Rock-fill dam multi-source data assimilation method based on multi-physical information neural network

Abstract

The invention relates to a rock-fill dam multi-source data assimilation method based on a multi-physical information neural network, and the method comprises the steps: extracting the pore water pressure, the soil pressure monitoring value, the permeability coefficient and the compression modulus of a rock-fill dam; constructing a differential equation of a filling and water storage process of a soil body in the rock-fill dam; constructing a random field of the permeability coefficient and the compression modulus; and based on a pre-constructed multi-physical information neural network model, embedding the differential equation and the random field into a loss function, performing common back propagation of a network structure and a random field vector by using a preset gradient, and performing iterative training of a neural network under the supervision of multi-source data to obtain a multi-source data assimilation result of the rock-fill dam. The heterogeneous soil consolidation theory differential equation is used as a control equation, the random field theory is combined to represent the spatial variability of the soil, the multi-physical information neural network is constructed to solve the stress-seepage multi-field coupling model of the heterogeneous soil in the rock-fill dam, and assimilation of multi-source data can be achieved.

Description

Technical Field

[0001] This application relates to the field of seepage safety analysis technology in hydraulic engineering and geotechnical engineering, and in particular to a method for assimilation of multi-source data for rockfill dams based on a multi-physical information neural network. Background Technology

[0002] Complex stress-seepage multi-field coupling exists in rockfill dams, and the interactions between these physical fields affect the safety and stability of the dam. Accurately calculating the stress-seepage multi-field coupling process and identifying changes in the stress and seepage fields are crucial for ensuring the stable operation of dam projects. Achieving a thorough understanding of the multi-physics fields is essential for building a digital twin system and promoting high-quality development of water conservancy. During the filling and impoundment process of rockfill dams, the pore water pressure inside the dam, especially within the core wall, cannot dissipate in time, leading to excessively high pore pressure and even hydraulic fracturing. Due to the strong nonlinearity, time lag, and spatial heterogeneity of multi-physics field interactions, establishing multi-field coupling models and calibrating model parameters present significant challenges.

[0003] In existing research, traditional methods mainly include numerical simulation and data-driven methods, but both have certain limitations in solving the aforementioned problems. Numerical simulation calculates the filling and impoundment process of a rockfill dam by jointly solving the constitutive equations and seepage equations, and can determine the state of the dam at any given time. However, numerical simulation requires significant computational resources and time, and is limited by the incompleteness of the governing equations, often resulting in significant discrepancies between the solutions and actual monitoring data. Data-driven methods collect large amounts of real data from monitoring instruments or field experiments, and use neural networks, such as deep neural networks, convolutional neural networks, or recurrent neural networks, to train the measured data. However, data-driven methods typically require a large amount of labeled data for training, and the quantity and quality of labeled data affect the network training effect. Furthermore, due to the complex multi-field coupling effects, analyzing these data alone is insufficient to comprehensively reflect the operational behavior of the rockfill dam. Therefore, an efficient and accurate data assimilation method is needed to process multi-source data, thereby achieving a thorough understanding of multi-physics fields. Summary of the Invention

[0004] This application provides a multi-source data assimilation method for rockfill dams based on a multi-physics information neural network. This addresses the problems in related technologies, such as the need for numerical simulation methods to consume a large amount of computational resources and time, the limitations of the incompleteness of the governing equations leading to significant discrepancies between the solution and actual monitoring data, the requirement for a large amount of labeled data for training, the impact of the quantity and quality of labeled data on network training performance, and the difficulty in comprehensively reflecting the working behavior of rockfill dams due to complex multi-field coupling effects.

[0005] The first aspect of this application provides a method for assimilating multi-source data of a rockfill dam based on a multi-physics information neural network, comprising the following steps: extracting multi-source data of the rockfill dam, wherein the multi-source data includes pore water pressure, earth pressure monitoring values, permeability coefficient, and compression modulus; constructing a differential equation for the filling and water storage process of the soil in the rockfill dam; constructing a random field for the permeability coefficient and the compression modulus; embedding the differential equation and the random field into a loss function based on a pre-constructed multi-physics information neural network model, and performing backpropagation of the network structure and the random field vector using a preset gradient based on the loss function, and iteratively training the neural network under the supervision of the multi-source data to obtain the multi-source data assimilation result of the rockfill dam.

[0006] Optionally, in one embodiment of this application, after obtaining the multi-source data assimilation results of the rockfill dam, the method further includes: based on the multi-source data assimilation results of the rockfill dam, verifying the forward calculation accuracy of the pore water pressure and earth pressure and the inverse inversion accuracy of the permeability coefficient compression modulus to generate verification data; and using the spatial extrapolation of the verification data to reconstruct the pore water pressure field and earth pressure field of the entire domain, so as to evaluate the safety of the rockfill dam based on the reconstructed pore water pressure field and the reconstructed earth pressure field.

