Method for predicting transient electromagnetic response of core wall dam

Abstract

The application discloses a kind of core wall dam transient electromagnetic response prediction methods, comprising: constructing the core wall dam boundary parameter space including the geometric dimension characteristics of core wall dam and the electrical property characteristics of medium;Accordingly generate the response constraint sample set for constraining the relationship between dam structure and electromagnetic field diffusion;Constitute the electromagnetic response mapping network for executing nonlinear transformation from parameter space to electromagnetic response space;By minimizing the loss function including physical field constraint or data fitting error, iteratively update network parameters, obtain the convergent electromagnetic response mapping network;When working, the target boundary parameter vector to be predicted is input into the convergent electromagnetic response mapping network, and the corresponding time-domain transient electromagnetic vertical magnetic field component attenuation curve is output.The application solves the network convergence problem in strong heterogeneous medium by partition interface joint constraint, and uses sensitivity equation constraint to ensure the physical consistency of derivative, realizes the high-precision, real-time intelligent prediction of core wall dam disease.

Description

Technical Field

[0001] This invention belongs to the field of geophysical exploration, and in particular, it is a method for predicting the transient electromagnetic response of a core wall dam. Background Technology

[0002] As the core barrier of a water conservancy project, the non-destructive testing of internal leakage and cracks in core-wall dams is crucial for ensuring dam safety. Transient electromagnetic method (TEM) has become a key means of detecting such hazards due to its sensitivity to low-resistivity bodies and its large detection depth. However, core-wall dams have a multi-layered structure of water body-core wall-dam shell-bedrock and complex trapezoidal boundaries. The diffusion law of electromagnetic fields in such highly non-homogeneous media is extremely complex, and traditional detection interpretation heavily relies on high-precision forward modeling.

[0003] Currently, forward modeling of core-wall dams primarily relies on numerical simulation methods such as the finite element method (FEM) or finite difference method (FDTD). While these methods can theoretically simulate complex structures, the computational process requires fine mesh generation and large-scale matrix solving, often taking several hours for a single forward modeling run. Although data-driven neural network methods have begun to be applied to geophysical inversion in recent years, most are limited to simple layered models or homogeneous half-space models, using only simple black-box networks to fit the input-output relationship, failing to deeply integrate the physical structural characteristics of the dam.

[0004] Existing technologies for handling composite structures like core-wall dams suffer from three major bottlenecks: low computational efficiency, physical discontinuities at interfaces, and unreliable sensitivity analysis. Specifically, the high time cost of traditional numerical methods cannot meet the demands of real-time inversion and massive operational condition analysis in engineering projects. When introducing conventional physical information neural networks (PINNs), the conductivity abrupt changes spanning several orders of magnitude between the core wall and dam shell, and between the water body and bedrock, lead to severe gradient ill-conditioning during network training, preventing convergence at strongly discontinuous interfaces and making it difficult to guarantee the continuity of physical quantities such as normal current density. Existing parameter sensitivity analysis is usually treated as an independent post-processing step (such as the finite difference method), and the calculated sensitivity information often does not satisfy the differential constraints of the governing equations. This lack of physically consistent gradient information easily leads to subsequent inversions getting trapped in local minima, reducing the accuracy of hazard diagnosis. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the transient electromagnetic response of a core wall dam, so as to solve the above-mentioned problems existing in the prior art.

[0006] Technical solution, a method for predicting the transient electromagnetic response of a core wall dam, including:

[0007] Construct a boundary parameter space for the core-wall dam that includes both geometric and dielectric electrical characteristics;

[0008] Based on the boundary parameter space of the core wall dam, a response constraint sample set is generated to constrain the relationship between the dam structure and the electromagnetic field diffusion.

[0009] Construct an electromagnetic response mapping network for performing nonlinear transformations from parameter space to electromagnetic response space;

[0010] The electromagnetic response mapping network is trained using a set of response constraint samples. The network parameters are iteratively updated by minimizing a loss function that includes physical field constraints or data fitting errors, resulting in a converged electromagnetic response mapping network.

[0011] During operation, the target boundary parameter vector to be predicted is input into the convergent electromagnetic response mapping network, and the corresponding transient electromagnetic vertical magnetic field component decay curve in the time domain is output.

[0012] Beneficial effects: This invention solves the network convergence problem in strongly non-uniform media by using partitioned interface joint constraints, and ensures the physical consistency of derivatives by using sensitivity equation constraints, thus realizing high-precision, real-time intelligent prediction of heart wall dam defects. Attached Figure Description

[0013] Figure 1 A flowchart illustrating the steps of a method for predicting the transient electromagnetic response of a core wall dam, as provided in this application embodiment.

[0014] Figure 2 This is a flowchart illustrating the steps of training an electromagnetic response mapping network using a response constraint sample set, as provided in an embodiment of this application.

[0015] Figure 3 A flowchart illustrating the steps for constructing interface continuity residual loss in an embodiment of this application.

[0016] Figure 4 A flowchart illustrating the steps for constructing sensitive physical consistency constraints provided in this application embodiment. Detailed Implementation

[0017] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0018] It should be noted that the terms include and have, and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such process, method, product, or device.

[0019] like Figure 1 As shown, a method for predicting the transient electromagnetic response of a core wall dam includes the following steps:

[0020] Construct a boundary parameter space for the core-wall dam that includes both the geometric and dielectric electrical characteristics of the core-wall dam.

[0021] In this embodiment, the boundary parameter space of the core wall dam is a multi-dimensional set of parameters used to comprehensively describe the physical properties of the core wall dam. Specifically, this parameter space includes two types of key parameters: geometric boundary parameters and electrical boundary parameters. Geometric boundary parameters are used to define the shape and structural dimensions of the dam, specifically including the dam height H, dam body slope ratio b, core wall slope ratio bc, and upstream water level height Hw. Dam height H refers to the vertical distance from the base to the top of the dam; dam body slope ratio b refers to the ratio of the horizontal length to the vertical height of the outer slope of the dam; core wall slope ratio bc refers to the slope of the internal seepage-proof core wall of the dam; upstream water level height Hw refers to the elevation of the reservoir water surface relative to the dam foundation. Electrical boundary parameters are used to define the electrical conductivity of each component of the dam, specifically including the dam body resistivity ρ. d Dam foundation resistivity ρ f Core wall resistivity ρ c and the resistivity ρ of the upstream water body w These parameters constitute the boundary conditions for the transient electromagnetic forward modeling of the core-wall dam, determining the diffusion law of the electromagnetic field inside the dam and in the surrounding medium.

[0022] Based on the boundary parameter space of the core wall dam, a response constraint sample set is generated to constrain the relationship between the dam structure and the electromagnetic field diffusion.

[0023] Alternatively, based on the boundary parameter space of the core wall dam, a response constraint sample set containing sampling points inside the subdomain and at the interface is generated.

[0024] Specifically, the response constraint sample set serves as the data foundation for training the neural network. The form of the response constraint sample set varies across different implementations. For example, in a data-driven implementation, the response constraint sample set consists of a large number of input-output pairs, where the inputs are discrete parameter combinations sampled from the boundary parameter space, and the outputs are the corresponding true values ​​of the transient electromagnetic response calculated using numerical methods such as the finite element method. In a physics-driven implementation, the response constraint sample set comprises a set of spatial sampling points within the computational domain, including subdomain points within the dam and interface points at the junctions of different media, used to calculate the residuals of the physical equations during training. Regardless of the form, this sample set carries information about the correlation between the dam's structural characteristics and the physical laws governing electromagnetic field diffusion.

[0025] Construct an electromagnetic response mapping network for performing nonlinear transformations from parameter space to electromagnetic response space.

