An electrical and hydrological coupling inversion method, device and medium

Abstract

The present application relates to the technical field of geophysical inversion and artificial intelligence, and particularly relates to an electrical and hydrological coupling inversion method, device and medium, the method comprising: obtaining inversion data; preprocessing the inversion data to generate a training data set; constructing an electrical and hydrological coupling control equation, establishing a differentiable proxy model for outputting a predicted inversion result; setting hydrological physical constraints, electrical physical constraints and hydrological and electrical coupling boundaries; constructing a comprehensive loss function of the differentiable proxy model, updating the weights in the comprehensive loss function through a back propagation algorithm; updating the neural network parameters of the differentiable proxy model until the loss decreases without fluctuation; after the model converges, the differentiable proxy model outputs the inversion result. Compared with the traditional method, the present application can quickly output the water head, permeability coefficient and electrical parameter distribution after the training is completed, and the time consumption of a single prediction is significantly lower than that of the traditional repeated forward iteration method.

Description

Technical Field

[0001] This invention relates to the fields of geophysical inversion and artificial intelligence technology, and in particular to a method, equipment and medium for coupled electrical and hydrological inversion. Background Technology

[0002] In dam leakage monitoring, the electrical resistivity tomography (EDT) response is controlled by hydrological parameters such as groundwater level and permeability coefficient. Traditional inversion methods have the following drawbacks: (1) Ignoring time series coupling results in large dynamic monitoring errors. The computational efficiency is low, and multiple time-series data need to be repeatedly calculated in forward modeling, making it difficult to respond quickly.

[0003] (2) The physical constraints are weak, the nonlinear hydrological-electrical relationship and boundary conditions are not fully utilized, and errors are easily generated.

[0004] (3) The coupling relationship between hydrology and electrical properties is complex, and traditional optimization methods are prone to getting trapped in local optima.

[0005] (4) Poor generalization ability. The model is trained for a single cross section and is difficult to apply to multiple regions or long time sequences. The loss function has large differences in the dimensions of each item, making training unstable and the cost of large-scale parameter inversion calculation is high.

[0006] In summary, there is an urgent need for a coupled electrical and hydrological inversion method, equipment, and medium. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention proposes a method, equipment, and medium for coupled electrical and hydrological inversion.

[0008] In a first aspect, the present invention provides a coupled electrical and hydrological inversion method, comprising the following steps: S1. Obtain inversion data; S2. Preprocess the inverted data to generate a training dataset; S3. Based on the groundwater flow control equation, electric field control equation and hydrological and electrical relationship, construct the electrical and hydrological coupled control equation, establish a differentiable surrogate model, and use it to output the prediction and inversion results; S4. Set hydrophysical constraints, electrical physical constraints, and hydro-electric coupling boundaries; S5. Construct the comprehensive loss function of the differentiable surrogate model, and update the weights in the comprehensive loss function through the backpropagation algorithm; S6. Update the neural network parameters of the differentiable surrogate model until the loss decreases without fluctuation; S7. After the model converges, the differentiable surrogate model outputs the inversion results.

[0009] Optionally, in S1, the inversion data includes inversion borehole depth, well logging and geophysical and electrical data, boundary conditions, time-varying parameters, measurement point coordinates, and observation distribution information.

[0010] Optionally, in S2, the preprocessing includes unifying units, timestamp processing, removing outlier data, filtering, handling missing values, data standardization, difference sets, and generating Gaussian training point clouds.

[0011] Optionally, in S3, the coupled control equations of electrical and hydrological methods include groundwater flow control equations, electric field control equations, and the relationship between hydrology and electrical properties. The expression for the governing equation of groundwater flow is as follows: ; in, For pressure head; Elevation; The unsaturated permeability coefficient; The specific water storage coefficient; For source and sink terms, it represents the external input or extraction of water into the system; The expression for the electric field control equation is as follows: ; in, Represents the gradient operator. Represents electric potential The gradient; Electrical conductivity; The expression for the relationship between hydrology and electrical properties is as follows: ; in, The electrical conductivity of pore water; Tortuosity factor; The cementation index; This represents the pore water saturation level.