[0007] Optionally, in one embodiment of this application, the formula of the differential equation is:

[0008] in, Poisson's ratio, For the specific gravity of water, Indicates time, Represents a point in space , , These are the permeability coefficient and the compressibility modulus, respectively, which are functions of spatial location. Pore ​​water pressure, This represents the total earth pressure.

[0009] Optionally, in one embodiment of this application, the method further includes: determining the physical loss term of the control equation based on the mean square error of the differential equation of the collocation points, and establishing a stress-seepage multi-field coupling relationship based on the physical loss term of the control equation; obtaining the pore water pressure boundary conditions of the upstream and downstream, and determining the physical loss term of the pore water pressure boundary conditions based on the mean square error of the collocation points at the boundary; taking the state of the rockfill dam in the early stage of construction as the initial condition, and determining the physical loss term of the initial condition based on the mean square error of the collocation points at the initial time; and, based on the physical loss term of the control equation, the stress-seepage multi-field coupling relationship, and the physical loss term, fitting the physical laws of the central wall portion of the rockfill dam by setting collocation point iterative training, and generating a fitting result.

[0010] Optionally, in one embodiment of this application, the formula for the random field is:

[0011] in, and These are the mean and standard deviation of the random field, respectively. Let be the number of terms in the series expansion. and These are the autocorrelation functions. The Each eigenvalue and eigenfunction Let be a set of mutually independent random variables that follow a normal distribution. It belongs to the probability space.

[0012] Optionally, in one embodiment of this application, the step of embedding the differential equation and the random field into a loss function based on a pre-constructed multi-physics information neural network model, and using a preset gradient to perform joint backpropagation of the network structure and the random field vector based on the loss function, and performing iterative training of the neural network under the supervision of the multi-source data to obtain the multi-source data assimilation result of the rockfill dam, includes: embedding a stress-seepage multi-field coupling model and a parametric random field into the multi-physics information neural network model, and supervising the training of the multi-physics information neural network model to couple the stress field and seepage field under a heterogeneous parametric field to obtain a coupling result; during the training process of the multi-physics information neural network model, based on the coupling result, incorporating the random field vector into the network parameters, and performing joint backpropagation of the network structure and the random field vector through the preset gradient to assimilate the pore water pressure, the earth pressure monitoring value, the permeability coefficient, and the compression modulus of the rockfill dam to obtain the multi-source data assimilation result of the rockfill dam.

[0013] Optionally, in one embodiment of this application, the method further includes: calculating the mean square error between the network training values ​​and the geotechnical test values ​​of the permeability coefficient and the compression modulus to obtain the detection data-driven loss; calculating the mean square error between the network training values ​​and the sensor monitoring values ​​of the pore water pressure and the earth pressure to obtain the monitoring data-driven loss; and determining the data-driven loss of the multi-physics information neural network model based on the detection data-driven loss and the monitoring data-driven loss.

[0014] Optionally, in one embodiment of this application, the iterative training of the neural network under the supervision of the multi-source data to obtain the multi-source data assimilation result of the rockfill dam further includes: constructing a data-physical dual-drive model based on the loss function, data loss term, and physical loss term of the multi-physical information neural network model; and continuously adjusting the network parameters of the data-physical dual-drive model through the network feedback mechanism to assimilate the multi-source data and obtain the multi-source data assimilation result of the rockfill dam.

[0015] Optionally, in one embodiment of this application, the formula for calculating the loss function is:

[0016] in, Indicates the loss driven by physics. This represents the data-driven loss of the monitored values. This represents the data-driven loss of the detected values. Represents the initial condition loss. This represents the loss due to boundary conditions. , , , These are the weight coefficients for the corresponding terms, used to balance the loss terms during the training process.

[0017] Optionally, in one embodiment of this application, the method further includes: dividing the multiphysics neural network model into a training set, a validation set, and a test set; training the neural network using the training set to obtain a preliminary network structure; selecting hyperparameters based on the preliminary network structure using the validation set to select the multiphysics neural network model and obtain a selection result; inputting the test set into the multiphysics neural network model based on the selection result to solve for the training accuracy of the test set, and outputting the multiphysics neural network model if the training accuracy meets a preset condition; otherwise, adjusting the network parameters until the test set meets the training accuracy.

