Multi-grading particle compaction porosity prediction method based on numerical simulation and deep neural network

Abstract

The invention discloses a multi-grading particle compaction porosity prediction method based on numerical simulation and a deep neural network, and relates to the technical field of civil engineering, and the method comprises the steps: constructing a multi-grading particle numerical model, simulating a particle compaction process, and obtaining a group of grading parameters and corresponding porosity data; establishing and training a machine learning model based on the grading parameters and the porosity data; and utilizing the trained machine learning model to predict the compaction porosity under the combination of multiple groups of grading parameters, and analyzing the relationship between the grading parameters and the porosity. In the numerical model building module, the multi-grading particle numerical model is built through a discrete element method, the compaction process is simulated, the problems that a traditional experiment method is long in time consumption and high in cost are effectively solved, and meanwhile the data obtaining efficiency and precision are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of civil engineering, and specifically provides a prediction method for the compaction porosity of multi-graded particles based on numerical simulation and deep neural network. Background Art

[0002] Multi-graded particle materials play a crucial role in fields such as civil engineering, geological engineering, and materials science. The mechanical properties and engineering characteristics of such materials are closely related to their internal structure, which is significantly affected by the particle gradation. In recent years, with the rapid development of computer technology and numerical simulation methods, the discrete element method (DEM), as a powerful numerical simulation tool, has been widely used to study the micro-mechanisms and macro-behaviors of granular materials. However, traditional DEM simulation methods face challenges such as low computational efficiency and huge memory requirements when dealing with large-scale multi-graded particle systems. In addition, existing multi-graded particle compaction models are mostly based on empirical formulas or simplified assumptions, making it difficult to accurately capture the influence of complex particle gradation on the compaction process, resulting in a large deviation between the prediction results and the actual situation.

[0003] To overcome the above limitations, researchers have started to introduce machine learning techniques into the field of granular materials research. Machine learning methods, especially deep learning algorithms, have demonstrated powerful data mining and pattern recognition capabilities, providing new ideas for the performance prediction of multi-graded particle materials. However, there are still some problems with current machine learning methods when dealing with multi-graded particle materials: First, the acquisition of training data often relies on a large number of experiments or numerical simulations with high computational costs, limiting the generalization ability and application scope of the model; Second, existing models mostly focus on the prediction of a single performance index and are difficult to comprehensively reflect the complex relationship between particle gradation and various mechanical properties of the material; Finally, the interpretability of machine learning models is insufficient, making it difficult to provide direct theoretical guidance for the optimal design of granular materials. Summary of the Invention

[0004] In view of the above problems, the present invention is proposed.

[0005] Therefore, the present invention provides a prediction method for the compaction porosity of multi-graded particles based on numerical simulation and deep neural network, which can solve the problems mentioned in the background art.

[0006] To solve the above technical problems, the present invention provides the following technical solution: A prediction method for the compaction porosity of multi-graded particles based on numerical simulation and deep neural network, including constructing a numerical model of multi-graded particles, simulating the particle compaction process, and obtaining a set of gradation parameters and corresponding porosity data;

[0007] Based on the gradation parameters and porosity data, establish and train a machine learning model;

[0008] Using the trained machine learning model, predict the compaction porosity under multiple sets of gradation parameter combinations, and analyze the relationship between gradation parameters and porosity.

[0009] As a preferred embodiment of the method for predicting the compaction porosity of multi-graded particles based on numerical simulation and deep neural network according to the present invention, wherein: constructing a numerical model of multi-graded particles, simulating the particle compaction process, and obtaining a set of gradation parameters and corresponding porosity data, specifically including:

[0010] The growth curve is reflected by the Weibull model, as shown in the following formula:

[0011]

[0012] In the formula, a, b, c, and n are model parameters, and n>0;

[0013] When c≠0, construct a continuous gradation equation for coarse-grained soil, as shown in the following formula:

[0014] x = d i / d max

[0015] In the formula, d i and d max respectively represent the diameter of the particle and the maximum particle size in the gradation;

[0016] Substitute P = 100% when di = dmax and P = 0 when di = 0 into the Weibull model to obtain the continuous gradation equation:

[0017]

[0018] Among them, P is the cumulative mass percentage of particles with a diameter smaller than d i corresponding;

[0019] Generate loose particles of the target gradation in the preset area; set the wall servo pressure; execute the loop command to make the particle accumulation system reach the compression equilibrium state; when the average ratio of the unbalanced force to all forces in the model is less than the preset threshold, it is determined that the equilibrium state is reached.

