A mine ventilation network flow field solving method and system

Abstract

The application discloses a kind of mine ventilation network flow field resolving method and system, the method is by introducing dynamics neural differential equation and depth space-time attention mechanism, constructs and trains the flow field simulation model of mine ventilation network, realizes the accurate simulation and fast resolving of space-time process flow field in mining engineering calculation field.The ventilation network space-time solving model based on dynamics neural differential equation is used in the method of the application, the dynamic change in physical process can be simulated using deep learning model, complex flow patterns can be automatically captured, without explicitly establishing all physical equations, so that the model has strong adaptability and generalization ability.The fluid dynamics deep neural network solver based on space-time self-attention is used in the method of the application, which can replace multiple numerical solving iteration processes of the solving model, reduce the number of iterations, improve the calculation efficiency and reduce the solving period.

Description

Technical Field

[0001] This invention belongs to the field of flow field calculation technology, and in particular relates to a method and system for calculating the flow field of a mine ventilation network. Background Technology

[0002] Intelligent ventilation is a crucial component of intelligent mine construction, and the demand for accurate calculation and intelligent management of mine ventilation systems is becoming increasingly urgent. However, existing ventilation network calculation models have many shortcomings, failing to fully consider the precise spatiotemporal evolution of airflow or hazards in complex mine environments. Traditional numerical calculation methods suffer from low computational efficiency and long calculation cycles, making it difficult to provide real-time intelligent decision support, which severely restricts the intelligent construction of mine ventilation systems.

[0003] Currently, the integration of deep learning and fluid mechanics offers a novel approach to solving these problems. Deep learning, especially neural network-based methods, has demonstrated powerful capabilities in various complex data processing and modeling tasks. By applying deep learning to the field of fluid mechanics, from physical model integration to complex flow simulation, and from data-driven research to intelligent flow field analysis, deep learning is reshaping the field with unprecedented force. This new research paradigm opens up entirely new avenues for addressing the theoretical and technical bottlenecks in the solution and intelligent analysis of mine ventilation networks.

[0004] However, effectively applying deep learning and attention mechanisms to flow field calculation in mine ventilation networks still faces many challenges. For example, mine ventilation networks have complex boundary conditions and dynamically changing flow fields, requiring models with strong adaptability and generalization capabilities. Furthermore, how to effectively integrate deep learning models with traditional fluid dynamics models to achieve more efficient and accurate flow field calculations is also a problem that urgently needs to be solved. For instance, the prior art published in CN116227359A provides a flow field prediction method based on attention and convolutional neural network encoders and decoders. However, this method only considers the spatial characteristics of the flow field data, thus lacking the capture of features in the temporal dimension and making it difficult to establish long-term dependencies across multiple time steps. The prior art published in CN114611381A provides a method and system for aerodynamic data modeling based on residual neural networks. However, the residual neural network in this method cannot effectively capture the long-term spatiotemporal sequence features of the flow field data, making it difficult to model the long-term evolutionary effects caused by initial disturbances. Summary of the Invention:

[0005] To address the problems existing in the prior art, this invention proposes a method and system for calculating the flow field of a mine ventilation network.

[0006] The technical solution of the present invention is as follows:

[0007] A method for calculating the flow field in a mine ventilation network includes:

[0008] Acquire boundary environment data, flow field data, and long-term spatiotemporal distribution data of the mine ventilation network; the flow field data includes wind speed, wind pressure, wind resistance, temperature, and gas concentration composed of methane concentration and dust concentration at various measuring points inside the mine; the long-term spatiotemporal distribution data of the flow field is the actual value of the long-term spatiotemporal distribution data composed of wind speed, wind pressure, and methane concentration.

[0009] A flow field simulation model for a mine ventilation network is constructed, comprising a spatiotemporal solution model for the ventilation network based on dynamic neural differential equations and a deep neural network solver for fluid dynamics based on spatiotemporal self-attention.

[0010] Based on the historical boundary environment data and flow field data, the fluid dynamics deep neural network solver is used to perform iterative numerical solution of the ventilation network spatiotemporal solution model to obtain the predicted value of the long-sequence distribution data of the flow field spatiotemporal data. Then, based on the error between the predicted value and the actual value of the long-sequence distribution data of the flow field spatiotemporal data, the model parameters of the ventilation network spatiotemporal solution model and the fluid dynamics deep neural network solver are adjusted to perform iterative training of the flow field simulation model of the mine ventilation network.

[0011] Based on the flow field simulation model of the pre-trained mine ventilation network, the target boundary environment data and the corresponding spatiotemporal long sequence distribution data of the flow field are obtained and used as the flow field solution results.

[0012] Furthermore, the specific steps for acquiring the boundary environment data and flow field data of the mine ventilation network include:

[0013] Collect boundary environmental data and flow field data of the mine ventilation network;

[0014] The collected boundary environment data and flow field data are preprocessed to remove noise and outliers.

[0015] Furthermore, the air intake volume in the boundary environment data is the sum of the air intake volumes of each air inlet in the mine ventilation network, expressed as:

[0016]

[0017] Where Q is the total air intake volume; Q i Let n be the air volume of the i-th air inlet, and n be the number of air inlets.

[0018] Furthermore, the expression for the wind speed in the flow field data is:

[0019]

[0020] In the formula, v is the wind speed; Q is the total air volume; and S is the cross-sectional area of ​​the tunnel.

[0021] The expression for the wind pressure is:

[0022]

[0023] In the formula, P is the wind pressure; ρ is the air density; Δh is the air height difference; and g is the acceleration due to gravity.

[0024] The expression for wind resistance is:

[0025]

[0026] In the formula, R is the air resistance; ΔP is the pressure difference between the two ends of the roadway;

[0027] The expression for the temperature is:

[0028] T = T0 + ΔT

[0029] In the formula, T0 is the reference temperature; ΔT is the temperature rise;

[0030] The gas concentration includes methane concentration and dust concentration, expressed as follows:

[0031]

[0032] In the formula, C g V represents the gas concentration. gas V is the volume of gas; air C is the volume of air. d Dust concentration; m dust For dust quality.

[0033] Furthermore, the data preprocessing specifically includes:

[0034] A) Data cleaning and filtering:

[0035] Data interpolation and smoothing filtering are used to fill in short-term missing data at measurement points. If a measurement point has long-term missing data, the measurement point is directly removed or data from a neighboring measurement point is used as a substitute.

