Temperature prediction method and system of particle flow system based on interpretable machine learning

Abstract

The invention provides a temperature prediction method and system of a particle flow system based on interpretable machine learning, and relates to the technical field of particle flow system research and application, the method comprises the steps that a data set of the particle flow system is acquired, and the data set comprises experiment translation particle temperatures and experiment rotation particle temperatures at multiple time points; forming a state variable dictionary matrix based on each alternative item in a pre-constructed control equation; performing equalization processing on alternative items in the state variable dictionary matrix to obtain an equalized dictionary matrix; based on an interpretable machine learning method and the data set, screening out reasonable alternative items from the equalized dictionary matrix, determining corresponding weights, and obtaining a target particle flow system control equation; and solving a target particle flow system control equation to predict the translational particle temperature and the rotating particle temperature. The reliability of the control equation of the particle flow system can be improved, and the accuracy of temperature prediction of the particle flow system is further improved.

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] Average the translational velocity of all single particles at each time point to generate the average particle translational velocity at the time point; average the rotational velocity of all single particles at each time point to generate the average particle rotational velocity at the time point;

[0021] Generate the translational fluctuation velocity of a single particle at the time point according to the average particle translational velocity at the time point and the translational velocity of a single particle; generate the rotational fluctuation velocity of a single particle at the time point according to the average particle rotational velocity at the time point and the rotational velocity of a single particle;

[0022] Generate the translational fluctuation energy of a single particle at the time point according to the translational fluctuation velocity of a single particle at the time point; generate the rotational fluctuation energy of a single particle at the time point according to the rotational fluctuation velocity of a single particle at the time point;

[0023] Average the translational fluctuation energy of all single particles at each time point to obtain the experimental translational particle temperature at the time point; average the rotational fluctuation energy of all single particles at each time point to obtain the experimental rotational particle temperature at the time point.

[0024] In an embodiment of the present application, the equalization processing of each alternative in the state variable dictionary matrix to obtain an equalized dictionary matrix comprises:

[0025] Divide each column element in the state variable dictionary matrix by the column length to obtain an equalized dictionary matrix.

[0026] In an embodiment of the present application, the data set comprises: a training set and a test set;

[0027] Based on the interpretable machine learning method and the data set, reasonable alternatives are screened from the equalized dictionary matrix and corresponding weights are determined to obtain a target particle flow system control equation, which comprises:

[0028] The training set is input into a preset optimization objective function, and a sequential ridge regression method is used to iteratively optimize a sparse vector to obtain a learning result, wherein the learning result comprises a first sparse vector with a preset cutoff value of the optimization objective function and a minimum value of the optimization objective function;

[0029] The learning result is used on the test set, a training sequential ridge regression method is called to optimize the preset cutoff value to obtain an optimized cutoff value; and a second sparse vector is determined according to the optimized cutoff value;

[0030] Reasonable alternatives are screened from each alternative in the equalized dictionary matrix according to the second sparse vector.

[0031] According to a linear relationship between a pre-acquired second sparse vector and a third sparse vector and an inverse linear relationship conversion of the second sparse vector, the third sparse vector is obtained, and the third sparse vector is determined as a weight corresponding to the reasonable candidate, so that the target granular flow system control equation is obtained.

[0032] In an embodiment of the present application, before solving the target granular flow system control equation to predict the translational particle temperature and the rotational particle temperature, the method further comprises:

[0033] Formally comparing the target granular flow system control equation with an analytical control equation derived by using the kinetic theory of granular flow, it is determined that the target granular flow system control equation passes the first verification;

[0034] Solving the target granular flow system control equation and the analytical control equation respectively, and comparing the solving results of the target granular flow system control equation and the analytical control equation with the translational particle temperature and the rotational particle temperature statistically averaged from the data set by using the discrete element method, it is determined that the target granular flow system control equation passes the second verification.

[0035] In a second aspect, the present application provides a granular flow system temperature prediction system based on interpretable machine learning, comprising:

[0036] An acquisition module is configured to acquire 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;

[0037] A formation module is configured to form a state variable dictionary matrix based on each candidate in a pre-constructed control equation, wherein a list of the state variable dictionary matrix represents the candidate;

[0038] A processing module is configured to perform equalization processing on each candidate in the state variable dictionary matrix to obtain an equalized dictionary matrix;

[0039] A screening module is configured to screen out reasonable candidates and determine corresponding weights from the equalized dictionary matrix based on an interpretable machine learning method and the data set, so as to obtain a target granular flow system control equation, wherein the interpretable machine learning method specifically refers to an equalized sparse regression method combining a sequential ridge regression method and a training sequential ridge regression method;

[0040] A prediction module is configured to solve the target granular flow system control equation to predict the translational particle temperature and the rotational particle temperature.

[0041] In an embodiment of the present application, the granular flow system temperature prediction system based on interpretable machine learning further comprises:

[0042] a generating module configured to substitute the particle property parameters of the granular flow system into the discrete element method to generate the data set.

[0043] In a third aspect, the present application provides a computer readable medium having stored thereon a computer program which, when executed by a processor, implements the temperature prediction method for granular flow system based on interpretable machine learning.

[0044] In a fourth aspect, the present application provides an electronic device comprising a memory configured to store information including program instructions, and a processor configured to control execution of the program instructions, wherein the program instructions, when loaded and executed by the processor, implement the temperature prediction method for granular flow system based on interpretable machine learning.

[0045] In a fifth aspect, the present application provides a computer program product comprising computer programs / instructions which, when executed by a processor, implement the temperature prediction method for granular flow system based on interpretable machine learning.

