​are obtained using the response surface methodology and the GA-BP-GA optimization method.

[0065] Figure 13 The fitness change curve;

[0066] Figure 14 Comparison of the experimental angle of packing of cassava seed stems and the simulated angle of packing;

[0067] Figure 15 The collision damage probability-seed stalk collision damage specific energy curve;

[0068] Figure 16 The variation of impact damage force of cassava seed stem with the depth of seed stem damage is shown. Detailed Implementation

[0069] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0070] 1. Materials and Methods

[0071] 1.1 Test Materials and Measurement of Intrinsic Parameters

[0072] In this embodiment, the experimental material used was cassava seed stems of the "Gui Re 7" variety, sourced from the cassava planting base in Ziyuan County, Guilin City, Guangxi, China. Sampling was conducted in early June 2025. The seed stems were free from pests and diseases, straight without bending, and without significant mechanical damage. They were cut into 150 mm long segments (including the seed bud). After multiple measurements, the average diameter of the seed stems was 30 mm, and the average moisture content was 62.73%. The seed stem density was determined using the water displacement method. [The last sentence appears to be incomplete and possibly refers to a different material.] The seed stem was placed in a 250 mL graduated cylinder. To prevent it from floating after adding water, a 150 g weight was fixed to the seed stem. 125 mL of water was added to the graduated cylinder, and the total volume was measured. The volume of the weights was determined using the same method. The seed tuber density is as follows:

[0073]

[0074] The seed tuber density was determined to be 693–747 kg / m² through 10 repeated experiments. 3 between.

[0075] Compression tests were conducted using an ENS-DVU multifunctional texture analyzer to determine the Poisson's ratio μ and shear modulus K of the seed stalk. The Poisson's ratio was calculated as follows:

[0076]

[0077] In the formula, ε1 is the strain perpendicular to the load direction; ε2 is the strain in the direction of the applied load; L1 is the transverse dimension before compression, m; L2 is the transverse dimension after compression, m; H1 is the axial dimension before compression, m; H2 is the axial dimension after compression, m.

[0078] After obtaining Poisson's ratio, calculate the shear modulus:

[0079]

[0080] In the formula, F is the maximum bearing capacity of the test specimen during the elastic deformation stage, in N; L is the initial length of the test specimen, in m; and S is the cross-sectional area of ​​the test specimen, in m². 2 ΔL represents the length difference of the sample before and after compression, in meters.

[0081] Through 10 repeated experiments, the Poisson's ratio of cassava seed stems was measured to be in the range of 0.37 to 0.45, and the shear modulus was measured to be in the range of 16.40 to 17.60 MPa.

[0082] 1.2 Physical Test Methods

[0083] 1.2.1 Measurement of the angle of embrittlement of cassava seed stems

[0084] The angle of accumulation of seed stalks was measured using the sidewall collapse method. The sidewalls and intermediate baffles of the device were made of steel plates, and the baffles could move freely vertically under external force. 250 seed stalk segments were placed between the sidewalls and the baffles of the measuring device. After the seed stalks came to rest, the baffles were pulled upwards, causing the seed stalks to flow towards the unobstructed side. After the flow stopped, the angle of the slope formed by the accumulated seed stalks was measured. Since using a protractor to measure the angle of accumulation had a large error, an image processing method was used to measure the angle of accumulation. The experiment was repeated 10 times, and the average angle of accumulation was 30.28° with a coefficient of variation of 3.61%. The simulated angle of accumulation measurement was consistent with the physical experimental method.

[0085] 1.2.2 Static friction coefficient of cassava seed stem

[0086] The static friction coefficient is the ratio of the maximum static friction force to the normal pressure between the contact surfaces. The static friction coefficients between seed stems and between seed stems and steel plates are measured using an inclinometer. To measure the static friction coefficient between seed stems and steel plates, the steel plate is fixed to the measuring plane of the inclinometer with a nut. The seed stem is placed on the steel plate along the length of the measuring plane. The measuring plane is slowly rotated clockwise. When the seed stem just begins to slide on the steel plate, the rotation is stopped, and the inclination angle of the measuring plane is measured using a protractor. The static friction coefficient between the seed stem and the steel plate is calculated using equation (4). When measuring the static friction coefficient between seed stems, the steel plate can be replaced with a uniformly arranged row of seed stems.

[0087]

[0088] In the formula f s α is the static friction coefficient; α is the critical angle for the static friction coefficient. o ).

[0089] The static friction coefficient test was repeated 10 times, and the static friction coefficient between the seed stalk and the steel plate was found to be between 0.39 and 0.63. Similarly, the static friction coefficient between seed stalks was measured to be between 0.42 and 0.66.

[0090] 1.2.3 Cassava seed stem rolling friction coefficient

[0091] The coefficient of rolling friction refers to the resistance to rolling caused by deformation at the contact surface when one object rolls without slipping or has a tendency to roll on the surface of another object. Place the seed stem radially along the length of the measuring plane on a steel plate, and slowly rotate the measuring plane clockwise. Observe the seed stem just as it begins to roll purely on the steel plate, then stop rotating. Use a protractor to measure the angle of inclination of the measuring plane at this moment. The force exerted on the seed stem by the measuring device is as follows: Figure 1 During the rolling of the seed stalk, the rolling friction torque experienced on the inclined plane is proportional to the supporting force exerted by the inclined plane on it. When the inclined plane tilts to a certain degree, the seed stalk tends to roll.

