Temperature prediction method and system for granular flow system based on interpretable machine learning

Abstract

The application provides a granular flow system temperature prediction method and system based on an interpretable machine learning, relates to the technical field of granular flow system research and application, and the method comprises the following steps: acquiring a data set of a granular flow system, wherein the data set comprises experimental translational particle temperatures and experimental rotational particle temperatures at multiple time points; forming a state variable dictionary matrix based on each alternative in a pre-constructed control equation; performing equalization processing on the alternatives in the state variable dictionary matrix to obtain an equalized dictionary matrix; screening out reasonable alternatives from the equalized dictionary matrix and determining corresponding weights based on an interpretable machine learning method and the data set, so as to obtain a target granular flow system control equation; and solving the target granular flow system control equation to predict the translational particle temperature and the rotational particle temperature. The application can improve the reliability of the granular flow system control equation, and further improve the accuracy of the granular flow system temperature prediction.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of granular flow system research and application technology, and particularly relates to a temperature prediction method and system for a granular flow system based on an interpretable machine learning. BACKGROUND

[0002] Solids often exist in the form of particles, have fixed volume and shape, and are not easy to compress. When the particles are closely packed, the particle and fluid density difference is relatively large, and the fluid has a small effect on the particles. Ignoring the effect of the fluid on the particles, this flow state is called granular flow. Granular flow systems exist widely in nature and industrial production processes: mud flow in nature, medicine manufacturing in the pharmaceutical industry, ore crushing and sorting in the mining industry, and mixing and stirring of particulate materials. The flow characteristics of the granular flow system are very complex, but the study of the flow field characteristics of the system is crucial to understanding these engineering activities and natural phenomena. In order to balance the calculation efficiency and the accuracy of the calculation, the continuous medium simulation method is widely used to describe the model of the granular flow system. This is often composed of control equations and constitutive relations, and a reasonable numerical algorithm can be used to solve the granular flow system. However, the flow field characteristics of the real granular flow system are very complex, and the common modeling method is often difficult to accurately describe the complex interaction between particles, and it is difficult to accurately construct the constitutive relation, thereby resulting in a large calculation error of the numerical simulation method.

[0003] With the rapid development of machine learning methods, the sparse regression method, which is a strong explainable and data and mechanism driven machine learning method, is often used in the modeling of complex flow control systems. For example, a hot updraft flow positioning method based on data driving in patent CN119598687A. The invention considers estimating the updraft flow, and then estimates the position of the wind field through a sparse identification algorithm of nonlinear dynamics. The mathematical physics specification model is accurately identified through the proposed sparse identification method, thereby realizing hot positioning and improving the ability to identify hot updraft flow and reducing aircraft energy consumption. For example, patent CN119513825A is based on the idea of sparse regression to establish a sub-transport constitutive relationship and a low-dimensional control equation. By using the accurate calculation results of the neutron transport equation, grasping the reason for the large deviation of the calculation results of the neutron diffusion equation in a small scale range, and combining sparse regression, the neutron transport constitutive relationship is obtained, and then the low-dimensional macroscopic neutron transport control equation is obtained. The difficulty of theoretical analysis modeling is greatly reduced, the calculation accuracy is significantly improved, the applicability is better, the situation is similar to the actual reactor core working condition, and has certain practicality. Combining physical information neural network and sparse regression method, the partial differential control equation of the dynamic system is found from the scarce and noisy data. Patent CN120105365A describes a method for discovering control equations from scarce and noisy data based on physics, wherein on the one hand, the candidate function library covered by the dictionary matrix is determined by a deep neural network, which indicates that the explainability of the candidate matrix is weak. On the other hand, the differential is obtained through automatic differentiation techniques, which means that it is difficult to accurately capture the contribution of information around the complex physical field.

[0004] In summary of the above cited descriptions, the sparse regression method is a reasonable method for constructing perfect constitutive relationship and control equation from data, but it has not been applied to complex particle flow systems. The reason for this may be that the learning results are biased due to the difference in the number of orders of magnitude of each state variable involved in the flow control equation of the system, thereby affecting the accuracy of temperature prediction of the particle flow system.

[0005] Therefore, there is an urgent need for a scheme that can improve the reliability of the particle flow system control equation. SUMMARY

[0006] To solve the above technical problems, the present application provides the following technical solutions:

[0007] In order to solve the above technical problems, the present application provides the following technical solutions:

[0008] In a first aspect, the present application provides a temperature prediction method for a granular flow system based on an interpretable machine learning method, comprising:

[0009] obtaining a data set of the granular flow system, wherein the data set comprises experimental translational particle temperatures and experimental rotational particle temperatures at a plurality of time points;

[0010] forming a state variable dictionary matrix based on each alternative in a pre-constructed control equation, wherein each row of the state variable dictionary matrix represents an alternative;

[0011] performing equalization processing on each alternative in the state variable dictionary matrix to obtain an equalized dictionary matrix;

[0012] screening out reasonable alternatives and determining corresponding weights from the equalized dictionary matrix based on an interpretable machine learning method and the data set to obtain a target granular flow system control equation, wherein the interpretable machine learning method is specifically an equalized sparse regression method combining a sequential threshold ridge regression method (STRidge) and a train sequential threshold ridge regression method (TrainSTRidge);

[0013] solving the target granular flow system control equation to predict translational particle temperatures and rotational particle temperatures.

[0014] In an embodiment of the present application, before the step of obtaining the data set of the granular flow system, the method further comprises:

[0015] calibrating particle physical property parameters by using kinetic theory of granular flow.

[0016] In an embodiment of the present application, before the step of obtaining the data set of the granular flow system, the method further comprises:

[0017] substituting particle physical property parameters of the granular flow system into a discrete element method to generate the data set.

[0018] In an embodiment of the present application, the step of substituting particle physical property parameters of the granular flow system into a discrete element method to generate the data set comprises:

[0019] substituting the particle physical property parameters of the granular flow system into a single-particle motion equation determined by a linear interaction model between particles in the discrete element method to obtain single-particle information at each time point in the granular flow system, wherein the single-particle information comprises translational velocity and rotational velocity of a single particle;

[0020] The translational velocities of all individual particles at each time point are averaged to generate the average particle translational velocity at that time point; the rotational velocities of all individual particles at each time point are averaged to generate the average particle rotational velocity at that time point.

[0021] Based on the average particle translational velocity and the translational velocity of a single particle at each time point, the translational velocity of a single particle at that time point is generated; based on the average particle rotational velocity and the rotational velocity of a single particle at each time point, the rotational velocity of a single particle at that time point is generated.

[0022] Based on the plane pulse velocity of a single particle at each time point, the plane pulse kinetic energy of that single particle at that time point is generated; based on the axial pulse velocity of a single particle at each time point, the axial pulse kinetic energy of that single particle at that time point is generated.

[0023] The translational kinetic energy of all individual particles at each time point is averaged to obtain the experimental translational particle temperature at that time point; the rotational kinetic energy of all individual particles at each time point is averaged to obtain the experimental rotating particle temperature at that time point.

[0024] In one embodiment of the present invention, the step of equalizing each alternative option in the state variable dictionary matrix to obtain an equalized dictionary matrix includes:

[0025] Divide each column element in the state variable dictionary matrix by the magnitude of that column to obtain a balanced dictionary matrix.