[0046] According to the above technical solution, the present application provides a temperature prediction method and system for granular flow system based on interpretable machine learning. The method comprises: obtaining a data set of a granular flow system, the data set comprising: 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, wherein each alternative in the state variable dictionary matrix represents the alternative; 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 data set, screening out reasonable alternatives from the equalized dictionary matrix and determining corresponding weights to obtain a target granular flow system control equation, wherein the interpretable machine learning method specifically refers to an equalized sparse regression method combining a sequential ridge regression method and a training sequential ridge regression method; and solving the target granular flow system control equation to predict translational particle temperatures and rotational particle temperatures. The equalization processing on the state variable dictionary matrix reduces the gap in the number of orders of magnitude of each state variable, realizes the application of a sparse regression method in the construction process of the granular flow system control equation, improves the reliability of the granular flow system control equation, and further improves the accuracy of temperature prediction. According to the above description, the temperature prediction method for granular flow system based on interpretable machine learning provided by the present application can utilize bottom-layer high-precision simulation data to develop an equalized sparse regression method, which can successfully mine the flow control equation set of a uniformly cooled coarse granular flow system. The equalized high-precision sparse regression method proposed by the present application can be one of the interpretable machine learning methods in the future, and is expected to mine complex solid-solid interaction relationships from bottom-layer high-precision simulation data. BRIEF DESCRIPTION OF DRAWINGS

[0047] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative effort based on these drawings.

[0048] Figure 1 is the first flowchart of the temperature prediction method of the granular flow system based on interpretable machine learning in the embodiments of the present application;

[0049] Figure 2 is the second flowchart of the temperature prediction method of the granular flow system based on interpretable machine learning in the embodiments of the present application;

[0050] Figure 3 is the third flowchart of the temperature prediction method of the granular flow system based on interpretable machine learning in the embodiments of the present application;

[0051] Figure 4 is the fourth flowchart of the temperature prediction method of the granular flow system based on interpretable machine learning in the embodiments of the present application;

[0052] Figure 5 is the fifth flowchart of the temperature prediction method of the granular flow system based on interpretable machine learning in the embodiments of the present application;

[0053] Figure 6 is a comparison diagram of the relative error between the coefficients of the control equation solved by the normalized SINDy method and the analytical results of the granular kinetic theory in an example of the present application;

[0054] Figure 7 is a comparison diagram of the change of the particle temperature with time derived by the numerical solution of the control equation by the normalized SINDy method and the traditional granular kinetic theory method and the change of the particle temperature with time by the discrete element method in an example of the present application;

[0055] Figure 8 is a logic diagram of the temperature prediction method of the granular flow system based on interpretable machine learning in the embodiments of the present application;

[0056] Figure 9 is a structure diagram of the temperature prediction system of the granular flow system based on interpretable machine learning in the embodiments of the present application;

[0057] Figure 10 is a system structure schematic diagram of the electronic device in the embodiments of the present application. DETAILED DESCRIPTION

[0058] In the following, the technical solutions in the embodiments of the present application will be described clearly and completely in combination with the accompanying drawings in the embodiments of the present application, so that those skilled in the art can better understand the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by those skilled in the art without creative work should belong to the protection scope of the present application.

[0059] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can adopt a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt a computer program product in the form of being implemented on one or more computer usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer usable program codes.

[0060] It should be noted that the terms “include” and “have” and any variations thereof in the specification and claims of the present application and the above-described accompanying drawings are intended to cover non-exclusive inclusion, for example, a process, a method, a system, a product, or an apparatus including a series of steps or units does not have to be limited to those clearly listed steps or units, but can include other steps or units not clearly listed or inherent to these processes, methods, products, or apparatuses.

[0061] For large-scale industrial particle flow systems, in order to balance the calculation efficiency and the accuracy of the calculation, the current general simulation method is to use the continuous medium simulation method. In the continuous medium model, the particle phase is regarded as a kind of fluid, which is a kind of interpenetrating continuous medium. The mass and momentum conservation relations are described by using the continuous medium control equation, and the particle flow system is solved under the Euler grid, which has high calculation efficiency. Since the solid phase is treated as a pseudo-fluid, compared with the discrete element method which analyzes the motion of each single particle, the overall calculation amount of the solid phase is greatly reduced. However, the momentum equation, the fluctuation energy dissipation equation often involves additional solid phase stress, heat flux and energy dissipation source term, so it is necessary to use additional bottom simulation statistical analysis method, empirical correlation or granular dynamics theory modeling method to close. However, the continuous medium simulation method is often difficult to accurately describe the complex interaction between particles, and cannot accurately construct the constitutive relation, resulting in large calculation error of the numerical simulation method. Therefore, the present application provides a temperature prediction method and system for a particle flow system based on explainable machine learning, which can accurately calibrate the particle property parameters by using the granular dynamics theory, and finely describe the motion state of a single particle by combining the discrete element method. By statistical analysis, the continuous solid phase motion information is obtained, and a reasonable dictionary matrix is formed by combining the expert experience based on statistical mechanics to construct the optional items appearing in the control equation. Considering the order of magnitude gap between the various flow field state variables in the particle flow system, a strategy is proposed to introduce the balance of the various optional items in the dictionary matrix, and a new high-precision balanced sparse regression method is developed. The sequential ridge regression is combined with the trained sequential ridge regression algorithm, so as to select the reasonable items appearing in the control equation from the dictionary matrix composed of optional items, and then realize the mining of the form of the control equation of the complex particle flow system. The present application relates to the development of a sparse regression method for a particle flow system. Taking the uniform cooling of a rough particle flow system as an example, the execution process of the method is introduced in detail, and the feasibility of the method is verified.

[0062] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the drawings and in combination with the embodiments.

[0063] Figure 1 The first flowchart of the temperature prediction method for a particle flow system based on explainable machine learning provided by the embodiments of the present application is shown in the figure. In order to improve the reliability of the particle flow system control equation and thus improve the accuracy of temperature prediction, the present embodiment provides a temperature prediction method for a particle flow system based on explainable machine learning. The execution subject of the method can be a temperature prediction system for a particle flow system based on explainable machine learning, which includes but is not limited to a server, as shown in the figure. The method specifically includes the following contents. Figure 1

[0064] ​Step 101: obtaining a data set of a granular flow system, the data set comprising: experimental translational granular temperature and experimental rotational granular temperature at multiple time points.