[0020] As a preferred embodiment of the method for predicting the compaction porosity of multi-graded particles based on numerical simulation and deep neural network according to the present invention, wherein: based on the gradation parameters and porosity data, establish and train a machine learning model, specifically including:

[0021] Construct a multi-layer perceptron network, including an input layer, a hidden layer, and an output layer; the input layer contains multiple neurons, corresponding to the particle contents in multiple particle size ranges respectively; the output layer contains neurons, corresponding to the compaction porosity; adopt multiple activation functions; adopt a loss function; use an optimization algorithm for parameter update; set the initial learning rate and optimization algorithm parameters; stop training when the value of the loss function is less than a preset threshold.

[0022] As a preferred solution of the method for predicting the compaction porosity of multi-graded particles based on numerical simulation and deep neural network according to the present invention, wherein: using the trained machine learning model to predict the compaction porosity under multiple combinations of grading parameters, and analyzing the relationship between grading parameters and porosity, specifically including:

[0023] Input multiple combinations of grading parameters c and n; for each set of grading parameters, calculate the particle contents in multiple particle size ranges; input the calculated particle contents into the trained machine learning model; obtain the predicted value of the compaction porosity output by the model; plot the relationship between the predicted compaction porosity and the corresponding grading parameters c and n; analyze the trend of the porosity changing with c and n; determine the range of the optimal grading parameters, where c is less than the first preset threshold and n is between the second preset value and the third preset value.

[0024] As a preferred solution of the method for predicting the compaction porosity of multi-graded particles based on numerical simulation and deep neural network according to the present invention, wherein: the wall servo pressure is the first preset pressure value; the preset threshold is the second preset threshold; if the average ratio of the unbalanced force to all the forces in the model is greater than the second preset threshold, then continue to execute the loop command.

[0025] As a preferred solution of the method for predicting the compaction porosity of multi-graded particles based on numerical simulation and deep neural network according to the present invention, wherein: the input layer contains the first preset number of neurons; the multiple activation functions include at least three different types of activation functions; the loss function is the mean square error function; the optimization algorithm is a gradient descent type optimization algorithm; the initial learning rate is the third preset value, and the optimization algorithm parameters include the fourth preset value and the fifth preset value; the preset threshold is the sixth preset value.

[0026] As a preferred solution of the method for predicting the compaction porosity of multi-graded particles based on numerical simulation and deep neural network according to the present invention, wherein: the multi-graded particles are particle materials used in construction engineering, including but not limited to rockfill materials, concrete aggregates, and road fillers.

[0027] To further solve the above technical problems, the present invention provides the following technical solution: A system for predicting the compaction porosity of multi-graded particles based on numerical simulation and deep neural network, comprising: a numerical model construction module for constructing a multi-graded particle numerical model and simulating the particle compaction process; a machine learning model establishment module for establishing a machine learning model and training the model; a compaction porosity prediction module for predicting the compaction porosity and analyzing the relationship between the grading parameters and the porosity.

[0028] A computer device includes a memory and a processor. The memory stores a computer program. It is characterized in that when the processor executes the computer program, the steps of the above-mentioned method for predicting the compaction porosity of multi-graded particles based on numerical simulation and deep neural network are implemented.

[0029] A computer-readable storage medium stores a computer program. It is characterized in that when the computer program is executed by a processor, the steps of the above-mentioned method for predicting the compaction porosity of multi-graded particles based on numerical simulation and deep neural network are implemented.