[0026] In one embodiment of the present invention, the dataset includes: a training set and a test set;

[0027] The process, based on interpretable machine learning methods and the dataset, involves selecting reasonable alternatives from the balanced dictionary matrix and determining their corresponding weights to obtain the governing equations for the target granular flow system, including:

[0028] The training set is input into a preset optimization objective function, and the sparse vector is iteratively optimized using the sequential ridge regression method to obtain the learning result. The learning result includes: the first sparse vector when the cutoff value of the optimization objective function is a preset cutoff value and the value of the optimization objective function is minimized.

[0029] The learning results are applied to the test set, and the training order ridge regression method is called to optimize the preset cutoff value to obtain the optimized cutoff value; based on the optimized cutoff value, the second sparse vector is determined.

[0030] Based on the second sparse vector, reasonable alternatives are selected from the alternatives of the equalized dictionary matrix;

[0031] Based on the linear relationship between the pre-obtained second sparse vector and the third sparse vector, and by performing an inverse linear relationship transformation on the second sparse vector, the third sparse vector is obtained. The third sparse vector is then determined as the weight corresponding to the reasonable alternative, thereby obtaining the control equation of the target granular flow system.

[0032] In one embodiment of the present invention, before solving the governing equations of the target particle flow system to predict the temperature of translational and rotating particles, the method further includes:

[0033] The control equations of the target particle flow system are compared with the analytical control equations derived using particle kinetic theory, and it is determined that the control equations of the target particle flow system pass the first verification.

[0034] Solve the control equations and analytical control equations of the target particle flow system respectively. Compare the solution results of the target particle flow system control equations and analytical control equations with the translational particle temperature and rotational particle temperature obtained by statistical averaging of the dataset using the discrete element method. Determine that the control equations of the target particle flow system pass the second verification.

[0035] Secondly, the present invention provides a temperature prediction system for granular flow systems based on interpretable machine learning, comprising:

[0036] The acquisition module is used to acquire the dataset of the particle flow system, which includes: experimental translational particle temperature and experimental rotating particle temperature at multiple time points;

[0037] A forming module is used to form a state variable dictionary matrix based on each alternative in a pre-constructed control equation, wherein the columns of the state variable dictionary matrix represent the alternatives;

[0038] The processing module is used to perform equalization processing on each alternative in the state variable dictionary matrix to obtain an equalized dictionary matrix;

[0039] The filtering module is used to filter out reasonable alternatives and determine their corresponding weights from the balanced dictionary matrix based on the interpretable machine learning method and the dataset, so as to obtain the control equation of the target granular flow system. The interpretable machine learning method specifically refers to the balanced sparse regression method that combines the sequential ridge regression method and the training sequential ridge regression method.

[0040] The prediction module is used to solve the control equations of the target particle flow system to predict the temperature of translational particles and the temperature of rotating particles.

[0041] In one embodiment of the present invention, the temperature prediction system for granular flow systems based on interpretable machine learning further includes:

[0042] The generation module is used to substitute the particulate property parameters of the granular flow system into the discrete element method to generate the dataset.

[0043] Thirdly, the present invention provides a computer-readable medium having a computer program stored thereon, which, when executed by a processor, implements the temperature prediction method for particulate flow systems based on interpretable machine learning.

[0044] Fourthly, the present invention provides an electronic device including a memory and a processor, wherein the memory is used to store information including program instructions, and the processor is used to control the execution of the program instructions, wherein when the program instructions are loaded and executed by the processor, the temperature prediction method for granular flow systems based on interpretable machine learning is implemented.

[0045] Fifthly, the present invention provides a computer program product, including a computer program / instructions, which, when executed by a processor, implement the temperature prediction method for granular flow systems based on interpretable machine learning.

[0046] As can be seen from the above technical solution, the present invention provides a method and system for temperature prediction of granular flow systems based on interpretable machine learning. The method includes: acquiring a dataset of the granular flow system, the dataset including experimental translational particle temperatures and experimental rotating particle temperatures at multiple time points; forming a state variable dictionary matrix based on various alternatives in a pre-constructed control equation, where the columns of the state variable dictionary matrix represent the alternatives; performing equalization processing on each alternative in the state variable dictionary matrix to obtain an equalized dictionary matrix; based on an interpretable machine learning method and the dataset, selecting reasonable alternatives from the equalized dictionary matrix and determining their corresponding weights to obtain the target granular flow system control equation, wherein the interpretable machine learning method specifically refers to an equalized sparse regression method combining sequential ridge regression and training sequential ridge regression; solving the target granular flow system control equation to predict the translational and rotating particle temperatures. This method can equalize the state variable dictionary matrix, reduce the order-of-magnitude differences between various state variables, realize the application of sparse regression methods in the construction of the granular flow system control equation, improve the reliability of the granular flow system control equation, and thus improve the accuracy of temperature prediction. As described above, the temperature prediction method for granular flow systems based on interpretable machine learning provided by this invention can utilize high-precision underlying simulation data to develop an equalized sparse regression method, successfully extracting the flow control equations for uniformly cooled coarse granular flow systems. The equalized high-precision sparse regression method proposed in this invention can serve as one of the interpretable machine learning methods in the future, and is expected to extract complex solid-phase interactions from high-precision underlying simulation data. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is a schematic diagram of the first process of the temperature prediction method for a particle flow system based on interpretable machine learning in an embodiment of the present invention.

[0049] Figure 2 This is a schematic diagram of the second process of the temperature prediction method for granular flow systems based on interpretable machine learning in an embodiment of the present invention.

[0050] Figure 3 This is a schematic diagram of the third process of the temperature prediction method for granular flow systems based on interpretable machine learning in an embodiment of the present invention.

[0051] Figure 4 This is a schematic diagram of the fourth process of the temperature prediction method for granular flow systems based on interpretable machine learning in an embodiment of the present invention.

[0052] Figure 5 This is a schematic diagram of the fifth process of the temperature prediction method for granular flow systems based on interpretable machine learning in an embodiment of the present invention.

[0053] Figure 6 This is a schematic diagram comparing the relative errors between the coefficients of the governing equations solved by the Normalized SINDy method and the discrete element method in an example of this invention and the analytical results of particle kinetic theory.

[0054] Figure 7 This is a schematic diagram comparing the particle temperature variation over time obtained by the equalization sparse regression method, the traditional particle kinetic theory method for deriving the control equation numerical solution, and the particle temperature variation over time obtained by the discrete element method.

[0055] Figure 8 This is a logic block diagram of the temperature prediction method for particulate flow systems based on interpretable machine learning in an embodiment of the present invention.

[0056] Figure 9 This is a schematic diagram of the structure of a temperature prediction system for a particle flow system based on interpretable machine learning in an embodiment of the present invention;

[0057] Figure 10 This is a schematic block diagram of the system configuration of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0058] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0059] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0060] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification, claims and accompanying drawings of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such processes, methods, products or devices.

