Underground water flow field streamline drawing method based on information entropy feature extraction

Abstract

The invention discloses an underground water flow field streamline drawing method based on information entropy feature extraction, and relates to the technical field of underground water visualization. The method comprises the following steps: calculating the three-dimensional information entropy of each sub-region in an underground water flow field, and quantifying the change degree of a flow state; critical point detection: identifying a source point, a sink point, a saddle point and a vortex point in the flow field by using the characteristic value of the Jacobian matrix; carrying out feature fusion on the three-dimensional information entropy feature value and the feature value of the Jacobian matrix to obtain a comprehensive feature, and taking the comprehensive feature as an input feature of the convolutional neural network; training a convolutional neural network model; utilizing the trained convolutional neural network model to predict the position of a seed point; drawing and displaying the flow line of the underground water flow field; and predicting the underground water flow field flow velocity and the underground water flow field direction by using the trained convolutional neural network model. According to the method, the information entropy and the critical point are combined, the convolutional neural network is constructed, the position of the seed point is optimized, and the underground water flow field streamline diagram is drawn.

Description

Technical Field

[0001] The invention relates to the technical field of groundwater visualization, and in particular to a method for drawing groundwater flow field streamlines based on information entropy feature extraction. Background Art

[0002] In the field of geological research, the visualization of groundwater flow field streamlines is crucial for the study of groundwater flow field streamlines. Flow field visualization has always been a hot spot and difficulty in scientific visualization. Streamline is a commonly used method for flow field visualization. It starts from a seed point, moves forward and backward along the point, obtains the next point through flow field integration, and finally connects all generated points to form a streamline. The difficulty lies in how to obtain suitable streamlines. If there are too many streamlines, the drawn image will produce visual confusion; and if there are too few streamlines, the characteristic information of the flow field will be lost. Therefore, how to set the seed point is a key issue in streamline visualization. At present, there are many methods for studying streamline placement, with two main focuses: on the one hand, focusing on the uniformity of streamlines to avoid a large number of blanks in the flow field; on the other hand, paying attention to the topological structure of the flow field, which focuses on the characteristic information of the flow field; but these two aspects cannot be fully taken into account. Summary of the invention

[0003] The purpose of the present invention is to provide a method for drawing groundwater flow field streamlines based on information entropy feature extraction to solve the problems raised in the above background technology.

[0004] In order to solve the above technical problems, the present invention provides the following technical solutions: A method for drawing streamlines of groundwater flow field based on information entropy feature extraction, the method comprising the following steps: S1. Calculate the three-dimensional information entropy of each sub-region in the groundwater flow field to quantify the degree of change in flow state; S2, critical point detection, and use the eigenvalues ​​of the Jacobian matrix to identify the source points, sink points, saddle points and vortex points in the flow field; S3, fusion of the eigenvalues ​​of the three-dimensional information entropy and the eigenvalues ​​of the Jacobian matrix to obtain comprehensive features, and use them as input features of the convolutional neural network; S4, training convolutional neural network model; S5, optimizing the seed point position using the trained convolutional neural network model; S6. Draw and display the streamlines of groundwater flow field; S7. Use the trained convolutional neural network model to predict the groundwater flow velocity and direction.

[0005] According to the above scheme, in step S1, the groundwater flow field is divided into i sub-areas, and s is the scanning span of the X, Y, and Z coordinates; O, P, and Q are the number of grids divided by the X, Y, and Z axes, respectively; W, H, and D are the total lengths in the X, Y, and Z axes, respectively; and the size of each grid is s. X =W / O,s Y =H / P,s Z =D / Q; subdividing the groundwater flow field into multiple sub-areas helps to analyze the flow characteristics of each part in more detail; If the remaining length after scanning to the end of the coordinate axis is less than one s, the end of the coordinate is regarded as the end of the last sub-region, which increases the flexibility of the method.

[0006] According to the above scheme, in step S1, a unit sphere is placed in the sub-region, and the unit sphere is divided into j spherical patches x of equal area using the Leopardi sphere equal area segmentation method. j , each spherical patch has a center point. The angle between the center position vector of the spherical patch and the velocity vector at the vertex in the sub-region is calculated using the following formula:

[0007] Among them, θ represents the angle between the center position vector of the spherical patch and the velocity vector at the vertex in the sub-region; It is represented as the center position vector of the spherical patch; Represented as the velocity vector at the vertex in the sub-region; The spherical patch with the smallest angle is taken as the spherical patch that the velocity vector falls into, and the spherical patch that the velocity vector of each vertex falls into is obtained; according to the number of velocity vectors falling into each spherical patch, the spherical patch x is calculated. j The distribution probability of the internal velocity vector is as follows:

[0008] Among them, p j Represented as a spherical patch x j Distribution probability of internal velocity vector; m j Represented as a spherical patch x j The number of velocity vectors falling into the sub-region; d represents the total number of velocity vectors of all vertices in the sub-region; vertices refer to the vertices of polygons or figures formed after the Leopardi sphere equal area partitioning method; According to the velocity vector distribution probability obtained by statistics, the three-dimensional information entropy of each sub-area is calculated, and the formula is as follows:

[0009] Among them, Entropy is represented by the three-dimensional information entropy; m is represented by the total number of spherical patches, and p is represented by thej It is expressed as the distribution probability of the velocity vector in the jth spherical patch. By calculating the three-dimensional information entropy, the degree of change of the flow state in different regions of the flow field can be quantified. When calculating the three-dimensional information entropy, p i If it is 0, it means that no velocity vector falls into the patch, and this item does not participate in the summation; If the size of the last sub-region in the X, Y or Z axis direction is smaller than s, the calculation of the three-dimensional information entropy of the sub-region needs to be adjusted.