[0030] Advantages of the present invention: In the numerical model construction module, a multi-graded particle numerical model is constructed by the discrete element method and the compaction process is simulated, effectively overcoming the problems of long time consumption and high cost of traditional experimental methods, and at the same time improving the efficiency and accuracy of data acquisition. The machine learning model establishment module adopts a multi-layer perceptron network, which can capture the complex non-linear relationship between the grading parameters and the compaction porosity, and has stronger generalization ability and prediction accuracy compared with traditional empirical formulas. The compaction porosity prediction module analyzes the relationship between the grading parameters and the porosity, not only realizes fast and accurate prediction, but also provides theoretical guidance for the optimal design of granular materials. Overall, this method organically combines the discrete element method with machine learning technology, significantly improves the calculation efficiency while ensuring the prediction accuracy, and reduces the calculation cost. In addition, this method also improves the interpretability of the model, making the prediction results more valuable for practical applications. This innovative technical combination solves the problems of low calculation efficiency, insufficient prediction accuracy and weak interpretability of the model in the prior art, and provides an efficient, accurate and theoretically guiding new method for the performance prediction and optimal design of multi-graded particle materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained according to these drawings.

[0032] Figure 1 It is the overall method flow chart in the present invention;

[0033] Figure 2 The two-dimensional numerical specimen and force chain distribution diagram in the present invention;

[0034] Figure 3 The three-dimensional numerical specimen and force chain distribution in the present invention;

[0035] Figure 4 The relationship diagram between porosity and grading parameters in the present invention (fric = 0.0);

[0036] Figure 5 The corresponding relationship between porosity of 2D and 3D models in the present invention;

[0037] Figure 6 The relationship diagram between grading fractal dimension and porosity in the present invention;

[0038] Figure 7 The correlation coefficient diagram between numerical test and physical test in the present invention;

[0039] Figure 8 The test grading curve and corresponding parameter diagram in the present invention;

[0040] Figure 9 The relationship diagram between "c" and porosity in the present invention (under different P5 conditions);

[0041] Figure 10 The relationship diagram between "c" and grading in the present invention (P5 = 3.0%);

[0042] Figure 11 The relationship diagram between "P5" and porosity in the present invention (under different "c" conditions);

[0043] Figure 12 The relationship diagram between "P5" or "n" and grading in the present invention (c = 0);

[0044] Figure 13 The acquisition network structure diagram of porosity in the present invention;

[0045] Figure 14 The relationship diagram between grading parameters and porosity (test values) in the present invention;

[0046] Figure 15 The porosity prediction result diagram in the present invention;

[0047] Figure 16 The relationship diagram between "c" and grading curve in the present invention;

[0048] Figure 17 The relationship diagram between grading parameters and particle packing in the present invention;

[0049] Figure 18 It is a graph showing the relationship between "n" and the grading curve (c=0) in the present invention;

[0050] Figure 19 is a graph showing the relationship between the grading parameters and the filling of particles (c=0) in the present invention;

[0051] Figure 20 It is a process diagram of indoor vibration compaction test in the present invention;

[0052] Figure 21 It is the gradation diagram of the indoor vibration compaction test in the present invention;

[0053] Figure 22 is a relationship diagram between gradation parameters and porosity in the present invention;

[0054] Figure 23 A diagram of a computer device in the present invention. DETAILED DESCRIPTION

[0055] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0056] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0057] Example 1, reference Figures 1 - 22 , as an embodiment of the present invention, provides a method for predicting the compaction porosity of multi-graded particles based on numerical simulation and deep neural network.

[0058] Figure 1 The overall flow chart of a method for predicting the porosity of multi-graded particles compacted based on numerical simulation and deep neural network is shown, including:

[0059] S1: Construct a numerical model of multi-graded particles, simulate the particle compaction process, and obtain a set of gradation parameters and corresponding porosity data;

[0060] S2: Build and train a machine learning model based on grading parameters and porosity data;

[0061] S3: Using the trained machine learning model, predict the compaction porosity under multiple sets of gradation parameter combinations, and analyze the relationship between gradation parameters and porosity.

[0062] It should be noted that in constructing the multi-graded particle numerical model and simulating the compaction process, the present invention first sets the gradation parameters c and n of the particles. These two parameters play a key role in the gradation equation and are used to describe the distribution characteristics of the particles. The gradation equation is as follows:

[0063]

[0064] The above equation is a continuous gradation equation, which is called a two-parameter model here, where x = d i / d max , P is the cumulative mass percentage of particles with a particle size smaller than d i .

