Method for predicting stiffness matrix of fluid-filled fractured rock based on multi-task neural network

Abstract

The application discloses a fluid-filled fractured rock stiffness matrix prediction method based on a multi-task neural network, and comprises the following steps: constructing a numerical upscaling sample set of fluid-filled fractured rock based on fluid-structure coupling numerical upscaling simulation; constructing a multi-task multilayer perceptron model, training the multi-task multilayer perceptron model by using the dimensionless fracture geometry descriptor of each sample in the numerical upscaling sample set, and obtaining the trained multi-task multilayer perceptron model; inputting the dimensionless fracture geometry descriptor of fluid-filled fractured rock to be predicted into the trained multi-task multilayer perceptron model, obtaining six stiffness coefficients, and reconstructing the full equivalent stiffness matrix of the fluid-filled fractured rock according to the matrix symmetry relationship. The application can reduce the calculation cost of a large number of repeated finite element numerical upscaling simulation, improve the efficiency of fracture parameter space rapid exploration, and be suitable for equivalent elastic modeling of fluid-filled fractured rock, fracture parameter sensitivity analysis and earthquake response prediction.

Description

Technical Field

[0001] This invention relates to the field of rock physics numerical simulation technology, and in particular to a method for predicting the stiffness matrix of fluid-filled fractured rocks based on a multi-task neural network. Background Technology

[0002] Fractures, microfractures, and other flexible heterogeneous structures are widely present in subsurface rock media. Their geometry, spatial distribution, and fluid-filled state significantly affect the equivalent elastic properties of the rock and the seismic wave propagation response. For fractured reservoirs, fracture density, fracture aspect ratio, fracture size, fracture spatial distribution, and fluid properties within the fractures can all influence the equivalent stiffness, seismic anisotropy, and related seismic responses of the rock. Therefore, accurately predicting the equivalent stiffness matrix of fluid-filled fractured rock is of great significance for rock physics modeling, seismic response prediction, and reservoir parameter evaluation in fractured reservoirs.

[0003] Existing methods typically predict the equivalent elastic parameters of fractured rocks using theoretical equivalent medium models or numerical upscaling methods. Theoretical equivalent medium models offer high computational efficiency, but usually require simplifications of fracture morphology, fracture interactions, spatial distribution, and boundary conditions. When fracture density increases, fracture spacing decreases, or fracture arrangement changes, the interactions between fractures alter the local stress and displacement fields, making it difficult for the simplified assumptions of the theoretical model to fully reflect the equivalent stiffness response under complex fracture configurations.

[0004] In contrast, finite element numerical simulation and numerical upscaling methods can more directly describe fracture geometry, local stress disturbances, fluid response within fractures, and fluid-structure interaction effects, thus obtaining a physically consistent equivalent stiffness matrix. For representative volumetric elements of rock containing fluid-filled fractures, mean stress and mean strain can be calculated using fluid-structure interaction governing equations and oscillatory relaxation tests, and the two-dimensional anisotropic equivalent stiffness matrix can be further recovered. However, when parameters such as fracture density, fracture aspect ratio, fracture length, and fracture spatial distribution change, repeated finite element simulations and oscillatory relaxation tests are required for a large number of fracture configurations, resulting in high computational costs and hindering large-scale parameter space exploration and rapid prediction applications.

[0005] In recent years, machine learning methods have been increasingly used for predicting rock mechanical parameters and estimating rock physical properties. However, existing machine learning methods mostly focus on predicting single elastic moduli, strength parameters, or simplified elastic indices, making it difficult to directly predict stability using the fully equivalent stiffness matrix of anisotropic media. For two-dimensional fluid-filled fractured rocks, the equivalent stiffness matrix not only includes... , , and Equal stiffness components also include and The weakly coupled stiffness components reflect the anisotropic coupling effect. There are significant differences in numerical magnitude and regression difficulty among the different stiffness components. If a conventional single-branch multi-output neural network is used for prediction, large numerical stiffness components may dominate the updating of shared parameters during training, thereby reducing the prediction stability of the weakly coupled stiffness components and intermediate stiffness components.

[0006] Therefore, it is urgent to propose a method for predicting the stiffness matrix of fluid-filled fractured rock based on multi-task neural networks, which can reduce the cost of repetitive finite element numerical upscaling simulations while achieving fast and stable prediction of the fully equivalent stiffness matrix of fluid-filled fractured rock. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a simple algorithm with high prediction accuracy for predicting the stiffness matrix of fluid-filled fractured rocks based on a multi-task neural network.