[0092] Measure the coefficient of rolling friction between seed stalks, and replace the steel plate with a uniformly arranged row of seed stalks.

[0093]

[0094] In the formula, M is the rolling friction torque, N·m; f is the rolling friction coefficient; F N The force exerted by the inclined plane on the seed stalk is N; G is the weight of the seed stalk, N; α1 is the critical angle of rolling friction of the seed stalk, ( o ); r is the radius of the seed stem, in meters.

[0095] The rolling friction coefficient test was repeated 10 times, and the rolling friction coefficient between the seed stalk and the steel plate was measured to be between 0.13 and 0.25. Similarly, the rolling friction coefficient between seed stalks was measured to be between 0.09 and 0.17.

[0096] 1.2.4 Collision Recovery Coefficient

[0097] The coefficient of restitution is a parameter that measures an object's ability to recover its original shape after deformation. It is the ratio of the instantaneous normal separation velocity at the point of contact at the end of a collision to the normal approach velocity before the collision. The measurement principle is as follows: Figure 2 During the experiment, the seed stalks were dropped from the discharge port at a height H of the collision plate, undergoing free fall and colliding with the collision plate below. The tilt angle of the collision plate was adjustable, and air resistance was ignored. During this process, the seed stalks were only subject to gravity. According to the principles of kinematics, the instantaneous velocity of the seed stalks before contact and collision with the collision plate was:

[0098]

[0099] In the formula, v0 is the velocity of the seed stalk before the collision, m / s; t is the free fall time of the seed stalk, s.

[0100] From equation (9), we can see that the instantaneous velocity v0 of the seed stalk before the collision at point O on the collision plate is:

[0101]

[0102] Assume the trajectory of the seed stem after the collision with the impact plate is projectile motion, i.e., its horizontal velocity component is v. x Uniform linear motion, with a vertical velocity component v. y Given uniformly accelerated linear motion, the trajectory of the rebounding stem is a parabola. According to the principle of projectile motion, we can deduce:

[0103]

[0104] In the formula, t1 is the time of the seed stem's rebound motion, s; s is the horizontal displacement of the seed stem, m; and h is the height of the seed stem's free fall after the collision, m.

[0105] The time t from the seed stalk falling freely from the discharge port to the collision with the impact plate is difficult to measure, making it challenging to determine the horizontal velocity component v after the rebound. x and vertical component of velocity v y The height of the receiving tray was adjusted, and two experiments were conducted. A high-speed camera was used to film the rebound trajectories of the cassava seed stalks under two different receiving tray heights. The horizontal displacements s1 and s2 and the vertical displacements h1 and h2 were measured, yielding the horizontal velocity component v of the seed stalks. x The vertical component of velocity v y The calculation formula is:

[0106]

[0107] According to the definition of the collision restitution coefficient, we can obtain:

[0108]

[0109] In the formula, e is the collision recovery coefficient; v n v is the normal separation velocity after the collision, in m / s; 0n θ is the normal velocity before the collision, m / s; θ is the tilt angle of the collision plate, ( o ).

[0110] After 10 repeated experiments, the coefficient of restitution for seed-to-seed-to-steel collision was measured to be between 0.3 and 0.5, and the coefficient of restitution for seed-to-steel-plate collision was between 0.3 and 0.6.

[0111] 1.3 Establishment of Discrete Element Model for Cassava Seed Stems

[0112] 1.3.1 Tavares Model Theory

[0113] like Figure 3 As shown, the Tavares model describes the material damage principle through particle collision processes. The particle collision damage condition depends on the intrinsic properties of the material and the forces exerted on it by the geometry and surrounding materials. The relationship between collision damage energy and normal energy and tangential energy is as follows:

[0114]

[0115] In the formula , For normal energy and tangential energy, ; is the tangential energy coefficient.

[0116] Furthermore, each particle possesses a unique collision damage energy, which is calibrated according to the particle size. for:

[0117]

[0118] In the formula Let be the error function. This represents the median collision damage energy. ; The standard deviation of collision damage energy. This is the upper limit cutoff value of the distribution. .

[0119] Median particle collision damage energy as follows:

[0120]

[0121] In the formula The limiting impact damage energy at the maximum particle size. ; is the median particle size, in meters; The parameters that can be fitted to the collision damage are... Particle size, in meters (m); Particle stiffness, GPa; It is the collision stiffness, GPa.

[0122] 1.3.2 Establishment of Discrete Element Model for Cassava Seed Stems

[0123] Considering the actual shape of the seed stem, simplifying it into a non-spherical granule composed of multiple triangular planes better reflects its characteristics. For example... Figure 4 A seed stem outline model was obtained using 3D scanning technology. The number of facets in the model was then reduced using software to construct a discrete element model (DEM) of the seed stem. The steps are as follows: 1) Scan the seed stem outline using a scanner to obtain point cloud data. 2) Process the point cloud data to obtain the seed stem outline model. 3) Import the seed stem outline model into SolidWorks 2023 software and use the mesh modeling function to reduce the number of facets in the seed stem model, exporting an STL format model file. The model was imported into EDEM for preliminary testing, and it was found that the DEM models of the seed stem with different numbers of facets showed differences in volume and simulation time. Figure 5 The number of facets in the model was set to 7922, 10192, 13870, 15790, 17678, 19889, 22164, 24448, and 27158 to investigate the impact of the number of facets on the model's accuracy and improve simulation efficiency while ensuring model accuracy. The seed stem model was imported into EDEM, and a preliminary experiment on the angle of packing was conducted using parameters from the literature. The results were then imported into Origin software to generate images. As the number of facets in the seed stem model increased, the relative volume error decreased; however, the simulation time increased with the increase in the number of facets. Considering all factors, this study selected a seed stem discrete element model with 15790 facets for simulation.