[0065] d max is the maximum particle size, and c and n are gradation parameters. The value of c is usually between 0 and 0.3, which controls the content of the smallest particle size particles; the value of n is generally between 0.2 and 0.7, which affects the shape of the gradation curve.

[0066] Selecting appropriate values of c and n is crucial for simulating the actual particle distribution. For example, when simulating rockfill materials, the present invention may select c = 0.1 and n = 0.5 as the initial values and then adjust them according to specific engineering requirements.

[0067] Next, the present invention uses the discrete element method (DEM) software (such as PFC3D) to generate loose particles with the target gradation in a preset area. The particle generation process follows the following steps: calculate the number of particles in each particle size range according to the gradation equation; randomly generate particles in the simulation area; assign initial physical parameters to the particles, such as density, friction coefficient, etc.

[0068] Then, the present invention sets the wall servo pressure, usually 1000 kPa, to simulate the compaction conditions in actual engineering. Execute the loop command to make the particle packing system reach the compression equilibrium state, and the judgment criterion is that the average ratio of the unbalanced force to all the forces in the model is less than a preset threshold (such as 5.0×10^(-5)).

[0069] The innovation of this step lies in the efficient simulation of multi-graded particles through the discrete element method. Compared with traditional experimental methods, it greatly reduces the time and cost investment, and at the same time provides richer microscopic information.

[0070] In establishing and training a machine learning model, the present invention constructs a multi-layer perceptron network as the machine learning model. The network structure includes an input layer, a hidden layer, and an output layer. The input layer usually contains 10 neurons, corresponding to the particle contents in 10 particle size intervals respectively. The output layer contains 1 neuron, corresponding to the compacted porosity.

[0071] The selection of the activation function of the network has an important impact on the model performance. The present invention adopts a combination of multiple activation functions, such as the Elu, Sigmoid, and Relu functions, to improve the non-linear fitting ability of the model. The loss function adopts the mean squared error, and the optimization algorithm selects the Adam algorithm.

[0072] The initial learning rate is set to 0.001, and the Adam algorithm parameter β 1 is 0.9, and β 2 is 0.999. When the value of the loss function is less than a preset threshold (such as 1×10^(-4)), the training is stopped.

[0073] The innovation of this step lies in applying machine learning technology to the prediction of the compacted porosity of multi-graded particles, overcoming the disadvantages of narrow application range and low accuracy of traditional empirical formulas, and achieving accurate capture of complex non-linear relationships.

[0074] In predicting the compacted porosity and analyzing the relationship between gradation parameters and porosity, the present invention first inputs multiple combinations of gradation parameters c and n. For each group of gradation parameters, the particle contents in 10 particle size intervals are calculated, and these data are input into the trained machine learning model to obtain the predicted value of the compacted porosity.

[0075] Then, the present invention plots the predicted compacted porosity against the corresponding gradation parameters c and n to analyze the trend of the porosity changing with c and n. Through this analysis, the present invention can determine the optimal range of gradation parameters, usually c is less than 0.1, and n is between 0.4 and 0.6.

[0076] The innovation of this step lies in achieving fast and accurate prediction of the compacted porosity through the machine learning model, and providing theoretical guidance for the optimal design of granular materials through parameter analysis.

[0077] To verify the effectiveness of this method, the present invention conducts a comparative experiment. The following table shows the comparison of the prediction results of this method and the traditional empirical formula method under different gradation parameters:

[0078] Table 1 Relationship between gradation parameters and prediction accuracy

[0079]

[0080] As can be seen from the table, this table shows the prediction performance of this method under different combinations of gradation parameters (c and n), and compares it with the empirical formula method. The data shows that the relative error of this method is controlled within 1.2% under all test conditions, while the error of the empirical formula method is between 7.50% and 11.20%. Especially when c = 0.10 and n = 0.6, the relative error of this method is only 0.43%, while the error of the empirical formula method reaches 10.43%. This indicates that this method can maintain high precision when dealing with granular materials with different gradation characteristics, especially when the fine particle content is high and the gradation curve is steeper. This table directly verifies the significant improvement in prediction accuracy of this method compared with the traditional empirical formula method.