[0008] The technical solution of this invention to solve the above-mentioned technical problems is: a method for predicting the stiffness matrix of fluid-filled fractured rock based on multi-task neural networks, comprising the following steps:

[0009] Step 1: Construct a numerical upscaling sample set of fluid-filled fractured rock based on fluid-structure interaction numerical upscaling simulation. Each sample in the numerical upscaling sample set includes a dimensionless fracture geometry descriptor and independent stiffness coefficients of the equivalent stiffness matrix corresponding to the dimensionless fracture geometry descriptor in the sample. The dimensionless fracture geometry descriptor includes fracture density, fracture aspect ratio, vertical uniformity ratio and normalized fracture length.

[0010] Step 2: Construct a multi-task multilayer perceptron model. Use the dimensionless crack geometry descriptor of each sample in the numerical upscaling sample set to train the multi-task multilayer perceptron model to obtain the trained multi-task multilayer perceptron model.

[0011] Step 3: Input the dimensionless fracture geometry descriptor of the fluid-filled fractured rock to be predicted into the trained multi-task multilayer perceptron model to obtain six stiffness coefficients, and reconstruct the full equivalent stiffness matrix of the fluid-filled fractured rock according to the matrix symmetry relationship.

[0012] The above-mentioned method for predicting the stiffness matrix of fluid-filled fractured rock based on multi-task neural networks, in step 1, the construction of the numerical upscaling sample set includes the following steps:

[0013] Step 11: Based on the dimensionless fracture geometry descriptor, construct a representative volumetric unit of rock containing fluid-filled fractures. The representative volumetric unit of rock includes a solid rock matrix region and a fluid-filled fracture region.

[0014] Step 12: Perform fluid-structure interaction numerical simulation on representative volume elements of rock based on the coupled Lamé-Navier equation and Navier-Stokes equation;

[0015] Step 13: Apply oscillatory relaxation tests to representative volumetric elements of rocks with different fracture configurations to obtain mean stress and mean strain;

[0016] Step 14: Calculate the equivalent stiffness matrix based on the relationship between mean stress and mean strain, and obtain the independent stiffness coefficients in the equivalent stiffness matrix.

[0017] In the above-mentioned method for predicting the rock stiffness matrix based on multi-task neural network fluid-filled fractures, step 11 represents the fluid-filled fractures as non-intersecting flattened elliptical fractures, each flattened elliptical fracture consisting of a semi-major axis. and semi-short axis Characterization, crack length for The aspect ratio of the crack The expression is:

[0018] ;

[0019] Crack density The expression is:

[0020] ;

[0021] Vertical uniformity ratio The expression is:

[0022] ;

[0023] in, The number of cracks; The area of ​​a representative volume unit of rock; The horizontal spacing between adjacent cracks; The vertical spacing between adjacent cracks; The width of the representative volume unit of the rock.

[0024] In the above-mentioned method for predicting the stiffness matrix of fractured rock based on multi-task neural network fluid filling, the fluid-structure interaction control equation in step 12 is:

[0025] ;

[0026] ;

[0027] in, Represents the divergence operator; For stress tensor; For strain tensor; For strain tensor The biased portion; This is the biased portion; For volumetric strain; Unit tensor; For phase indicator functions, Indicates the solid rock matrix region. This indicates that the fluid has filled the crack area; The shear modulus of the solid rock matrix; The bulk modulus of the solid rock matrix; For fluid dynamic viscosity; Bulk modulus of the fluid; The imaginary unit; ω is the angular frequency.

[0028] In the above-mentioned method for predicting the stiffness matrix of fluid-filled fractured rock based on multi-task neural networks, in step 13, for the k-th oscillatory relaxation test, the mean stress, mean strain, and equivalent stiffness matrix satisfy the following relationship:

[0029] ;

[0030] in, These correspond to three different oscillation relaxation tests; , and The first normal stress component, the second normal stress component, and the shear stress component are obtained in a representative volume element of rock under the kth oscillatory relaxation test. , and Indicates the first The first normal strain component, the second normal strain component, and the shear strain component were obtained in a representative volume element of rock under an oscillatory relaxation test. , , , , and These are the six independent stiffness coefficients in the equivalent stiffness matrix.

[0031] In the above-mentioned method for predicting the stiffness matrix of fluid-filled fractured rock based on multi-task neural networks, step 14 involves an equivalent stiffness matrix that is a two-dimensional anisotropic equivalent stiffness matrix, expressed as follows:

[0032] ;

[0033] in, The equivalent stiffness matrix, , , , , and They are respectively , , , , and The real part of .