[0124] 1.3.3 Establishment of Simulation Model for Cassava Stem Accumulation Angle

[0125] Based on the discrete element model of cassava seed stems, a packing angle measuring device with the same structure and dimensions as the experimental setup was established. This device was saved as an STP file and imported into EDEM. 250 segments of cassava seed stems were statically generated. After the seed stems were stably packed, a baffle was moved to form a packing angle. The packing angle simulation device formed the packing angle as shown in the image. Figure 6 As shown.

[0126] 1.4 Experimental Design and Methods

[0127] 1.4.1 Response Surface Methodology

[0128] (1) Plackett-Burman Design experiments were conducted using Design-Expert software to screen intrinsic parameters of the seed stalk (density X1, Poisson's ratio X2, shear modulus X3) and contact parameters (seed stalk-to-seed stalk collision recovery coefficient X4, seed stalk-to-steel plate collision recovery coefficient X5, seed stalk-to-steel plate static friction coefficient X6, seed stalk-to-seed stalk static friction coefficient X7, seed stalk-to-steel plate rolling friction coefficient X8, and seed stalk-to-seed stalk rolling friction coefficient X9), prioritizing parameters that significantly affect the angle of repose. The required calibration parameter values ​​were obtained through experiments and relevant references, as shown in Table 1.

[0129] Table 1 PBD Factor Coding

[0130]

[0131] (2) The steepest climb test can quickly determine the optimal value range of factors. The Plackett-Burman Design test was used to screen the significant influencing factors (the static friction coefficient between the seed stalk and the steel plate X6, the static friction coefficient between the seed stalk and the seed stalk X7, and the rolling friction coefficient between the seed stalk and the seed stalk X9). The corresponding horizontal intervals were divided into 6 equal parts. The non-significant parameters were selected at the middle level, and the angle of repose was simulated. The upper and lower limits of the central composite response surface test were determined with the goal of minimizing the relative error.

[0132]

[0133] In the formula The relative error is %; To determine the angle of accumulation of the seed stalk (°); To simulate and determine the seed stalk accumulation angle (°).

[0134] Based on the results of the steepest climb test, a central composite response surface methodology was used to conduct a response surface experiment to determine the optimal parameters. The range of the steepest climb test results was used as the upper and lower limits for the response surface experiment. The intermediate level was selected for non-significant parameters. The codes for significant parameters and simulation factors are shown in Table 2.

[0135] Table 2 CCD Factor Codes

[0136]

[0137] 1.4.2 Machine Learning Regression Fitting Modeling

[0138] Using the same data as the response surface methodology, MATLAB was employed to perform regression fitting modeling using support vector machine (SVR), backpropagation neural network (BP) and GA-BP algorithm, in order to find the optimal regression fitting algorithm.

[0139] 1) Support Vector Machine (SVR): This method finds a regression hyperplane that minimizes the distance to all data points in a given set. Let the sample set be (x1, y1), (x2, y2), ..., (x...). i y i x∈R n Let y ∈ R, where R represents the set of real numbers. If y is replaced by a function f(x) of x, then y and x in the sample set can be represented by the following equation:

[0140]

[0141] In the formula and represents the coefficients of the hyperplane.

[0142] If the original data fits well with the support vector machine regression, then:

[0143]

[0144] In the formula Let be any positive number.

[0145] However, real-world data often fails to fully satisfy the above strict constraints, hence the introduction of slack variables. , At the same time, a penalty parameter is introduced. Balancing model complexity and fitting error, the optimized form is obtained:

[0146]

[0147] By introducing Lagrange multipliers to transform equation (21), we obtain:

[0148]

[0149] In the formula and These are the Lagrange multipliers for the corresponding samples, most of which take the value of 0.

[0150] For nonlinear regression problems, kernel functions can be used. (x) iThe data (x) is mapped to a high-dimensional feature space. The regression function then becomes:

[0151]

[0152] In summary, the SVR type is set to epsilon-SVR regression, the loss function is 0.05, and the gamma function value is 0.2.

[0153] 2) The more layers a BP neural network has, the better its ability to fit the function; however, more layers can lead to overfitting, making the model difficult to converge. The transfer functions for the hidden and output layers are the sigmoid function and a linear function, respectively. The training objective error is set to 0.0001, the learning rate to 0.005, and the maximum training steps to 100. The input layer has three neurons: seed stem-stem plate static friction coefficient X6, seed stem-seed stem static friction coefficient X7, and seed stem-seed stem rolling friction coefficient X9. The stacking angle is set to the output layer. The number of nodes in the hidden layers is... The trial-and-error method needs to be used to determine this.

[0154]

[0155] In the formula and This represents the number of neurons in the input and output layers. The constant is 1 to 11; The value range is 3 to 13.