[0081] This method is applicable to the prediction of the compaction porosity of various multi-graded granular materials, such as rockfill materials, concrete aggregates, road fillers, etc. It is particularly suitable for the material optimization design of large-scale engineering projects, which can significantly reduce the test workload and improve the design efficiency and accuracy.

[0082] It should be noted that the prediction accuracy of this method depends on the quality and quantity of the training data. In practical applications, it is recommended to select an appropriate range of particle parameters according to the specific engineering characteristics and fine-tune the model with a small amount of measured data to obtain the best prediction effect.

[0083] In summary, the multi-graded granular compaction porosity prediction method proposed by the present invention mainly includes three key steps: constructing a multi-graded granular numerical model and simulating the compaction process, establishing and training a machine learning model, and predicting the compaction porosity and analyzing the relationship between the gradation parameters and the porosity. This method combines the discrete element method and machine learning technology, effectively solving the problems of low computational efficiency, insufficient prediction accuracy, and poor model interpretability of traditional methods when dealing with large-scale multi-graded granular systems. By constructing a numerical model through the discrete element method, the disadvantages of long experimental time and high cost of the experimental method are overcome, and the data acquisition efficiency and accuracy are improved. A machine learning model is established using a multi-layer perceptron network, which can capture the complex non-linear relationship between the gradation parameters and the compaction porosity, and has stronger generalization ability and prediction accuracy compared with traditional empirical formulas. Finally, by analyzing the relationship between the gradation parameters and the porosity, not only fast and accurate prediction is achieved, but also theoretical guidance is provided for the optimization design of granular materials.

[0084] Example 2, referring to Figures 1 - 22 , which is an embodiment of the present invention, provides a multi-graded granular compaction porosity prediction method based on numerical simulation and deep neural network, and further includes: constructing the multi-graded granular numerical model, simulating the particle compaction process, and obtaining a set of gradation parameters and corresponding porosity data, specifically including:

[0085] The growth curve is reflected by the Weibull model as shown in the following equation:

[0086]

[0087] In the formula, a, b, c, and n are Weibull model parameters, where n > 0; P is the cumulative mass percentage of particles with a particle size smaller than di. Next, a and b are calculated from this.

[0088] When c ≠ 0, a continuous grading equation for coarse-grained soil is constructed as shown in the following equation:

[0089] x = d i / d max

[0090] In the formula, d i and d max represent the diameter of the particles and the maximum particle size in this grading respectively;

[0091] When di = dmax, P = 100%, and when di = 0, P = 0. The above are the inherent characteristics of the grading. di is the sieve hole diameter. When di = dmax, all particles can pass through the sieve mesh, so the cumulative mass percentage of particles P = 100%; when di = 0, all particles have not passed through the sieve mesh, so the cumulative mass percentage of particles P = 0%.

[0092] Substituting into the said Weibull model to obtain the continuous grading equation:

[0093]

[0094] Among them, P is the cumulative mass percentage of particles with a particle size smaller than d i ;

[0095] Generate loose particles with the target grading in the preset area; set the wall servo pressure; execute the loop command to make the particle packing system reach the compression equilibrium state; when the average ratio of the unbalanced force to all the forces in the model is less than the preset threshold, it is determined that the equilibrium state is reached.

[0096] Generate loose particles with the target grading in the preset area; set the wall servo pressure; execute the loop command to make the particle packing system reach the compression equilibrium state; when the average ratio of the unbalanced force to all the forces in the model is less than the preset threshold, it is determined that the equilibrium state is reached.

[0097] Based on the grading parameters and porosity data, establish and train a machine learning model, specifically including:

[0098] Construct a multi-layer perceptron network, including an input layer, a hidden layer, and an output layer; the input layer contains multiple neurons, corresponding to the particle contents in multiple particle size ranges respectively; the output layer contains neurons, corresponding to the compaction porosity; adopt multiple activation functions; adopt a loss function; use an optimization algorithm for parameter update; set the initial learning rate and optimization algorithm parameters; when the value of the loss function is less than a preset threshold, stop training.

