A method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN

Abstract

This invention belongs to the field of machine learning and ground mechanics prediction technology, and discloses a method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN. The method includes the following steps: collecting data on the movement of a robot's feet on a wet particulate surface and identifying the factors that have the greatest impact on the results; establishing a high-fidelity fluid-solid-particle coupled simulation environment based on the VOF model; using a GAN neural network to enhance the distribution of the dataset; deriving physical formulas based on the RFT model; constructing a CNN-BPNN neural network model and inserting the derived physical formulas into the loss function; and using the constructed network model to predict the data. This invention, employing the above-mentioned method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN, not only improves the accuracy and efficiency of prediction but also provides support for the research and engineering applications of the mechanical properties of particulate surfaces.

Description

Technical Field

[0001] This invention relates to the field of machine learning and ground mechanics prediction technology, and in particular to a method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN. Background Technology

[0002] Robots experience severe degradation in mobility on unstructured surfaces composed of granular media, such as sand and seabed sediment. Granular surfaces exhibit fluidity under low-speed disturbances but also display certain solid-like properties under high-speed impacts; these complex physical characteristics pose a significant challenge to efficient robot operation. In amphibious environments, the seabed and near-water areas of beaches are typically composed of wet granular media formed by water-sand mixtures. The mixing of sand and water further complicates the mechanical properties, making the prediction of foot-ground interaction mechanics on such surfaces a key issue that needs to be addressed in the development of amphibious robots.

[0003] To date, while machine learning methods have greatly advanced research on nonlinear dynamics prediction, applying these methods to predict the mechanical properties of robot foot-to-ground interactions on granular surfaces remains a challenge. On one hand, most traditional machine learning methods struggle to adapt to the complex mechanisms, high nonlinearity, and high dimensionality of data in granular surfaces because their feature extraction capabilities are shallow. Furthermore, compared to models based on physical formulas, the feature information extracted by traditional neural networks is difficult to interpret intuitively from a physical perspective, and most parameters in the model lack clear physical meaning. On the other hand, a well-trained ML model typically requires a large amount of experimental data, which is both time-consuming and expensive.

[0004] Therefore, there is an urgent need for a method to predict the foot-ground interaction mechanical properties of robots on saturated wet particulate ground. The aim is to contribute to this developing research field by exploring the combination of machine learning and physical models to predict the foot-ground interaction mechanical properties of robots moving on complex ground surfaces. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN. Through innovative approaches such as establishing high-fidelity multiphase flow coupling simulation based on data obtained from physical experiments and VOF model, enhancing dataset distribution with GAN neural network, CNN-BPNN neural network model, and integrating physical knowledge, this invention provides a more accurate and effective means for predicting the mechanical properties of wet particulate media ground surfaces. This not only improves the accuracy and efficiency of prediction but also provides better support for the research and engineering application of the mechanical properties of particulate media ground surfaces.

[0006] To achieve the above objectives, this invention provides a method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN, comprising the following steps:

[0007] Step S1: Collect data on the movement of the robot's feet on a wet granular surface, and identify the factors that have the greatest impact on the results.

[0008] Step S2: Based on the data obtained from the physical experiment, establish a high-fidelity fluid-solid-particle coupling simulation environment based on the VOF model;

[0009] Step S3: Use a GAN neural network to enhance the distribution of the dataset;

[0010] Step S4: Derivation of physical formulas based on the RFT model;

[0011] Step S5: Construct a CNN-BPNN neural network model and insert the derived physical formulas into the loss function;

[0012] Step S6: Use the established network model to predict the data of the robot's foot movement on the wet granular ground and obtain the predicted value.

[0013] Preferably, the mechanical parameter collection of wet particulate media ground includes two parts. The first part is to determine the variables to be studied through data collection and to design experiments using orthogonal experimental design. The second part is to accurately test the data and strictly measure and analyze each variable according to the experimental design table.

[0014] Preferably, based on the collected data, an experiment is designed using the orthogonal experimental method to determine the variables to be studied, and each variable is measured and analyzed. The specific process is as follows:

[0015] Step S11: Select the test indicators;

[0016] Step S12: Select factors and levels;

[0017] Step S13: Design an orthogonal array using SPSS Statistics 23;

[0018] Step S14: Measure each set of experimental data three times and take the arithmetic mean;

[0019] Step S15: Analyze the test results using range analysis.

[0020] Preferably, in step S2, a high-fidelity fluid-solid-particle coupled simulation environment is established based on the data obtained from the physical experiment and the VOF model. The specific process is as follows:

[0021] Step S21: The applicability of the RFT model micro-element method and inertial force model in saturated wet granular media is studied by using multiphase flow coupling simulation test, and the key factors for the study of the ground resistance model of the foot in saturated wet granular media are clarified.