[0026] In this embodiment, the electromagnetic response mapping network is a deep learning model that establishes a nonlinear mapping relationship between the input boundary parameters and the output transient electromagnetic response. This network can be a standard feedforward neural network (FNN), which fits data through a weighted summation of multiple neurons and a nonlinear activation function; or it can be a physical information neural network (PINN), whose network structure not only includes the data stream for prediction but also embeds an automatic differentiation mechanism to calculate the partial derivatives of the physical field with respect to space and time. The network's input layer receives normalized boundary parameters and time information, and the output layer outputs the vertical magnetic field component Bz or its logarithmic form at the corresponding time moment.

[0027] The electromagnetic response mapping network is trained using a set of response constraint samples. The network parameters are iteratively updated by minimizing a loss function that includes physical field constraints or data fitting errors, resulting in a converged electromagnetic response mapping network.

[0028] Specifically, the training process involves adjusting the weights and biases within the network to minimize the prediction error. The specific form of the loss function depends on the chosen network type. For feedforward neural networks (FNNs), the loss function primarily consists of the mean squared error (MSE) between the predicted values ​​and the true values, i.e., the data fitting error. For physics-information neural networks (PINNs), the loss function is more complex, potentially including a small amount of data fitting error, but primarily incorporating physical constraints, i.e., whether the network output satisfies the partial differential equation residuals of Maxwell's equations and the boundary condition residuals. The network parameters are iteratively updated using optimization algorithms such as Adam, L-BFGS, or Levenberg-Marquardt until the loss function converges to a preset threshold, resulting in a well-trained, converged network model.

[0029] During operation, the target boundary parameter vector to be predicted is input into the convergent electromagnetic response mapping network, and the corresponding transient electromagnetic vertical magnetic field component decay curve in the time domain is output.

[0030] In this embodiment, once the network is trained, it can be used for rapid prediction. The specific parameters of the target core wall dam, i.e., the target boundary parameter vector, are input into the network after necessary preprocessing, such as normalization. The network calculates through forward propagation and instantly outputs a series of predicted values. These predicted values ​​are post-processed, such as inverse normalization and exponential transformation, and arranged in a time series to form a complete transient electromagnetic vertical magnetic field component decay curve. This curve reflects the decay law of the secondary field over time under the specific boundary parameter conditions, providing a direct basis for subsequent engineering inversion and interpretation.

[0031] In one possible implementation, the electromagnetic response mapping network is a physical information neural network; the response constraint sample set includes sampling points inside subdomains distributed within the computational domain and interface sampling points distributed at the junctions of different media.

[0032] In this embodiment, to address the challenges of numerical simulation caused by drastic changes in conductivity within the core dam, a Physical Information Neural Network (PINN) architecture is employed. The response constraint sample set no longer relies on time-consuming finite element forward modeling results, but is instead generated by distributing points in physical space. Specifically, the sampling points within the subdomain are spatial coordinate points randomly or uniformly distributed within various physical regions of the dam, including the upstream water region ω. w Heart wall region ω c , Dam shell and transition zone region ω d and bedrock region ω r Points within the interface. Interface sampling points are points distributed at the interfaces between these different media, such as the interface γ between the core wall and the dam shell. cd γ at the interface between the dam shell and the bedrock dr And so on. The set of these points is used for subsequent calculations of how well the physical equations are satisfied at different locations.

[0033] Furthermore, such as Figure 2 As shown, the electromagnetic response mapping network is trained using a response constraint sample set, including:

[0034] By utilizing sampling points within the subdomain, the physical residual loss of the subdomain is constructed based on the transient electromagnetic control equation.

[0035] Specifically, the subdomain physical residual loss is used to constrain the network output to conform to the electromagnetic field diffusion law within each homogeneous medium. Under the quasi-static approximation that neglects displacement current, the Maxwell's equations satisfied by the transient electromagnetic field can be simplified to diffusion equations. For example, for each subdomain ω... iUsing automatic differentiation techniques, the first derivative of the network output electric field E with respect to time t and the second derivative with respect to space x are calculated, and a residual operator of the following form is constructed:

[0036] L i (E) = ▽×(▽×E)+μ i *σ i *(ΨE / Ψt);

[0037] Where ▽× represents curl operation, μ i Let σ be the permeability of this subdomain. i Let Ψ be the conductivity of the subdomain, E be the electric field intensity vector, and Ψ be the partial derivative. The perpendicular magnetic field component Bz can be obtained through Faraday's law of electromagnetic induction: ΨB / Ψt = -▽×E. The subdomain physical residual loss L... phys That is, the residual operator L at all sampling points within the subdomain. i The sum of squares of the values. Minimizing this loss forces the network predictions to satisfy the physical diffusion equations within each medium. Optionally, the subdomain physical residual loss applies to physical subdomains including the upstream water subdomain, the core wall subdomain, the dam shell and transition zone subdomain, and the bedrock subdomain.

[0038] Using interface sampling points, an interface continuity residual loss is constructed based on electromagnetic field boundary conditions.

[0039] In this embodiment, an interface continuity residual loss is constructed to address the problem of abrupt changes in physical quantities at multi-medium interfaces.

[0040] like Figure 3 As shown, in a preferred implementation, the interface continuity residual loss is constructed by including:

[0041] The interface continuity residual operator is invoked to calculate the electromagnetic field components on both sides of the interface sampling point. Based on the electromagnetic field components, the interface continuity residual operator is used to constrain the normal current density or tangential electric field between adjacent physical subdomains to maintain continuity, thus obtaining the interface continuity residual loss.

[0042] In this embodiment, at the interface γ of different conductive media ij Above, the electromagnetic field components must satisfy specific continuity conditions. Specifically, constructing the interface continuity residual operator includes two constraints: one is the continuity of the tangential electric field, i.e., R t = n×(E i - E j ) = 0; secondly, the normal current density is continuous, i.e., R n = n · (σ i * E i -σ j *E jE = 0; where n is the unit normal vector of the interface, E i and E j σ represents the electric field vectors in subdomains i and j on either side of the interface. i and σ j Let R be the conductivity of the two media. The residual R is calculated at the interface sampling point. t and R n The sum of squares of the moduli constitutes the interface continuity residual loss L. interface This ensures that the current can pass correctly through interfaces with large resistivity differences, such as from a high-resistivity dam shell to a low-resistivity core wall, preventing numerical solutions from diverging at the interface.

[0043] A loss function is constructed by combining the subdomain physical residual loss, the interface continuity residual loss, and the data fitting loss calculated based on pre-stored observation or simulation data.

[0044] In a further embodiment, training the electromagnetic response mapping network using a response constraint sample set further includes:

[0045] During the training iteration, the mean, variance, or gradient norm of the subdomain physical residual loss, interface continuity residual loss, and data fitting loss are calculated to generate residual statistical features.

[0046] Specifically, because the dimensions and orders of magnitude of the subdomain residuals, interface residuals, and data fitting residuals differ significantly, direct summation will cause the optimizer to fail to converge. Therefore, it is necessary to monitor the statistical characteristics of each part of the loss in real time. In each training batch, each loss term L is calculated separately. k The expected value of the gradient norm G k :

[0047] G k = mean(|▽ θ L k |);

[0048] Where θ represents the network parameters, ▽ θ Let be the gradient operator for the network parameters θ. The expected value of the gradient norm reflects the contribution of each loss term to the update of the network parameters at the current time step.

[0049] The residual statistical characteristics are processed according to the adaptive weight scheduling strategy, and the dynamic weights used to balance the contribution of each loss term are calculated. The loss function is updated by weighting and summing the subdomain physical residual loss, interface continuity residual loss and data fitting loss using the dynamic weights.