[0065] Specifically, the granular flow system can be a uniformly cooled rough granular flow system. The data set can comprise: a batch of samples, each sample comprising: experimental translational granular temperature and experimental rotational granular temperature of the granular flow system, both of which are a time series corresponding to the translational temperature and rotational temperature of the particles at different times, and the data samples available for sampling are the time series of experimental translational granular temperature and experimental rotational granular temperature. In the execution process of the present application, a random sampling method can be used to reduce the amount of data samples used for prediction and reduce the learning difficulty of the interpretable machine learning method. In the subsequent steps, the batch of samples can be divided into a training set and a test set.

[0066] Step 102: forming a state variable dictionary matrix based on each alternative in the pre-constructed control equation, and the list of the state variable dictionary matrix representing the alternatives.

[0067] Step 103: equalizing each alternative in the state variable dictionary matrix to obtain an equalized dictionary matrix.

[0068] Step 104: based on an interpretable machine learning method and the data set, filtering out reasonable alternatives from the equalized dictionary matrix and determining corresponding weights to obtain a target granular flow system control equation, and the interpretable machine learning method specifically refers to an equalized sparse regression method combining a sequential ridge regression method and a training sequential ridge regression method.

[0069] Specifically, the machine learning method provides a breakthrough research paradigm for the mining of fluid mechanics constitutive relations, the determination of control equation forms, due to its complex nonlinear relationship representation ability, multi-scale modeling adaptive optimization ability and dynamic system real-time prediction ability.

[0070] Step 105: solving the target granular flow system control equation to predict the translational granular temperature and the rotational granular temperature.

[0071] Specifically, the time series can be discretized into a sequence of time points to be predicted, and a numerical solution method is used to solve the target granular flow system control equation to predict the translational granular temperature and the rotational granular temperature corresponding to the sequence of time points to be predicted.

[0072] Figure 2is a second flow schematic diagram of the temperature prediction method of the granular flow system based on the interpretable machine learning provided by the embodiment of the present application, in the prior art, the sparse regression method has not been applied to the complex granular flow system, which may be due to the difficulty in determining the real particle properties, resulting in difficulty in generating high-precision simulation data of the real granular flow, based on this, in order to obtain high-precision simulation data, such as Figure 2 As shown in the embodiment of the present application, before step 101, it also includes:

[0073] Step 201: calibrate the particle property parameters by using the granular dynamics theory.

[0074] In the embodiment, the particle property parameters can include: particle size, particle density, Poisson ratio, normal spring stiffness coefficient, tangential spring stiffness coefficient, normal restitution coefficient, tangential restitution coefficient, time step, initial translational particle temperature, rotational particle temperature, solid content, particle number, simulation domain length, simulation time and friction coefficient, etc.

[0075] In an embodiment of the present application, the particle properties can be calibrated by using the granular dynamics theory developed based on statistical mechanics, as follows: uniformly cool the rough granular flow system, which is uniformly distributed with surface rough spherical particles under three periodic boundary conditions, the particle velocity distribution in the system satisfies the Maxwell distribution, and the translational / rotational particle temperature gradually decreases with time evolution due to the non-elastic collision and contact friction between particles, the particles in the system remain uniformly distributed in space within a period of time, that is, the solid content and average velocity in the system are constants, and the evolution law of the flow field characteristics of the system is described by the control equation of the translational / rotational particle temperature with time evolution. Therefore, the present application can determine the control equation of the uniformly cooled rough granular flow system by using the granular dynamics theory developed based on statistical mechanics, that is:

[0076] Translational particle temperature T equation:

[0077] (1)

[0078] Rotational particle temperature R equation:

[0079] (2)

[0080] Wherein, the translational / rotational energy dissipation source terms are respectively denoted as: γ and Γ. When the granular dynamics theory derives the above energy dissipation source terms, it is assumed that the sliding friction coefficient μ is close to 0, the tangential restitution coefficient and the normal restitution coefficient The recovery coefficient close to 1, the particle temperature caused by the fluctuation energy of the inelastic collision is also consumed, and the friction coefficient marks the fluctuation energy dissipation caused by the constant interaction between particles, and the energy dissipation in the system is less, so it is assumed that the friction coefficient is also a small value. The core constitutive relation involved in the translational / rotational particle energy conservation equation of the homogeneous cooling rough particle flow system determined in this way is in the form of:

[0081] The translational energy dissipation rate γ:

[0082] (3)

[0083] The rotational energy dissipation rate Γ:

[0084] (4)

[0085] (5)

[0086] Where: g o is the radial pair correlation function, ɛ s is the solid volume fraction, e n is the particle normal restitution coefficient, d p is the particle diameter, is the density.

[0087] (6)

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

[0089] (7)

[0090] (8)

[0091] (9)

[0092] (10)

[0093] Where: μ0 is the critical friction coefficient, which is related to the judgment condition of dynamic friction or static friction between particles, μ is the sliding friction coefficient, and the critical friction coefficient is assumed to be equal to the sliding friction coefficient in the kinetic theory of particles .

[0094] Combined with the derivation process and assumptions of the above kinetic theory of particles, the calibration of particle physical parameters can be further realized, as follows: the sliding friction coefficient μ is close to 0, the tangential restitution coefficient e t , the normal restitution coefficient e nApproaching 1, the sliding friction coefficient μ is set to 0.001, and the tangential recovery coefficient is equal to the normal recovery coefficient e t = e n = 0.95. The particle property settings in the above discrete element method can directly ensure that the energy loss in the overall system is small, and the energy dissipation is concentrated in the normal direction, which is consistent with the particle properties in the kinetic theory of granular flow. Therefore, the rationality of the high-precision data generation of the bottom layer can be further ensured, and since the data is the core of the equalization sparse regression method, by accurately calibrating the particle property parameters, the accuracy of the learning process can be further ensured through the high-precision discrete element simulation method in the subsequent steps.

[0095] In this embodiment, the reasonable kinetic theory of granular flow can be first determined for the particle flow system to preliminarily depict the constitutive relation in the control equation, wherein the reasonable kinetic theory of granular flow contains related assumptions about particle properties, so these assumptions are followed when simulating the particle flow system by the discrete element method; and thus the particle property parameters involved in the discrete element method based on the soft sphere model are determined, such as the normal / tangential recovery coefficients e n / e t , the sliding friction coefficient μ, the normal elastic coefficients k n and the tangential elastic coefficients k t involved in the contact force model between particles, the normal / tangential damping coefficients γ n / γ t , etc.