[0034] In the above-mentioned method for predicting the stiffness matrix of fluid-filled fractured rock based on multi-task neural networks, step 2 of the multi-task multilayer perceptron model includes a shared feature extraction module, a coupled stiffness branch, an intermediate stiffness branch, and a dominant stiffness branch. The shared feature extraction module is used to extract shared features from the dimensionless fracture geometric descriptor of the sample and feed them into the coupled stiffness branch, the intermediate stiffness branch, and the dominant stiffness branch. The coupled stiffness branch is used to predict the weakly coupled stiffness coefficient, the intermediate stiffness branch is used to predict the intermediate stiffness coefficient, and the dominant stiffness branch is used to predict the dominant stiffness coefficient.

[0035] Input vector of a multi-task multilayer perceptron model for:

[0036] ;

[0037] Among them, superscript Represents the transpose of a matrix;

[0038] The output vector of the multi-task multilayer perceptron model for:

[0039] ;

[0040] in, and Corresponding to the coupled stiffness branch, and Corresponding to the intermediate stiffness branch, and Corresponding to the dominant stiffness branch; when reconstructing the fully equivalent stiffness matrix, according to , , , , and The matrix positions are arranged and reconstructed into the following form:

[0041] ;

[0042] in, For fully equivalent stiffness matrices, , , , , and represents the real part of the six independent stiffness coefficients in the fully equivalent stiffness matrix.

[0043] In the above-mentioned method for predicting the stiffness matrix of fluid-filled fractured rock based on multi-task neural networks, in step 2, the shared feature extraction module is used to extract features from the input vector. Extracting shared features Shared features Represented as:

[0044] ;

[0045] in, This indicates a shared feature extraction module. The trainable parameters of the shared feature extraction module are represented as follows: The outputs of the coupled stiffness branch, intermediate stiffness branch, and dominant stiffness branch are respectively represented as follows:

[0046] ;

[0047] ;

[0048] ;

[0049] in, , and These represent the coupled stiffness branch, intermediate stiffness branch, and dominant stiffness branch, respectively. , and These represent the trainable parameters of the coupled stiffness branch, intermediate stiffness branch, and dominant stiffness branch, respectively. Indicates stopping the gradient operator; The predicted value for the coupled stiffness branch; This is the predicted value for the intermediate stiffness branch; The predicted value for the dominant stiffness branch; superscript This indicates the matrix transpose.

[0050] In the above-mentioned method for predicting the stiffness matrix of fluid-filled fractured rock based on multi-task neural network, in step 2, a stopping gradient operator is set before the dominant stiffness branch. The stopping gradient operator transmits the shared features to the dominant stiffness branch during forward propagation and blocks the gradient update of the parameters of the shared feature extraction module by the loss of the dominant stiffness branch during backward propagation.

[0051] Stop gradient operator The following relationship must be satisfied:

[0052] Forward propagation process:

[0053] ;

[0054] Backpropagation process: The dominant stiffness branch loss does not affect the trainable parameters of the shared feature extraction module. Generate gradient updates;

[0055] The stopping gradient operator is used to reduce , The prediction task has a dominant influence on the parameter updates of the shared feature extraction module.

[0056] Step 4: When training the multi-task multilayer perceptron model, a branch-weighted loss function is used to balance the training contributions of the coupled stiffness branch, intermediate stiffness branch and dominant stiffness branch.

[0057] The above-mentioned method for predicting the stiffness matrix of fluid-filled fractured rock based on multi-task neural networks, in step 2, employs a branch-weighted Huber loss function when training the multi-task multilayer perceptron model. Represented as:

[0058] ;

[0059] in, Here is the Huber loss function. and These are the predicted and reference values ​​for the coupled stiffness branch, respectively. and These are the predicted and reference values ​​for the intermediate stiffness branch, respectively. and These are the predicted and reference values ​​for the dominant stiffness branch, respectively. , and These are the loss weights for the coupled stiffness branch, intermediate stiffness branch, and dominant stiffness branch, respectively.

[0060] The beneficial effects of this invention are as follows:

[0061] 1. This invention constructs a training sample set through fluid-structure interaction numerical upscaling simulation, so that the training data of the model has a clear physical basis and can reflect the equivalent elastic response of fluid filling fractured rock.

[0062] 2. This invention can simultaneously predict six independent stiffness coefficients and reconstruct a fully equivalent stiffness matrix, rather than predicting only a single elastic modulus or simplified elastic parameters.