[0036] Smoothing filters are used to suppress high-frequency noise, and wavelet decomposition is performed on non-stationary signals to retain low-frequency effective components and remove high-frequency noise.

[0037] Outliers were detected and removed using statistical methods and physical constraint methods.

[0038] B) Data Standardization:

[0039] For the air intake volume, a central logarithmic ratio transformation is used;

[0040] For wind pressure and temperature, Min-Max Scaling normalization is used to scale the data to the [0,1] range;

[0041] For normally distributed data including wind speed and gas concentration, Z-score normalization is used.

[0042] For non-normally distributed data including wind resistance, quantile transformation is used to map them to a uniform or normal distribution;

[0043] C) Feature extraction and selection:

[0044] For the time dimension, sliding window statistics are extracted, and frequency domain features are extracted through Fourier transform;

[0045] For the spatial dimension, the topological relationship between the measurement points is constructed, the spatial correlation is calculated, and the spatiotemporal correlation strength between the measurement points is quantified using the synchronization event matrix.

[0046] Features with high correlation to the target variable are selected by mutual information, and then the high-dimensional spatiotemporal data are reduced in dimensionality by principal component analysis, retaining more than 90% of the variance components.

[0047] Furthermore, the specific method for iterative training includes:

[0048] A dataset is constructed based on the aforementioned environmental data, flow field data, and spatiotemporal long-sequence distribution data.

[0049] The flow field simulation model of the mine ventilation network is trained based on the dataset. Boundary environment data and flow field data are used as input data for the spatiotemporal solution model of the ventilation network based on dynamic neural differential equations. A fluid dynamics deep neural network solver based on spatiotemporal self-attention is used to solve the ventilation network spatiotemporal solution model numerically to obtain the predicted values ​​of the long-sequence distribution data of the flow field. Then, based on the error between the predicted values ​​and the actual values ​​of the long-sequence distribution data of the flow field, the model parameters of the spatiotemporal solution model of the ventilation network and the fluid dynamics deep neural network solver are adjusted to perform iterative training of the flow field simulation model of the mine ventilation network.

[0050] During training, model parameters are adjusted using backpropagation and gradient descent algorithms, and regularization is used to prevent overfitting. Furthermore, a learning rate scheduling method is employed to improve training efficiency.

[0051] Furthermore, the specific construction method of the spatiotemporal solution model of the ventilation network based on dynamic neural differential equations is as follows:

[0052] First, the grid points i and j in the lattice Boltzmann model where the wind speed is higher than the threshold p are denoted as the set of ventilation events. and In the formula, Let be the time of occurrence of the μ-th ventilation event at grid point i; Let be the time of occurrence of the v-th ventilation event at grid point j; s i and s j These represent the total number of ventilation events at grid points i and j during the study period;

[0053] Based on the time difference of events occurring at a pair of grid points (i,j) in the synchronous event method, the spatiotemporal correlation characteristics are constructed. Therefore, for a ventilation network system, if the time delay between any two ventilation events μ,v in space... If the values ​​are less than a threshold, the two events are considered to have occurred synchronously and are called synchronous events. The formula for calculating the threshold is as follows:

[0054]

[0055] In the formula, and These represent the time interval between the μ-th and μ-1-th events at grid point i, and the time interval between the μ+1-th and μ-th events at grid point i, respectively. and These represent the time interval between the νth and ν-1th events at grid point j, and the time interval between the ν+1th and νth events at grid point j, respectively.

[0056] The number of synchronization events for any grid point pair (i,j) is:

[0057]

[0058] In the formula, ES(i|j) represents the total number of synchronization events for the grid pair (i,j); J μv For indicator functions;

[0059]

[0060] This yields the synchronization event matrix ES, thus completing the dynamic statistical construction of ventilation events at the grid points. For the spatiotemporal correlation between grid points in the ventilation network, a symmetric matrix Q and an asymmetric matrix q are constructed, with the elements of the matrices being:

[0061]

[0062] Among them, Q ij and q ij The synchronization intensity and time delay relationship of ventilation events at grid points i and j are given by Q. ij ∈[0,1],q ij∈[-1,1]; Thus, by setting a threshold to eliminate secondary spatial correlations, the synchronous correlation characteristics and time delay direction characteristics of wind velocity on grid points are obtained; ES(j|τ) is the number of times an event occurs at grid point j within the time delay τ of an event occurring at grid point i;

[0063] Secondly, a simulation prediction and solution model based on dynamic neural differential equations is constructed, which describes time dynamics on the lattice Boltzmann model based on the differential equation system:

[0064]

[0065] in, G(t) represents the state or characteristic value of a dynamic system consisting of n lattice points at any given time; G(t) represents the complex network structure capturing how the lattice points interact; W(t) represents the parameters of how the control system evolves over time; X(0) = X0 represents the initial state of the ventilation network system based on the lattice Boltzmann model at time t = 0; the function Control the dynamic instantaneous rate of change of the grid points.

[0066] Define G j (t) is used to characterize the degree to which lattice point j is affected by the magnitude of the velocity of other lattice points.

[0067]

[0068] In the formula, n is the total number of lattice points, M(t) is the set of lattice points where velocity collisions occur at time t, and d ij It is the distance between grid points i and j. These are the correlation strength and correlation direction factors between grid points.

[0069] Furthermore, the spatiotemporal self-attention-based deep neural network solver for fluid dynamics includes constructing a patch-based two / three-dimensional CNN spatial self-attention module and a one-dimensional CNN temporal self-attention module; wherein, the two / three-dimensional CNN spatial self-attention module utilizes the spatial correlation between the features of the central grid point and the surrounding grid points to traverse each grid point and improve its spatial feature representation; the one-dimensional CNN temporal self-attention module captures long-distance temporal correlation through short-distance temporal features;

[0070] Based on the mine gas state equation, the discrete particle density is calculated using temperature, wind pressure, wind resistance, and gas concentration from the flow field data. Then, based on the discrete particle density and the wind speed and temperature from the flow field data, the Maxwell-Boltzmann distribution function describing the particle velocity distribution is obtained. Finally, this function is vector-decomposed into components of each discrete velocity direction in the D2Q9 model, forming the initial velocity distribution function f. i (x, y, t) are stored in a three-dimensional array (N). x N y Ni In ), f i (x,y,t) represents the particle density at the lattice point (x,y) in the i-th velocity direction at time t; N in the three-dimensional array i Each (x,y) point in the intermediate layer of the dimension is centered on an adjacent cuboid as a patch composed of discrete velocity numbers.