[0018] This application uses the differential equation of consolidation theory for heterogeneous soil as the governing equation, and combines random field theory to represent the spatial variability of the soil. A multi-physics information neural network is constructed to solve the stress-seepage multi-field coupling model of heterogeneous soil in rockfill dams. This effectively achieves the assimilation of multi-source data for rockfill dams, enabling thorough perception of multi-physics fields at a lower cost. This solves the problems in related technologies, such as the need for large amounts of computational resources and time for numerical simulation methods, the significant discrepancies between the solution and actual monitoring data due to the incompleteness of the governing equations, the requirement for large amounts of labeled data for training (the quantity and quality of labeled data affect network training performance), and the difficulty in comprehensively reflecting the working behavior of rockfill dams due to complex multi-field coupling effects.

[0019] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0020] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a flowchart of a multi-source data assimilation method for rockfill dams based on a multi-physics information neural network, according to an embodiment of this application. Figure 2 This is a flowchart illustrating a multi-source data assimilation method for rockfill dams based on a multi-physics information neural network according to an embodiment of this application. Figure 3 This is a schematic diagram of the model structure of a multi-source data assimilation method for rockfill dams based on a multi-physics information neural network according to an embodiment of this application; Figure 4 This is a schematic diagram of the material partitioning of a core wall rockfill dam according to an embodiment of the present application, which describes a multi-source data assimilation method for rockfill dams based on a multi-physics information neural network. Figure 5 This is a scatter plot of training results for a multi-source data assimilation method for rockfill dams based on a multi-physics information neural network according to an embodiment of this application. Figure 6 This is a schematic diagram of the predicted global distribution of core wall pore water pressure according to an embodiment of this application of a multi-physical information neural network-based multi-source data assimilation method for rockfill dams. Figure 7 This is a schematic diagram illustrating the predicted global distribution of core wall earth pressure according to an embodiment of this application of a multi-physical information neural network-based multi-source data assimilation method for rockfill dams. Detailed Implementation

[0021] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0022] The following description, with reference to the accompanying drawings, illustrates an embodiment of this application of a multi-source data assimilation method for rockfill dams based on a multi-physics information neural network. In the related technologies mentioned in the background section, numerical simulation methods require significant computational resources and time, and are often limited by the incompleteness of the governing equations, resulting in significant discrepancies between the solutions and actual monitoring data. Data-driven methods typically require a large amount of labeled data for training, and the quantity and quality of the labeled data affect the network training effect. Due to complex multi-field coupling effects, analyzing these data alone is insufficient to comprehensively reflect the working behavior of rockfill dams. This application provides a multi-source data assimilation method for rockfill dams based on a multi-physics information neural network. In this method, the differential equation of consolidation theory for heterogeneous soil is used as the governing equation, combined with random field theory to represent the spatial variability of the soil, and a multi-physics information neural network is constructed to solve the stress-seepage multi-field coupling model of heterogeneous soil in rockfill dams. This effectively achieves the assimilation of multi-source data for rockfill dams, enabling thorough perception of multi-physics fields at a lower cost. This solves the problems in related technologies, such as the fact that numerical simulation methods require a lot of computing resources and time, and the results often differ significantly from actual monitoring data due to the incompleteness of the control equations; data-driven methods usually require a large amount of labeled data for training, and the quantity and quality of labeled data will affect the network training effect; and due to the complex multi-field coupling effect, it is difficult to fully reflect the working behavior of rockfill dams by analyzing these data alone.

[0023] Specifically, Figure 1 This is a flowchart illustrating a multi-source data assimilation method for rockfill dams based on a multi-physics information neural network, provided in an embodiment of this application.

[0024] like Figure 1 As shown, this method for multi-source data assimilation of rockfill dams based on multi-physics information neural networks includes the following steps: In step S101, multi-source data of the rockfill dam is extracted, including pore water pressure, earth pressure monitoring value, permeability coefficient and compression modulus.

[0025] In practical implementation, the embodiments of this application can extract spatiotemporal datasets of seepage-stress from pore pressure gauges and earth pressure gauges. ,in, , , These are the three-dimensional coordinates of the core wall. For time, , These are the upstream and downstream water levels of the rockfill dam, respectively. Pore ​​water pressure, For earth pressure.

[0026] Obtain field material datasets from field testing data. ,in Permeability coefficient, It is the compressibility modulus.

[0027] In step S102, the differential equations for the filling and water storage process of the soil in the rockfill dam are constructed.

[0028] In practical implementation, the embodiments of this application can construct differential equations for the filling and water storage process of soil in rockfill dams based on the theory of consolidation of heterogeneous soil: In one embodiment of this application, the differential equation for the consolidation of heterogeneous soil satisfying the stress-seepage multi-field coupling process is derived based on Biot's consolidation theory. This equation is composed of pore water pressure, earth pressure, permeability coefficient, and compression modulus. Biot's consolidation theory is a three-dimensional consolidation equation that accurately reflects the relationship between pore water pressure dissipation and soil skeleton deformation. Based on this, the differential equation for the consolidation of heterogeneous soil is expressed as follows:

[0029] in, Poisson's ratio, For the specific gravity of water, Indicates time, Represents a point in space , , These are the permeability coefficient and the compressibility modulus, respectively, which are functions of spatial location. Pore ​​water pressure, This represents the total earth pressure.

