A Data-Driven Model-Based Method for Predicting and Classifying Particle Flow Inside a Rotary Drum

Abstract

A data-driven model-based method for predicting and classifying particle flow inside a rotary drum is presented. This method combines particle flow data generated by a discrete element method (DEM) model of the rotary drum to extract features related to particle motion behavior. A data-driven model is constructed using a Long Short-Term Memory (LSTM) method to predict the temporal characteristics of the flow data of mixed particles inside the rotary drum, and further classifies the rotary drum under various operating conditions. This method, combined with the DEM model, provides visualization of the trajectory of each particle and collects macroscopic and microscopic data representing the characteristics of particle flow inside the drum. Based on the data-driven model, this method extracts feature representations related to particle motion behavior from historical data of the DEM simulation and establishes a mapping relationship related to the motion state by mining the entire process data of mixed particle motion. Therefore, the prediction and classification method for mixed particle flow inside a rotary drum can be implemented at low cost, higher efficiency, and faster.

Description

Technical Field

[0001] This invention relates to the field of rotary drum particle motion, and in particular to a method for predicting and classifying particle flow inside a rotary drum based on a data-driven model. Background Technology

[0002] Rotary drum mills are common industrial equipment widely used in various industries involving particle materials. However, the different particle flows within a rotary drum often exhibit various phenomena, such as mixing, avalanche, and segregation. These characteristics unique to rotary drums, especially the homogeneity of the particle mixture, have a significant impact on overall industry production, including mass and heat transfer, particle crushing, and mill wear. Therefore, it is necessary to quantify and predict optimal operating conditions to achieve better crushing and grinding efficiency while reducing energy consumption.

[0003] In the past, the mixing and segregation processes of rotary drums have been studied based on data collected from various experiments and semi-empirical models. Due to differences in particle density, size, and shape, mixing and segregation behaviors are common during the movement of rotary drums. In particular, when axial segregation occurs in rotary drums, the axial distribution of media and material particles is not uniform, resulting in alternating segregation bands. Under these circumstances, the axial segregation structure in the mixed particle system reduces the overall grinding efficiency.

[0004] Currently, traditional model-based methods often require extensive domain knowledge and cumbersome parameter calibration and experimental verification. Despite the significant increases in computational performance observed in the past, physical model-based numerical methods remain difficult to apply in large-scale industrial applications. In contrast, data-driven methods do not rely on extensive prior expert knowledge, can extract feature representations related to motion behavior from historical data, and establish mapping relationships between these features and motion states by mining data from the entire particle motion process.

[0005] Therefore, it is necessary to study a prediction and classification method based on a data-driven model, which combines discrete element simulation data to effectively learn the flow behavior of a rotary drum mixing particle system, thereby achieving low-cost, rapid prediction of operating parameters and real-time classification of operating conditions. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a data-driven model-based method for predicting and classifying particle flow inside a rotary drum, enabling low-cost, rapid prediction of operating parameters and real-time classification of operating conditions.

[0007] The technical solution adopted in this invention is as follows: Based on the particle axial segregation data and collision energy data of the rotary drum at different times, a data-driven model for predicting and classifying particle flow inside the rotary drum is constructed using the long short-term memory method. This model predicts the time-series characteristics of the flow data of mixed particles inside the rotary drum and further classifies the various working condition labels of the rotary drum.

[0008] Furthermore, the following steps are included:

[0009] S1. The motion of particles inside the rotary drum was simulated based on the discrete element method, and the simulation parameters were consistent with the experimental parameters.

[0010] S2. The particle mixing and segregation process is captured by cameras at different positions and angles. Information on each particle inside the rotating drum is collected, including coordinates, velocity, energy, contact detection and motion state. Then, the correlation between different feature information and the overall flow of mixed particles is analyzed, and particle flow characteristics that can significantly characterize macroscopic and microscopic angles are extracted.

[0011] S3. Using the axial segregation data of particles in the rotary drum as the macroscopic flow characteristics and the collision energy as the microscopic flow characteristics, the axial segregation data and collision energy data of particles in the rotary drum at different times are statistically analyzed and calculated.