[0061] For large-scale industrial granular flow systems, to balance computational efficiency and accuracy, continuum simulation methods are generally used for simulation studies. In continuum models, particles are treated as interpenetrating fluids, and the mass and momentum conservation relationships are described using continuum governing equations. Solving the granular flow system using an Eulerian grid results in high computational efficiency. Because the solid phase is treated as a pseudo-fluid, the overall computational load is significantly reduced compared to the discrete element method, which analyzes the motion of individual particles one by one. However, the momentum equations and pulsating energy dissipation equations often introduce additional solid-state forces, heat fluxes, and energy dissipation source terms, requiring additional low-level simulation statistical analysis methods, empirical correlations, or particle kinetic theory modeling for closure. However, continuum simulation methods often struggle to accurately characterize the complex interactions between particles and cannot accurately construct constitutive relations, leading to significant computational errors in numerical simulations. Therefore, this invention proposes a temperature prediction method and system for granular flow systems based on interpretable machine learning. This method can accurately calibrate particle physical parameters using particle kinetic theory and finely characterize the motion state of individual particles using the discrete element method. This invention obtains continuous solid-phase motion information through statistical analysis, and constructs reasonable alternatives for the governing equations based on expert experience in statistical mechanics, forming a reasonable dictionary matrix. Taking into account the order-of-magnitude differences between the various flow field state variables within the granular flow system, a strategy is proposed to introduce alternatives into the equalized dictionary matrix, developing a novel high-precision equalized sparse regression method. By combining sequential ridge regression with a trained sequential ridge regression algorithm, the reasonable forms of the governing equations are selected from the dictionary matrix composed of alternatives, thereby enabling the mining of the governing equation forms for complex granular flow systems. This invention relates to the development of sparse regression methods for granular flow systems. Taking a uniformly cooled coarse granular flow system as an example, the method execution process is described in detail, and the feasibility of the method is verified.

[0062] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0063] Figure 1 This is a schematic diagram of the first process of a temperature prediction method for granular flow systems based on interpretable machine learning provided in an embodiment of the present invention. To improve the reliability of the governing equations of the granular flow system and thus improve the accuracy of temperature prediction, this embodiment provides a temperature prediction method for granular flow systems based on interpretable machine learning. The executing entity of this method can be the temperature prediction system for granular flow systems based on interpretable machine learning, which includes, but is not limited to, a server, such as... Figure 1 As shown, this method specifically includes the following:

[0064] Step 101: Obtain the dataset of the particle flow system, which includes: experimental translational particle temperature and experimental rotating particle temperature at multiple time points.

[0065] Specifically, the particle flow system can be a uniformly cooled coarse particle flow system. The dataset can include: batch samples, each sample comprising: experimental translational particle temperature and experimental rotating particle temperature of the particle flow system. Both the experimental translational and rotating particle temperatures are time series, corresponding to the particle translational and rotating temperatures at different times. The data samples available for sampling are the experimental translational particle temperature time series and the experimental rotating particle temperature time series. During the execution of this invention, a random sampling method can be used to reduce the amount of data samples used for prediction and lower the learning difficulty of interpretable machine learning methods. In subsequent steps, the batch samples can be divided into a training set and a test set.

[0066] Step 102: Based on the various alternatives in the pre-constructed control equations, form a state variable dictionary matrix, where the columns of the state variable dictionary matrix represent the alternatives.

[0067] Step 103: Perform equalization processing on each option in the state variable dictionary matrix to obtain an equalized dictionary matrix.

[0068] Step 104: Based on the interpretable machine learning method and the dataset, select reasonable alternatives from the equalized dictionary matrix and determine their corresponding weights to obtain the control equations of the target granular flow system. The interpretable machine learning method specifically refers to the equalized sparse regression method that combines the sequential ridge regression method and the training sequential ridge regression method.

[0069] Specifically, machine learning methods have provided a groundbreaking research paradigm for the discovery of constitutive relations in fluid mechanics and the determination of the form of governing equations due to their ability to represent complex nonlinear relationships, adaptive optimization capabilities in multi-scale modeling, and real-time prediction capabilities for dynamic systems.

[0070] Step 105: Solve the control equations of the target particle flow system to predict the temperature of translational particles and the temperature of rotating particles.

[0071] Specifically, the time series can be discretized into a sequence of time points to be predicted, and the control equations of the target particle flow system can be solved using numerical methods to predict the translational particle temperature and the rotational particle temperature corresponding to the sequence of time points to be predicted.

[0072] Figure 2This is a schematic diagram of the second process of the temperature prediction method for granular flow systems based on interpretable machine learning provided in this embodiment of the invention. In the prior art, sparse regression methods have not yet been applied to complex granular flow systems, possibly because the actual particle properties are difficult to define, making it difficult to generate high-precision simulation data of real granular flow. Therefore, in order to obtain high-precision simulation data, such as... Figure 2 As shown, in one embodiment of the present invention, before step 101, the following steps are further included:

[0073] Step 201: Use particle kinetic theory to calibrate particle physical property parameters.

[0074] In this embodiment, the particle physical properties may include: particle size, particle density, Poisson's ratio, normal spring stiffness coefficient, tangential spring stiffness coefficient, normal restitution coefficient, tangential restitution coefficient, time step, initial translational particle temperature, rotating particle temperature, solid content, number of particles, simulation domain side length, simulation time, and friction coefficient, etc.

[0075] In one embodiment of the present invention, particle properties can be calibrated using particle kinetic theory developed from statistical mechanics, as follows: A uniformly cooled rough particle flow system consists of uniformly distributed, rough-surfaced spherical particles under three-period boundary conditions. The particle velocity distribution within the system follows a Maxwell distribution. Inelastic collisions and contact friction between particles cause the temperature of translational / rotational particles to gradually decrease over time. For a period of time, the particles within the system remain spatially uniformly distributed; that is, the solid content and average velocity within the system are constants. The evolution of the system's flow field characteristics is described only by the governing equations governing the evolution of the temperature of translational / rotational particles over time. Therefore, the present invention can sequentially determine the governing equations of the uniformly cooled rough particle flow system using particle kinetic theory developed from statistical mechanics, namely:

[0076] Equation for temperature T of translational particles:

[0077] (1)

[0078] Equation for the temperature R of rotating particles:

[0079] (2)

[0080] The translational / rotational energy dissipation source terms are denoted as γ and Γ, respectively. When deriving these energy dissipation source terms from particle kinetic theory, it is assumed that the sliding friction coefficient μ is close to 0, and the tangential restitution coefficient... and normal recovery coefficient The coefficient of restitution, close to 1, characterizes the pulsating energy (i.e., particle temperature loss) caused by inelastic collisions, while the coefficient of friction indicates the dissipation of pulsating energy due to constant-range interactions between particles. Since energy dissipation within the system is relatively low, the coefficient of friction is assumed to be small as well. Therefore, the core constitutive relation in the translational / rotational particle energy conservation equations of the uniformly cooled coarse particle flow system is as follows:

[0081] Translational energy dissipation rate γ:

[0082] (3)

[0083] Rotational energy dissipation rate Γ:

[0084] (4)

[0085] (5)

[0086] Wherein: g o For radial correlation function, ɛ s For solid content, e n For particle normal restitution coefficient, d p For particle diameter, For density.