[0012] Optionally, in S4, the hydrophysical constraints are: the continuity of the water flow velocity field is constrained by Darcy's law and the mass conservation equation; the electrical physical constraints are: the electric potential field and current density field are calculated by the electrical volume charge equation and Ohm's law; the hydrological and electrical coupling boundary is: the coupling relationship between groundwater flow and resistivity change is established by fitting the saturation relationship using the Archie model.

[0013] Optionally, in S5, the expression for the comprehensive loss function L is as follows: ; in, , , , These represent the residual losses of groundwater flow, respectively. Electric field residual loss Data error loss Regularization loss The weights; ; ; ; ; in, Indicates the number of calculation points for the hydrological control equations; Indicates the water storage coefficient; Indicates the first The head value at each calculation point; Indicates the calculation point Corresponding head value The permeability coefficient below; Indicates the calculation point Spatial elevation; Indicates source and sink terms; This indicates the number of calculation points for the electric field control equations; Show the first Dielectric conductivity at each calculation point; This represents the electric potential at the calculation point. Indicates the number of observation data; Indicates the first A set of actual observation data; This represents the corresponding predicted value calculated by the model; Indicates the number of regularization calculation points; Indicates the first Medium parameters at a spatial location; This represents the spatial variation gradient of the medium parameter.

[0014] Optionally, in S6, the neural network parameters are updated based on the Adam optimizer. The expression is as follows: ; in, Indicates the parameters to be inverted; The expression for the differentiable surrogate model is as follows: ; The differentiable surrogate model is used for backpropagation optimization.

[0015] Optionally, S6 also includes adaptive loss weight updates, expressed as follows: ; in, For the first Term gradient norm; For the average gradient, Indicates the (k+1)th iteration when the... The unnormalized weights of each loss term; Indicates the k-th iteration. The weights of each loss term.

[0016] In a second aspect, the present invention also provides a computer device, including a memory and a processor; The memory stores computer programs; When the processor executes the computer program, it implements the steps of the above-described electrical and hydrological coupled inversion method.

[0017] In a third aspect, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described electrical and hydrological coupled inversion method.

[0018] The application of the technical solution of the present invention has at least the following beneficial effects: (1) This invention provides a method, equipment and medium for coupled inversion of electrical and hydrological methods. The method of this invention introduces a differentiable surrogate model and learns the mapping relationship between model parameters and electrical response through a neural network, which replaces the traditional finite element forward model solver and improves the speed of single iteration.

[0019] (2) The method of the present invention incorporates the groundwater seepage equation and the electric field control equation as physical constraints into the loss function, and constructs a joint inversion framework of surrogate model and geophysical information neural network, which improves the inversion accuracy.

[0020] (3) The method of the present invention avoids the single loss from dominating the model training by updating the loss weights adaptively. The method of the present invention improves the training stability by using adaptive weights to change the loss function from oscillating decline to relatively stable and synchronous decline. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0022] Figure 1 This is a flowchart illustrating the steps of a preferred embodiment of the electrical and hydrological coupled inversion method of the present invention. Figure 2This is a comparison chart of head pressure in a numerical simulation of a preferred embodiment of the present invention; Figure 3 This is a training data graph of numerical simulation without adaptive weights in a preferred embodiment of the present invention; Figure 4 The training data graph for numerical simulation using adaptive weights is shown in the preferred embodiment of the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0024] Example 1: like Figure 1 As shown, this embodiment provides a coupled electrical and hydrological inversion method, including the following steps (S1 to S7): S1. Obtain inversion data; inversion data includes inversion borehole depth, well logging and geophysical and electrical data, boundary conditions, time-varying parameters, measurement point coordinates, and observation distribution information.

[0025] S2. Preprocess the inversion data to generate a training dataset; the preprocessing includes unifying units, timestamp processing, removing outlier data, filtering, handling missing values, data standardization, difference set, and generating Gaussian training point cloud.

[0026] S3. Based on the groundwater flow control equation, electric field control equation, and the relationship between hydrology and electrical properties, construct the coupled control equation of electrical method and hydrology, and establish a differentiable surrogate model. The differentiable surrogate model receives the parameters to be inverted, the coordinates of the measuring points, and the time variable, and outputs the predicted electrical method response and hydrological state variables.