[0156] 3) GA-BP model: Before executing the BP neural network, the initial weights of the hidden and output layers are set using a genetic algorithm. , And the thresholds for hidden and output layers , Optimization. The individual population is iteratively optimized through selection, crossover, and mutation. The initial weights and thresholds obtained from the genetic algorithm optimization are assigned to the BP neural network for updating until a termination criterion is met. The number of evolutionary iterations is 200, the population size is 150, the selection function is geometric programming sorting with a selection coefficient of 0.12, a crossover coefficient of 0.9, and a mutation coefficient of 0.1.

[0157] 1.4.3 GA optimization

[0158] For unknown nonlinear functions, it is difficult to accurately find the function's extrema through the function's input and output data. Combining the nonlinear optimization capability of genetic algorithms, a neural network model is established using the genetic algorithm's fitness function. With a stacking angle of 30.28° as the optimization objective, the values ​​of the static friction coefficient X6 between the seed stalk and the steel plate, the static friction coefficient X7 between seed stalks, and the rolling friction coefficient X9 between seed stalks are optimized. The genetic algorithm is assumed to have 150 evolutionary iterations, a population size of 200, a geometric programming sorting selection coefficient of 0.08, a crossover coefficient of 0.9, and a mutation coefficient of 0.1.

[0159] 1.4.4 Data Analysis and Processing

[0160] Design-Expert was used for experimental design and processing, and the coefficient of determination was used. Mean squared error (MSE) and mean absolute deviation (AAD) are used to evaluate the predictive performance of response surface experimental and machine learning models.

[0161] 2 Results and Discussion

[0162] 2.1 PBD Test Results and Analysis

[0163] The PBD test scheme and results are shown in Table 3, and the variance analysis of parameters on the angle of repose is shown in Table 4. The results show that the static friction coefficients X6 (seed stalk-steel plate), X7 (seed stalk-seed stalk static friction coefficient), and X9 (seed stalk-seed stalk rolling friction coefficient) have significant effects on the angle of repose, while the effects of other parameters are not significant. The t-tests of the effects of each factor were performed using Design-Expert software, as shown below. Figure 7 Based on the confidence levels of the factors, significant factors were selected for further research. The t-test results showed that the order of influence of each factor on the angle of repose was: seed stem-stem plate static friction coefficient X6 > seed stem-seed stem static friction coefficient X7 > seed stem-seed stem rolling friction coefficient X9. Specifically, the p-values ​​for seed stem-seed stem static friction coefficient X7 and seed stem-seed stem rolling friction coefficient X9 were less than 0.05, indicating that these factors had a significant impact on the target. The p-value for seed stem-stem plate static friction coefficient X6 was less than 0.01, indicating that this factor had an extremely significant impact on the target. The same conclusion was also reached through the Pareto Chart t-value test. Furthermore, the seed stem-stem plate static friction coefficient X6, seed stem-seed stem static friction coefficient X7, and seed stem-seed stem rolling friction coefficient X9 significantly affected the angle of repose. The effect value is positive. The first-order model fitting each factor to the angle of packing is as follows:

[0164]

[0165] Table 3. PBD test protocol and results

[0166]

[0167] Table 4. Analysis of Variance of PBD Test Results

[0168]

[0169] Note: * indicates a significant effect (0.01≤P≤0.05), and ** indicates an extremely significant effect (P<0.01).

[0170] 2.2 Results and Analysis of the Steepest Climb Test

[0171] Based on the PBD test results, the intermediate level was selected for factors with insignificant effects on the angle of repose. The three significant parameters were determined using values ​​from the PBD test factor level table for the steepest ramp test, and the relative error between the simulated and actual angle of repose was calculated. The results are shown in Table 5. The results indicate that the simulated angle of repose continuously increases with the increase of the static friction coefficient X6 between the seed stalk and the steel plate, the static friction coefficient X7 between the seed stalks, and the rolling friction coefficient X9 between the seed stalks. The relative error of the angle of repose first decreases and then increases, with the third group of tests showing the smallest relative error. Therefore, the level near the selected level in the third group of tests (i.e., the levels selected in the second, third, and fourth groups of tests) was chosen for response surface methodology (RSM) experiments, and a RSM regression model was established.

[0172] Table 5. Test plan and results for the steepest climb.

[0173]

[0174] 2.3 Response Surface Analysis Experimental Results and Analysis

[0175] The CCD experimental design and results are shown in Table 6. The results were analyzed using Design-Expert software, yielding a quadratic regression model. Factors with insignificant effects on the quadratic regression model were eliminated. The analysis of variance for the optimized regression model is shown in Table 7, and the regression equation is as follows:

[0176]

[0177] Table 6 CCD Test Protocol and Results

[0178]

[0179] Table 7. Analysis of Variance of CCD Optimized Regression Model

[0180]