[0071] The patch consisting of discrete velocity numbers is input into the two / three-dimensional CNN spatial self-attention module and the one-dimensional CNN temporal self-attention module respectively. The outputs of the two / three-dimensional CNN spatial self-attention module and the one-dimensional CNN temporal self-attention module are fused using a fractional weighted fusion method to obtain the flow field solution results of the spatiotemporal process simulation.

[0072] Furthermore, the expression for the spatial correlation between the features of the central grid point and the surrounding grid points is:

[0073]

[0074] In the formula, S i,t The central grid point vector A i Spatiotemporal similarity with adjacent grid points and time t;

[0075] A i Let A be the vectorized representation of the center grid data, where A is the first feature map generated after two parallel convolutional layers are input to a patch composed of discrete velocity numbers; A i,1 A i,2 A i,3 ,......,A i,n These are respectively related to the central grid point A i Adjacent grid points;

[0076] Use the softmax function to evaluate S. i,t After normalization, we obtain the spatiotemporal self-attention representation:

[0077]

[0078] Based on the spatiotemporal self-attention features, a weighted matrix is ​​calculated to enhance the representation of feature information related to the central grid point and suppress unnecessary spatiotemporal features:

[0079]

[0080] V spa =W spa +X

[0081] Among them W spa Let V be the weight matrix. spaFor incremental representation, B is the second feature map generated after the patch consisting of discrete velocity numbers is input to two parallel convolutional layers;

[0082] Applying the same processing to the time features yields the increment V. tpe The output of the one-dimensional CNN temporal self-attention module is fed back to the fully connected layer FC, and the transformation is obtained as F. spa and F tpe Finally, a fractional weighted fusion method was used to obtain the prediction results of the spatiotemporal process simulation:

[0083] F=σ(λ×F spa +(1-λ)×F tpe )

[0084] Where σ(·) is the softmax function, and λ∈[0,1] is the weight parameter.

[0085] A mine ventilation network flow field calculation system includes a data acquisition module, a model building module, a model training module, and a calculation module;

[0086] The data acquisition module is used to acquire boundary environment data, flow field data, and long-term spatiotemporal distribution data of the mine ventilation network. The flow field data includes wind speed, wind pressure, wind resistance, temperature, and gas concentration composed of methane concentration and dust concentration at various measuring points inside the mine. The long-term spatiotemporal distribution data of the flow field consists of the actual values ​​of the long-term spatiotemporal distribution data composed of wind speed, wind pressure, and methane concentration.

[0087] The model building module is used to build a flow field simulation model of the mine ventilation network. The flow field simulation model of the mine ventilation network includes a spatiotemporal solution model of the ventilation network based on dynamic neural differential equations and a fluid dynamics deep neural network solver based on spatiotemporal self-attention.

[0088] The model training module is used to perform iterative numerical solutions on the ventilation network spatiotemporal solution model based on the historical boundary environment data and flow field data, using the fluid dynamics deep neural network solver, to obtain the predicted values ​​of the long-sequence distribution data of the flow field spatiotemporal data. Then, based on the error between the predicted values ​​and the actual values ​​of the long-sequence distribution data of the flow field spatiotemporal data, the model parameters of the ventilation network spatiotemporal solution model and the fluid dynamics deep neural network solver are adjusted to perform iterative training of the flow field simulation model of the mine ventilation network.

[0089] The solution module is used to acquire target boundary environment data and the corresponding spatiotemporal long sequence distribution data of the flow field based on the flow field simulation model of the trained mine ventilation network, and use them as the flow field solution results.

[0090] An electronic device includes a memory and a processor, the memory storing a computer program, the processor being configured to invoke and run the computer program stored in the memory to perform the method as described in any of the preceding methods.

[0091] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method described in any of the preceding claims.

[0092] Compared with the prior art, the present invention has the following beneficial effects:

[0093] This invention proposes a method and system for solving the flow field of a mine ventilation network. The method introduces dynamic neural differential equations and a deep spatiotemporal attention mechanism to construct and train a flow field simulation model of the mine ventilation network. Based on boundary environment data and flow field data, it can obtain long-term spatiotemporal distribution data of the flow field with long-term dependencies across multiple time steps, thereby realizing accurate simulation and rapid solution of the spatiotemporal process flow field in the field of mining engineering calculation.

[0094] The method of this invention adopts a spatiotemporal solution model of ventilation network based on dynamic neural differential equations. It can use deep learning models to simulate dynamic changes in physical processes, automatically capture complex flow patterns, and eliminate the need to explicitly establish all physical equations, giving the model strong adaptability and generalization ability.

[0095] The method of this invention employs a deep neural network solver for fluid dynamics based on spatiotemporal self-attention, which can replace multiple numerical solution iterations in the solution model, reduce the number of iterations, improve computational efficiency, and shorten the solution cycle. Attached Figure Description

[0096] Figure 1 This is a flowchart of the flow field calculation method for the mine ventilation network in the embodiment;

[0097] Figure 2 This is a block diagram illustrating the principle of the flow field calculation method for the mine ventilation network in the embodiment.

[0098] Figure 3 This is a schematic diagram of the neural differential equation training structure on the Lattice Boltzmann Model (LBM) in the embodiment. Detailed Implementation

[0099] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0100] Example 1:

[0101] The present invention provides a method for calculating the flow field of a mine ventilation network, such as... Figure 1 and Figure 2 As shown, the specific steps include the following:

[0102] S1. Obtain boundary environment data, flow field data, and long-term spatiotemporal distribution data of the mine ventilation network; the flow field data includes wind speed, wind pressure, wind resistance, temperature, and gas concentration composed of methane concentration and dust concentration at various measuring points inside the mine; the long-term spatiotemporal distribution data of the flow field is the actual value of the long-term spatiotemporal distribution data composed of wind speed, wind pressure, and methane concentration.

[0103] S2. Construct a flow field simulation model for the mine ventilation network. The flow field simulation model for the mine ventilation network includes a spatiotemporal solution model for the ventilation network based on dynamic neural differential equations and a deep neural network solver for fluid dynamics based on spatiotemporal self-attention.