[0096] In order to improve the reliability of obtaining the data set, in an embodiment of the present application, as shown in Figure 2 , before step 101, it further includes:

[0097] Step 202: substituting the particle property parameters of the particle flow system into the discrete element method to generate the data set.

[0098] Figure 3 is a third flow diagram of the temperature prediction method for the particle flow system based on the interpretable machine learning provided by the embodiment of the present application, as shown in Figure 3 , in order to improve the reliability of obtaining the experimental translational particle temperature and the experimental rotational particle temperature, in an embodiment of the present application, step 301 includes:

[0099] Step 301: substituting the particle property parameters of the particle flow system into the single particle motion equation determined by the linear interaction model between particles in the discrete element method to obtain the single particle information of each of the time points in the particle flow system, the single particle information including the translational velocity and the rotational velocity of the single particle.

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

[0101] Step 303: generate the translational fluctuation velocity of single particles at each time point according to the average particle translational velocity at the time point and the translational velocity of single particles; generate the rotational fluctuation velocity of single particles at each time point according to the average particle rotational velocity at the time point and the rotational velocity of single particles.

[0102] Step 304: generate the translational fluctuation energy of single particles at each time point according to the translational fluctuation velocity of single particles at the time point; generate the rotational fluctuation energy of single particles at each time point according to the rotational fluctuation velocity of single particles at the time point.

[0103] Step 305: average the translational fluctuation energy of all single particles at each time point to obtain the experimental translational particle temperature at the time point; average the rotational fluctuation energy of all single particles at each time point to obtain the experimental rotational particle temperature at the time point.

[0104] In an embodiment of the present application, the particle property parameters determined by the particle dynamics theory calibration are used to determine the discrete element method related parameter settings as shown in Table 1:

[0105] Table 1

[0106]

[0107] Further, the particle motion equation is determined by Newton's second law of motion as follows:

[0108] The particle translational equation is:

[0109] (11)

[0110] The particle rotational equation is:

[0111] (12)

[0112] Wherein: m a is the mass of particle a, r a is the position vector of particle a, I is the moment of inertia, ω a is the rotational velocity of particle a, R a is the radius of particle a, n ab is the normal unit vector of the centroid of particle a pointing to particle b, which is defined as:

[0113] (13)

[0114] Normal force between particles F ab,n is defined as:

[0115] (14)

[0116] Normal damping coefficient of particles is:

[0117] (15)

[0118] where: k n is normal spring stiffness coefficient, e n is normal restitution coefficient, m i , m j is the mass of particle i, j.

[0119] Normal relative velocity u ab,n involved in normal force is the normal component of relative velocity u ab between two particles in contact; Tangential relative velocity u ab,t involved in tangential force is the tangential component of relative velocity u ab between two particles in contact. Where the overall relative velocity u ab between two particles in contact is defined as:

[0120] (16)

[0121] Then the normal unit relative velocity u ab,n :

[0122] (17)

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

[0124] (18)

[0125] δ ab.n involved in particle force is the overlap of normal particle contact:

[0126] (19)

[0127] In the early dynamic theory calibration of particle properties, it is assumed that the sliding friction coefficient of the particle is the same as the static friction coefficient, which can ensure the continuity of the tangential force of the particle. Therefore, the tangential contact force F ab,t of the particle in the discrete element can be closed using the Coulomb friction law, which is specifically:

[0128] (20)

[0129] where: k t is the tangential spring stiffness coefficient, η t is the tangential damping coefficient, μ f is the sliding friction coefficient, t ab is the tangential unit vector.

[0130] Tangential damping coefficient of the particle :

[0131] (21)

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

[0133] In this embodiment, the discrete element method can be used to accurately depict the motion and position information of the particles in the uniform cooling rough particle flow system. Further combining the definition of the translational particle temperature T (i.e., translational kinetic energy) and the rotational particle temperature R (i.e., rotational kinetic energy) according to the kinetic theory of particles, the information of the physical quantities (T(t), R(t)) varying with time in the uniform cooling particle flow system obtained from the bottom-layer high-precision simulation method can be obtained, i.e., the experimental translational particle temperature and the experimental rotational particle temperature required in this application example. The definition of the particle temperature involved is as follows:

[0134] The experimental translational particle temperature is:

[0135] (22)

[0136] The particle fluctuation velocity is:

[0137] (23)

[0138] where: N represents the number of particles in the statistical region, c i represents the translational velocity of the particle i, represents the average solid phase velocity in the statistical region.

[0139] The experimental rotational particle temperature is:

[0140] (24)

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

[0142] (25)

[0143] Therefore, the experimental rotational particle temperature R is:

[0144] (26)

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

[0146] In this embodiment, after the geometric size of the particle flow system and the particle motion state distribution are given, the relationship between the particle acceleration and the force can be determined by using the discrete element method based on Newton's second law of motion, wherein the inter-particle interaction force is determined by a linear model, wherein the particle properties involved in the linear model, such as the tangential / normal collision restitution coefficient, the sliding friction coefficient, the normal / tangential spring elastic coefficient, the damping coefficient, etc. are obtained by step 201. Through gradual deduction of time, the speed, position, force and other related information of all particles in the system at each time can be obtained. According to the control equation itself, the size of the statistical region and the statistical state variable are determined, and then the particle information in the region is statistically averaged to obtain the average information of the solid phase in the specified statistical region, such as the average solid concentration, the average solid phase velocity, the particle fluctuation energy, i.e. the particle temperature, etc. In this embodiment, the experimental translational particle temperature and the experimental fluctuation particle temperature are obtained, thereby completing the step of generating high-precision particle flow system data using the underlying high-precision simulation method.