[0181] 2.4 Influence of Interaction Factors on Angle of Packing

[0182] The rolling friction coefficient between seed stalks is fixed, and the response surfaces of the static friction coefficient between seed stalks and steel plates and the static friction coefficient between seed stalks are as follows: Figure 8a. When the static friction coefficient between the seed stalk and the steel plate remains constant, the angle of repose gradually increases with the increase of the static friction coefficient between the seed stalk and the steel plate. When the static friction coefficient between the seed stalk and the steel plate remains constant, the angle of repose gradually increases with the increase of the static friction coefficient between the seed stalk and the steel plate, and both trends are significant. When the static friction coefficient between the seed stalk and the steel plate is fixed, the response surfaces of the static friction coefficient between the seed stalk and the rolling friction coefficient between the seed stalk and the steel plate are as follows: Figure 8 b. When the static friction coefficient between the seed stalk and the steel plate remains constant, the angle of repose gradually increases with the increase of the rolling friction coefficient between the seed stalk and the steel plate; when the rolling friction coefficient between the seed stalk and the steel plate remains constant, the angle of repose gradually increases with the increase of the static friction coefficient between the seed stalk and the steel plate, and the trend of change is significant. With the static friction coefficient between the seed stalk and the steel plate fixed, the response surfaces of the static friction coefficient between the seed stalk and the rolling friction coefficient between the seed stalk and the steel plate are as follows: Figure 8 c. When the static friction coefficient between seed stalks remains constant, the angle of repose gradually increases with the increase of the rolling friction coefficient between seed stalks; when the rolling friction coefficient between seed stalks remains constant, the angle of repose gradually increases with the increase of the static friction coefficient between seed stalks.

[0183] 2.5 Comparison of Machine Learning Regression Models

[0184] By comparing the determination coefficients of three regression model algorithms The mean squared error (MSE) and mean absolute deviation (AAD) were used to determine the regression model suitable for subsequent experiments. For the BP neural network model, a trial-and-error method was used to study the number of neurons in the hidden layer from 3 to 13. Due to the small number of training samples, errors occurred during regression fitting; therefore, the training was repeated 5 times. The results are shown in Table 8.

[0185] Table 8 Comparison of Machine Learning Regression Models

[0186]

[0187] Table 8 shows that the SVR and GA-BP models have more accurate predictive power than the BP neural network. SVR has the lowest coefficient of variation and the most stable fitting effect, but SVR's... The scores (0.9651), AAD (0.5867), and MSE (0.4691) are lower than those of the GA-BP network with 10 hidden neurons, which has the largest... (0.9685), minimum AAD (0.4163), and minimum MSE (0.2995), and its coefficient of variation is relatively small, indicating stable fitting effect. Therefore, 10 hidden neurons in the GA-BP model were selected as the regression model of this invention, and the topological structure of the GA-BP model was established as follows: Figure 9 As shown. Figure 10As the training cycle increases, the mean squared error (MSE) of the training, validation, and test groups is used for evaluation. A smaller MSE indicates a better accuracy in describing the experimental results. The best validation performance is achieved at step 1, with an MSE of 0.0021, indicating successful neural network training. Based on this optimization, a high-performance neural network model is further obtained. Figure 11 This indicates a good correlation between the predictions and the actual data.

[0188] 2.6 Comparison of Response Surface Methodology and GA-BP-GA Method

[0189] Figure 12 This section compares the measured and predicted values ​​of two models: the response surface methodology (RSM) model and the GA-BP-GA model. The results show that the GA-BP-GA model's evaluation metrics, AAD (0.6049) and MSE (0.6187), are superior to those of the RSM model (AAD 1.2167, MSE 2.1967), with AAD and MSE decreasing by 50.28% and 71.84%, respectively. This indicates that the GA-BP-GA model has better predictive ability and higher prediction accuracy than the RSM experimental method model.

[0190] 2.6.1 Parameter Optimization of Response Surface Method

[0191] Using Design-Expert software, with the average actual angle of packing of seed stalks (30.28°) as the target, the regression model was optimized using the Numerical module. The optimization constraints are as follows:

[0192]

[0193] To verify the obtained solutions using repose angle simulation, an optimal solution was found that closely approximates the shape of the physical experiment: the static friction coefficient X6 between the seed stalk and the steel plate is 0.492, the static friction coefficient X7 between the seed stalks is 0.469, and the rolling friction coefficient X9 between the seed stalks is 0.137. The simulated repose angle was measured to be 31.17°, with a relative error of 2.94% compared to the actual repose angle.

[0194] 2.6.2 Parameter Optimization Based on GA-BP-GA Method

[0195] Figure 13The figure shows the fitness curve as the number of generations increases. Initially, GA utilizes its population search characteristics to cause a sharp drop in the fitness of selected individuals. Subsequently, GA performs multiple crossover and selection processes, resulting in small positive changes in the fitness of selected individuals, gradually approaching the target value. Analysis shows that by the 95th iteration, the fitness curve gradually converges to 0, indicating that the difference between the predicted and target values ​​is minimal. Through multiple generations, when the number of iterations reaches the target value of 150, GA stops selecting and obtains the individual with the closest fitness. Therefore, the optimal parameter combination obtained is a seed-stem plate static friction coefficient of 0.488, a seed-seed stem static friction coefficient of 0.489, and a seed-seed stem rolling friction coefficient of 0.131. At this point, the simulated angle of packing is 30.73°, with a relative error of 1.49% compared to the actual angle of packing. The angle of packing prediction errors of both the response surface methodology and the GA-BP-GA method are less than 3%, indicating that the optimal values ​​of the three significant parameters obtained are accurate, and both methods can be used for angle of packing prediction. The prediction accuracy of GA-BP is higher than that of the response surface methodology, and the prediction error of the angle of packing after GA-BP-GA optimization is smaller than that of the response surface methodology. This indicates that the prediction results of GA-BP-GA are closer to the true values.