[0063] 3. The present invention sets up coupled stiffness branches, intermediate stiffness branches and dominant stiffness branches according to the physical meaning and numerical magnitude of stiffness components, which can improve the stability of multi-output stiffness prediction.

[0064] 4. This invention reduces the impact of the dominant stiffness branch on the parameter update of the shared feature extraction module by stopping the gradient operator, thereby reducing the interference of large numerical stiffness components on the prediction tasks of weakly coupled stiffness components and intermediate stiffness components.

[0065] 5. This invention balances the training difficulty of different task branches through the branch-weighted Huber loss function, thereby improving the joint prediction effect of stiffness coefficients of different numerical magnitudes.

[0066] 6. This invention can reduce the computational cost of a large number of repetitive finite element numerical upscaling simulations, improve the efficiency of rapid exploration of fracture parameter space, and is suitable for equivalent elastic modeling of fluid-filled fractured rocks, fracture parameter sensitivity analysis, and seismic response prediction. Attached Figure Description

[0067] Figure 1 This is the overall flowchart of the present invention.

[0068] Figure 2 This is a schematic diagram of a representative volume unit of fluid filling fractured rock in this invention.

[0069] Figure 3 This is a schematic diagram of a vertical compression oscillation relaxation test.

[0070] Figure 4 This is a schematic diagram of a transverse compression oscillation relaxation test.

[0071] Figure 5 This is a schematic diagram of a shear oscillation relaxation test.

[0072] Figure 6 This is a schematic diagram of the prediction of six independent stiffness coefficients in this invention, wherein (a) is The prediction diagram, (b) is The prediction diagram, (c) is The prediction diagram, (d) is The prediction diagram, (e) is The prediction diagram, (f) is The prediction diagram. Detailed Implementation

[0073] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0074] like Figure 1 As shown, the method for predicting the stiffness matrix of fluid-filled fractured rock based on multi-task neural networks includes the following steps:

[0075] Step 1: Construct a numerical upscaling sample set of fluid-filled fractured rock based on fluid-structure interaction numerical upscaling simulation. Each sample in the numerical upscaling sample set includes a dimensionless fracture geometry descriptor and independent stiffness coefficients of the equivalent stiffness matrix corresponding to the dimensionless fracture geometry descriptor in the sample. The dimensionless fracture geometry descriptor includes fracture density, fracture aspect ratio, vertical uniformity ratio and normalized fracture length.

[0076] The construction of the numerical upscaling sample set includes the following steps:

[0077] Step 11: Based on the dimensionless fracture geometry descriptor, construct a representative volumetric unit of rock containing fluid-filled fractures. The representative volumetric unit of rock includes a solid rock matrix region and a fluid-filled fracture region. The solid rock matrix region is used to represent the elastic response of the rock skeleton, and the fluid-filled fracture region is used to represent the viscous compressible response of the fluid within the fracture.

[0078] like Figure 2 As shown, in this embodiment, the representative volume unit of the rock is a two-dimensional square rock model with a side length of 0.2m. The model includes a solid rock matrix region and multiple fluid-filled fracture regions. The solid rock matrix region is set as an isotropic linear elastic solid region, and the fluid-filled fracture regions are set as viscous compressible fluid regions. The fluid-filled fractures are represented by non-intersecting flat elliptical fractures, and each fracture is characterized by a semi-major axis a and a semi-minor axis b.

[0079] Fluid-filled fractures are represented by non-intersecting flattened elliptical fractures, each consisting of a semi-major axis. and semi-short axis Characterization, crack length for The aspect ratio of the crack The expression is:

[0080] ;

[0081] Crack density The expression is:

[0082] ;

[0083] Vertical uniformity ratio The expression is:

[0084] ;

[0085] in, The number of cracks; The area of ​​a representative volume unit of rock; The horizontal spacing between adjacent cracks; The vertical spacing between adjacent cracks; The width of the representative volume unit of the rock.

[0086] In this embodiment, the aspect ratio of the crack is... The value range is from 0.01 to 0.10, and the semi-major axis... The value ranges from 0.005m to 0.010m, corresponding to the crack length. The value ranges from 0.010m to 0.020m. The number of cracks in the horizontal and vertical directions are denoted as follows: and Total number of cracks Crack density The aspect ratio of the cracks Vertical uniformity ratio and normalized crack length These parameters together constitute the input parameters of the multi-task multilayer perceptron model. By changing the number, size, and arrangement of fractures, multiple fluid-filled fracture rock configurations can be obtained.