[0022] For the study of wet particulate media, coupled simulation was performed using the fluid dynamics simulation software ANSYS Fluent and EDEM.

[0023] Step S22: The VOF model models immiscible fluids by solving a set of momentum equations and tracking the volume fraction of each fluid in the entire computational domain. For each immiscible additional fluid phase added to the model, a corresponding variable is introduced—the volume fraction of that phase in the cell.

[0024] Step S23: By solving the continuity equation of the phase volume fraction, the interface between phases is traced, as shown below:

[0025]

[0026] Where, ρ q α represents the density of the fluid. q This indicates the volume fraction of fluid in the unit; The velocity vector represents the fluid; p and q represent two interacting phases. and S represents mass transfer between phases; αq Indicates the source phase;

[0027] Step S24: The volume fraction equation for the initial phase will not be solved; the volume fraction will be calculated based on the following constraints:

[0028]

[0029] Step S25: Solve the VOF-based model using implicit formulas. The volume fraction equation is then discretized as follows:

[0030]

[0031] Where n+1 is the index of the current time step; n is the index of the previous time step; This represents the unit value of the volume fraction at time step n+1; This represents the unit value of the volume fraction at time step n; This is the face value of the volume fraction at step n+1; is the volume flux through the surface at step n+1; V is the unit volume.

[0032] Preferably, the sum of the volume fractions of all phases is 1, and the volume fraction is usually represented by the symbol α; the volume fraction of the i-th term in the multiphase fluid is α.i Then there are three possible scenarios:

[0033] (1)α i =0, at this time the element does not contain the fluid term;

[0034] (2)α i =1, at this time the entire cell contains this fluid term;

[0035] (3) 0 < α i <1, at this time the cell contains the interface between the fluid item and one or more other fluid phases.

[0036] Preferably, in step S3, a GAN neural network is used to enhance the distribution of the dataset, and the specific process is as follows:

[0037] Step S31, Data Preprocessing and Normalization: Read the data and normalize it using MinMaxScaler, scaling all feature values ​​to the range of [0,1].

[0038] Step S32: Build a basic GAN framework, including a generator and a discriminator.

[0039] Step S33: During the training process of GAN, the generator and discriminator are optimized alternately;

[0040] Step S34: Data generation and denormalization, restoring the generated data to the original numerical range;

[0041] Step S35: Post-process the data, discretize and limit the range, and save the data as an Excel file.

[0042] Preferably, in step S4, the physical formula is derived based on the RFT model, and the specific process is as follows:

[0043] Step S41: Use the RFT theoretical model as the theoretical basis for studying the mechanical properties of robots on particulate media surfaces;

[0044] Step S42: Simulation experiment based on advanced discrete element method to analyze and verify the conditions and key factors for the establishment of the RFT model in particulate media;

[0045] Step S43: Through fluid-solid-particle coupling simulation test, the magnitude and corresponding relationship of the resistance of the three components in the wet particulate medium when they move at the same speed are tested, and the test results are analyzed.

[0046] Step S44: Determine a simplified model suitable for the neural network, as shown below:

[0047] F x =kDα V β t γ ;

[0048] Among them, F x denoted by , where is the force on the robot's foot along the x-axis; D is the depth, V is the velocity, t is the type of robot foot propeller; k is the proportionality coefficient; α, β, and γ are the powers of D, V, and t, respectively.

[0049] Preferably, in step S41, based on the idea of ​​infinitesimal elements, it is assumed that the resultant force on the moving object moving under the dry granular interface is a linear superposition of each independent force-bearing unit; the model is divided into two parts, namely the horizontal RFT model and the vertical RFT model.

[0050] The horizontal RFT model is shown below:

[0051]

[0052] Among them, F N For normal force, F L For tangential force, F X The resultant force is horizontal; tanβ0=cotγ0sinψ, where γ0 is the angle of internal friction of the ground, ψ is the angle between the axis of the unit and its velocity; θ is the angle between the axis of the discrete unit and the horizontal direction, and l and r are the length and radius of the unit; C S C F β0 is the drag force constant, which is related to the particulate medium;

[0053] The vertical plane RFT model is shown below:

[0054] The vertical plane RFT model is shown below:

[0055]

[0056] Where, σ z,x The vertical and horizontal forces acting on the unit cell are represented by |z|, the embedment depth, β, the angle of attack, γ, and α. z,x (β,γ) represent the vertical and horizontal stresses, respectively.