[0030] Optionally, in one embodiment of this application, the method further includes: determining the physical loss term of the control equation based on the mean square error of the differential equation of the collocation points, and establishing a stress-seepage multi-field coupling relationship based on the physical loss term of the control equation; obtaining the pore water pressure boundary conditions of the upstream and downstream, and determining the physical loss term of the pore water pressure boundary conditions based on the mean square error of the collocation points at the boundary; taking the state of the rockfill dam in the early stage of construction as the initial condition, and determining the physical loss term of the initial condition based on the mean square error of the collocation points at the initial time; and, based on the physical loss term of the control equation, the stress-seepage multi-field coupling relationship, and the physical loss term, fitting the physical laws of the central wall part of the rockfill dam by setting collocation point iterative training, and generating fitting results.

[0031] In this embodiment, the consolidation theory differential equation for heterogeneous soil can be set as the governing equation of MPINN, and the physical laws of the central wall of the rockfill dam can be fitted by setting collocation point iterative training. The physical loss term of the network includes: The mean square error of the differential equation for the collocation points is set as the physical loss term of the governing equation, establishing a multi-field coupling relationship between stress and seepage. Upstream and downstream pore water pressure boundary conditions are set, with the area above the free water surface as the drainage boundary and the area below the free water surface as the seepage boundary. The mean square error of the collocation points at the boundary is used as the physical loss term of the boundary conditions. The state of the rockfill dam in the early stage of construction is set as the initial condition to meet the actual engineering conditions. The mean square error of the collocation points at the initial time is set as the physical loss term of the initial condition.

[0032] In step S103, a random field of permeability coefficient and compressibility modulus is constructed.

[0033] Specifically, embodiments of this application can construct random fields with permeability coefficients and compressibility moduli based on series expansion theory: 1. Construct an autocorrelation function that reflects the spatial variability of soil:

[0034] in, , For spatial coordinates, These are the coordinate components of the spatial coordinates. , These are the autocorrelation distances in the horizontal and vertical coordinate directions, respectively.

[0035] 2. Construct the series expansion of the random field for the permeability coefficient and the compressibility modulus. The autocorrelation function cannot directly form a random field in practical calculations; it needs to be discretized into a finite number of random variables, which can be achieved through series expansion.

[0036] In one embodiment of this application, a random field of permeability coefficient and elastic modulus is constructed, and the autocorrelation function reflecting the spatial variability of soil is a three-dimensional separable Gaussian autocorrelation function. The continuous random field satisfying the above relationship is discretized into a finite number of random variables by a series expansion method.

[0037] in, and These are the mean and standard deviation of the random field, respectively. Let be the number of terms in the series expansion. and These are the autocorrelation functions. The Each eigenvalue and eigenfunction Let be a set of mutually independent random variables that follow a normal distribution. It belongs to the probability space.

[0038] The continuous random fields of permeability coefficient and compression modulus are reduced in dimension to establish vectorized parameter fields. Both the permeability coefficient and compression modulus in soil follow a log-normal distribution. The vectorized parameter fields are expressed as follows: and .

[0039] In step S104, based on the pre-constructed multi-physics information neural network model, differential equations and random fields are embedded into the loss function. Based on the loss function, the network structure and random field vectors are backpropagated using a preset gradient. The neural network is iteratively trained under the supervision of multi-source data to obtain the multi-source data assimilation result of the rockfill dam.

[0040] It is understood that the embodiments of this application can assimilate the monitoring data of pore water pressure and earth pressure of rockfill dams and the detection data of permeability coefficient and compression modulus during the training process of MPINN.

[0041] In actual implementation, the embodiments of this application can construct a Multiphysics-Informed Neural Network (MPINN) model, embed the theory in steps S102 and S103 into the loss function, complete the common backpropagation of the network structure and random field vector through a custom gradient, and assimilate the data in step S101 during the training process to obtain a trained surrogate model.

[0042] This application enables the construction of an MPINN network model. When establishing the MPINN structure, a five-layer fully connected neural network is constructed, with 50 neurons in each layer. Bayesian optimization is used to adjust the hyperparameters of the MPINN model. The input and output of the MPINN network model are a seepage-stress spatiotemporal dataset. The structure specifically includes an input layer, a fully connected layer, an output layer, and a loss function.