[0147] In order to use expert experience to guide the form of the alternative in the dictionary matrix, in an embodiment of the present application, step 102 comprises:

[0148] Using expert experience based on statistical mechanics to guide the pre-constructed options in the control equation, forming a dictionary matrix, and constituting 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 based on the kinetic theory of granular flow, it can be seen that, in the translational / rotational control equation, in addition to the non-steady term of the particle temperature changing with time, only the term is included. The energy dissipation source term can be expressed in the form of a constant term, a term related to the particle temperature, and thus the form of the dictionary matrix can be determined as The established equalization sparse regression method can help to screen out the terms in the dictionary matrix that appear in the control equation, which is equivalent to the target sparse vector that is expected to be obtained. Therefore, the form of the linear regression system can be:

[0150] (27)

[0151] Since in this linear regression system, only the experimental translational temperature T and the experimental rotational particle temperature R change with time, the time information is substituted into the above linear regression system, and the left non-steady term and right end dictionary matrix Part of the expansion according to the time information, get:

[0152] (28)

[0153] Where: m represents the number of sample data samples in the specific implementation process, n represents the total number of options, in the specific implementation process, this sparse sampling method can be used to further reduce the calculation amount and reduce the complexity of solving the linear regression system.

[0154] In this embodiment, the control equation involved in the statistical mechanics determined particle flow continuum medium method is the non-steady term with respect to the partial derivative of time, and the convection term and diffusion term with respect to the spatial derivative. Therefore, the left end term of the regression system is the non-steady term of the time derivative of the state variable; At the same time, it is found in the previous modeling process that it is difficult to determine the form of the spatial derivative term of the state variable, so in this step, the invention first determines the possible dissipation source term form by using the kinetic theory of particles, and then lists the terms involved one by one, and then constructs the complete dictionary matrix in the regression system. The right end term of the regression system will be composed of the product of the complete dictionary matrix and the sparse vector that can be used to screen the options. Then the space-time information of the spatial physical field state variable is substituted one by one, that is, the left non-steady term and the right end dictionary matrix part of the above regression system are expanded in turn, and the core regression system of the equalization sparse regression method can be obtained.

[0155] In an embodiment of the present application, considering that there is a difference in order of magnitude between different state variables, which directly leads to the difference between the elements of each column in the dictionary matrix in step 102, therefore, it is necessary to consider introducing an equalization strategy to optimize the dictionary matrix. In an embodiment of the present application, step 103 comprises:

[0156] Divide each column element in the state variable dictionary matrix by the column length to obtain an equalized dictionary matrix, and the specific implementation scheme is as follows:

[0157] After statistics of the translational / rotational particle temperature of the system, it is found that there is a difference in order of magnitude between the column vectors composed of each option in the dictionary matrix, and the module length of each column vector in the dictionary matrix is 100, 2.48e-4, 1.76e-1, 3.94e-7, 2.47e-4, 4.43e-6, 2.6e-2. The difference in order of magnitude of these column elements directly leads to the involvement of a completely ill-conditioned matrix in the above linear regression system, which makes it impossible to accurately solve the target sparse vector . Therefore, the form of normalizing each column vector in the dictionary matrix is introduced, and thus the equalization sparse regression method is developed. Specifically, the following operations are performed on the linear regression system expanded according to the time:

[0158] Firstly, the above normalization system is rewritten in the form of matrix, which can be expressed in matrix form as follows:

[0159] (29)

[0160] The dictionary matrix A can be abstracted as follows:

[0161] (30)

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

[0163] (31)

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

[0165] (32)

[0166] The normalized dictionary matrix can be equivalent to the above-mentioned equalized dictionary matrix. Meanwhile, the normalized dictionary matrix B can be further expressed as:

[0167] (33)

[0168] In which, the matrix C -1 can be expressed in the form as follows:

[0169] (34)

[0170] Then, the natural matrix C is a diagonal matrix, which is in the form as follows:

[0171] (35)

[0172] Thus, the normalized linear regression system is rewritten as:

[0173] (36)

[0174] The linear regression system (equation (36)) can be solved by using the classical sparse regression method. However, the sparse vector obtained by the above normalization operation of the dictionary matrix (i.e., the second sparse vector involved in the present application) is not the sparse vector (i.e., the third sparse vector involved in the present application) which appears in the final balance control equation. Further, by comparing the initial form of the dictionary matrix (equation (30)) with the form of the linear regression system after normalization (equation (32)), the second sparse vector obtained by the normalization of the dictionary matrix can be further transformed into the final target third sparse vector The conversion relationship between the second sparse vector and the third sparse vector is as follows:

[0175] (37)

[0176] In the embodiment, the elements in each column of the dictionary matrix represent different alternative functions (i.e., alternatives), and there are differences in the number of orders of the alternative functions due to the differences in the forms of the alternative functions and the state variables involved, which leads to large differences in the numerical values of the elements in each column of the dictionary matrix, and further leads to strong ill-conditioning of the dictionary matrix, which is difficult to converge and calculate. Therefore, the embodiment proposes that each column element in the dictionary matrix can be divided by its module length, so that the sizes of each column in the dictionary matrix are balanced, the module length is 1, the ill-conditioning of the dictionary matrix is reduced, and the solution is facilitated.

[0177] Figure 4 is the fourth flow diagram of the temperature prediction method of the granular flow system based on the interpretable machine learning provided by the embodiment of the application, as shown in Figure 4 In order to improve the reliability of obtaining the target granular flow system control equation, in an embodiment of the application, the data set includes: a training set and a test set; and step 104 includes:

[0178] Step 401: inputting the training set into a preset optimization objective function, and using a sequential ridge regression method to iteratively optimize a sparse vector to obtain a learning result, the learning result including a first sparse vector with a preset cutoff value of the optimization objective function and a minimum value of the optimization objective function.

[0179] Step 402: using the learning result on the test set, calling a training sequential ridge regression method, optimizing the preset cutoff value to obtain an optimized cutoff value; and determining a second sparse vector according to the optimized cutoff value.

[0180] Step 403: screening reasonable alternatives from each alternative of the balanced dictionary matrix according to the second sparse vector.