[0057] A scaled-down model was obtained by performing Fourier transforms on stress data from various ground surfaces with different particle sizes, using angles of attack and penetration. The model is shown below:

[0058]

[0059] M = (A 0,0 A 1,0 B 1,1 B 0,1 B -1,1 C 1,1 C0,1 C -1,1 D 1,0 ) T

[0060] ξ=0.8α z,x (0,π / 2)

[0061] in, ξ is the unit horizontal and vertical stress; β is the scale ratio; γ is the angle of attack; M is the Fourier coefficient; α is the angle of attack. z,x (β,γ) represent the horizontal and vertical stresses of the actual granular ground surface;

[0062] Using this scaled-down model, even with a certain loss of precision, a complete mechanical model can be obtained simply by measuring the experimental mechanical data of the vertical downward pressure of the plate.

[0063] Preferably, in step S5, the construction of the CNN-BPNN neural network model involves inserting the derived physical formula into the loss function. The specific process is as follows:

[0064] Step S51: First, the input data is processed by the CNN module to extract features. Then, the extracted features are input into the BPNN for further processing. Finally, the prediction result is output.

[0065] Step S52: Set up the CNN module: consisting of convolutional layers, pooling layers, and flattening layers; taking one-dimensional data with a single channel as input; wherein, the first convolutional layer has 16 output channels, uses a convolutional kernel of size 2, a stride of 1, and padding of 1; the purpose of this layer is to extract low-level features; the second convolutional layer has 32 output channels, also with a convolutional kernel of size 2, padding of 1, and a stride of 1, used to further extract higher-level features; a pooling layer of size 2 is used for downsampling to reduce the data dimensionality; the output of the convolutional layer is flattened into one dimension so that it can be input into the fully connected layer;

[0066] Step S53: Set up the BPNN module: It consists of fully connected layers and hidden layers; the fully connected layer is a fully connected network used to further process the features extracted by the CNN; this module contains two linear transformations; the input size of the first layer is the feature dimension output by the CNN module, and the output size is 16; each linear transformation has input size × 16 + 16 parameters; the second linear transformation maps 16 hidden units to 1 output.

[0067] Step S54: Optimize using the Adam optimizer with a learning rate set to 0.001;

[0068] Step S55: Determine the loss function. The loss function consists of two parts: model loss and physical loss.

[0069] Preferably, the model loss is calculated using the mean squared error loss function, as shown below:

[0070]

[0071] Where ModelLoss represents the model loss; y pred y represents the predicted value of the CNN-BPNN neural network model; true Indicates the true target value;

[0072] Physical loss: Calculated by comparing the model's predictions with the predicted values ​​calculated based on physical formulas. The aim is to ensure that the model output aligns with physical laws, as shown below:

[0073]

[0074] Where PhysicsLoss represents the physical loss; physics pred This represents the predicted value using only physical formulas;

[0075] The total loss is a weighted sum of the model loss and the physical loss, as shown below:

[0076] TotalLoss = ModelLoss + λ physics ×PhysicsLoss;

[0077] Where TotalLoss represents the total loss; λ physics It is the weight of the physical loss, which controls the degree to which physical constraints affect model training.

[0078] Therefore, the present invention employs the above-mentioned method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN, and the beneficial effects are as follows:

[0079] (1) High-fidelity multiphase flow coupling simulation based on data obtained from physical experiments and VOF model: A fluid-solid-particle coupling simulation environment was established based on VOF model. The application conditions of RFT model micro-element method and inertial force model in saturated wet particle medium were studied by multiphase flow coupling simulation test, and the key factors of the research on the ground resistance model of foot in saturated wet particle medium were clarified.

[0080] (2) GAN neural network enhances dataset distribution: Using GAN-based regression data generation method, by constructing generators and discriminators suitable for regression tasks, and post-processing and evaluating the generated results, high-quality synthetic data similar to the distribution of real data is generated, solving the problem of small dataset prediction and reducing the problems of long test cycles and high test costs caused by relying on physical experiments.

[0081] (3) CNN-BPNN neural network model: Combining CNN and BPNN, the CNN-BPNN neural network model has both the powerful feature extraction capability of CNN and the excellent nonlinear mapping capability, adaptability and learning capability of BPNN, which greatly improves the accuracy and efficiency of model prediction.

[0082] (4) Integrating physical knowledge: Physical information is added to the CNN-BPNN neural network model as a loss function, which makes the model physically interpretable and improves the prediction accuracy.

[0083] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0084] Figure 1 This is a flowchart of a method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN;

[0085] Figure 2 This is a schematic diagram of the fluid-solid-particle coupling simulation test component of the present invention;

[0086] Figure 3 This is a structural diagram of the CNN-BPNN neural network model of this invention;

[0087] Figure 4 This is a comparison chart of the predicted results and the actual values ​​in an embodiment of the present invention. Detailed Implementation

[0088] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0089] like Figure 1 As shown, the present invention provides a method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN, comprising the following steps:

[0090] Step S1: Collect data on the movement of the robot's feet on a wet granular surface, and identify the factors that have the greatest impact on the results.