[0027] In this embodiment, the coupled control equations of electrical and hydrological methods include groundwater flow control equations, electric field control equations, and the relationship between hydrological and electrical properties.

[0028] Specifically, the expression for the groundwater flow control equation is as follows: ; in, Pressure head (unit: m); Elevation (unit: m); The unsaturated permeability coefficient (unit: m / s); Specific water storage coefficient (unit: 1 / m); For source and sink terms, it represents the external input or extraction of water into the system.

[0029] It should be noted that source and sink terms are not necessarily required in dam seepage monitoring; they are used when only natural seepage occurs inside the dam body. (In this embodiment, the value is 0). When there are concentrated leakage channels, drainage holes or water injection conditions, non-zero source-sink terms are used to describe local water exchange, and the unit is uniformly 1 / s.

[0030] Specifically, the expression for the electric field control equation is as follows: ; in, Represents the gradient operator, Represents electric potential The gradient; is the electrical conductivity.

[0031] Specifically, the expression for the relationship between hydrology and electrical properties is as follows: ; in, The electrical conductivity of pore water; Tortuosity factor; The cementation index; For pore water saturation, This represents the reference pore water saturation under fully saturated conditions.

[0032] S4. Set hydrophysical constraints, electrical physical constraints, and hydro-electric coupling boundaries to constrain the continuity of the water flow velocity field, the calculation of the electric potential field / current density field, and the coupling relationship between saturation and resistivity changes.

[0033] In this embodiment, the hydrophysical constraints are: the continuity of the water flow velocity field is constrained by Darcy's law and the mass conservation equation; the electrical physical constraints are: the electric potential field and current density field are calculated by the electrical volume charge equation and Ohm's law; the hydrological and electrical coupling boundary is: the coupling relationship between groundwater flow and resistivity change is established by fitting the saturation relationship using the Archie model.

[0034] S5. Construct a comprehensive loss function for the differentiable surrogate model. The comprehensive loss function includes groundwater flow residual loss, electric field residual loss, data error loss, and regularization loss. Update the loss weights through the backpropagation algorithm.

[0035] In this embodiment, the expression for the comprehensive loss function L is as follows: ; in, , , , These represent the residual losses of groundwater flow, respectively. Electric field residual loss Data error loss Regularization loss The weights; ; ; ; ; groundwater flow residual loss In the calculation expression, This indicates the number of calculation points for the hydrological control equations. Indicates the water storage coefficient; Indicates the first The head value at each calculation point; Represents the calculation point Corresponding head value The permeability coefficient below; Indicates the calculation point Spatial elevation; Indicates source and sink terms.

[0036] electric field residual loss In the calculation expression, This indicates the number of calculation points for the electric field control equations; Show the first Dielectric conductivity at each calculation point; This represents the electric potential at the calculation point.

[0037] Data error loss In the calculation expression, Indicates the number of observation data; Indicates the first A set of actual observation data; This represents the corresponding predicted value calculated by the model.

[0038] In regularization loss In the calculation expression, Indicates the number of regularization calculation points; Indicates the first Medium parameters at a spatial location; This represents the spatial variation gradient of the medium parameter.

[0039] in, This indicates the number of sampling points for the residuals of the hydrological control equations; This indicates the number of residual sampling points in the electric field control equation; Indicates the number of observation data samples; This indicates the number of sampling points or parameter nodes for regularization constraints.

[0040] Furthermore, in this embodiment, the neural network includes four fully connected layers, with each layer containing 128-128-128-2 neurons; the activation function is tanh; and the learning rate is set to 1.0e. -4 (Adam).

[0041] S6. Update the neural network parameters of the differentiable surrogate model until the loss decreases without fluctuation.

[0042] In this embodiment, the Adam optimizer is used to update the neural network parameters of the differentiable surrogate model, and an adaptive loss weight strategy is used to suppress the dominance of single-item loss in the training process until the loss decreases without fluctuation or reaches the preset convergence condition.