[0010] According to the above scheme, a three-dimensional information entropy threshold Threshold is determined to screen the sub-regions where the fluid state changes drastically. The formula of the three-dimensional information entropy threshold Threshold is as follows: Threshold = f × max (Entropy i ) Where f represents the influencing factor of the three-dimensional information entropy of the screening sub-region; Entropy i It is expressed as the three-dimensional information entropy of the i-th sub-region; max(Entropy i ) is expressed as taking the maximum value of the three-dimensional information entropy of the sub-region; by setting the three-dimensional information entropy threshold, the sub-regions where the fluid state changes dramatically can be screened out, and then these key regions can be focused on for more in-depth research; To filter sub-regions where the fluid state changes dramatically, the following conditions need to be met: Entropy i ≥Threshold The screened sub-regions represent areas where the fluid state changes drastically or the flow complexity is high.

[0011] According to the above scheme, in step S2, By using the linear interpolation method, critical points are detected in the sub-regions where the fluid state changes dramatically. Only focusing on the regions with high three-dimensional information entropy can reduce unnecessary computational burden and improve overall processing efficiency. The source points, sink points, saddle points and vortex points in the flow field are identified by the eigenvalues ​​of the Jacobian matrix J; let the velocity field be expressed as (x,y,z)=(v x ,v y ,v z ), where v x , v y , v z are the velocity components in the x, y, and z directions respectively, and the Jacobian matrix J is:

[0012] When the Jacobian matrix has one positive eigenvalue and one negative eigenvalue, it is represented as a source point or a sink point; when all eigenvalues ​​of the Jacobian matrix are zero or the real part is zero, it is represented as a saddle point; when the Jacobian matrix has a pair of conjugate complex eigenvalues, it is represented as a vortex point; Critical point detection can accurately identify source points, sink points, saddle points and vortex points in the flow field; identifying these points helps to simplify subsequent streamline tracing and flow field analysis; and by identifying different types of key points, the physical interpretability of the model can be increased, making the research results easier to understand.

[0013] According to the above scheme, in step S3, the three-dimensional information entropy value and the eigenvalue of the Jacobian matrix are preprocessed, and the preprocessing includes: standardization processing, converting the three-dimensional information entropy value and the eigenvalue of the Jacobian matrix to the same range; data cleaning processing, processing the abnormal values ​​and missing values ​​in the eigenvalue data of the three-dimensional information entropy value and the Jacobian matrix; data alignment processing, ensuring that the eigenvalue data of the three-dimensional information entropy value and the Jacobian matrix are aligned at the same space or time point; weighted fusion of the preprocessed three-dimensional information entropy value and the eigenvalue of the Jacobian matrix to obtain comprehensive features; By fusing the eigenvalues ​​of three-dimensional information entropy and the eigenvalues ​​of the Jacobian matrix, the flow field characteristics can be more comprehensively characterized; the fused features can provide richer information for the convolutional neural network, thereby improving the prediction accuracy of the model.

[0014] According to the above scheme, in step S4, a convolutional neural network is constructed, and the convolutional neural network includes an input layer, a convolutional layer, a pooling layer, a fully connected layer, and an output layer; through the convolutional layer, the pooling layer, the fully connected layer, and the output layer structure, pattern recognition and feature extraction can be effectively performed; According to forward propagation, the comprehensive features are input into the input layer of the convolutional neural network, and the comprehensive features are transmitted to the convolution layer through the input layer for convolution operation. The formula is as follows:

[0015] Among them, S I,J It is represented as the output of the convolutional layer at the Ith row and the Jth column position; w E,F,T It is represented as the weight at the channel T position in the Eth row and the Fth column in the convolutional layer; f I+E,J+F,T It is represented as the value of the comprehensive feature f at the position of channel T in the I+E row, J+F column; B is represented as the bias term of the convolutional layer; weights and biases are parameters that the model needs to learn during training; The convolutional layer is followed by a nonlinear activation function to introduce nonlinear transformations. The formula is as follows: ReLU I,J =max(0,S I,J ) Among them, ReLUI,J Represented as the output after the activation function; max(0,S I,J ) means taking the larger value; The data after the activation function is transferred to the pooling layer, and after the maximum pooling, the dimension of the feature value is reduced while keeping the most important features; The fully connected layer flattens the pooled features into a one-dimensional vector V through the flatten function flat , and is calculated by matrix multiplication and bias terms as follows: Z fc =w fc V flat +b fc Among them, Z fc Represented as the output of the fully connected layer; w fc Represented as the weight matrix of the fully connected layer; b fc Represented as the bias vector of the fully connected layer; The output layer outputs the seed point location, groundwater flow velocity and groundwater flow direction.