[0043] The input layer is used to receive spatial features. and time characteristics ; The hidden layers in a fully connected layer use ReLU as the activation function; The output layer is used for output. Seepage-stress at any point in time The derivative terms relative to spatial and temporal features are automatically differentiated, making it easier to include them in the loss function to calculate the physical loss during backpropagation. loss function It can be represented as:

[0044] in, Indicates the loss driven by physics. Indicates data-driven loss. Represents the initial condition loss. This represents the loss due to boundary conditions. , , , These are the weight coefficients for the corresponding terms, used to balance the loss term during training. Each loss term is expressed as:

[0045]

[0046]

[0047]

[0048] in, , , , These represent the number of collocation points, marker points, initial condition points, and boundary condition points, respectively. For network training values, including pore water pressure Earth pressure , To monitor and test the measured values ​​of the data. The initial values ​​are the network training values. The measured value is the initial value. These are the network training values ​​for the boundary values. These are the measured values ​​of the boundary values. These are network parameters.

[0049] This application uses the differential equation of the consolidation theory of heterogeneous soil as the governing equation, combines random field theory to represent the spatial variability of soil, and constructs a multi-physics information neural network to solve the stress-seepage multi-field coupling model of heterogeneous soil in rockfill dams, which can achieve the assimilation of multi-source data.

[0050] Optionally, in one embodiment of this application, based on a pre-constructed multi-physics information neural network model, differential equations and random fields are embedded into a loss function. Based on the loss function, a preset gradient is used to perform joint backpropagation of the network structure and random field vectors. Under the supervision of multi-source data, iterative training of the neural network is performed to obtain the multi-source data assimilation result of the rockfill dam. This includes: embedding a stress-seepage multi-field coupling model and a parametric random field into the multi-physics information neural network model, and supervising the training of the multi-physics information neural network model to couple the stress field and seepage field under a heterogeneous parametric field to obtain a coupling result; during the training process of the multi-physics information neural network model, based on the coupling result, random field vectors are incorporated into the network parameters, and a preset gradient is used to perform joint backpropagation of the network structure and random field vectors to assimilate the multi-source data to obtain the multi-source data assimilation result of the rockfill dam.

[0051] Specifically, embodiments of this application can embed a stress-seepage multi-field coupling model and a parametric random field into a neural network and supervise model training to achieve coupling between the stress field and the seepage field under a heterogeneous parametric field. During network training, the random field vector... and By incorporating network parameters and using a custom gradient, convergence is achieved during iterative training and backpropagation, thus enabling the simultaneous solution of forward and inverse problems during network training. This allows for the acquisition of an optimal set of random variables through network training. Thus obtain and The distribution of the permeability coefficient and compressibility modulus. That is, this application can combine the random fields of the permeability coefficient and compressibility modulus with MPINN: by combining the random variables... and By incorporating network parameters, a combination of random fields and MPINN can be achieved. An optimal set of random variables can be obtained through network training. Thus obtain and The distribution of the physical driving loss term, after being combined with the random field, can be expressed as:

[0052]

[0053]

[0054] After introducing a random field, the residual between the network training data and the actual geotechnical survey data is incorporated into the data-driven loss term, expressed as:

[0055] in, and The number of on-site survey points for permeability coefficient and compression modulus, respectively. and These are the actual measured values ​​of permeability coefficient and compression modulus, respectively. and These are the network training values ​​for the permeability coefficient and compression modulus, respectively.

[0056] Optionally, in one embodiment of this application, iterative training of the neural network is performed under the supervision of multi-source data to obtain the multi-source data assimilation result of the rockfill dam. This also includes: constructing a data-physical dual-drive model based on the loss function, data loss term, and physical loss term of the multi-physical information neural network model; and continuously adjusting the network parameters of the data-physical dual-drive model through the network feedback mechanism to assimilate the pore water pressure, earth pressure monitoring value, permeability coefficient, and compression modulus of the rockfill dam to obtain the multi-source data assimilation result of the rockfill dam.

[0057] Specifically, embodiments of this application can construct the loss function of the MPINN model, combine data loss terms and physical loss terms to construct a data-physical dual-driven model, and continuously adjust network parameters through the network feedback mechanism to ultimately achieve assimilation of multi-source data.

[0058] In one embodiment of this application, a loss function can be constructed and an MPINN model can be trained. Based on the aforementioned technical features, the loss function of the joint random field PINN model can be expressed as:

[0059] in, Indicates the loss driven by physics. This represents the data-driven loss of the monitored values. This represents the data-driven loss of the detected values. Represents the initial condition loss. This represents the loss due to boundary conditions. , , , These are the weight coefficients for the corresponding terms, used to balance the loss terms during the training process.