[0181] Step 404: obtaining a third sparse vector according to a linear relationship between the second sparse vector and the third sparse vector and inverse linear relationship conversion of the second sparse vector, determining the third sparse vector as a weight corresponding to the reasonable alternative, and obtaining the target granular flow system control equation.

[0182] In an embodiment of the application, the balanced dictionary matrix form can be introduced into the core algorithm of the sparse regression method to realize accurate solution of the balanced regression system, and the specific implementation scheme is as follows:

[0183] Further defined And The above form is rewritten and simplified as:

[0184] (38)

[0185] The sparse vector to be solved in the equalized sparse regression method is The essence of the sparse regression method is to sort the importance of the candidate items by solving the sparse vector, and to filter out the important items that must appear in the control equation. Then the problem of solving the sparse vector can be expressed as the following conditional extreme value problem:

[0186] (39)

[0187] The equalized sparse regression method is converted into a relaxed unconditional extreme value problem as follows:

[0188] (40)

[0189] wherein represents the regularization term coefficient of the two-norm. 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 preliminary learning result is sparse. The specific process is as follows: set the truncation value of the sparse vector to be solved, when each element of the sparse vector is less than the truncation value, it is considered that the candidate item corresponding to the element is very small and can be ignored in the entire control equation; further, the elements in the sparse vector that are greater than the truncation value are reserved, and it is considered that the candidate items corresponding to these elements should appear in the entire control equation, so these candidate items are retained in the next learning process. Further, regression is performed on these selected candidate items with a large weight proportion, and the STRidge algorithm is continuously run multiple times until no new candidate function is selected. The key of STRidge in the above iteration process is the setting of the truncation value of the sparse vector, which directly affects the determination of which items should be finally retained in the control equation.

[0190] The specific method of setting the truncation value is to use 80% of the samples in the data set as the training set and 20% of the samples in the data set as the test set. Further, the result of STRidge learning on the training set is used in the 20% test set, and the TrainSTRidge method is called to continuously optimize the arbitrarily selected truncation value in the early stage, and further improve the reliability of the overall sparse regression method. The result of STRidge learning on the training set can be equivalent to the above first sparse vector.

[0191] By combining the above STRidge and TrainSTRidge algorithms, the correct solution of the equalized regression system can be realized, and the sparse vector It can be determined which options in the dictionary matrix finally appear, and the whole control equation form is completed. In order to determine the weight of the options in the control equation, the process analyzed in step 103 needs to be continued , and . It can be equivalent to the second sparse vector described above. It can be equivalent to the third sparse vector described above. The second sparse vector determines the term in the control equation, and the third sparse vector determines the specific weight of each term in the control equation.

[0192] Therefore, in the above working conditions, the balanced sparse regression method is realized for the form of the uniform cooling rough particle flow planar / rotational energy dissipation source term, that is, the balanced sparse regression method is successfully used to mine the control equation of the uniform cooling rough particle flow system, and the control equation of the uniform cooling rough particle flow system can be equivalent to the target particle flow system control equation:

[0193] (41)

[0194] Figure 5 is the fifth flowchart of the temperature prediction method of the particle flow system based on the interpretable machine learning provided by the embodiment of the present application. In order to further verify the rationality and reliability of the target particle flow system control equation, in an embodiment of the present application, as shown in Figure 5 , after step 105, it further includes:

[0195] Step 501: comparing the target particle flow system control equation with the analytical control equation derived by the kinetic theory of granular, and determining that the target particle flow system control equation passes the first verification.

[0196] Step 502: respectively solving the target particle flow system control equation and the analytical control equation, and comparing the solving results of the target particle flow system control equation and the analytical control equation with the translational particle temperature and the rotational particle temperature statistically averaged by the discrete element method, and determining that the target particle flow system control equation passes the second verification.

[0197] In an embodiment of the present application, the rationality of the balanced sparse regression method learning the control equation form is verified, and the specific execution process is as follows: first, the particle properties calibrated by the kinetic theory of granular in Table 1 are substituted into the control equation form derived by the kinetic theory of granular:

[0198] (42)

[0199] (43)

[0200] The final form of the translational / rotational particle temperature equation under this target system is obtained:

[0201] (44)

[0202] Further, comparing the learning result (formula (41)) with the control equation result (formula (44)) derived by the granular dynamics theory, it can be found that the equalization sparse regression method successfully identifies the form of the energy dissipation source term and T 3 / 2 , T 1 / 2 R are related.

[0203] In this embodiment, the target granular flow system control equation solved by the equalization sparse regression method can be solved to obtain the first translational particle temperature curve changing with time and the first rotational particle temperature curve changing with time; the analytical control equation is solved to obtain the second translational particle temperature curve changing with time and the second rotational particle temperature curve changing with time; the data set is statistically averaged to obtain the third translational particle temperature curve changing with time and the third rotational particle temperature curve changing with time; if the difference between the first translational particle temperature curve changing with time and the third translational particle temperature curve changing with time is less than the difference between the second translational particle temperature curve changing with time and the third translational particle temperature curve changing with time, and the difference between the first rotational particle temperature curve changing with time and the third rotational particle temperature curve changing with time is less than the difference between the second rotational particle temperature curve changing with time and the third rotational particle temperature curve changing with time, it can be determined that the target granular flow system control equation passes the second verification.

[0204] Figure 6 is a comparison diagram of the relative error between the coefficients of the control equation solved by the equalization sparse regression method and the discrete element method in an example of the present application and the analytical results of the granular dynamics theory. Specifically:

[0205] The relative error between the energy dissipation source term coefficients mined by the equalization sparse regression method in the uniform cooling granular flow system and the coefficients of the granular dynamics theory is small, and formula (44) can be equivalent to the analytical control equation derived by the granular dynamics theory. However, in the translational control equation, the learning result only appears T 3 / 2 term, and the reason is that the order of magnitude of the T 3 / 2 term is generally 1e-3, and the order of magnitude of the T 1 / 2 R term is generally 1e-10. It can be seen that the two terms in the translational energy dissipation source term differ greatly, and the sparse regression method can only find the term with relatively large value in essence. 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 uniform cooling coarse granular flow system, that is, the target granular flow system control equation passes the first verification.