[0016] According to the above scheme, the difference between the predicted value and the actual value is measured by the loss function to obtain the loss value; the loss function formula is as follows: The output value of the seed point position uses the mean square error to calculate the loss function, and the formula is as follows:

[0017] Among them, L position It is represented as the loss function value of the seed point position; N is represented as the number of seed points; (x true,n ,y true,n , z true,n ) represents the true position of the nth seed point; Represents the predicted position of the nth seed point; The output value of groundwater flow field velocity uses mean square error to calculate the loss function, and the formula is as follows:

[0018] Among them, L velocity Expressed as the loss function value of groundwater flow velocity; v true,n It represents the actual groundwater flow velocity at the nth seed point; It is represented as the predicted groundwater flow velocity of the nth seed point; The output value of the groundwater flow field direction uses the cosine similarity loss function to calculate the loss function, and the formula is as follows:

[0019] Among them, Ldirection Expressed as the loss function of the groundwater flow direction; θ ture,n It is represented as the real groundwater flow direction vector of the nth seed point; It is represented as the predicted groundwater flow direction vector of the nth seed point; It is expressed as the cosine similarity between the true groundwater flow field direction vector and the predicted groundwater flow field direction vector; According to L position , L velocity and L direction Calculate the comprehensive loss function, the formula is as follows: L=λ1•L position +λ2•L velocity +λ3•L direction Among them, L represents the comprehensive loss function; λ1, λ2 and λ3 are L position , L velocity and L direction The weight coefficient indicates the relative importance in the comprehensive loss; Starting from the output layer, use the back-propagation algorithm to adjust the network parameters; calculate the gradient of each loss function weight and bias, which represents the sensitivity of the loss function to the change of weight and bias; through a reasonable loss function and back-propagation mechanism, the performance of the model on unseen data can be improved; Calculate the gradient according to the loss function; The loss gradient at the seed point position is as follows:

[0020] in, Expressed as the gradient of the predicted x-coordinate; Expressed as the gradient of the predicted y coordinate; Expressed as the gradient of the predicted z-coordinate; The loss gradient of groundwater flow velocity is as follows:

[0021] in, It is expressed as the gradient of the predicted groundwater flow velocity; The loss gradient in the direction of groundwater flow field is as follows:

[0022] in, It is expressed as the gradient of the direction vector of the predicted groundwater flow field; Backward propagation of error signals, based on which the gradients of the fully connected layer, pooling layer, and convolutional layer are calculated; during the back propagation process, all relevant gradients are added together to obtain the final gradient; using the gradient descent method, the weights and biases in the network are updated based on the calculated gradients; In each training iteration, the forward propagation and back propagation processes are repeated until the model has reached convergence on the training set, and the performance of the model is evaluated to verify the generalization ability of the model.

[0023] According to the above scheme, the seed point positions are placed according to the predicted seed point positions output by the convolutional neural network; starting from each seed point, the streamlines are traced along the velocity vector direction of the flow field by the fourth-order Runge-Kutta method; the traced paths are plotted on the groundwater flow field to form a groundwater flow field streamline diagram; By optimizing the position of seed points through the trained model, the accuracy and stability of streamline tracing can be improved; more precise and reliable streamline trajectories can be generated.

[0024] According to the above scheme, the trained convolutional neural network model is used to predict the groundwater flow field velocity and groundwater flow field direction, and the groundwater flow field streamline prediction map is drawn based on the prediction results of the convolutional neural network; the prediction results can be used for decision support in the fields of groundwater management, pollution control, etc.

[0025] Compared with the prior art, the beneficial effects achieved by the present invention are: 1. Combine information entropy and critical points to construct a convolutional neural network, and use the convolutional neural network to predict the position of the seed point; 2. Optimize the seed point position through convolutional neural network and draw a clear streamline map of groundwater flow field; 3. Using the trained model to predict the speed and direction of groundwater flow can help hydrogeologists better understand the flow characteristics of groundwater and make more accurate hydrogeological predictions; 4. Convolutional neural networks can be adjusted according to different application scenarios to adapt to different groundwater flow field environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings: Figure 1 It is a schematic diagram of the steps of a method for drawing streamlines of groundwater flow field based on information entropy feature extraction of the present invention; Figure 2 It is a schematic diagram of the steps of extracting three-dimensional information entropy by a method for drawing streamlines of groundwater flow field based on information entropy feature extraction according to the present invention; Figure 3 It is a schematic diagram of the steps of calculating the eigenvalues ​​of the Jacobian matrix in a groundwater flow field streamline drawing method based on information entropy feature extraction of the present invention. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0028] See also Figure 1-Figure 3 , the present invention provides a technical solution: According to an embodiment of the present invention, a method for drawing streamlines of groundwater flow field based on information entropy feature extraction comprises the following steps: S1. Calculate the three-dimensional information entropy of each sub-region in the groundwater flow field to quantify the degree of change in flow state; S2, critical point detection, and use the eigenvalues ​​of the Jacobian matrix to identify the source points, sink points, saddle points and vortex points in the flow field; S3, fusion of the eigenvalues ​​of the three-dimensional information entropy and the eigenvalues ​​of the Jacobian matrix to obtain comprehensive features, and use them as input features of the convolutional neural network; S4, training convolutional neural network model; S5, optimizing the seed point position using the trained convolutional neural network model; S6. Draw and display the streamlines of groundwater flow field; S7. Use the trained convolutional neural network model to predict the groundwater flow velocity and direction.