[0091] Step S2: Based on the data obtained from the physical experiment, establish a high-fidelity fluid-solid-particle coupling simulation environment based on the VOF (Volume of Fluid) model;

[0092] Step S3: Use a GAN (Generative Adversarial Network) neural network to enhance the distribution of the dataset;

[0093] Step S4: Derivation of physical formulas based on the RFT (Resistive Force Theory) model;

[0094] Step S5: Construct a CNN-BPNN (a combined convolutional neural network and backpropagation neural network) neural network model and insert the derived physical formulas into the loss function;

[0095] Step S6: Use the established network model to predict the data of the robot's foot movement on the wet granular ground and obtain the predicted value.

[0096] Example

[0097] This invention discloses a method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN, the specific implementation process of which is as follows:

[0098] Step S1: Collect data on the movement of the robot's feet on a wet granular surface and determine the factors that have the greatest impact on the results.

[0099] The acquisition of mechanical parameters for wet particulate ground surfaces mainly consists of two parts. The first part involves collecting a large amount of data to determine the variables to be studied and designing experiments using orthogonal experimental design. The second part involves precise data testing, rigorously measuring and analyzing each variable according to the experimental design table. Based on the large amount of data collected, experiments were designed using orthogonal experimental design to determine the variables to be studied, and each variable was measured and analyzed. The specific process is as follows:

[0100] Step S11: Select test index: The resistance experienced by the foot during the interaction with the saturated wet particulate ground plays a decisive role in the robot's motion capability, so it is used as the test index and denoted as F.

[0101] Step S12: Selecting Factors and Levels: To study drag phenomena in a 2D plane, the relevant experimental factors include velocity, width, and depth; three levels are selected for each factor, as shown below:

[0102] A-Speed: 30mm / s, 60mm / s, 90mm / s;

[0103] B-Depth: 20mm, 30mm, 40mm;

[0104] C-Width: 10mm, 25mm, 40mm.

[0105] Step S13: Design the orthogonal array: Use SPSS Statistics 23 to complete the design of the L9(33) orthogonal array, as shown in Table 1.

[0106] Table 1 L9(33) Orthogonal Experiment Table

[0107]

[0108]

[0109] Step S14: Conduct the experiment according to the plan: Measure the experimental data of each group three times and take the arithmetic mean. Record the measurement results and variance in Table 1.

[0110] Step S15: Analyze the test results using range analysis.

[0111] Based on the test device, all tests in the orthogonal experimental design table were completed. The orthogonal test results of L9(33) are shown in Table 2. The range analysis method was used to analyze the test results. The importance of each level to the result was judged according to the size of the range of each level.

[0112] Table 2 Range Statistics Table

[0113]

[0114] According to the statistical results in Table 2, the resistance is most affected by depth, followed by width, and least affected by speed. The relationship between resistance and the three parameters is that the resistance increases with increasing speed, increasing with increasing depth, and increasing with increasing width.

[0115] Step S2: Based on the data obtained from the physical experiment, establish a high-fidelity fluid-solid-particle coupling simulation environment based on the VOF model.

[0116] Step S21: Multiphase flow coupled simulation tests are used to study the applicability of the RFT model micro-element method and inertial force model in saturated wet particulate media, clarifying the key factors in the study of the ground resistance model of the foot in saturated wet particulate media. For the study of wet particulate media, coupled simulations are performed using the computational fluid dynamics (CFD) simulation software ANSYS Fluent (ANSYS is a company, Fluent is the name of one of its simulation software programs, commonly used in fluid dynamics simulations) and the general-purpose simulation analysis software EDEM (the world's first general-purpose simulation analysis software based on the advanced discrete element method).

[0117] Step S22: The VOF model models two or more immiscible fluids by solving a set of momentum equations and tracking the volume fraction of each fluid throughout the computational domain.

[0118] The VOF model only applies to cases where two or more fluids (or phases) are immiscible. For each immiscible additional fluid phase added to the model, a corresponding variable is introduced—the volume fraction of that phase in the element.

[0119] The sum of the volume fractions of all phases is 1. Volume fractions are usually represented by the symbol α. If the volume fraction of the i-th phase in a multiphase fluid is α... i Then there are three possible scenarios:

[0120] (1)α i =0, at this time the element does not contain the fluid term;

[0121] (2)α i =1, at this time the entire cell contains this fluid term;

[0122] (3) 0 < α i <1, at this time the cell contains the interface between the fluid item and one or more other fluid phases.

