An artificial intelligence-based bagged sand cofferdam MPM simulation method and system

Abstract

The application belongs to the technical field of the cross of artificial intelligence and computational mechanics, and particularly relates to a bagged sand cofferdam MPM simulation method and system based on artificial intelligence, a three-dimensional simulation system of the bagged sand cofferdam is constructed by combining the MPM method, a penetration state of the sand and the geotextile is detected by using a penetration tracking algorithm and a space hash acceleration, an artificial intelligence algorithm is introduced to design a reward function with the minimum penetration depth and penetration times as the target, penetration prediction of the bagged sand MPM particle is driven, further based on the predicted contact model and the artificial intelligence algorithm, the MPM particle velocity and stress are dynamically regulated to prevent penetration and ensure numerical stability, and the implicit integration and gradient descent method are adopted to improve the calculation precision, and the two-way coupling of the sand and the geotextile is realized through a visualization module. The problems of low coupling simulation efficiency, easy penetration and numerical instability of the sand and the flexible structure in the traditional method are solved, and the accuracy and reliability of the simulation analysis of the bagged sand cofferdam structure under complex working conditions are significantly improved.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of artificial intelligence and computational mechanics, specifically relating to an artificial intelligence-based method and system for simulating MPM (Multi-Mesh Mooring) cofferdams. Background Technology

[0002] Geotextile sand cofferdams are widely used in various temporary cofferdam projects. Their structural performance is significantly affected by the interaction between sand and geotextile. Traditional simulation methods mostly use the finite element method or discrete element method, but it is difficult to effectively simulate the dynamic coupling behavior of flexible geotextile and loose sand particles. The following problems exist: (1) The large deformation of geotextile and the discrete characteristics of sand particles make the calculation extremely complicated and inefficient; (2) Sand particles are prone to penetration during the contact process with the fabric, resulting in simulation distortion; (3) Insufficient numerical stability, which easily leads to abnormal results such as sand particle leakage or fabric tearing.

[0003] In existing technologies, the nonlinear mechanical response of geotextiles is not fully considered; some methods reduce the amount of computation by simplifying the contact model, but at the expense of simulation accuracy.

[0004] Furthermore, traditional methods lack intelligent control for dynamic optimization of coupled systems, making them difficult to adapt to complex engineering scenarios. Summary of the Invention

[0005] To address the aforementioned problems in existing technologies, this invention proposes a manhole cover sand cofferdam MPM simulation method integrating artificial intelligence technology. This method accurately characterizes the mechanical properties of the geotextile using a mass-spring model, combines MPM simulation with sand particle movement simulation, and utilizes artificial intelligence algorithms and a prediction-based contact model to correct particle states in real time. Simultaneously, artificial intelligence algorithms are introduced to optimize fabric penetration parameters, and bidirectional data interaction enables collaborative simulation of sand and geotextile. This method significantly improves computational efficiency and stability while ensuring high-precision simulation, providing reliable technical support for the design and safety assessment of manhole cover sand cofferdams.

[0006] The objective of this invention can be achieved through the following technical solution: an artificial intelligence-based method for simulating the MPM (Multi-Purpose Membrane Model) of a geotextile sand cofferdam, comprising the following steps:

[0007] S1: Data collection, including geotextile data and filling sand data:

[0008] A simulation system was constructed based on the MLS-MPM algorithm, in which sand particles filling the sand were represented by MPM material point particles, geotextile was represented by a non-volume grid, and simulation control parameters were collected to determine the simulation parameters.

[0009] S2: Generate the initial state and set the boundary conditions:

[0010] A three-dimensional simulation model of geotextile bag sand was established by using a mass-spring model to simulate geotextile.

[0011] Based on the filling sand parameters, material point particles are randomly generated within the geotextile grid, and given initial velocity and gravitational acceleration.

[0012] Through small-step pre-calculation, the particle-spring model is expected to reach static equilibrium under the action of gravity.

[0013] S3: Generate a contact model and detect the penetration state of sand particles: Use a spatial hashing algorithm to accelerate the search, locate the nearest contact surface between the sand particles and the geotextile mesh, use the nearest contact surface as the contact model, and detect the penetration state of the sand particles.

[0014] S4: Calculate contact force, monitor and update node status in real time.

[0015] After the timing starts, based on the contact model, the grid point velocity and displacement of sand particles in the contact area are updated, and the number of penetrating sand particles and the average penetration depth are monitored and modified in real time until the sand in the mold bag is destroyed or the simulation is manually stopped.