[0012] S4. Establish a data-driven model framework using the LSTM method:

[0013] Repeat steps S1 and S3 to simulate particle flow cases inside the rotary drum under different working conditions. Select three different working conditions, namely rotary drum speed, filling rate and length-to-diameter ratio, as input variables of the LSTM model. Use axial segregation index and relative region energy as output variables of the LSTM model to establish a data-driven model framework for predicting and classifying particle flow inside the rotary drum.

[0014] S5. Optimize the hyperparameter model and establish a standard data-driven model:

[0015] Based on the established data-driven model framework, after determining the input and output parameters of the data-driven model, the standard data-driven model is trained by minimizing the difference between the predicted value and the target value. Then, the parameters of the standard data-driven model, namely the time window length, the number of hidden layer neurons, and the number of hidden layers, are optimized. After comparison, the optimal data-driven model parameters are determined.

[0016] S6. Train the data-driven model and validate its prediction and classification performance:

[0017] During model training, datasets from different working conditions were shuffled, and 80% of the discrete metadata was randomly selected as the training set. The constructed standard data-driven model was then used for training and cross-validation, while the remaining 20% ​​of the data served as the test set. Images were plotted, and the particle flow prediction and classification results of the trained data-driven model were compared with the discrete element simulation results to verify the potential of the data-driven model for rapid prediction and parameter optimization in the industrial application of rotary drum mixing particles.

[0018] Furthermore, in step S1, when simulating the movement of particles inside the rotary drum based on discrete element method, it is necessary to establish a discrete element rotary drum model of equal scale according to the experimental parameters; the experimental device for obtaining the experimental parameters includes a rotary drum and a multi-camera acquisition system, the discrete element model is a transparent rotary drum, and the interior of the transparent rotary drum is filled with transparent glass particles of two diameter types in a completely segregated state.

[0019] Furthermore, in step S1, in order to simulate the particle motion behavior under different conditions, the operating parameters of the rotary drum include: length-to-diameter ratio of 0.5 to 3, filling rate of 10% to 30%, and rotational speed of 40 rpm to 80 rpm; the time step used in the model is 25% of the Rayleigh time step.

[0020] Furthermore, in step S3, when extracting the axial segregation data, each radial section of each rotary drum is regarded as a calculation unit, and the mixing index and the weight of the particles in the drum of each radial section are calculated.

[0021] Then, based on the axial center compensation distance of the radial section, the axial segregation ACNN data of the particles inside the drum is calculated;

[0022] The formula for the axial segregation ACNN data is: ;

[0023] In the formula, The actual axial center compensation distance for the two types of particles; , These are the axial segregation distance when fully mixed and the axial distance when fully segregated, respectively.

[0024] Furthermore, in step S3, when extracting data with collision energy, the entire computational region is... × × The grid is divided, the number of collisions and the energy loss of each collision are counted during the particle flow, and the total energy loss of each region is calculated.

[0025] Next, count the total number of related objects in each group, that is, the total number of media and material particles;

[0026] Then use the total energy of the region Divide by the total number of related objects This means obtaining relative regional energy RRTE data;

[0027] In the longer drum, the energy from each region is superimposed radially onto the axial section, as shown in the following formula:

[0028] In the formula, This represents the total number of time steps during the crushing process. This represents the total number of related objects.

[0029] Furthermore, in step S4, the data-driven model established using the LSTM method includes an input gate, a forget gate, and an output gate; by adjusting the states of the input gate, forget gate, and output gate, the information flow between the hidden layers of the LSTM network is controlled.

[0030] Furthermore, in step S5, the cross-entropy loss function is mainly used during the training of the prediction model. : ;

[0031] In the formula, and These are the indexes for the target working condition and the category index, respectively. and These are the actual and predicted labels, respectively; yes Regularization term, The set of optimizable parameters for the model.

[0032] During the training of the classification model, the main consideration is to classify targets under multiple working conditions, which requires the introduction of dimensionless weights. The cross-entropy loss function is modified, resulting in the modified multi-objective cross-entropy loss function. for: ;

[0033] Furthermore, in step S6, when comparing the prediction results of the data-driven model with the discrete element simulation results, the following evaluation indicators are selected: goodness of fit R2, mean absolute percentage error MAPE, root mean square error RMSE, etc.

[0034] Furthermore, when evaluating the classification results of the data-driven model, accuracy is used as an indicator to assess the performance and effectiveness of the proposed model. ;

[0035] In the formula, The total number of cases that can be accurately classified as positive examples, The total number of cases misclassified as positive. The total number of cases misclassified as negative. It is the total number of cases that are accurately classified as negative.