[0123] Step S23: By solving the continuity equation for the volume fraction of one (or more) phases, trace the interfaces between phases, as shown below:

[0124]

[0125] Where, ρ q α represents the density of the fluid. q This indicates the volume fraction of fluid in the unit; The velocity vector represents the fluid; p and q represent two interacting phases. and S represents mass transfer between phases; αq Indicates the source phase.

[0126] Typically, the source phase S on the right-hand side of the equation αq It can be 0, but a constant can also be specified for each stage based on the specific characteristics of the fluid phase.

[0127] Step S24: The volume fraction equation for the initial phase will not be solved; the volume fraction will be calculated based on the following constraints:

[0128]

[0129] Step S25: During the solution process based on the VOF model, the implicit formula iteratively solves the scalar transport equation for each second-phase volume fraction within each time step. The coupled simulation of the Fluent and EDEM simulation platforms relies on the mutual transfer and solution of parameters between the two software programs within each time step. Therefore, using the implicit formula to solve the VOF model, the volume fraction equation is discretized as follows:

[0130]

[0131] Where n+1 is the index of the current time step; n is the index of the previous time step; This represents the unit value of the volume fraction at time step n+1; This represents the unit value of the volume fraction at time step n; This is the face value of the volume fraction at step n+1; is the volume flux through the surface at step n+1; V is the unit volume.

[0132] Since the volume fraction in the current time step is a function of other quantities in the current time step, the scalar transport equation for each second-phase volume fraction is solved iteratively in each time step. The surface flux is interpolated using the selected spatial discretization scheme; the implicit formula can perform both time-varying and steady-state calculations.

[0133] The control volume formulas in ANSYS Fluent require calculating the convection and diffusion fluxes across the control volume surface and balancing them with the source terms within the control volume. In both the geometric reconstruction and donor-acceptor schemes, ANSYS Fluent performs special interpolation on cells located near the interface between two phases, revealing the actual interface shape. In the geometric reconstruction method, the standard interpolation format in ANSYS Fluent is used to obtain the surface flux when an element completely fills one or more phases. A geometric reconstruction scheme is employed when elements are close to the two-phase interface.

[0134] Step S3: Use a GAN neural network to enhance the distribution of the dataset.

[0135] Step S31: Data preprocessing and normalization.

[0136] The data was read and normalized using MinMaxScaler (MinMaxScaler is a tool in the scikit-learn library for feature scaling that works by scaling each feature to a specified range (usually 0 to 1); this transformation is often used as an alternative to zero-mean and unit-variance scaling, the code content) to scale all feature values ​​to the range [0,1].

[0137] Step S32: Build a basic GAN framework, including two core parts: the generator and the discriminator.

[0138] The generator is responsible for generating fake data that resembles real data from a potential noisy space. It is a multi-layer fully connected neural network. The input is a random noise vector (10 dimensions). After several layers of linear transformations and activation functions (such as ReLU), it generates an output with the same feature dimensions as the input data. The final output layer uses a linear activation function, suitable for regression tasks, to ensure that the generated data are continuous values.

[0139] The discriminator is also a fully connected neural network, and its task is to determine whether the input data is real or generated. The discriminator outputs a probability value between 0 and 1, representing the probability that the data is real. Through adversarial training against the generator, the discriminator gradually learns to distinguish between real and generated data.

[0140] Step S33: During the training process of GAN, the generator and discriminator are optimized alternately.

[0141] The training process of GANs is adversarial, with the generator and discriminator competing against each other. The generator continuously generates fake data, attempting to make the discriminator unable to distinguish between real and fake data; while the discriminator continuously optimizes itself, enhancing its ability to differentiate between real and fake data. Through this "adversarial training," the generator gradually learns the distribution of real data.

[0142] Step S34: Data generation and inverse normalization.

[0143] After training, the generator can generate a large number of new data samples. The generator's output is normalized data, and in order to compare it with the original data, an inverse normalization operation is used to restore the generated data to the original numerical range.

[0144] Step S35: Post-process the data, discretize and limit the range, and save the data as an Excel file.

[0145] For certain specific features, the generated data needs to meet certain constraints. The code processes these features by mapping them to a discrete set of multiples and limiting the range of values, ensuring that the generated data meets the requirements of practical applications.

[0146] Step S4: Derivation of physical formulas based on the RFT model.

[0147] Step S41: Use the RFT theoretical model as the theoretical basis for studying the mechanical properties of robots on particulate media surfaces.

[0148] Based on the concept of infinitesimal elements, it is assumed that the net force on a moving object moving underground in a dry granular medium is a linear superposition of the individual force-bearing elements. The model is divided into two parts: the horizontal RFT model and the vertical RFT model.