[0029] According to the above scheme, in step S1, the groundwater flow field is divided into i sub-areas, and s is the scanning span of the X, Y, and Z coordinates; O, P, and Q are the number of grids divided by the X, Y, and Z axes, respectively; W, H, and D are the total lengths in the X, Y, and Z axes, respectively; and the size of each grid is s. X =W / O,s Y =H / P,s Z =D / Q; subdividing the groundwater flow field into multiple sub-areas helps to analyze the flow characteristics of each part in more detail If the remaining length after scanning to the end of the coordinate axis is less than one s, the end of the coordinate is regarded as the end of the last sub-region, which increases the flexibility of the method.

[0030] According to the above scheme, in step S1, a unit sphere is placed in the sub-region, and the unit sphere is divided into j spherical patches x of equal area using the Leopardi sphere equal area segmentation method. j , each spherical patch has a center point. The angle between the center position vector of the spherical patch and the velocity vector at the vertex in the sub-region is calculated using the following formula:

[0031] Among them, θ represents the angle between the center position vector of the spherical patch and the velocity vector at the vertex in the sub-region; It is represented as the center position vector of the spherical patch; Represented as the velocity vector at the vertex in the sub-region; The spherical patch with the smallest angle is taken as the spherical patch that the velocity vector falls into, and the spherical patch that the velocity vector of each vertex falls into is obtained; according to the number of velocity vectors falling into each spherical patch, the spherical patch x is calculated. j The distribution probability of the internal velocity vector is as follows:

[0032] Among them, p j Represented as a spherical patch x j Distribution probability of internal velocity vector; m j Represented as a spherical patch x j The number of velocity vectors falling into the sub-region; d represents the total number of velocity vectors of all vertices in the sub-region; vertices refer to the vertices of polygons or figures formed after the Leopardi sphere equal area partitioning method; Suppose the unit sphere is divided into 20 spherical patches, each with 100 vertices, and the velocity vector of each vertex points in a different direction; suppose there are 10 velocity vectors in spherical patch x1, 15 velocity vectors in spherical patch x2, and 4 velocity vectors in the remaining spherical patches; we get d=100, n1=10, n2=15, n j =4; According to the velocity vector distribution probability formula, the probabilities p1 and p2 within the spherical patches x1 and x2 are calculated: p1=n1 / d=10 / 100=0.1 P2=n2 / d=15 / 100=0.15 P j =n j / d=4 / 100=0.04 According to the velocity vector distribution probability obtained by statistics, the three-dimensional information entropy of each sub-area is calculated, and the formula is as follows:

[0033] Among them, Entropy is represented by the three-dimensional information entropy; m is represented by the total number of spherical patches, and p is represented by the j It is expressed as the distribution probability of the velocity vector in the jth spherical patch. By calculating the three-dimensional information entropy, the degree of change of the flow state in different regions of the flow field can be quantified. Entropy=-(0.1log(0.1)+0.15log(0.15)+18×0.04log(0.04)) When calculating the three-dimensional information entropy, p i If it is 0, it means that no velocity vector falls into the patch, and this item does not participate in the summation; If the size of the last sub-region in the X, Y or Z axis direction is smaller than s, the calculation of the three-dimensional information entropy of the sub-region needs to be adjusted.

[0034] According to the above scheme, a three-dimensional information entropy threshold Threshold is determined to screen the sub-regions where the fluid state changes drastically. The formula of the three-dimensional information entropy threshold Threshold is as follows: Threshold = f × max (Entropy i ) Where f represents the influencing factor of the three-dimensional information entropy of the screening sub-region; Entropy i It is expressed as the three-dimensional information entropy of the i-th sub-region; max(Entropy i ) is expressed as taking the maximum value of the three-dimensional information entropy of the sub-region; by setting the three-dimensional information entropy threshold, the sub-regions where the fluid state changes dramatically can be screened out, and then these key regions can be focused on for more in-depth research; The influence factor f of the three-dimensional information entropy is usually 0.7-0.9. When f=0.9, the three-dimensional information entropy of all sub-areas is calculated, and the maximum three-dimensional information entropy max (Entropy i )=0.5; Then the three-dimensional information entropy threshold Threshold = f×max(Entropy i )=0.9×0.5=0.45; To filter sub-regions where the fluid state changes dramatically, the following conditions need to be met: Entropy i ≥Threshold The selected sub-regions represent areas with drastic changes in fluid state or high flow complexity; Any sub-region with a three-dimensional information entropy greater than or equal to 0.45 will be regarded as a sub-region where the fluid state changes dramatically.