[0043] Furthermore, neural networks The expression is as follows: ; in, Indicates the parameters to be inverted; The network training parameters in this embodiment are as follows: Network layers: 4 fully connected layers; Neurons per layer: 128-128-128-2; Activation function: tanh; Learning rate: 1.0e-4 (Adam); Loss function weights: Adaptive weights with automatic parameter tuning.

[0044] The expression for the differentiable surrogate model is as follows: ; The differentiable surrogate model is used for backpropagation optimization.

[0045] Furthermore, this embodiment also includes adaptive loss weight update, expressed as follows: ; in, For the first Term gradient norm; For the average gradient, Indicates the (k+1)th iteration when the... The unnormalized weights of each loss term; Indicates the k-th iteration. The weights of each loss term.

[0046] S7. After the model converges, the differentiable surrogate model outputs the inversion results.

[0047] Specifically, after the model in this embodiment converges, the differentiable surrogate model outputs the pressure head, permeability coefficient, conductivity or resistivity distribution, and the location of the leakage anomaly area or leakage channel determined by the above distribution.

[0048] It should be noted that traditional electrical resistivity-hydrological coupled inversion typically requires repeated hydrological seepage forward modeling, electrical resistivity forward modeling, and sensitivity matrix or Jacobian matrix calculations in each iteration. When the model is extended to multiple time steps, multi-electrode arrays, or large-scale 3D grids, the computational load increases rapidly with the number of grid nodes, the amount of observation data, and the number of time steps. For medium-scale 2D time-shift coupled inversion, the computation time can typically reach several hours; for 3D or long-term series coupled inversion, the computation time may reach tens of hours or even days, making it difficult to meet the needs of long-term monitoring and rapid early warning of dam leakage. Compared to existing technologies, the method in this embodiment only requires 45s-130s of computation time, and can quickly output the distribution of head, permeability coefficient, and electrical parameters after training. Furthermore, the time required for a single prediction is significantly lower than that of traditional iterative forward modeling methods.

[0049] The beneficial effects of the method in this embodiment are verified through numerical simulation below: Data: 12 days x 4236 nodes = 50832 data points; the resistivity range obtained from hydrological simulation calculation is: 99.21 - 16819.20 ohm-m.

[0050] like Figure 2 The inversion accuracy shown is from Figure 2 As can be seen from the scatter plot, the predicted pressure head of the method in this embodiment is consistent with the actual pressure head.

[0051] like Figure 3 and Figure 4 As shown, Figure 3 The training data before adaptive weights were applied. Figure 4 For training data with adaptive weights, from Figure 3 and Figure 4 It can be seen that the convergence curve of the loss function changes significantly before and after the adaptive weights. After adopting the adaptive weights, the loss function changes from oscillating decline to a relatively stable and synchronous decline, that is, the method in this embodiment improves the training stability.

[0052] In addition, this embodiment also provides a computer device, including a memory and a processor; The memory stores computer programs; When the processor executes the computer program, it implements the steps of the above-described electrical and hydrological coupled inversion method.

[0053] It should be noted that computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof. These programming languages ​​include object-oriented programming languages—such as Java, Smalltalk, and C++—as well as conventional procedural programming languages—such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a Local Area Network (LAN) or a Wide Area Network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0054] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0055] In addition, this embodiment also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described electrical and hydrological coupled inversion method.

[0056] The readable storage medium provided in this application is a computer-readable storage medium, which stores computer-readable program instructions (i.e., a computer program) for executing the above-described electrical and hydrological coupled inversion method. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided in this application are the same as the beneficial effects of the electrical and hydrological coupled inversion method provided in the above embodiments, and will not be repeated here.

[0057] The above description is only a preferred embodiment of the present invention and does not limit the scope of the present invention. All equivalent structural transformations made under the inventive concept of the present invention using the contents of the present invention specification and drawings, or direct / indirect applications in other related technical fields, are included within the protection scope of the present invention.

