Wet granular medium mechanical property prediction method based on GAN and CNN-BPNN

Abstract

The invention belongs to the technical field of machine learning and ground mechanics prediction, and discloses a wet particle medium mechanical property prediction method based on GAN and CNN-BPNN, and the method comprises the following steps: collecting the data of the movement of the feet of a robot on the ground of a wet particle medium, determining the factor which has the greatest influence on the result, and determining the factor which has the greatest influence on the result; establishing a high-fidelity fluid-solid-particle coupling simulation environment based on a VOF model; enhancing data set distribution by using a GAN neural network; carrying out physical formula derivation based on an RFT model; constructing a CNN-BPNN neural network model, and inserting the derived physical formula into a loss function; and predicting the data by using the established network model. According to the wet granular medium mechanical property prediction method based on the GAN and the CNN-BPNN, the prediction accuracy and efficiency are improved, and support is provided for granular medium ground mechanical property research and engineering application.

Description

Technical Field

[0001] The present invention relates to the technical field of machine learning and ground mechanics prediction, and in particular to a method for predicting mechanical properties of wet granular media based on GAN and CNN-BPNN. Background Art

[0002] The robot's ability to move on unstructured ground formed by granular media such as star soil and seabed mud is extremely attenuated. Granular medium ground shows fluidity when disturbed at low speed, and shows certain solid properties when impacted at high speed. Its complex physical properties pose a huge challenge to the efficient operation of robots. The seabed and the area near the water on the beach in an amphibious environment are usually wet granular medium ground formed by a mixture of water and sand. The mechanical properties of sand and water become more complex after mixing. The prediction of the mechanical properties of the robot's foot-ground interaction on this ground is a key issue that needs to be solved in the development of amphibious robots.

[0003] To date, although machine learning methods have greatly promoted the research of nonlinear dynamics prediction, it is still a challenge to apply these methods to the prediction of mechanical properties of robot foot-ground interaction on granular media surfaces. On the one hand, most traditional machine learning methods are difficult to adapt to the complex mechanism, high nonlinearity and high dimensionality of data of granular media surfaces because their feature extraction capabilities are shallow, and compared with models based on physical formulas, the feature information extracted in traditional neural networks is difficult to intuitively explain from physical principles, and most parameters in the model lack clear physical meanings. On the other hand, a well-trained ML model usually requires a large amount of experimental data, which is time-consuming and expensive.

[0004] Therefore, there is an urgent need for a method to predict the foot-ground interaction mechanical properties of a robot moving on a saturated wet granular medium ground. This method aims to contribute to this growing research field by exploring the combination of machine learning and physical models to predict the foot-ground interaction mechanical properties of a robot moving on a complex mechanism ground. Summary of the invention

[0005] The purpose of the present invention is to provide a method for predicting the mechanical properties of wet granular media based on GAN and CNN-BPNN. By establishing a high-fidelity multiphase flow coupling simulation based on data obtained from actual experiments and a VOF model, using a GAN neural network to enhance data set distribution, using a CNN-BPNN neural network model, and integrating physical knowledge, a more accurate and effective means for predicting the ground mechanical properties of wet granular media is provided, which not only improves the accuracy and efficiency of the prediction, but also provides better support for the research and engineering application of the ground mechanical properties of granular media.

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

[0007] Step S1, collecting data of the robot's feet moving on the wet granular medium ground, and determining the factors that have the greatest impact on the results;

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

[0009] Step S3, using GAN neural network to enhance data set distribution;

[0010] Step S4, deriving physical formulas based on the RFT model;

[0011] Step S5, constructing a CNN-BPNN neural network model, and inserting the derived physical formula into the loss function;

[0012] Step S6: Use the constructed network model to predict the data of the robot's feet moving on the wet granular medium ground to obtain a predicted value.

[0013] Preferably, the mechanical parameter collection of the wet granular medium ground includes two parts. The first part is to determine the variables to be studied through data collection, and to design the experiment through the orthogonal experimental method; the second part is the precise data testing, and each variable is strictly measured and analyzed according to the experimental design table.