[0035] According to the above scheme, in step S2, By using the linear interpolation method, critical points are detected in the sub-regions where the fluid state changes dramatically. Only focusing on the regions with high three-dimensional information entropy can reduce unnecessary computational burden and improve overall processing efficiency. The source points, sink points, saddle points and vortex points in the flow field are identified by the eigenvalues ​​of the Jacobian matrix J; let the velocity field be expressed as (x,y,z)=(v x ,v y ,v z ), where v x , v y , v z are the velocity components in the x, y, and z directions respectively, and the Jacobian matrix J is:

[0036] When the Jacobian matrix has one positive eigenvalue and one negative eigenvalue, it is represented as a source point or a sink point; when all eigenvalues ​​of the Jacobian matrix are zero or the real part is zero, it is represented as a saddle point; when the Jacobian matrix has a pair of conjugate complex eigenvalues, it is represented as a vortex point; Assume that the velocity field (x, y, z) = (v x ,v y ,v z ) at a certain point is: v x =2x+3y+4z;v y =x-3y+2z;v z =4x+2y-3z; Based on these velocity components, the Jacobian matrix J can be obtained:

[0037] Calculate the Jacobian matrix solution to obtain eigenvalues ​​λ1=1, λ2=-2, λ3=0; Since there is a positive and a negative eigenvalue, this point can be identified as a source or sink; Critical point detection can accurately identify source points, sink points, saddle points and vortex points in the flow field; identifying these points helps to simplify subsequent streamline tracing and flow field analysis; and by identifying different types of key points, the physical interpretability of the model can be increased, making the research results easier to understand.

[0038] According to the above scheme, in step S3, the three-dimensional information entropy value and the eigenvalue of the Jacobian matrix are preprocessed, and the preprocessing includes: standardization processing, converting the three-dimensional information entropy value and the eigenvalue of the Jacobian matrix to the same range; data cleaning processing, processing the abnormal values ​​and missing values ​​in the eigenvalue data of the three-dimensional information entropy value and the Jacobian matrix; data alignment processing, ensuring that the eigenvalue data of the three-dimensional information entropy value and the Jacobian matrix are aligned at the same space or time point; weighted fusion of the preprocessed three-dimensional information entropy value and the eigenvalue of the Jacobian matrix to obtain comprehensive features; By fusing the eigenvalues ​​of three-dimensional information entropy and the eigenvalues ​​of the Jacobian matrix, the flow field characteristics can be more comprehensively characterized; the fused features can provide richer information for the convolutional neural network, thereby improving the prediction accuracy of the model.

[0039] According to the above scheme, in step S4, a convolutional neural network is constructed, and the convolutional neural network includes an input layer, a convolutional layer, a pooling layer, a fully connected layer, and an output layer; through the convolutional layer, the pooling layer, the fully connected layer, and the output layer structure, pattern recognition and feature extraction can be effectively performed; According to forward propagation, the comprehensive features are input into the input layer of the convolutional neural network, and the comprehensive features are transmitted to the convolution layer through the input layer for convolution operation. The formula is as follows:

[0040] Among them, S I,J It is represented as the output of the convolutional layer at the Ith row and the Jth column position; w E,F,T It is represented as the weight at the channel T position in the Eth row and the Fth column in the convolutional layer; f I+E,J+F,T It is represented as the value of the comprehensive feature f at the position of channel T in the I+E row, J+F column; B is represented as the bias term of the convolutional layer; weights and biases are parameters that the model needs to learn during training; The convolutional layer is followed by a nonlinear activation function to introduce nonlinear transformations. The formula is as follows: ReLU I,J =max(0,S I,J ) Among them, ReLU I,J Represented as the output after the activation function; max(0,S I,J ) means taking the larger value; The data after the activation function is transferred to the pooling layer, and after the maximum pooling, the dimension of the feature value is reduced while keeping the most important features; The fully connected layer flattens the pooled features into a one-dimensional vector V through the flatten function flat , and is calculated by matrix multiplication and bias terms as follows: Zfc =w fc V flat +b fc Among them, Z fc Represented as the output of the fully connected layer; w fc Represented as the weight matrix of the fully connected layer; b fc Represented as the bias vector of the fully connected layer; The output layer outputs the seed point location, groundwater flow velocity and groundwater flow direction.

[0041] According to the above scheme, the difference between the predicted value and the actual value is measured by the loss function to obtain the loss value; the loss function formula is as follows: The output value of the seed point position uses the mean square error to calculate the loss function, and the formula is as follows:

[0042] Among them, L position It is represented as the loss function value of the seed point position; N is represented as the number of seed points; (x true,n ,y true,n , z true,n ) represents the true position of the nth seed point; Represents the predicted position of the nth seed point; The output value of groundwater flow field velocity uses mean square error to calculate the loss function, and the formula is as follows:

[0043] Among them, L velocity Expressed as the loss function value of groundwater flow velocity; v true,n It represents the actual groundwater flow velocity at the nth seed point; It is represented as the predicted groundwater flow velocity of the nth seed point; The output value of the groundwater flow field direction uses the cosine similarity loss function to calculate the loss function, and the formula is as follows:

[0044] Among them, L direction Expressed as the loss function of the groundwater flow direction; θ ture,n It is represented as the real groundwater flow direction vector of the nth seed point; It is represented as the predicted groundwater flow direction vector of the nth seed point; It is expressed as the cosine similarity between the true groundwater flow field direction vector and the predicted groundwater flow field direction vector; According to L position , L velocity and L directionCalculate the comprehensive loss function, the formula is as follows: L=λ1•L position +λ2•L velocity +λ3•L direction Among them, L represents the comprehensive loss function; λ1, λ2 and λ3 are L position , L velocity and L direction The weight coefficient indicates the relative importance in the comprehensive loss; Starting from the output layer, use the back-propagation algorithm to adjust the network parameters; calculate the gradient of each loss function weight and bias, which represents the sensitivity of the loss function to the change of weight and bias; through a reasonable loss function and back-propagation mechanism, the performance of the model on unseen data can be improved; Calculate the gradient according to the loss function; The loss gradient at the seed point position is as follows:

[0045] in, Expressed as the gradient of the predicted x-coordinate; Expressed as the gradient of the predicted y coordinate; Expressed as the gradient of the predicted z-coordinate; The loss gradient of groundwater flow velocity is as follows:

[0046] in, It is expressed as the gradient of the predicted groundwater flow velocity; The loss gradient in the direction of groundwater flow field is as follows:

[0047] in, It is expressed as the gradient of the direction vector of the predicted groundwater flow field; Backward propagation of error signals, based on which the gradients of the fully connected layer, pooling layer, and convolutional layer are calculated; during the back propagation process, all relevant gradients are added together to obtain the final gradient; using the gradient descent method, the weights and biases in the network are updated based on the calculated gradients; In each training iteration, the forward propagation and back propagation processes are repeated until the model has reached convergence on the training set, and the performance of the model is evaluated to verify the generalization ability of the model.

[0048] According to the seed point positions predicted by the convolutional neural network output, the seed point positions are placed according to the predicted seed point positions; the groundwater flow field velocity and groundwater flow field direction are predicted.

[0049] In this embodiment, a coal consumption control system based on the Internet of Things draws a streamline diagram of the groundwater flow field; The seed point positions are placed according to the predicted seed point positions output by the convolutional neural network; starting from each seed point, the streamlines are traced along the velocity vector direction of the flow field using the fourth-order Runge-Kutta method; the traced paths are plotted on the groundwater flow field to form a groundwater flow field streamline diagram; The convolutional neural network has predicted the positions of 5 seed points: P1=(20m, 20m, 5m); P2=(60m, 40m, 5m); P3=(40m, 30m, 0m); P4=(80m, 20m, 5m); P5=(30m, 10m, 0m); The formula for the fourth-order Runge-Kutta method is: K x1 =Δt•v x (x,y,z), K y1 =Δt•v x (x,y,z), K z1 =Δt•v x (x,y,z); K x2 =Δt•v x (x+K x1 / 2,y+K y1 / 2,z+K z1 / 2), K y2 =Δt•v x (x+K x1 / 2,y+K y1 / 2,z+K z1 / 2), K z2 =Δt•v x (x+K x1 / 2,y+K y1 / 2,z+K z1 / 2); K x3 =Δt•v x (x+K x2 / 2,y+K y2 / 2,z+K z2 / 2), K y3 =Δt•v x (x+K x2 / 2,y+K y2 / 2,z+K z2 / 2), K z3 =Δt•vx (x+K x2 / 2,y+K y2 / 2,z+K z2 / 2); K x4 =Δt•v x (x+K x3 / 2,y+K y3 / 2,z+K z3 / 2), K y4 =Δt•v x (x+K x3 / 2,y+K y3 / 2,z+K z3 / 2), K z4 =Δt•v x (x+K x3 / 2,y+K y3 / 2,z+K z3 / 2); The new location is: x new =x+1 / 6(K x1 +K x2 +K x3 +K x4 ), y new =x+1 / 6(K y1 +K y2 +K y3 +K y4 ), z new =x+1 / 6(K z1 +K z2 +K z3 +K z4 ); Calculate the position of the first time step starting from the first seed point P1=(20m,20m,5m): K x1 =0.1•(2•20+3•20+4•5)=0.1•(40+60+20)=0.1•120=12, K y1 =0.1•(20−3•20+2•5)=0.1•(−40+10)=0.1•(−30)=−3, K z1 =0.1•(4•20+2•20−3•5)=0.1•(80+40−15)=0.1•105=10.5; By calculating according to the above method, we can get the new position of the first time step: x new =20+1 / 6(12+2•15.15+2•15.15+15.15), y new =20+1 / 6(−3+2•(−1.2)+2•(−1.2)+(−1.2)), z new =5+1 / 6(10.5+2•11.225+2•11.225+11.225); By the above method, the streamlines are traced, and the traced paths are plotted on the groundwater flow field to form a groundwater flow field streamline diagram; By optimizing the position of seed points through the trained model, the accuracy and stability of streamline tracing can be improved; more accurate and reliable streamline trajectories can be generated; According to the above scheme, the trained convolutional neural network model is used to predict the groundwater flow field velocity and groundwater flow field direction, and the groundwater flow field streamline prediction map is drawn based on the prediction results of the convolutional neural network; the prediction results can be used for decision support in the fields of groundwater management, pollution control, etc.