[0016] S5: Generate visualization results and iteratively optimize the model based on the results:

[0017] Repeat steps S1-S5.

[0018] Preferably, step S2 further includes setting the overall horizontal friction boundary conditions of the mass-spring model, with the boundary plane moving vertically downward at an initial velocity until it contacts the geotextile mesh.

[0019] Preferably, the detection of the penetration state of sand particles in step S3 includes:

[0020] The distance calculation defines a binary penetration state for each particle. The penetration condition is determined by comparing the normal direction. The minimum distance from the sand centroid to the geotextile mesh surface is calculated. If the minimum distance is less than the set distance, the particle is determined to be in the penetration state, and the penetration normal direction is recorded.

[0021] Preferably, in step S1, the simulation control parameters include: the relevant properties of particles and meshes, time step, and material parameters, wherein the material parameters include the elastic parameters and plastic parameters of sand and the mechanical properties of geotextile;

[0022] Setting parameters required for a prediction-based contact model: Threshold coefficient of friction Smoothing factor and step length The simulated control parameters are obtained by simulating using the implicit integration method.

[0023] Preferably, in step S2, the geotextile is represented by mass points, which are connected by springs. The tensile and compressive strength of the fabric is characterized by the warp and weft spring characteristics between adjacent mass points, and the shear strength of the fabric is characterized by the spring characteristics between diagonally opposite mass points. Each mass point includes position, velocity, and mass.

[0024] Preferably, step S3 further includes updating the inverse gradient of the model by introducing a policy gradient algorithm, as follows:

[0025] Assign a binary penetration state to each particle The simulation is based on the positional changes of particles and geotextile.

[0026] By pre-compiling the adjacent triangles of each face and defining a consistent orientation, the positional relationship between the particle and the face is compared at adjacent time points. If the particle moves to the other side of the mesh, the penetration state is updated. ,otherwise ;

[0027] Extract the feature parameters of geotextile and sand particles, use the extracted feature parameters as the state input strategy gradient algorithm, and adjust the output parameters.

[0028] The training process employs a policy gradient-based algorithm to maximize cumulative rewards and update the model's weights.

[0029] Preferably, step S3 further includes designing a reward function with the objective of minimizing the penetration depth and the number of penetrations, wherein the reward function R is calculated using the following formula:

[0030] ;

[0031] in , These are the weighting coefficients. Let be the penetration depth of the i-th sand particle. This represents the number of times the device penetrates the ground.

[0032] Preferably, in step S4, the calculation based on the contact model includes prediction, optimization, speed adjustment, and contact force calculation;

[0033] In the mesh operation phase of the MPM simulation, P2G is first executed to process the area around the material point particles. Within the range grid, based on the nearest grid point of the material point particle, a second-order B-spline function is applied. Interpolation:

[0034] ;

[0035] in, This represents the distance of a particle's projection onto the mesh in a certain direction, using... Interpolation calculation of grid point quality With momentum The formula is:

[0036] ;

[0037] ;

[0038] in, Indicates the mass of a point particle of matter. This indicates the number of matter particles within the affected area of ​​the lattice. Indicates the first Shape function at each grid point , They represent the first The coordinates of each grid point and the material particle. express The affine velocity matrix of each particle.

[0039] Preferably, the stress of the material point particles is calculated using an explicit integration method, which is based on a modified least squares method as follows:

[0040] ;

[0041] in, , These represent the displacement of the material point particle and the simulation step size, respectively. This represents the initial volume of each point particle. Represents the energy density function Plastic deformation The partial derivative, , Let represent the deformation gradient matrix and its transpose matrix of each material point particle, respectively. This indicates the internal stress caused by material deformation in the first... The equivalent effect generated on each grid node.

[0042] An artificial intelligence-based MPM (Multi-Purpose Movable Bag) cofferdam simulation system includes:

[0043] The data processing module is used to read initial data, which includes material parameters, simulation environment parameters, and initial state data. The data processing module then transmits the initial data to the simulation engine module.

[0044] The data processing module includes a data storage unit, which is used to store the running data generated during the simulation process. The running data includes particle and mesh state data, gradient data, and simulation result data.

[0045] The visualization module is used to organize and output simulation results data, generating visualized data files or data tables for subsequent analysis.

[0046] The simulation engine module is used to simulate the movement and deformation of sand particles and the mechanical behavior of geotextiles.