[0087] Step 12: Perform fluid-structure interaction numerical simulation on representative volume elements of rock based on the coupled Lamé-Navier equation and Navier-Stokes equation.

[0088] The governing equations for fluid-structure interaction are:

[0089] ;

[0090] ;

[0091] in, Represents the divergence operator; For stress tensor; For strain tensor; For strain tensor The biased portion; This is the biased portion; For volumetric strain; Unit tensor; For phase indicator functions, Indicates the solid rock matrix region. This indicates that the fluid has filled the crack area; The shear modulus of the solid rock matrix; The bulk modulus of the solid rock matrix; For fluid dynamic viscosity; Bulk modulus of the fluid; The imaginary unit; ω is the angular frequency.

[0092] In this embodiment, the shear modulus of the solid rock matrix is... The bulk modulus of the solid rock matrix is ​​set to 44 GPa. Set to 36.4 GPa, hydrodynamic viscosity Set to 0.003 Pa·s, fluid bulk modulus The oscillation frequency was set to 2.4 GPa. The oscillation frequency for the numerical upscaling simulation was set to 30 Hz.

[0093] Step 13: As Figures 3-5 As shown, vertical compression oscillation relaxation tests, transverse compression oscillation relaxation tests, and shear oscillation relaxation tests were applied to representative volumetric elements of rocks with different fracture configurations to obtain the corresponding mean stress and mean strain. Three independent loading conditions were used to recover the six independent stiffness coefficients in the equivalent stiffness matrix.

[0094] For the k-th oscillatory relaxation test, the mean stress, mean strain, and equivalent stiffness matrix satisfy the following relationship:

[0095] ;

[0096] in, These correspond to three different oscillation relaxation tests; , and The first normal stress component, the second normal stress component, and the shear stress component are obtained in a representative volume element of rock under the kth oscillatory relaxation test. , and Indicates the first The first normal strain component, the second normal strain component, and the shear strain component were obtained in a representative volume element of rock under an oscillatory relaxation test. , , , , and These are the six independent stiffness coefficients in the equivalent stiffness matrix.

[0097] Step 14: Calculate the equivalent stiffness matrix based on the relationship between mean stress and mean strain, and obtain the independent stiffness coefficients in the equivalent stiffness matrix.

[0098] The equivalent stiffness matrix is ​​a two-dimensional anisotropic equivalent stiffness matrix, expressed as:

[0099] ;

[0100] in, The equivalent stiffness matrix, , , , , and They are respectively , , , , and The real part of .

[0101] After forming the sample set, the samples were screened to remove those that did not converge in the finite element calculation and those with non-physical stiffness values. In this embodiment, 4714 valid crack configuration samples were finally obtained. Subsequently, the samples were subjected to Min-Max normalization and divided into training, validation, and test sets with a ratio of 60%, 20%, and 20%, respectively.

[0102] Step 2: Construct a multi-task multilayer perceptron model. Use the dimensionless crack geometry descriptor of each sample in the numerical upscaling sample set to train the multi-task multilayer perceptron model to obtain the trained multi-task multilayer perceptron model.

[0103] The multi-task multilayer perceptron model includes a shared feature extraction module, a coupled stiffness branch, an intermediate stiffness branch, and a dominant stiffness branch. The shared feature extraction module is used to extract shared features from the dimensionless crack geometric descriptor of the sample and feed them into the coupled stiffness branch, the intermediate stiffness branch, and the dominant stiffness branch. The coupled stiffness branch is used to predict the weakly coupled stiffness coefficient, the intermediate stiffness branch is used to predict the intermediate stiffness coefficient, and the dominant stiffness branch is used to predict the dominant stiffness coefficient.

[0104] Input vector of a multi-task multilayer perceptron model for:

[0105] ;

[0106] Among them, superscript Represents the transpose of a matrix;

[0107] The output vector of the multi-task multilayer perceptron model for:

[0108] ;

[0109] in, and Corresponding to the coupled stiffness branch, and Corresponding to the intermediate stiffness branch, and Corresponding to the dominant stiffness branch; when reconstructing the fully equivalent stiffness matrix, according to , , , , and The matrix positions are arranged and reconstructed into the following form:

[0110] ;

[0111] in, For fully equivalent stiffness matrices, , , , , and represents the real part of the six independent stiffness coefficients in the fully equivalent stiffness matrix.