[0104] S3. Based on historical boundary environment data and flow field data, a fluid dynamics deep neural network solver is used to perform numerical iterative solution of the ventilation network spatiotemporal solution model to obtain the predicted value of the long-sequence distribution data of the flow field spatiotemporal data. Then, based on the error between the predicted value and the actual value of the long-sequence distribution data of the flow field spatiotemporal data, the model parameters of the ventilation network spatiotemporal solution model and the fluid dynamics deep neural network solver are adjusted to perform iterative training of the flow field simulation model of the mine ventilation network.

[0105] S4. Based on the well-trained mine ventilation network flow field simulation model, acquire the target boundary environment data and the corresponding spatiotemporal long sequence distribution data of the flow field data, and use them as the flow field solution results.

[0106] Example 2:

[0107] This embodiment, based on Embodiment 1, further incorporates the following specific steps for acquiring boundary environment data and flow field data of the mine ventilation network:

[0108] Collect boundary environmental data and flow field data of the mine ventilation network;

[0109] The collected boundary environment data and flow field data are preprocessed to remove noise and outliers.

[0110] Example 3:

[0111] This embodiment, based on Embodiment 2, further designs the following: In this example, the air intake volume in the boundary environment data is the sum of the air intake volumes of each air inlet in the mine ventilation network, expressed as:

[0112]

[0113] Where Q is the total air intake volume; Q i Let m be the air volume of the i-th air inlet. 3 / s, where n is the number of air inlets;

[0114] Example 4:

[0115] This embodiment, based on Embodiment 2, is further designed in that the wind speed in the flow field data represents the air velocity within the tunnel, and the expression for the wind speed at a certain measuring point is:

[0116]

[0117] In the formula, v is the wind speed; Q is the total air volume (m³). 3 / s, where S is the cross-sectional area of ​​the tunnel, m 2 ;

[0118] Wind pressure represents the total air pressure in the roadway, including static pressure and dynamic pressure. The expression for the wind pressure at a certain measuring point is:

[0119]

[0120] In the formula, P is the wind pressure; ρ is the air density; Δh is the air height difference; and g is the acceleration due to gravity.

[0121] Air resistance represents the air resistance of the roadway, calculated using Darcy's formula. The expression for the air resistance at a certain measuring point is:

[0122]

[0123] In the formula, R is the air resistance; ΔP is the pressure difference between the two ends of the roadway, in Pa;

[0124] Temperature represents the temperature at the measuring point. The expression for the temperature at a given measuring point is:

[0125] T = T0 + ΔT

[0126] In the formula, T0 is the reference temperature; ΔT is the temperature rise, in °C;

[0127] Gas concentration includes methane concentration and dust concentration, expressed as follows:

[0128]

[0129] In the formula, C g Gas concentration, volume percentage; V gas V is the volume of gas; air C is the volume of air. d Dust concentration, mass concentration, mg / m³ 3 ;m dust For dust quality.

[0130] The table is as follows:

[0131]

[0132] Example 5:

[0133] This embodiment, based on Embodiment 2, is further designed in that the data preprocessing in this example specifically includes:

[0134] A) Data cleaning and filtering:

[0135] Data interpolation and smoothing filtering techniques are used to fill in short-term missing data at sensor measurement points. If a measurement point has long-term missing data, such as more than 50%, the measurement point is directly removed or replaced with data from neighboring measurement points.

[0136] Smoothing filters are used to suppress high-frequency noise, and wavelet decomposition is performed on non-stationary signals (such as sudden changes in wind speed) to retain low-frequency effective components and remove high-frequency noise.

[0137] Outliers were detected and removed using statistical methods and physical constraint methods.

[0138] B) Data Standardization:

[0139] For the air intake volume, the Central Logarithmic Ratio Transform (CLR) is used for processing, and the expression is as follows:

[0140]

[0141] In the formula, x clr denoted as the standardized intake air volume; x represents the intake air volume; g(x) is the geometric mean of the intake air volume.

[0142] For wind pressure and temperature, Min-Max Scaling normalization is used to scale the data to the [0,1] interval. The formula is:

[0143]

[0144] In the formula, X represents wind pressure or temperature; X max X represents the maximum value of wind pressure or temperature. min This represents the minimum value of wind pressure or temperature; X norm Standardized wind pressure or temperature;

[0145] For normally distributed data including wind speed and gas concentration, Z-score standardization is used, with the formula:

[0146]

[0147] In the formula, X represents wind speed and gas concentration; μ represents the mean of wind speed and gas concentration; and σ represents the standard deviation of wind speed and gas concentration.

[0148] For non-normally distributed data including wind resistance, a quantile transformation is used to map it to a uniform or normal distribution.

[0149] C) Feature extraction and selection:

[0150] For the time dimension, sliding window statistics such as mean, variance, and trend slope are extracted, and frequency domain features such as dominant frequency and energy spectrum are extracted through Fourier transform (FFT).

[0151] For the spatial dimension, construct the topological relationship between measuring points, such as the tunnel connection diagram, calculate the spatial correlation, such as the Pearson correlation coefficient, and use the synchronous event matrix (ES matrix) to quantify the spatiotemporal correlation strength between measuring points.

[0152] Features highly correlated with the target variable (such as flow field distribution) are selected by mutual information, and then the high-dimensional spatiotemporal data are reduced in dimensionality by principal component analysis (PCA) to retain more than 90% of the variance components.

[0153] Example 6:

[0154] This embodiment, based on Embodiment 1, is further designed in that the specific method of iterative training in this example includes:

[0155] A dataset is constructed based on environmental data, flow field data, and spatiotemporal long-sequence distribution data; generally, the dataset is divided into a training set and a validation set.

[0156] The flow field simulation model of the mine ventilation network is trained based on the training set in the dataset. Boundary environment data and flow field data are used as input data for the spatiotemporal solution model of the ventilation network based on dynamic neural differential equations. A fluid dynamics deep neural network solver based on spatiotemporal self-attention is used to solve the ventilation network spatiotemporal solution model numerically, and the predicted values ​​of the long-sequence distribution data of the flow field are obtained. Then, based on the error between the predicted values ​​and the actual values ​​of the long-sequence distribution data of the flow field, the model parameters of the spatiotemporal solution model of the ventilation network and the fluid dynamics deep neural network solver are adjusted to carry out iterative training of the flow field simulation model of the mine ventilation network.