[0050] In this embodiment, the adaptive weight scheduling strategy can dynamically balance the gradient contributions of each loss term, preventing a dominant term from obscuring the optimization direction of other terms. Specifically, a strategy such as maximum gradient can be used to calculate the dynamic weight λ.k (t) = max(G all ) / G k Alternatively, a moving average method can be used for smooth updates, where G all This is the set or population of expected gradient norms for all loss terms in the current training batch. The final total loss function is constructed as follows:

[0051] L total = λ data * L data +λ phys * L phys +λ interface * L interface ;

[0052] Where λ data For the dynamic weighting coefficients of the data fitting loss, L data For data fitting loss, λ phys λ is the dynamic weighting coefficient for the subdomain physical residual loss. interface This refers to the dynamic weighting coefficients for the interface continuity residual loss. By continuously updating the λ parameter during training, the residuals of each part can decrease synchronously, thereby training a network model that both conforms to the observed data and strictly satisfies the complex physical boundary conditions.

[0053] According to one aspect of this application, the electromagnetic response mapping network is configured with an automatic differentiation interface; the method for predicting the transient electromagnetic response of the core wall dam further includes:

[0054] While outputting the attenuation curve of the transient electromagnetic vertical magnetic field component, an automatic differentiation technique is applied to calculate the partial derivative of the output of the electromagnetic response mapping network with respect to the target boundary parameter vector; based on the partial derivative, parameter sensitivity information is generated to characterize the rate of change of the response with respect to the parameters.

[0055] Specifically, the electromagnetic response mapping network not only outputs the vertical magnetic field component Bz, but also functions as a differentiable operator, supporting differentiation with respect to its input parameters. Utilizing the automatic differentiation capabilities provided by deep learning frameworks, the output vertical magnetic field component Bz can be accurately calculated with respect to the input boundary parameters θ. k For example, the core wall resistivity ρ c partial derivative S k =Ψ Bz / Ψθ k This process involves a combination of one forward propagation and one backward propagation, resulting in extremely high computational efficiency and no truncation error. The generated parameter sensitivity information S... k This directly quantifies the degree of influence of the parameter change on the electromagnetic response, which is the core basis for the calculation of the Jacobian matrix in the subsequent inversion algorithm.

[0056] like Figure 4As shown, in a further embodiment, the method also includes constructing sensitive physical consistency constraints, specifically:

[0057] Based on the transient electromagnetic control equations, the target boundary parameter vector is symbolically differentiated to construct a sensitivity equation residual operator to describe the physical dependence between the rate of change of electromagnetic response and the rate of change of parameters.

[0058] In this embodiment, in order to ensure the sensitivity S obtained by automatic differentiation k It's not just a mathematical derivative; it also conforms to the physical laws of electromagnetic fields, requiring the construction of sensitivity equations. Specifically, for the original Maxwell's equation L(B) = 0 with respect to the parameter θ... k By performing chain rule differentiation, we obtain the sensitivity control equation:

[0059] (ΨL / ΨB) *(ΨB / Ψθ k )+ ΨL / Ψθ k = 0;

[0060] Where L is the original Maxwell's governing equation operator, and B is the magnetic flux density vector in the electromagnetic field. This forms the residual operator of the sensitivity equation:

[0061] R sens (S k ) = Op L (S k ) + Q k ;

[0062] Among them Op L It acts on the sensitive field S k Differential operators on Q are usually similar in form to the original field operators; k It is a source term, derived from the medium parameter θ. k The derivative of θ. For example, if θ k If the conductivity is σ, then the source term is proportional to the electric field E.

[0063] Substitute the partial derivatives into the residual operator of the sensitivity equation to calculate the residual loss of the sensitivity equation; add the residual loss of the sensitivity equation to the loss function, and perform joint training of response and sensitivity on the electromagnetic response mapping network to constrain the partial derivatives to meet the physical conditions defined by the residual operator of the sensitivity equation.

[0064] Specifically, the parameter sensitivity information S obtained by automatic differentiation k Substitute into residual operator R sens In the process, calculate its imbalance, i.e., the residual loss of the sensitivity equation:

[0065] L sens = || R sens (S k) || 2 .

[0066] This loss is added to the total loss function with a certain weight, that is:

[0067] L new_total = L total + λ s * L sens ;

[0068] Where L new_total For the updated loss function, λ s These are the weight parameters for the residual loss of the sensitivity equation. Through joint training, the update of the network parameters is simultaneously constrained by the field equation and the sensitivity equation, resulting in the final output sensitivity information S. k It has clear physical consistency, which can more accurately guide the direction of inversion optimization and avoid the problem of inversion getting trapped in local minima caused by inaccurate calculation of sensitivity matrix in traditional methods.

[0069] In a further embodiment, a ternary sensitivity field is constructed to drive network closed-loop optimization, specifically as follows:

[0070] By integrating parameter sensitivity information, candidate measurement point set, and candidate time channels, a time-space-parameter ternary sensitivity field is constructed, which includes time dimension, spatial dimension, and parameter dimension.

[0071] In this embodiment, the ternary sensitivity field is a high-dimensional data structure used to provide a panoramic view of the parameter sensitivity distribution across the entire spatiotemporal domain. Specifically, for each candidate measurement point location x... j (Spatial dimension), each sampling time t k (Time dimension) and each parameter to be inverted θ i (Parameter dimension), extract its sensitivity value:

[0072] S ijk = |ΨBz(x j , t k ) / Ψθ i |;

[0073] Organize all these values ​​into a three-dimensional tensor T sens This reflects when and where the data was observed and which parameter it was most sensitive to. For example, the three-dimensional tensor T sens Analysis may show that the core wall resistivity parameter is most sensitive when the measuring point is located at the center of the dam crest and the observation time is in the middle.

[0074] Based on the time-space-parameter ternary sensitivity field, sample weights are calculated to characterize the importance of different observation locations and time windows. The sample weights are then used to weight the samples in the response constraint sample set, and a closed-loop update is performed on the electromagnetic response mapping network to enhance the network's learning of physical consistency in highly sensitive regions.

[0075] Specifically, the attention allocation during network training is guided using a ternary sensitivity field. An observation information content metric is defined as follows:

[0076] I(x j , t k ) = ∑ (w i * S ijk );

[0077] Where w i These are the engineering attention weights for each parameter. Calculate the engineering attention weights for each training sample point (x). j , t k The information content I is normalized to the sample weight W. sample (j, k). For highly sensitive regions with abundant information, assign greater weight; for regions with less information, reduce the weight. Apply this weighting to the data fitting term of the loss function, i.e.:

[0078] L data_weighted = ∑ (W sample * (Bz pred - Bz true ) 2 );

[0079] Where L data_weighted Bz is the weighted data fitting loss. pred Bz represents the vertical magnetic field component predicted by the network. true This represents the vertical magnetic field components observed in reality. The network is retrained or fine-tuned using the weighted dataset, a process known as closed-loop update. This tilts network resources towards key areas, improving the accuracy and resolution of inversion for key disease parameters.

[0080] In one exemplary embodiment, the electromagnetic response mapping network is a feedforward neural network;

[0081] Constructing an electromagnetic response mapping network includes:

[0082] Construct a network topology containing at least two hidden layers, each with a predetermined number of neurons, and use either the hyperbolic tangent sigmoid function or the log sigmoid function as the activation function; use the Levenberg-Marquardt algorithm or the Bayesian regularization algorithm as the training algorithm, and update the weight parameters of the feedforward neural network by minimizing the data fitting error.

[0083] In this embodiment, a lightweight yet efficient feedforward neural network (FNN) structure is designed. Preferably, each hidden layer is configured with 15 to 20 neurons, meaning the network comprises an input layer (9 nodes), two hidden layers (15-20 nodes each), and an output layer (1 node). The hyperbolic tangent sigmoid function tansig(n) = 2 / (1+exp(-2n))-1 is used as the activation function for the hidden layers to introduce nonlinearity. The Levenberg-Marquardt algorithm is used for training, combining the advantages of gradient descent and Gauss-Newton methods, resulting in extremely fast convergence and making it particularly suitable for small- to medium-sized function approximation problems.