Claims

1. A coupled electrical and hydrological inversion method, characterized in that, Includes the following steps: S1. Obtain inversion data; S2. Preprocess the inverted data to generate a training dataset; S3. Based on the groundwater flow control equation, electric field control equation and hydrological and electrical relationship, construct the electrical and hydrological coupled control equation, establish a differentiable surrogate model, and use it to output the prediction and inversion results; S4. Set hydrophysical constraints, electrical physical constraints, and hydro-electric coupling boundaries; S5. Construct the comprehensive loss function of the differentiable surrogate model, and update the weights in the comprehensive loss function through the backpropagation algorithm; S6. Update the neural network parameters of the differentiable surrogate model until the loss decreases without fluctuation; S7. After the model converges, the differentiable surrogate model outputs the inversion results.

2. The electrical and hydrological coupled inversion method according to claim 1, characterized in that, In S1, the inversion data includes inversion borehole depth, well logging and geophysical and electrical data, boundary conditions, time-varying parameters, measurement point coordinates, and observation distribution information.

3. The electrical and hydrological coupled inversion method according to claim 2, characterized in that, In S2, the preprocessing includes unifying units, timestamp processing, removing outlier data, filtering, handling missing values, data standardization, difference set, and generating Gaussian training point clouds.

4. The electrical and hydrological coupled inversion method according to claim 3, characterized in that, In S3, the coupled control equations of electrical and hydrological methods include the groundwater flow control equation, the electric field control equation, and the relationship between hydrology and electrical properties. The expression for the governing equation of groundwater flow is as follows: ； in, For pressure head; Elevation; The unsaturated permeability coefficient; The specific water storage coefficient; For source and sink terms, it represents the external input or extraction of water into the system; The expression for the electric field control equation is as follows: ； in, Represents the gradient operator, Represents electric potential The gradient; Electrical conductivity; The expression for the relationship between hydrology and electrical properties is as follows: ； in, The electrical conductivity of pore water; Tortuosity factor; The cementation index; This represents the pore water saturation level.

5. The electrical and hydrological coupled inversion method according to claim 4, characterized in that, In S4, the hydrophysical constraints are: the continuity of the water flow velocity field is constrained by Darcy's law and the mass conservation equation; the electrical physical constraints are: the electric potential field and the current density field are calculated by the electrical volume charge equation and Ohm's law; the hydrological and electrical coupling boundary is: the coupling relationship between groundwater flow and resistivity change is established by fitting the saturation relationship using the Archie model.

6. The electrical and hydrological coupled inversion method according to claim 5, characterized in that, In S5, the expression for the comprehensive loss function L is as follows: ； in, , , , These represent the residual losses of groundwater flow, respectively. Electric field residual loss Data error loss Regularization loss The weights; ； ； ； ； in, Indicates the number of calculation points for the hydrological control equations; Indicates the water storage coefficient; Indicates the first The head value at each calculation point; Represents the calculation point Corresponding head value The permeability coefficient below; Indicates the calculation point Spatial elevation; Indicates source and sink terms; This indicates the number of calculation points for the electric field control equations; Show the first Dielectric conductivity at each calculation point; This represents the electric potential at the calculation point. Indicates the number of observation data; Indicates the first A set of actual observation data; This represents the corresponding predicted value calculated by the model; Indicates the number of regularization calculation points; Indicates the first Medium parameters at a spatial location; This represents the spatial variation gradient of the medium parameter.

7. The electrical and hydrological coupled inversion method according to claim 6, characterized in that, In S6, the neural network parameters are updated based on the Adam optimizer. The expression is as follows: ； in, Indicates the parameters to be inverted; The expression for the differentiable surrogate model is as follows: ； The differentiable surrogate model is used for backpropagation optimization.

8. The electrical and hydrological coupled inversion method according to claim 7, characterized in that, S6 also includes adaptive loss weight updates, expressed as follows: ； in, For the first Term gradient norm; For the average gradient, Indicates the (k+1)th iteration when the... The unnormalized weights of each loss term; Indicates the k-th iteration. The weights of each loss term.

9. A computer device, characterized in that, Including memory and processor; The memory stores computer programs; When the processor executes the computer program, it implements the steps of the electrical and hydrological coupled inversion method as described in any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the electrical and hydrological coupled inversion method as described in any one of claims 1-8.

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