[0014] Preferably, based on the collected data, an experiment is designed by an 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, selecting test indicators;

[0016] Step S12, selecting factors and levels;

[0017] Step S13, designing an orthogonal array using SPSS Statistics 23;

[0018] Step S14, measuring each set of experimental data three times and taking the arithmetic mean;

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

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

[0021] Step S21, using multiphase flow coupling simulation test to study the applicable conditions of the RFT model microelement method and the inertial force model in the saturated wet granular medium, and clarify the key factors of the research on the ground resistance model of the foot in the saturated wet granular medium;

[0022] For the study of wet granular media, the fluid mechanics simulation software ANSYS Fluent and EDEM were used for coupled simulation;

[0023] Step S22, the VOF model models the immiscible fluid 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, which is the volume fraction of the phase in the unit.

[0024] Step S23: Track the interface between the phases by solving the continuity equation for the volume fraction of the phases, as shown below:

[0025]

[0026] Among them, ρ q represents the density of the fluid; α q represents the volume fraction of the fluid in the unit; represents the velocity vector of the fluid; p and q represent the two interacting phases; and Represents the mass transfer between phases; S αq represents the source phase;

[0027] Step S24: The volume fraction equation of the initial phase will not be solved, and the volume fraction will be calculated according to the following constraints:

[0028]

[0029] Step S25: Using an implicit formula to solve the VOF model, the volume fraction equation is discretized in the following manner:

[0030]

[0031] Among them, n+1 is the index of the current time step; n is the index of the previous time step; is the unit value of volume fraction at the n+1th time step; is the unit value of volume fraction at the nth time step; is the nominal value of the volume fraction at step n+1; is the volume flux through the surface at the n+1th step; 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 a multiphase fluid is αi , there are three situations:

[0033] (1)α i =0, the unit does not contain the fluid item;

[0034] (2)α i =1, then all the cells are this fluid item;

[0035] (3) 0<α i <1, in which case the cell contains the interface between the fluid term and one or more other fluid phases.

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

[0037] Step S31, data preprocessing and normalization: read the data, and use MinMaxScaler to normalize the data, scaling all eigenvalues ​​to the range of [0,1];

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

[0039] Step S33, alternately optimizing the generator and the discriminator during the training process of the GAN;

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

[0041] Step S35: post-process the data, perform discretization and range limitation, and save the data as an Excel file.

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

[0043] Step S41, using the RFT theoretical model as a theoretical basis for studying the mechanical properties of the robot on granular medium ground;

[0044] Step S42: Analyze and verify the establishment conditions and key factors of the RFT model in the granular medium based on the simulation experiment of the advanced discrete element method;

[0045] Step S43, through a fluid-solid-particle coupling simulation test, the resistance magnitudes and corresponding relationships of the three components in the wet granular medium when moving 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 is the force on the robot's foot in the x-axis direction; D is the depth, V is the speed, t is the type of the robot's foot paddle; k is the proportional coefficient; α, β, γ are the powers of D, V, and t, respectively.

[0049] Preferably, in step S41, based on the idea of ​​microelement, it is assumed that the resultant force on the moving object moving underground in the dry granular medium is the linear superposition of each independent force unit; the model is divided into two parts, namely, the horizontal plane RFT model and the vertical plane RFT model;

[0050] The horizontal plane RFT model is as follows:

[0051]

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

[0053] The vertical RFT model is as follows:

[0054] The vertical RFT model is as follows:

[0055]

[0056] Among them, σ z,x is the vertical and horizontal force of the unit body; |z| is the embedding depth; β is the attack angle; γ is the invasion angle; α z,x (β,γ) are the vertical and horizontal stresses;

[0057] The scaled model is obtained by performing Fourier transformation on the stress data of various granular grounds with respect to the invasion angle and attack angle, as 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, is the unit horizontal and vertical stress; ξ is the scale ratio, β is the angle of attack, γ is the angle of invasion, M is the Fourier coefficient, α z,x (β,γ) are the horizontal and vertical stresses of the actual granular ground;

[0062] By using this scaled model, a complete mechanical model can be obtained by measuring only the experimental mechanical data of the vertical downward pressure of the plate at the expense of a certain degree of accuracy.