[0157] During training, the model parameters are adjusted using the backpropagation algorithm and the gradient descent algorithm to enable the model to accurately fit and predict the spatiotemporal changes of the ventilation network. Regularization is used to prevent overfitting, and learning rate scheduling is used to improve training efficiency.

[0158] Finally, the trained flow field simulation model was evaluated using a validation set to verify its predictive and generalization capabilities under different mine environments and boundary conditions.

[0159] Example 7:

[0160] This embodiment, based on Embodiment Six, further designs a specific method for constructing the spatiotemporal solution model of the ventilation network based on the dynamic neural differential equation:

[0161] First, the grid points i and j in the lattice Boltzmann model where the wind speed is higher than the threshold p are denoted as the set of ventilation events. and In the formula, Let be the time of occurrence of the μ-th ventilation event at grid point i; Let be the time of occurrence of the v-th ventilation event at grid point j; s i and s j These represent the total number of ventilation events at grid points i and j during the study period;

[0162] Based on the time difference of events occurring at a pair of grid points (i,j) in the synchronous event method, the spatiotemporal correlation characteristics are constructed. Therefore, for a ventilation network system, if the time delay between any two ventilation events μ,v in space... If the values ​​are less than a threshold, the two events are considered to have occurred synchronously and are called synchronous events. The formula for calculating the threshold is as follows:

[0163]

[0164] In the formula, and These represent the time interval between the μ-th and μ-1-th events at grid point i, and the time interval between the μ+1-th and μ-th events at grid point i, respectively. and These represent the time interval between the νth and ν-1th events at grid point j, and the time interval between the ν+1th and νth events at grid point j, respectively.

[0165] The number of synchronization events for any grid point pair (i,j) is:

[0166]

[0167] In the formula, ES(i|j) represents the total number of synchronization events for the grid pair (i,j); J μv For indicator functions;

[0168]

[0169] This yields the synchronization event matrix ES, thus completing the dynamic statistical construction of ventilation events at the grid points. Matrix ES can represent the correlation strength between grid points based on directed and weighted network links. For the spatiotemporal correlation between ventilation network grid points, a symmetric matrix Q and an asymmetric matrix q are constructed, with the following elements:

[0170]

[0171] Among them, Q ij and q ij The synchronization intensity and time delay relationship of ventilation events at grid points i and j are given by Q. ij ∈[0,1],q ij ∈[-1,1]; Thus, by setting a threshold to eliminate secondary spatial correlations, the synchronous correlation characteristics and time delay direction characteristics of wind velocity on grid points are obtained; ES(j|τ) is the number of times an event occurs at grid point j within the time delay τ of an event occurring at grid point i;

[0172] Secondly, a simulation prediction and solution model based on dynamic neural differential equations is constructed, such as... Figure 3 The diagram shows the training structure for neural differential equations on a lattice Boltzmann model (LBM). Time dynamics are described on the lattice Boltzmann model based on a system of differential equations.

[0173]

[0174] in, G(t) represents the state or characteristic value of a dynamic system consisting of n lattice points at any given time; G(t) represents the complex network structure capturing how the lattice points interact; W(t) represents the parameters of how the control system evolves over time; X(0) = X0 represents the initial state of the ventilation network system based on the lattice Boltzmann model at time t = 0; the function Control the dynamic instantaneous rate of change of the grid points.

[0175] The problem to be solved is how to predict the dynamic state of grid points in a ventilation network lattice model at any given time. If grid point i experiences a velocity collision at time t, based on spatiotemporal correlation characteristics, it will affect surrounding grid points j. Therefore, in establishing the complex network structure of equation G, it is necessary to consider information such as grid point wind speed, distance between grid points, correlation strength, and correlation direction. Define G j (t) is used to characterize the degree to which lattice point j is affected by the magnitude of the velocity of other lattice points.

[0176]

[0177] In the formula, n is the total number of lattice points, M(t) is the set of lattice points where velocity collisions occur at time t, and d ij It is the distance between grid points i and j. These are the correlation strength and correlation direction factors between grid points.

[0178] Example 8:

[0179] This embodiment, based on Embodiment 1, is further designed in that the hydrodynamic deep neural network solver based on spatiotemporal self-attention includes constructing a patch-based two / three-dimensional CNN spatial self-attention module and a one-dimensional CNN temporal self-attention module; wherein, the two / three-dimensional CNN spatial self-attention module utilizes the spatial correlation between the features of the central grid point and the surrounding grid points, traverses each grid point and improves its spatial feature representation; the one-dimensional CNN temporal self-attention module captures long-distance temporal correlation through short-distance temporal features;

[0180] Based on the mine gas state equation, the discrete particle density is calculated using temperature, wind pressure, wind resistance, and gas concentration from the flow field data. Then, based on the discrete particle density and the wind speed and temperature from the flow field data, the Maxwell-Boltzmann distribution function describing the particle velocity distribution is obtained. Finally, this (numerical distribution function) is vector-decomposed into components of each discrete velocity direction in the D2Q9 model, forming the initial velocity distribution function f. i (x, y, t) are stored in a three-dimensional array (N). x N y N i In ), f i (x,y,t) represents the particle density at the lattice point (x,y) in the i-th velocity direction at time t; N in the three-dimensional array i Each (x,y) point in the intermediate layer of the dimension is centered on an adjacent cuboid as a patch composed of discrete velocity numbers.

[0181] In the Boltzmann model calculation, by adjusting the velocity distribution function, it is ensured that the calculated mass of gas entering the mine through the inlet boundary per unit time is equal to the known air intake, thus ensuring the conservation of mass and momentum at the inlet.

[0182] The patch consisting of discrete velocity numbers is input into the two / three-dimensional CNN spatial self-attention module and the one-dimensional CNN temporal self-attention module respectively. The outputs of the two / three-dimensional CNN spatial self-attention module and the one-dimensional CNN temporal self-attention module are fused using a fractional weighted fusion method to obtain the flow field solution results of the spatiotemporal process simulation.

[0183] Example 9:

[0184] This embodiment, based on Embodiment 8, is further designed in that it uses a two-dimensional D2Q9 model to represent the velocity distribution function f. i (x, y, t) are stored in a three-dimensional array with dimensions N. x(Number of grid points in the x-direction), N y (number of grid points in the y-direction) and N i (Number of discrete velocity directions, N in the D2Q9 model) i =9). Feature maps A and B are generated by inputting a patch consisting of discrete velocity numbers into two parallel convolutional layers.