[0047] The optimization control module is used to calculate the gradients of each state variable and control action with respect to the objective function based on the computational graph of the simulation process, and to optimize the control actions based on the calculated gradients.

[0048] The beneficial effects of this invention are as follows:

[0049] This invention combines the MPM method to construct a three-dimensional simulation system for geotextile sand cofferdams. It utilizes penetration tracking algorithms and spatial hashing to accelerate the detection of the penetration state between sand and geotextile. A reward function is designed with the goal of minimizing the penetration depth and number of penetrations to drive the penetration prediction of geotextile sand MPM particles. Furthermore, based on the predicted contact model, the velocity and force of MPM particles are dynamically adjusted to prevent penetration and ensure numerical stability. Implicit integration and gradient descent methods are used to improve the calculation accuracy, and a visualization module is used to realize the bidirectional coupling between sand and geotextile. Attached Figure Description

[0050] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to the accompanying drawings.

[0051] Figure 1 This is a system structure block diagram of the present invention;

[0052] Figure 2 This is a flowchart of the method steps of the present invention. Detailed Implementation

[0053] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided.

[0054] Please see Figures 1-2 This embodiment provides an artificial intelligence-based method for simulating the MPM (Multi-Purpose Model) of geotextile sand cofferdams, including the following steps:

[0055] S1: Collect data, including:

[0056] S11: Collect geotextile data for the geotextile bag cofferdam. This data includes geometric dimensions, physical parameters, and layout.

[0057] Based on the specific operation manual and actual construction data, obtain the geometric dimensions of the geotextile used in the actual scenario, including length, width and thickness, and control the error range according to the test requirements;

[0058] Obtain the physical parameters of the geotextile, including density and porosity, and conduct multiple tests to take the average value of the data to improve accuracy;

[0059] Obtain information on the actual layout of geotextiles during construction, including laying angle, number of layers, and connection method.

[0060] S12: Collect filling sand data. This data includes the volume and physical parameters of the filling sand, including:

[0061] The volume of the filling sand was measured using the drainage method;

[0062] Particle size distribution curves were obtained by conducting particle analysis tests on the filler sand, and physical parameters such as moisture content and density were measured at the same time.

[0063] S13: Construct a 3D simulation model of the molding bag sand:

[0064] A three-dimensional simulation model of geotextile bag sand is constructed based on the MLS-MPM algorithm (Moving Least Squares Material Point Method, hereinafter referred to as MPM for ease of description). The sand particles filling the sand are represented by MPM material points, and the geotextile is represented by a non-volume mesh.

[0065] S14: Acquire analog control parameters:

[0066] The simulation control parameters here include the relevant properties of particles and meshes, time steps, and material parameters, including the elastic and plastic parameters of sand and the mechanical properties of geotextiles.

[0067] Simultaneously, set the parameters required for the prediction-based contact model, such as threshold. coefficient of friction Smoothing factor Step length wait;

[0068] The simulations all employed implicit integration methods to improve the stability of the constructed models.

[0069] S2: Generate the initial state and set the boundary conditions:

[0070] S21: Convert the geotextile into a point-spring model.

[0071] Geotextiles are represented by mass points, which are connected by springs. The warp and weft spring characteristics between adjacent mass points characterize the tensile and compressive strength of the fabric, while the spring characteristics between diagonally opposite mass points characterize the shear strength of the fabric.

[0072] Each particle is assigned an initial position, velocity, and mass. The position of the particle is determined based on the geometry and arrangement of the geotextile. The velocity is initialized to zero, and the mass is calculated based on the density and volume of the geotextile.

[0073] S22: Model initialization and pre-computation:

[0074] Initialize the geotextile mesh as a closed cuboid structure;

[0075] The fabric surface is formed by searching each particle and its adjacent particles to create a triangular mesh.

[0076] Perform small-step pre-calculations to further couple the actual engineering usage of geotextile sand cofferdams, so that the geotextile model reaches its initial equilibrium state.

[0077] S23: Generate filling sand particles:

[0078] Based on the volume parameters of the filling sand, material point particles are randomly generated within the geotextile grid, and given initial velocity and gravitational acceleration. The initial velocity can be set according to the actual engineering conditions, and the gravitational acceleration is taken as the standard value of the construction site.

[0079] Through small-step pre-calculation, the three-dimensional simulation model of the sand bag to be molded reaches a static equilibrium state under the action of gravity.