[0036] The beneficial effects of this invention are as follows:

[0037] 1. Compared to existing technologies, this method combines particle flow data generated by a rotary drum discrete element model to extract features related to particle motion behavior. It then constructs a data-driven model using the Long Short-Term Memory (LSTM) method to predict the temporal characteristics of the flow data of mixed particles inside the rotary drum and further classifies various operating condition labels of the rotary drum. This method, combined with the discrete element model, can provide visualization of the trajectory of each particle and collect macroscopic and microscopic data representing the flow characteristics of particles inside the drum.

[0038] 2. This method is based on a data-driven model. It extracts feature representations related to particle motion behavior from historical data of discrete element simulation and establishes a mapping relationship related to motion state by mining the data of the entire process of mixed particle motion. This not only makes up for the limitations of traditional physical model-based methods that rely on a large amount of prior expert knowledge, but also eliminates the need for repeated experimental verification on complex equipment. As a result, the prediction and classification method of mixed particle flow inside the rotary drum can be realized at low cost, higher efficiency and faster.

[0039] 3. This method is beneficial for better analysis and research on the overall flow behavior of large-scale, multi-scale particles. It has the potential for real-time process control and parameter optimization in industrial applications. In actual production processes, it has important research value for real-time monitoring and status identification of actual working conditions through the collection of historical data. Attached Figure Description

[0040] Figure 1 This is a flowchart of the process of this invention;

[0041] Figure 2 This is a discrete element model diagram of the rotary drum worktable in this invention;

[0042] Figure 3 This is an axial segregation data graph representing macroscopic flow characteristics in this invention;

[0043] Figure 4 This is a collision energy data graph representing the micro-flow characteristics in this invention;

[0044] Figure 5 This is a diagram of the data-driven model structure based on the LSTM framework in this invention;

[0045] Figure 6 This is a graph showing the hyperparameter optimization results of the data-driven model in this invention;

[0046] Figure 7 Yes, this is the prediction result of particle flow data in the data-driven model of this invention;

[0047] Figure 8 This is the data-driven model classification result of the rotary drum under multiple working conditions in this invention. Detailed Implementation

[0048] The present invention will be further described below with reference to specific embodiments, which should not be construed as limiting the technical solution. Any modifications and / or alterations made to the present invention will fall within the protection scope of the present invention.

[0049] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0050] This invention provides a data-driven model-based method for predicting and classifying particle flow inside a rotating drum, such as... Figure 1 As shown, it includes the following steps:

[0051] S1. The motion of particles inside the rotary drum was simulated based on the discrete element method, and the simulation parameters were consistent with the experimental parameters.

[0052] S2. Generation and feature extraction of mixed particle flow data:

[0053] The particle mixing and segregation process is captured by cameras at different positions and angles. Information on each particle inside the rotating drum is statistically analyzed, including coordinates, velocity, energy, contact detection, and motion state. Then, the correlation between different feature information and the overall flow characteristics of the mixed particles is compared and analyzed, extracting particle flow characteristics that can significantly characterize both macroscopic and microscopic perspectives.

[0054] S3. Axial segregation data and collision energy data are used to characterize macroscopic and microscopic features:

[0055] Based on the highly correlated particle flow data extracted from the feature extraction, and after comparison, the axial segregation data of particles in the rotating drum was taken as the macroscopic flow characteristic, and the collision energy was taken as the microscopic flow characteristic. The axial segregation data and collision energy data of particles in the rotating drum at different times were statistically analyzed and calculated.

[0056] S4. Establish a data-driven model framework using the LSTM method:

[0057] Repeat steps S1 and S3 to simulate particle flow cases inside the rotary drum under different operating conditions. Select the operating conditions (rotary drum speed, filling rate, length-to-diameter ratio) and the statistically obtained mixed particle flow data (axial segregation index, relative region energy) as the input and output variables of the LSTM model to establish a data-driven model framework for predicting and classifying particle flow inside the rotary drum.

[0058] S5. Optimize the hyperparameter model and establish a standard data-driven model:

[0059] Based on the data-driven model framework, after determining the input and output parameters of the model, the standard LSTM model is trained by minimizing the difference between the predicted and target values. Then, the LSTM model parameters (time window length, number of hidden layer neurons, number of hidden layers) are optimized, and the optimal model parameters are determined by comparison.