[0185] The expression for the spatial correlation between the features of the central grid point and the surrounding grid points is:

[0186]

[0187] In the formula, S i,t The central grid point vector A i Spatiotemporal similarity with adjacent grid points and time t;

[0188] A i Let A be the vectorized representation of the center grid data, where A is the first feature map generated after two parallel convolutional layers are input to a patch composed of discrete velocity numbers; A i,1 A i,2 A i,3 ,......,A i,n These are respectively related to the central grid point A i Adjacent grid points;

[0189] Use the softmax function to evaluate S. i,t After normalization, we obtain the spatiotemporal self-attention representation:

[0190]

[0191] Based on the spatiotemporal self-attention features, a weighted matrix is ​​calculated to enhance the representation of feature information related to the central grid point and suppress unnecessary spatiotemporal features:

[0192]

[0193] V spa =W spa +X

[0194] Among them W spa Let V be the weight matrix. spa As an incremental representation, B is the second feature map generated after two parallel convolutional layers, with a patch composed of discrete velocity numbers as input. This allows inference of whether features relevant to the central grid point are enhanced and whether irrelevant features are suppressed, thereby further improving the ability to represent the spatiotemporal features of the central grid point. Similarly, performing the same processing on the temporal features yields the incremental V. tpe The output of the one-dimensional CNN temporal self-attention module is fed back to the fully connected layer FC, and the transformation is obtained as F. spa and F tpeFinally, a fractional weighted fusion method was used to obtain the prediction results of the spatiotemporal process simulation:

[0195] F=σ(λ×F spa +(1-λ)×F tpe )

[0196] Where σ(·) is the softmax function, and λ∈[0,1] is the weight parameter, which is generally given an initial value of 0.5 and is adaptively and dynamically adjusted during the network optimization process to finally obtain the optimal solution of the simulation prediction.

[0197] Example 10:

[0198] The present invention provides a mine ventilation network flow field calculation system, comprising a data acquisition module, a model building module, a model training module, and a calculation module;

[0199] The data acquisition module is used to acquire boundary environment data, flow field data, and long-term spatiotemporal distribution data of the mine ventilation network. The flow field data includes wind speed, wind pressure, wind resistance, temperature, and gas concentration composed of methane concentration and dust concentration at various measuring points inside the mine. The long-term spatiotemporal distribution data of the flow field consists of the actual values ​​of the long-term spatiotemporal distribution data composed of wind speed, wind pressure, and methane concentration.

[0200] The model building module is used to build a flow field simulation model of the mine ventilation network. The flow field simulation model of the mine ventilation network includes a spatiotemporal solution model of the ventilation network based on dynamic neural differential equations and a fluid dynamics deep neural network solver based on spatiotemporal self-attention.

[0201] The model training module is used to perform iterative numerical solutions on the ventilation network spatiotemporal solution model based on historical boundary environment data and flow field data, using a fluid dynamics deep neural network solver. This obtains predicted values ​​of the long-sequence distribution data of the flow field spatiotemporal distribution data. Then, based on the error between the predicted and actual values ​​of the long-sequence distribution data of the flow field spatiotemporal distribution data, the model parameters of the ventilation network spatiotemporal solution model and the fluid dynamics deep neural network solver are adjusted to perform iterative training of the flow field simulation model of the mine ventilation network.

[0202] The solution module is used to acquire target boundary environment data and the corresponding spatiotemporal long sequence distribution data of the flow field based on the trained flow field simulation model of the mine ventilation network, and use them as the flow field solution results.

[0203] Example 11:

[0204] An electronic device includes a memory and a processor, the memory storing a computer program, and the processor being configured to invoke and run the computer program stored in the memory to perform the method described in any of the preceding methods.

[0205] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method as described in any of the preceding claims.

[0206] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for solving a flow field of a mine ventilation network, characterized in that, include: Acquire boundary environment data, flow field data, and long-term spatiotemporal distribution data of the mine ventilation network; the flow field data includes wind speed, wind pressure, wind resistance, temperature, and gas concentration composed of methane concentration and dust concentration at various measuring points inside the mine; the long-term spatiotemporal distribution data of the flow field is the actual value of the long-term spatiotemporal distribution data composed of wind speed, wind pressure, and methane concentration. A flow field simulation model for a mine ventilation network is constructed, comprising a spatiotemporal solution model for the ventilation network based on dynamic neural differential equations and a deep neural network solver for fluid dynamics based on spatiotemporal self-attention. Based on historical boundary environment data and flow field data, the fluid dynamics deep neural network solver is used to perform iterative numerical solution of the ventilation network spatiotemporal solution model to obtain the predicted value of the long-sequence distribution data of the flow field spatiotemporal data. Then, based on the error between the predicted value and the actual value of the long-sequence distribution data of the flow field spatiotemporal data, the model parameters of the ventilation network spatiotemporal solution model and the fluid dynamics deep neural network solver are adjusted to perform iterative training of the flow field simulation model of the mine ventilation network. Based on the flow field simulation model of the well-trained mine ventilation network, the target boundary environment data and the corresponding spatiotemporal long sequence distribution data of the flow field are obtained and used as the flow field solution results. The specific construction method of the spatiotemporal solution model of the ventilation network based on the dynamic neural differential equation is as follows: First, the lattice Boltzmann model lattice points i , j above the threshold value of the wind speed p are recorded as the set of ventilation events and ; in the formula, is the occurrence time of the first ventilation event at the lattice point i ; μ is the occurrence time of the first ventilation event at the lattice point ; j is the occurrence time of the first ventilation event at the lattice point v ; s i and s j These are grid point i and 1 within the research period, respectively. j The total number of ventilation incidents at the location; Based on a pair of grid points in the synchronous event method ( i,j The spatiotemporal correlation characteristics are constructed by the time difference of the occurrence of the events. Therefore, for a ventilation network system, if any two ventilation events in space... μ, v Time delay between If the values ​​are less than a threshold, the two events are considered to have occurred synchronously and are called synchronous events. The formula for calculating the threshold is as follows: In the formula, and Grid points i No. μ The second event and the first μ -1 event time interval and grid points i No. μ+ 1st incident and the first μ The time interval between events; and Grid points j No. v The second event and the first v -1 event time interval and grid points j No. v+ 1st incident and the first v The time interval between events; Arbitrary lattice pairs ( i, j The number of synchronization events is: In the formula, For grid pairs ( i,j The total number of synchronization events; For indicator functions; ; This yields the synchronization event matrix ES, thus completing the dynamic statistical construction of ventilation events at the grid points. A symmetric matrix is ​​then constructed to address the spatiotemporal correlations between grid points in the ventilation network. Q and symmetric matrix q The elements in the matrix are: ; ;in, Q ij and q ij Grid points i, j The relationship between the synchronization intensity and time delay of ventilation events. Q ij ∈[0,1], q ij ∈[-1,1]; Thus, by setting a threshold to eliminate secondary spatial correlations, the synchronous correlation characteristics and time delay direction characteristics of wind velocity on the grid points are obtained; For grid points i Time delay of event occurrence τ inside, grid point j The number of events occurring; secondly, a simulation prediction and solution model based on dynamic neural differential equations is constructed, and the time dynamics are described on the lattice Boltzmann model based on the differential equation system: ; in, For any time by n The state or characteristic value of a dynamic system composed of 10 lattice points; To capture the complex network structures of how grid points interact; The parameters that define how the control system evolves over time; for The initial state of the ventilation network system based on the lattice Boltzmann model at any given time; function Control the dynamic instantaneous rate of change of the grid points; define To characterize lattice points j The degree to which it is affected by the velocity magnitude of other grid points. In the formula, n It is the total number of grid points. M(t) Is t The set of lattice points where velocity collisions occur at any given time. d ij It is a grid. i, j distance, These are the correlation strength and correlation direction factors between grid points.