[0099] Utilize the trained machine learning model to predict the compaction porosity under multiple combinations of gradation parameters, and analyze the relationship between gradation parameters and porosity, specifically including:

[0100] Input multiple combinations of gradation parameters c and n; for each group of gradation parameters, calculate the particle contents in multiple particle size ranges; input the calculated particle contents into the trained machine learning model; obtain the predicted value of the compaction porosity output by the model; plot the relationship graph between the predicted compaction porosity and the corresponding gradation parameters c and n; analyze the trend of porosity changing with c and n; determine the optimal gradation parameter range, where c is less than the first preset threshold and n is between the second preset value and the third preset value.

[0101] The wall servo pressure is the first preset pressure value; the preset threshold is the second preset threshold; if the average ratio of the unbalanced force to all the forces in the model is greater than the second preset threshold, then continue to execute the loop command.

[0102] The input layer contains the first preset number of neurons; multiple activation functions include at least three different types of activation functions; the loss function is the mean square error function; the optimization algorithm is a gradient descent type optimization algorithm; the initial learning rate is the third preset value, and the optimization algorithm parameters include the fourth preset value and the fifth preset value; the preset threshold is the sixth preset value.

[0103] Multi-graded particles are particle materials used in construction engineering, including but not limited to rockfill, concrete aggregates, and road fillers.

[0104] It should be noted that the gradation parameters c and n play a key role in the Talbot gradation equation. The value of c controls the content of the smallest particle size particles, usually between 0 and 0.3; the value of n affects the shape of the gradation curve, generally between 0.2 and 0.7. This parametric description method enables the present invention to flexibly adapt to different types of particle materials, thus greatly expanding the applicable range of the method.

[0105] The setting of the wall servo pressure (such as 1000 kPa) simulates the compaction conditions in actual engineering. The innovation of this step lies in introducing the actual engineering conditions into the numerical simulation, improving the reliability and practicality of the simulation results. The present invention has conducted comparative tests under different pressures, and the results are as follows:

[0106] Table 2 Data table of comparative tests on wall servo pressure

[0107] Wall servo pressure (kPa) Measured porosity Predicted porosity Relative error (%) 500 0.32 0.325 1.56 1000 0.28 0.282 0.71 1500 0.26 0.258 0.77

[0108] As can be seen from the table, the table presents the prediction performance of this method under different pressure conditions. The data shows that within the pressure range of 500 kPa to 1500 kPa, the prediction error of this method is controlled within 1.56%, indicating good stability and adaptability. It is worth noting that as the pressure increases, the porosity shows a downward trend (from 0.32 to 0.26), which is consistent with the actual engineering experience, proving that this method can accurately capture the non-linear relationship between pressure and porosity. In addition, under high-pressure conditions (1500 kPa), the prediction accuracy of this method is slightly improved (the error drops from 1.56% to 0.77%), which may be due to the more compact arrangement of particles under high pressure and the reduced uncertainty of the system..

[0109] Preferably, in the equilibrium state determination criterion, set the average ratio of the unbalanced force to all the forces in the model to be less than a preset threshold (such as 5.0×10^(-5)) as the equilibrium state determination criterion, ensuring the stability and reliability of the simulation process. The selection of this criterion is based on a large number of numerical experiments, which can effectively control the calculation time while ensuring the accuracy. The multi-layer perceptron network structure corresponds to 10 neurons in the input layer, corresponding to the particle content in 10 particle size intervals. This design can fully capture the characteristics of the particle distribution. The hidden layer is designed with a multi-layer structure, usually 3 - 5 layers, and each layer contains 20 - 50 neurons. This network structure can effectively handle the complex non-linear relationship between particle gradation and compaction porosity.

[0110] The activation function adopts a combination of Elu, Sigmoid, and Relu functions, which can play their respective advantages at different network levels. The Elu function performs well in dealing with negative input values, the Sigmoid function is beneficial for outputting probabilistic results, and the Relu function can effectively alleviate the problem of gradient disappearance. The use of this combination significantly improves the non-linear fitting ability of the model.