[0112] In this embodiment, the shared feature extraction module includes three fully connected hidden layers with 512, 512, and 256 neurons respectively; the coupling stiffness branch includes two fully connected hidden layers with 128 and 64 neurons respectively; the intermediate stiffness branch includes three fully connected hidden layers with 512, 256, and 128 neurons respectively; and the dominant stiffness branch includes a stopping gradient operator and a bottleneck hidden layer with 32 neurons. The output layer of each branch uses a linear activation function to output continuous stiffness coefficient predictions. The model is trained using the Adam optimizer with an initial learning rate of 0.001, 1200 training epochs, a batch size of 64, and a learning rate decay strategy based on validation set loss, with a learning rate decay factor of 0.5 and a patience value of 40.

[0113] The shared feature extraction module is used to extract features from the input vector. Extracting shared features Shared features Represented as:

[0114] ;

[0115] in, This indicates a shared feature extraction module. The trainable parameters of the shared feature extraction module are represented as follows: The outputs of the coupled stiffness branch, intermediate stiffness branch, and dominant stiffness branch are respectively represented as follows:

[0116] ;

[0117] ;

[0118] ;

[0119] in, , and These represent the coupled stiffness branch, intermediate stiffness branch, and dominant stiffness branch, respectively. , and These represent the trainable parameters of the coupled stiffness branch, intermediate stiffness branch, and dominant stiffness branch, respectively. Indicates stopping the gradient operator; The predicted value for the coupled stiffness branch; This is the predicted value for the intermediate stiffness branch; The predicted value for the dominant stiffness branch; superscript This indicates the matrix transpose.

[0120] A stopping gradient operator is set before the dominant stiffness branch. The stopping gradient operator will pass the shared features to the dominant stiffness branch during forward propagation and block the gradient update of the parameters of the shared feature extraction module by the dominant stiffness branch loss during back propagation.

[0121] Stop gradient operator The following relationship must be satisfied:

[0122] Forward propagation process:

[0123] ;

[0124] Backpropagation process: The dominant stiffness branch loss does not affect the trainable parameters of the shared feature extraction module. Gradient updates are generated; by setting a stopping gradient operator, the gradient can be reduced. and The dominant stiffness component has a dominant influence on the parameter update of the shared feature extraction module, thereby reducing the interference of large numerical stiffness components on the prediction tasks of weakly coupled stiffness components and intermediate stiffness components, and improving the joint prediction stability of the multi-task multilayer perceptron model for stiffness coefficients of different numerical magnitudes.

[0125] When training a multi-task multilayer perceptron model, the branch-weighted Huber loss function is used. Represented as:

[0126] ;

[0127] in, Here is the Huber loss function. and These are the predicted and reference values ​​for the coupled stiffness branch, respectively. and These are the predicted and reference values ​​for the intermediate stiffness branch, respectively. and These are the predicted and reference values ​​for the dominant stiffness branch, respectively. , and These are the loss weights for the coupled stiffness branch, intermediate stiffness branch, and dominant stiffness branch, respectively.

[0128] In this embodiment, the loss weight of the coupled stiffness branch is... The loss weight for the intermediate stiffness branch is set to 30.0. Set to 50.0, the loss weight of the dominant stiffness branch. Set to 1.0. By using a branch-weighted strategy, the differences in regression difficulty that still exist for different stiffness components after normalization can be compensated for, thereby improving the stability of the model's joint prediction of stiffness components of different numerical magnitudes.

[0129] Step 3: Input the dimensionless fracture geometry descriptor of the fluid-filled fractured rock to be predicted into the trained multi-task multilayer perceptron model to obtain six stiffness coefficients, and reconstruct the full equivalent stiffness matrix of the fluid-filled fractured rock according to the matrix symmetry relationship.

[0130] The trained multi-task multilayer perceptron model is used for prediction on an independent test set, and the prediction results are compared with numerical upscaling reference results. Figure 6 As shown, the test results indicate that the multi-task multilayer perceptron model can reproduce the equivalent stiffness response obtained by numerical upscaling quite well. and The predicted results show a high degree of consistency with the reference results, among which... The coefficient of determination (all coefficients of determination are expressed as R²) is 0.9993, and the root mean square error (RMSE) is 0.0205. The coefficient of determination was 0.9990, and the root mean square error (RMSE) was 0.0087. The coefficient of determination was 0.9803, and the root mean square error (RMSE) was 1.6473. The coefficient of determination was 0.9057, and the root mean square error (RMSE) was 1.5134. and The magnitude of the value is much smaller than that of the dominant stiffness component and the intermediate stiffness component, with coefficients of determination of 0.9128 and 0.9380, respectively, and corresponding root mean square errors (RMSE) of 8.38 × 10⁻⁶. -7 and 1.06×10 -5 The above results demonstrate that the multi-task multilayer perceptron model in this embodiment can simultaneously predict six independent stiffness coefficients of different numerical magnitudes and maintain the main variation law of the equivalent stiffness response of fluid-filled fractured rock.