[0060] Under the constraint of the loss function, the MPINN model can meet the solution requirements of differential equations while gradually reducing the training data error, realizing the joint stress-seepage multi-field coupling model and parametric random field.

[0061] This application presents a multi-physics information neural network-based method for assimilating multi-source data of rockfill dams. This method combines a stress-seepage multi-field coupling model with a parametric random field, effectively assimilating multi-source data for rockfill dams and achieving thorough multi-physics perception at a lower cost. By combining the stress-seepage multi-field coupling model with the parametric random field, the method assimilates pore water pressure, earth pressure monitoring data, compression modulus, and permeability coefficient detection data of the rockfill dam during the calculation process, thus improving the difficulty of handling multi-source data in traditional methods.

[0062] Optionally, in one embodiment of this application, after obtaining the multi-source data assimilation results of the rockfill dam, the method further includes: verifying the forward calculation accuracy of pore water pressure and earth pressure and the inverse inversion accuracy of the permeability coefficient compression modulus based on the multi-source data assimilation results of the rockfill dam, so as to generate verification data; and using the spatial extrapolation of the verification data to reconstruct the pore water pressure field and earth pressure field of the entire domain, so as to evaluate the safety of the rockfill dam based on the reconstructed pore water pressure field and the reconstructed earth pressure field.

[0063] In actual implementation, the embodiments of this application can verify the data assimilation effect, test the forward calculation accuracy of pore water pressure and earth pressure and the inverse inversion accuracy of the permeability coefficient compression modulus, test the spatial extrapolation of the data assimilation method, and achieve a comprehensive perception of the pore water pressure field and earth pressure field.

[0064] This application embodiment constructs a data-physical dual-driven multi-source data assimilation method to calculate the stress-seepage problem of heterogeneous soil in rockfill dams, realizes the forward calculation of pore water pressure and earth pressure and the inverse inversion of the permeability coefficient and compression modulus, and then realizes the reconstruction of the pore water pressure field and earth pressure field of the whole domain from sparse monitoring and detection data, so as to conduct a more comprehensive assessment of the overall safety of rockfill dams.

[0065] Optionally, in one embodiment of this application, the method further includes: calculating the mean square error between the network training values ​​and the geotechnical test values ​​of the permeability coefficient and the compression modulus to obtain the detection data-driven loss; calculating the mean square error between the network training values ​​and the sensor monitoring values ​​of the pore water pressure and the earth pressure to obtain the monitoring data-driven loss; and determining the data-driven loss of the multi-physics information neural network model based on the detection data-driven loss and the monitoring data-driven loss.

[0066] As one possible implementation, embodiments of this application can construct the data loss of MPINN, and achieve fitting of the actual engineering values ​​through feedback training of the data-driven loss term. The mean square error between the network training values ​​of permeability coefficient and compression modulus and the geotechnical investigation test values ​​is set as the detection data-driven loss, and the mean square error between the network training values ​​of pore water pressure and soil pressure and the sensor monitoring values ​​is set as the monitoring data-driven loss, thus finally determining the data-driven loss of the multi-physics information neural network model.

[0067] Optionally, in one embodiment of this application, the method further includes: dividing the multi-physics information neural network model into a training set, a validation set, and a test set; training the neural network using the training set to obtain a preliminary network structure; selecting hyperparameters using the validation set based on the preliminary network structure to select the multi-physics information neural network model and obtain a selection result; inputting the test set into the multi-physics information neural network model based on the selection result to solve for the training accuracy of the test set, and outputting the multi-physics information neural network model if the training accuracy meets a preset condition; otherwise, adjusting the network parameters until the test set meets the training accuracy.

[0068] It is understood that the dataset of MPINN in this application embodiment includes a training set (60%), a validation set (20%), and a test set (10%).

[0069] In actual implementation, the specific training process of this application embodiment includes: using the training set for training the neural network, obtaining a preliminary network structure through iterative training; using the validation set for selecting hyperparameters to achieve specific selection of the model; inputting the test set into the model, solving the training accuracy of the test set, and if it meets the preset ideal value, saving and outputting the neural network model; otherwise, adjusting the network parameters and repeating the above training process until the test set meets the accuracy.

[0070] Specifically, it can be combined with Figures 2 to 7 As shown, the working principle of the multi-source data assimilation method for rockfill dams based on multi-physical information neural networks in this application is explained in detail with a specific embodiment.