[0206] Figure 7 is a comparison diagram of the particle temperature change with time obtained by numerical solving of the control equation derived by the traditional granular dynamics theory method and the particle temperature change with time curve obtained by the discrete element method in an example of the equalization sparse regression method of the present application.

[0207] Specifically, the Runge-Kutta 45 method can be used to directly solve the ordinary differential equation set (formula (41)) learned by the sparse regression method and the ordinary differential equation set (formula (44)) derived by the granular dynamics theory, and the law of the change of the particle temperature with time in the system obtained by statistical averaging of the discrete element method can also be directly drawn, wherein T_Normalized SINDy represents the translational particle temperature change with time law obtained by solving the ordinary differential equation set learned by the sparse regression method, T_KTGF represents the translational particle temperature change with time law obtained by solving the ordinary differential equation set derived by the granular dynamics theory, T_DEM represents the translational particle temperature change with time law in the system obtained by statistical averaging of the discrete element method, R_Normalized SINDy represents the rotational particle temperature change with time law obtained by solving the ordinary differential equation set learned by the sparse regression method, R_KTGF represents the rotational particle temperature change with time law obtained by solving the ordinary differential equation set derived by the granular dynamics theory, and R_DEM represents the rotational particle temperature change with time law in the system obtained by statistical averaging of the discrete element method. The particle temperatures quantitatively determined by the three methods are compared, and it is found that the laws of the translational / rotational particle temperature change with time described by the learning results are consistent with the underlying high-precision simulation data, that is, the control equation of the target granular flow system is verified through the second verification, and the effectiveness of the normalized dictionary matrix strategy proposed in the embodiment in mining the control equation of the granular flow system by the sparse regression method is further verified.

[0208] Figure 8 is a logic block diagram of the temperature prediction method of the granular flow system based on the interpretable machine learning in the embodiment of the present application.

[0209] Specifically, in an embodiment of the present application, the sparse sampling method can be used to reduce the number of data samples in an example of the present application, and the original linear regression system can be converted into a subsampling linear regression system. The subsampling of data means reducing the number of rows of the dictionary matrix and reducing the learning difficulty. The equalization sparse regression method is used to normalize each column of the dictionary matrix to obtain a new linear regression system. The sequential ridge regression and the training sequential ridge regression core algorithm are used to calculate the pseudo-sparse vector, and the real sparse vector is obtained through linear transformation. The particle temperature equation is found, and the algorithm and identification result of the uniform cooling rough granular flow system are obtained.

[0210] In the embodiment, the control equation form obtained by the balanced high-precision sparse regression method in the target particle flow system can be solved by a numerical or analytical method to obtain the full flow field system information, and further compared with the high-precision full flow field information obtained by the discrete element method in the early stage to verify the reliability of the control equation mined in the embodiment.

[0211] In order to improve the reliability of the particle flow system control equation and further improve the accuracy of temperature prediction from the software level, the embodiment of the temperature prediction system of the particle flow system based on the interpretable machine learning for implementing all or part of the contents of the temperature prediction method of the particle flow system based on the interpretable machine learning is provided, which is described with reference to Figure 9 , and the temperature prediction system of the particle flow system based on the interpretable machine learning specifically includes the following contents:

[0212] The acquisition module 01 is used to acquire the data set of the particle flow system, and the data set includes the experimental translational particle temperature and the experimental rotational particle temperature at multiple time points.

[0213] The forming module 02 is used to form a state variable dictionary matrix based on each alternative in the pre-constructed control equation, and the list of the state variable dictionary matrix represents the alternative.

[0214] The processing module 03 is used to perform balanced processing on each alternative in the state variable dictionary matrix to obtain a balanced dictionary matrix.

[0215] The screening module 04 is used to screen out reasonable alternatives and determine corresponding weights from the balanced dictionary matrix based on an interpretable machine learning method and the data set to obtain a target particle flow system control equation, and the interpretable machine learning method specifically refers to a balanced sparse regression method combining a sequential ridge regression method and a training sequential ridge regression method.

[0216] The prediction module 05 is used to solve the target particle flow system control equation to predict the translational particle temperature and the rotational particle temperature.

[0217] The embodiment of the temperature prediction system of the particle flow system based on the interpretable machine learning provided in the specification can be specifically used to execute the processing flow of the above-mentioned embodiment of the temperature prediction method of the particle flow system based on the interpretable machine learning, and the functions thereof will not be described here again, and can be referred to the detailed description of the above-mentioned embodiment of the temperature prediction method of the particle flow system based on the interpretable machine learning.

[0218] The temperature prediction method and system of the particle flow system based on the interpretable machine learning provided in the embodiment mainly have the following 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 10 As 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] The embodiment provides a computer readable storage medium, the computer readable storage medium stores a computer program, and the computer program is executed by a processor to implement steps of the temperature prediction method of the granular flow system based on the interpretable machine learning.

[0225] The present application is described with reference to flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and combinations of flows and / or blocks in the flowcharts 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, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing apparatus generate a means for implementing the functions specified in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 means for performing the functions specified in the flowchart or flows and / or blocks.

[0226] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to work in a specific manner, so that the instructions stored in the computer readable memory produce a product including instruction means, which implement the functions specified in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 means for performing the functions specified in the flowchart or flows and / or blocks.

[0227] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus, so that a series of operation steps are performed on the computer or other programmable data processing apparatus to produce a computer implemented process, so that the instructions executed on the computer or other programmable data processing apparatus provide a means for implementing the functions specified in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 means for performing the functions specified in the flowchart or flows and / or blocks.