[0084] In another exemplary embodiment, generating a response constraint sample set includes:

[0085] For each parameter in the boundary parameter space of the core wall dam, a range of values ​​is set, and an orthogonal experimental design method is used to combine the parameters to generate a representative set of working conditions.

[0086] Specifically, to efficiently cover the high-dimensional parameter space, an orthogonal experimental design was adopted. The engineering value ranges for each parameter were set as follows: dam height H ranged from 30m to 120m, for example, 30m, 60m, 90m, and 120m; dam slope ratio b ranged from 1:1 to 1:2.5; upstream water level Hw ranged from 0m to 50m; and resistivity ρ for each part ranged from 10 ohm-meters to 1000 ohm-meters. The orthogonal array L was then used. n (r c The combination generates thousands of representative working conditions, making the samples uniformly distributed and representative in the parameter space, thus avoiding the combinatorial explosion problem caused by comprehensive experiments. Here, n is the number of trials in the orthogonal array, r is the number of factors, and c is the number of levels.

[0087] For each set of working conditions in the representative set of working conditions, a parameterized core wall dam finite element model is established; the finite element model is used to solve the pre-configured time-domain Maxwell equations to calculate the transient electromagnetic response within the observation time window; the obtained transient electromagnetic response data is combined with the corresponding working condition parameters to form a response constraint sample set.

[0088] In this embodiment, a two-dimensional or three-dimensional finite element model is established for each working condition using COMSOL or a self-developed finite element code. The model needs to be accurately meshed in areas such as the core wall, dam shell, and water body. The time-domain Maxwell's equations are solved to obtain the observation points at 10... -7 s to 10 -2 The decay curves of the vertical magnetic field component Bz within the s-time window. These [parameter combinations, Bz curves] data pairs constitute the offline training sample library.

[0089] In yet another exemplary embodiment, the boundary parameter space of the core wall dam includes length-type parameters and resistivity-type parameters; the method further includes normalizing the parameters within the boundary parameter space of the core wall dam, specifically:

[0090] For length parameters, a linear normalization method is used to map them to a preset numerical range; for resistivity parameters, a logarithmic transformation is performed, and the logarithmically transformed values ​​are then mapped to a preset numerical range using a linear normalization method to obtain normalized boundary parameters.

[0091] In this embodiment, to eliminate the influence of dimensions and improve network training efficiency, the input parameters are finely normalized. For length-type parameters such as dam height H, a linear formula H' = (H - H) is used. min ) / (H max - H min Mapped to the interval [0, 1], where H' is the normalized value of the dam height H, and H min H is the minimum dam height. max This represents the maximum value of the dam height. Preferably, for resistivity parameters, a base-10 logarithmic transformation is performed. Specifically, for resistivity parameters ρ spanning multiple orders of magnitude, the logarithm is taken. ρ =log 10 (ρ), then perform linear normalization ρ' = (log ρ - log ρmin ) / (log ρmax - log ρmin ), where ρ' is the normalized value of the resistivity parameter, ρ min ρ is the minimum value of the resistivity parameter. max This represents the maximum value of the resistivity parameter. For example, if the resistivity range is 10 to 1000 and the true value is 100, then the normalized value is (2 - 1) / (3 - 1) = 0.5. This effectively compresses the dynamic range of the input data, preventing gradient vanishing or exploding.

[0092] In yet another exemplary embodiment, the boundary parameter space of the core wall dam contains parameters in at least eight dimensions; training the electromagnetic response mapping network using a response constraint sample set includes:

[0093] For each time point within the observation time window, calculate the normalized logarithmic time corresponding to each time point; concatenate the normalized boundary parameters with the normalized logarithmic time to construct the input feature vector.

[0094] Specifically, to enable the network to process time-varying signals, time is used as an explicit input feature. The logarithm of the observation time t is taken and normalized to obtain t'. The eight normalized boundary parameters [H', b', ..., ρ] are then... w The feature vector V is formed by concatenating the time parameter [t] with the time parameter [t]. in = [P1, ..., P8, t'], where b' is the normalized result of the dam slope ratio, ρ w ' represents the normalized result of the upstream water resistivity, P1 is the first normalized boundary parameter, and P8 is the eighth normalized boundary parameter. This allows a single network to predict the response value at any given time.

[0095] The input feature vector is fed into the electromagnetic response mapping network, and the logarithmic transformation value of the transient electromagnetic response at that time point is used as the training target to supervise the learning of the electromagnetic response mapping network.

[0096] In yet another exemplary embodiment, the output transient electromagnetic vertical magnetic field component attenuation curve includes:

[0097] The target boundary parameter vector is normalized and combined with each time point in the given time series to generate the input feature vector set to be tested. The input feature vector set to be tested is input into a convergent electromagnetic response mapping network to obtain the predicted logarithmic response sequence. The predicted logarithmic response sequence is subjected to exponential operation and inverse normalization to reconstruct the attenuation curve of the transient electromagnetic vertical magnetic field component.

[0098] In this embodiment, during the prediction phase, the parameters of the dam to be measured and a series of prediction times are combined into a batch input vector matrix. This matrix is ​​then input into a trained feedforward neural network (FNN), which outputs the corresponding logarithmic values. 10 (Bz) Predicted value. Perform inverse transform:

[0099] Bz = 10 output *Scale factor ;

[0100] The Bz decay curve with true physical dimensions is recovered, where output is the logarithm of the vertical magnetic field component predicted by the feedforward neural network. Scale factor This is the scaling factor required for inverse normalization. The process is computationally insignificant and can achieve real-time prediction at the millisecond level.

[0101] In one embodiment of this application, the method further includes performing parameter sensitivity quantitative analysis on the prediction results, specifically:

[0102] For a single boundary parameter change in the normalized boundary parameters, multiple transient electromagnetic vertical magnetic field component attenuation curves are obtained. The cumulative area index method is used to calculate the area of ​​difference between the attenuation curves of the transient electromagnetic vertical magnetic field components before and after the single boundary parameter change within the entire observation time window. The overall influence index is generated based on the area of ​​difference to quantify the overall influence and direction of the single boundary parameter on the electromagnetic response.

[0103] For example, the cumulative area index (CAI) is defined to quantify the overall sensitivity of the parameter. The formula is:

[0104] CAI =∫ tmin tmax (log 10 (Bz case (t)) - log 10 (Bz ref (t))) d(log 10 t);

[0105] Among them Bz case It is the transient electromagnetic vertical magnetic field component response after parameter changes, Bz ref This is the transient electromagnetic vertical magnetic field component response under reference conditions, t min and t max These represent the start and end times of the observation time window, respectively. The magnitude of the integral value reflects the degree of influence, and the positive or negative sign indicates the direction of influence, i.e., enhancement or suppression.

[0106] In another embodiment of this application, the method further includes performing time-series sensitivity analysis using a permutation importance analysis method, specifically:

[0107] For each time point within the observation window, the original prediction accuracy of the converged electromagnetic response mapping network on the test samples is calculated; a random permutation operation is performed on the target parameter in the normalized boundary parameters along the sample dimension, and the prediction is re-performed using the converged electromagnetic response mapping network to calculate the interference prediction accuracy; based on the difference between the original prediction accuracy and the interference prediction accuracy, the degree of accuracy degradation is calculated, and the degree of accuracy degradation is used as the temporal sensitivity index of the target parameter at that time point.

[0108] In this embodiment, the time-varying characteristics of sensitivity are analyzed using the concept of permutation importance. For a specific time t, the order of a parameter in the test set, such as the core-wall slope ratio bc, is randomly shuffled to disrupt its correlation with the results, while keeping other parameters unchanged. The increase in prediction error after shuffling is calculated, such as the increase in mean squared error (MSE) or the decrease in the coefficient of determination (R²). The greater the increase in error, the more important the parameter is at that time. Sensitivity curves for each parameter over time are generated, revealing physical patterns such as early control by shallow geometric parameters and later control by deep resistivity.