[0060] S6. Train the data-driven model and validate its prediction and classification performance:

[0061] During model training, datasets from different working conditions were shuffled, and 80% of the discrete metadata was randomly selected as the training set. This training set was then used to train the constructed standard data-driven model and for cross-validation. The remaining 20% ​​of the data served as the test set. Images were plotted, and the particle flow prediction and classification results of the trained data-driven model were compared with the discrete element simulation results. This verified the potential of the data-driven model for rapid prediction and parameter optimization in the industrial application of rotary drum mixing particles.

[0062] For reference Figure 2 In step S1, when simulating the particle motion inside the rotary drum based on discrete element method (DEM), a discrete element model of equal scale needs to be established according to the experimental parameters. The discrete element model of the rotary drum is as follows: Figure 2 As shown, it can be simplified to a transparent rotary drum 1, and the filling particles are selected as large black particles 2 with a diameter of 22mm and small white particles 3 with a diameter of 12mm.

[0063] The experimental setup for verifying the rotary drum workbench includes, in addition to the rotary drum 1, the large black particles 2, and the small white particles 3, a multi-camera acquisition system consisting of a data acquisition laptop and a high-speed camera. The image quality during the acquisition process is improved by using supplementary lighting and a black background cloth. The supplementary lighting is located on one side of the rotary drum 1, and the black background cloth is located behind the rotary drum 1. The entire rotary drum device is driven by a drive motor to rotate.

[0064] Specifically, in the discrete element model, the rotating drum is like... Figure 2 As shown, the diameter of the rotary drum 1 is D, and the axial length L is determined by the length-to-diameter ratio L / D of the drum, which is used to study the influence of the drum's rotation direction on the axial flow characteristics.

[0065] Furthermore, the rotating drum is made of acrylic material with a density of 1,250 kg / m³, a shear modulus of 3 GPa, and a Poisson's ratio of 0.35. The glass beads filling has a density of 2,500 kg / m³, a shear modulus of 22 GPa, and a Poisson's ratio of 0.25.

[0066] According to existing technology, the larger the particle size ratio in a rotary drum and the lower the filling rate, the more prone axial segregation will occur. To simulate particle motion behavior under different conditions, the rotary drum operating parameters included: aspect ratio 0.5–3, filling rate 10%–30%, and rotational speed 40–80 rpm. The time step used in the model was 25% of the Rayleigh time step. All other simulation parameters remained consistent with the experimental results.

[0067] In step S2, the particle mixing and segregation process is captured by cameras at different positions and angles. When the particle mixing system inside the rotary drum reaches a stable mixing and segregation state, the information of each particle inside the rotary drum is analyzed and statistically analyzed, including coordinates, velocity, energy, contact detection, and motion state. Then, the correlation between different feature information and the overall flow characteristics of the mixed particles is compared and analyzed, thereby extracting particle flow characteristics that can significantly characterize both macroscopic and microscopic perspectives.

[0068] In this embodiment, the flow behavior of particles inside a rotating drum is simulated using the Discrete Element Method (DEM). Therefore, based on the DEM's ability to update position information in real time, the position, velocity, energy, and collision state information of any particle in each time period can be extracted using commercial EDEM software. Furthermore, principal component analysis is used to reduce the dimensionality of the collected particle data and extract highly correlated feature information, which is then used as new samples input into the subsequent data-driven model.

[0069] In step S3, axial segregation data and collision energy data are selected to characterize macroscopic and microscopic features. Specifically, based on the particle flow data with high correlation extracted from the above features, and after comparison, the axial segregation data of particles in the rotating drum is taken as the macroscopic flow feature, such as... Figure 3 As shown, collision energy is used as a microscopic flow characteristic, such as Figure 4 As shown, the axial segregation data and collision energy data of particles in the rotating drum at different times were statistically analyzed and calculated.

[0070] In this embodiment, when extracting data with axial segregation characteristics, each radial section of each rotating drum needs to be treated as a computational unit, and the mixing index and the weight of the particles in that section within the drum are calculated for each radial section. Then, based on the axial center compensation distance of the radial section, the axial segregation ACNN data of the particles inside the drum is calculated.