[0196] 3. Verification Experiment

[0197] 3.1 Angle of Concentration Test

[0198] The combination of parameters obtained from the optimization solution is verified by an angle-of-repose experiment, such as... Figure 14 As shown, the simulated and experimental seed pile contours are close, with a simulated pile angle of 30.54° and an experimental pile angle of 29.93°. The relative error between the simulated and experimental values ​​is 2.04%, indicating that the calibrated contact parameters are accurate and reliable and can be used in subsequent collision damage tests of cassava seed piles using the Tavares model.

[0199] 3.2 Tavares model collision damage test

[0200] The Tavares model allows for cassava stem impact damage testing via compression, yielding pressure-displacement curves, impact damage force, and impact damage energy. Four groups of cassava stems with average diameters of 24–27 mm, 27–30 mm, 30–33 mm, and 33–36 mm were selected for testing. Thirty intact stem segments from each group were tested using a universal testing machine to obtain their pressure-displacement curves. The results showed that 81% of the stems were damaged radially, and 19% were damaged axially. Differences in impact damage force and energy among stems of different average diameters indicate significant variations in the mechanical properties of the same material.

[0201] Based on the seed stalk pressure-displacement curve, the specific energy of seed stalk impact damage was calculated:

[0202]

[0203] In the formula The impact damage force on the seed stalk is N; The depth of the seed stem damage is in meters (m). The depth of the severely damaged point on the seed stem, in meters (m). The weight of the seed stem is in grams.

[0204] Table 9 Results of Cassava Seed Stem Collision Damage Test

[0205]

[0206] Import the data into Origin software to obtain the specific energy of seed stem collision damage in each group of experiments, and plot the collision damage probability-specific energy curve of seed stem collision damage, as shown below. Figure 15 It can be seen that the median specific energy of stem collision damage obtained from the fitting is... The standard deviation of the log-normal distribution of the probability of collision damage to seed stems The values ​​were 62.23, 80.57, 105.06, and 137.99 J / kg, and 0.34, 0.25, 0.20, and 0.18, respectively. Furthermore, the average values ​​of the impact damage force and impact damage energy were statistically analyzed and compared with the experimental results to complete the verification of the Tavares seed stalk impact damage model. A graph showing the variation of seed stalk impact damage force with seed stalk damage depth was plotted. Figure 16 a) Figure 16 Figure b shows the variation of the impact damage force of the simulated seed stalk with the depth of seed stalk damage, which is similar to the experimental situation. The average values ​​of the impact damage force and impact damage energy were statistically analyzed based on the variation of the impact damage force with the depth of seed stalk damage, as shown in Table 9. Analysis shows that the relative errors of both are less than 3%, indicating that the Tavares model calibration parameters are accurate and can well describe the impact process of the seed stalk.

[0207] 4. Conclusion

[0208] To address the limitation of discrete element method (DEM) simulation due to the lack of accurate parameters in the study of cassava precision planting mechanism and seed stem damage and fracture mechanism, this study used the seed stem of 'Gui Re 7' cassava variety as the research object and calibrated the DEM parameters of cassava seed stem by combining physical experiments with DEM simulation. The main conclusions are as follows:

[0209] (1) A non-spherical cassava seed stem model was constructed in EDEM to investigate the effect of different facet numbers on model accuracy and simulation efficiency. As the number of facets of the seed stem model increases, the volume relative error decreases. The simulation time increases with the number of facets. In this invention, a seed stem discrete element model with 15790 facets was selected for simulation.

[0210] (2) The parameters that significantly affect the angle of repose and their optimal value ranges were screened using Plackett-Burman Design and the steepest climb test. Using the angle of repose as the response value, the central composite design test was applied in combination with three machine learning regression model algorithms to optimize and compare the significantly affecting parameters. The results showed that the genetic algorithm optimization yielded a static friction coefficient of 0.488 between the seed stalk and the steel plate, a static friction coefficient of 0.489 between the seed stalk and the seed stalk, and a rolling friction coefficient of 0.131 between the seed stalk and the seed stalk. The simulated angle of repose was 30.73°, and the relative error between the simulated angle of repose and the actual angle of repose was 1.49%. The optimization effect of the GA-BP-GA method was better than that of the central composite design test method.

[0211] (3) The Tavares model parameters were calibrated by physical experiments on the seed stems. The collision damage force and collision damage energy were used as indicators for verification. The relative errors of the collision damage force and collision damage energy were both less than 3%, which was within the allowable error range, thus confirming the correctness of the calibration of the discrete element parameters of the seed stems.