[0149] The horizontal RFT model is shown below:

[0150]

[0151] Among them, F N For normal force, F L For tangential force, F X The resultant force is horizontal; tanβ0=cotγ0sinψ, where γ0 is the angle of internal friction of the ground, ψ is the angle between the axis of the unit and its velocity; θ is the angle between the axis of the discrete unit and the horizontal direction, and l and r are the length and radius of the unit; C S C F β0 and β0 are drag force constants, which are related to particulate media.

[0152] The horizontal plane RFT model assumes that the object moves at a constant speed and is suitable for low-speed swimming motion of body wave propulsion robots in a horizontal plane.

[0153] The vertical plane RFT model is shown below:

[0154]

[0155] Where, σ z,x The vertical and horizontal forces acting on the unit cell are represented by |z|, the embedment depth, β, the angle of attack (the angle between the unit cell and the horizontal direction), γ, the angle of penetration (the angle between the unit cell's velocity and the horizontal direction), and α. z,x (β,γ) represent the vertical and horizontal stresses, respectively.

[0156] The relationship between stress and angle of attack / impact (RFT) in the vertical surface RFT model is difficult to describe with precise mathematical formulas and requires experimental measurement. However, the stress variation trends with RFT / impact are similar for different particle sizes. A scaled-down model was obtained by performing Fourier transforms on stress data from various particle sizes with respect to RFT / impact, as shown below:

[0157]

[0158] M = (A 0,0 A 1,0 B 1,1 B 0,1 B -1,1 C 1,1 C 0,1 C -1,1 D 1,0 ) T

[0159]

[0160] in, ξ is the unit horizontal and vertical stress; β is the scale ratio; γ is the angle of attack; M is the Fourier coefficient; α is the angle of attack. z,x (β, γ) represent the horizontal and vertical stresses of the actual granular ground surface. Using this scaled-down model, with a certain loss of accuracy, a complete mechanical model can be obtained by measuring only the experimental mechanical data of the vertical downward pressure of the plate.

[0161] The vertical plane RFT model is based on the horizontal plane RFT model and is suitable for calculating the force of low-speed motion embedded at shallow depths in dry granular ground. It is also suitable for calculating the contact force between small legged robots and the ground.

[0162] Therefore, the RFT theoretical model was chosen as the theoretical basis for the study of the mechanical properties of robots on particulate media surfaces.

[0163] Step S42: Based on the advanced discrete element method, simulation experiments are conducted to analyze and verify the conditions and key factors for the establishment of the RFT model in particulate media.

[0164] The most critical condition for realizing RFT in particulate media is the establishment of the infinitesimal element method, that is, for a component moving in particulate media, it is discretized into multiple tiny elements, and the resistance of the entire component is obtained by calculating the force of each tiny element and superimposing them.

[0165] Step S43: Through fluid-solid-particle coupling simulation test, the resistance magnitude and corresponding relationship of the three components in the wet particulate medium when they move at the same speed are tested, and the test results are analyzed.

[0166] like Figure 2 As shown, both component 1 and component 2 are flat plates with a thickness of 2mm and a front surface size of 20mm×20mm; component 3 is the state after component 1 and component 2 are combined together.

[0167] In saturated wet granular media, some research methods and ideas of RFT theory are still applicable, but the infinitesimal method has errors in calculation. Therefore, specific models need to be improved to suit the characteristics of wet granular media.

[0168] Step S44: Determine a simplified model suitable for the neural network, as shown below:

[0169] F x =kD α V β t γ ;

[0170] Among them, F x denoted by , where is the force on the robot's foot along the x-axis; D is the depth, V is the velocity, t is the type of robot foot propeller; k is the proportionality coefficient; α, β, and γ are the powers of D, V, and t, respectively.

[0171] The final values ​​obtained are k = 0.0071, α = 1.5381, β = 0.0027, and γ = 0.1105.

[0172] Step S5, Construction of the CNN-BPNN neural network model, as follows Figure 3 As shown, the derived physical formula is inserted into the loss function.

[0173] Step S51: First, the input data is processed by the CNN module to extract features. Then, the extracted features are input into the BPNN for further processing. Finally, the prediction results are output.

[0174] Step S52: Set up the CNN module: consisting of convolutional layers, pooling layers, and flattening layers; taking single-channel one-dimensional data (each data point is composed of multiple features) as input. The first convolutional layer (Conv1d) has 16 output channels, uses a kernel size of 2, a stride of 1, and padding of 1. The purpose of this layer is to extract low-level features. The second convolutional layer (Conv1d) has 32 output channels, also with a kernel size of 2, padding of 1, and a stride of 1, used to further extract higher-level features. A pooling layer of size 2 is used for downsampling to reduce the data dimensionality. The output of the convolutional layers is flattened into one dimension for input to the fully connected layer.