[0071] The following formula is used to extract axial segregation features from ACNN data:

[0072]

[0073] In the formula, The actual axial center compensation distance for the two types of particles; , These represent the axial segregation distance when fully mixed and the axial distance when fully segregated, respectively.

[0074] like Figure 3 As shown, due to the large difference in particle size, radial segregation occurs at the end caps on both sides during the mixing process of the two particles, and then axial segregation gradually occurs as the drum continues to rotate.

[0075] Specifically, when L / D < 1.0, for short drums, the particulate media forms a random mixture on the axial cross section, and axial segregation is not obvious.

[0076] When 1.0 ≤ L / D < 2.0, as the length-to-diameter ratio of the roller increases, large particles aggregate on both sides, forming an axial segregation center zone shape dominated by small particles.

[0077] When L / D ≥ 2.0, an axial segregation zone is formed with two types of particle bands alternating.

[0078] Therefore, the overall or local segregation characteristics of binary particles in a rotary drum, especially under different drum length-to-diameter ratios (L / D), can describe particle flow information from a macroscopic perspective.

[0079] Furthermore, when extracting data with collision energy characteristics, it is necessary to perform a process on the entire computational domain. × × The grid was divided, and the number of collisions and energy loss per collision during particle flow were counted to calculate the total energy loss for each region. Next, the total number of related objects in each group was counted, i.e., the sum of the number of media and material particles, and then the total energy loss for the region was used. Divide by the total number of related objects This means obtaining relative regional energy RRTE data.

[0080] Specifically, in a longer drum, the energy from each region is superimposed radially onto the axial section, as shown in the following formula:

[0081]

[0082] In the formula, This represents the total number of time steps during the crushing process. This represents the total number of related objects.

[0083] Specifically, such as Figure 4As shown, the regional distribution of RRTE collision energy in the rotary drum over time is plotted. Observed from the axial surface of the rotary drum, all RRTE distribution characteristics are similar to the axial segregation characteristics of the particle flow. In the initial stage, the mixing of medium and material particles along the axial direction of the drum is relatively uniform, indicating that the grinding and crushing efficiency of each shaft section is basically consistent under uniform mixing conditions. However, as the drum continues to move, the axial segregation characteristics that subsequently form cause significant changes in the grinding and crushing efficiency of each shaft section. Obviously, as the overall segregation degree inside the rotary drum increases, the RRTE also decreases monotonically. Therefore, similar to axial segregation, RRTE can also describe particle flow information at the microscopic level.

[0084] In step S4, the LSTM method is used to establish a data-driven model framework. Steps S1 and S3 are repeated to simulate particle flow cases inside the rotary drum under different working conditions.

[0085] Specifically, three different operating conditions—rotary drum speed, filling rate, and length-to-diameter ratio—were selected as input variables for the LSTM model; axial segregation index and relative region energy were used as output variables for the LSTM model to establish a data-driven model framework for predicting and classifying particle flow inside the rotary drum.

[0086] like Figure 5 As shown, the hidden layer cell structure of the data-driven model built based on the LSTM network has three types of gates: input gates... Forgotten Gate and output gate Its forward computation method can be expressed as follows:

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] In the formula, and These are the corresponding coefficient matrix and bias vector, respectively. For input gates; Forgotten Gate; For output gate; This is a memory gate. This is the activation function.

[0093] By adjusting the state of these gates, the flow of information between LSTM network layers can be controlled.

[0094] Typically, the LSTM model training process uses the backpropagation time-propagation (BPTT) algorithm, which can be divided into four steps: (a) solving for the output value of the LSTM cells using the forward calculation method given above; (b) performing backpropagation calculation for the error term of each LSTM cell, including backpropagation by time and backpropagation by network layer; (c) solving for the gradient of each weight based on the calculated error term; and (d) updating the weights using a gradient-based optimization algorithm.

[0095] In step S5, the hyperparameters of the model are optimized and a standard data-driven model is established. Based on the established data-driven model framework, after determining the model's input and output parameters, a standard LSTM model is trained by minimizing the difference between the predicted and target values. Then, the parameters of the standard data-driven model—time window length, number of hidden layer neurons, and number of hidden layers—are optimized. After comparison, the optimal model parameters are determined.