[0109] In a further embodiment, the method further includes calculating an interaction sensitivity index between parameters, specifically:

[0110] For any two different parameters in the normalized boundary parameters, perform a joint random permutation operation simultaneously and calculate the resulting joint accuracy reduction. Compare the joint accuracy reduction with the sum of the accuracy reductions caused by performing random permutation operations on the two parameters independently to evaluate the nonlinear synergistic effect of the two parameters on the electromagnetic response and obtain the interaction sensitivity index.

[0111] Specifically, the coupling effect between parameters is investigated. If the increase in error caused by simultaneously shuffling parameters A and B is significantly greater than the sum of the error increases from shuffling A and B separately, it indicates a positive synergistic effect between A and B (1+1>2); otherwise, there is redundancy or inhibition. The interaction sensitivity index helps identify which parameters need to be jointly inverted and cannot be decoupled independently.

[0112] As an optional implementation, the method further includes performing engineering safety diagnosis based on the prediction results, specifically:

[0113] Obtain the field measured data of the core wall dam to be tested, and compare the field measured data with the transient electromagnetic vertical magnetic field component decay curve output by the converged electromagnetic response mapping network, and perform residual analysis.

[0114] Specifically, the measured TEM data collected in the field and processed by noise reduction is imported into the system. The trained network is then used to quickly generate the theoretical curve under the current assumed model. The fitting residual vectors between the measured curve and the theoretical curve at each time channel are calculated.

[0115] Based on the results of residual analysis, the deviation between the target boundary parameter vector and the actual situation is deduced in reverse, and a dam safety assessment conclusion containing information on leakage or crack determination is generated.

[0116] In this embodiment, residual vectors and ternary sensitivity fields are used to identify the main parameter sources causing fitting errors. For example, if the residuals of late-stage data are large and the core wall resistivity is highly sensitive in the late stage, it is inferred that the model value of the core wall resistivity deviates significantly from the true value. By iteratively correcting the model parameters to minimize the residuals, the inverted value of the true core wall resistivity is obtained. If the inverted core wall resistivity is significantly lower than the normal value, for example, below 10 ohm-meters, it is determined that there are highly conductive seepage channels or water-bearing cracks inside the core wall. Based on this, a dam safety assessment report is generated to guide engineering reinforcement.

[0117] In a preferred implementation, the method further includes constructing optimized configuration data for observation points and optimized configuration data for observation time windows, specifically as follows:

[0118] Read the ternary sensitive field data and set the weights of the observation cost constraint data and the parameters of engineering concern.

[0119] In this embodiment, the time-space-parameter ternary sensitivity field data is loaded, denoted as tensor T. sens Define the observation cost constraints for the engineering site. Specifically, the constraints include: an upper limit N for the number of measurement points. max For example, limitations include the number of instruments, with no more than 50 observation points allowed simultaneously; the allowed density of receiver points along each survey line, for example, a spacing of no less than 5 meters; and the number of available sampling time channels, for example, the minimum sampling interval and maximum recording duration supported by the instrument. Simultaneously, based on the dam risk assessment requirements, the weights w of the engineering focus parameters are set. i For example, if the primary focus is on the seepage prevention performance of the core wall, then the resistivity parameter of the core wall is given a very high weight, while the resistivity of the bedrock is given a low weight.

[0120] For each measurement point and time channel combination, calculate the measurement point time information content evaluation data.

[0121] In this embodiment, the system traverses all candidate measurement point positions x j and time sampling point t k For each combination (x) j , t k The comprehensive information content index I is calculated using a formula. For example: the sensitivity values ​​S of all parameters corresponding to this spatiotemporal point in the ternary sensitivity field. ijk Extract the values ​​and multiply them by the corresponding engineering focus parameter weights w. i Then sum them. That is:

[0122] I(x j , t k ) = ∑(w i * S ijk );

[0123] The comprehensive information content index I quantifies the potential contribution of observations at a specific location and time to the retrieval of key parameters. The calculation results form a two-dimensional information content distribution map, visually displaying high-value observation areas.

[0124] Under the constraint of observation cost data, a heuristic search algorithm is used to optimize the observation configuration and generate observation design optimization results data.

[0125] Preferably, to select the observation scheme that satisfies the constraints and maximizes the total information content from a massive number of candidate combinations, a combinatorial optimization algorithm is employed. Specifically, a genetic algorithm or a greedy algorithm can be used. Taking the greedy strategy as an example, the system selects the point with the largest information content index I and adds it to the observation set, deducting the corresponding cost, such as occupying a measurement point quota; among the remaining candidate points, it continues to search for the point with the largest information content that satisfies the spatial density constraints, such as a point that is not too close to the already selected point; this process is repeated until the upper limit N of the number of measurement points is reached. max As for the selection of the time window, the optimal observation time window is selected based on the time sensitivity curve of the selected measurement point, with the cumulative information content reaching 95%.

[0126] Output optimized configuration data for observation points and optimized configuration data for observation time windows to guide on-site deployment or simulation encryption.

[0127] Specifically, the optimized list of measurement point coordinates and time sampling parameters are exported and used directly to guide the electromagnetic exploration wiring on the engineering site, enabling the acquisition of the most valuable data within a limited budget.

[0128] This embodiment utilizes a pre-constructed ternary sensitivity field to automatically search for the optimal combination of observation points and time windows while meeting engineering cost constraints, in order to maximize the information content of the observation data.

[0129] In one optional embodiment, a method for predicting the transient electromagnetic response of a core-wall dam includes: constructing a boundary parameter space containing the geometric and electrical characteristics of the core-wall dam; generating a response constraint sample set containing sampling points inside the subdomain and at the interface; constructing a physical information neural network configured with an automatic differentiation interface; constructing a joint loss function using the subdomain physical residual, the interface continuity residual, and the data fitting error, and training the network using an adaptive weighting strategy; and finally outputting the transient electromagnetic response and parameter sensitivity information that conforms to the physical equation constraints.

[0130] According to one aspect of this application, a method for predicting the transient electromagnetic response of a core-wall dam can also be:

[0131] S1. Establish a parameterized core wall dam finite element model, combine multiple core wall dam boundary parameters to generate multiple working conditions, and obtain the transient electromagnetic response Bz attenuation curves corresponding to each working condition through numerical forward modeling to construct a sample library.

[0132] Specifically, two types of dam boundary condition parameters affecting the TEM response are defined: geometric boundary parameters, including dam height H, dam body slope ratio b, core wall slope ratio bc, and upstream water level height Hw; and electrical boundary parameters, including dam body resistivity ρ. d Dam foundation resistivity ρ f Core wall resistivity ρ c Upstream water resistivity ρ w To determine the appropriate value ranges for each boundary condition parameter to align with engineering realities, orthogonal experimental design methods were used to generate a large number of representative working conditions. For each set of working condition parameters, a corresponding two-dimensional or three-dimensional finite element model of the core-wall dam was established. By solving Maxwell's equations in the time domain, the transient electromagnetic response was calculated, and the observation time window was obtained, such as 10... -7 s to 10 -2 The attenuation curve of the vertical component Bz of the magnetic field within s is obtained, which yields the TEM forward response for this operating condition. A sample library is created by combining all operating condition parameters and their corresponding Bz attenuation curves {(X... i Y i )}, where X i Y is an 8-dimensional parameter vector. i This represents the corresponding time series Bz value.

[0133] S2. Perform parameter sensitivity analysis on the boundary parameters in the sample library to determine the degree, direction and dominant time period of influence of each boundary parameter on the transient electromagnetic response Bz decay curve.