[0087] (6)

[0088] The coefficients a1, a2, b1, and b2 in the energy dissipation source terms involved in the translational particle temperature and the rotational particle temperature are as follows:

[0089] (7)

[0090] (8)

[0091] (9)

[0092] (10)

[0093] Where: μ0 is the critical friction coefficient, which is related to the condition for determining whether the particles experience kinetic or static friction; μ is the sliding friction coefficient, which is assumed to be equal to the sliding friction coefficient in particle kinetic theory. .

[0094] Based on the above derivation process and assumptions of the particle kinetic theory, the particle physical property parameters can be further calibrated, specifically as follows: the sliding friction coefficient μ is close to 0, and the tangential restitution coefficient e t Normal restoration coefficient e nApproximately 1, the sliding friction coefficient μ = 0.001, and the tangential restitution coefficient equals the normal restitution coefficient e. t =e n =0.95. The particle property settings in the discrete element method above directly ensure minimal energy loss within the overall system, with energy dissipation concentrated in the normal direction, consistent with particle properties in particle kinetic theory. Therefore, the rationality of generating high-precision underlying data can be further guaranteed. Since data is the core of the equalization sparse regression method, accurate calibration of particle property parameters, followed by high-precision discrete element simulation in subsequent steps, further ensures the accuracy of the learning process.

[0095] In this embodiment, a reasonable kinetic theory of particles can be determined first to preliminarily characterize the constitutive relations in the governing equations of the granular flow system. This reasonable kinetic theory includes relevant assumptions about particle properties, which are then used in the subsequent discrete element method simulation of the granular flow system. This determines the particle property parameters involved in the discrete element method based on the soft sphere model, such as the particle normal / tangential coefficient of restitution e. n / e t The sliding friction coefficient μ and the normal elastic coefficient k involved in the interparticle contact force model. n and tangential elastic modulus k t Normal / tangential damping coefficient γ n / γ t wait.

[0096] To improve the reliability of obtaining the dataset, in one embodiment of the present invention, such as Figure 2 As shown, before step 101, the procedure further includes:

[0097] Step 202: Substitute the particle property parameters of the granular flow system into the discrete element method to generate the dataset.

[0098] Figure 3 This is a schematic diagram of the third process of the temperature prediction method for granular flow systems based on interpretable machine learning provided in this embodiment of the invention, as shown below. Figure 3 As shown, in order to improve the reliability of obtaining the experimental translational particle temperature and the experimental rotating particle temperature, in one embodiment of the present invention, step 301 includes:

[0099] Step 301: Substitute the particle property parameters of the particle flow system into the single particle motion equation determined by Newton's second law of motion, which is closed by the linear interaction model between particles, in the discrete element method to obtain the single particle information at each time point in the particle flow system. The single particle information includes the translational velocity and rotational velocity of the single particle.

[0100] Step 302: Average the translational velocity of all individual particles at each time point to generate the average particle translational velocity at that time point; average the rotational velocity of all individual particles at each time point to generate the average particle rotational velocity at that time point.

[0101] Step 303: Generate the translational velocity of a single particle at each time point based on the average particle translational velocity and the translational velocity of a single particle at that time point; generate the rotational velocity of a single particle at each time point based on the average particle rotational velocity and the rotational velocity of a single particle at that time point.

[0102] Step 304: Generate the kinetic energy of a single particle at each time point based on its lateral kinetic velocity; generate the kinetic energy of a single particle at each time point based on its axial kinetic velocity.

[0103] Step 305: Averaging the translational kinetic energy of all individual particles at each time point to obtain the experimental translational particle temperature at that time point; Averaging the rotational kinetic energy of all individual particles at each time point to obtain the experimental rotational particle temperature at that time point.

[0104] In one embodiment of the present invention, the relevant parameter settings for the discrete element method are determined according to the particle property parameters calibrated using particle kinetic theory, as shown in Table 1:

[0105] Table 1

[0106]

[0107] Furthermore, the equation of motion for the particles is determined by Newton's second law of motion as follows:

[0108] The equation for particle translation is:

[0109] (11)

[0110] The equation for particle rotation is:

[0111] (12)

[0112] Where: m a Let r be the mass of particle a. a Let I be the position vector of particle a, and ω be the moment of inertia. a Let R be the rotational speed of particle a. a Let n be the radius of particle a. ab Let be the unit normal vector pointing from the centroid of particle a to particle b, defined as:

[0113] (13)

[0114] Interparticle normal force F ab,n Defined as:

[0115] (14)

[0116] Normal damping coefficient of particles for:

[0117] (15)

[0118] Where: k n For the normal spring stiffness coefficient, e n For normal restitution coefficient, m i m j Let be the mass of particles i and j.

[0119] The normal relative velocity u involved in the normal force ab,n The relative velocity u between two particles in contact ab The normal component; the tangential relative velocity u involved in the tangential force. ab,t The relative velocity u between two particles in contact ab The tangential component. The overall relative velocity u between the two contacting particles. ab Defined as:

[0120] (16)

[0121] Therefore, the normal relative velocity u can be determined. ab,n :

[0122] (17)

[0123] Tangential unit relative velocity u ab,t :

[0124] (18)

[0125] δ involved in particle forces ab.n The overlap of normal particle contact:

[0126] (19)

[0127] In the initial calibration of particle properties using kinetic theory, it was assumed that the sliding friction coefficient and static friction coefficient of the particles were the same, thus ensuring the continuity of tangential forces on the particles. Therefore, the tangential contact force F of the particles in the discrete element... ab,t Coulomb's law of friction can be used to close the loop, and its specific form is as follows:

[0128] (20)

[0129] Where: k t For the tangential spring stiffness coefficient, η t For the tangential damping coefficient, μ f For the coefficient of sliding friction, t ab It is a tangential unit vector.

[0130] Tangential damping coefficient of particles :

[0131] (twenty one)

[0132] Where: e t For the tangential restitution coefficient, k t This is the tangential spring stiffness coefficient.

[0133] In this embodiment, the discrete element method can be used to accurately characterize the particle motion and position information within a uniformly cooled coarse particle flow system. Further, by combining the definitions of translational particle temperature T (i.e., translational kinetic energy) and rotational particle temperature R (i.e., rotational kinetic energy) from particle kinetic theory, the time-varying physical quantities (T(t), R(t)) that need to be characterized in the uniformly cooled particle flow system obtained from the underlying high-precision simulation method can be obtained; that is, the experimental translational particle temperature and experimental rotational particle temperature required in this application example. The definitions of the particle temperatures involved are as follows:

[0134] The temperature of the experimentally translated particles is:

[0135] (twenty two)

[0136] The particle pulsation velocity is:

[0137] (twenty three)

[0138] Where: N represents the number of particles in the statistical region, c i Let i represent the translational velocity of particle i. It represents the average solid phase velocity within the statistical region.

[0139] The temperature of the rotating particles in the experiment was:

[0140] (twenty four)

[0141] The moment of inertia I of the spherical particle is:

[0142] (25)

[0143] Therefore, the temperature R of the rotating particle in the experiment is:

[0144] (26)

[0145] Where: ω ij It is the difference between the instantaneous angular velocity and the average angular velocity of the particle.