[0175] Step S53: Set up the BPNN module: It consists of fully connected layers and hidden layers. The fully connected layer is a fully connected network used to further process the features extracted by the CNN. This module contains two linear transformation layers; the input size of the first layer is the feature dimension output by the CNN module (depending on the size of the input data), and the output size is 16. Each linear transformation has input size × 16 + 16 parameters. The second linear transformation layer maps 16 hidden units to 1 output.

[0176] Step S54: Optimize using the Adam optimizer with a learning rate set to 0.001. This is a commonly used adaptive learning rate optimization algorithm that typically provides good training results.

[0177] Step S55: Determine the loss function. The loss function consists of two parts: model loss and physical loss.

[0178] Model Loss: Using the Mean Squared Error (MSE) loss function, the difference between the model's predicted value and the true target value is calculated, as shown below:

[0179]

[0180] Among them, ypred y represents the predicted value of the CNN-BPNN neural network model; true This represents the actual target value.

[0181] Physics Loss: Calculated by comparing the model's predictions with predictions based on physical formulas. The goal is to ensure that the model output aligns with physical laws, as shown below:

[0182]

[0183] Among them, physics pred This represents the predicted value using only physical formulas.

[0184] The total loss is a weighted sum of the model loss and the physical loss, as shown below:

[0185] TotalLoss = ModelLoss + λ physics ×PhysicsLoss;

[0186] Where, λ physics The weight of the physical loss is λ. physics =0.1, controls the degree of influence of physical constraints on model training.

[0187] Step S6: Use the constructed network model to predict the motion data of the robot's feet on the wet granular surface, obtain the predicted value, and compare the predicted value with the actual value as follows: Figure 4 As shown, the experimental results verify the predictive effect of the method of the present invention.

[0188] Therefore, this invention employs the aforementioned method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN. Through innovative features such as establishing high-fidelity multiphase flow coupling simulation based on data obtained from physical experiments and the VOF model, enhancing dataset distribution using GAN neural networks, employing CNN-BPNN neural network models, and integrating physical knowledge, this method provides a more accurate and effective means for predicting the mechanical properties of wet particulate media surfaces. This approach not only improves the accuracy and efficiency of prediction but also provides better support for the research and engineering applications of the mechanical properties of particulate media surfaces.

[0189] Finally, it should be noted that 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 preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN, characterized in that, Includes the following steps: Step S1: Collect data on the movement of the robot's feet on a wet granular surface and determine the factors that have the greatest impact on the results; Step S2: Based on the data obtained from the physical experiment, establish a high-fidelity fluid-solid-particle coupling simulation environment based on the VOF model; Step S3: Use a GAN neural network to enhance the distribution of the dataset; Step S4: Derivation of physical formulas based on the RFT model; Step S5: Construct the CNN-BPNN neural network model and insert the derived physical formulas into the loss function. The specific process is as follows: Step S51: First, the input data is processed by the CNN module to extract features. Then, the extracted features are input into the BPNN for further processing. Finally, the prediction result is output. Step S52: Set up the CNN module: consisting of convolutional layers, pooling layers, and flattening layers; taking one-dimensional data with a single channel as input; wherein, the first convolutional layer has 16 output channels, uses a convolutional kernel of size 2, a stride of 1, and padding of 1; the purpose of this layer is to extract low-level features; the second convolutional layer has 32 output channels, also with a convolutional kernel of size 2, padding of 1, and a stride of 1, used to further extract higher-level features; a pooling layer of size 2 is used for downsampling to reduce the data dimensionality; the output of the convolutional layer is flattened into one dimension so that it can be input into the fully connected layer; Step S53: Set up the BPNN module: It consists of fully connected layers and hidden layers; the fully connected layer is a fully connected network used to further process the features extracted by the CNN; this module contains two linear transformations; the input size of the first layer is the feature dimension output by the CNN module, and the output size is 16; each linear transformation has input size × 16 + 16 parameters; the second linear transformation maps 16 hidden units to 1 output. Step S54: Optimize using the Adam optimizer with a learning rate set to 0.001; Step S55: Determine the loss function. The loss function consists of two parts: model loss and physical loss. Step S6: Use the established network model to predict the data of the robot's foot movement on the wet granular ground and obtain the predicted value.

2. The method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN according to claim 1, characterized in that: The mechanical parameter collection of wet particulate media ground consists of two parts. The first part is to determine the variables to be studied through data acquisition and to design experiments using orthogonal experimental methods. The second part is to accurately test the data and strictly measure and analyze each variable according to the experimental design table.