[0212] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calibrating discrete element parameters of non-spherical particles, characterized in that, Includes the following steps: Step 1: By measuring the intrinsic parameters of the non-spherical granular seed stem, the basic physical and mechanical parameters of the non-spherical granular seed stem are obtained; Step 2: Conduct physical experiments based on the same batch of non-spherical granular seed stem samples used in Step 1, measure the angle of accumulation, and simultaneously determine the contact characteristic parameters required for discrete element simulation. Step 3: Based on the intrinsic parameters and contact parameters obtained in Steps 1 and 2, construct a generalized discrete element model of non-spherical granular seed stems, and at the same time build a simulation test model of the angle of repose. Step 4: Based on the simulation test model of non-spherical particle packing angle obtained in Step 3, and combined with the intrinsic parameters and contact parameter value ranges in Steps 1 and 2, parameter screening and optimal range determination are completed through generalized experiments, while CCD test data are obtained. Step 5: Based on the CCD test data obtained in Step 4, using the packing angle as the response value, perform generalized machine learning modeling and genetic algorithm optimization, determine the optimal method after comparison, obtain the optimal combination of contact parameters, and construct a high-precision discrete element simulation model for non-spherical particles. Step 6: Based on the high-precision discrete element simulation model of non-spherical particles obtained in Step 5, and combined with the Tavares model, conduct generalized collision damage parameter calibration and dual verification experiments to fully verify the correctness of the overall parameter calibration.

2. The method for calibrating discrete element parameters of non-spherical particles according to claim 1, characterized in that, Step 1 is as follows: Step 1.1: Select the target non-spherical particle test material, process it into test samples that are free from pests and diseases and have uniform specifications, and measure the basic physical properties of the samples; Step 1.2: The particle density is determined using the water displacement method. This is done by placing the test sample and weights together in a graduated cylinder and then using the formula... The density range was obtained through repeated experiments, among which For the quality of the test samples, The total volume of the sample, weights, and water. The volume of the weight; Step 1.3: Perform a compression test using a multi-functional texture analyzer, and first calculate Poisson's ratio using the formula. Where ε1 is the strain perpendicular to the load direction, ε2 is the strain in the direction of applied load, L1 is the transverse dimension before compression, L2 is the transverse dimension after compression, and H1 is the axial dimension before compression; then, using the formula... Calculate the shear modulus, where F is the maximum force that the test sample can withstand during the elastic deformation stage, L is the initial length of the test sample, S is the cross-sectional area of ​​the test sample, and ΔL is the length difference of the sample before and after compression.

3. The method for calibrating discrete element parameters of non-spherical particles according to claim 2, characterized in that, Step 2 is as follows: Step 2.1, Angle of repose determination: Using the sidewall collapse method, the quantitative test sample is placed into a steel plate measuring device. After the baffle is removed, the angle of repose is measured by image processing. The average value is obtained by repeating the test multiple times. Step 2.2, Static Friction Coefficient Determination: Using an inclined plane apparatus, the static friction coefficient is determined using the formula... The static friction coefficients between particles and the contact medium, and between particles, were measured respectively, where f s α is the static friction coefficient, and α is the critical angle for the static friction coefficient; the range of the coefficient was obtained through repeated experiments. Step 2.3, Rolling Friction Coefficient Determination: Based on the force analysis of the inclined plane apparatus, the rolling friction coefficients between particles and the contact medium, and between particles, are determined using the following set of formulas: ， ， ， ； in For rolling friction torque, The coefficient of rolling friction is To provide support for the seed stem at an angle, For the weight of the seed stem, The critical angle of rolling friction of the seed stem. The radius of the seed stem; the range of coefficients was obtained through repeated experiments; Step 2.4, Collision Recovery Coefficient Determination: By observing the free fall of the material and capturing the rebound trajectory using high-speed video recording, the velocity before the collision is first obtained using the free fall formula. Then, through two tests with different receiving tray heights, the horizontal component velocity was derived. and vertical component velocity Ultimately, it is determined by the formula. The collision recovery coefficients between particles and between particles and the contact medium were determined. The collision recovery coefficient is... The normal separation velocity after the collision. The normal velocity before the collision. The angle of inclination of the collision plate; the coefficient range was obtained through repeated experiments.

4. The method for calibrating discrete element parameters of non-spherical particles according to claim 3, characterized in that, Step 3 specifically involves: Step 3.1, Construction of non-spherical particle model: Obtain target particle point cloud data through 3D scanning, process it and import it into SolidWorks for mesh modeling; Step 3.2, Optimal facet number selection: Set multiple gradient facet numbers, explore the impact of facet number on volume relative error and simulation time, and finally select the optimal facet number model that balances simulation accuracy and efficiency, and export the STL format file to EDEM software; Step 3.3, Building the Angle of Accumulation Simulation Model: Construct an angle of accumulation measuring device in EDEM that is consistent with the physical test size in Step 2, statically generate quantitative test samples, simulate the accumulation process after the baffle is removed, and extract the simulated angle of accumulation using the same image processing method as the physical test to obtain a basic model for angle of accumulation simulation test that can be used for subsequent parameter tests.