[0146] In this embodiment, given the geometric dimensions and particle motion distribution of the granular flow system, the relationship between particle acceleration and force is determined using the discrete element method based on Newton's second law of motion. The interaction forces between particles are determined using a linear model, where particle properties such as tangential / normal collision restitution coefficient, sliding friction coefficient, normal / tangential spring elastic coefficient, and damping coefficient are obtained in step 201. Through gradual time regression, the velocity, position, and force of all particles in the system at each moment can be obtained. Based on the governing equations of interest, the size of the statistical region and statistical state variables are determined. Then, the particle information within this region is statistically averaged to obtain the average solid phase information within the specified statistical region, such as average solid concentration, average solid phase velocity, and particle kinetic energy (i.e., particle temperature). This embodiment primarily obtains the experimental translational particle temperature and the experimental pulsating particle temperature, thus completing the step of generating high-precision granular flow system data using a low-level high-precision simulation method.

[0147] In order to utilize expert experience to guide the form of the options in the dictionary matrix, in one embodiment of the present invention, step 102 includes:

[0148] By leveraging expert experience based on statistical mechanics to pre-construct the alternative options in the governing equations, forming a dictionary matrix, and constructing a reasonable regression system form, the specific implementation process is as follows:

[0149] From the form of the translational / rotational energy dissipation source term derived from the particle kinetic theory based on statistical mechanics, it can be seen that, apart from the unsteady-state term of particle temperature changing with time, the translational / rotational governing equations contain... In addition, it only includes energy dissipation source terms. Energy dissipation source terms can be expressed as constant terms or terms related to particle temperature. From this, the form of the dictionary matrix can be determined as follows: The established equilibrium sparse regression method can help filter out terms in the dictionary matrix that appear in the governing equations, which is equivalent to obtaining the target sparse vector. Therefore, the form of a linear regression system can be:

[0150] (27)

[0151] Since only the state variables, experimental translational temperature T and experimental rotating particle temperature R, change with time in this linear regression system, substituting the time information into the above linear regression system will change the unsteady-state term on the left side of the linear regression system. and the dictionary matrix on the right. Partially expanded according to time information, we obtain:

[0152] (28)

[0153] Where: m represents the number of data samples collected during the specific execution process, and n represents the total number of alternatives. In the specific implementation process, this sparse sampling method can be used to further reduce the amount of computation and reduce the complexity of solving the linear regression system.

[0154] In this embodiment, the governing equations involved in the granular flow continuum method, which can be determined by statistical mechanics, consist of unsteady-state terms with partial derivatives in time, and convection and diffusion terms with spatial derivatives. Therefore, the left-hand side of the regression system is the unsteady-state term, which is the time derivative of the state variable. Simultaneously, during the initial modeling process, it was found difficult to determine the form of the spatial derivative of the state variable. Therefore, in this step, the invention first uses granular kinetic theory to determine the possible forms of dissipation source terms, listing each involved term to construct a complete dictionary matrix for the regression system. The right-hand side of the regression system consists of the product of the complete dictionary matrix and sparse vectors that can be used to select alternatives. Then, by substituting the spatiotemporal information of the spatial physical field state variables one by one, the left-hand unsteady-state term and the right-hand dictionary matrix in the above regression system can be expanded sequentially, thus obtaining the core regression system of the equilibrium sparse regression method.

[0155] In one embodiment of the present invention, considering that the different state variables have orders of magnitude differences in size, which directly leads to differences in the elements of each column in the dictionary matrix in step 102, it is necessary to consider introducing an equalization strategy to optimize the dictionary matrix. In one embodiment of the present invention, step 103 includes:

[0156] Divide each column element in the state variable dictionary matrix by the magnitude of that column to obtain a balanced dictionary matrix. The specific implementation scheme is as follows:

[0157] Statistical analysis of the translational / rotational particle temperatures revealed a significant order-of-magnitude difference in the column vectors composed of the candidate options in the dictionary matrix. Specifically, the magnitudes of the column vectors were 100, 2.48e-4, 1.76e-1, 3.94e-7, 2.47e-4, 4.43e-6, and 2.6e-2, respectively. This significant difference in magnitude directly resulted in a completely ill-conditioned matrix in the aforementioned linear regression system, making it impossible to perform target sparse vector analysis. To achieve an accurate solution, the form of column vectors in the normalized dictionary matrix is ​​introduced, thereby developing a balanced sparse regression method. Specifically, the following operations are performed on the above-mentioned linear regression system expanded over time:

[0158] First, the above normalization system can be rewritten in matrix form, which can be represented as a matrix:

[0159] (29)

[0160] The dictionary matrix A can be abstracted into the following form:

[0161] (30)

[0162] After normalizing each column of the dictionary matrix, the new linear regression system form is obtained as follows:

[0163] (31)

[0164] The normalized dictionary matrix form is as follows:

[0165] (32)

[0166] The normalized dictionary matrix can be equated to the aforementioned balanced dictionary matrix. Furthermore, this normalized dictionary matrix B can be further expressed as:

[0167] (33)

[0168] Where, matrix C -1 It can be represented in the following form:

[0169] (34)

[0170] Therefore, the natural matrix C is a diagonal matrix, and its form is as follows:

[0171] (35)

[0172] Therefore, the normalized linear regression system can be rewritten as:

[0173] (36)

[0174] This linear regression system can be solved using the classical sparse regression method (Equation (36)). However, the sparse vector obtained after the above dictionary matrix normalization operation... (That is, the second sparse vector involved in this invention) is not the final sparse vector that measures the terms appearing in the governing equation (that is, the third sparse vector involved in this invention). Furthermore, by comparing the initial form of the dictionary matrix (Equation (30)) with the normalized form of the linear regression system (Equation (32)), the second sparse vector obtained after normalizing the dictionary matrix can be... Further transformation into the final desired target third sparse vector The transformation relationship between the second and third sparse vectors is as follows:

[0175] (37)

[0176] In this embodiment, each column of the dictionary matrix represents a different candidate function (i.e., an option). Because the candidate functions differ in form and the state variables involved, they vary by order of magnitude, resulting in significant differences in the numerical values ​​of the elements in each column of the dictionary matrix. This leads to a strong ill-conditioned nature in the dictionary matrix, making convergence difficult. Therefore, this embodiment proposes dividing each column element of the dictionary matrix by its modulus to ensure balanced column sizes and a modulus of 1, thereby reducing the ill-conditioned nature of the dictionary matrix and facilitating solution.

[0177] Figure 4 This is a schematic diagram of the fourth process of the temperature prediction method for granular flow systems based on interpretable machine learning provided in this embodiment of the invention, as shown below. Figure 4 As shown, to improve the reliability of obtaining the governing equations for the target granular flow system, in one embodiment of the present invention, the dataset includes: a training set and a test set; step 104 includes:

[0178] Step 401: Input the training set into a preset optimization objective function, and use the sequential ridge regression method to iteratively optimize the sparse vector to obtain the learning result. The learning result includes: the first sparse vector when the cutoff value of the optimization objective function is a preset cutoff value and the value of the optimization objective function is minimized.