[0096] Specifically, we simulated a total of 162 cases under three different operating conditions: drum filling rate, rotational speed, and length-to-diameter ratio. Table 1 lists the detailed information of the parameters for different operating conditions in the simulation and the amount of data generated by the discrete element method.

[0097] Table 1 Simulation schemes with different variables and generated data.

[0098] Simulation scheme Roller filling rate Drum speed Roller length-to-diameter ratio (D = 400 mm) 1 ~ 54 10 % 40 / 60 / 80 rpm 0.5 / 1.0 / 1.5 / 2.0 / 2.5 / 3.0 56 ~ 108 20 % 40 / 60 / 80 rpm 0.5 / 1.0 / 1.5 / 2.0 / 2.5 / 3.0 109 ~ 162 30 % 40 / 60 / 80 rpm 0.5 / 1.0 / 1.5 / 2.0 / 2.5 / 3.0

[0099] The datasets selected for the hyperparameters were derived from the particle flow data generated in 162 DEM simulation experiments in Table 1. Each set of experimental data is a time-dependent sequence.

[0100] Rotary drum speed, fill rate, aspect ratio, overall segregation index, and relative region energy are selected as the input and output variables of the model. After determining the input and output parameters of the data-driven model, the standard LSTM model parameters—time window length, hidden layer dimension, and number of hidden layers—need to be trained by minimizing the difference between the predicted and target values.

[0101] The cross-entropy loss function is mainly used in the training of the prediction model. :

[0102]

[0103] In the formula, and These are the indexes for the target working condition and the category index, respectively. and These are actual and predicted labels, respectively. yes Regularization term, The set of optimizable parameters for the model.

[0104] In the process of training the classification model, it is necessary to introduce dimensionless weights to classify targets under multiple working conditions. The cross-entropy loss function is modified, resulting in the modified multi-objective cross-entropy loss function. for:

[0105]

[0106] Figure 6 The impact of different time window lengths on prediction results is presented. The model's iteration count is set to 2000, and the learning rate to 0.001. During training, the loss function (Loss) is calculated every 100 iterations. The time window length is optimized sequentially with window lengths of 5, 15, 25, 35, and 45. Comparing the error and goodness of fit between the predicted and reference values ​​shows that a window length of 25 is appropriate. Accordingly, after comparison, the optimal parameters are finally determined to be 3 hidden layers and 50 hidden layer dimensions.

[0107] In step S6, the data-driven model is trained and its prediction and classification performance is verified. During model training, the datasets for different working conditions are shuffled, and 80% of the data is randomly selected as the training set, including ACNN time-series data and RRTE energy data. This data is then input into the constructed standard data-driven model for training and cross-validation, with the remaining 20% ​​of the data used as the test set. Images are plotted, and the particle flow prediction and classification results of the trained data-driven model are compared with the discrete element simulation results to verify the potential of this data-driven model for rapid prediction and parameter optimization in industrial applications of rotary drum mixing particles.

[0108] Specifically, Figure 7 The results show the predictions for the last 24 seconds from the data-driven model and discrete element simulation. In the shorter rotating drum, with L / D = 0.5, the model's predictive ability is only average, as indicated by the R² goodness-of-fit results. This is because the end cap effect is significant in the short drum, causing the mixed particles to maintain axial convection throughout their movement.

[0109] Therefore, the mixing inside the rotary drum is good and the axial segregation is not obvious. However, when the length-to-diameter ratio of the rotary drum increases, the prediction accuracy is higher in the long drum and the fluctuation of its sample points is much lower than that in the short drum.

[0110] In addition, the test data included data from L / D = 1.5 and L / D = 3.0. The model rotational speed and fill rate were the same as in the training data, but the aspect ratio of the rotary drum was different to test the model's interpolation ability and extrapolation ability under larger aspect ratio conditions.

[0111] like Figure 7 As shown in (e) with L / D = 1.5, for the steady-state case, the ACNN model's prediction fit is close to the accuracy of other long rollers, which is reasonable. Furthermore, Figure 7 (f) shows the extrapolated predictions for L / D = 3.0. Clearly, the predictions for L / D = 3.0 are more accurate than those for L / D = 1.5. This is attributed to the reduced influence of the end cap effect on the axial segregation of the mixed particles as the aspect ratio of the rotary drum increases.