[0080] S24: Set model boundary conditions: Set overall horizontal friction boundary conditions. The boundary plane moves vertically downward at an initial velocity until it contacts the geotextile mesh. The initial velocity is set according to the actual engineering situation.

[0081] S3: Generate a contact model and detect the penetration state of sand particles;

[0082] S31: Locating the contact surface: Using a spatial hashing algorithm to accelerate the search, locate the nearest contact surface between the sand particles and the geotextile mesh, and use the nearest contact surface as the contact model;

[0083] S32: Detect Penetration Status: Calculate the distance to define a binary penetration status for each particle. Determine the penetration condition by comparing the normal direction. Calculate the minimum distance from the sand centroid to the geotextile mesh surface. If the minimum distance is less than the set distance, determine that the particle is in a penetration state and record the penetration normal direction.

[0084] S4: Calculate contact force, monitor and update node status in real time.

[0085] After the timing starts, based on the contact model, a reaction force is applied to the geotextile mesh nodes for sand particles in the contact area, the node velocity and displacement are updated, penetration is suppressed and numerical stability is enhanced, and the geotextile and sand in the geotextile sand cofferdam do not penetrate each other.

[0086] The simulation ends when the sand in the molding bag is destroyed or the simulation is manually stopped.

[0087] S5: Generate visualization results and iteratively optimize the model based on the results:

[0088] At each simulation time step, the model output results are displayed in a visualization window to show the deformation, stress distribution, etc. of the geotextile sand cofferdam in real time. The MPM simulation is performed with the geotextile state as the boundary condition to update the sand state and calculate the reaction force. Then, the reaction force is used as an external force input to the geotextile to simulate and update its state.

[0089] Repeat steps S1-S5.

[0090] In step S3, to further improve the accuracy of the 3D simulation model of the sand bag, in one embodiment, a policy gradient algorithm is introduced to update the network weights of the model. The specific steps are as follows:

[0091] First, assign a binary penetration state to each sand particle. In the simulation, the penetration is checked based on the positional changes of particles and geotextile using the principle of locality of motion.

[0092] By pre-compiling the adjacent triangles of each face and defining a consistent orientation, the positional relationship between the particle and the face is compared at adjacent time points. If the particle moves to the other side of the mesh, the penetration state is updated. ,otherwise .

[0093] Extract features from geotextile and sand particles, use the extracted features as state input to the policy network, and adjust the action by outputting parameters from the policy network.

[0094] The training process employs a policy gradient-based method to maximize cumulative reward and update weights.

[0095] Design a reward function R with the goal of minimizing the penetration depth and the number of penetrations:

[0096] ;

[0097] in , These are the weighting coefficients. Let be the penetration depth of the i-th sand particle. This represents the number of times the device penetrates the ground.

[0098] Next, the gradient of the model weight parameters is calculated based on the simulation results, and the parameters are dynamically optimized using the gradient descent method, thereby training the model to optimize the penetration performance between fabrics and between material points.

[0099] By comparing the momentum and affine velocity of the material point, the penetration relationship between the material point and the fabric surface can be predicted, thereby optimizing the coupling performance between two different systems, accelerating the calculation, and effectively preventing sand particles from leaking out of the geotextile due to numerical instability in the simulation.

[0100] In one embodiment, in step S4, the calculation of the contact model based on the optimized parameters of the artificial intelligence algorithm includes prediction, optimization, speed adjustment, and force calculation.

[0101] In prediction and optimization, during the grid operation phase of the MPM simulation in each simulation cycle, P2G (particle to grid) is first performed to optimize the area around the material point particles. The range grid, based on its nearest grid point, applies a second-order B-spline function. Interpolation:

[0102] ;

[0103] in, This represents the distance a particle projects onto the grid in a specific direction. (Used...) Interpolation calculation of grid quality With momentum :

[0104] ;

[0105] ;

[0106] in, Indicates the mass of a point particle of matter. This indicates the number of matter particles within the affected area of ​​the lattice. Indicates the first Shape function at each grid point , They represent the first Total mass and total velocity at each grid point express The affine velocity matrix of each particle. , They represent the first The coordinates of each grid point and a material particle.

[0107] To prevent sand particles within the contact area from penetrating. In one embodiment, the nearest grid point to the fabric is made to approximate the contact point, and the relative velocity is decomposed over the fabric triangular grid. Then, the parameter optimization problem of the model is solved by one-step gradient descent.