[0179] Step 402: Apply the learning results to the test set, call the training order ridge regression method, optimize the preset cutoff value, and obtain the optimized cutoff value; determine the second sparse vector based on the optimized cutoff value.

[0180] Step 403: Based on the second sparse vector, select reasonable alternatives from the alternatives of the equalized dictionary matrix.

[0181] Step 404: Based on the linear relationship between the pre-acquired second sparse vector and the third sparse vector, and the inverse linear relationship transformation of the second sparse vector, the third sparse vector is obtained. The third sparse vector is determined as the weight corresponding to the reasonable alternative, and the control equation of the target particle flow system is obtained.

[0182] In one embodiment of the present invention, the core algorithm of the sparse regression method can be introduced based on the form of an equalized dictionary matrix to achieve an accurate solution of the equalized regression system. The specific implementation scheme is as follows:

[0183] Further definition and The above form can be rewritten and simplified as follows:

[0184] (38)

[0185] The sparse vector to be solved by the equalization sparse regression method is The essence of sparse regression is to rank the importance of alternatives by solving for sparse vectors and then select the important terms that must appear in the governing equations. The sparse vectors to be solved... The problem can be represented as the following conditional extremum problem:

[0186] (39)

[0187] The equilibrium sparse regression method is transformed into a relaxed unconditional extremum problem as follows:

[0188] (40)

[0189] in, The coefficients represent the L2 regularization term. Equation (40) can be equivalent to the above optimization objective function; further, the core algorithm of the sparse regression method, the sequential ridge regression algorithm, is used to ensure that the initial learning result is sparse. The specific process is as follows: set the cutoff value for solving the sparse vector. When each element of the sparse vector is less than the cutoff value, it is considered that the candidate corresponding to the element is very small in the whole control equation and can be ignored. Further, the part of the sparse vector whose elements are larger than the cutoff value is retained. It is considered that the candidate corresponding to these elements should appear in the whole control equation. Therefore, these candidate options are retained in the next learning process. Further, regression is performed on these selected candidate options with relatively large weights, and the STRidge algorithm is run many more times until no new candidate functions are selected. The key in the STRidge algorithm in the above iteration process is the setting of the cutoff value of the sparse vector. This cutoff value directly affects which terms should be retained in the control equation.

[0190] The specific method for setting the cutoff value is to use 80% of the samples in the dataset as the training set and 20% as the test set. The results learned by STRidge on the training set are then applied to the 20% test set, and the sequential ridge regression method is called to continuously optimize the arbitrarily selected cutoff value, further improving the reliability of the overall sparse regression method. The results learned by STRidge on the training set can be equivalent to the first sparse vector mentioned above.

[0191] By combining the STRidge and TrainSTRidge algorithms above, the equilibrium regression system can be optimized. The correct solution is obtained from the sparse vector. This determines which candidate options in the dictionary matrix will ultimately appear, completing the mining of the entire governing equation form. To determine the specific weights of these governing equation candidates, the analysis in step 103 needs to be performed. ,get . It can be equivalent to the second sparse vector mentioned above. This can be equivalent to the third sparse vector mentioned above. The second sparse vector determines the terms in the mined governing equations, while the third sparse vector determines the specific weights of each term in the governing equations.

[0192] Thus, under the above operating conditions, the equalization sparse regression method is used to mine the translational / rotational energy dissipation source terms of a uniformly cooled coarse particle flow. In other words, the high-precision equalization sparse regression method is used to successfully mine the governing equations of the uniformly cooled coarse particle flow system. The governing equations of the uniformly cooled coarse particle flow system are equivalent to the governing equations of the target particle flow system mentioned above.

[0193] (41)

[0194] Figure 5 This is a schematic diagram of the fifth step in the temperature prediction method for granular flow systems based on interpretable machine learning provided in this embodiment of the invention. To further verify the rationality and reliability of the governing equations of the target granular flow system, in one embodiment of the invention, as follows... Figure 5 As shown, after step 105, the following steps are also included:

[0195] Step 501: Compare the formal equations of the target particle flow system with the analytical equations derived using particle kinetic theory to determine that the target particle flow system control equations pass the first verification.

[0196] Step 502: Solve the control equations of the target particle flow system and the analytical control equations respectively. Compare the solution results of the control equations of the target particle flow system and the analytical control equations with the translational particle temperature and the rotational particle temperature obtained by statistical averaging of the dataset using the discrete element method, and determine that the control equations of the target particle flow system pass the second verification.

[0197] In one embodiment of the present invention, the rationality of the equalization sparse regression method in learning the form of the governing equation is verified. The specific execution process is as follows: First, the particle properties calibrated using particle kinetic theory in Table 1 are substituted into the specific governing equation form derived from particle kinetic theory:

[0198] (42)

[0199] (43)

[0200] The final form of the temperature equations for translational / rotational particles in this target system is obtained:

[0201] (44)

[0202] Furthermore, by comparing the learning results (Equation (41)) with the control equation results derived from the particle kinetic theory (Equation (44)), it can be found that the equalization sparse regression method successfully identified the energy dissipation source term form and T. 3 / 2 T 1 / 2 R-related.

[0203] In this embodiment, the control equations of the target particle flow system, solved using the equalization sparse regression method, are obtained to yield the temperature variation curves of the first translational particle and the first rotating particle over time. The analytical control equations are then solved to obtain the temperature variation curves of the second translational particle and the second rotating particle over time. The datasets are statistically averaged to obtain the temperature variation curves of the third translational particle and the third rotating particle over time. If the difference between the temperature variation curves of the first and third translational particles over time is less than the difference between the temperature variation curves of the second and third translational particles over time, and the difference between the temperature variation curves of the first and third rotating particles over time is also less than the difference between the temperature variation curves of the second and third rotating particles over time, then the control equations of the target particle flow system pass the second verification.

[0204] Figure 6 This is a schematic diagram comparing the relative errors between the coefficients of the governing equations solved by the equalization sparse regression method and the discrete element method, as exemplified in this invention, and the analytical results of particle kinetic theory. Specifically:

[0205] The relative error between the energy dissipation source term coefficients and the particle kinetic theory coefficients in the uniformly cooled granular flow system mined by the equalization sparse regression method is small, and equation (44) can be equivalent to the analytical control equations derived from particle kinetic theory. However, in the translational control equations, the learning result only appears T. 3 / 2 The reason for this is that T is under this system. 3 / 2 The order of magnitude of the terms is generally in the range of 1e-3, T 1 / 2The order of magnitude of R terms is generally in the range of 1e-10. It can be seen that the two terms in the translational energy dissipation source term are quite different. The sparse regression method can essentially only find terms with relatively large values ​​and importance. Therefore, from the perspective of mining the form of the control equation, the equalization high-precision sparse regression method can mine the translational / rotational particle control equation of the uniformly cooled coarse particle flow system. That is, the control equation of the target particle flow system passes the first verification.

[0206] Figure 7 This is a schematic diagram comparing the particle temperature variation over time obtained by the equalization sparse regression method, the traditional particle kinetic theory method for deriving the control equation numerical solution, and the particle temperature variation over time curve obtained by the discrete element method.