[0134] In this embodiment, to address the issue of differences in the dimensions and orders of magnitude of the parameters, a linear or logarithmic mapping method is used to normalize each parameter to the [0, 1] interval. The cumulative area index (CAI) is defined to quantify the overall impact (enhancement or suppression) of a single parameter change on the entire decay curve.

[0135] CAI =∫ x1 x2 (log 10 (Bz case (x)) - log 10 (Bz ref (x))) dx;

[0136] Where x1 and x2 are the logarithmic times of the acquisition window, i.e., log 10 t, t∈[10 -7 10 -2 ];Bz case To compare the response curves under parametric operating conditions; Bz refThe response curve is shown for the baseline operating condition. It can be seen that the upstream water level enhances the response (CAI>0), while dam height and slope ratio inhibit it (CAI<0); low resistivity materials enhance the response, while high resistivity materials inhibit it. Gaussian process regression or random forest models are selected as surrogate models. For each observation time point, the sensitivity of a parameter at that moment is quantified by randomly permuting the sample values ​​of that parameter and evaluating the degree of decrease in the surrogate model's prediction accuracy.

[0137] ;

[0138] Where ρ i，t ρ' is the predictive correlation coefficient of the original model. i，t S is the predicted correlation coefficient after replacing parameter k. i，t , where N is the number of repetitions or sample size of the random permutation experiment in the sensitivity analysis. This reveals the controlling roles of different parameters in the early, middle, and late stages of the response. An extended permutation importance method is used, simultaneously randomly permuting two parameters to assess the synergistic effect of their combination on the response, and the interactive sensitivity of different parameters to different time periods is displayed in the form of a heatmap.

[0139] S3. Construct a feedforward neural network model and train it using a sample library to establish a nonlinear mapping relationship from boundary parameters to the transient electromagnetic response Bz decay curve.

[0140] Specifically, for each representative working condition in the sample library, the eight boundary parameters are normalized. For each time point t on the decay curve corresponding to each representative working condition, the normalized logarithmic time t' is concatenated with the normalized eight boundary parameters to form a 9-dimensional input feature vector. The output layer outputs the logarithm of the corresponding time. 10 (Bz) value. The preferred network structure is a double-hidden-layer structure with 15-20 neurons per layer. The preferred activation function is either the hyperbolic tangent function (tansig) or the logarithmic sigmoid function (logsig). For example, the input layer has 9 neurons, each of the two hidden layers contains 20 neurons, and the activation function is tansig. The output layer has 1 neuron, and the activation function is the linear activation function (purelin). The training algorithm uses the Levenberg-Marquardt (LM) algorithm or the Bayesian regularization (BR) algorithm, with mean squared error (MSE) as the loss function. During training, the sample library is divided into training and test sets proportionally. For example, 80% of all samples are used as the training set, and 20% as the test set. Training continues until the model's prediction accuracy on the test set meets the requirements, such as MSE < 0.0001, and the coefficient of determination Rz is [value missing]. 2 >0.999.

[0141] S4. Receive the boundary parameters of the heart wall dam to be predicted, input the trained feedforward neural network model, and output the predicted transient electromagnetic response Bz decay curve.

[0142] Specifically, the eight boundary condition parameters of the core wall dam to be predicted are normalized. For example, the parameters are: H=90m, b=1:2, Hw=50m, bc=1:0.2, ρ d =100Ω·m, ρ f =500Ω·m, ρ c =10Ω·m, ρ w =1Ω·m. Normalize all 8 parameters. For example, b=1:2=0.5, b'=(0.5-0.4) / (1.0-0.4)=0.1667, (assuming b min =0.4 corresponds to a ratio of 1:2.5, b max =1.0 corresponds to a 1:1 ratio). ρ c =10, ρ c '=(log 10 (10)-log 10 (1)) / (log) 10 (10000)-log 10 (1) = 0.25, and other parameters are similar. For a given time series t1, t2, ..., t n Calculate the normalized logarithmic time for each. For example, t=[10 -7 10 -6.9 , ..., 10 -2 The time interval is calculated in seconds, and the normalized logarithmic time t' corresponding to each time point is calculated. The eight normalization parameters are combined with each normalized logarithmic time to form multiple 9-dimensional input vectors, which are then input into the trained feedforward neural network (FNN) model. The model outputs a series of log... 10 The predicted (Bz) value is used to reconstruct the complete Bz decay curve after exponential operation and inverse normalization.

[0143] In one possible embodiment, the process of constructing the electromagnetic response mapping network can also be:

[0144] The process reads the dam's geometric structure data, initial data on dam physical properties, and operational configuration data, including geometric information and resistivity, conductivity, and permeability ranges for regions such as the core wall, upstream shell, downstream shell, bedrock, and water body. Based on the engineering structure of the core wall dam, the target computational domain is divided into multiple physical subdomains, generating dam body partition structure data. The dam body partition structure data records the subdomain's number, spatial extent, and associated physical property parameter names for subsequent constraint physical equations. At the boundaries of adjacent subdomains, based on geometric relationships and engineering design drawings, interfaces such as the core wall / shell interface, water-dam body interface, and bedrock interface are identified, generating interface definition data. This interface definition data includes the interface number, the numbers of the two adjacent subdomains, and the interface's normal information. Within each subdomain and on the interfaces, physical constraint sampling point data is generated according to a specific sampling strategy, including sets of sampling points within the subdomain and sets of sampling points at the interfaces, for subsequent construction of physical residuals.

[0145] The dam body zoning structure data and operating condition configuration data are read. For each physical subdomain, a physical control operator is constructed based on the transient electromagnetic control equations, yielding subdomain physical residual operator data. This subdomain physical residual operator data defines the relationship between electromagnetic field components and conductivity parameters and current sources at any point within the subdomain. Interface definition data is read, and based on the physical continuity conditions of electric field and current density at different material interfaces, interface condition operators are constructed for each interface, yielding interface continuity residual operator data. This interface continuity residual operator data describes the continuity or abrupt change relationships that the electric field components, current density, or magnetic field components on both sides of the interface should satisfy. The subdomain physical residual operator data and the interface continuity residual operator data are kept in the same interface format as the used observation data residual operators for unified subsequent calls within the same physical information neural network PINN loss function.

[0146] The system reads subdomain physical residual operator data, interface continuity residual operator data, and observation data residual operator data used for fitting observations. During the initial training or pre-training phase, it statistically analyzes the values ​​of each residual term on a batch of training samples to obtain the mean, variance, and gradient norm of each type of residual, generating residual statistical feature data. Based on the residual statistical feature data, an adaptive weight update rule is constructed to calculate the initial weights of each subdomain physical residual, each interface continuity residual, and the observation data residual, obtaining physical residual normalization parameter data and initial loss weight configuration data. The physical residual normalization parameter data is used to scale residuals of different dimensions and orders of magnitude, while the initial loss weight configuration data is used to balance the impact of each loss term on the overall training. During network training, the residual statistical feature data is periodically re-analyzed, and the weights of each loss term are iteratively adjusted according to the pre-set update rule, generating loss weight scheduling time series data that changes with the training process. Through this process, when a subdomain or interface is in a high residual state for a long time, the system will automatically and appropriately increase the weight of that residual term, guiding the network to focus on correcting the physical consistency of this subdomain or interface.

[0147] Data on dam zoning structure, interface definition, and physical constraint sampling points are read, along with training sample data, including dam parameters, operating condition configurations, and corresponding transient electromagnetic responses or numerical forward modeling results. This data is organized into input-output batches suitable for network training. Multiple loss functions are constructed based on subdomain physical residual operator data, interface continuity residual operator data, observation data residual operator data, and physical residual normalized parameter data. The loss function is a weighted sum of data fitting loss, subdomain physical residual loss, and interface continuity residual loss, with weights dynamically adjusted as training iterations using time-series data. Backpropagation and optimization algorithms are employed to calculate the loss function on each batch of training data and update the network parameters. This process iterates until the loss converges or a preset stopping condition is met, resulting in an electromagnetic response mapping network model trained with joint constraints of the core-wall dam zoning and interfaces. The model's input remains dam parameters and operating condition configuration, and its output is the transient electromagnetic response. During training, the variation curves and residual statistics of each loss component are recorded to form training process diagnostic data, so as to evaluate the physical consistency of the model across different subdomains and interfaces in subsequent training.