[0112] Therefore, even in rotary drums under different operating conditions, the data-driven model established by combining discrete element simulation has good prediction accuracy for the steady-state mixing and segregation of particles inside the rotary drum, indicating its potential for rapid optimization of operating parameters and equipment parameters in industrial applications.

[0113] When comparing the prediction results of the data-driven model with the discrete element simulation results, the following evaluation metrics are used: goodness of fit R², mean absolute percentage error (MAPE), and root mean square error (RMSE). Furthermore, when evaluating the classification results of the data-driven model, accuracy is used as the metric to assess the performance and effectiveness of the proposed model.

[0114]

[0115] In the formula, The total number of cases that can be accurately classified as positive examples, The total number of cases misclassified as positive. The total number of cases misclassified as negative. It is the total number of cases that are accurately classified as negative.

[0116] Similarly, after hyperparameter optimization, the LSTM model's iteration count is set to 1000, the learning rate to 0.01, and the loss function (Loss) is given every 100 iterations during training. Correspondingly, when the number of hidden layers is 2, the hidden layer dimension is 5, and the weights are dimensionless... The optimized model performed best when the values ​​were 1, 1.1, and 2.5 respectively.

[0117] To facilitate comparison of the classification accuracy of rotary drum operating conditions, the classification results of this data-driven model are plotted on... Figure 8It is evident that the data-driven model, integrating ACNN time-series data and RRTE energy data, achieved a classification accuracy exceeding 85% for all three types of labeled data. Particularly noteworthy is its 100% accuracy in classifying rotary drum speed and fill rate conditions. Therefore, the combination of discrete element simulation and data-driven methods validates the potential of this data-driven model for rapid prediction and parameter optimization in the industrial application of rotary drum mixing particles. Rapid prediction and parameter optimization of particle behavior in various industrial applications will be realized in the future.

[0118] This embodiment combines historical data from discrete element method (DEM) simulations to extract features related to particle motion behavior. Based on a data-driven model, it mines data on the entire process of mixed particle motion inside a rotary drum, establishing a mapping relationship between motion states. This not only overcomes the limitations of traditional physics-based methods that rely on extensive prior expert knowledge but also eliminates the need for repeated experimental verification on complex equipment. Therefore, the prediction and classification method for mixed particle flow inside a rotary drum can be implemented more cost-effectively, efficiently, and quickly. This will facilitate better analysis and research on the overall flow behavior of large-scale, multi-scale particles, and has the potential for real-time process control and parameter optimization in industrial applications. In actual production processes, the collection of historical data for real-time monitoring and state identification of actual operating conditions has significant research value.

[0119] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A method for predicting and classifying particle flow inside a rotating drum based on a data-driven model, characterized in that: Based on the particle axial segregation data and collision energy data of the rotary drum at different times, a data-driven model for predicting and classifying particle flow inside the rotary drum is constructed using the long short-term memory method. This model predicts the time-series characteristics of the flow data of mixed particles inside the rotary drum and further classifies various operating condition labels of the rotary drum. Includes the following steps, S1. The motion of particles inside the rotary drum was simulated based on the discrete element method, and the simulation parameters were consistent with the experimental parameters. S2. The particle mixing and segregation process is captured by cameras at different positions and angles. Information on each particle inside the rotating drum is collected, including coordinates, velocity, energy, contact detection and motion state. Then, the correlation between different feature information and the overall flow of mixed particles is analyzed, and particle flow characteristics that can significantly characterize macroscopic and microscopic angles are extracted. S3. Using the axial segregation data of particles in the rotary drum as the macroscopic flow characteristics and the collision energy as the microscopic flow characteristics, the axial segregation data and collision energy data of particles in the rotary drum at different times are statistically analyzed and calculated. S4. Establish a data-driven model framework using the LSTM method: Repeat steps S1 and S3 to simulate particle flow cases inside the rotary drum under different working conditions. Select three different working conditions, namely rotary drum speed, filling rate and length-to-diameter ratio, as input variables of the LSTM model. Use axial segregation index and relative region energy as output variables of the LSTM model to establish a data-driven model framework for predicting and classifying particle flow inside the rotary drum. S5. Optimize the hyperparameter model and establish a standard data-driven model: Based on the established data-driven model framework, after determining the input and output parameters of the data-driven model, the standard data-driven model is trained by minimizing the difference between the predicted value and the target value. Then, the parameters of the standard data-driven model, namely the time window length, the number of hidden layer neurons, and the number of hidden layers, are optimized. After comparison, the optimal data-driven model parameters are determined. S6. Train the data-driven model and validate its prediction and classification performance: During model training, the datasets for different working conditions are shuffled, and 80% of the discrete metadata is randomly selected as the training set. The standard data-driven model is then input into the training set and used for cross-validation. The remaining 20% ​​of the data is used as the test set. By plotting images and comparing the particle flow prediction and classification results of the trained data-driven model with the discrete element simulation results, the potential of the data-driven model for rapid prediction and parameter optimization in the industrial application of rotary drum mixing particles is verified.