[0131] Physical consistency verification can also be performed on the trained multi-task multilayer perceptron model. The physical consistency verification includes: selecting a fixed crack aspect ratio. and fixed normalized crack length The crack configuration path, resulting in crack density The model follows this path; the stiffness coefficients predicted by the multi-task multilayer perceptron model are compared with the numerical upscaling results to determine whether the model maintains the component-dependent response law of the stiffness coefficients as a function of crack density. Furthermore, the prediction results can also be compared with the results of the analytical crack baseline model to help illustrate the model's ability to maintain the stiffness variation trend under different crack density conditions.

Claims

1. A method for predicting the stiffness matrix of fractured rock based on multi-task neural network fluid filling, characterized in that, Includes the following steps: Step 1: Construct a numerical upscaling sample set of fluid-filled fractured rock based on fluid-structure interaction numerical upscaling simulation. Each sample in the numerical upscaling sample set includes a dimensionless fracture geometry descriptor and independent stiffness coefficients of the equivalent stiffness matrix corresponding to the dimensionless fracture geometry descriptor in the sample. The dimensionless fracture geometry descriptor includes fracture density, fracture aspect ratio, vertical uniformity ratio and normalized fracture length. Step 2: Construct a multi-task multilayer perceptron model. Use the dimensionless crack geometry descriptor of each sample in the numerical upscaling sample set to train the multi-task multilayer perceptron model to obtain the trained multi-task multilayer perceptron model. Step 3: Input the dimensionless fracture geometry descriptor of the fluid-filled fractured rock to be predicted into the trained multi-task multilayer perceptron model to obtain six stiffness coefficients, and reconstruct the full equivalent stiffness matrix of the fluid-filled fractured rock according to the matrix symmetry relationship.

2. The method for predicting the stiffness matrix of fractured rock based on multi-task neural network fluid filling as described in claim 1, characterized in that, In step 1, the construction of the numerical upscaling sample set includes the following steps: Step 11: Based on the dimensionless fracture geometry descriptor, construct a representative volumetric unit of rock containing fluid-filled fractures. The representative volumetric unit of rock includes a solid rock matrix region and a fluid-filled fracture region. Step 12: Perform fluid-structure interaction numerical simulation on representative volume elements of rock based on the coupled Lamé-Navier equation and Navier-Stokes equation; Step 13: Apply oscillatory relaxation tests to representative volumetric elements of rocks with different fracture configurations to obtain mean stress and mean strain; Step 14: Calculate the equivalent stiffness matrix based on the relationship between mean stress and mean strain, and obtain the independent stiffness coefficients in the equivalent stiffness matrix.

3. The method for predicting the stiffness matrix of fractured rock based on multi-task neural network fluid filling as described in claim 2, characterized in that, In step 11, the fluid-filled cracks are represented by non-intersecting flat elliptical cracks, each flat elliptical crack consisting of a semi-major axis. and semi-short axis Characterization, crack length for The aspect ratio of the crack The expression is: ； Crack density The expression is: ； Vertical uniformity ratio The expression is: ； in, The number of cracks; The area of ​​a representative volume unit of rock; The horizontal spacing between adjacent cracks; The vertical spacing between adjacent cracks; The width of the representative volume unit of the rock.

4. The method for predicting the stiffness matrix of fractured rock based on multi-task neural network fluid filling as described in claim 3, characterized in that, In step 12, the fluid-structure interaction control equation is: ； ； in, Represents the divergence operator; For stress tensor; For strain tensor; For strain tensor The biased portion; This is the biased portion; For volumetric strain; Unit tensor; For phase indicator functions, Indicates the solid rock matrix region. This indicates that the fluid has filled the crack area; The shear modulus of the solid rock matrix; The bulk modulus of the solid rock matrix; For fluid dynamic viscosity; Bulk modulus of the fluid; The imaginary unit; ω is the angular frequency.