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

[0064] Step S51: First, input data to perform feature extraction through the CNN module, then input the extracted features into the BPNN for further processing, and finally output the prediction results;

[0065] Step S52, set up a CNN module: consisting of a convolution layer, a pooling layer, and a flattening layer; use single-channel one-dimensional data as input; wherein the first convolution layer has 16 output channels, uses a convolution kernel of size 2, a stride of 1, and a padding of 1; the purpose of this layer is to extract low-level features; the second convolution layer has 32 output channels, the convolution kernel size is also 2, the padding is 1, and the stride is 1, which is used to further extract higher-level features; use a pooling layer of size 2 for downsampling to reduce the data dimension; flatten the output of the convolution layer into one dimension for input to the fully connected layer;

[0066] Step S53, setting a BPNN module: consisting of a fully connected layer and a hidden layer; the fully connected layer is a fully connected network for further processing the features extracted by CNN; the module contains two layers of linear transformation; the input size of the first layer is the feature dimension of the output of the CNN module, and the output size is 16; each linear transformation has input size×16+16 parameters; the second layer of linear transformation maps 16 hidden units to 1 output;

[0067] Step S54, use the Adam optimizer for optimization, and set the learning rate to 0.001;

[0068] Step S55, determine the loss function, which consists of two parts, one is the model loss and the other is the physical loss.

[0069] Preferably, model loss: Use the mean squared error loss function to calculate the difference between the model prediction value and the true target value, as follows:

[0070]

[0071] Among them, ModelLoss represents the model loss; y pred Represents the predicted value of the CNN-BPNN neural network model; y true represents the true target value;

[0072] Physical loss: Calculated by comparing the model's predictions with the predictions calculated based on physical formulas, with the goal of making the model output consistent with physical laws, as shown below:

[0073]

[0074] Among them, PhysicsLoss represents physical loss; physics pred It represents the predicted value using only physical formula;

[0075] The total loss is the weighted sum of the model loss and the physical loss as follows:

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

[0077] Among them, TotalLoss represents the total loss; λ physics is the weight of the physical loss, which controls the influence of physical constraints on model training.

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

[0079] (1) Establish high-fidelity multiphase flow coupling simulation based on the data obtained from physical experiments and the VOF model: A fluid-solid-particle coupling simulation environment was established based on the VOF model. The multiphase flow coupling simulation test was used to study the applicable conditions of the RFT model microelement method and the inertial force model in saturated wet granular media, and the key factors in the study of the ground resistance model of the foot in saturated wet granular media were clarified;

[0080] (2) GAN neural network to enhance data set distribution: Using the GAN-based regression data generation method, by constructing a generator and discriminator suitable for regression tasks, and post-processing and evaluating the generated results, high-quality synthetic data similar to the real data distribution is generated, solving the small data set prediction problem and reducing the long test cycle and high test cost caused by relying on physical tests;

[0081] (3) CNN-BPNN neural network model: Combining CNN with 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 ability of BPNN, which greatly improves the accuracy and efficiency of model prediction;

[0082] (4) Integration of physical knowledge: Physical information is added to the CNN-BPNN neural network model in the form of a loss function, making the model physically interpretable and improving prediction accuracy.

[0083] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 It is a flow chart of a method for predicting mechanical properties of wet granular media based on GAN and CNN-BPNN;

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

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

[0087] Figure 4 1 is a comparison diagram between the prediction results and the true values ​​in the embodiment of the present invention. DETAILED DESCRIPTION

[0088] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

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

[0090] Step S1, collecting data of the robot's feet moving on the wet granular medium ground, and determining the factors that have the greatest impact on the results;

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

[0092] Step S3, using GAN (Generative Adversarial Network) neural network to enhance the data set distribution;

[0093] Step S4, deriving physical formulas based on the RFT model (Resistive Force Theory);

[0094] Step S5, constructing a CNN-BPNN (a convolutional neural network and a back propagation neural network combined neural network model) neural network model, and inserting the derived physical formula into the loss function;

[0095] Step S6: Use the constructed network model to predict the data of the robot's feet moving on the wet granular medium ground to obtain a predicted value.