[0148] In a further embodiment, the electromagnetic response mapping network model is trained as follows:

[0149] The electromagnetic response mapping network model data and parameter definition data are read to identify which dam parameters require sensitivity analysis, such as core wall resistivity, transition zone resistivity, and bedrock resistivity. Operating condition configuration data and measuring point sampling configuration data are also read, including transmitter circuit parameters, turn-off time series, and receiver coil positions and time channel configurations. For each set of dam parameters and operating condition inputs, the electromagnetic response mapping network model is invoked to obtain transient electromagnetic response predictions, forming model response prediction data. Simultaneously, the partial derivatives of the response are calculated for each analyzed dam parameter using an automatic differentiation mechanism to obtain the sensitivity with respect to each parameter, forming the automatic differentiation sensitivity raw data. The automatic differentiation sensitivity raw data provides the partial derivatives of the transient electromagnetic response with respect to the dam parameters at each measuring point and time channel. The automatic differentiation sensitivity raw data is organized into a unified data structure with parameter, spatial, and temporal dimensions to facilitate physical consistency constraints and joint optimization.

[0150] The process involves reading subdomain physical residual operator data, interface continuity residual operator data, and parameter definition data. Starting from the expressions of the governing equations and interface conditions, symbolic differentiation is performed on each parameter to be analyzed to construct a theoretical sensitivity equation, yielding the theoretical form of the sensitivity equation data. Then, the process reads the raw data of the automatic differential sensitivity and the physical constraint sampling point data. At each sampling point, the automatic differential sensitivity value is substituted into the theoretical form of the sensitivity equation, and the residual value on the left-hand side of the equation is calculated to obtain the subdomain sensitivity equation residual data. This data measures whether the automatic differential sensitivity satisfies the sensitivity relationship derived from the governing equation within each subdomain. Similarly, at the interface sampling points, the automatic differential sensitivity is substituted into the sensitivity interface relationship derived from the interface conditions, and the residual is calculated to obtain the interface sensitivity equation residual data. This reflects whether the automatic differential sensitivity follows the interface continuity or abrupt change conditions at the interface between different materials. Finally, the subdomain sensitivity equation residual data and the interface sensitivity equation residual data are uniformly encapsulated into sensitivity residual operator data.

[0151] The electromagnetic response mapping network model data, model response prediction data, and original automatic differential sensitivity data are read as the output baseline of the current model. Simultaneously, the time series data of loss weight scheduling and sensitivity residual operator data are read. A sensitivity residual component is added to the original loss function to construct a new total loss function. The new total loss function includes the observation data fitting loss, the physical residual loss of each subdomain, the continuity residual loss of each interface, and the sensitivity equation residual loss. The sensitivity residual loss consists of two parts: the residual of the subdomain sensitivity equation and the residual of the interface sensitivity equation. Their weights can be obtained by extending the weight scheduling strategy, forming the sensitivity loss weight configuration data. Incremental training or joint training is used to further optimize the network: in each iteration, a new total loss is calculated, and the network parameters are updated, so that while maintaining or improving the transient electromagnetic response prediction accuracy, the automatic differential sensitivity result is closer to the sensitivity equation that satisfies the control equation and interface conditions. After training convergence, an electromagnetic response mapping network model with physical consistent response and sensitivity output capability is obtained. Its output adds sensitivity data for each key dam body parameter to the original transient electromagnetic response. During training, the changes in the residuals of the sensitivity equation with iteration are recorded to generate sensitivity consistency evaluation data.

[0152] In a further embodiment, the process of obtaining a converged electromagnetic response mapping network includes:

[0153] The process involves reading an electromagnetic response mapping network model with physical consistency response and sensitivity output capabilities, along with candidate measurement point configuration data and time sampling candidate configuration data. The candidate measurement point configuration data provides all feasible measurement point locations, while the time sampling candidate configuration data provides available sampling time channels. Parameter definition data and engineering-related parameter weight data provided by the project are then read to determine which dam parameters are key parameters for evaluating core wall leakage risk and overall dam stability. For each candidate measurement point and each candidate time channel, the electromagnetic response mapping network model with physical consistency response and sensitivity output capabilities is invoked to calculate the transient electromagnetic response and corresponding sensitivity under the current parameter estimates or design values, yielding candidate observation sensitivity sample data. This candidate observation sensitivity sample data records the absolute or normalized values ​​of the sensitivity of each key parameter at different measurement points and time channels. The candidate observation sensitivity sample data is then organized into a unified ternary sensitivity field data according to the measurement point dimension, time dimension, and parameter dimension. Each element in the ternary sensitivity field data corresponds to the sensitivity intensity of a measurement point, a time channel, and a parameter.

[0154] The process involves reading ternary sensitivity field data, engineering-critical parameter weight data, and observation cost constraint data. The observation cost constraint data includes the upper limit on the number of measurement points, the allowed number of receiving points per measurement line, and the number of available sampling time channels. For each combination of measurement points and time channels, a comprehensive information content index is calculated based on the ternary sensitivity field data and the engineering-critical parameter weight data, forming the measurement point time information content evaluation data. This information content index can be a weighted sum or nonlinear function of the sensitivity to key parameters, reflecting the potential for acquiring key parameter information at that location and time channel. Under the joint constraints of the measurement point time information content evaluation data and the observation cost constraint data, a heuristic search or combinatorial optimization algorithm is used to select an optimal or near-optimal observation configuration from all candidate measurement points and time channels, resulting in optimized measurement point configuration data and optimized observation time window configuration data. The optimized measurement point configuration data indicates the actual locations of the measurement points that should be deployed, and the optimized observation time window configuration data indicates the time channel intervals that should be collected. The optimized configuration data of observation points and the optimized configuration data of observation time windows are output according to the original observation design interface format to generate the optimized observation design result data, which can be used to guide the on-site observation deployment or guide the intensive sampling of numerical simulation samples in key areas.

[0155] The process involves reading the ternary sensitivity field data and the metadata of the training samples used in the current stage. The training sample metadata records the measurement point location, time trace, and dam parameter configuration corresponding to each training sample. For each training sample, based on the measurement point location and time trace, the corresponding sensitivity values ​​for each parameter are found or interpolated in the ternary sensitivity field data. This is then combined with the weight data of the engineering-related parameters to calculate the comprehensive sensitivity intensity of the sample, resulting in comprehensive sensitivity assessment data. Based on this comprehensive sensitivity assessment data, a sample weighting strategy is set, for example, assigning larger weights to samples with higher comprehensive sensitivity and smaller weights to samples with lower comprehensive sensitivity, thus constructing sample weight data. This sample weight data is used to weight and calculate the data fitting loss during training. Simultaneously, the comprehensive sensitivity assessment data is combined with the physical residual weight scheduling time series data to appropriately amplify or reduce the physical residual weights in highly sensitive areas, forming a closed-loop data for loss weighting configuration that comprehensively considers sensitivity and physical consistency. This data provides variable weights for each loss type in different spatial and temporal regions, which is beneficial for strengthening physical constraints in critical parameter sensitive areas. The sample weight data and loss weighted configuration closed-loop data are organized into a weight configuration format compatible with the original training framework, providing input for the closed-loop network update.