2. The method for predicting and classifying particle flow inside a rotary drum according to claim 1, characterized in that, In step S1, when simulating the movement of particles inside a rotary drum based on discrete element method (DEM), it is necessary to establish a discrete element rotary drum model of equal scale according to the experimental parameters. The experimental device for obtaining the experimental parameters includes a rotary drum and a multi-camera acquisition system. The discrete element model is a transparent rotary drum, and the interior of the transparent rotary drum is filled with transparent glass particles of two diameter types in a completely segregated state.

3. The method for predicting and classifying particle flow inside a rotary drum according to claim 2, characterized in that, In step S1, in order to simulate the particle motion behavior under different conditions, the operating parameters of the rotary drum include: length-to-diameter ratio of 0.5 to 3, filling rate of 10% to 30%, and rotation speed of 40 rpm to 80 rpm; the time step used in the model is 25% of the Rayleigh time step.

4. The method for predicting and classifying particle flow inside a rotary drum according to claim 1, characterized in that, In step S3, when extracting the axial segregation data, each radial section of each rotary drum is regarded as a calculation unit, and the mixing index and the weight of the particles in the drum of each radial section are calculated. Then, based on the axial center compensation distance of the radial section, the axial segregation ACNN data of the particles inside the drum is calculated; The formula for the axial segregation ACNN data is: In the formula, L now The actual axial center compensation distance for the two types of particles; L min L max These are the axial segregation distance when fully mixed and the axial distance when fully segregated, respectively.

5. The method for predicting and classifying particle flow inside a rotary drum according to claim 1, characterized in that, In step S3, When extracting data with collision energy, the entire computational domain is... × × The grid is divided, the number of collisions and the energy loss of each collision are counted during the particle flow, and the total energy loss of each region is calculated. Next, count the total number of related objects in each group, that is, the total number of media and material particles; Then use the total energy of the region Divide by the total number of related objects This means obtaining relative regional energy RRTE data; In the longer drum, the energy from each region is superimposed radially onto the axial section, as shown in the following formula: In the formula, This represents the total number of time steps during the crushing process. This represents the total number of related objects.

6. The method for predicting and classifying particle flow inside a rotary drum according to claim 5, characterized in that, In step S4, the data-driven model established using the LSTM method includes an input gate, a forget gate, and an output gate; by adjusting the states of the input gate, forget gate, and output gate, the information flow between the hidden layers of the LSTM network is controlled.

7. The method for predicting and classifying particle flow inside a rotary drum according to claim 1, characterized in that, In step S5, the cross-entropy loss function is mainly used during the training of the prediction model. : In the formula, and These are the indexes for the target working condition and the category index, respectively. and These are the actual and predicted labels, respectively; yes Regularization term, The set of optimizable parameters of the representative model; During the training of the classification model, the main consideration is to classify targets under multiple working conditions, which requires the introduction of dimensionless weights. The cross-entropy loss function is modified, resulting in the modified multi-objective cross-entropy loss function. for: .

8. The method for predicting and classifying particle flow inside a rotary drum according to claim 1, characterized in that, In step S6, when comparing the prediction results of the data-driven model with the discrete element simulation results, the following evaluation indicators are selected: goodness of fit R2, mean absolute percentage error MAPE, and root mean square error RMSE.

9. The method for predicting and classifying particle flow inside a rotary drum according to claim 1, characterized in that, When evaluating the classification results of the data-driven model, accuracy is used as an indicator to assess the performance and effectiveness of the proposed model. In the formula, The total number of cases that can be accurately classified as positive examples. The total number of cases misclassified as positive. The total number of cases that were misclassified as negative. It is the total number of cases that are accurately classified as negative.

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