[0096] Example

[0097] The present invention provides a method for predicting mechanical properties of wet granular media based on GAN and CNN-BPNN, and the specific implementation process is as follows:

[0098] Step S1, collecting data of the robot's feet moving on the wet granular medium ground, and determining the factors that have the greatest impact on the results.

[0099] The mechanical parameter collection of wet granular medium ground mainly includes two parts. The first part is to determine the variables to be studied through a large amount of data collection, and to design the experiment through the orthogonal experimental method; the second part is the data precision test, and each variable is strictly measured and analyzed according to the experimental design table. Based on the large amount of data collected, the experiment is designed through the orthogonal experimental method, the variables to be studied are determined, and each variable is measured and analyzed. The specific process is as follows:

[0100] Step S11, selecting a test index: The resistance encountered by the foot during the interaction with the saturated wet granular medium ground plays a decisive role in the robot's movement ability, so it is used as a test index, denoted by F.

[0101] Step S12, select factors and levels: To study the resistance phenomenon in the 2D plane, the relevant experimental factors include speed, 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, designing an orthogonal array: using SPSS Statistics 23 to complete the design of the L9(33) orthogonal array, as shown in Table 1.

[0106] Table 1L9(33) orthogonal test table

[0107]

[0108]

[0109] Step S14, conduct the experiment according to the plan: measure each set of experimental data three times and take the arithmetic mean value, and the measurement results and variance are recorded in Table 1.

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

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

[0112] Table 2 Range Statistics

[0113]

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

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

[0116] Step S21, using multiphase flow coupling simulation test to study the applicable conditions of RFT model microelement method and inertial force model in saturated wet granular medium, and clarify the key factors of the foot ground resistance model in saturated wet granular medium. For the study of wet granular medium, the computational fluid dynamics (CFD) simulation software ANSYS Fluent (ANSYS is a company, Fluent is the name of a simulation software of the company, commonly used in fluid dynamics simulation) and EDEM (the world's first general simulation analysis software based on advanced discrete element method) Discrete Element Method) are used for coupling simulation.

[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 in the entire computational domain.

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

[0119] The sum of the volume fractions of all phases is 1, and the volume fraction is usually represented by the symbol α. If the volume fraction of the i-th term in a multiphase fluid is α i , there are three situations:

[0120] (1)α i =0, the unit does not contain the fluid item;

[0121] (2)α i =1, then all the cells are this fluid item;

[0122] (3) 0<α i <1, in which case the cell contains the interface between the fluid term and one or more other fluid phases.

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

[0124]

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

[0126] Usually, the source phase S on the right side of the equation αq is 0, but a constant can be assigned to each phase depending on the specific characteristics of the fluid phase.

[0127] Step S24: The volume fraction equation of the initial phase will not be solved, and the volume fraction will be calculated according to the following constraints:

[0128]

[0129] Step S25, in the process of solving the problem based on the VOF model, the implicit equation (The Implicit Formulation) iteratively solves the scalar transport equation for each second phase volume fraction in each time step. The coupled simulation of the two simulation platforms Fluent and EDEM depends on the mutual transfer and solution of parameters between the two software in each time step. Therefore, the implicit formula is used to solve the VOF model, and the volume fraction equation is discretized in the following way:

[0130]

[0131] Among them, n+1 is the index of the current time step; n is the index of the previous time step; is the unit value of volume fraction at the n+1th time step; is the unit value of volume fraction at the nth time step; is the nominal value of the volume fraction at step n+1; is the volume flux through the surface at the n+1th step; V is the unit volume.

[0132] Since the volume fraction at the current time step is a function of other quantities at the current time step, the scalar transport equation for each second phase volume fraction is solved iteratively at each time step. The areal flux is interpolated using the selected spatial discretization scheme, and the implicit formulation can be used for both time-dependent and steady-state calculations.