[0228] In the description of the present specification, the description of the terms "one embodiment", "one specific embodiment", "some embodiments", "for example", "exemplary", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0229] The above-described specific embodiments further illustrate the purpose, technical solutions and beneficial effects of the present application. It should be understood that the above-described specific embodiments are merely examples of the present application and are not intended to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A temperature prediction method of a granular flow system based on interpretable machine learning, characterized by, The method comprises the following steps: obtaining a data set of a granular flow system, the data set comprising: experimental translational particle temperature and experimental rotational particle temperature at multiple time points; forming a state variable dictionary matrix based on each alternative in a pre-constructed control equation, wherein a list of the state variable dictionary matrix represents the alternatives; balancing each alternative in the state variable dictionary matrix to obtain a balanced dictionary matrix; screening reasonable alternatives from the balanced dictionary matrix and determining corresponding weights 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 a balanced sparse regression method combining a sequential ridge regression method and a training sequential ridge regression method; solving the target granular flow system control equation to predict translational particle temperature and rotational particle temperature.

2. The temperature prediction method of a granular flow system based on interpretable machine learning according to claim 1, characterized in that, Before the step of obtaining the data set of the granular flow system, the method further comprises the following step: calibrating particle property parameters by using kinetic theory of granular flow.

3. The temperature prediction method of a granular flow system based on interpretable machine learning according to claim 1, characterized in that, Before the step of obtaining the data set of the granular flow system, the method further comprises the following step: substituting particle property parameters of the granular flow system into a discrete element method to generate the data set.

4. The temperature prediction method of a granular flow system based on interpretable machine learning according to claim 3, characterized in that, The step of substituting particle property parameters of the granular flow system into the discrete element method to generate the data set comprises the following steps: substituting the particle 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; averaging translational velocities of all single particles at each time point to generate average particle translational velocity at the time point; and averaging rotational velocities of all single particles at each time point to generate average particle rotational velocity at the time point; generating translational fluctuation velocity of a single particle at each time point according to the average particle translational velocity and the translational velocity of the single particle at the time point; and generating rotational fluctuation velocity of a single particle at each time point according to the average particle rotational velocity and the rotational velocity of the single particle at the time point; generating translational fluctuation energy of a single particle at each time point according to the translational fluctuation velocity of the single particle at the time point; and generating rotational fluctuation energy of a single particle at each time point according to the rotational fluctuation velocity of the single particle at the time point; averaging translational fluctuation energies of all single particles at each time point to obtain the experimental translational particle temperature at the time point; and averaging rotational fluctuation energies of all single particles at each time point to obtain the experimental rotational particle temperature at the time point.

5. The temperature prediction method of a granular flow system based on interpretable machine learning according to claim 1, wherein, The step of balancing each alternative in the state variable dictionary matrix to obtain a balanced dictionary matrix comprises the following step: dividing each column in the state variable dictionary matrix by the length of the column to obtain a balanced dictionary matrix.

6. The temperature prediction method of a granular flow system based on interpretable machine learning according to claim 1, wherein, The data set comprises a training set and a test set. The reasonable options are screened from the balanced dictionary matrix based on the interpretable machine learning method and the data set, and corresponding weights are determined to obtain a target granular flow system control equation, including: The training set is input into a preset optimization objective function, and a sequential ridge regression method is used to iteratively optimize a sparse vector to obtain a learning result, the learning result including a first sparse vector when a cutoff value of the optimization objective function is a preset cutoff value and a value of the optimization objective function is a minimum value; The learning result is used on the test set, a training sequential ridge regression method is called, the preset cutoff value is optimized to obtain an optimized cutoff value, and a second sparse vector is determined according to the optimized cutoff value; Reasonable options are screened from each option of the balanced dictionary matrix according to the second sparse vector; A third sparse vector is obtained by performing inverse linear relationship conversion on the second sparse vector according to a linear relationship between the second sparse vector and the third sparse vector and the second sparse vector, the third sparse vector is determined as the weight corresponding to the reasonable options, and the target granular flow system control equation is obtained.

7. The temperature prediction method of a granular flow system based on interpretable machine learning according to claim 1, characterized in that, Before solving the target granular flow system control equation to predict translational particle temperature and rotational particle temperature, the following steps are further included: The target granular flow system control equation is compared in form with an analytical control equation derived using granular dynamics theory to determine that the target granular flow system control equation passes a first verification; The target granular flow system control equation and the analytical control equation are respectively solved, and the respective solving results of the target granular flow system control equation and the analytical control equation are respectively compared with translational particle temperature and rotational particle temperature statistically averaged from the data set using a discrete element method to determine that the target granular flow system control equation passes a second verification.

8. A temperature prediction system for a granular flow system based on interpretable machine learning, characterized by, The following are included: An acquisition module is configured to acquire a data set of a granular flow system, the data set including experimental translational particle temperature and experimental rotational particle temperature at multiple time points; A formation module is configured to form a state variable dictionary matrix based on each option in a pre-constructed control equation, a list of the state variable dictionary matrix representing the options; A processing module is configured to perform balancing processing on each option in the state variable dictionary matrix to obtain a balanced dictionary matrix; A screening module is configured to screen reasonable options from the balanced dictionary matrix based on an interpretable machine learning method and the data set, and determine corresponding weights to obtain a target granular flow system control equation, the interpretable machine learning method being specifically a balanced sparse regression method combining a sequential ridge regression method and a training sequential ridge regression method; A prediction module is configured to solve the target granular flow system control equation to predict translational particle temperature and rotational particle temperature.

9. The interpretable machine learning-based temperature prediction system for a granular flow system of claim 8, wherein, The following are further included: A generation module is configured to substitute particle physical property parameters of a granular flow system into a discrete element method to generate the data set.

10. A computer readable medium having stored thereon a computer program, characterized in that, The program is executed by a processor to implement the temperature prediction method of the granular flow system based on the interpretable machine learning according to any one of claims 1 to 7.

11. An electronic device comprising a memory for storing information including program instructions, and a processor for controlling execution of the program instructions, characterized in that, The program instructions, when loaded and executed by a processor, implement the temperature prediction method for a granular flow system based on interpretable machine learning according to any one of claims 1 to 7.

12. A computer program product comprising computer programs / instructions, characterized in that, The computer program / instructions, when executed by a processor, implement the temperature prediction method for a granular flow system based on interpretable machine learning according to any one of claims 1 to 7.

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