2. The method for calculating the flow field of a mine ventilation network according to claim 1, characterized in that, The specific steps for obtaining boundary environment data and flow field data of the mine ventilation network include: Collect boundary environmental data and flow field data of the mine ventilation network; The collected boundary environment data and flow field data are preprocessed to remove noise and outliers.

3. The method for calculating the flow field of a mine ventilation network according to claim 2, characterized in that, The air intake volume in the boundary environment data is the sum of the air intake volumes of each air inlet in the mine ventilation network, expressed as: ;in, Total air intake volume; For the first i The air volume of each air inlet is n, where n is the number of air inlets.

4. The method for calculating the flow field of a mine ventilation network according to claim 2, characterized in that, The expression for the wind speed in the flow field data is: In the formula, Wind speed; Q Total air volume S Let be the cross-sectional area of ​​the tunnel; the expression for the air pressure is: ; In the formula, Wind pressure; air density; This refers to the difference in air altitude. It is the acceleration due to gravity; The expression for wind resistance is: ; In the formula, For wind resistance; The pressure difference between the two ends of the tunnel; The expression for the temperature is: ; In the formula, Reference temperature; For temperature rise; The gas concentration includes methane concentration and dust concentration, expressed as follows: ; ; In the formula, Gas concentration; For gas volume; For air volume; Dust concentration; For dust quality.

5. The method for calculating the flow field of a mine ventilation network according to claim 2, characterized in that, The data preprocessing specifically includes: A) Data cleaning and filtering: Data interpolation and smoothing filtering are used to fill in short-term missing data at measurement points. If a measurement point has long-term missing data, the measurement point is directly removed or data from a neighboring measurement point is used as a substitute. Smoothing filters are used to suppress high-frequency noise, and wavelet decomposition is performed on non-stationary signals to retain low-frequency effective components and remove high-frequency noise. Outliers were detected and removed using statistical methods and physical constraint methods. B) Data Standardization: For the air intake volume, a central logarithmic ratio transformation is used; For wind pressure and temperature, Min-Max Scaling normalization is used to scale the data to the [0,1] range; For normally distributed data including wind speed and gas concentration, Z-score normalization is used. For non-normally distributed data including wind resistance, quantile transformation is used to map them to a uniform or normal distribution; C) Feature extraction and selection: For the time dimension, sliding window statistics are extracted, and frequency domain features are extracted through Fourier transform; For the spatial dimension, the topological relationship between the measurement points is constructed, the spatial correlation is calculated, and the spatiotemporal correlation strength between the measurement points is quantified using the synchronization event matrix. Features with high correlation to the target variable are selected by mutual information, and then the high-dimensional spatiotemporal data are reduced in dimensionality by principal component analysis, retaining more than 90% of the variance components.

6. The method for calculating the flow field of a mine ventilation network according to claim 1, characterized in that, The specific methods for iterative training include: A dataset is constructed based on the aforementioned environmental data, flow field data, and spatiotemporal long-sequence distribution data. The flow field simulation model of the mine ventilation network is trained based on the dataset. Boundary environment data and flow field data are used as input data for the spatiotemporal solution model of the ventilation network based on dynamic neural differential equations. A fluid dynamics deep neural network solver based on spatiotemporal self-attention is used to solve the ventilation network spatiotemporal solution model numerically to obtain the predicted values ​​of the long-sequence distribution data of the flow field. Then, based on the error between the predicted values ​​and the actual values ​​of the long-sequence distribution data of the flow field, the model parameters of the spatiotemporal solution model of the ventilation network and the fluid dynamics deep neural network solver are adjusted to perform iterative training of the flow field simulation model of the mine ventilation network. During training, model parameters are adjusted using backpropagation and gradient descent algorithms, and regularization is used to prevent overfitting. Furthermore, a learning rate scheduling method is employed to improve training efficiency.