[0133] The control volume formulation in ANSYS FLUENT requires that the convection and diffusion fluxes through the control volume surface be calculated and balanced with the source terms within the control volume. In both the geometry reconstruction and donor-acceptor schemes, ANSYS FLUENT performs a special interpolation treatment on cells located near the interface between two phases, showing the actual interface shape. In the geometry reconstruction method, the standard interpolation format in ANSYS FLUENT is used to obtain the surface flux when a cell is completely filled with one or the other phase. When the cell is close to the interface between two phases, the geometry reconstruction scheme is used.

[0134] Step S3: Use GAN neural network to enhance the data set distribution.

[0135] Step S31: data preprocessing and normalization.

[0136] The data is read and normalized using MinMaxScaler (MinMaxScaler is a feature scaling tool in the scikit-learn library 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, see 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 similar to real data from a potential noise space. It is a multi-layer fully connected neural network. The input is a random noise vector (dimension is 10). After several layers of linear transformation and activation function (such as ReLU), an output with the same feature dimension as the input data is generated. The final output layer uses a linear activation function, which is suitable for regression tasks to ensure that the generated data is a continuous value.

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

[0140] Step S33: Alternately optimize the generator and the discriminator during the training process of GAN.

[0141] The training process of GAN is adversarial, with the generator and the discriminator competing with each other. The generator continuously generates fake data in an attempt to make the discriminator unable to distinguish between true and false; while the discriminator continuously optimizes to enhance its ability to distinguish between true and false data. Through this "adversarial training", the generator gradually learns the distribution of real data.

[0142] Step S34: data generation and denormalization.

[0143] After training, the generator can generate a large number of new data samples. The output of the generator is normalized data. In order to be able to compare with the original data, the denormalization operation is used to restore the generated data to the original numerical range.

[0144] Step S35: post-process the data, perform discretization and range limitation, and save the data as an Excel file.

[0145] For some specific features, the generated data needs to meet certain constraints. The code processes these features by mapping them to discrete sets of multiples and limiting the value range to ensure that the generated data meets the needs of the actual application.

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

[0147] Step S41, using the RFT theoretical model as the theoretical basis for studying the mechanical properties of the robot on granular medium ground.

[0148] Based on the idea of ​​microelement, it is assumed that the resultant force on the moving object moving underground in dry granular medium is the linear superposition of each independent force unit. The model is divided into two parts, namely the horizontal plane RFT model and the vertical plane RFT model.

[0149] The horizontal plane RFT model is as follows:

[0150]

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

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

[0153] The vertical RFT model is as follows:

[0154]

[0155] Among them, σ z,x is the vertical and horizontal force of the unit body; |z| is the embedding depth; β is the attack angle (the angle between the unit body and the horizontal direction); γ is the invasion angle (the angle between the unit body movement speed and the horizontal direction); α z,x (β,γ) are the vertical and horizontal stresses.

[0156] The relationship between the stress and the angle of invasion and the angle of attack of the vertical RFT model is difficult to describe with an accurate mathematical formula and requires experimental measurement, but the stress of different granular grounds has a similar trend with the angle of invasion and the angle of attack. The scaled model is obtained by performing Fourier transformation on the stress data of various different granular grounds with respect to the angle of invasion and the angle of attack, 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, is the unit horizontal and vertical stress; ξ is the scale ratio, β is the angle of attack, γ is the angle of invasion, M is the Fourier coefficient, α z,x (β,γ) are the horizontal and vertical stresses of the actual granular ground. Using this scaled model, with a certain loss of accuracy, only the mechanical data of the vertical downward pressure test of the flat plate need to be measured to obtain a complete mechanical model.

[0161] The vertical plane RFT model is based on the horizontal plane RFT model. It is suitable for calculating the forces of low-speed motion with shallow embedding depth under dry granular ground, and is suitable for calculating the contact force between small footed robots and the ground.

[0162] Therefore, the RFT theoretical model was chosen as the theoretical basis for studying the mechanical properties of robots on granular media ground.