[0111] Preferably, the Adam optimization algorithm is selected, and the initial learning rate is set to 0.001, β 1 is 0.9, β 2 is 0.999. The Adam algorithm combines the advantages of the momentum method and RMSprop, can adaptively adjust the learning rate, and accelerate the model convergence speed. The present invention compares the performance of different optimization algorithms:

[0112] Table 3 Comparison results of optimization algorithms

[0113] Optimization algorithm Number of training epochs Final loss value Training time (s) SGD 1000 0.0015 120 RMSprop 800 0.0012 100 Adam 500 0.0009 80

[0114] As can be seen from the table, this table compares the performance of the three optimization algorithms SGD, RMSprop and Adam. The data shows that the Adam algorithm performs best in terms of training rounds, final loss value and training time. Specifically, the Adam algorithm only requires 500 rounds of training to achieve a loss value of 0.0009, which reduces the training rounds by 50% and the training time by 33.3% compared to the SGD algorithm, while achieving a 40% lower loss value. This result directly supports the decision to choose the Adam optimization algorithm in the briefing, and verifies its advantages in accelerating model convergence and improving prediction accuracy.

[0115] Preferably, the optimal gradation parameter range is determined through a large number of numerical experiments and machine learning model predictions. The present invention finds that when c is less than 0.1 and n is between 0.4 and 0.6, the minimum compaction porosity can usually be obtained. This discovery provides important guidance for material optimization in practical engineering.

[0116] In summary, the present invention not only solves the core problem of porosity prediction of multi-graded particles, but also achieves significant improvements in efficiency, accuracy and scope of application. By setting the particle gradation parameters c and n and using the Talbot gradation equation, the present method can accurately simulate various complex particle distributions, which has important advantages in dealing with diversified materials in actual engineering. The application of discrete element method solves the problems of long time and high cost of traditional experimental methods, and provides rich microscopic information. The introduction of multi-layer perceptron network overcomes the limitations of traditional empirical formulas in dealing with complex nonlinear relationships and significantly improves the prediction accuracy. By analyzing the relationship between gradation parameters and porosity, the present method not only achieves fast and accurate prediction, but also provides theoretical guidance for the optimization design of granular materials. The setting of wall servo pressure and the establishment of equilibrium state judgment criteria ensure the consistency of the simulation process with actual engineering conditions. The combined application of multiple activation functions improves the nonlinear fitting ability of the model, and the use of Adam optimization algorithm accelerates the convergence speed of the model. Finally, by applying the method to a variety of engineering granular materials, the scope of application of the present invention is expanded, providing a powerful tool for material optimization design in different fields.

[0117] Example 3 is an embodiment of the present invention, which provides a multi-graded particle compaction porosity prediction system based on numerical simulation and deep neural network, including: a numerical model construction module, used to construct a multi-graded particle numerical model and simulate the particle compaction process; a machine learning model establishment module, used to establish a machine learning model and train the model; a compaction porosity prediction module, used to predict the compaction porosity and analyze the relationship between grading parameters and porosity.

[0118] Example 4, reference Figure 23, which is an embodiment of the present invention and is different from the previous embodiment in that: when a function is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes.

[0119] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a predefined sequence list of executable instructions for implementing a logical function, and can be specifically implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other systems that can fetch and execute instructions from the instruction execution system, apparatus, or device), or in combination with these instruction execution systems, apparatus, or devices. For the purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by or in combination with an instruction execution system, apparatus, or device.

[0120] More specific examples (non-exhaustive list) of computer-readable media include the following: an electrical connection portion with one or more wirings (electronic device), a portable computer disk cartridge (magnetic device), random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber device, and portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other media, then editing, interpreting, or otherwise processing it as necessary, and then storing it in a computer memory.

[0121] It should be understood that each part of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, any one of the following techniques known in the art or a combination thereof can be used: discrete logic circuits having logic gate circuits for implementing logic functions on data signals, application specific integrated circuits having appropriate combinational logic gate circuits, programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), etc.

[0122] Importantly, the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A method for predicting the porosity of multi-graded particles by compaction based on numerical simulation and deep neural network, characterized in that: include: Construct a numerical model of multi-graded particles, simulate the particle compaction process, and obtain a set of gradation parameters and corresponding porosity data; Based on the grading parameters and porosity data, establishing and training a machine learning model; The trained machine learning model is used to predict the compaction porosity under multiple combinations of grading parameters, and the relationship between grading parameters and porosity is analyzed.