[0108] By adjusting the mesh velocity instead of directly modifying the particle velocity, we prevent particles from passing through the cloth. Therefore, we apply boundary conditions to the mesh velocity after particle P2G. This means that the target velocity of the mesh is obtained by forcibly constraining the boundary mesh velocity. :

[0109]

[0110] Therefore, the particle stress can be calculated at each grid point.

[0111] When calculating the stress of point particles in a material, methods such as explicit integration, implicit integration, and semi-implicit integration are used.

[0112] Among them, when using the explicit integration method to calculate the stress of material particles, its modified form based on the least squares method is as follows:

[0113] ;

[0114] in, , These represent the displacement of the material point particle and the simulation step size, respectively;

[0115] This represents the initial volume of each material point particle;

[0116] Represents the energy density function Plastic deformation The partial derivative;

[0117] , These represent the deformation gradient matrix and its transpose matrix for each material point particle, respectively.

[0118] This indicates the internal stress caused by material deformation in the first... The equivalent effect generated on each grid node.

[0119] Then, perform G2P (grid to particle), which is similar to the previous P2G process, returning the calculated information at the grid points to the material particles to update the data. .

[0120] Update deformation gradient Used for the next long calculation, and recorded. The contact force is then distributed to the corresponding nodes of the geotextile.

[0121] This embodiment provides an artificial intelligence-based MPM (Multi-Purpose Movable Bag) cofferdam simulation system, including a simulation engine module, a data processing module, an optimization control module, and a visualization module;

[0122] The data processing module is used to read initial data, including material parameters, simulation environment parameters, and initial state data, and pass them to the simulation engine module;

[0123] The data processing module includes a data storage unit, which stores the running data generated during the simulation. The running data includes particle and mesh state data, gradient data, and simulation result data.

[0124] The visualization module is used to organize and output the simulation results data, generating visualized data files or data tables for subsequent analysis. The visualization files include files for drawing deformation diagrams and stress distribution diagrams.

[0125] The visualization file is used for scene rendering and data visualization. It reads key simulation results data from the model and renders a 3D scene of the geotextile sand cofferdam, including the sand accumulation pattern and the deformation of the geotextile.

[0126] The simulation engine module is used to simulate the movement and deformation of sand particles and the mechanical behavior of geotextiles.

[0127] The optimization control module is used to calculate the gradients of each state variable and control action with respect to the objective function based on the computation graph of the simulation process. Based on the calculated gradients, the control actions are optimized, and the optimization function is further optimized. The optimization control module interacts with the simulation engine module and feeds back the optimized control actions to the simulation engine to achieve dynamic optimization of the simulation process.

[0128] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. An artificial intelligence-based method for simulating the MPM (Multi-Purpose Model) of geotextile sand cofferdams, characterized in that: Includes the following steps: S1: Data collection, including geotextile data and filling sand data: A simulation system was constructed based on the MLS-MPM algorithm, in which sand particles filling the sand were represented by MPM material point particles, geotextile was represented by a non-volume grid, and simulation control parameters were collected to determine the simulation parameters. S2: Generate the initial state and set the boundary conditions: A three-dimensional simulation model of geotextile bag sand was established by using a mass-spring model to simulate geotextile. Based on the filling sand parameters, material point particles are randomly generated within the geotextile area, and given initial velocity and gravitational acceleration. Through small-step pre-calculation, the mass-spring model is expected to reach static equilibrium under the action of gravity. S3: Generate a contact model and detect the penetration state of sand particles: Use a spatial hashing algorithm to accelerate the search, locate the nearest contact surface between the sand particles and the geotextile mesh, use the nearest contact surface as the contact model, and detect the penetration state of the sand particles. S4: Calculate contact force, monitor and update node status in real time. After the timing starts, based on the contact model, the grid point velocity and displacement of the sand particles in the contact area are updated, and the number of penetrating sand particles and the average penetration depth are monitored and modified in real time until the sand in the mold bag is destroyed or the simulation is manually stopped. S5: Generate visualization results and iteratively optimize the model based on the results: Repeat steps S1-S5.

2. The method for simulating MPM (Multi-Purpose Modeling) cofferdams based on artificial intelligence according to claim 1, characterized in that: Step S2 also includes setting the overall horizontal friction boundary conditions of the mass-spring model, with the boundary plane moving vertically downward at an initial velocity until it contacts the geotextile mesh.