7. The method for calculating the flow field of a mine ventilation network according to claim 1, characterized in that, The spatiotemporal self-attention-based deep neural network solver for fluid dynamics includes a patch-based two / three-dimensional CNN spatial self-attention module and a one-dimensional CNN temporal self-attention module. The two / three-dimensional CNN spatial self-attention module utilizes the spatial correlation between the features of the central grid point and the surrounding grid points to traverse each grid point and improve its spatial feature representation. The one-dimensional CNN temporal self-attention module captures long-distance temporal correlation through short-distance temporal features. Based on the mine gas state equation, discrete particle density is calculated using temperature, wind pressure, wind resistance, and gas concentration from the flow field data. Then, based on the discrete particle density and the wind speed and temperature from the flow field data, the Maxwell-Boltzmann distribution function describing the particle velocity distribution is obtained. Finally, this function is vector-decomposed into... D 2 Q The components of each discrete velocity direction in the 9 model form the initial velocity distribution function. f i ( x , y ,t) are stored in a three-dimensional array ( N x ,N y ,N i )middle, f i ( x , y ,t) represents a lattice point ( x,y At that moment t Time i Particle density in each velocity direction; in the three-dimensional array N i Each of the intermediate layers in the dimension ( x,y The adjacent cuboids centered at point ) serve as patches composed of discrete velocity numbers; The patch consisting of discrete velocity numbers is input into the two / three-dimensional CNN spatial self-attention module and the one-dimensional CNN temporal self-attention module respectively. The outputs of the two / three-dimensional CNN spatial self-attention module and the one-dimensional CNN temporal self-attention module are fused using a fractional weighted fusion method to obtain the flow field solution results of the spatiotemporal process simulation.

8. The method for calculating the flow field of a mine ventilation network according to claim 7, characterized in that, The expression for the spatial correlation between the features of the central grid point and the surrounding grid points is: In the formula, The center grid point vector With adjacent grid points and time The similarity of spatiotemporal features between them; for A The vectorized representation of the central grid point data. A The first feature map generated after inputting two parallel convolutional layers into a patch consisting of discrete velocity numbers; They are respectively with the central grid point Adjacent grid points; Use the softmax function to After normalization, we obtain the spatiotemporal self-attention representation: ; Based on the spatiotemporal self-attention features, a weighted matrix is ​​calculated to enhance the representation of feature information related to the central grid point and suppress unnecessary spatiotemporal features: ; ; in, This is the weight matrix. Incremental representation, The second feature map is generated after inputting two parallel convolutional layers into a patch consisting of discrete velocity numbers; The increment can be obtained by performing the same processing on the time features. The output of the one-dimensional CNN temporal self-attention module is fed back to the fully connected layer (FC) to transform the result. and Finally, a fractional weighted fusion method was used to obtain the prediction results of the spatiotemporal process simulation: ; in, For the softmax function, For weight parameters, .

9. A flow field calculation system for a mine ventilation network, characterized in that, It includes a data acquisition module, a model building module, a model training module, and a solution module; The data acquisition module is used to acquire boundary environment data, flow field data, and long-term spatiotemporal distribution data of the mine ventilation network. The flow field data includes wind speed, wind pressure, wind resistance, temperature, and gas concentration composed of methane concentration and dust concentration at various measuring points inside the mine. The long-term spatiotemporal distribution data of the flow field consists of the actual values ​​of the long-term spatiotemporal distribution data composed of wind speed, wind pressure, and methane concentration. The model building module is used to build a flow field simulation model of the mine ventilation network. The flow field simulation model of the mine ventilation network includes a spatiotemporal solution model of the ventilation network based on dynamic neural differential equations and a fluid dynamics deep neural network solver based on spatiotemporal self-attention. The model training module is used to perform iterative numerical solutions on the ventilation network spatiotemporal solution model based on historical boundary environment data and flow field data, using the fluid dynamics deep neural network solver to obtain predicted values ​​of the long-sequence distribution data of the flow field spatiotemporal data. Then, based on the error between the predicted values ​​and the actual values ​​of the long-sequence distribution data of the flow field spatiotemporal data, the model parameters of the ventilation network spatiotemporal solution model and the fluid dynamics deep neural network solver are adjusted to perform iterative training of the flow field simulation model of the mine ventilation network. The solution module is used to acquire target boundary environment data and the corresponding spatiotemporal long-sequence distribution data of the flow field based on the trained flow field simulation model of the mine ventilation network, and use these as the flow field solution results; the specific construction method of the spatiotemporal solution model of the ventilation network based on the dynamic neural differential equation is as follows: First, the lattice Boltzmann model is divided into lattice points. i , j Upwind speed above the threshold p The grid points are denoted as the ventilation event set. and In the formula, For grid points i Upper μ The timing of the secondary ventilation incident; For grid points j Upper v The timing of the secondary ventilation incident; s i and s j These are grid point i and 1 within the research period, respectively. j The total number of ventilation incidents at the location; Based on a pair of grid points in the synchronous event method ( i,j The spatiotemporal correlation characteristics are constructed by the time difference of the occurrence of the events. Therefore, for a ventilation network system, if any two ventilation events in space... μ, v Time delay between If the values ​​are less than a threshold, the two events are considered to have occurred synchronously and are called synchronous events. The formula for calculating the threshold is as follows: In the formula, and Grid points i No. μ The second event and the first μ -1 event time interval and grid points i No. μ+ 1st incident and the first μ The time interval between events; and Grid points j No. v The second event and the first v -1 event time interval and grid points j No. v+ 1st incident and the first v The time interval between events; Arbitrary lattice pairs ( i, j The number of synchronization events is: In the formula, For grid pairs ( i,j The total number of synchronization events; For indicator functions; ; This yields the synchronization event matrix ES, thus completing the dynamic statistical construction of ventilation events at the grid points. A symmetric matrix is ​​then constructed to address the spatiotemporal correlations between grid points in the ventilation network. Q and symmetric matrix q The elements in the matrix are: ; ;in, Q ij and q ij Grid points i, j The relationship between the synchronization intensity and time delay of ventilation events. Q ij ∈[0,1], q ij ∈[-1,1]; Thus, by setting a threshold to eliminate secondary spatial correlations, the synchronous correlation characteristics and time delay direction characteristics of wind velocity on the grid points are obtained; For grid points i Time delay of event occurrence τ inside, grid point j The number of events occurring; secondly, a simulation prediction and solution model based on dynamic neural differential equations is constructed, and the time dynamics are described on the lattice Boltzmann model based on the differential equation system: ; in, For any time by n The state or characteristic value of a dynamic system composed of 10 lattice points; To capture the complex network structures of how grid points interact; The parameters that define how the control system evolves over time; for The initial state of the ventilation network system based on the lattice Boltzmann model at any given time; function Control the dynamic instantaneous rate of change of the grid points; define To characterize lattice points j The degree to which it is affected by the velocity magnitude of other grid points. In the formula, n It is the total number of grid points. M(t) Is t The set of lattice points where velocity collisions occur at any given time. d ij It is a grid. i, j distance, These are the correlation strength and correlation direction factors between grid points.

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