[0156] The process involves reading an electromagnetic response mapping network model with physically consistent response and sensitivity output capabilities, sample weight data, and loss-weighted configuration closed-loop data. Simultaneously, it reads the updated set of observation data or simulation data guided by the observation design optimization results. This updated set includes transient electromagnetic response data collected or generated at newly selected measurement points and time windows. The original training samples and newly collected or added simulation samples are merged. Differential weights are assigned to different samples using sample weight data, and the weights for different regions and loss terms are adjusted based on the loss-weighted configuration closed-loop data to construct a new weighted training dataset and loss function, generating closed-loop training configuration data. Using the electromagnetic response mapping network model with physically consistent response and sensitivity output capabilities as the initial model, the new weighted training dataset is retrained or continuously trained. This further improves the response prediction accuracy and sensitivity physical consistency in key regions under the constraint of newly added highly sensitive observation data, resulting in a closed-loop converged electromagnetic response mapping network model. During training, prediction errors and sensitivity equation residuals at key measurement points, key time traces, and key parameters are compared before and after training to generate closed-loop training effect evaluation data. This data demonstrates the effectiveness of the ternary sensitivity field-driven closed-loop strategy in improving the interpretation accuracy and physical consistency of key regions. The electromagnetic response mapping network model after closed-loop convergence is then encapsulated according to the original fast forward modeling and sensitivity calculation interface to form the final fast forward modeling and sensitivity service interface data.

[0157] This invention addresses the problem of low computational efficiency by employing parametric modeling and neural network mapping techniques. Through offline training, it achieves millisecond-level online prediction for any working condition, overcoming the bottlenecks of traditional finite element methods, such as excessive time consumption and inability to perform real-time analysis. To address the issues of interface physical discontinuities and network non-convergence, a joint constraint strategy for partitioned interfaces is described. By introducing specific interface continuity residual operators and an adaptive dynamic weight scheduling mechanism, the network is forced to satisfy physical conservation at high-contrast interfaces, effectively overcoming gradient ill-conditioning and training divergence problems caused by highly non-uniform media. To address the unreliability of sensitivity analysis, a residual constraint on the sensitivity equation and a joint training mechanism are introduced. The derivatives calculated by automatic differentiation are substituted into the sensitivity partial differential equation derived from the governing equations, forcing the gradient information output by the network to strictly conform to physical laws. This yields sensitivity information with high physical consistency, solving the misjudgment problem caused by inaccurate gradient calculations in traditional methods.

[0158] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A method for predicting the transient electromagnetic response of a core-wall dam, characterized in that, include: Construct a boundary parameter space for the core-wall dam that includes both geometric and dielectric electrical characteristics; Based on the boundary parameter space of the core wall dam, a response constraint sample set is generated to constrain the relationship between the dam structure and the electromagnetic field diffusion. Construct an electromagnetic response mapping network for performing nonlinear transformations from parameter space to electromagnetic response space; The electromagnetic response mapping network is trained using a set of response constraint samples. The network parameters are iteratively updated by minimizing a loss function that includes physical field constraints or data fitting errors, resulting in a converged electromagnetic response mapping network. During operation, the target boundary parameter vector to be predicted is input into the converged electromagnetic response mapping network, and the corresponding transient electromagnetic vertical magnetic field component decay curve in the time domain is output. Electromagnetic response mapping networks are physical information neural networks; The response constraint sample set includes sampling points within subdomains distributed within the computational domain and interface sampling points distributed at the junctions of different media; The electromagnetic response mapping network is trained using a set of response-constrained samples, including: Using sampling points within the subdomain, the physical residual loss of the subdomain is constructed based on the transient electromagnetic control equations. Using interface sampling points, an interface continuity residual loss is constructed based on electromagnetic field boundary conditions; A loss function is constructed by combining the subdomain physical residual loss, the interface continuity residual loss, and the data fitting loss calculated based on pre-stored observation or simulation data.

2. The method according to claim 1, characterized in that, The physical subdomains targeted by the subdomain physical residual loss include the upstream water body subdomain, the core wall subdomain, the dam shell and transition zone subdomain, and the bedrock subdomain; Constructing the interface continuity residual loss includes: Call the interface continuity residual operator to calculate the electromagnetic field components on both sides of the interface sampling point; Based on electromagnetic field components, the interface continuity residual loss is obtained by using the interface continuity residual operator to constrain the normal current density or tangential electric field between adjacent physical subdomains to maintain continuity.

3. The method according to claim 1, characterized in that, The electromagnetic response mapping network is trained using a response constraint sample set, further including: During the training iteration, the mean, variance, or gradient norm of the subdomain physical residual loss, interface continuity residual loss, and data fitting loss are calculated respectively to generate residual statistical features. The residual statistical characteristics are processed according to the adaptive weight scheduling strategy, and the dynamic weights used to balance the contribution of each loss term are calculated. The loss function is updated by weighting and summing the subdomain physical residual loss, interface continuity residual loss, and data fitting loss using dynamic weights.

4. The method according to claim 1, characterized in that, The electromagnetic response mapping network is equipped with an automatic differentiation interface; The method further includes: While outputting the attenuation curve of the transient electromagnetic vertical magnetic field component, the automatic differentiation technique is applied to calculate the partial derivative of the output of the electromagnetic response mapping network with respect to the target boundary parameter vector. Based on the partial derivatives, parameter sensitivity information is generated to characterize the rate of change of the response with respect to the parameters.

5. The method according to claim 4, characterized in that, This also includes constructing sensitive physical consistency constraints, specifically: Based on the transient electromagnetic control equation, the target boundary parameter vector is symbolically differentiated to construct a sensitivity equation residual operator to describe the physical dependence between the rate of change of electromagnetic response and the rate of change of parameters. Substitute the partial derivatives into the residual operator of the sensitivity equation to calculate the residual loss of the sensitivity equation. The residual loss of the sensitivity equation is added to the loss function, and joint training of response and sensitivity is performed on the electromagnetic response mapping network to constrain the partial derivatives to satisfy the physical conditions defined by the residual operator of the sensitivity equation.

6. The method according to claim 1, characterized in that, The electromagnetic response mapping network is a feedforward neural network; Constructing an electromagnetic response mapping network includes: Construct a network topology containing at least two hidden layers, where each hidden layer is configured with a predetermined number of neurons, and the tansig function or the logsig function is used as the activation function; The Levenberg-Marquardt algorithm or Bayesian regularization algorithm is used as the training algorithm to update the weight parameters of the feedforward neural network by minimizing the data fitting error.

7. The method according to claim 6, characterized in that, Generate a sample set of response constraints, including: For each parameter in the boundary parameter space of the core wall dam, a range of values ​​is set, and an orthogonal experimental design method is used to combine the parameters to generate a representative set of working conditions. For each set of working conditions in the representative set of working conditions, a parameterized core wall dam finite element model is established; The finite element model is used to solve the pre-configured time-domain Maxwell's equations to calculate the transient electromagnetic response within the observation time window. This response is then combined with the corresponding operating parameters to form a response constraint sample set.

8. The method according to claim 7, characterized in that, The boundary parameter space of the core wall dam includes length-type parameters and resistivity parameters; The method further includes normalizing the parameters within the boundary parameter space of the core wall dam, specifically: For length-type parameters, a linear normalization method is used to map them to a preset numerical range; For resistivity parameters, a logarithmic transformation is performed, and the logarithmically transformed values ​​are mapped to a preset numerical range using a linear normalization method to obtain normalized boundary parameters.

9. The method according to claim 8, characterized in that, The boundary parameter space of the core wall dam contains parameters in at least eight dimensions; The electromagnetic response mapping network is trained using a set of response-constrained samples, including: For each time point within the observation time window, calculate its corresponding normalized logarithm time; The normalized boundary parameters are concatenated with the normalized logarithmic time to construct the input feature vector; The input feature vector is fed into the electromagnetic response mapping network, and the logarithmic transformation value of the transient electromagnetic response at that time point is used as the training target to supervise the learning of the electromagnetic response mapping network.

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