[0071] Figure 2 The process includes: S1: Extracting pore water pressure, earth pressure monitoring values, and permeability coefficient and compression modulus detection values ​​for rockfill dams; S2: Constructing differential equations for the filling and water storage process of soil in rockfill dams based on the theory of heterogeneous soil consolidation; S3: Constructing random fields for permeability coefficient and compression modulus based on series expansion theory; S4: Constructing a multi-physics information neural network model, embedding the theories from S2 and S3 into the loss function, and completing the common backpropagation of the network structure and random field vector through a custom gradient. During training, the data in S1 is assimilated to obtain a trained surrogate model; S5: Verifying the data assimilation effect, checking the forward calculation accuracy of pore water pressure and earth pressure, and the inverse inversion accuracy of permeability coefficient and compression modulus; S6: Checking the spatial extrapolation of the data assimilation method to achieve a comprehensive and thorough perception of the pore water pressure field and earth pressure field.

[0072] The multi-source data assimilation method for rockfill dams based on multi-physics information neural networks provided in this application was used to analyze the filling and impoundment process of a core-wall rockfill dam. The model structure is as follows: Figure 3 As shown, the material zoning diagram of this core-wall rockfill dam is as follows: Figure 4As shown.

[0073] S1: Extract the monitoring values ​​of pore water pressure and earth pressure, as well as the test values ​​of permeability coefficient and compression modulus of the rockfill dam. For the core wall area, there are a total of 60 monitoring points and 41 test sampling points. Extract the spatiotemporal seepage-stress dataset and material dataset from them. S2: Constructing differential equations for the filling and water storage process of soil in rockfill dams based on the consolidation theory of heterogeneous soil; S3: Constructing random fields with permeability coefficient and compressibility modulus based on series expansion theory: S3.1: Construct an autocorrelation function that reflects the spatial variability of soil, and calculate the correlation length using the recursive spatial method; S3.2: Construct the random field series expansion of the permeability coefficient and the compressibility modulus, with the mean and standard deviation taken from the field test data; S4: Construct a multi-physics information neural network model, embedding the theories from S2 and S3 into the loss function. A custom gradient is used to perform backpropagation of the network structure and random field vectors. During training, the data from S1 is assimilated to obtain a trained surrogate model. The training effect is as follows: Figure 5 As shown: S4.1: Construct the MPINN network model; S4.2: Simultaneous random fields; S4.3: Construct the loss function and train the MPINN model; S5: Using the coefficient of determination (R²) 2 The MPINN model was validated using the R-Squared method, enabling positive prediction of pore water pressure and earth pressure, and inverse inversion of permeability coefficient and compression modulus. S6: Verify the spatial extrapolation of the data assimilation method to achieve a comprehensive understanding of the pore water pressure field and earth pressure field. The core wall area is verified using three typical time points: completion period (December 2021), water storage period (July 2022), and operation period (July 2024).

[0074] The global distribution of pore water pressure calculated by the multi-source data assimilation method for rockfill dams based on multi-physics information neural networks provided in this application is as follows: Figure 6 As shown, the earth pressure distribution across the entire region is as follows: Figure 7 As shown in the figure. The comparison results show that the calculation results of the multi-source data assimilation method provided in this application are close to the measured values, which can achieve thorough perception of multi-physics fields, demonstrating the scientific nature and reliability of the method provided in this application.

[0075] This application proposes a method for assimilating multi-source data of rockfill dams based on a multi-physics information neural network. Using the differential equation of consolidation theory for heterogeneous soil as the governing equation, and combining it with random field theory to represent the spatial variability of the soil, a multi-physics information neural network is constructed to solve the stress-seepage multi-field coupling model of heterogeneous soil in the rockfill dam. This effectively achieves the assimilation of multi-source data for the rockfill dam, enabling thorough perception of the multi-physics field at a lower cost. This addresses the problems in related technologies, such as the need for large amounts of computational resources and time in numerical simulation methods, the inherent limitations of the governing equations leading to significant discrepancies between the solutions and actual monitoring data, the requirement for large amounts of labeled data for training (the quantity and quality of which affect network training performance), and the difficulty in comprehensively reflecting the operational behavior of the rockfill dam due to complex multi-field coupling effects when analyzing these data alone.

[0076] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0077] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0078] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

Claims

1. A method for multi-source data assimilation of rockfill dams based on multi-physics information neural networks, characterized in that, Includes the following steps: Extract multi-source data of the rockfill dam, wherein the multi-source data includes pore water pressure, earth pressure monitoring value, permeability coefficient and compression modulus; Construct the differential equations for the filling and water storage process of the soil in the rockfill dam; Construct a random field for the permeability coefficient and the compressibility modulus; Based on a pre-constructed multi-physics information neural network model, the differential equation and the random field are embedded in a loss function. Based on the loss function, a preset gradient is used to perform joint backpropagation of the network structure and the random field vector. Under the supervision of the multi-source data, the neural network is iteratively trained to obtain the multi-source data assimilation result of the rockfill dam.