[0163] Step S42: Based on the simulation experiment of the advanced discrete element method, the establishment conditions and key factors of the RFT model in the granular medium are analyzed and verified.

[0164] The most critical condition for the realization of RFT in granular media is the establishment of the infinitesimal method, that is, for a component moving in a granular medium, it is discretized into multiple tiny units, and the force of each tiny unit is calculated and superimposed to obtain the resistance of the entire component.

[0165] Step S43: Through a fluid-solid-particle coupling simulation test, the resistance magnitudes and corresponding relationships of the three components in the wet granular medium when moving 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 2 mm and a leading surface size of 20 mm×20 mm; 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 there are errors in the calculation of the differential element method, so the specific model needs to be improved according to the characteristics of the 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 is the force on the robot's foot in the x-axis direction; D is the depth, V is the speed, t is the type of the robot's foot paddle; k is the proportional coefficient; α, β, γ are the powers of D, V, and t, respectively.

[0171] Finally, we get k=0.0071, α=1.5381, β=0.0027, and γ=0.1105.

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

[0173] Step S51: First, input data and extract features through the CNN module, then input the extracted features into the BPNN for further processing, and finally output the prediction results.

[0174] Step S52, set up a CNN module: consisting of a convolution layer, a pooling layer, and a flattening layer; use single-channel one-dimensional data (each data point consists of multiple features) as input. Among them, the first convolution layer (Conv1d) has 16 output channels, uses a convolution kernel of size 2, a stride of 1, and a padding of 1. The purpose of this layer is to extract low-level features. The second convolution layer (Conv1d) has 32 output channels, the convolution kernel size is also 2, the padding is 1, and the stride is 1, which is used to further extract higher-level features. Use a pooling layer of size 2 for downsampling to reduce the data dimension. Flatten the output of the convolution layer into one dimension for input to the fully connected layer.

[0175] Step S53, set up a BPNN module: consisting of a fully connected layer and a hidden layer. The fully connected layer is a fully connected network used to further process the features extracted by CNN. The module contains two layers of linear transformations; the input size of the first layer is the feature dimension of the output of 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 layer of linear transformation maps 16 hidden units to 1 output.

[0176] Step S54: Use the Adam optimizer for optimization, and set the learning rate to 0.001. This is a commonly used adaptive learning rate optimization algorithm, which can usually provide better training results.

[0177] Step S55, determine the loss function, which consists of two parts, one is the model loss (ModelLoss), and the other is the physical loss (Physics Loss).

[0178] Model Loss: Use the mean squared error (MSE) loss function to calculate the difference between the model prediction value and the true target value, as shown below:

[0179]

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

[0181] Physics Loss: It is calculated by comparing the model's predictions with the predictions calculated based on physical formulas. The purpose is to make the model output consistent with the laws of physics, as shown below:

[0182]

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

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

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

[0186] Among them, λ physics is the weight of physical loss, let λ physics =0.1, controls the influence of physical constraints on model training.

[0187] Step S6: Use the established network model to predict the data of the robot's foot moving on the wet granular medium ground, obtain the predicted value, and compare the predicted value with the actual value. Figure 4 As shown, the experimental results verify the prediction effect of the method of the present invention.

[0188] Therefore, the present invention adopts the above-mentioned method for predicting the mechanical properties of wet granular media based on GAN and CNN-BPNN, and establishes high-fidelity multiphase flow coupling simulation based on the data obtained from actual experiments and the VOF model, GAN neural network enhanced data set distribution, CNN-BPNN neural network model, and integration of physical knowledge and other innovations, which provides a more accurate and effective means for predicting the ground mechanical properties of wet granular media; this method not only improves the accuracy and efficiency of the prediction, but also provides better support for the research and engineering application of the ground mechanical properties of granular media.