[0207] Specifically, the ordinary differential equations learned by the sparse regression method (Equation (41)) and the ordinary differential equations derived from the particle kinetic theory (Equation (44)) can be directly solved using the Runge-Kutta 45 method. Alternatively, the variation of particle temperature over time within the system obtained by statistical averaging using the discrete element method can be directly plotted. Here, T_Normalized SINDy represents the variation of translational particle temperature over time obtained by solving the ordinary differential equations learned by the sparse regression method, T_KTGF represents the variation of translational particle temperature over time obtained by solving the ordinary differential equations derived from the particle kinetic theory, T_DEM represents the variation of translational particle temperature over time within the system obtained by statistical averaging using the discrete element method, and R_Normalized SINDy represents the temperature variation of rotating particles over time obtained by solving the set of ordinary differential equations learned by the sparse regression method; R_KTGF represents the temperature variation of rotating particles over time obtained by solving the set of ordinary differential equations derived from particle kinetic theory; and R_DEM represents the temperature variation of rotating particles over time within the system obtained by statistical averaging using the discrete element method. Comparing the particle temperatures quantitatively determined by the three methods, it was found that the temperature variation of translational / rotational particles over time described by the learning results is consistent with the underlying high-precision simulation data. That is, the control equation of the target particle flow system passed the second verification, further verifying the effectiveness of the normalized dictionary matrix strategy proposed in this embodiment in mining the control equation of particle flow systems using the sparse regression method.

[0208] Figure 8 This is a logic block diagram of a temperature prediction method for granular flow systems based on interpretable machine learning, as described in an embodiment of the present invention.

[0209] Specifically, in one embodiment of the present invention, sparse sampling can be used to reduce the number of data samples in one example of the present invention. At the same time, the original linear regression system can be transformed into a subsampled linear regression system. Subsampling of data means reducing the number of rows in the dictionary matrix and reducing the learning difficulty. Using the equalization sparse regression method, the columns of the dictionary matrix are normalized to obtain a new linear regression system. The pseudo-sparse vector is calculated using the sequential ridge regression and training sequential ridge regression core algorithm. Then, the real sparse vector is obtained through linear transformation. The particle temperature equation is discovered, and the algorithm and recognition results of the uniformly cooled coarse particle flow system are obtained.

[0210] In this embodiment, the governing equations obtained by the equalization high-precision sparse regression method can be solved numerically or analytically within the target particle flow system to obtain the full flow field system information. This information is then compared with the high-precision full flow field information obtained by the discrete element method in the previous step to verify the reliability of the governing equations mined in this embodiment.

[0211] From a software perspective, to improve the reliability of the governing equations of granular flow systems and thus enhance the accuracy of temperature prediction, this invention provides an embodiment of a temperature prediction system for granular flow systems based on interpretable machine learning, used to implement all or part of the aforementioned temperature prediction method for granular flow systems based on interpretable machine learning. See [link to embodiment]. Figure 9 The temperature prediction system for granular flow systems based on interpretable machine learning specifically includes the following:

[0212] Acquisition module 01 is used to acquire the dataset of the particle flow system, the dataset including: experimental translational particle temperature and experimental rotating particle temperature at multiple time points;

[0213] Forming module 02 is used to form a state variable dictionary matrix based on each alternative in the pre-constructed control equation, wherein the columns of the state variable dictionary matrix represent the alternatives;

[0214] Processing module 03 is used to perform equalization processing on each alternative in the state variable dictionary matrix to obtain an equalized dictionary matrix;

[0215] The filtering module 04 is used to filter out reasonable alternatives and determine their corresponding weights from the balanced dictionary matrix based on the interpretable machine learning method and the dataset, so as to obtain the control equation of the target granular flow system. The interpretable machine learning method specifically refers to the balanced sparse regression method that combines the sequential ridge regression method and the training sequential ridge regression method.

[0216] Prediction module 05 is used to solve the control equations of the target particle flow system to predict the temperature of translational particles and the temperature of rotating particles.

[0217] The embodiments of the temperature prediction system for granular flow systems based on interpretable machine learning provided in this specification can be used to execute the processing flow of the embodiments of the temperature prediction method for granular flow systems based on interpretable machine learning described above. Its functions will not be repeated here, but can be referred to the detailed description of the embodiments of the temperature prediction method for granular flow systems based on interpretable machine learning described above.

[0218] The temperature prediction method and system for granular flow systems based on interpretable machine learning provided in this invention have the following main technical effects:

[0219] 1. Traditional methods for determining the key governing equations and constitutive relations in granular flow systems include granular kinetic theory modeling, direct statistical analysis, and empirical correlation. All three methods rely on certain assumptions, resulting in poor universality and low accuracy in the modeling results. In contrast, the sparse regression method developed in this invention combines high-precision simulation data with expert experience derived from statistical mechanics, using a data-driven and mechanism-based approach to uncover the governing equations and constitutive relations of complex granular flow systems. The overall method exhibits strong universality and relies on virtually no assumptions.

[0220] 2. The classic sparse regression method, without improvement or development, is directly applied to granular flow systems, resulting in a highly ill-conditioned system and an inability to obtain accurate governing equations. The equilibration strategy effectively introduces and develops the sparse regression method, which can effectively control the size of each option in the dictionary matrix, thereby solving the problem of strong ill-conditioned regression systems. The implementation process of the patent example proves that this method can effectively obtain the governing equations of uniformly cooled coarse granular flow, and can be used to mine the governing equations and constitutive relations of complex granular flow systems that are difficult to model.

[0221] 3. When high-precision granular flow simulation data obtained through traditional discrete element method (DIB) simulations are compared with the results of continuous medium modeling based on kinetic theory of particles (KDP) through statistical analysis, the calibration of particle properties is often neglected. This is because the particles used in the traditional DIB simulation are determined by soft sphere models, while the models involved in KDP are hard sphere models, and the interaction models between particles differ significantly. Therefore, without calibrating particle properties using KDP, the two methods will have discrepancies in the initial selection of particle models, leading to unreliable comparison results. Therefore, to improve the accuracy of granular flow system information obtained through traditional DIB simulations, this invention first employs a KDP method suitable for the physical characteristics of the system to calibrate particle properties.

[0222] Figure 10 This is a schematic diagram of the physical structure of an electronic device provided in an embodiment of the present invention, such as... Figure 10As shown, the electronic device includes: a memory 1001, a processor 1002, and a computer program stored in the memory 1001 and executable on the processor 1002. When the processor 1002 executes the computer program, it implements the steps of the above-described temperature prediction method for granular flow systems based on interpretable machine learning.

[0223] This embodiment discloses a computer program product, which includes a computer program that, when executed by a processor, implements the steps of the above-described temperature prediction method for granular flow systems based on interpretable machine learning.

[0224] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described temperature prediction method for granular flow systems based on interpretable machine learning.