3. The method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN according to claim 2, characterized in that, Based on the collected data, an experiment was designed using the orthogonal experimental method to determine the variables to be studied, and each variable was measured and analyzed. The specific process is as follows: Step S11: Select the test indicators; Step S12: Select factors and levels; Step S13: Design an orthogonal array using SPSS Statistics 23; Step S14: Measure each set of experimental data three times and take the arithmetic mean; Step S15: Analyze the test results using range analysis.

4. The method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN according to claim 1, characterized in that, In step S2, based on the data obtained from the physical experiment, a high-fidelity fluid-solid-particle coupled simulation environment is established based on the VOF model. The specific process is as follows: Step S21: The applicability of the RFT model micro-element method and inertial force model in saturated wet particulate media is studied by using multiphase flow coupling simulation test, and the key factors for the study of the ground resistance model of the foot in saturated wet particulate media are clarified. For the study of wet particulate media, coupled simulation was performed using the fluid dynamics simulation software ANSYS Fluent and EDEM. Step S22: The VOF model models immiscible fluids by solving a set of momentum equations and tracking the volume fraction of each fluid in the entire computational domain. For each immiscible additional fluid phase added to the model, a corresponding variable is introduced—the volume fraction of that phase in the cell. Step S23: By solving the continuity equation of the phase volume fraction, the interface between phases is traced, as shown below: ； in, Indicates the density of the fluid; This indicates the volume fraction of fluid in the unit; Represents the velocity vector of the fluid; and This represents two phases interacting; and This indicates mass transfer between phases; Indicates the source phase; Step S24: The volume fraction equation for the initial phase will not be solved; the volume fraction will be calculated based on the following constraints: ； Step S25: Solve the VOF-based model using implicit formulas. The volume fraction equation is then discretized as follows: ； in, The index of the current time step; This is the index of the previous time step; In the first The unit value of volume fraction at the time step; In the first The unit value of volume fraction at the time step; For the first The face value of the volume fraction at step time; For the first The volume flux through the surface during the step; V is the unit volume.

5. The method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN according to claim 4, characterized in that, The sum of the volume fractions of all phases is 1. Volume fractions are represented by the symbol 1. Indicates; the first in a multiphase fluid The volume fraction of each item is Then there are three possible scenarios: (1) =0, at this time the element does not contain the fluid term; (2) =1, at this time all the elements in the cell are this fluid term; (3) 0 < <1, at this time the cell contains the interface between the fluid item and one or more other fluid phases.

6. The method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN according to claim 1, characterized in that, In step S3, a GAN neural network is used to enhance the distribution of the dataset. The specific process is as follows: Step S31, Data Preprocessing and Normalization: Read the data and normalize it using MinMaxScaler, scaling all feature values ​​to the range of [0,1]. Step S32: Build a basic GAN framework, including a generator and a discriminator. Step S33: During the training process of GAN, the generator and discriminator are optimized alternately; Step S34: Data generation and denormalization, restoring the generated data to the original numerical range; Step S35: Post-process the data, discretize and limit the range, and save the data as an Excel file.

7. The method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN according to claim 1, characterized in that, In step S4, the physical formulas are derived based on the RFT model. The specific process is as follows: Step S41: Use the RFT theoretical model as the theoretical basis for studying the mechanical properties of robots on particulate media surfaces; Step S42: Simulation experiment based on advanced discrete element method to analyze and verify the conditions and key factors for the establishment of the RFT model in particulate media; Step S43: Through fluid-solid-particle coupling simulation test, the magnitude and corresponding relationship of the resistance of the three components in the wet particulate medium when they move at the same speed are tested, and the test results are analyzed. Step S44: Determine a simplified model suitable for the neural network, as shown below: ； in, For the robot's feet in Force in the axial direction; For depth, For speed, Types of robot propeller parts; This is the proportionality coefficient; , , They are respectively , , The power of .

8. The method for predicting the mechanical properties of wet particulate media based on GAN and CNN-BPNN according to claim 1, characterized in that, Model loss: The mean squared error loss function is used to calculate the difference between the model's predicted value and the true target value, as shown below: ； in, Indicates the model loss; This represents the predicted value of the CNN-BPNN neural network model; Indicates the true target value; Physical loss: Calculated by comparing the model's predictions with the predicted values ​​calculated based on physical formulas. The aim is to ensure that the model output aligns with physical laws, as shown below: ； in, Indicates physical loss; This represents the predicted value using only physical formulas; The total loss is a weighted sum of the model loss and the physical loss, as shown below: ； in, Indicates the total loss; It is the weight of the physical loss, which controls the degree to which physical constraints affect model training.

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