[0189] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for predicting mechanical properties of wet granular media based on GAN and CNN-BPNN, characterized in that: The following steps are involved: Step S1, collecting data of the robot's feet moving on the wet granular medium ground, and determining the factors that have the greatest impact on the results; Step S2: establishing a high-fidelity fluid-solid-particle coupling simulation environment based on the VOF model according to the data obtained from the physical experiment; Step S3, using GAN neural network to enhance data set distribution; Step S4, deriving physical formulas based on the RFT model; Step S5, constructing a CNN-BPNN neural network model, and inserting the derived physical formula into the loss function; Step S6: Use the constructed network model to predict the data of the robot's feet moving on the wet granular medium ground to obtain a predicted value.

2. The method for predicting mechanical properties of wet granular media based on GAN and CNN-BPNN according to claim 1, characterized in that: The collection of mechanical parameters of wet granular medium ground includes two parts. The first part is to determine the variables to be studied through data collection, and to design the experiment through the orthogonal experimental method; the second part is the precise data testing, which strictly measures and analyzes each variable according to the experimental design table.

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

4. The method for predicting mechanical properties of wet granular media based on GAN and CNN-BPNN according to claim 1, characterized in that: In step S2, according to the data obtained from the physical experiment, a high-fidelity fluid-solid-particle coupling simulation environment is established based on the VOF model. The specific process is as follows: Step S21, using multiphase flow coupling simulation test to study the applicable conditions of the RFT model microelement method and the inertial force model in the saturated wet granular medium, and clarify the key factors of the research on the ground resistance model of the foot in the saturated wet granular medium; For the study of wet granular media, the fluid mechanics simulation software ANSYS Fluent and EDEM were used for coupled simulation; Step S22, the VOF model models the immiscible fluid 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, which is the volume fraction of the phase in the unit. Step S23: Track the interface between the phases by solving the continuity equation for the volume fraction of the phases, as shown below: Among them, ρ q represents the density of the fluid; α q represents the volume fraction of the fluid in the unit; represents the velocity vector of the fluid; p and q represent the two interacting phases; and Represents the mass transfer between phases; S αq represents the source phase; Step S24: The volume fraction equation of the initial phase will not be solved, and the volume fraction will be calculated according to the following constraints: Step S25: Using an implicit formula to solve the VOF model, the volume fraction equation is discretized in the following manner: Among them, n+1 is the index of the current time step; n is the index of the previous time step; is the unit value of volume fraction at the n+1th time step; is the unit value of volume fraction at the nth time step; is the nominal value of the volume fraction at step n+1; is the volume flux through the surface at the n+1th step; V is the unit volume.

5. A method for predicting mechanical properties of wet granular 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. The volume fraction is usually represented by the symbol α. The volume fraction of the i-th term in a multiphase fluid is α i , there are three situations: (1)α i =0, the unit does not contain the fluid item; (2)α i =1, then all the cells are this fluid item; (3) 0<α i <1, in which case the cell contains the interface between the fluid term and one or more other fluid phases.

6. The method for predicting mechanical properties of wet granular media based on GAN and CNN-BPNN according to claim 1, characterized in that: In step S3, the GAN neural network is used to enhance the distribution of the data set. The specific process is as follows: Step S31, data preprocessing and normalization: read the data, and use MinMaxScaler to normalize the data, scaling all eigenvalues ​​to the range of [0,1]; Step S32: Build a basic GAN framework, including a generator and a discriminator; Step S33, alternately optimizing the generator and the discriminator during the training process of the GAN; Step S34: data generation and denormalization, restoring the generated data to the original value range; Step S35: post-process the data, perform discretization and range limitation, and save the data as an Excel file.

7. The method for predicting mechanical properties of wet granular media based on GAN and CNN-BPNN according to claim 1, characterized in that: In step S4, the physical formula is derived based on the RFT model. The specific process is as follows: Step S41, using the RFT theoretical model as the theoretical basis for studying the mechanical properties of the robot on granular medium ground; Step S42: Analyze and verify the establishment conditions and key factors of the RFT model in the granular medium based on the simulation experiment of the advanced discrete element method; Step S43, through a fluid-solid-particle coupling simulation test, the resistance magnitudes and corresponding relationships of the three components in the wet granular medium when moving 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: F x =kD α V β t γ ; Among them, F x is the force on the robot's foot in the x-axis direction; D is the depth, V is the speed, t is the type of the robot's foot paddle; k is the proportional coefficient; α, β, γ are the powers of D, V, and t, respectively.