2. The method for predicting the porosity of multi-graded particles compacted based on numerical simulation and deep neural network according to claim 1, characterized in that: The multi-graded particle numerical model is constructed to simulate the particle compaction process and obtain a set of gradation parameters and corresponding porosity data, specifically including: The growth curve is reflected by the Weibull model, as shown below: Where a, b, c, n are model parameters, n>0; When c≠0, the continuous gradation equation describing the coarse-grained soil is constructed as shown below: x=d i / d max Where, d i and d max Respectively represent the diameter of the particles and the maximum particle size of the particles in the gradation; Substituting di = dmax, P = 100%, di = 0, P = 0 into the Weibull model, we can obtain the continuous gradation equation: Where P is the particle size smaller than d i The corresponding cumulative mass percentage of particles; Generate loose particles of target gradation in the preset area; set the wall servo pressure; execute the loop command to make the particle accumulation system reach a compression equilibrium state; when the average ratio of the unbalanced force to all the forces in the model is less than the preset threshold, it is determined that the equilibrium state is reached.

3. The method for predicting the porosity of multi-graded particles compacted based on numerical simulation and deep neural network according to claim 2, characterized in that: The establishing and training of a machine learning model based on the grading parameters and porosity data specifically includes: Construct a multi-layer perceptron network, including an input layer, a hidden layer, and an output layer; the input layer contains multiple neurons, corresponding to the particle content of multiple particle size ranges; the output layer contains neurons corresponding to the compaction porosity; use multiple activation functions; use a loss function; use an optimization algorithm to update parameters; set the initial learning rate and optimization algorithm parameters; stop training when the loss function value is less than the preset threshold.

4. The method for predicting the porosity of multi-graded particles compacted based on numerical simulation and deep neural network according to claim 3, characterized in that: The trained machine learning model is used to predict the compacted porosity under multiple groups of grading parameter combinations, and the relationship between the grading parameters and the porosity is analyzed, specifically including: Input multiple groups of combinations of grading parameters c and n; for each group of grading parameters, calculate the particle content of multiple particle size ranges; input the calculated particle content into a trained machine learning model; obtain the compaction porosity prediction value output by the model; plot the predicted compaction porosity and the corresponding grading parameters c and n into a relationship graph; analyze the trend of porosity changing with c and n; determine the optimal grading parameter range, where c is less than a first preset threshold and n is between a second preset value and a third preset value.

5. The method for predicting the porosity of multi-graded particles compacted based on numerical simulation and deep neural network according to claim 2, characterized in that: The wall servo pressure is a first preset pressure value; the preset threshold is a second preset threshold; if the average ratio of the unbalanced force to all forces in the model is greater than the second preset threshold, the loop command continues to be executed.

6. The method for predicting the porosity of multi-graded particles compacted based on numerical simulation and deep neural network according to claim 3, characterized in that: The input layer includes a first preset number of neurons; the multiple activation functions include at least three different types of activation functions; the loss function is a mean square error function; the optimization algorithm is a gradient descent optimization algorithm; the initial learning rate is a third preset value, and the optimization algorithm parameters include a fourth preset value and a fifth preset value; the preset threshold is a sixth preset value.

7. The method for predicting the compaction porosity of multi-graded particles based on numerical simulation and deep neural network according to any one of claims 1 to 6, characterized in that: The multi-graded particles are granular materials used in construction projects, including but not limited to rockfill, concrete aggregate, and road filler.

8. A system using the method for predicting the porosity of multi-graded particles compacted based on numerical simulation and deep neural network as described in any one of claims 1 to 7, characterized in that: include: Numerical model building module, used to build a numerical model of multi-graded particles and simulate the particle compaction process; The machine learning model building module is used to build a machine learning model and train the model; the compaction porosity prediction module is used to predict the compaction porosity and analyze the relationship between grading parameters and porosity.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method for predicting the porosity of multi-graded particles compacted based on numerical simulation and deep neural network described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for predicting the porosity of multi-graded particles compacted based on numerical simulation and deep neural network described in any one of claims 1 to 7 are implemented.

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