5. The method for predicting the stiffness matrix of fractured rock based on multi-task neural network fluid filling as described in claim 4, characterized in that, In step 13, for the k-th oscillatory relaxation test, the mean stress, mean strain, and equivalent stiffness matrix satisfy the following relationship: ； in, These correspond to three different oscillation relaxation tests; , and The first normal stress component, the second normal stress component, and the shear stress component are obtained in a representative volume element of rock under the kth oscillatory relaxation test. , and Indicates the first The first normal strain component, the second normal strain component, and the shear strain component were obtained in a representative volume element of rock under an oscillatory relaxation test. , , , , and These are the six independent stiffness coefficients in the equivalent stiffness matrix.

6. The method for predicting the stiffness matrix of fractured rock based on multi-task neural network fluid filling as described in claim 5, characterized in that, In step 14, the equivalent stiffness matrix is ​​a two-dimensional anisotropic equivalent stiffness matrix, expressed as: ； in, The equivalent stiffness matrix, , , , , and They are respectively , , , , and The real part of .

7. The method for predicting the stiffness matrix of fractured rock based on multi-task neural network fluid filling as described in claim 6, characterized in that, In step 2, the multi-task multilayer perceptron model includes a shared feature extraction module, a coupled stiffness branch, an intermediate stiffness branch, and a dominant stiffness branch. The shared feature extraction module is used to extract shared features from the dimensionless crack geometric descriptor of the sample and feed them into the coupled stiffness branch, the intermediate stiffness branch, and the dominant stiffness branch. The coupled stiffness branch is used to predict the weakly coupled stiffness coefficient, the intermediate stiffness branch is used to predict the intermediate stiffness coefficient, and the dominant stiffness branch is used to predict the dominant stiffness coefficient. Input vector of a multi-task multilayer perceptron model for: ； Among them, superscript Represents the transpose of a matrix; The output vector of the multi-task multilayer perceptron model for: ； in, and Corresponding to the coupled stiffness branch, and Corresponding to the intermediate stiffness branch, and Corresponding to the dominant stiffness branch; when reconstructing the fully equivalent stiffness matrix, according to , , , , and The matrix positions are arranged and reconstructed into the following form: ； in, For fully equivalent stiffness matrices, , , , , and represents the real part of the six independent stiffness coefficients in the fully equivalent stiffness matrix.

8. The method for predicting the stiffness matrix of fractured rock based on multi-task neural network fluid filling as described in claim 7, characterized in that, In step 2, the shared feature extraction module is used to extract features from the input vector. Extracting shared features Shared features Represented as: ； in, This indicates a shared feature extraction module. The trainable parameters of the shared feature extraction module are represented as follows: The outputs of the coupled stiffness branch, intermediate stiffness branch, and dominant stiffness branch are respectively represented as follows: ； ； ； in, , and These represent the coupled stiffness branch, intermediate stiffness branch, and dominant stiffness branch, respectively. , and These represent the trainable parameters of the coupled stiffness branch, intermediate stiffness branch, and dominant stiffness branch, respectively. Indicates stopping the gradient operator; The predicted value for the coupled stiffness branch; This is the predicted value for the intermediate stiffness branch; The predicted value for the dominant stiffness branch; superscript This indicates the matrix transpose.

9. The method for predicting the stiffness matrix of fractured rock based on multi-task neural network fluid filling as described in claim 8, characterized in that, In step 2, a stopping gradient operator is set before the dominant stiffness branch. The stopping gradient operator will pass the shared features to the dominant stiffness branch during the forward propagation process and block the gradient update of the parameters of the shared feature extraction module by the loss of the dominant stiffness branch during the back propagation process. Stop gradient operator The following relationship must be satisfied: Forward propagation process: ； Backpropagation process: The dominant stiffness branch loss does not affect the trainable parameters of the shared feature extraction module. Generate gradient updates; The stopping gradient operator is used to reduce , The dominant influence of the prediction task on the parameter update of the shared feature extraction module; Step 4: When training the multi-task multilayer perceptron model, a branch-weighted loss function is used to balance the training contributions of the coupled stiffness branch, intermediate stiffness branch, and dominant stiffness branch.

10. The method for predicting the stiffness matrix of fractured rock based on multi-task neural network fluid filling as described in claim 9, characterized in that, In step 2, the branch-weighted Huber loss function is used when training the multi-task multilayer perceptron model. Represented as: ； in, Here is the Huber loss function. and These are the predicted and reference values ​​for the coupled stiffness branch, respectively. and These are the predicted and reference values ​​for the intermediate stiffness branch, respectively. and These are the predicted and reference values ​​for the dominant stiffness branch, respectively. , and These are the loss weights for the coupled stiffness branch, intermediate stiffness branch, and dominant stiffness branch, respectively.

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