8. The method for predicting mechanical properties of wet granular media based on GAN and CNN-BPNN according to claim 7, characterized in that: In step S41, based on the idea of ​​micro-element, it is assumed that the resultant force on the moving object moving underground in the dry granular medium is the linear superposition of each independent force unit; the model is divided into two parts, namely the horizontal plane RFT model and the vertical plane RFT model; The horizontal plane RFT model is as follows: Among them, F N is the normal force, F L is the tangential force, F X is the horizontal resultant force; tanβ0=cotγ0sinψ, γ0 is the ground internal friction angle, ψ is the angle between the unit axis and its moving speed; θ is the angle between the discrete unit axis and the horizontal direction, l and r are the unit length and radius; C S , C F and β0 are the drag force constants, which are related to the granular medium; The vertical RFT model is as follows: The vertical RFT model is as follows: Among them, σ z,x is the vertical and horizontal force of the unit body; |z| is the embedding depth; β is the attack angle; γ is the invasion angle; α z,x (β,γ) are the vertical and horizontal stresses; The scaled model is obtained by performing Fourier transformation on the stress data of various granular grounds with respect to the invasion angle and attack angle, as shown below: 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 in, is the unit horizontal and vertical stress; ξ is the scale ratio, β is the angle of attack, γ is the angle of invasion, M is the Fourier coefficient, α z,x (β,γ) are the horizontal and vertical stresses of the actual granular ground; By using this scaled model, a complete mechanical model can be obtained by measuring only the experimental mechanical data of the vertical downward pressure of the plate at the expense of a certain degree of accuracy.

9. The method for predicting mechanical properties of wet granular media based on GAN and CNN-BPNN according to claim 1, characterized in that: In step S5, the CNN-BPNN neural network model is constructed by inserting the derived physical formula into the loss function. The specific process is as follows: Step S51: First, input data to perform feature extraction through the CNN module, then input the extracted features into the BPNN for further processing, and finally output the prediction results; Step S52, set up a CNN module: consisting of a convolution layer, a pooling layer, and a flattening layer; use single-channel one-dimensional data as input; wherein the first convolution layer has 16 output channels, uses a convolution kernel of size 2, a stride of 1, and a padding of 1; the purpose of this layer is to extract low-level features; the second convolution layer has 32 output channels, the convolution kernel size is also 2, the padding is 1, and the stride is 1, which is used to further extract higher-level features; use a pooling layer of size 2 for downsampling to reduce the data dimension; flatten the output of the convolution layer into one dimension for input to the fully connected layer; Step S53, setting a BPNN module: consisting of a fully connected layer and a hidden layer; the fully connected layer is a fully connected network for further processing the features extracted by CNN; the module contains two layers of linear transformation; the input size of the first layer is the feature dimension of the output of the CNN module, and the output size is 16; each linear transformation has input size×16+16 parameters; the second layer of linear transformation maps 16 hidden units to 1 output; Step S54, use the Adam optimizer for optimization, and set the learning rate to 0.001; Step S55, determine the loss function, which consists of two parts, one is the model loss and the other is the physical loss.

10. A method for predicting mechanical properties of wet granular media based on GAN and CNN-BPNN according to claim 9, characterized in that: Model loss: Use the mean squared error loss function to calculate the difference between the model prediction value and the true target value, as shown below: Among them, ModelLoss represents the model loss; y pred Represents the predicted value of the CNN-BPNN neural network model; y true represents the true target value; Physical loss: Calculated by comparing the model's predictions with the predictions calculated based on physical formulas, with the goal of making the model output consistent with physical laws, as shown below: Among them, PhysicsLoss represents physical loss; physics pred It represents the predicted value using only physical formula; The total loss is the weighted sum of the model loss and the physical loss as follows: TotalLoss=ModelLoss+λ physics ×PhysicsLoss; Among them, TotalLoss represents the total loss; λ physics is the weight of the physical loss, which controls the influence of physical constraints on model training.

Images