5. The method for calibrating discrete element parameters of non-spherical particles according to claim 4, characterized in that, Step 4 specifically involves: Step 4.1, Plackett-Burman Design Experiment: Using particle density (X1), Poisson's ratio (X2), and shear modulus (X3) as factors, and the angle of repose as the response value, an experiment was designed using Design-Expert software. Through analysis of variance and factor effect t-tests, parameters with significant influence on the angle of repose were selected, and a first-order fitting model was obtained. Where X4 is the collision recovery coefficient between seed stalks, X5 is the collision recovery coefficient between seed stalks and steel plate, X6 is the static friction coefficient between seed stalks and steel plate, X7 is the static friction coefficient between seed stalks, X8 is the rolling friction coefficient between seed stalks and steel plate, and X9 is the rolling friction coefficient between seed stalks. Step 4.2, Steepest Slope Test: Divide the range of values ​​for the selected significant parameters into equal parts, and take the middle level for the non-significant parameters, using the relative error between the simulation and the measured angle of repose in Step 2. To achieve this goal, simulation experiments were conducted on the basic simulation test model in step 3 to determine the optimal range of parameter values. This is a relative error. To determine the angle of accumulation of seed stems, To simulate and determine the angle of accumulation of seed stems; Step 4.3, CCD Experiment: Using the optimal value range determined by the steepest slope test as the upper and lower limits, CCD experiment design is carried out for significant parameters. Full-scale simulation experiments are conducted in the simulation test basic model of step 3. The parameter combination and corresponding repose angle simulation results of each group of experiments are recorded to obtain CCD experiment data. At the same time, the experiment data are analyzed by Design-Expert software to obtain a quadratic regression model. After eliminating insignificant factors, the model is optimized to determine the interaction law of significant parameters.

6. The method for calibrating discrete element parameters of non-spherical particles according to claim 5, characterized in that, Step 5 specifically involves: Step 5.1, Construction of three types of machine learning models: In MATLAB, using the significant parameters selected in Step 4 as the input layer and the stacking angle as the output layer, support vector machine (SVR), backpropagation (BP) neural network, and GA-BP neural network models are constructed based on the CCD experimental data from Step 4. Support Vector Machine (SVR): Set to epsilon-SVR regression, loss function 0.05, gamma function value 0.2, and fit CCD experimental data through hyperplane fitting; Backpropagation Neural Network: The number of hidden layer nodes is determined through trial and error. Confirmed, among which and The number of neurons in the input and output layers. The constant is 1 to 11. The value range is 3~13; the transfer function is a sigmoid function and a linear function; the training target error is 0.0001; the learning rate is 0.005; and the model training is completed based on CCD experimental data. GA-BP Neural Network: First, optimize the initial weights of the BP neural network using GA. / and threshold / The evolutionary iterations were performed 200 times, the population size was 150, the crossover coefficient was 0.9, and the mutation coefficient was 0.

1. The optimized weights / thresholds were then assigned to the backpropagation algorithm for training, and the training was completed based on experimental data designed with the center combination. Step 5.2, Model Performance Comparison: Using the coefficient of determination The mean square error (MSE) and mean absolute deviation (AAD) were used to evaluate the fitting and prediction capabilities of the three types of models for CCD experimental data, and the GA-BP model with the best performance was determined. Step 5.3, GA-BP-GA optimization: The training objective error between the predicted and actual stacking angle values ​​obtained from the best-performing GA-BP model is used as the fitness function of GA. The measured stacking angle in Step 2 is used as the optimization objective. Global optimization is performed on the significant parameters selected in Step 4. The evolutionary iteration is 150 times, the population size is 200, the crossover coefficient is 0.9, and the mutation coefficient is 0.1 to obtain the optimal combination of contact parameters. Step 5.4, Method Comparison and High-Precision Model Construction: The GA-BP-GA method is compared with the CCD response surface method to verify that the GA-BP-GA method has a better optimization effect; the optimal combination of contact parameters is substituted into the discrete element model in step 3 to obtain a high-precision discrete element simulation model for non-spherical particles.

7. The method for calibrating discrete element parameters of non-spherical particles according to claim 6, characterized in that, Step 6 specifically involves: Step 6.1, Angle of Accumulation Verification: Directly use the angle of accumulation simulation results of the high-precision discrete element simulation model in Step 5, and compare them with the measured angle of accumulation values ​​and sample accumulation contours in Step 2 to verify the accuracy of the contact parameters; Step 6.2, Tavares model parameter derivation: Based on the particle collision damage principle, determine: Relationship between impact damage energy and normal / tangential energy: ;in , For normal energy and tangential energy, The tangential energy coefficient; Collision damage energy distribution formula: , ;in Let be the error function. This represents the median collision damage energy. The standard deviation of collision damage energy. This is the upper limit cutoff value of the distribution; Damage energy median formula: ;in The limiting impact damage energy at the maximum particle size. This represents the median particle size. The parameters that can be fitted to the collision damage are... For particle size, For particle stiffness, It is the collision stiffness; Step 6.3, Tavares model parameter calibration: Select multiple groups of target particle test samples with different particle sizes / specifications. For each group, quantitatively select samples with intact surfaces. Conduct compression tests using a universal testing machine to obtain pressure-displacement curves. Then, use the formula... Calculate the specific energy of the collision damage, where For the impact damage force of the seed stem, The depth of the seed stem damage. The depth of the severely damaged point on the seed stem. To determine the seed stem quality, the median damage energy for each sample size was obtained through fitting. and standard deviation Substitute the damage parameters obtained from the physical experiment into the Tavares model framework in step 6.3, and combine and adapt them with the high-precision discrete element simulation model in step 5 to complete the full parameter calibration of the Tavares model. Step 6.4, Collision Damage Verification: Using collision damage force and collision damage energy as the core indicators, conduct collision damage simulation experiments in the Tavares model after parameter calibration and integration with the high-precision model. Compare the simulated values ​​with the measured values ​​from physical experiments to verify whether the error is within the allowable range. At the same time, plot the curve of collision damage force as a function of damage depth to verify the consistency between the simulation and experimental patterns.

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