[0050] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0051] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for drawing streamlines of groundwater flow field based on information entropy feature extraction, characterized in that: The method comprises the following steps: S1. Calculate the three-dimensional information entropy of each sub-region in the groundwater flow field to quantify the degree of change in flow state; S2, critical point detection, and use the eigenvalues ​​of the Jacobian matrix to identify the source points, sink points, saddle points and vortex points in the flow field; S3, fusion of the eigenvalues ​​of the three-dimensional information entropy and the eigenvalues ​​of the Jacobian matrix to obtain comprehensive features, and use them as input features of the convolutional neural network; S4, training convolutional neural network model; S5, optimizing the seed point position using the trained convolutional neural network model; S6, drawing a streamline diagram of groundwater flow field through the seed point position; S7. Use the trained convolutional neural network model to predict the groundwater flow velocity and direction.

2. The method for drawing streamlines of groundwater flow field based on information entropy feature extraction according to claim 1 is characterized in that: In step S1, The groundwater flow field is divided into i sub-areas, and s is the scanning span of X, Y, and Z coordinates; O, P, and Q are the number of grids divided by X, Y, and Z axes, respectively; W, H, and D are the total lengths in the X, Y, and Z axes, respectively; and the size of each grid is s. X =W / O,s Y =H / P,s Z =D / Q; If the remaining length after scanning to the end of the coordinate axis is less than one s, the end of the coordinate is regarded as the end of the last sub-region.

3. The method for drawing streamlines of groundwater flow field based on information entropy feature extraction according to claim 2 is characterized in that: In step S1, A unit sphere is placed in the sub-region, and the unit sphere is divided into j spherical patches x of equal area using the Leopardi sphere equal area segmentation method. j , each spherical patch has a center point. The angle between the center position vector of the spherical patch and the velocity vector at the vertex in the sub-region is calculated using the following formula: Among them, θ represents the angle between the center position vector of the spherical patch and the velocity vector at the vertex in the sub-region; It is represented as the center position vector of the spherical patch; Represented as the velocity vector at the vertex in the sub-region; The spherical patch with the smallest angle is taken as the spherical patch that the velocity vector falls into, and the spherical patch that the velocity vector of each vertex falls into is obtained; according to the number of velocity vectors falling into each spherical patch, the spherical patch x is calculated. j The distribution probability of the internal velocity vector is as follows: Among them, p j Represented as a spherical patch x j Distribution probability of internal velocity vector; m j Represented as a spherical patch x j The number of velocity vectors falling into the sub-region; d represents the total number of velocity vectors of all vertices in the sub-region; vertices refer to the vertices of polygons or figures formed after the Leopardi sphere equal area partitioning method; According to the velocity vector distribution probability obtained by statistics, the three-dimensional information entropy of each sub-area is calculated, and the formula is as follows: Among them, Entropy is represented by the three-dimensional information entropy; m is represented by the total number of spherical patches, and p is represented by the j Expressed as the distribution probability of the velocity vector within the jth spherical patch; When calculating the three-dimensional information entropy, p i =0, indicating that no velocity vector falls into the patch, and this item does not participate in the summation; If the size of the last sub-region in the X, Y or Z axis direction is smaller than s, the calculation of the three-dimensional information entropy of the sub-region needs to be adjusted.

4. The method for drawing streamlines of groundwater flow field based on information entropy feature extraction according to claim 3 is characterized in that: A three-dimensional information entropy threshold Threshold is determined to screen sub-regions where the fluid state changes dramatically. The formula of the three-dimensional information entropy threshold Threshold is as follows: Threshold=f×max(Entropy i ) Where f represents the influencing factor of the three-dimensional information entropy of the screening sub-region; Entropy i It is expressed as the three-dimensional information entropy of the i-th sub-region; max(Entropy i ) represents the maximum value of the three-dimensional information entropy of the sub-region; To filter sub-regions where the fluid state changes dramatically, the following conditions need to be met: Entropy i ≥Threshold The screened sub-regions represent areas where the fluid state changes drastically or the flow complexity is high.

5. The method for drawing streamlines of groundwater flow field based on information entropy feature extraction according to claim 4 is characterized in that: In step S2, The linear interpolation method is used to detect the critical points of the sub-regions where the fluid state changes dramatically, and the source points, sink points, saddle points and vortex points in the flow field are identified by the eigenvalues ​​of the Jacobian matrix J. The velocity field is expressed as (x,y,z)=(v x ,v y ,v z ), where v x , v y , v z are the velocity components in the x, y, and z directions respectively, and the Jacobian matrix J is: When the Jacobian matrix has one positive eigenvalue and one negative eigenvalue, it is represented as a source point or a sink point; when all eigenvalues ​​of the Jacobian matrix are zero or the real part is zero, it is represented as a saddle point; when the Jacobian matrix has a pair of conjugate complex eigenvalues, it is represented as a vortex point.

6. The method for drawing streamlines of groundwater flow field based on information entropy feature extraction according to claim 1 is characterized in that: In step S3, The three-dimensional information entropy value and the eigenvalue of the Jacobian matrix are preprocessed, and the preprocessing includes: standardization processing, converting the three-dimensional information entropy value and the eigenvalue of the Jacobian matrix to the same range; data cleaning processing, processing the abnormal values ​​and missing values ​​in the eigenvalue data of the three-dimensional information entropy value and the Jacobian matrix; data alignment processing, ensuring that the eigenvalue data of the three-dimensional information entropy value and the Jacobian matrix are aligned at the same space or time point; and weighted fusion of the preprocessed three-dimensional information entropy value and the eigenvalue of the Jacobian matrix to obtain comprehensive features.