2. The method according to claim 1, characterized in that, After obtaining the multi-source data assimilation results of the rockfill dam, the following is also included: Based on the multi-source data assimilation results of the rockfill dam, the forward calculation accuracy of the pore water pressure and earth pressure and the inverse inversion accuracy of the permeability coefficient and compression modulus are tested to generate test data. By utilizing the spatial extrapolation of the test data, the pore water pressure field and earth pressure field of the entire domain are reconstructed, so as to assess the safety of the rockfill dam based on the reconstructed pore water pressure field and the reconstructed earth pressure field.

3. The method according to claim 1, characterized in that, The formula for the differential equation is: in, Poisson's ratio, For the specific gravity of water, Indicates time, Represents a point in space , , These are the permeability coefficient and the compressibility modulus, respectively, which are functions of spatial location. Pore ​​water pressure, This represents the total earth pressure.

4. The method according to claim 1, characterized in that, Also includes: The physical loss term of the control equation is determined based on the mean square error of the differential equation of the collocation points, and the stress-seepage multi-field coupling relationship is established based on the physical loss term of the control equation. Obtain the pore water pressure boundary conditions upstream and downstream, and determine the physical loss term of the pore water pressure boundary conditions based on the mean square error of the points at the boundary. Using the state of the rockfill dam in the early stage of construction as the initial condition, the physical loss term of the initial condition is determined based on the mean square error of the points at the initial time. Based on the physical loss term of the governing equation, the stress-seepage multi-field coupling relationship, and the physical loss term, the physical laws of the central wall of the rockfill dam are fitted by setting collocation points for iterative training, and the fitting results are generated.

5. The method according to claim 1, characterized in that, The formula for the random field is: in, and These are the mean and standard deviation of the random field, respectively. Let be the number of terms in the series expansion. and These are the autocorrelation functions. The Each eigenvalue and eigenfunction Let be a set of mutually independent random variables that follow a normal distribution. It belongs to the probability space.

6. The method according to claim 1, characterized in that, The pre-constructed multi-physics information neural network model embeds the differential equation and the random field into a loss function, and performs joint backpropagation of the network structure and random field vectors using a preset gradient based on the loss function. Iterative training of the neural network is then performed under the supervision of the multi-source data to obtain the multi-source data assimilation result of the rockfill dam, including: The stress-seepage multi-field coupling model and the parametric random field are embedded into the multi-physics information neural network model, and the training of the multi-physics information neural network model is supervised to couple the stress field and seepage field under the heterogeneous parametric field to obtain the coupling result. During the training process of the multi-physics information neural network model, based on the coupling result, the random field vector is incorporated into the network parameters, and the network structure and the random field vector are backpropagated together through the preset gradient to assimilate the pore water pressure, the earth pressure monitoring value, the permeability coefficient and the compression modulus of the rockfill dam, thereby obtaining the multi-source data assimilation result of the rockfill dam.

7. The method according to claim 1, characterized in that, Also includes: The mean square error between the network training values ​​and the geotechnical test values ​​of the permeability coefficient and the compression modulus is calculated to obtain the detection data-driven loss. The mean square error between the network training values ​​and the sensor monitoring values ​​of the pore water pressure and the soil pressure is calculated to obtain the monitoring data-driven loss. Based on the detection data-driven loss and the monitoring data-driven loss, the data-driven loss of the multi-physics information neural network model is determined.

8. The method according to claim 1, characterized in that, The iterative training of the neural network under the supervision of the multi-source data to obtain the multi-source data assimilation result of the rockfill dam further includes: Based on the loss function, data loss term, and physical loss term of the multi-physics information neural network model, a data-physical dual-drive model is constructed. The network parameters of the data-physical dual-drive model are continuously adjusted through the network feedback mechanism to assimilate the multi-source data and obtain the multi-source data assimilation result of the rockfill dam.

9. The method according to claim 8, characterized in that, The formula for calculating the loss function is as follows: in, Indicates the loss driven by physics. This represents the data-driven loss of the monitored values. This represents the data-driven loss of the detected values. Represents the initial condition loss. This represents the loss due to boundary conditions. , , , These are the weight coefficients for the corresponding terms, used to balance the loss terms during the training process.

10. The method according to claim 1, characterized in that, Also includes: The multiphysics information neural network model is divided into a training set, a validation set, and a test set; The neural network is trained using the training set to obtain a preliminary network structure; Based on the preliminary network structure, the validation set is used to select hyperparameters to select the multi-physics information neural network model and obtain the selection result; Based on the selection result, the test set is fed into the multi-physics information neural network model to solve for the training accuracy of the test set. If the training accuracy meets the preset conditions, the multi-physics information neural network model is output; otherwise, the network parameters are adjusted until the test set meets the training accuracy.

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