[0225] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0226] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0227] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0228] In the description of this specification, the references to terms such as "an embodiment," "a specific embodiment," "some embodiments," "for example," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0229] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for temperature prediction of granular flow systems based on interpretable machine learning, characterized in that, include: Obtain a dataset of the granular flow system, the dataset including: experimental translational particle temperature and experimental rotating particle temperature at multiple time points; Based on the various alternatives in the pre-constructed control equations, a state variable dictionary matrix is ​​formed, wherein the columns of the state variable dictionary matrix represent the alternatives; The alternative options in the state variable dictionary matrix are subjected to equalization processing to obtain an equalized dictionary matrix; Based on the interpretable machine learning method and the dataset, reasonable alternatives are selected from the balanced dictionary matrix and their corresponding weights are determined to obtain the control equations of the target granular flow system. The interpretable machine learning method specifically refers to the balanced sparse regression method that combines the sequential ridge regression method and the training sequential ridge regression method. Solve the governing equations of the target particle flow system to predict the temperatures of translational and rotating particles; The dataset includes: a training set and a test set; The process, based on interpretable machine learning methods and the dataset, involves selecting reasonable alternatives from the balanced dictionary matrix and determining their corresponding weights to obtain the governing equations for the target granular flow system, including: The training set is input into a preset optimization objective function, and the sparse vector is iteratively optimized using the sequential ridge regression method to obtain the learning result. The learning result includes: the first sparse vector when the cutoff value of the optimization objective function is a preset cutoff value and the value of the optimization objective function is minimized. The learning results are applied to the test set, and the training order ridge regression method is called to optimize the preset cutoff value to obtain the optimized cutoff value; based on the optimized cutoff value, the second sparse vector is determined. Based on the second sparse vector, reasonable alternatives are selected from the alternatives of the equalized dictionary matrix; Based on the linear relationship between the pre-obtained second sparse vector and the third sparse vector, and by performing an inverse linear relationship transformation on the second sparse vector, the third sparse vector is obtained. The third sparse vector is then determined as the weight corresponding to the reasonable alternative, thereby obtaining the control equation of the target granular flow system.

2. The temperature prediction method for granular flow systems based on interpretable machine learning according to claim 1, characterized in that, Before acquiring the dataset of the granular flow system, the following is also included: The particle physical property parameters were calibrated using particle kinetic theory.

3. The temperature prediction method for granular flow systems based on interpretable machine learning according to claim 1, characterized in that, Before acquiring the dataset of the granular flow system, the following is also included: The dataset is generated by substituting the particulate property parameters of the granular flow system into the discrete element method.

4. The temperature prediction method for granular flow systems based on interpretable machine learning according to claim 3, characterized in that, The step of substituting the particulate property parameters of the granular flow system into the discrete element method to generate the dataset includes: Substituting the particle properties of the particle flow system into the single-particle motion equation determined by Newton's second law of motion, which is closed by the linear interaction model between particles, in the discrete element method, the single-particle information at each time point in the particle flow system is obtained. The single-particle information includes the translational velocity and rotational velocity of the single particle. The translational velocities of all individual particles at each time point are averaged to generate the average particle translational velocity at that time point; the rotational velocities of all individual particles at each time point are averaged to generate the average particle rotational velocity at that time point. Based on the average particle translational velocity and the translational velocity of a single particle at each time point, the translational velocity of a single particle at that time point is generated; based on the average particle rotational velocity and the rotational velocity of a single particle at each time point, the rotational velocity of a single particle at that time point is generated. Based on the plane pulse velocity of a single particle at each time point, the plane pulse kinetic energy of that single particle at that time point is generated; based on the axial pulse velocity of a single particle at each time point, the axial pulse kinetic energy of that single particle at that time point is generated. The translational kinetic energy of all individual particles at each time point is averaged to obtain the experimental translational particle temperature at that time point; the rotational kinetic energy of all individual particles at each time point is averaged to obtain the experimental rotating particle temperature at that time point.

5. The temperature prediction method for granular flow systems based on interpretable machine learning according to claim 1, characterized in that, The process of equalizing each option in the state variable dictionary matrix to obtain an equalized dictionary matrix includes: Divide each column element in the state variable dictionary matrix by the magnitude of that column to obtain a balanced dictionary matrix.

6. The temperature prediction method for granular flow systems based on interpretable machine learning according to claim 1, characterized in that, Before solving the governing equations of the target particle flow system to predict the temperatures of translational and rotating particles, the method further includes: The control equations of the target particle flow system are compared with the analytical control equations derived using particle kinetic theory, and it is determined that the control equations of the target particle flow system pass the first verification. Solve the control equations and analytical control equations of the target particle flow system respectively. Compare the solution results of the target particle flow system control equations and analytical control equations with the translational particle temperature and rotational particle temperature obtained by statistical averaging of the dataset using the discrete element method. Determine that the control equations of the target particle flow system pass the second verification.

7. A temperature prediction system for granular flow systems based on interpretable machine learning, characterized in that, include: The acquisition module is used to acquire the dataset of the particle flow system, which includes: experimental translational particle temperature and experimental rotating particle temperature at multiple time points; A forming module is used to form a state variable dictionary matrix based on each alternative in a pre-constructed control equation, wherein the columns of the state variable dictionary matrix represent the alternatives; The processing module is used to perform equalization processing on each alternative in the state variable dictionary matrix to obtain an equalized dictionary matrix; The filtering module is used to filter out reasonable alternatives and determine their corresponding weights from the balanced dictionary matrix based on the interpretable machine learning method and the dataset, so as to obtain the control equation of the target granular flow system. The interpretable machine learning method specifically refers to the balanced sparse regression method that combines the sequential ridge regression method and the training sequential ridge regression method. The prediction module is used to solve the control equations of the target particle flow system to predict the temperature of translational particles and the temperature of rotating particles. The dataset includes: a training set and a test set; The process, based on interpretable machine learning methods and the dataset, involves selecting reasonable alternatives from the balanced dictionary matrix and determining their corresponding weights to obtain the governing equations for the target granular flow system, including: The training set is input into a preset optimization objective function, and the sparse vector is iteratively optimized using the sequential ridge regression method to obtain the learning result. The learning result includes: the first sparse vector when the cutoff value of the optimization objective function is a preset cutoff value and the value of the optimization objective function is minimized. The learning results are applied to the test set, and the training order ridge regression method is called to optimize the preset cutoff value to obtain the optimized cutoff value; based on the optimized cutoff value, the second sparse vector is determined. Based on the second sparse vector, reasonable alternatives are selected from the alternatives of the equalized dictionary matrix; Based on the linear relationship between the pre-obtained second sparse vector and the third sparse vector, and by performing an inverse linear relationship transformation on the second sparse vector, the third sparse vector is obtained. The third sparse vector is then determined as the weight corresponding to the reasonable alternative, thereby obtaining the control equation of the target granular flow system.

8. The temperature prediction system for granular flow systems based on interpretable machine learning according to claim 7, characterized in that, Also includes: The generation module is used to substitute the particulate property parameters of the granular flow system into the discrete element method to generate the dataset.

9. A computer-readable medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the temperature prediction method for granular flow systems based on interpretable machine learning as described in any one of claims 1 to 6.

10. An electronic device comprising a memory and a processor, the memory for storing information including program instructions, and the processor for controlling the execution of the program instructions, characterized in that, When the program instructions are loaded and executed by the processor, they implement the temperature prediction method for granular flow systems based on interpretable machine learning as described in any one of claims 1 to 6.

11. A computer program product, comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the temperature prediction method for granular flow systems based on interpretable machine learning as described in any one of claims 1 to 6.

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