3. The method for simulating MPM (Multi-Purpose Modeling) cofferdams based on artificial intelligence according to claim 1, characterized in that: Step S3, which involves detecting the penetration state of sand particles, includes: The distance calculation defines a binary penetration state for each particle. The penetration condition is determined by comparing the normal direction. The minimum distance from the sand centroid to the geotextile mesh surface is calculated. If the minimum distance is less than the set distance, the particle is determined to be in the penetration state, and the penetration normal direction is recorded.

4. The artificial intelligence-based MPM simulation method for geotextile sand cofferdams according to claim 1, characterized in that: In step S1, the simulation control parameters include: the relevant properties of particles and meshes, time step and material parameters, wherein the material parameters include the elastic parameters and plastic parameters of sand and the mechanical properties of geotextile; Setting parameters required for a prediction-based contact model: Threshold coefficient of friction Smoothing factor and step length The simulated control parameters are obtained by simulating using the implicit integration method.

5. The artificial intelligence-based MPM simulation method for geotextile sand cofferdams according to claim 1, characterized in that: In step S2, the geotextile is represented by mass points, which are connected by springs. The tensile and compressive strength of the fabric is characterized by the warp and weft spring characteristics between adjacent mass points, and the shear strength of the fabric is characterized by the spring characteristics between diagonally opposite mass points. Each mass point includes position, velocity, and mass.

6. The artificial intelligence-based MPM simulation method for geotextile sand cofferdams according to claim 3, characterized in that: Step S3 also includes updating the inverse gradient of the model by introducing a policy gradient algorithm, as follows: Assign a binary penetration state to each particle The simulation is based on the positional changes of particles and geotextile. By pre-compiling the adjacent triangles of each face and defining a consistent orientation, the positional relationship between the particle and the face is compared at adjacent time points. If the particle moves to the other side of the mesh, the penetration state is updated. ,otherwise ; Extract the feature parameters of geotextile and sand particles, use the extracted feature parameters as the state input strategy gradient algorithm, and adjust the output parameters. The training process employs a policy gradient-based algorithm to maximize cumulative rewards and update the model's weights.

7. The artificial intelligence-based MPM simulation method for geotextile sand cofferdams according to claim 6, characterized in that: Step S3 further includes designing a reward function with the objective of minimizing the penetration depth and the number of penetrations. The formula for calculating the reward function R is as follows: ； in , These are the weighting coefficients. Let be the penetration depth of the i-th sand particle. This represents the number of times the device penetrates the ground.

8. The artificial intelligence-based MPM simulation method for geotextile sand cofferdams according to claim 1, characterized in that: In step S4, the calculations based on the contact model include prediction, optimization, speed adjustment, and contact force calculation; In the mesh operation phase of the MPM simulation, P2G is first executed to perform mesh operations around the material point particles. Within the range grid, based on the nearest grid point of the material point particle, a second-order B-spline function is applied. Interpolation: ； in, This represents the distance of a particle's projection onto the mesh in a certain direction, using... Interpolation calculation of grid point quality With momentum The formula is: ； ； in, Indicates the mass of a point particle of matter. This indicates the number of matter particles within the affected area of ​​the lattice. Indicates the first Shape function at each grid point , They represent the first The coordinates of each grid point and the material particle. express The affine velocity matrix of each particle.

9. The artificial intelligence-based MPM simulation method for geotextile sand cofferdams according to claim 8, characterized in that: The stress of the material point particles is calculated using an explicit integration method, which is based on a modified least squares method as follows: ； in, , These represent the displacement of the material point particle and the simulation step size, respectively. This represents the initial volume of each point particle. Represents the energy density function Plastic deformation The partial derivative, , Let represent the deformation gradient matrix and its transpose matrix of each material point particle, respectively. This indicates the internal stress caused by material deformation in the first... The equivalent effect generated on each grid node.

10. An AI-based MPM simulation system for geotextile sand cofferdams, used to execute the AI-based MPM simulation method for geotextile sand cofferdams as described in any one of claims 1-9, characterized in that: include: The data processing module is used to read initial data, which includes material parameters, simulation environment parameters, and initial state data. The data processing module then transmits the initial data to the simulation engine module. The data processing module includes a data storage unit, which is used to store the running data generated during the simulation process. The running data includes particle and mesh state data, gradient data, and simulation result data. The visualization module is used to organize and output simulation results data, generating visualized data files or data tables for subsequent analysis. The simulation engine module is used to simulate the movement and deformation of sand particles and the mechanical behavior of geotextiles. The optimization control module is used to calculate the gradients of each state variable and control action with respect to the objective function based on the computational graph of the simulation process, and to optimize the control action based on the calculated gradients.

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