7. The method for drawing streamlines of groundwater flow field based on information entropy feature extraction according to claim 1 is characterized in that: Constructing a convolutional neural network, wherein the convolutional neural network includes an input layer, a convolution layer, a pooling layer, a fully connected layer and an output layer; According to forward propagation, the comprehensive features are input into the input layer of the convolutional neural network, and the comprehensive features are transmitted to the convolution layer through the input layer for convolution operation. The formula is as follows: Among them, S I,J It is represented as the output of the convolutional layer at the Ith row and the Jth column position; w E,F,T It is represented as the weight at the channel T position in the Eth row and the Fth column in the convolutional layer; f I+E,J+F,T It is represented as the value of the comprehensive feature f at the position of channel T in the I+E row, J+F column; B is represented as the bias term of the convolutional layer; weights and biases are parameters that the model needs to learn during training; The convolutional layer is followed by a nonlinear activation function to introduce nonlinear transformations. The formula is as follows: resume I,J =max(0,S I,J ) Among them, ReLU I,J Represented as the output after the activation function; max(0,S I,J ) means taking the larger value; The data after the activation function is transferred to the pooling layer, and after the maximum pooling, the dimension of the feature value is reduced while keeping the most important features; The fully connected layer flattens the pooled features into a one-dimensional vector V through the flatten function flat , and is calculated by matrix multiplication and bias terms as follows: Z fc =w fc V flat +b fc Among them, Z fc Represented as the output of the fully connected layer; w fc Represented as the weight matrix of the fully connected layer; b fc Represented as the bias vector of the fully connected layer; The output layer outputs the seed point location, groundwater flow velocity and groundwater flow direction.

8. The method for drawing streamlines of groundwater flow field based on information entropy feature extraction according to claim 7 is characterized in that: The loss function is used to measure the difference between the predicted value and the actual value to obtain the loss value; the loss function formula is as follows: The output value of the seed point position uses the mean square error to calculate the loss function, and the formula is as follows: Among them, L position It is represented as the loss function value of the seed point position; N is represented as the number of seed points; (x true,n ,y true,n , z true,n ) represents the true position of the nth seed point; Represents the predicted position of the nth seed point; The output value of groundwater flow field velocity uses mean square error to calculate the loss function, and the formula is as follows: Among them, L velocity Expressed as the loss function value of groundwater flow velocity; v true,n It represents the actual groundwater flow velocity at the nth seed point; It is represented as the predicted groundwater flow velocity of the nth seed point; The output value of the groundwater flow field direction uses the cosine similarity loss function to calculate the loss function, and the formula is as follows: Among them, L direction Expressed as the loss function of the groundwater flow direction; θ ture,n It is represented as the real groundwater flow direction vector of the nth seed point; It is represented as the predicted groundwater flow direction vector of the nth seed point; It is expressed as the cosine similarity between the true groundwater flow field direction vector and the predicted groundwater flow field direction vector; According to L position , L velocity and L direction Calculate the comprehensive loss function, the formula is as follows: L=λ1•L position +λ2•L velocity +λ3•L direction Among them, L represents the comprehensive loss function; λ1, λ2 and λ3 are L position , L velocity and L direction The weight coefficient indicates the relative importance in the comprehensive loss; Starting from the output layer, the back-propagation algorithm is used to adjust the network parameters; the gradient of each loss function weight and bias is calculated, which represents the sensitivity of the loss function to changes in weights and biases; Calculate the gradient according to the loss function; The loss gradient at the seed point position is as follows: in, Expressed as the gradient of the predicted x-coordinate; Expressed as the gradient of the predicted y coordinate; Expressed as the gradient of the predicted z-coordinate; The loss gradient of groundwater flow velocity is as follows: in, It is expressed as the gradient of the predicted groundwater flow velocity; The loss gradient in the direction of groundwater flow field is as follows: in, It is expressed as the gradient of the direction vector of the predicted groundwater flow field; Backward propagation of error signals, based on which the gradients of the fully connected layer, pooling layer, and convolutional layer are calculated; during the back propagation process, all relevant gradients are added together to obtain the final gradient; using the gradient descent method, the weights and biases in the network are updated based on the calculated gradients; In each training iteration, the forward propagation and back propagation processes are repeated until the model has reached convergence on the training set, and the performance of the model is evaluated to verify the generalization ability of the model.

9. The method for drawing streamlines of groundwater flow field based on information entropy feature extraction according to claim 1, characterized in that: The seed point positions are placed according to the predicted seed point positions output by the convolutional neural network; starting from each seed point, the streamlines are traced along the velocity vector direction of the flow field using the fourth-order Runge-Kutta method; the traced paths are plotted on the groundwater flow field to form a groundwater flow field streamline diagram.

10. The method for drawing groundwater flow field streamlines based on information entropy feature extraction according to claim 1, characterized in that: The trained convolutional neural network model is used to predict the groundwater flow velocity and direction, and a groundwater flow field streamline prediction map is drawn based on the prediction results of the convolutional neural network.

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